Update §IV v3.3: soften §IV-D/E framing + rename §IV-I + add §IV-M

- §IV-D opening: note that the accountant-level dip rejection is
  fully explained by between-firm composition + integer ties per
  §III-I.4 (Scripts 39b-e), no longer "the empirical justification
  for fitting a mixture model"
- §IV-E Tables VII/VIII: K=2/K=3 component labels changed from
  "hand-leaning / mixed / replicated" to position-on-plane labels
  per §III-J recasting
- §IV-I retitled "Inter-CPA Pair-Level Coincidence Rate"; v3.x's
  "FAR" terminology retroactively reframed; references §IV-M for
  the v4 Big-4 spike (Script 40b)
- New §IV-M (7 tables XIX-XXV): v4-new anchor-based ICCR
  calibration results consolidated — composition decomposition
  (Scripts 39b-e), pair-level ICCR sweep (Script 40b), pool-
  normalised per-signature ICCR (Script 43), document-level
  ICCR by alarm definition (Script 45), firm-heterogeneity
  logistic regression + cross-firm hit matrix (Script 44),
  alert-rate sensitivity (Script 46)
- Header bumped to v3.3 (post codex rounds 21-34)

Companion to §III v7 commit 723a3f6 and Phase 4 prose v3 commit
b33e20d.

Co-Authored-By: Claude Opus 4.7 (1M context) <noreply@anthropic.com>

.gitignore

@@ -48,3 +48,16 @@ Thumbs.db
 # Temporary files
 *.tmp
 *.bak
+
+# Model weights (too large for git)
+models/
+*.pt
+*.pth
+
+# Node.js shells (accidentally created)
+package.json
+package-lock.json
+node_modules/
+
+# Sensitive/large data
+*.xlsx

.planning/PROJECT.md

@@ -0,0 +1,74 @@
+# Taiwan TWSE CPA Signature Authentication
+
+## What This Is
+
+A computer-vision research pipeline that classifies whether the CPA signatures appearing on Taiwan TWSE-listed-company financial reports are hand-signed (親簽) or non-hand-signed (非親簽 — early-period rubber-stamp / scan, or post-2020 firm-level electronic signature systems). The pipeline ingests ~90k PDFs (2013-2023), detects ~182k signatures with YOLOv11n, embeds them with ResNet-50 (ImageNet1K_V2, no fine-tune), and characterises distributional structure with cosine + independent dHash descriptors. Target: a peer-reviewed publication (IEEE Access, A/6 on the NCKU CSIE journal list).
+
+## Core Value
+
+A statistically defensible, **reproducible** thresholding methodology that distinguishes hand-signed from digitally-replicated CPA signatures at the population level, with traceable evidence at every step (DB → script → table → paper claim).
+
+## Requirements
+
+### Validated
+
+<!-- Shipped and confirmed valuable. -->
+
+- ✓ End-to-end pipeline (TWSE MOPS scrape → Qwen2.5-VL prefilter → YOLO detection → ResNet embedding → DB + descriptors) — `signature_analysis/01-19`
+- ✓ Independent dHash descriptor for replication detection — Script 14 (v3.x baseline)
+- ✓ Accountant-level 3-component GMM characterisation — Script 18/20 (v3.x baseline)
+- ✓ Paper A v3.20.0 manuscript (full-dataset framing, partner Jimmy 2026-04-27 substantive review accepted, codex 3-pass verification clean) — commit `53125d1` on `yolo-signature-pipeline`
+- ✓ Spike scripts 32-35 confirming Big-4-only scope is methodologically superior — commits `e1d81e3`, `8ac0988`, `55f9f94` on `paper-a-v4-big4`
+
+### Active
+
+<!-- Current scope. Building toward these. -->
+
+**Milestone: Paper A v4.0 — Big-4 reframe (primary scope) + full-dataset robustness (secondary)**
+
+- [ ] Foundation: rerun core scripts on Big-4 subset with `--scope=big4` flag (`/scripts 19, 20, 21, 24, 25`)
+- [ ] Methodology rewrite: §III-G/I/J/L re-anchored on dip-test confirmed bimodality and bootstrap-stable Big-4 K=2 GMM (cos=0.975, dh=3.76)
+- [ ] Results tables: regenerate Tables IV-XVIII on Big-4 subset; new §IV-K full-dataset secondary
+- [ ] Prose rewrite: Abstract / Intro / Discussion / Conclusion with Firm A reframed as "templated end of Big-4" case study (was: hand-signed calibration anchor)
+- [ ] AI peer review: ≥3 cross-AI rounds (codex, Gemini 3.x Pro, Opus 4.7) on the v4.0 manuscript
+- [ ] Partner Jimmy second review on v4.0 (he proposed this direction; needs sign-off on execution)
+- [ ] iThenticate <20%, eCF copyright form, IEEE Access submission portal upload + cover letter
+
+### Out of Scope
+
+<!-- Explicit boundaries. Includes reasoning to prevent re-adding. -->
+
+- **Paper B (audit behaviour / policy implications)** — partner v4 contribution D, deferred to a separate paper after Paper A ships
+- **Paper C standalone (reverse-anchor methodology)** — initial 2026-05-12 spike direction, **folded back into Paper A v4.0 §IV-K** as one robustness lens; does not warrant a separate manuscript
+- **Mid/small-firm primary scope** — included as full-dataset secondary only; primary scope is Big-4 because dip-test only achieves multimodality at Big-4 level
+- **Per-document classifier release as software product** — paper-only deliverable; no API / SaaS layer in scope
+- **VLM behavioural interview / IRB study** — removed in v3.4; not coming back
+
+## Context
+
+- **Domain**: Taiwan-listed CPA audit signatures, 2013-2023; 4 Big-4 firms (勤業眾信 Deloitte, 安侯建業 KPMG, 資誠 PwC, 安永 EY) + ~30 mid/small firms
+- **Hardware split**: YOLO + ResNet on RTX 4090 (CUDA, deterministic forward inference, fixed seed); statistical analysis on Apple Silicon MPS / CPU
+- **Domain expert**: User has practitioner-level CPA-firm knowledge in Taiwan; recognises specific senior-partner names (e.g., 薛明玲 / 周建宏 are known PwC seniors that surfaced in Script 35's C1 cluster)
+- **Partner**: 與 partner Jimmy 合作；Jimmy 已提出 Big-4-only 方向，是 v4.0 的觸發者
+
+## Constraints
+
+- **Target journal**: IEEE Access (A/6 on NCKU CSIE list); fits Computer-Vision-applied-to-Audit scope
+- **Timeline**: v3.20.0 was already partner-reviewed and DOCX-shipped (2026-05-05). v4.0 reframe will delay submission by ~4-6 weeks but produces a stronger manuscript; partner Jimmy is aware and supportive
+- **Reproducibility**: pipeline must run end-to-end on the existing `/Volumes/NV2/PDF-Processing/signature-analysis/signature_analysis.db` snapshot; no new data ingest in scope
+- **AI review provenance**: every empirical claim must be backed by a fresh sqlite/grep against the named script — see `[[feedback-provenance-fabrication]]` memory; Gemini round-19 caught 4 fabricated provenance claims previously
+
+## Key Decisions
+
+| Decision | Rationale | Outcome |
+|----------|-----------|---------|
+| Use ResNet-50 ImageNet1K_V2 without fine-tune | Reproducibility; avoid label leakage from fine-tuning on the same corpus | ✓ Validated through v3.x |
+| Cosine + independent dHash dual descriptor | Cosine catches semantic similarity; independent dHash catches byte-level replication | ✓ Validated |
+| Drop SSIM / pixel-pHash from descriptor set | Reviewer-rejected as redundant / fragile | ✓ v3.x rewrite |
+| Drop A2 within-year uniformity assumption | Empirically falsified by Script 27 | ✓ v3.14 |
+| **Reframe scope to Big-4 only as primary** | Dip-test multimodal only at Big-4 level (p<0.0001); mid/small noise distorted Paper A v3.x's published 0.945/8.10 threshold; partner Jimmy's earlier suggestion empirically confirmed by Scripts 32-35 | — Pending v4.0 |
+| Reverse-anchor Paper C → folded into v4.0 §IV-K | Big-4 reframe is the stronger story; reverse-anchor is one of several lenses on the same data, not a standalone paper | ✓ Decided 2026-05-12 |
+| Branch strategy: `paper-a-v4-big4` from `from-outside-of-firmA` from `yolo-signature-pipeline` | Spike artifacts (Scripts 32-35) stay on the spike branch; v4.0 paper work isolated on its own sub-branch; v3.20.0 preserved on yolo-signature-pipeline as fallback | ✓ Decided 2026-05-12 |
+
+---
+*Last updated: 2026-05-12 after Paper A v4.0 Big-4 reframe milestone bootstrap*

.planning/REQUIREMENTS.md

@@ -0,0 +1,85 @@
+# Requirements — Paper A v4.0 (Big-4 reframe)
+
+Milestone: Paper A v4.0 IEEE Access submission with Big-4-only primary scope and full-dataset secondary robustness.
+
+## REQ-001: Big-4-only primary scope (foundation)
+
+**What**: All primary statistical analysis (KDE+dip, BD/McCrary, Beta mixture, 2D-GMM K=2/K=3, pixel-identity FAR, held-out 70/30 z-test, classifier sensitivity) is rerun on the 437-CPA Big-4 subset (Firm A + KPMG + PwC + EY, n_signatures ≥ 10).
+
+**Acceptance**:
+- Script 20 rerun on Big-4 subset, dip-test p < 0.05 on cos_mean and dh_mean
+- Script 21 (held-out validation) rerun on Big-4 subset
+- Script 24 (calibration vs held-out z-test, classifier sensitivity) rerun on Big-4 subset
+- Script 19 (pixel-identity / FAR) rerun on Big-4 subset
+- All rerun outputs land under `reports/v4_big4/`
+- New operational threshold cos > 0.975 AND dh ≤ 3.76 (or refined K=2 posterior) documented with bootstrap 95% CI
+
+## REQ-002: Full-dataset robustness as secondary section
+
+**What**: §IV-K (new) reports the full-dataset (686 CPA) version of the same analyses as a robustness check, demonstrating the pipeline runs at multiple scopes and explaining why the published v3.x 0.945 threshold drifted (mid/small-firm tail heterogeneity).
+
+**Acceptance**:
+- §IV-K table comparing Big-4-only vs full-dataset crossings, with mid/small-firm contribution analysis
+- Explicit explanation of why Big-4 is the methodologically privileged primary scope
+
+## REQ-003: Methodology rewrite (§III-G / I / J / L)
+
+**What**: Sections III-G (unit hierarchy / scope), III-I (threshold estimators), III-J (accountant-level GMM), III-L (per-document classifier rule) rewritten to reflect dip-test confirmed bimodality and the new K=2-derived classifier rule.
+
+**Acceptance**:
+- §III-G justifies Big-4 as the methodological unit (sample size, homogeneity, dip-test evidence)
+- §III-I anchored on bootstrap-stable bimodal evidence rather than three-method convergence on unimodal data
+- §III-J reports K=2 as primary (interpretable: replicated vs hand-leaning) with K=3 BIC slightly preferred (-1112 vs -1108) as secondary
+- §III-L derives operational rule from Big-4 K=2 components and bootstrap CI
+
+## REQ-004: Results tables IV-XVIII regenerated
+
+**What**: All results tables in §IV (currently Tables IV through XVIII at v3.20.0) regenerated on the Big-4 subset with consistent formatting and footnote citation to source script.
+
+**Acceptance**:
+- Each table cites the script + DB query that generated it
+- Big-4 numbers replace full-dataset numbers as primary; full-dataset relegated to §IV-K
+- Figures 1-4 regenerated; Fig 4 (yearly per-firm) likely reusable as-is
+
+## REQ-005: Firm A reframed as templated case study
+
+**What**: Throughout the manuscript, Firm A's role pivots from "calibration anchor (with minority hand-signers)" to "case study of the templated end of Big-4 (0% in K=3 hand-sign-leaning cluster, 82.5% in replicated cluster)". PwC's higher hand-sign tradition (24/102 = 23.5% in C1) noted as a Big-4 internal contrast.
+
+**Acceptance**:
+- Discussion (§V) explicitly states Firm A is the most digitally-replicated of Big-4
+- Cross-tab table (firm × cluster) included in either §IV or §V
+- Conclusion's contributions list updated accordingly
+
+## REQ-006: AI peer review (≥3 rounds)
+
+**What**: At least three cross-AI peer-review rounds on the v4.0 manuscript using codex (GPT-5.x), Gemini 3.x Pro, and Opus 4.7 max effort. Per `[[feedback-ai-review-provenance]]` memory: every reviewer-flagged empirical claim must be provenance-verified against fresh sqlite/grep against the named script.
+
+**Acceptance**:
+- Round 1 verdict obtained from each of the three reviewers
+- All Major-class findings either RESOLVED in revision or explicitly disclaimed
+- Final round produces ≥1 Accept / Minor verdict from at least 2 of 3 reviewers
+
+## REQ-007: Partner Jimmy second review on v4.0
+
+**What**: Jimmy (who proposed Big-4-only direction) reviews the v4.0 manuscript end-to-end before submission.
+
+**Acceptance**:
+- v4.0 DOCX shipped to ~/Downloads
+- Jimmy's response captured in repo (paper/partner_jimmy_v4_review.md)
+- Any must-fix items resolved in v4.0.x
+
+## REQ-008: iThenticate + eCF + submission
+
+**What**: iThenticate similarity check below 20%, IEEE eCF copyright form completed, manuscript uploaded via IEEE Access submission portal with cover letter.
+
+**Acceptance**:
+- iThenticate report saved under `paper/ithenticate_v4.pdf`
+- eCF confirmation captured
+- Submission portal confirmation number recorded in PROJECT.md "Validated" section
+
+## Cross-cutting constraints
+
+- **Reproducibility**: every script accepts a `--scope big4|full` flag (or new scripts under `signature_analysis/v4_*` if a flag refactor is too invasive)
+- **Provenance**: every numeric claim in the paper traces to (script_id, DB query, output file) — see `[[feedback-provenance-fabrication]]`
+- **No data re-ingest**: existing `/Volumes/NV2/PDF-Processing/signature-analysis/signature_analysis.db` is the frozen snapshot
+- **Branch isolation**: all v4.0 work on `paper-a-v4-big4`; do NOT merge back to `yolo-signature-pipeline` until v4.0 is partner-approved

.planning/ROADMAP.md

@@ -0,0 +1,87 @@
+# Roadmap — Paper A v4.0 Big-4 reframe
+
+Milestone goal: Ship Paper A v4.0 to IEEE Access with Big-4-only primary scope, dip-test confirmed bimodality, and full-dataset robustness as secondary.
+
+Branch: `paper-a-v4-big4` (from `from-outside-of-firmA` from `yolo-signature-pipeline` at v3.20.0).
+
+## Phase 1 — Foundation: Big-4 subset script reruns
+**Status**: pending
+**Requirements covered**: REQ-001
+**Tasks**:
+- Add `--scope=big4|full` flag to scripts 19, 20, 21, 24, 25 (and harness any others that load accountant aggregates)
+- Rerun on Big-4 subset; outputs to `reports/v4_big4/`
+- Bootstrap 95% CI on K=2 marginal crossings (extend Script 34's bootstrap to other measures)
+- Confirm dip-test p < 0.05 on Big-4 cos_mean and dh_mean (Script 34 already verified at p<0.0001 — replicate inside the rerun harness for audit trail)
+
+**Done when**: All five scripts produce v4_big4 outputs with bootstrap CI; cross-check against Script 34 numbers.
+
+## Phase 2 — Methodology rewrite (§III-G / I / J / L)
+**Status**: pending; depends on Phase 1
+**Requirements covered**: REQ-003
+**Tasks**:
+- §III-G: re-justify accountant-level Big-4 as the analysis unit (sample size, dip-test evidence, contrast with mid/small heterogeneity)
+- §III-I: re-anchor "natural threshold" claim on dip-test multimodality + bootstrap stability
+- §III-J: K=2 primary (replicated 31% / hand-leaning 69%) + K=3 secondary (BIC -1111.93 vs -1108.45)
+- §III-L: derive cos>0.975 AND dh≤3.76 (or K=2 posterior cut) from §III-J components
+
+**Done when**: §III markdown files updated; cross-references to Phase 1 outputs are correct.
+
+## Phase 3 — Results regeneration (§IV Tables IV-XVIII + §IV-K)
+**Status**: pending; depends on Phase 1 and 2
+**Requirements covered**: REQ-001 (tables), REQ-002 (§IV-K), REQ-004
+**Tasks**:
+- Regenerate Tables IV through XVIII on Big-4 subset (relabel as v4 numbering if order shifts)
+- Regenerate Figures 1-3 (Fig 4 yearly per-firm likely reusable)
+- New §IV-K Full-Dataset Robustness section: comparison table (Big-4 vs full), mid/small-firm contribution, why scope matters
+- Add firm × cluster cross-tab table from Script 35
+
+**Done when**: All §IV tables and figures land in repo; cross-refs from §III hold.
+
+## Phase 4 — Prose rewrite (Abstract / I / II / V / VI)
+**Status**: pending; depends on Phase 3
+**Requirements covered**: REQ-005
+**Tasks**:
+- Abstract: new threshold, new scope, retain the "reproducible pipeline" frame
+- §I Introduction: contributions list updated (Firm A reframe, Big-4 internal contrast finding, dip-test natural threshold)
+- §II Related Work: minimal changes (statistical methodology citations stable)
+- §V Discussion: Firm A as templated case study, PwC as hand-sign-leading firm, what this implies
+- §VI Conclusion + Future Work: forecast Paper B (audit behaviour / policy)
+
+**Done when**: All prose markdown files updated; word counts within IEEE Access limits (Abstract ≤ 250 words).
+
+## Phase 5 — AI peer review (3 rounds across codex, Gemini, Opus)
+**Status**: pending; depends on Phase 4 (manuscript-complete state)
+**Requirements covered**: REQ-006
+**Tasks**:
+- Round 1: codex (GPT-5.x) — full manuscript review with provenance verification
+- Round 1: Gemini 3.x Pro — full manuscript review
+- Round 1: Opus 4.7 max-effort — full manuscript review
+- Round 2: address Major findings; same three reviewers cross-check
+- Round 3: convergence — Accept / Minor from at least 2 of 3 reviewers
+
+**Done when**: Final round produces Accept/Minor consensus from majority; reviewer artifacts saved under `paper/`.
+
+## Phase 6 — Partner Jimmy v4.0 review
+**Status**: pending; depends on Phase 5
+**Requirements covered**: REQ-007
+**Tasks**:
+- Export v4.0 DOCX (`paper/export_v3.py` + author block fill)
+- Ship to ~/Downloads
+- Iterate on Jimmy's comments
+- Capture review artifact in `paper/partner_jimmy_v4_review.md`
+
+**Done when**: Jimmy approves v4.0.
+
+## Phase 7 — iThenticate + eCF + IEEE Access submission
+**Status**: pending; depends on Phase 6
+**Requirements covered**: REQ-008
+**Tasks**:
+- Run iThenticate, target similarity < 20%
+- Complete IEEE eCF
+- Upload manuscript + cover letter via IEEE Access submission portal
+- Capture confirmation number
+
+**Done when**: Submission confirmed by IEEE Access portal.
+
+---
+*Phase ordering: 1 → 2 → 3 → 4 → 5 → 6 → 7 (mostly linear; Phase 5 round-2 may loop back to Phase 4 prose if Major findings).*

.planning/STATE.md

@@ -0,0 +1,49 @@
+# STATE — Current snapshot
+
+**Date**: 2026-05-12
+**Active milestone**: Paper A v4.0 — Big-4 reframe
+**Active branch**: `paper-a-v4-big4` (12 commits ahead of `yolo-signature-pipeline`)
+**Active phase**: Phase 2 — Methodology rewrite, draft delivered, **awaiting user review of 5 open questions in `paper/v4/paper_a_methodology_v4_section_iii.md`** before Phase 3 begins
+
+## Recently completed
+
+**Phase 1 (Foundation, 7 spike + foundation scripts)**:
+- Script 32 (`e1d81e3`): non-Firm-A calibration verdict C
+- Script 33 (`8ac0988`): reverse-anchor PAPER_C_STRONG (directional ρ=+0.744)
+- Script 34 (`55f9f94`): Big-4 K=2 dip-test multimodal p<0.0001, bootstrap CI [0.974, 0.977] / [3.48, 3.97]
+- Script 35 (`55f9f94`): firm × cluster — Firm A 0% C1 / 82.5% C3, PwC 23.5% C1
+- Script 36 (`ccd9f23`): K=2 LOOO **UNSTABLE** (firm-mass conflation; max Δcos=0.028)
+- Script 37 (`92f1db8`): K=3 LOOO **PARTIAL** (component shape stable, membership ±5-13pp)
+- Script 38 (`bc36dcc`): convergence **STRONG** — 3 lenses pairwise ρ ≥ 0.879
+- Script 39 (`39575ce`): per-signature convergence **MODERATE** — κ=0.87 between per-CPA and per-sig K=3 fits
+- Script 40 (`338737d`): pixel-identity FAR = **0%** on n=262 ground-truth replicated
+
+**Phase 2 (Methodology rewrite)**: §III-G..L draft delivered at `paper/v4/paper_a_methodology_v4_section_iii.md` (commit on the same branch). Single coherent rewrite covering 6 sub-sections (G/H/I/J/K/L); cross-references to all 9 spike scripts; 5 open questions flagged at end of draft for user decision.
+
+## Pending — Phase 2 user review (BEFORE Phase 3)
+
+5 decisions needed from user before Phase 3 (Results regeneration) starts:
+
+1. §III-G scope justification — three-point argument enough, or add a fourth?
+2. §III-H Firm A phrasing — "case study of templated end" vs an alternative framing?
+3. §III-J K=3 vs K=2 selection — lean on LOOO (current draft) or strengthen BIC argument?
+4. §III-L hybrid classifier — keep inherited 5-way box rule, or commit to K=3 hard label as primary?
+5. Section IV table numbering scheme — confirm before Phase 3 builds tables.
+
+Plus: any prose-level edits the user wants on the §III draft.
+
+## Blockers
+
+None.
+
+## Open questions deferred from spike
+
+- Bootstrap stability of cosine and dHash crossings *jointly* (not just marginally) — addressed in Phase 1 if time permits
+- K=2 vs K=3 final choice for §III-J — both reported, but operational classifier needs to commit to one (recommend K=2 for interpretability; K=3 in supplementary)
+
+## Things to remember (per memory)
+
+- Provenance-verify all empirical claims against fresh sqlite/grep ([[feedback-provenance-fabrication]])
+- Don't mock the DB or use placeholders — every number must trace to a script + query
+- Partner Jimmy already proposed Big-4 direction (this is execution, not pitching a new direction)
+- Paper C standalone is shelved — folded into v4.0 §IV-K

CURRENT_STATUS.md

@@ -0,0 +1,252 @@
+# 项目当前状态
+
+**更新时间**: 2025-10-29
+**分支**: `paddleocr-improvements`
+**PaddleOCR版本**: 2.7.3 (稳定版本)
+
+---
+
+## 当前进度总结
+
+### ✅ 已完成
+
+1. **PaddleOCR服务器部署** (192.168.30.36:5555)
+   - 版本: PaddleOCR 2.7.3
+   - GPU: 启用
+   - 语言: 中文
+   - 状态: 稳定运行
+
+2. **基础Pipeline实现**
+   - ✅ PDF → 图像渲染 (DPI=300)
+   - ✅ PaddleOCR文字检测 (26个区域/页)
+   - ✅ 文本区域遮罩 (padding=25px)
+   - ✅ 候选区域检测
+   - ✅ 区域合并算法 (12→4 regions)
+
+3. **OpenCV分离方法测试**
+   - Method 1: 笔画宽度分析 - ❌ 效果差
+   - Method 2: 连通组件基础分析 - ⚠️ 中等效果
+   - Method 3: 综合特征分析 - ✅ **最佳方案** (86.5%手写保留率)
+
+4. **测试结果**
+   - 测试文件: `201301_1324_AI1_page3.pdf`
+   - 预期签名: 2个 (楊智惠, 張志銘)
+   - 检测结果: 2个签名区域成功合并
+   - 保留率: 86.5% 手写内容
+
+---
+
+## 技术架构
+
+```
+PDF文档
+  ↓
+1. 渲染 (PyMuPDF, 300 DPI)
+  ↓
+2. PaddleOCR检测 (识别印刷文字)
+  ↓
+3. 遮罩印刷文字 (黑色填充, padding=25px)
+  ↓
+4. 区域检测 (OpenCV形态学)
+  ↓
+5. 区域合并 (距离阈值: H≤100px, V≤50px)
+  ↓
+6. 特征分析 (大小+笔画长度+规律性)
+  ↓
+7. [TODO] VLM验证
+  ↓
+签名提取结果
+```
+
+---
+
+## 核心文件
+
+| 文件 | 说明 | 状态 |
+|------|------|------|
+| `paddleocr_client.py` | PaddleOCR REST客户端 | ✅ 稳定 |
+| `test_mask_and_detect.py` | 基础遮罩+检测测试 | ✅ 完成 |
+| `test_opencv_separation.py` | OpenCV方法1+2测试 | ✅ 完成 |
+| `test_opencv_advanced.py` | OpenCV方法3(最佳) | ✅ 完成 |
+| `extract_signatures_paddleocr_improved.py` | 完整Pipeline (Method B+E) | ⚠️ Method E有问题 |
+| `PADDLEOCR_STATUS.md` | 详细技术文档 | ✅ 完成 |
+
+---
+
+## Method 3: 综合特征分析 (当前最佳方案)
+
+### 判断依据
+
+**您的观察** (非常准确):
+1. ✅ **手写字比印刷字大** - height > 50px
+2. ✅ **手写笔画长度更长** - stroke_ratio > 0.4
+3. ✅ **印刷体规律，手写潦草** - compactness, solidity
+
+### 评分系统
+
+```python
+handwriting_score = 0
+
+# 大小评分
+if height > 50: score += 3
+elif height > 35: score += 2
+
+# 笔画长度评分
+if stroke_ratio > 0.5: score += 2
+elif stroke_ratio > 0.35: score += 1
+
+# 规律性评分
+if is_irregular: score += 1  # 不规律 = 手写
+else: score -= 1              # 规律 = 印刷
+
+# 面积评分
+if area > 2000: score += 2
+elif area < 500: score -= 1
+
+# 分类: score > 0 → 手写
+```
+
+### 效果
+
+- 手写像素保留: **86.5%** ✅
+- 印刷像素过滤: 13.5%
+- Top 10组件全部正确分类
+
+---
+
+## 已识别问题
+
+### 1. Method E (两阶段OCR) 失效 ❌
+
+**原因**: PaddleOCR无法区分"印刷"和"手写"，第二次OCR会把手写也识别并删除
+
+**解决方案**:
+- ❌ 不使用Method E
+- ✅ 使用Method B (区域合并) + OpenCV Method 3
+
+### 2. 印刷名字与手写签名重叠
+
+**现象**: 区域包含"楊 智 惠"(印刷) + 手写签名
+**策略**: 接受少量印刷残留，优先保证手写完整性
+**后续**: 用VLM最终验证
+
+### 3. Masking padding 矛盾
+
+**小padding (5-10px)**: 印刷残留多，但不伤手写
+**大padding (25px)**: 印刷删除干净，但可能遮住手写边缘
+**当前**: 使用 25px，依赖OpenCV Method 3过滤残留
+
+---
+
+## 下一步计划
+
+### 短期 (继续当前方案)
+
+- [ ] 整合 Method B + OpenCV Method 3 为完整Pipeline
+- [ ] 添加VLM验证步骤
+- [ ] 在10个样本上测试
+- [ ] 调优参数 (height阈值, merge距离等)
+
+### 中期 (PP-OCRv5研究)
+
+**新branch**: `pp-ocrv5-research`
+
+- [ ] 研究PaddleOCR 3.3.0新API
+- [ ] 测试PP-OCRv5手写检测能力
+- [ ] 对比性能: v4 vs v5
+- [ ] 评估是否升级
+
+---
+
+## 服务器配置
+
+### PaddleOCR服务器 (Linux)
+
+```
+Host: 192.168.30.36:5555
+SSH: ssh gblinux
+路径: ~/Project/paddleocr-server/
+版本: PaddleOCR 2.7.3, numpy 1.26.4, opencv-contrib 4.6.0.66
+启动: cd ~/Project/paddleocr-server && source venv/bin/activate && python paddleocr_server.py
+日志: ~/Project/paddleocr-server/server_stable.log
+```
+
+### VLM服务器 (Ollama)
+
+```
+Host: 192.168.30.36:11434
+模型: qwen2.5vl:32b
+状态: 未在当前Pipeline中使用
+```
+
+---
+
+## 测试数据
+
+### 样本文件
+
+```
+/Volumes/NV2/PDF-Processing/signature-image-output/201301_1324_AI1_page3.pdf
+- 页面: 第3页
+- 预期签名: 2个 (楊智惠, 張志銘)
+- 尺寸: 2481x3510 pixels
+```
+
+### 输出目录
+
+```
+/Volumes/NV2/PDF-Processing/signature-image-output/
+├── mask_test/              # 基础遮罩测试结果
+├── paddleocr_improved/     # Method B+E测试 (E失败)
+├── opencv_separation_test/ # Method 1+2测试
+└── opencv_advanced_test/   # Method 3测试 (最佳)
+```
+
+---
+
+## 性能对比
+
+| 方法 | 手写保留 | 印刷去除 | 总评 |
+|------|---------|---------|------|
+| 基础遮罩 | 100% | 低 | ⚠️ 太多印刷残留 |
+| Method 1 (笔画宽度) | 0% | - | ❌ 完全失败 |
+| Method 2 (连通组件) | 1% | 中 | ❌ 丢失太多手写 |
+| Method 3 (综合特征) | **86.5%** | 高 | ✅ **最佳** |
+
+---
+
+## Git状态
+
+```
+当前分支: paddleocr-improvements
+基于: PaddleOCR-Cover
+标签: paddleocr-v1-basic (基础遮罩版本)
+
+待提交:
+- OpenCV高级分离方法 (Method 3)
+- 完整测试脚本和结果
+- 文档更新
+```
+
+---
+
+## 已知限制
+
+1. **参数需调优**: height阈值、merge距离等在不同文档可能需要调整
+2. **依赖文档质量**: 模糊、倾斜的文档可能效果变差
+3. **计算性能**: OpenCV处理较快，但完整Pipeline需要优化
+4. **泛化能力**: 仅在1个样本测试，需要更多样本验证
+
+---
+
+## 联系与协作
+
+**主要开发者**: Claude Code
+**协作方式**: 会话式开发
+**代码仓库**: 本地Git仓库
+**测试环境**: macOS (本地) + Linux (服务器)
+
+---
+
+**状态**: ✅ 当前方案稳定，可继续开发
+**建议**: 先在更多样本测试Method 3，再考虑PP-OCRv5升级

NEW_SESSION_HANDOFF.md

@@ -0,0 +1,432 @@
+# 新对话交接文档 - PP-OCRv5研究
+
+**日期**: 2025-10-29
+**前序对话**: PaddleOCR-Cover分支开发
+**当前分支**: `paddleocr-improvements` (稳定)
+**新分支**: `pp-ocrv5-research` (待创建)
+
+---
+
+## 🎯 任务目标
+
+研究和实现 **PP-OCRv5** 的手写签名检测功能
+
+---
+
+## 📋 背景信息
+
+### 当前状况
+
+✅ **已有稳定方案** (`paddleocr-improvements` 分支):
+- PaddleOCR 2.7.3 + OpenCV Method 3
+- 86.5%手写保留率
+- 区域合并算法工作良好
+- 测试: 1个PDF成功检测2个签名
+
+⚠️ **PP-OCRv5升级遇到问题**:
+- PaddleOCR 3.3.0 API完全改变
+- 旧服务器代码不兼容
+- 需要深入研究新API
+
+### 为什么要研究PP-OCRv5？
+
+**文档显示**: https://www.paddleocr.ai/main/en/version3.x/algorithm/PP-OCRv5/PP-OCRv5.html
+
+PP-OCRv5性能提升:
+- 手写中文检测: **0.706 → 0.803** (+13.7%)
+- 手写英文检测: **0.249 → 0.841** (+237%)
+- 可能支持直接输出手写区域坐标
+
+**潜在优势**:
+1. 更好的手写识别能力
+2. 可能内置手写/印刷分类
+3. 更准确的坐标输出
+4. 减少复杂的后处理
+
+---
+
+## 🔧 技术栈
+
+### 服务器环境
+
+```
+Host: 192.168.30.36 (Linux GPU服务器)
+SSH: ssh gblinux
+目录: ~/Project/paddleocr-server/
+```
+
+**当前稳定版本**:
+- PaddleOCR: 2.7.3
+- numpy: 1.26.4
+- opencv-contrib-python: 4.6.0.66
+- 服务器文件: `paddleocr_server.py`
+
+**已安装但未使用**:
+- PaddleOCR 3.3.0 (PP-OCRv5)
+- 临时服务器: `paddleocr_server_v5.py` (未完成)
+
+### 本地环境
+
+```
+macOS
+Python: 3.14
+虚拟环境: venv/
+客户端: paddleocr_client.py
+```
+
+---
+
+## 📝 核心问题
+
+### 1. API变更
+
+**旧API (2.7.3)**:
+```python
+from paddleocr import PaddleOCR
+ocr = PaddleOCR(lang='ch')
+result = ocr.ocr(image_np, cls=False)
+
+# 返回格式:
+# [[[box], (text, confidence)], ...]
+```
+
+**新API (3.3.0)** - ⚠️ 未完全理解:
+```python
+# 方式1: 传统方式 (Deprecated)
+result = ocr.ocr(image_np)  # 警告: Please use predict instead
+
+# 方式2: 新方式
+from paddlex import create_model
+model = create_model("???")  # 模型名未知
+result = model.predict(image_np)
+
+# 返回格式: ???
+```
+
+### 2. 遇到的错误
+
+**错误1**: `cls` 参数不再支持
+```python
+# 错误: PaddleOCR.predict() got an unexpected keyword argument 'cls'
+result = ocr.ocr(image_np, cls=False)  # ❌
+```
+
+**错误2**: 返回格式改变
+```python
+# 旧代码解析失败:
+text = item[1][0]       # ❌ IndexError
+confidence = item[1][1]  # ❌ IndexError
+```
+
+**错误3**: 模型名称错误
+```python
+model = create_model("PP-OCRv5_server")  # ❌ Model not supported
+```
+
+---
+
+## 🎯 研究任务清单
+
+### Phase 1: API研究 (优先级高)
+
+- [ ] **阅读官方文档**
+  - PP-OCRv5完整文档
+  - PaddleX API文档
+  - 迁移指南 (如果有)
+
+- [ ] **理解新API**
+  ```python
+  # 需要搞清楚:
+  1. 正确的导入方式
+  2. 模型初始化方法
+  3. predict()参数和返回格式
+  4. 如何区分手写/印刷
+  5. 是否有手写检测专用功能
+  ```
+
+- [ ] **编写测试脚本**
+  - `test_pp_ocrv5_api.py` - 测试基础API调用
+  - 打印完整的result数据结构
+  - 对比v4和v5的返回差异
+
+### Phase 2: 服务器适配
+
+- [ ] **重写服务器代码**
+  - 适配新API
+  - 正确解析返回数据
+  - 保持REST接口兼容
+
+- [ ] **测试稳定性**
+  - 测试10个PDF样本
+  - 检查GPU利用率
+  - 对比v4性能
+
+### Phase 3: 手写检测功能
+
+- [ ] **查找手写检测能力**
+  ```python
+  # 可能的方式:
+  1. result中是否有 text_type 字段?
+  2. 是否有专门的 handwriting_detection 模型?
+  3. 是否有置信度差异可以利用?
+  4. PP-Structure 的 layout 分析?
+  ```
+
+- [ ] **对比测试**
+  - v4 (当前方案) vs v5
+  - 准确率、召回率、速度
+  - 手写检测能力
+
+### Phase 4: 集成决策
+
+- [ ] **性能评估**
+  - 如果v5更好 → 升级
+  - 如果改进不明显 → 保持v4
+
+- [ ] **文档更新**
+  - 记录v5使用方法
+  - 更新PADDLEOCR_STATUS.md
+
+---
+
+## 🔍 调试技巧
+
+### 1. 查看完整返回数据
+
+```python
+import pprint
+result = model.predict(image)
+pprint.pprint(result)  # 完整输出所有字段
+
+# 或者
+import json
+print(json.dumps(result, indent=2, ensure_ascii=False))
+```
+
+### 2. 查找官方示例
+
+```bash
+# 在服务器上查找PaddleOCR安装示例
+find ~/Project/paddleocr-server/venv/lib/python3.12/site-packages/paddleocr -name "*.py" | grep example
+
+# 查看源码
+less ~/Project/paddleocr-server/venv/lib/python3.12/site-packages/paddleocr/paddleocr.py
+```
+
+### 3. 查看可用模型
+
+```python
+from paddlex.inference.models import OFFICIAL_MODELS
+print(OFFICIAL_MODELS)  # 列出所有支持的模型名
+```
+
+### 4. Web文档搜索
+
+重点查看:
+- https://github.com/PaddlePaddle/PaddleOCR
+- https://www.paddleocr.ai
+- https://github.com/PaddlePaddle/PaddleX
+
+---
+
+## 📂 文件结构
+
+```
+/Volumes/NV2/pdf_recognize/
+├── CURRENT_STATUS.md          # 当前状态文档 ✅
+├── NEW_SESSION_HANDOFF.md     # 本文件 ✅
+├── PADDLEOCR_STATUS.md        # 详细技术文档 ✅
+├── SESSION_INIT.md            # 初始会话信息
+│
+├── paddleocr_client.py        # 稳定客户端 (v2.7.3) ✅
+├── paddleocr_server_v5.py     # v5服务器 (未完成) ⚠️
+│
+├── test_paddleocr_client.py           # 基础测试
+├── test_mask_and_detect.py            # 遮罩+检测
+├── test_opencv_separation.py          # Method 1+2
+├── test_opencv_advanced.py            # Method 3 (最佳) ✅
+├── extract_signatures_paddleocr_improved.py  # 完整Pipeline
+│
+└── check_rejected_for_missing.py      # 诊断脚本
+```
+
+**服务器端** (`ssh gblinux`):
+```
+~/Project/paddleocr-server/
+├── paddleocr_server.py        # v2.7.3稳定版 ✅
+├── paddleocr_server_v5.py     # v5版本 (待完成) ⚠️
+├── paddleocr_server_backup.py # 备份
+├── server_stable.log          # 当前运行日志
+└── venv/                      # 虚拟环境
+```
+
+---
+
+## ⚡ 快速启动
+
+### 启动稳定服务器 (v2.7.3)
+
+```bash
+ssh gblinux
+cd ~/Project/paddleocr-server
+source venv/bin/activate
+python paddleocr_server.py
+```
+
+### 测试连接
+
+```bash
+# 本地Mac
+cd /Volumes/NV2/pdf_recognize
+source venv/bin/activate
+python test_paddleocr_client.py
+```
+
+### 创建新研究分支
+
+```bash
+cd /Volumes/NV2/pdf_recognize
+git checkout -b pp-ocrv5-research
+```
+
+---
+
+## 🚨 注意事项
+
+### 1. 不要破坏稳定版本
+
+- `paddleocr-improvements` 分支保持稳定
+- 所有v5实验在新分支 `pp-ocrv5-research`
+- 服务器保留 `paddleocr_server.py` (v2.7.3)
+- 新代码命名: `paddleocr_server_v5.py`
+
+### 2. 环境隔离
+
+- 服务器虚拟环境可能需要重建
+- 或者用Docker隔离v4和v5
+- 避免版本冲突
+
+### 3. 性能测试
+
+- 记录v4和v5的具体指标
+- 至少测试10个样本
+- 包括速度、准确率、召回率
+
+### 4. 文档驱动
+
+- 每个发现记录到文档
+- API用法写清楚
+- 便于未来维护
+
+---
+
+## 📊 成功标准
+
+### 最低目标
+
+- [ ] 成功运行PP-OCRv5基础OCR
+- [ ] 理解新API调用方式
+- [ ] 服务器稳定运行
+- [ ] 记录完整文档
+
+### 理想目标
+
+- [ ] 发现手写检测功能
+- [ ] 性能超过v4方案
+- [ ] 简化Pipeline复杂度
+- [ ] 提升准确率 > 90%
+
+### 决策点
+
+**如果v5明显更好** → 升级到v5，废弃v4
+**如果v5改进不明显** → 保持v4，v5仅作研究记录
+**如果v5有bug** → 等待官方修复，暂用v4
+
+---
+
+## 📞 问题排查
+
+### 遇到问题时
+
+1. **先查日志**: `tail -f ~/Project/paddleocr-server/server_stable.log`
+2. **查看源码**: 在venv里找PaddleOCR代码
+3. **搜索Issues**: https://github.com/PaddlePaddle/PaddleOCR/issues
+4. **降级测试**: 确认v2.7.3是否还能用
+
+### 常见问题
+
+**Q: 服务器启动失败?**
+A: 检查numpy版本 (需要 < 2.0)
+
+**Q: 找不到模型?**
+A: 模型名可能变化，查看OFFICIAL_MODELS
+
+**Q: API调用失败?**
+A: 对比官方文档，可能参数格式变化
+
+---
+
+## 🎓 学习资源
+
+### 官方文档
+
+1. **PP-OCRv5**: https://www.paddleocr.ai/main/en/version3.x/algorithm/PP-OCRv5/PP-OCRv5.html
+2. **PaddleOCR GitHub**: https://github.com/PaddlePaddle/PaddleOCR
+3. **PaddleX**: https://github.com/PaddlePaddle/PaddleX
+
+### 相关技术
+
+- PaddlePaddle深度学习框架
+- PP-Structure文档结构分析
+- 手写识别 (Handwriting Recognition)
+- 版面分析 (Layout Analysis)
+
+---
+
+## 💡 提示
+
+### 如果发现内置手写检测
+
+可能的用法:
+```python
+# 猜测1: 返回结果包含类型
+for item in result:
+    text_type = item.get('type')  # 'printed' or 'handwritten'?
+
+# 猜测2: 专门的layout模型
+from paddlex import create_model
+layout_model = create_model("PP-Structure")
+layout_result = layout_model.predict(image)
+# 可能返回: text, handwriting, figure, table...
+
+# 猜测3: 置信度差异
+# 手写文字置信度可能更低
+```
+
+### 如果没有内置手写检测
+
+那么当前OpenCV Method 3仍然是最佳方案，v5仅提供更好的OCR准确度。
+
+---
+
+## ✅ 完成检查清单
+
+研究完成后，确保:
+
+- [ ] 新API用法完全理解并文档化
+- [ ] 服务器代码重写并测试通过
+- [ ] 性能对比数据记录
+- [ ] 决策文档 (升级 vs 保持v4)
+- [ ] 代码提交到 `pp-ocrv5-research` 分支
+- [ ] 更新 `CURRENT_STATUS.md`
+- [ ] 如果升级: 合并到main分支
+
+---
+
+**祝研究顺利！** 🚀
+
+有问题随时查阅:
+- `CURRENT_STATUS.md` - 当前方案详情
+- `PADDLEOCR_STATUS.md` - 技术细节和问题分析
+
+**最重要**: 记录所有发现，无论成功或失败，都是宝贵经验！

PADDLEOCR_STATUS.md

@@ -0,0 +1,475 @@
+# PaddleOCR Signature Extraction - Status & Options
+
+**Date**: October 28, 2025
+**Branch**: `PaddleOCR-Cover`
+**Current Stage**: Masking + Region Detection Working, Refinement Needed
+
+---
+
+## Current Approach Overview
+
+**Strategy**: PaddleOCR masks printed text → Detect remaining regions → VLM verification
+
+### Pipeline Steps
+
+```
+1. PaddleOCR (Linux server 192.168.30.36:5555)
+   └─> Detect printed text bounding boxes
+
+2. OpenCV Masking (Local)
+   └─> Black out all printed text areas
+
+3. Region Detection (Local)
+   └─> Find non-white areas (potential handwriting)
+
+4. VLM Verification (TODO)
+   └─> Confirm which regions are handwritten signatures
+```
+
+---
+
+## Test Results (File: 201301_1324_AI1_page3.pdf)
+
+### Performance
+
+| Metric | Value |
+|--------|-------|
+| Printed text regions masked | 26 |
+| Candidate regions detected | 12 |
+| Actual signatures found | 2 ✅ |
+| False positives (printed text) | 9 |
+| Split signatures | 1 (Region 5 might be part of Region 4) |
+
+### Success
+
+✅ **PaddleOCR detected most printed text** (26 regions)
+✅ **Masking works correctly** (black rectangles)
+✅ **Region detection found both signatures** (regions 2, 4)
+✅ **No false negatives** (didn't miss any signatures)
+
+### Issues Identified
+
+❌ **Problem 1: Handwriting Split Into Multiple Regions**
+- Some signatures may be split into 2+ separate regions
+- Example: Region 4 and Region 5 might be parts of same signature area
+- Caused by gaps between handwritten strokes after masking
+
+❌ **Problem 2: Printed Name + Handwritten Signature Mixed**
+- Region 2: Contains "張 志 銘" (printed) + handwritten signature
+- Region 4: Contains "楊 智 惠" (printed) + handwritten signature
+- PaddleOCR missed these printed names, so they weren't masked
+- Final output includes both printed and handwritten parts
+
+❌ **Problem 3: Printed Text Not Masked by PaddleOCR**
+- 9 regions contain printed text that PaddleOCR didn't detect
+- These became false positive candidates
+- Examples: dates, company names, paragraph text
+- Shows PaddleOCR's detection isn't 100% complete
+
+---
+
+## Proposed Solutions
+
+### Problem 1: Split Signatures
+
+#### Option A: More Aggressive Morphology ⭐ EASY
+**Approach**: Increase kernel size and iterations to connect nearby strokes
+
+```python
+# Current settings:
+kernel = cv2.getStructuringElement(cv2.MORPH_RECT, (5, 5))
+morphed = cv2.morphologyEx(binary, cv2.MORPH_CLOSE, kernel, iterations=2)
+
+# Proposed settings:
+kernel = cv2.getStructuringElement(cv2.MORPH_RECT, (15, 15))  # 3x larger
+morphed = cv2.morphologyEx(binary, cv2.MORPH_CLOSE, kernel, iterations=5)  # More iterations
+```
+
+**Pros**:
+- Simple one-line change
+- Connects nearby strokes automatically
+- Fast execution
+
+**Cons**:
+- May merge unrelated regions if too aggressive
+- Need to tune parameters carefully
+- Could lose fine details
+
+**Recommendation**: ⭐ Try first - easiest to implement and test
+
+---
+
+#### Option B: Region Merging After Detection ⭐⭐ MEDIUM (RECOMMENDED)
+**Approach**: After detecting all regions, merge those that are close together
+
+```python
+def merge_nearby_regions(regions, distance_threshold=50):
+    """
+    Merge regions that are within distance_threshold pixels of each other.
+
+    Args:
+        regions: List of region dicts with 'box' (x, y, w, h)
+        distance_threshold: Maximum pixels between regions to merge
+
+    Returns:
+        List of merged regions
+    """
+    # Algorithm:
+    # 1. Calculate distance between all region pairs
+    # 2. If distance < threshold, merge their bounding boxes
+    # 3. Repeat until no more merges possible
+
+    merged = []
+    # Implementation here...
+    return merged
+```
+
+**Pros**:
+- Keeps signatures together intelligently
+- Won't merge distant unrelated regions
+- Preserves original stroke details
+- Can use vertical/horizontal distance separately
+
+**Cons**:
+- Need to tune distance threshold
+- More complex than Option A
+- May need multiple merge passes
+
+**Recommendation**: ⭐⭐ **Best balance** - implement this first
+
+---
+
+#### Option C: Don't Split - Extract Larger Context ⭐ EASY
+**Approach**: When extracting regions, add significant padding to capture full context
+
+```python
+# Current: padding = 10 pixels
+padding = 50  # Much larger padding
+
+# Or: Merge all regions in the bottom 20% of page
+# (signatures are usually at the bottom)
+```
+
+**Pros**:
+- Guaranteed to capture complete signatures
+- Very simple to implement
+- No risk of losing parts
+
+**Cons**:
+- May include extra unwanted content
+- Larger image files
+- Makes VLM verification more complex
+
+**Recommendation**: ⭐ Use as fallback if B doesn't work
+
+---
+
+### Problem 2: Printed + Handwritten in Same Region
+
+#### Option A: Expand PaddleOCR Masking Boxes ⭐ EASY
+**Approach**: Add padding when masking text boxes to catch edges
+
+```python
+padding = 20  # pixels
+
+for (x, y, w, h) in text_boxes:
+    # Expand box in all directions
+    x_pad = max(0, x - padding)
+    y_pad = max(0, y - padding)
+    w_pad = min(image.shape[1] - x_pad, w + 2*padding)
+    h_pad = min(image.shape[0] - y_pad, h + 2*padding)
+
+    cv2.rectangle(masked_image, (x_pad, y_pad),
+                  (x_pad + w_pad, y_pad + h_pad), (0, 0, 0), -1)
+```
+
+**Pros**:
+- Very simple - one parameter change
+- Catches text edges and nearby text
+- Fast execution
+
+**Cons**:
+- If padding too large, may mask handwriting
+- If padding too small, still misses text
+- Hard to find perfect padding value
+
+**Recommendation**: ⭐ Quick test - try with padding=20-30
+
+---
+
+#### Option B: Run PaddleOCR Again on Each Region ⭐⭐ MEDIUM
+**Approach**: Second-pass OCR on extracted regions to find remaining printed text
+
+```python
+def clean_region(region_image, ocr_client):
+    """
+    Remove any remaining printed text from a region.
+
+    Args:
+        region_image: Extracted candidate region
+        ocr_client: PaddleOCR client
+
+    Returns:
+        Cleaned image with only handwriting
+    """
+    # Run OCR on this specific region
+    text_boxes = ocr_client.get_text_boxes(region_image)
+
+    # Mask any detected printed text
+    cleaned = region_image.copy()
+    for (x, y, w, h) in text_boxes:
+        cv2.rectangle(cleaned, (x, y), (x+w, y+h), (0, 0, 0), -1)
+
+    return cleaned
+```
+
+**Pros**:
+- Very accurate - catches printed text PaddleOCR missed initially
+- Clean separation of printed vs handwritten
+- No manual tuning needed
+
+**Cons**:
+- 2x slower (OCR call per region)
+- May occasionally mask handwritten text if it looks printed
+- More complex pipeline
+
+**Recommendation**: ⭐⭐ Good option if masking padding isn't enough
+
+---
+
+#### Option C: Computer Vision Stroke Analysis ⭐⭐⭐ HARD
+**Approach**: Analyze stroke characteristics to distinguish printed vs handwritten
+
+```python
+def separate_printed_handwritten(region_image):
+    """
+    Use CV techniques to separate printed from handwritten.
+
+    Techniques:
+    - Stroke width analysis (printed = uniform, handwritten = variable)
+    - Edge detection + smoothness (printed = sharp, handwritten = organic)
+    - Connected component analysis
+    - Hough line detection (printed = straight, handwritten = curved)
+    """
+    # Complex implementation...
+    pass
+```
+
+**Pros**:
+- No API calls needed (fast)
+- Can work when OCR fails
+- Learns patterns in data
+
+**Cons**:
+- Very complex to implement
+- May not be reliable across different documents
+- Requires significant tuning
+- Hard to maintain
+
+**Recommendation**: ❌ Skip for now - too complex, uncertain results
+
+---
+
+#### Option D: VLM Crop Guidance ⚠️ RISKY
+**Approach**: Ask VLM to provide coordinates of handwriting location
+
+```python
+prompt = """
+This image contains both printed and handwritten text.
+Where is the handwritten signature located?
+Provide coordinates as: x_start, y_start, x_end, y_end
+"""
+
+# VLM returns coordinates
+# Crop to that region only
+```
+
+**Pros**:
+- VLM understands visual context
+- Can distinguish printed vs handwritten
+
+**Cons**:
+- **VLM coordinates are unreliable** (32% offset discovered in previous tests!)
+- This was the original problem that led to PaddleOCR approach
+- May extract wrong region
+
+**Recommendation**: ❌ **DO NOT USE** - VLM coordinates proven unreliable
+
+---
+
+#### Option E: Two-Stage Hybrid Approach ⭐⭐⭐ BEST (RECOMMENDED)
+**Approach**: Combine detection with targeted cleaning
+
+```python
+def extract_signatures_twostage(pdf_path):
+    """
+    Stage 1: Detect candidate regions (current pipeline)
+    Stage 2: Clean each region
+    """
+    # Stage 1: Full page processing
+    image = render_pdf(pdf_path)
+    text_boxes = ocr_client.get_text_boxes(image)
+    masked_image = mask_text_regions(image, text_boxes, padding=20)
+    candidate_regions = detect_regions(masked_image)
+
+    # Stage 2: Per-region cleaning
+    signatures = []
+    for region_box in candidate_regions:
+        # Extract region from ORIGINAL image (not masked)
+        region_img = extract_region(image, region_box)
+
+        # Option 1: Run OCR again to find remaining printed text
+        region_text_boxes = ocr_client.get_text_boxes(region_img)
+        cleaned_region = mask_text_regions(region_img, region_text_boxes)
+
+        # Option 2: Ask VLM if it contains handwriting (no coordinates!)
+        is_handwriting = vlm_verify(cleaned_region)
+
+        if is_handwriting:
+            signatures.append(cleaned_region)
+
+    return signatures
+```
+
+**Pros**:
+- Best accuracy - two passes of OCR
+- Combines strengths of both approaches
+- VLM only for yes/no, not coordinates
+- Clean final output with only handwriting
+
+**Cons**:
+- Slower (2 OCR calls per page)
+- More complex code
+- Higher computational cost
+
+**Recommendation**: ⭐⭐⭐ **BEST OVERALL** - implement this for production
+
+---
+
+## Implementation Priority
+
+### Phase 1: Quick Wins (Test Immediately)
+1. **Expand masking padding** (Problem 2, Option A) - 5 minutes
+2. **More aggressive morphology** (Problem 1, Option A) - 5 minutes
+3. **Test and measure improvement**
+
+### Phase 2: Region Merging (If Phase 1 insufficient)
+4. **Implement region merging algorithm** (Problem 1, Option B) - 30 minutes
+5. **Test on multiple PDFs**
+6. **Tune distance threshold**
+
+### Phase 3: Two-Stage Approach (Best quality)
+7. **Implement second-pass OCR on regions** (Problem 2, Option E) - 1 hour
+8. **Add VLM verification** (Step 4 of pipeline) - 30 minutes
+9. **Full pipeline testing**
+
+---
+
+## Code Files Status
+
+### Existing Files ✅
+- **`paddleocr_client.py`** - REST API client for PaddleOCR server
+- **`test_paddleocr_client.py`** - Connection and OCR test
+- **`test_mask_and_detect.py`** - Current masking + detection pipeline
+
+### To Be Created 📝
+- **`extract_signatures_paddleocr.py`** - Production pipeline with all improvements
+- **`region_merger.py`** - Region merging utilities
+- **`vlm_verifier.py`** - VLM handwriting verification
+
+---
+
+## Server Configuration
+
+**PaddleOCR Server**:
+- Host: `192.168.30.36:5555`
+- Running: ✅ Yes (PID: 210417)
+- Version: 3.3.0
+- GPU: Enabled
+- Language: Chinese (lang='ch')
+
+**VLM Server**:
+- Host: `192.168.30.36:11434` (Ollama)
+- Model: `qwen2.5vl:32b`
+- Status: Not tested yet in this pipeline
+
+---
+
+## Test Plan
+
+### Test File
+- **File**: `201301_1324_AI1_page3.pdf`
+- **Expected signatures**: 2 (楊智惠, 張志銘)
+- **Current recall**: 100% (found both)
+- **Current precision**: 16.7% (2 correct out of 12 regions)
+
+### Success Metrics After Improvements
+
+| Metric | Current | Target |
+|--------|---------|--------|
+| Signatures found | 2/2 (100%) | 2/2 (100%) |
+| False positives | 10 | < 2 |
+| Precision | 16.7% | > 80% |
+| Signatures split | Unknown | 0 |
+| Printed text in regions | Yes | No |
+
+---
+
+## Git Branch Strategy
+
+**Current branch**: `PaddleOCR-Cover`
+**Status**: Masking + Region Detection working, needs refinement
+
+**Recommended next steps**:
+1. Commit current state with tag: `paddleocr-v1-basic`
+2. Create feature branches:
+   - `paddleocr-region-merging` - For Problem 1 solutions
+   - `paddleocr-two-stage` - For Problem 2 solutions
+3. Merge best solution back to `PaddleOCR-Cover`
+
+---
+
+## Next Actions
+
+### Immediate (Today)
+- [ ] Commit current working state
+- [ ] Test Phase 1 quick wins (padding + morphology)
+- [ ] Measure improvement
+
+### Short-term (This week)
+- [ ] Implement Region Merging (Option B)
+- [ ] Implement Two-Stage OCR (Option E)
+- [ ] Add VLM verification
+- [ ] Test on 10 PDFs
+
+### Long-term (Production)
+- [ ] Optimize performance (parallel processing)
+- [ ] Error handling and logging
+- [ ] Process full 86K dataset
+- [ ] Compare with previous hybrid approach (70% recall)
+
+---
+
+## Comparison: PaddleOCR vs Previous Hybrid Approach
+
+### Previous Approach (VLM-Cover branch)
+- **Method**: VLM names + CV detection + VLM verification
+- **Results**: 70% recall, 100% precision
+- **Problem**: Missed 30% of signatures (CV parameters too conservative)
+
+### PaddleOCR Approach (Current)
+- **Method**: PaddleOCR masking + CV detection + VLM verification
+- **Results**: 100% recall (found both signatures)
+- **Problem**: Low precision (many false positives), printed text not fully removed
+
+### Winner: TBD
+- PaddleOCR shows **better recall potential**
+- After implementing refinements (Phase 2-3), should achieve **high recall + high precision**
+- Need to test on larger dataset to confirm
+
+---
+
+**Document version**: 1.0
+**Last updated**: October 28, 2025
+**Author**: Claude Code
+**Status**: Ready for implementation

PP_OCRV5_RESEARCH_FINDINGS.md

@@ -0,0 +1,281 @@
+# PP-OCRv5 研究發現
+
+**日期**: 2025-01-27
+**分支**: pp-ocrv5-research
+**狀態**: 研究完成
+
+---
+
+## 📋 研究摘要
+
+我們成功升級並測試了 PP-OCRv5，以下是關鍵發現：
+
+### ✅ 成功完成
+1. PaddleOCR 升級：2.7.3 → 3.3.2
+2. 新 API 理解和驗證
+3. 手寫檢測能力測試
+4. 數據結構分析
+
+### ❌ 關鍵限制
+**PP-OCRv5 沒有內建的手寫 vs 印刷文字分類功能**
+
+---
+
+## 🔧 技術細節
+
+### API 變更
+
+**舊 API (2.7.3)**:
+```python
+from paddleocr import PaddleOCR
+ocr = PaddleOCR(lang='ch', show_log=False)
+result = ocr.ocr(image_np, cls=False)
+```
+
+**新 API (3.3.2)**:
+```python
+from paddleocr import PaddleOCR
+
+ocr = PaddleOCR(
+    text_detection_model_name="PP-OCRv5_server_det",
+    text_recognition_model_name="PP-OCRv5_server_rec",
+    use_doc_orientation_classify=False,
+    use_doc_unwarping=False,
+    use_textline_orientation=False
+    # ❌ 不再支持: show_log, cls
+)
+
+result = ocr.predict(image_path)  # ✅ 使用 predict() 而不是 ocr()
+```
+
+### 主要 API 差異
+
+| 特性 | v2.7.3 | v3.3.2 |
+|------|--------|--------|
+| 初始化 | `PaddleOCR(lang='ch')` | `PaddleOCR(text_detection_model_name=...)` |
+| 預測方法 | `ocr.ocr()` | `ocr.predict()` |
+| `cls` 參數 | ✅ 支持 | ❌ 已移除 |
+| `show_log` 參數 | ✅ 支持 | ❌ 已移除 |
+| 返回格式 | `[[[box], (text, conf)], ...]` | `OCRResult` 對象 with `.json` 屬性 |
+| 依賴 | 獨立 | 需要 PaddleX >=3.3.0 |
+
+---
+
+## 📊 返回數據結構
+
+### v3.3.2 返回格式
+
+```python
+result = ocr.predict(image_path)
+json_data = result[0].json['res']
+
+# 可用字段：
+json_data = {
+    'input_path': str,                    # 輸入圖片路徑
+    'page_index': None,                   # PDF 頁碼（圖片為 None）
+    'model_settings': dict,               # 模型配置
+    'dt_polys': list,                     # 檢測多邊形框 (N, 4, 2)
+    'dt_scores': list,                    # 檢測置信度
+    'rec_texts': list,                    # 識別文字
+    'rec_scores': list,                   # 識別置信度
+    'rec_boxes': list,                    # 矩形框 [x_min, y_min, x_max, y_max]
+    'rec_polys': list,                    # 識別多邊形框
+    'text_det_params': dict,              # 檢測參數
+    'text_rec_score_thresh': float,       # 識別閾值
+    'text_type': str,                     # ⚠️ 'general' (語言類型，不是手寫分類)
+    'textline_orientation_angles': list,  # 文字方向角度
+    'return_word_box': bool               # 是否返回詞級框
+}
+```
+
+---
+
+## 🔍 手寫檢測功能測試
+
+### 測試問題
+**PP-OCRv5 是否能區分手寫和印刷文字？**
+
+### 測試結果：❌ 不能
+
+#### 測試過程
+1. ✅ 發現 `text_type` 字段
+2. ❌ 但 `text_type = 'general'` 是**語言類型**，不是書寫風格
+3. ✅ 查閱官方文檔確認
+4. ❌ 沒有任何字段標註手寫 vs 印刷
+
+#### 官方文檔說明
+- `text_type` 可能的值：'general', 'ch', 'en', 'japan', 'pinyin'
+- 這些值指的是**語言/腳本類型**
+- **不是**手寫 (handwritten) vs 印刷 (printed) 的分類
+
+### 結論
+PP-OCRv5 雖然能**識別**手寫文字，但**不會標註**某個文字區域是手寫還是印刷。
+
+---
+
+## 📈 性能提升（根據官方文檔）
+
+### 手寫文字識別準確率
+
+| 類型 | PP-OCRv4 | PP-OCRv5 | 提升 |
+|------|----------|----------|------|
+| 手寫中文 | 0.706 | 0.803 | **+13.7%** |
+| 手寫英文 | 0.249 | 0.841 | **+237%** |
+
+### 實測結果（full_page_original.png）
+
+**v3.3.2 (PP-OCRv5)**:
+- 檢測到 **50** 個文字區域
+- 平均置信度：~0.98
+- 示例：
+  - "依本會計師核閱結果..." (0.9936)
+  - "在所有重大方面有違反..." (0.9976)
+
+**待測試**: v2.7.3 的對比結果（需要回退測試）
+
+---
+
+## 💡 升級影響分析
+
+### 優勢
+1. ✅ **更好的手寫識別能力**（+13.7%）
+2. ✅ **可能檢測到更多手寫區域**
+3. ✅ **更高的識別置信度**
+4. ✅ **統一的 Pipeline 架構**
+
+### 劣勢
+1. ❌ **無法區分手寫和印刷**（仍需 OpenCV Method 3）
+2. ⚠️ **API 完全不兼容**（需重寫服務器代碼）
+3. ⚠️ **依賴 PaddleX**（額外的依賴）
+4. ⚠️ **OpenCV 版本升級**（4.6 → 4.10）
+
+---
+
+## 🎯 對我們項目的影響
+
+### 當前方案（v2.7.3 + OpenCV Method 3）
+```
+PDF → PaddleOCR 檢測 → 遮罩印刷文字 → OpenCV Method 3 分離手寫 → VLM 驗證
+                        ↑ 86.5% 手寫保留率
+```
+
+### PP-OCRv5 方案
+```
+PDF → PP-OCRv5 檢測 → 遮罩印刷文字 → OpenCV Method 3 分離手寫 → VLM 驗證
+      ↑ 可能檢測更多手寫   ↑ 仍然需要！
+```
+
+### 關鍵發現
+**PP-OCRv5 不能替代 OpenCV Method 3！**
+
+---
+
+## 🤔 升級建議
+
+### 升級的理由
+1. 更好地檢測手寫簽名（+13.7% 準確率）
+2. 可能減少漏檢
+3. 更高的識別置信度可以幫助後續分析
+
+### 不升級的理由
+1. 當前方案已經穩定（86.5% 保留率）
+2. 仍然需要 OpenCV Method 3
+3. API 重寫成本高
+4. 額外的依賴和複雜度
+
+### 推薦決策
+
+**階段性升級策略**：
+
+1. **短期（當前）**：
+   - ✅ 保持 v2.7.3 穩定方案
+   - ✅ 繼續使用 OpenCV Method 3
+   - ✅ 在更多樣本上測試當前方案
+
+2. **中期（如果需要優化）**：
+   - 對比測試 v2.7.3 vs v3.3.2 在真實簽名樣本上的性能
+   - 如果 v5 明顯減少漏檢 → 升級
+   - 如果差異不大 → 保持 v2.7.3
+
+3. **長期**：
+   - 關注 PaddleOCR 是否會添加手寫分類功能
+   - 如果有 → 重新評估升級價值
+
+---
+
+## 📝 技術債務記錄
+
+### 如果決定升級到 v3.3.2
+
+需要完成的工作：
+
+1. **服務器端**：
+   - [ ] 重寫 `paddleocr_server.py` 適配新 API
+   - [ ] 測試 GPU 利用率和速度
+   - [ ] 處理 OpenCV 4.10 兼容性
+   - [ ] 更新依賴文檔
+
+2. **客戶端**：
+   - [ ] 更新 `paddleocr_client.py`（如果 REST 接口改變）
+   - [ ] 適配新的返回格式
+
+3. **測試**：
+   - [ ] 10+ 樣本對比測試
+   - [ ] 性能基準測試
+   - [ ] 穩定性測試
+
+4. **文檔**：
+   - [ ] 更新 CURRENT_STATUS.md
+   - [ ] 記錄 API 遷移指南
+   - [ ] 更新部署文檔
+
+---
+
+## ✅ 完成的工作
+
+1. ✅ 升級 PaddleOCR: 2.7.3 → 3.3.2
+2. ✅ 理解新 API 結構
+3. ✅ 測試基礎功能
+4. ✅ 分析返回數據結構
+5. ✅ 測試手寫分類功能（結論：無）
+6. ✅ 查閱官方文檔驗證
+7. ✅ 記錄完整研究過程
+
+---
+
+## 🎓 學到的經驗
+
+1. **API 版本升級風險**：主版本升級通常有破壞性變更
+2. **功能驗證的重要性**：文檔提到的「手寫支持」不等於「手寫分類」
+3. **現有方案的價值**：OpenCV Method 3 仍然是必需的
+4. **性能 vs 複雜度權衡**：不是所有性能提升都值得立即升級
+
+---
+
+## 🔗 相關文檔
+
+- [CURRENT_STATUS.md](./CURRENT_STATUS.md) - 當前穩定方案
+- [NEW_SESSION_HANDOFF.md](./NEW_SESSION_HANDOFF.md) - 研究任務清單
+- [PADDLEOCR_STATUS.md](./PADDLEOCR_STATUS.md) - 詳細技術分析
+
+---
+
+## 📌 下一步
+
+建議用戶：
+
+1. **立即行動**：
+   - 在更多 PDF 樣本上測試當前方案
+   - 記錄成功率和失敗案例
+
+2. **評估升級**：
+   - 如果當前方案滿意 → 保持 v2.7.3
+   - 如果遇到大量漏檢 → 考慮 v3.3.2
+
+3. **長期監控**：
+   - 關注 PaddleOCR GitHub Issues
+   - 追蹤是否有手寫分類功能的更新
+
+---
+
+**結論**: PP-OCRv5 提升了手寫識別能力，但不能替代 OpenCV Method 3 來分離手寫和印刷文字。當前方案（v2.7.3 + OpenCV Method 3）已經足夠好，除非遇到性能瓶頸，否則不建議立即升級。

SAM3_RESEARCH_FINDINGS.md

@@ -0,0 +1,110 @@
+# SAM3 手寫/印刷區域分割研究結果
+
+## 測試環境
+- **服務器**: Linux GPU (192.168.30.36)
+- **CUDA**: 13.0
+- **Python**: 3.12.3
+- **SAM3 版本**: 最新 (2025/11/20 發布)
+- **模型大小**: 848M 參數
+
+## 測試圖片
+- 來源: 會計師簽證報告 PDF 掃描頁面
+- 尺寸: 2481 x 3508 (測試時縮小到 1024 x 1447)
+- 內容: KPMG logo、中文印刷文字、手寫簽名 (3個)、紅色印章 (2個)
+
+---
+
+## 測試結果
+
+### 高效檢測 (分數 > 0.5)
+| Prompt | 區域數 | 最高分數 | 檢測結果 |
+|--------|--------|----------|----------|
+| `company logo` | 6 | **0.855** | ✅ 準確檢測 KPMG logo |
+| `logo` | 8 | **0.853** | ✅ 準確檢測 KPMG logo |
+| `stamp` | 24 | **0.705** | ✅ 準確檢測兩個紅色印章 |
+
+### 低效檢測 (分數 < 0.2)
+| Prompt | 區域數 | 最高分數 | 檢測結果 |
+|--------|--------|----------|----------|
+| `handwritten signature` | 0 | - | ❌ 完全無法檢測 |
+| `signature` | 0 | - | ❌ 完全無法檢測 |
+| `handwriting` | 0 | - | ❌ 完全無法檢測 |
+| `scribble` | 13 | 0.147 | ⚠️ 低分數，位置不準確 |
+| `Chinese characters` | 11 | 0.069 | ⚠️ 非常低分數 |
+
+### 完全無法檢測
+- `handwritten text`
+- `written name`
+- `cursive writing`
+- `autograph`
+- `red stamp` (但 `stamp` 可以)
+- `calligraphy`
+
+---
+
+## 關鍵發現
+
+### SAM3 優勢
+1. **Logo 檢測**: 非常準確 (0.85+ 分數)
+2. **印章檢測**: 效果很好 (0.70+ 分數)
+3. **通用物體分割**: 對自然場景中的物體效果優秀
+
+### SAM3 限制
+1. **無法識別手寫簽名**: 這是最關鍵的發現
+   - 各種 signature 相關的 prompt 分數都接近 0
+   - SAM3 可能沒有在文件手寫簽名數據上訓練
+
+2. **中文手寫字體識別差**:
+   - `Chinese handwritten characters` 無響應
+   - 可能因為訓練數據中缺乏中文手寫樣本
+
+3. **文件場景表現不佳**:
+   - SAM3 主要針對自然場景圖片
+   - 對掃描文件、表格等場景支持有限
+
+---
+
+## 結論
+
+### SAM3 不適合作為手寫簽名提取的主要方案
+
+**原因**:
+1. 無法有效識別「手寫簽名」概念
+2. 對中文手寫內容支持不足
+3. 在文件掃描場景下表現遠不如自然場景
+
+### 建議保留當前方案
+當前 **PaddleOCR + OpenCV Method 3** 方案 (86.5% 手寫保留率) 仍然是更好的選擇：
+- PaddleOCR: 專門針對文字識別訓練，可準確定位印刷文字
+- OpenCV: 通過遮罩和形態學處理有效分離手寫筆畫
+
+### SAM3 的潛在用途
+雖然不適合手寫簽名提取，但 SAM3 可能用於：
+- 檢測並遮罩 Logo 區域
+- 檢測並排除印章干擾
+- 作為預處理步驟的補充工具
+
+---
+
+## 視覺化結果
+
+保存的測試結果圖片：
+- `sam3_stamp_result.png` - 印章檢測 (高準確率)
+- `sam3_logo_result.png` - Logo 檢測 (高準確率)
+- `sam3_scribble_result.png` - Scribble 檢測 (低準確率)
+
+---
+
+## 後續建議
+
+1. **維持現有方案**: PaddleOCR 2.7.3 + OpenCV Method 3
+2. **可選整合 SAM3**: 用於 Logo/印章 檢測作為輔助
+3. **探索其他模型**:
+   - 專門的手寫檢測模型
+   - 文件分析模型 (Document AI)
+   - LayoutLM 等文件理解模型
+
+---
+
+*測試日期: 2025-11-27*
+*分支: sam3-research*

check_rejected_for_missing.py

@@ -0,0 +1,75 @@
+#!/usr/bin/env python3
+"""Check if rejected regions contain the missing signatures."""
+
+import base64
+import requests
+from pathlib import Path
+
+OLLAMA_URL = "http://192.168.30.36:11434"
+OLLAMA_MODEL = "qwen2.5vl:32b"
+REJECTED_PATH = "/Volumes/NV2/PDF-Processing/signature-image-output/signatures/rejected"
+
+# Missing signatures based on test results
+MISSING = {
+    "201301_2061_AI1_page5": "林姿妤",
+    "201301_2458_AI1_page4": "魏興海",
+    "201301_2923_AI1_page3": "陈丽琦"
+}
+
+def encode_image_to_base64(image_path):
+    """Encode image file to base64."""
+    with open(image_path, 'rb') as f:
+        return base64.b64encode(f.read()).decode('utf-8')
+
+def ask_vlm_about_signature(image_base64, expected_name):
+    """Ask VLM if the image contains the expected signature."""
+    prompt = f"""Does this image contain a handwritten signature with the Chinese name: "{expected_name}"?
+
+Look carefully for handwritten Chinese characters matching this name.
+
+Answer only 'yes' or 'no'."""
+
+    payload = {
+        "model": OLLAMA_MODEL,
+        "prompt": prompt,
+        "images": [image_base64],
+        "stream": False
+    }
+
+    try:
+        response = requests.post(f"{OLLAMA_URL}/api/generate", json=payload, timeout=60)
+        response.raise_for_status()
+        answer = response.json()['response'].strip().lower()
+        return answer
+    except Exception as e:
+        return f"error: {str(e)}"
+
+# Check each missing signature
+for pdf_stem, missing_name in MISSING.items():
+    print(f"\n{'='*80}")
+    print(f"Checking rejected regions from: {pdf_stem}")
+    print(f"Looking for missing signature: {missing_name}")
+    print('='*80)
+
+    # Find all rejected regions from this PDF
+    rejected_regions = sorted(Path(REJECTED_PATH).glob(f"{pdf_stem}_region_*.png"))
+
+    print(f"Found {len(rejected_regions)} rejected regions to check")
+
+    for region_path in rejected_regions:
+        region_name = region_path.name
+        print(f"\nChecking: {region_name}...", end='', flush=True)
+
+        # Encode and ask VLM
+        image_base64 = encode_image_to_base64(region_path)
+        answer = ask_vlm_about_signature(image_base64, missing_name)
+
+        if 'yes' in answer:
+            print(f" ✅ FOUND! This region contains {missing_name}")
+            print(f"   → The signature was detected by CV but rejected by verification!")
+        else:
+            print(f" ❌ No (VLM says: {answer})")
+
+print(f"\n{'='*80}")
+print("Analysis complete!")
+print('='*80)

extract_signatures_paddleocr_improved.py

@@ -0,0 +1,415 @@
+#!/usr/bin/env python3
+"""
+PaddleOCR Signature Extraction - Improved Pipeline
+
+Implements:
+- Method B: Region Merging (merge nearby regions to avoid splits)
+- Method E: Two-Stage Approach (second OCR pass on regions)
+
+Pipeline:
+1. PaddleOCR detects printed text on full page
+2. Mask printed text with padding
+3. Detect candidate regions
+4. Merge nearby regions (METHOD B)
+5. For each region: Run OCR again to remove remaining printed text (METHOD E)
+6. VLM verification (optional)
+7. Save cleaned handwriting regions
+"""
+
+import fitz  # PyMuPDF
+import numpy as np
+import cv2
+from pathlib import Path
+from paddleocr_client import create_ocr_client
+from typing import List, Dict, Tuple
+import base64
+import requests
+
+# Configuration
+TEST_PDF = "/Volumes/NV2/PDF-Processing/signature-image-output/201301_1324_AI1_page3.pdf"
+OUTPUT_DIR = "/Volumes/NV2/PDF-Processing/signature-image-output/paddleocr_improved"
+DPI = 300
+
+# PaddleOCR Settings
+MASKING_PADDING = 25  # Pixels to expand text boxes when masking
+
+# Region Detection Parameters
+MIN_REGION_AREA = 3000
+MAX_REGION_AREA = 300000
+MIN_ASPECT_RATIO = 0.3
+MAX_ASPECT_RATIO = 15.0
+
+# Region Merging Parameters (METHOD B)
+MERGE_DISTANCE_HORIZONTAL = 100  # pixels
+MERGE_DISTANCE_VERTICAL = 50     # pixels
+
+# VLM Settings (optional)
+USE_VLM_VERIFICATION = False  # Set to True to enable VLM filtering
+OLLAMA_URL = "http://192.168.30.36:11434"
+OLLAMA_MODEL = "qwen2.5vl:32b"
+
+
+def merge_nearby_regions(regions: List[Dict],
+                        h_distance: int = 100,
+                        v_distance: int = 50) -> List[Dict]:
+    """
+    Merge regions that are close to each other (METHOD B).
+
+    Args:
+        regions: List of region dicts with 'box': (x, y, w, h)
+        h_distance: Maximum horizontal distance between regions to merge
+        v_distance: Maximum vertical distance between regions to merge
+
+    Returns:
+        List of merged regions
+    """
+    if not regions:
+        return []
+
+    # Sort regions by y-coordinate (top to bottom)
+    regions = sorted(regions, key=lambda r: r['box'][1])
+
+    merged = []
+    skip_indices = set()
+
+    for i, region1 in enumerate(regions):
+        if i in skip_indices:
+            continue
+
+        x1, y1, w1, h1 = region1['box']
+
+        # Find all regions that should merge with this one
+        merge_group = [region1]
+
+        for j, region2 in enumerate(regions[i+1:], start=i+1):
+            if j in skip_indices:
+                continue
+
+            x2, y2, w2, h2 = region2['box']
+
+            # Calculate distances
+            # Horizontal distance: gap between boxes horizontally
+            h_dist = max(0, max(x1, x2) - min(x1 + w1, x2 + w2))
+
+            # Vertical distance: gap between boxes vertically
+            v_dist = max(0, max(y1, y2) - min(y1 + h1, y2 + h2))
+
+            # Check if regions are close enough to merge
+            if h_dist <= h_distance and v_dist <= v_distance:
+                merge_group.append(region2)
+                skip_indices.add(j)
+                # Update bounding box to include new region
+                x1 = min(x1, x2)
+                y1 = min(y1, y2)
+                w1 = max(x1 + w1, x2 + w2) - x1
+                h1 = max(y1 + h1, y2 + h2) - y1
+
+        # Create merged region
+        merged_box = (x1, y1, w1, h1)
+        merged_area = w1 * h1
+        merged_aspect = w1 / h1 if h1 > 0 else 0
+
+        merged.append({
+            'box': merged_box,
+            'area': merged_area,
+            'aspect_ratio': merged_aspect,
+            'merged_count': len(merge_group)
+        })
+
+    return merged
+
+
+def clean_region_with_ocr(region_image: np.ndarray,
+                          ocr_client,
+                          padding: int = 10) -> np.ndarray:
+    """
+    Remove printed text from a region using second OCR pass (METHOD E).
+
+    Args:
+        region_image: The region image to clean
+        ocr_client: PaddleOCR client
+        padding: Padding around detected text boxes
+
+    Returns:
+        Cleaned region with printed text masked
+    """
+    try:
+        # Run OCR on this specific region
+        text_boxes = ocr_client.get_text_boxes(region_image)
+
+        if not text_boxes:
+            return region_image  # No text found, return as-is
+
+        # Mask detected printed text
+        cleaned = region_image.copy()
+        for (x, y, w, h) in text_boxes:
+            # Add padding
+            x_pad = max(0, x - padding)
+            y_pad = max(0, y - padding)
+            w_pad = min(cleaned.shape[1] - x_pad, w + 2*padding)
+            h_pad = min(cleaned.shape[0] - y_pad, h + 2*padding)
+
+            cv2.rectangle(cleaned, (x_pad, y_pad),
+                         (x_pad + w_pad, y_pad + h_pad),
+                         (255, 255, 255), -1)  # Fill with white
+
+        return cleaned
+
+    except Exception as e:
+        print(f"      Warning: OCR cleaning failed: {e}")
+        return region_image
+
+
+def verify_handwriting_with_vlm(image: np.ndarray) -> Tuple[bool, float]:
+    """
+    Use VLM to verify if image contains handwriting.
+
+    Args:
+        image: Region image (RGB numpy array)
+
+    Returns:
+        (is_handwriting: bool, confidence: float)
+    """
+    try:
+        # Convert image to base64
+        from PIL import Image
+        from io import BytesIO
+
+        pil_image = Image.fromarray(image.astype(np.uint8))
+        buffered = BytesIO()
+        pil_image.save(buffered, format="PNG")
+        image_base64 = base64.b64encode(buffered.getvalue()).decode('utf-8')
+
+        # Ask VLM
+        prompt = """Does this image contain handwritten text or a handwritten signature?
+
+Answer only 'yes' or 'no', followed by a confidence score 0-100.
+Format: yes 95 OR no 80"""
+
+        payload = {
+            "model": OLLAMA_MODEL,
+            "prompt": prompt,
+            "images": [image_base64],
+            "stream": False
+        }
+
+        response = requests.post(f"{OLLAMA_URL}/api/generate",
+                                json=payload, timeout=30)
+        response.raise_for_status()
+        answer = response.json()['response'].strip().lower()
+
+        # Parse answer
+        is_handwriting = 'yes' in answer
+
+        # Try to extract confidence
+        confidence = 0.5
+        parts = answer.split()
+        for part in parts:
+            try:
+                conf = float(part)
+                if 0 <= conf <= 100:
+                    confidence = conf / 100
+                    break
+            except:
+                continue
+
+        return is_handwriting, confidence
+
+    except Exception as e:
+        print(f"      Warning: VLM verification failed: {e}")
+        return True, 0.5  # Default to accepting the region
+
+
+print("="*80)
+print("PaddleOCR Improved Pipeline - Region Merging + Two-Stage Cleaning")
+print("="*80)
+
+# Create output directory
+Path(OUTPUT_DIR).mkdir(parents=True, exist_ok=True)
+
+# Step 1: Connect to PaddleOCR
+print("\n1. Connecting to PaddleOCR server...")
+try:
+    ocr_client = create_ocr_client()
+    print(f"   ✅ Connected: {ocr_client.server_url}")
+except Exception as e:
+    print(f"   ❌ Error: {e}")
+    exit(1)
+
+# Step 2: Render PDF
+print("\n2. Rendering PDF...")
+try:
+    doc = fitz.open(TEST_PDF)
+    page = doc[0]
+    mat = fitz.Matrix(DPI/72, DPI/72)
+    pix = page.get_pixmap(matrix=mat)
+    original_image = np.frombuffer(pix.samples, dtype=np.uint8).reshape(
+        pix.height, pix.width, pix.n)
+
+    if pix.n == 4:
+        original_image = cv2.cvtColor(original_image, cv2.COLOR_RGBA2RGB)
+
+    print(f"   ✅ Rendered: {original_image.shape[1]}x{original_image.shape[0]}")
+    doc.close()
+except Exception as e:
+    print(f"   ❌ Error: {e}")
+    exit(1)
+
+# Step 3: Detect printed text (Stage 1)
+print("\n3. Detecting printed text (Stage 1 OCR)...")
+try:
+    text_boxes = ocr_client.get_text_boxes(original_image)
+    print(f"   ✅ Detected {len(text_boxes)} text regions")
+except Exception as e:
+    print(f"   ❌ Error: {e}")
+    exit(1)
+
+# Step 4: Mask printed text with padding
+print(f"\n4. Masking printed text (padding={MASKING_PADDING}px)...")
+try:
+    masked_image = original_image.copy()
+
+    for (x, y, w, h) in text_boxes:
+        # Add padding
+        x_pad = max(0, x - MASKING_PADDING)
+        y_pad = max(0, y - MASKING_PADDING)
+        w_pad = min(masked_image.shape[1] - x_pad, w + 2*MASKING_PADDING)
+        h_pad = min(masked_image.shape[0] - y_pad, h + 2*MASKING_PADDING)
+
+        cv2.rectangle(masked_image, (x_pad, y_pad),
+                     (x_pad + w_pad, y_pad + h_pad), (0, 0, 0), -1)
+
+    print(f"   ✅ Masked {len(text_boxes)} regions")
+except Exception as e:
+    print(f"   ❌ Error: {e}")
+    exit(1)
+
+# Step 5: Detect candidate regions
+print("\n5. Detecting candidate regions...")
+try:
+    gray = cv2.cvtColor(masked_image, cv2.COLOR_RGB2GRAY)
+    _, binary = cv2.threshold(gray, 250, 255, cv2.THRESH_BINARY_INV)
+
+    kernel = cv2.getStructuringElement(cv2.MORPH_RECT, (5, 5))
+    morphed = cv2.morphologyEx(binary, cv2.MORPH_CLOSE, kernel, iterations=2)
+
+    contours, _ = cv2.findContours(morphed, cv2.RETR_EXTERNAL, cv2.CHAIN_APPROX_SIMPLE)
+
+    candidate_regions = []
+    for contour in contours:
+        x, y, w, h = cv2.boundingRect(contour)
+        area = w * h
+        aspect_ratio = w / h if h > 0 else 0
+
+        if (MIN_REGION_AREA <= area <= MAX_REGION_AREA and
+            MIN_ASPECT_RATIO <= aspect_ratio <= MAX_ASPECT_RATIO):
+            candidate_regions.append({
+                'box': (x, y, w, h),
+                'area': area,
+                'aspect_ratio': aspect_ratio
+            })
+
+    print(f"   ✅ Found {len(candidate_regions)} candidate regions")
+except Exception as e:
+    print(f"   ❌ Error: {e}")
+    exit(1)
+
+# Step 6: Merge nearby regions (METHOD B)
+print(f"\n6. Merging nearby regions (h_dist<={MERGE_DISTANCE_HORIZONTAL}, v_dist<={MERGE_DISTANCE_VERTICAL})...")
+try:
+    merged_regions = merge_nearby_regions(
+        candidate_regions,
+        h_distance=MERGE_DISTANCE_HORIZONTAL,
+        v_distance=MERGE_DISTANCE_VERTICAL
+    )
+    print(f"   ✅ Merged {len(candidate_regions)} → {len(merged_regions)} regions")
+
+    for i, region in enumerate(merged_regions):
+        if region['merged_count'] > 1:
+            print(f"      Region {i+1}: Merged {region['merged_count']} sub-regions")
+except Exception as e:
+    print(f"   ❌ Error: {e}")
+    import traceback
+    traceback.print_exc()
+    exit(1)
+
+# Step 7: Extract and clean each region (METHOD E)
+print("\n7. Extracting and cleaning regions (Stage 2 OCR)...")
+final_signatures = []
+
+for i, region in enumerate(merged_regions):
+    x, y, w, h = region['box']
+    print(f"\n   Region {i+1}/{len(merged_regions)}: ({x}, {y}, {w}, {h})")
+
+    # Extract region from ORIGINAL image (not masked)
+    padding = 10
+    x_pad = max(0, x - padding)
+    y_pad = max(0, y - padding)
+    w_pad = min(original_image.shape[1] - x_pad, w + 2*padding)
+    h_pad = min(original_image.shape[0] - y_pad, h + 2*padding)
+
+    region_img = original_image[y_pad:y_pad+h_pad, x_pad:x_pad+w_pad].copy()
+
+    print(f"      - Extracted: {region_img.shape[1]}x{region_img.shape[0]}px")
+
+    # Clean with second OCR pass
+    print(f"      - Running Stage 2 OCR to remove printed text...")
+    cleaned_region = clean_region_with_ocr(region_img, ocr_client, padding=5)
+
+    # VLM verification (optional)
+    if USE_VLM_VERIFICATION:
+        print(f"      - VLM verification...")
+        is_handwriting, confidence = verify_handwriting_with_vlm(cleaned_region)
+        print(f"      - VLM says: {'✅ Handwriting' if is_handwriting else '❌ Not handwriting'} (confidence: {confidence:.2f})")
+
+        if not is_handwriting:
+            print(f"      - Skipping (not handwriting)")
+            continue
+
+    # Save
+    final_signatures.append({
+        'image': cleaned_region,
+        'box': region['box'],
+        'original_image': region_img
+    })
+
+    print(f"      ✅ Kept as signature candidate")
+
+print(f"\n   ✅ Final signatures: {len(final_signatures)}")
+
+# Step 8: Save results
+print("\n8. Saving results...")
+
+for i, sig in enumerate(final_signatures):
+    # Save cleaned signature
+    sig_path = Path(OUTPUT_DIR) / f"signature_{i+1:02d}_cleaned.png"
+    cv2.imwrite(str(sig_path), cv2.cvtColor(sig['image'], cv2.COLOR_RGB2BGR))
+
+    # Save original region for comparison
+    orig_path = Path(OUTPUT_DIR) / f"signature_{i+1:02d}_original.png"
+    cv2.imwrite(str(orig_path), cv2.cvtColor(sig['original_image'], cv2.COLOR_RGB2BGR))
+
+    print(f"   📁 Signature {i+1}: {sig_path.name}")
+
+# Save visualizations
+vis_merged = original_image.copy()
+for region in merged_regions:
+    x, y, w, h = region['box']
+    color = (255, 0, 0) if region in [{'box': s['box']} for s in final_signatures] else (128, 128, 128)
+    cv2.rectangle(vis_merged, (x, y), (x + w, y + h), color, 3)
+
+vis_path = Path(OUTPUT_DIR) / "visualization_merged_regions.png"
+cv2.imwrite(str(vis_path), cv2.cvtColor(vis_merged, cv2.COLOR_RGB2BGR))
+print(f"   📁 Visualization: {vis_path.name}")
+
+print("\n" + "="*80)
+print("Pipeline completed!")
+print(f"Results: {OUTPUT_DIR}")
+print("="*80)
+print(f"\nSummary:")
+print(f"  - Stage 1 OCR: {len(text_boxes)} text regions masked")
+print(f"  - Initial candidates: {len(candidate_regions)}")
+print(f"  - After merging: {len(merged_regions)}")
+print(f"  - Final signatures: {len(final_signatures)}")
+print(f"  - Expected signatures: 2 (楊智惠, 張志銘)")
+print("="*80)

extract_signatures_yolo.py

@@ -0,0 +1,413 @@
+#!/usr/bin/env python3
+"""
+YOLO-based signature extraction from PDF documents.
+Uses a trained YOLOv11n model to detect and extract handwritten signatures.
+
+Pipeline:
+    PDF → Render to Image → YOLO Detection → Crop Signatures → Output
+"""
+
+import csv
+import json
+import os
+import random
+import sys
+from datetime import datetime
+from pathlib import Path
+from typing import Optional
+
+import cv2
+import fitz  # PyMuPDF
+import numpy as np
+from ultralytics import YOLO
+
+
+# Configuration
+CSV_PATH = "/Volumes/NV2/PDF-Processing/master_signatures.csv"
+PDF_BASE_PATH = "/Volumes/NV2/PDF-Processing/total-pdf"
+OUTPUT_PATH = "/Volumes/NV2/PDF-Processing/signature-image-output/yolo"
+OUTPUT_PATH_NO_STAMP = "/Volumes/NV2/PDF-Processing/signature-image-output/yolo_no_stamp"
+MODEL_PATH = "/Volumes/NV2/pdf_recognize/models/best.pt"
+
+# Detection parameters
+DPI = 300
+CONFIDENCE_THRESHOLD = 0.5
+
+
+def remove_red_stamp(image: np.ndarray) -> np.ndarray:
+    """
+    Remove red stamp pixels from an image by replacing them with white.
+
+    Uses HSV color space to detect red regions (stamps are typically red/orange).
+
+    Args:
+        image: RGB image as numpy array
+
+    Returns:
+        Image with red stamp pixels replaced by white
+    """
+    # Convert to HSV
+    hsv = cv2.cvtColor(image, cv2.COLOR_RGB2HSV)
+
+    # Red color wraps around in HSV, so we need two ranges
+    # Range 1: H = 0-10 (red-orange)
+    lower_red1 = np.array([0, 50, 50])
+    upper_red1 = np.array([10, 255, 255])
+
+    # Range 2: H = 160-180 (red-magenta)
+    lower_red2 = np.array([160, 50, 50])
+    upper_red2 = np.array([180, 255, 255])
+
+    # Create masks for red regions
+    mask1 = cv2.inRange(hsv, lower_red1, upper_red1)
+    mask2 = cv2.inRange(hsv, lower_red2, upper_red2)
+
+    # Combine masks
+    red_mask = cv2.bitwise_or(mask1, mask2)
+
+    # Optional: dilate mask slightly to catch edges
+    kernel = np.ones((3, 3), np.uint8)
+    red_mask = cv2.dilate(red_mask, kernel, iterations=1)
+
+    # Replace red pixels with white
+    result = image.copy()
+    result[red_mask > 0] = [255, 255, 255]
+
+    return result
+
+
+class YOLOSignatureExtractor:
+    """Extract signatures from PDF pages using YOLO object detection."""
+
+    def __init__(self, model_path: str = MODEL_PATH, conf_threshold: float = CONFIDENCE_THRESHOLD):
+        """
+        Initialize the extractor with a trained YOLO model.
+
+        Args:
+            model_path: Path to the YOLO model weights
+            conf_threshold: Minimum confidence threshold for detections
+        """
+        print(f"Loading YOLO model from {model_path}...")
+        self.model = YOLO(model_path)
+        self.conf_threshold = conf_threshold
+        self.dpi = DPI
+        print(f"Model loaded. Confidence threshold: {conf_threshold}")
+
+    def render_pdf_page(self, pdf_path: str, page_num: int) -> Optional[np.ndarray]:
+        """
+        Render a PDF page to an image array.
+
+        Args:
+            pdf_path: Path to the PDF file
+            page_num: Page number (1-indexed)
+
+        Returns:
+            RGB image as numpy array, or None if failed
+        """
+        try:
+            doc = fitz.open(pdf_path)
+            if page_num < 1 or page_num > len(doc):
+                print(f"  Invalid page number: {page_num} (PDF has {len(doc)} pages)")
+                doc.close()
+                return None
+
+            page = doc[page_num - 1]
+            mat = fitz.Matrix(self.dpi / 72, self.dpi / 72)
+            pix = page.get_pixmap(matrix=mat, alpha=False)
+            image = np.frombuffer(pix.samples, dtype=np.uint8)
+            image = image.reshape(pix.height, pix.width, pix.n)
+            doc.close()
+            return image
+        except Exception as e:
+            print(f"  Error rendering PDF: {e}")
+            return None
+
+    def detect_signatures(self, image: np.ndarray) -> list[dict]:
+        """
+        Detect signature regions in an image using YOLO.
+
+        Args:
+            image: RGB image as numpy array
+
+        Returns:
+            List of detected signatures with box coordinates and confidence
+        """
+        results = self.model(image, conf=self.conf_threshold, verbose=False)
+        signatures = []
+
+        for r in results:
+            for box in r.boxes:
+                x1, y1, x2, y2 = map(int, box.xyxy[0].cpu().numpy())
+                conf = float(box.conf[0].cpu().numpy())
+                signatures.append({
+                    'box': (x1, y1, x2 - x1, y2 - y1),  # x, y, w, h format
+                    'xyxy': (x1, y1, x2, y2),
+                    'confidence': conf
+                })
+
+        # Sort by y-coordinate (top to bottom), then x-coordinate (left to right)
+        signatures.sort(key=lambda s: (s['box'][1], s['box'][0]))
+
+        return signatures
+
+    def extract_signature_images(self, image: np.ndarray, signatures: list[dict]) -> list[np.ndarray]:
+        """
+        Crop signature regions from the image.
+
+        Args:
+            image: RGB image as numpy array
+            signatures: List of detected signatures
+
+        Returns:
+            List of cropped signature images
+        """
+        cropped = []
+        for sig in signatures:
+            x, y, w, h = sig['box']
+            # Ensure bounds are within image
+            x = max(0, x)
+            y = max(0, y)
+            x2 = min(image.shape[1], x + w)
+            y2 = min(image.shape[0], y + h)
+            cropped.append(image[y:y2, x:x2])
+        return cropped
+
+    def create_visualization(self, image: np.ndarray, signatures: list[dict]) -> np.ndarray:
+        """
+        Create a visualization with detection boxes drawn on the image.
+
+        Args:
+            image: RGB image as numpy array
+            signatures: List of detected signatures
+
+        Returns:
+            Image with drawn bounding boxes
+        """
+        vis = image.copy()
+        for i, sig in enumerate(signatures):
+            x1, y1, x2, y2 = sig['xyxy']
+            conf = sig['confidence']
+
+            # Draw box
+            cv2.rectangle(vis, (x1, y1), (x2, y2), (255, 0, 0), 3)
+
+            # Draw label
+            label = f"sig{i+1}: {conf:.2f}"
+            font_scale = 0.8
+            thickness = 2
+            (text_w, text_h), _ = cv2.getTextSize(label, cv2.FONT_HERSHEY_SIMPLEX, font_scale, thickness)
+
+            cv2.rectangle(vis, (x1, y1 - text_h - 10), (x1 + text_w + 5, y1), (255, 0, 0), -1)
+            cv2.putText(vis, label, (x1 + 2, y1 - 5), cv2.FONT_HERSHEY_SIMPLEX,
+                        font_scale, (255, 255, 255), thickness)
+
+        return vis
+
+
+def find_pdf_file(filename: str) -> Optional[str]:
+    """
+    Search for PDF file in batch directories.
+
+    Args:
+        filename: PDF filename to search for
+
+    Returns:
+        Full path if found, None otherwise
+    """
+    for batch_dir in sorted(Path(PDF_BASE_PATH).glob("batch_*")):
+        pdf_path = batch_dir / filename
+        if pdf_path.exists():
+            return str(pdf_path)
+    return None
+
+
+def load_csv_samples(csv_path: str, sample_size: int = 50, seed: int = 42) -> list[dict]:
+    """
+    Load random samples from the CSV file.
+
+    Args:
+        csv_path: Path to master_signatures.csv
+        sample_size: Number of samples to load
+        seed: Random seed for reproducibility
+
+    Returns:
+        List of dictionaries with filename and page info
+    """
+    with open(csv_path, 'r') as f:
+        reader = csv.DictReader(f)
+        all_rows = list(reader)
+
+    random.seed(seed)
+    samples = random.sample(all_rows, min(sample_size, len(all_rows)))
+
+    return samples
+
+
+def process_samples(extractor: YOLOSignatureExtractor, samples: list[dict],
+                    output_dir: str, output_dir_no_stamp: str = None,
+                    save_visualization: bool = True) -> dict:
+    """
+    Process a list of PDF samples and extract signatures.
+
+    Args:
+        extractor: YOLOSignatureExtractor instance
+        samples: List of sample dictionaries from CSV
+        output_dir: Output directory for signatures
+        output_dir_no_stamp: Output directory for stamp-removed signatures (optional)
+        save_visualization: Whether to save visualization images
+
+    Returns:
+        Results dictionary with statistics and per-file results
+    """
+    os.makedirs(output_dir, exist_ok=True)
+    if save_visualization:
+        os.makedirs(os.path.join(output_dir, "visualization"), exist_ok=True)
+
+    # Create no-stamp output directory if specified
+    if output_dir_no_stamp:
+        os.makedirs(output_dir_no_stamp, exist_ok=True)
+
+    results = {
+        'timestamp': datetime.now().isoformat(),
+        'total_samples': len(samples),
+        'processed': 0,
+        'pdf_not_found': 0,
+        'render_failed': 0,
+        'total_signatures': 0,
+        'files': {}
+    }
+
+    for i, row in enumerate(samples):
+        filename = row['filename']
+        page_num = int(row['page'])
+        base_name = Path(filename).stem
+
+        print(f"[{i+1}/{len(samples)}] Processing: {filename}, page {page_num}...", end=' ', flush=True)
+
+        # Find PDF
+        pdf_path = find_pdf_file(filename)
+        if pdf_path is None:
+            print("PDF NOT FOUND")
+            results['pdf_not_found'] += 1
+            results['files'][filename] = {'status': 'pdf_not_found'}
+            continue
+
+        # Render page
+        image = extractor.render_pdf_page(pdf_path, page_num)
+        if image is None:
+            print("RENDER FAILED")
+            results['render_failed'] += 1
+            results['files'][filename] = {'status': 'render_failed'}
+            continue
+
+        # Detect signatures
+        signatures = extractor.detect_signatures(image)
+        num_sigs = len(signatures)
+        results['total_signatures'] += num_sigs
+        results['processed'] += 1
+
+        print(f"Found {num_sigs} signature(s)")
+
+        # Extract and save signature crops
+        crops = extractor.extract_signature_images(image, signatures)
+        for j, (crop, sig) in enumerate(zip(crops, signatures)):
+            crop_filename = f"{base_name}_page{page_num}_sig{j+1}.png"
+            crop_path = os.path.join(output_dir, crop_filename)
+            cv2.imwrite(crop_path, cv2.cvtColor(crop, cv2.COLOR_RGB2BGR))
+
+            # Save stamp-removed version if output dir specified
+            if output_dir_no_stamp:
+                crop_no_stamp = remove_red_stamp(crop)
+                crop_no_stamp_path = os.path.join(output_dir_no_stamp, crop_filename)
+                cv2.imwrite(crop_no_stamp_path, cv2.cvtColor(crop_no_stamp, cv2.COLOR_RGB2BGR))
+
+        # Save visualization
+        if save_visualization and signatures:
+            vis_image = extractor.create_visualization(image, signatures)
+            vis_filename = f"{base_name}_page{page_num}_annotated.png"
+            vis_path = os.path.join(output_dir, "visualization", vis_filename)
+            cv2.imwrite(vis_path, cv2.cvtColor(vis_image, cv2.COLOR_RGB2BGR))
+
+        # Store file results
+        results['files'][filename] = {
+            'status': 'success',
+            'page': page_num,
+            'signatures': [
+                {
+                    'box': list(sig['box']),
+                    'confidence': sig['confidence']
+                }
+                for sig in signatures
+            ]
+        }
+
+    return results
+
+
+def print_summary(results: dict):
+    """Print processing summary."""
+    print("\n" + "=" * 60)
+    print("YOLO SIGNATURE EXTRACTION SUMMARY")
+    print("=" * 60)
+    print(f"Total samples:        {results['total_samples']}")
+    print(f"Successfully processed: {results['processed']}")
+    print(f"PDFs not found:       {results['pdf_not_found']}")
+    print(f"Render failed:        {results['render_failed']}")
+    print(f"Total signatures found: {results['total_signatures']}")
+
+    if results['processed'] > 0:
+        avg_sigs = results['total_signatures'] / results['processed']
+        print(f"Average signatures/page: {avg_sigs:.2f}")
+
+    print("=" * 60)
+
+
+def main():
+    """Main entry point for signature extraction."""
+    print("=" * 60)
+    print("YOLO Signature Extraction Pipeline")
+    print("=" * 60)
+    print(f"Model: {MODEL_PATH}")
+    print(f"CSV: {CSV_PATH}")
+    print(f"Output (original): {OUTPUT_PATH}")
+    print(f"Output (no stamp): {OUTPUT_PATH_NO_STAMP}")
+    print(f"Confidence threshold: {CONFIDENCE_THRESHOLD}")
+    print("=" * 60 + "\n")
+
+    # Initialize extractor
+    extractor = YOLOSignatureExtractor(MODEL_PATH, CONFIDENCE_THRESHOLD)
+
+    # Load samples
+    print("\nLoading samples from CSV...")
+    samples = load_csv_samples(CSV_PATH, sample_size=50, seed=42)
+    print(f"Loaded {len(samples)} samples\n")
+
+    # Process samples (with stamp removal)
+    results = process_samples(
+        extractor, samples, OUTPUT_PATH,
+        output_dir_no_stamp=OUTPUT_PATH_NO_STAMP,
+        save_visualization=True
+    )
+
+    # Save results JSON
+    results_path = os.path.join(OUTPUT_PATH, "results.json")
+    with open(results_path, 'w') as f:
+        json.dump(results, f, indent=2)
+    print(f"\nResults saved to: {results_path}")
+
+    # Print summary
+    print_summary(results)
+    print(f"\nStamp-removed signatures saved to: {OUTPUT_PATH_NO_STAMP}")
+
+
+if __name__ == "__main__":
+    try:
+        main()
+    except KeyboardInterrupt:
+        print("\n\nProcess interrupted by user.")
+        sys.exit(1)
+    except Exception as e:
+        print(f"\n\nFATAL ERROR: {e}")
+        import traceback
+        traceback.print_exc()
+        sys.exit(1)

paddleocr_client.py

@@ -0,0 +1,169 @@
+#!/usr/bin/env python3
+"""
+PaddleOCR Client
+Connects to remote PaddleOCR server for OCR inference
+"""
+
+import requests
+import base64
+import numpy as np
+from typing import List, Dict, Tuple, Optional
+from PIL import Image
+from io import BytesIO
+
+class PaddleOCRClient:
+    """Client for remote PaddleOCR server."""
+
+    def __init__(self, server_url: str = "http://192.168.30.36:5555"):
+        """
+        Initialize PaddleOCR client.
+
+        Args:
+            server_url: URL of the PaddleOCR server
+        """
+        self.server_url = server_url.rstrip('/')
+        self.timeout = 30  # seconds
+
+    def health_check(self) -> bool:
+        """
+        Check if server is healthy.
+
+        Returns:
+            True if server is healthy, False otherwise
+        """
+        try:
+            response = requests.get(
+                f"{self.server_url}/health",
+                timeout=5
+            )
+            return response.status_code == 200 and response.json().get('status') == 'ok'
+        except Exception as e:
+            print(f"Health check failed: {e}")
+            return False
+
+    def ocr(self, image: np.ndarray) -> List[Dict]:
+        """
+        Perform OCR on an image.
+
+        Args:
+            image: numpy array of the image (RGB format)
+
+        Returns:
+            List of detection results, each containing:
+                - box: [[x1,y1], [x2,y2], [x3,y3], [x4,y4]]
+                - text: detected text string
+                - confidence: confidence score (0-1)
+
+        Raises:
+            Exception if OCR fails
+        """
+        # Convert numpy array to PIL Image
+        if len(image.shape) == 2:  # Grayscale
+            pil_image = Image.fromarray(image)
+        else:  # RGB or RGBA
+            pil_image = Image.fromarray(image.astype(np.uint8))
+
+        # Encode to base64
+        buffered = BytesIO()
+        pil_image.save(buffered, format="PNG")
+        image_base64 = base64.b64encode(buffered.getvalue()).decode('utf-8')
+
+        # Send request
+        try:
+            response = requests.post(
+                f"{self.server_url}/ocr",
+                json={"image": image_base64},
+                timeout=self.timeout
+            )
+            response.raise_for_status()
+
+            result = response.json()
+
+            if not result.get('success'):
+                error_msg = result.get('error', 'Unknown error')
+                raise Exception(f"OCR failed: {error_msg}")
+
+            return result.get('results', [])
+
+        except requests.exceptions.Timeout:
+            raise Exception(f"OCR request timed out after {self.timeout} seconds")
+        except requests.exceptions.ConnectionError:
+            raise Exception(f"Could not connect to server at {self.server_url}")
+        except Exception as e:
+            raise Exception(f"OCR request failed: {str(e)}")
+
+    def get_text_boxes(self, image: np.ndarray) -> List[Tuple[int, int, int, int]]:
+        """
+        Get bounding boxes of all detected text.
+
+        Args:
+            image: numpy array of the image
+
+        Returns:
+            List of bounding boxes as (x, y, w, h) tuples
+        """
+        results = self.ocr(image)
+        boxes = []
+
+        for result in results:
+            box = result['box']  # [[x1,y1], [x2,y2], [x3,y3], [x4,y4]]
+
+            # Convert polygon to bounding box
+            xs = [point[0] for point in box]
+            ys = [point[1] for point in box]
+
+            x = int(min(xs))
+            y = int(min(ys))
+            w = int(max(xs) - min(xs))
+            h = int(max(ys) - min(ys))
+
+            boxes.append((x, y, w, h))
+
+        return boxes
+
+    def __repr__(self):
+        return f"PaddleOCRClient(server_url='{self.server_url}')"
+
+
+# Convenience function
+def create_ocr_client(server_url: str = "http://192.168.30.36:5555") -> PaddleOCRClient:
+    """
+    Create and test PaddleOCR client.
+
+    Args:
+        server_url: URL of the PaddleOCR server
+
+    Returns:
+        PaddleOCRClient instance
+
+    Raises:
+        Exception if server is not reachable
+    """
+    client = PaddleOCRClient(server_url)
+
+    if not client.health_check():
+        raise Exception(
+            f"PaddleOCR server at {server_url} is not responding. "
+            "Make sure the server is running on the Linux machine."
+        )
+
+    return client
+
+
+if __name__ == "__main__":
+    # Test the client
+    print("Testing PaddleOCR client...")
+
+    try:
+        client = create_ocr_client()
+        print(f"✅ Connected to server: {client.server_url}")
+
+        # Create a test image
+        test_image = np.ones((100, 100, 3), dtype=np.uint8) * 255
+
+        print("Running test OCR...")
+        results = client.ocr(test_image)
+        print(f"✅ OCR test successful! Found {len(results)} text regions")
+
+    except Exception as e:
+        print(f"❌ Error: {e}")

paddleocr_server_v5.py

@@ -0,0 +1,91 @@
+#!/usr/bin/env python3
+"""
+PaddleOCR Server v5 (PP-OCRv5)
+Flask HTTP server exposing PaddleOCR v3.3.0 functionality
+"""
+
+from paddlex import create_model
+import base64
+import numpy as np
+from PIL import Image
+from io import BytesIO
+from flask import Flask, request, jsonify
+import traceback
+
+app = Flask(__name__)
+
+# Initialize PP-OCRv5 model
+print("Initializing PP-OCRv5 model...")
+model = create_model("PP-OCRv5_server")
+print("PP-OCRv5 model loaded successfully!")
+
+@app.route('/health', methods=['GET'])
+def health():
+    """Health check endpoint."""
+    return jsonify({
+        'status': 'ok',
+        'service': 'paddleocr-server-v5',
+        'version': '3.3.0',
+        'model': 'PP-OCRv5_server',
+        'gpu_enabled': True
+    })
+
+@app.route('/ocr', methods=['POST'])
+def ocr_endpoint():
+    """
+    OCR endpoint using PP-OCRv5.
+
+    Accepts: {"image": "base64_encoded_image"}
+    Returns: {"success": true, "count": N, "results": [...]}
+    """
+    try:
+        # Parse request
+        data = request.get_json()
+        image_base64 = data['image']
+
+        # Decode image
+        image_bytes = base64.b64decode(image_base64)
+        image = Image.open(BytesIO(image_bytes))
+        image_np = np.array(image)
+
+        # Run OCR with PP-OCRv5
+        result = model.predict(image_np)
+
+        # Format results
+        formatted_results = []
+
+        if result and 'dt_polys' in result[0] and 'rec_text' in result[0]:
+            dt_polys = result[0]['dt_polys']
+            rec_texts = result[0]['rec_text']
+            rec_scores = result[0]['rec_score']
+
+            for i in range(len(dt_polys)):
+                box = dt_polys[i].tolist()  # Convert to list
+                text = rec_texts[i]
+                confidence = float(rec_scores[i])
+
+                formatted_results.append({
+                    'box': box,
+                    'text': text,
+                    'confidence': confidence
+                })
+
+        return jsonify({
+            'success': True,
+            'count': len(formatted_results),
+            'results': formatted_results
+        })
+
+    except Exception as e:
+        print(f"Error during OCR: {str(e)}")
+        traceback.print_exc()
+        return jsonify({
+            'success': False,
+            'error': str(e)
+        }), 500
+
+if __name__ == '__main__':
+    print("Starting PP-OCRv5 server on port 5555...")
+    print("Model: PP-OCRv5_server")
+    print("Version: 3.3.0")
+    app.run(host='0.0.0.0', port=5555, debug=False)

paper/ablation_backbone_comparison.py

@@ -0,0 +1,493 @@
+#!/usr/bin/env python3
+"""
+Ablation Study: Backbone Comparison for Signature Feature Extraction
+====================================================================
+Compares ResNet-50 vs VGG-16 vs EfficientNet-B0 on:
+  1. Feature extraction speed
+  2. Intra/Inter class cosine similarity separation (Cohen's d)
+  3. KDE crossover point
+  4. Firm A (known replication) distribution
+
+Usage:
+  python ablation_backbone_comparison.py              # Run all backbones
+  python ablation_backbone_comparison.py --extract     # Feature extraction only
+  python ablation_backbone_comparison.py --analyze     # Analysis only (features must exist)
+"""
+
+import torch
+import torch.nn as nn
+import torchvision.models as models
+import torchvision.transforms as transforms
+from torch.utils.data import Dataset, DataLoader
+import numpy as np
+import sqlite3
+import time
+import argparse
+import json
+from pathlib import Path
+from collections import defaultdict
+from tqdm import tqdm
+import warnings
+warnings.filterwarnings('ignore')
+
+# === Configuration ===
+IMAGES_DIR = Path("/Volumes/NV2/PDF-Processing/yolo-signatures/images")
+FEATURES_DIR = Path("/Volumes/NV2/PDF-Processing/signature-analysis/features")
+DB_PATH = Path("/Volumes/NV2/PDF-Processing/signature-analysis/signature_analysis.db")
+OUTPUT_DIR = Path("/Volumes/NV2/PDF-Processing/signature-analysis/ablation")
+FILENAMES_PATH = FEATURES_DIR / "signature_filenames.txt"
+
+BATCH_SIZE = 64
+NUM_WORKERS = 4
+DEVICE = torch.device("mps" if torch.backends.mps.is_available() else
+                      "cuda" if torch.cuda.is_available() else "cpu")
+
+# Sampling for analysis
+INTER_CLASS_SAMPLE_SIZE = 500_000
+INTRA_CLASS_MIN_SIGNATURES = 3
+RANDOM_SEED = 42
+
+# Known replication firm (Deloitte Taiwan = 勤業眾信)
+FIRM_A_NAME = "勤業眾信聯合"
+
+BACKBONES = {
+    "resnet50": {
+        "model_fn": lambda: models.resnet50(weights=models.ResNet50_Weights.IMAGENET1K_V2),
+        "feature_dim": 2048,
+        "description": "ResNet-50 (ImageNet1K_V2)",
+    },
+    "vgg16": {
+        "model_fn": lambda: models.vgg16(weights=models.VGG16_Weights.IMAGENET1K_V1),
+        "feature_dim": 4096,
+        "description": "VGG-16 (ImageNet1K_V1)",
+    },
+    "efficientnet_b0": {
+        "model_fn": lambda: models.efficientnet_b0(weights=models.EfficientNet_B0_Weights.IMAGENET1K_V1),
+        "feature_dim": 1280,
+        "description": "EfficientNet-B0 (ImageNet1K_V1)",
+    },
+}
+
+
+class SignatureDataset(Dataset):
+    def __init__(self, image_paths, transform=None):
+        self.image_paths = image_paths
+        self.transform = transform
+
+    def __len__(self):
+        return len(self.image_paths)
+
+    def __getitem__(self, idx):
+        import cv2
+        img_path = self.image_paths[idx]
+        img = cv2.imread(str(img_path))
+        if img is None:
+            img = np.ones((224, 224, 3), dtype=np.uint8) * 255
+        else:
+            img = cv2.cvtColor(img, cv2.COLOR_BGR2RGB)
+        img = self._resize_with_padding(img, 224, 224)
+        if self.transform:
+            img = self.transform(img)
+        return img, str(img_path.name)
+
+    @staticmethod
+    def _resize_with_padding(img, target_w, target_h):
+        h, w = img.shape[:2]
+        scale = min(target_w / w, target_h / h)
+        new_w, new_h = int(w * scale), int(h * scale)
+        import cv2
+        resized = cv2.resize(img, (new_w, new_h), interpolation=cv2.INTER_AREA)
+        canvas = np.ones((target_h, target_w, 3), dtype=np.uint8) * 255
+        x_off = (target_w - new_w) // 2
+        y_off = (target_h - new_h) // 2
+        canvas[y_off:y_off+new_h, x_off:x_off+new_w] = resized
+        return canvas
+
+
+def build_feature_extractor(backbone_name):
+    """Build a feature extractor for the given backbone."""
+    config = BACKBONES[backbone_name]
+    model = config["model_fn"]()
+
+    if backbone_name == "vgg16":
+        features_part = model.features
+        avgpool = model.avgpool
+        # Drop last Linear (classifier) to get 4096-dim output
+        classifier_part = nn.Sequential(*list(model.classifier.children())[:-1])
+
+        class VGGFeatureExtractor(nn.Module):
+            def __init__(self, features, avgpool, classifier):
+                super().__init__()
+                self.features = features
+                self.avgpool = avgpool
+                self.classifier = classifier
+
+            def forward(self, x):
+                x = self.features(x)
+                x = self.avgpool(x)
+                x = torch.flatten(x, 1)
+                x = self.classifier(x)
+                return x
+
+        model = VGGFeatureExtractor(features_part, avgpool, classifier_part)
+
+    elif backbone_name == "resnet50":
+        model = nn.Sequential(*list(model.children())[:-1])
+
+    elif backbone_name == "efficientnet_b0":
+        model.classifier = nn.Identity()
+
+    model = model.to(DEVICE)
+    model.eval()
+    return model
+
+
+def extract_features(backbone_name):
+    """Extract features for all signatures using the given backbone."""
+    print(f"\n{'='*60}")
+    print(f"Extracting features: {BACKBONES[backbone_name]['description']}")
+    print(f"{'='*60}")
+
+    output_path = OUTPUT_DIR / f"features_{backbone_name}.npy"
+    if output_path.exists():
+        print(f"  Features already exist: {output_path}")
+        print(f"  Skipping extraction. Delete file to re-extract.")
+        return np.load(output_path)
+
+    # Load filenames
+    with open(FILENAMES_PATH) as f:
+        filenames = [line.strip() for line in f if line.strip()]
+    print(f"  Images: {len(filenames):,}")
+
+    image_paths = [IMAGES_DIR / fn for fn in filenames]
+
+    # Build model
+    model = build_feature_extractor(backbone_name)
+
+    transform = transforms.Compose([
+        transforms.ToTensor(),
+        transforms.Normalize(mean=[0.485, 0.456, 0.406], std=[0.229, 0.224, 0.225])
+    ])
+
+    dataset = SignatureDataset(image_paths, transform=transform)
+    dataloader = DataLoader(dataset, batch_size=BATCH_SIZE, shuffle=False,
+                           num_workers=NUM_WORKERS, pin_memory=True)
+
+    all_features = []
+    start_time = time.time()
+
+    with torch.no_grad():
+        for images, _ in tqdm(dataloader, desc=f"  {backbone_name}"):
+            images = images.to(DEVICE)
+            feats = model(images)
+            feats = feats.view(feats.size(0), -1)  # flatten
+            feats = nn.functional.normalize(feats, p=2, dim=1)  # L2 normalize
+            all_features.append(feats.cpu().numpy())
+
+    elapsed = time.time() - start_time
+    all_features = np.vstack(all_features)
+
+    print(f"  Feature shape: {all_features.shape}")
+    print(f"  Time: {elapsed:.1f}s ({elapsed/60:.1f}min)")
+    print(f"  Speed: {len(filenames)/elapsed:.1f} images/sec")
+
+    # Save
+    OUTPUT_DIR.mkdir(parents=True, exist_ok=True)
+    np.save(output_path, all_features)
+    print(f"  Saved: {output_path} ({all_features.nbytes / 1e9:.2f} GB)")
+
+    return all_features
+
+
+def load_accountant_data():
+    """Load accountant assignments and firm info from DB."""
+    conn = sqlite3.connect(DB_PATH)
+    cur = conn.cursor()
+
+    cur.execute('''
+        SELECT image_filename, assigned_accountant
+        FROM signatures
+        WHERE feature_vector IS NOT NULL
+        ORDER BY signature_id
+    ''')
+    sig_rows = cur.fetchall()
+
+    cur.execute('SELECT name, firm FROM accountants')
+    acct_firm = {r[0]: r[1] for r in cur.fetchall()}
+
+    conn.close()
+
+    filename_to_acct = {r[0]: r[1] for r in sig_rows}
+    return filename_to_acct, acct_firm
+
+
+def analyze_backbone(backbone_name, features, filenames, filename_to_acct, acct_firm):
+    """Compute intra/inter class stats for a backbone's features."""
+    print(f"\n{'='*60}")
+    print(f"Analyzing: {BACKBONES[backbone_name]['description']}")
+    print(f"{'='*60}")
+
+    np.random.seed(RANDOM_SEED)
+
+    # Map features to accountants
+    accountants = []
+    valid_indices = []
+    for i, fn in enumerate(filenames):
+        acct = filename_to_acct.get(fn)
+        if acct:
+            accountants.append(acct)
+            valid_indices.append(i)
+
+    valid_features = features[valid_indices]
+    print(f"  Valid signatures with accountant: {len(valid_indices):,}")
+
+    # Group by accountant
+    acct_groups = defaultdict(list)
+    for i, acct in enumerate(accountants):
+        acct_groups[acct].append(i)
+
+    # --- Intra-class ---
+    print("  Computing intra-class similarities...")
+    intra_sims = []
+    for acct, indices in tqdm(acct_groups.items(), desc="  Intra-class", leave=False):
+        if len(indices) < INTRA_CLASS_MIN_SIGNATURES:
+            continue
+        vecs = valid_features[indices]
+        sim_matrix = vecs @ vecs.T
+        n = len(indices)
+        triu_idx = np.triu_indices(n, k=1)
+        intra_sims.extend(sim_matrix[triu_idx].tolist())
+
+    intra_sims = np.array(intra_sims)
+    print(f"  Intra-class pairs: {len(intra_sims):,}")
+
+    # --- Inter-class ---
+    print("  Computing inter-class similarities...")
+    all_acct_list = list(acct_groups.keys())
+    inter_sims = []
+    for _ in range(INTER_CLASS_SAMPLE_SIZE):
+        a1, a2 = np.random.choice(len(all_acct_list), 2, replace=False)
+        i1 = np.random.choice(acct_groups[all_acct_list[a1]])
+        i2 = np.random.choice(acct_groups[all_acct_list[a2]])
+        sim = float(valid_features[i1] @ valid_features[i2])
+        inter_sims.append(sim)
+    inter_sims = np.array(inter_sims)
+    print(f"  Inter-class pairs: {len(inter_sims):,}")
+
+    # --- Firm A (known replication) ---
+    print(f"  Computing Firm A ({FIRM_A_NAME}) distribution...")
+    firm_a_accts = [acct for acct in acct_groups if acct_firm.get(acct) == FIRM_A_NAME]
+    firm_a_sims = []
+    for acct in firm_a_accts:
+        indices = acct_groups[acct]
+        if len(indices) < 2:
+            continue
+        vecs = valid_features[indices]
+        sim_matrix = vecs @ vecs.T
+        n = len(indices)
+        triu_idx = np.triu_indices(n, k=1)
+        firm_a_sims.extend(sim_matrix[triu_idx].tolist())
+    firm_a_sims = np.array(firm_a_sims) if firm_a_sims else np.array([])
+    print(f"  Firm A accountants: {len(firm_a_accts)}, pairs: {len(firm_a_sims):,}")
+
+    # --- Statistics ---
+    def dist_stats(arr, name):
+        return {
+            "name": name,
+            "n": len(arr),
+            "mean": float(np.mean(arr)),
+            "std": float(np.std(arr)),
+            "median": float(np.median(arr)),
+            "p1": float(np.percentile(arr, 1)),
+            "p5": float(np.percentile(arr, 5)),
+            "p25": float(np.percentile(arr, 25)),
+            "p75": float(np.percentile(arr, 75)),
+            "p95": float(np.percentile(arr, 95)),
+            "p99": float(np.percentile(arr, 99)),
+            "min": float(np.min(arr)),
+            "max": float(np.max(arr)),
+        }
+
+    intra_stats = dist_stats(intra_sims, "intra")
+    inter_stats = dist_stats(inter_sims, "inter")
+    firm_a_stats = dist_stats(firm_a_sims, "firm_a") if len(firm_a_sims) > 0 else None
+
+    # Cohen's d
+    pooled_std = np.sqrt((intra_stats["std"]**2 + inter_stats["std"]**2) / 2)
+    cohens_d = (intra_stats["mean"] - inter_stats["mean"]) / pooled_std if pooled_std > 0 else 0
+
+    # KDE crossover
+    try:
+        from scipy.stats import gaussian_kde
+        x_grid = np.linspace(0, 1, 1000)
+        kde_intra = gaussian_kde(intra_sims)
+        kde_inter = gaussian_kde(inter_sims)
+        diff = kde_intra(x_grid) - kde_inter(x_grid)
+        sign_changes = np.where(np.diff(np.sign(diff)))[0]
+        crossovers = x_grid[sign_changes]
+        valid_crossovers = crossovers[(crossovers > 0.5) & (crossovers < 1.0)]
+        kde_crossover = float(valid_crossovers[-1]) if len(valid_crossovers) > 0 else None
+    except Exception as e:
+        print(f"  KDE crossover computation failed: {e}")
+        kde_crossover = None
+
+    results = {
+        "backbone": backbone_name,
+        "description": BACKBONES[backbone_name]["description"],
+        "feature_dim": BACKBONES[backbone_name]["feature_dim"],
+        "intra": intra_stats,
+        "inter": inter_stats,
+        "firm_a": firm_a_stats,
+        "cohens_d": float(cohens_d),
+        "kde_crossover": kde_crossover,
+    }
+
+    # Print summary
+    print(f"\n  --- {backbone_name} Summary ---")
+    print(f"  Feature dim:    {results['feature_dim']}")
+    print(f"  Intra mean:     {intra_stats['mean']:.4f} +/- {intra_stats['std']:.4f}")
+    print(f"  Inter mean:     {inter_stats['mean']:.4f} +/- {inter_stats['std']:.4f}")
+    print(f"  Cohen's d:      {cohens_d:.4f}")
+    print(f"  KDE crossover:  {kde_crossover}")
+    if firm_a_stats:
+        print(f"  Firm A mean:    {firm_a_stats['mean']:.4f} +/- {firm_a_stats['std']:.4f}")
+        print(f"  Firm A 1st pct: {firm_a_stats['p1']:.4f}")
+
+    return results
+
+
+def generate_comparison_table(all_results):
+    """Generate a markdown comparison table."""
+    print(f"\n{'='*60}")
+    print("COMPARISON TABLE")
+    print(f"{'='*60}\n")
+
+    results_by_name = {r["backbone"]: r for r in all_results}
+
+    def get_val(backbone, key, sub=None):
+        r = results_by_name.get(backbone)
+        if not r:
+            return None
+        if sub:
+            section = r.get(sub)
+            if isinstance(section, dict):
+                return section.get(key)
+            return None
+        return r.get(key)
+
+    def fmt(val, fmt_str=".4f"):
+        if val is None:
+            return "---"
+        if isinstance(val, int):
+            return str(val)
+        return f"{val:{fmt_str}}"
+
+    names = ["resnet50", "vgg16", "efficientnet_b0"]
+    header = "| Metric | ResNet-50 | VGG-16 | EfficientNet-B0 |"
+    sep    = "|--------|-----------|--------|-----------------|"
+
+    rows = [
+        f"| Feature dim | {fmt(get_val('resnet50','feature_dim'),'')} | {fmt(get_val('vgg16','feature_dim'),'')} | {fmt(get_val('efficientnet_b0','feature_dim'),'')} |",
+        f"| Intra mean | {fmt(get_val('resnet50','mean','intra'))} | {fmt(get_val('vgg16','mean','intra'))} | {fmt(get_val('efficientnet_b0','mean','intra'))} |",
+        f"| Intra std | {fmt(get_val('resnet50','std','intra'))} | {fmt(get_val('vgg16','std','intra'))} | {fmt(get_val('efficientnet_b0','std','intra'))} |",
+        f"| Inter mean | {fmt(get_val('resnet50','mean','inter'))} | {fmt(get_val('vgg16','mean','inter'))} | {fmt(get_val('efficientnet_b0','mean','inter'))} |",
+        f"| Inter std | {fmt(get_val('resnet50','std','inter'))} | {fmt(get_val('vgg16','std','inter'))} | {fmt(get_val('efficientnet_b0','std','inter'))} |",
+        f"| **Cohen's d** | **{fmt(get_val('resnet50','cohens_d'))}** | **{fmt(get_val('vgg16','cohens_d'))}** | **{fmt(get_val('efficientnet_b0','cohens_d'))}** |",
+        f"| KDE crossover | {fmt(get_val('resnet50','kde_crossover'))} | {fmt(get_val('vgg16','kde_crossover'))} | {fmt(get_val('efficientnet_b0','kde_crossover'))} |",
+        f"| Firm A mean | {fmt(get_val('resnet50','mean','firm_a'))} | {fmt(get_val('vgg16','mean','firm_a'))} | {fmt(get_val('efficientnet_b0','mean','firm_a'))} |",
+        f"| Firm A 1st pct | {fmt(get_val('resnet50','p1','firm_a'))} | {fmt(get_val('vgg16','p1','firm_a'))} | {fmt(get_val('efficientnet_b0','p1','firm_a'))} |",
+    ]
+
+    table = "\n".join([header, sep] + rows)
+    print(table)
+
+    # Save report
+    report_path = OUTPUT_DIR / "ablation_comparison.md"
+    with open(report_path, 'w') as f:
+        f.write("# Ablation Study: Backbone Comparison\n\n")
+        f.write(f"Date: {time.strftime('%Y-%m-%d %H:%M')}\n\n")
+        f.write("## Comparison Table\n\n")
+        f.write(table + "\n\n")
+        f.write("## Interpretation\n\n")
+        f.write("- **Cohen's d**: Higher = better separation between same-CPA and different-CPA signatures\n")
+        f.write("- **KDE crossover**: The Bayes-optimal decision boundary (higher = easier to classify)\n")
+        f.write("- **Firm A**: Known replication firm; expect very high mean similarity\n")
+        f.write("- **Firm A 1st percentile**: Lower bound of known-replication similarity\n")
+
+    json_path = OUTPUT_DIR / "ablation_results.json"
+    with open(json_path, 'w') as f:
+        json.dump(all_results, f, indent=2, ensure_ascii=False)
+
+    print(f"\n  Report saved: {report_path}")
+    print(f"  Raw data saved: {json_path}")
+
+    return table
+
+
+def main():
+    parser = argparse.ArgumentParser(description="Ablation: backbone comparison")
+    parser.add_argument("--extract", action="store_true", help="Feature extraction only")
+    parser.add_argument("--analyze", action="store_true", help="Analysis only")
+    parser.add_argument("--backbone", type=str, help="Run single backbone (resnet50/vgg16/efficientnet_b0)")
+    args = parser.parse_args()
+
+    OUTPUT_DIR.mkdir(parents=True, exist_ok=True)
+
+    # Load filenames
+    with open(FILENAMES_PATH) as f:
+        filenames = [line.strip() for line in f if line.strip()]
+
+    backbones_to_run = [args.backbone] if args.backbone else list(BACKBONES.keys())
+
+    if not args.analyze:
+        # === Phase 1: Feature Extraction ===
+        print("\n" + "=" * 60)
+        print("PHASE 1: FEATURE EXTRACTION")
+        print("=" * 60)
+
+        # For ResNet-50, copy existing features instead of re-extracting
+        resnet_ablation_path = OUTPUT_DIR / "features_resnet50.npy"
+        resnet_existing_path = FEATURES_DIR / "signature_features.npy"
+        if "resnet50" in backbones_to_run and not resnet_ablation_path.exists() and resnet_existing_path.exists():
+            print(f"\nCopying existing ResNet-50 features...")
+            import shutil
+            resnet_ablation_path.parent.mkdir(parents=True, exist_ok=True)
+            shutil.copy2(resnet_existing_path, resnet_ablation_path)
+            print(f"  Copied: {resnet_ablation_path}")
+
+        for name in backbones_to_run:
+            if name == "resnet50" and resnet_ablation_path.exists():
+                continue
+            extract_features(name)
+
+    if args.extract:
+        print("\nFeature extraction complete. Run with --analyze to compute statistics.")
+        return
+
+    # === Phase 2: Analysis ===
+    print("\n" + "=" * 60)
+    print("PHASE 2: ANALYSIS")
+    print("=" * 60)
+
+    filename_to_acct, acct_firm = load_accountant_data()
+
+    all_results = []
+    for name in backbones_to_run:
+        feat_path = OUTPUT_DIR / f"features_{name}.npy"
+        if not feat_path.exists():
+            print(f"\n  WARNING: {feat_path} not found, skipping {name}")
+            continue
+        features = np.load(feat_path)
+        results = analyze_backbone(name, features, filenames, filename_to_acct, acct_firm)
+        all_results.append(results)
+
+    if len(all_results) > 1:
+        generate_comparison_table(all_results)
+    elif len(all_results) == 1:
+        print(f"\nOnly one backbone analyzed. Run all three for comparison table.")
+
+    print("\nDone!")
+
+
+if __name__ == "__main__":
+    main()

paper/build_docx.sh

@@ -0,0 +1,83 @@
+#!/bin/bash
+# Build complete Paper A Word document from section markdown files
+# Uses pandoc with embedded figures
+
+PAPER_DIR="/Volumes/NV2/pdf_recognize/paper"
+FIG_DIR="/Volumes/NV2/PDF-Processing/signature-analysis/paper_figures"
+OUTPUT="$PAPER_DIR/Paper_A_IEEE_TAI_Draft_v2.docx"
+
+# Create combined markdown with title page
+cat > "$PAPER_DIR/_combined.md" << 'TITLEEOF'
+---
+title: "Automated Detection of Digitally Replicated Signatures in Large-Scale Financial Audit Reports"
+author: "[Authors removed for double-blind review]"
+date: ""
+geometry: margin=1in
+fontsize: 11pt
+---
+
+TITLEEOF
+
+# Append each section (strip the # heading line if it duplicates)
+for section in \
+    paper_a_abstract.md \
+    paper_a_impact_statement.md \
+    paper_a_introduction.md \
+    paper_a_related_work.md \
+    paper_a_methodology.md \
+    paper_a_results.md \
+    paper_a_discussion.md \
+    paper_a_conclusion.md \
+    paper_a_references.md
+do
+    echo "" >> "$PAPER_DIR/_combined.md"
+    # Strip HTML comments and append
+    sed '/^<!--/,/-->$/d' "$PAPER_DIR/$section" >> "$PAPER_DIR/_combined.md"
+    echo "" >> "$PAPER_DIR/_combined.md"
+done
+
+# Insert figure references as actual images
+# Fig 1 after "Fig. 1 illustrates"
+sed -i '' "s|Fig. 1 illustrates the overall architecture.|Fig. 1 illustrates the overall architecture.\n\n![Fig. 1. Pipeline architecture for automated signature replication detection.]($FIG_DIR/fig1_pipeline.png){width=100%}\n|" "$PAPER_DIR/_combined.md"
+
+# Fig 2 after "Fig. 2 presents the cosine"
+sed -i '' "s|Fig. 2 presents the cosine similarity distributions|Fig. 2 presents the cosine similarity distributions|" "$PAPER_DIR/_combined.md"
+sed -i '' "/^Fig. 2 presents the cosine/a\\
+\\
+![Fig. 2. Cosine similarity distributions: intra-class vs. inter-class. KDE crossover at 0.837.]($FIG_DIR/fig2_intra_inter_kde.png){width=60%}\\
+" "$PAPER_DIR/_combined.md"
+
+# Fig 3 after "Fig. 3 presents"
+sed -i '' "/^Fig. 3 presents/a\\
+\\
+![Fig. 3. Per-signature best-match cosine similarity: Firm A vs. other CPAs.]($FIG_DIR/fig3_firm_a_calibration.png){width=60%}\\
+" "$PAPER_DIR/_combined.md"
+
+# Fig 4 after "we compared three pre-trained"
+sed -i '' "/^To validate the choice of ResNet-50.*we conducted/a\\
+\\
+![Fig. 4. Ablation study: backbone comparison.]($FIG_DIR/fig4_ablation.png){width=100%}\\
+" "$PAPER_DIR/_combined.md"
+
+# Build with pandoc
+pandoc "$PAPER_DIR/_combined.md" \
+    -o "$OUTPUT" \
+    --reference-doc=/dev/null \
+    -f markdown \
+    --wrap=none \
+    2>&1
+
+# If reference-doc fails, try without it
+if [ $? -ne 0 ]; then
+    pandoc "$PAPER_DIR/_combined.md" \
+        -o "$OUTPUT" \
+        -f markdown \
+        --wrap=none \
+        2>&1
+fi
+
+# Clean up
+rm -f "$PAPER_DIR/_combined.md"
+
+echo "Output: $OUTPUT"
+ls -lh "$OUTPUT"

paper/codex_bd_mccrary_opinion.md

@@ -0,0 +1,9 @@
+# Codex gpt-5.4 Opinion on BD/McCrary Option (a) vs (b)
+
+(read-only sandbox; full text captured verbatim from codex output log)
+
+**Recommendation: option (b) DEMOTE**, with a preferred hybrid (c) if time permits.
+
+---
+
+For an IEEE Access reviewer, option (b) is the more defensible choice. At this point the paper's own evidence no longer supports BD/McCrary as a co-equal threshold estimator: at the accountant level, which is now the methodologically decisive level for inference, it produces no significant transition at all, while at the signature level the reported cosine transition is 0.985 with very large adjacent Z values, meaning the procedure is finding a sharp local density irregularity inside the non-hand-signed mode rather than a boundary between the two mechanisms the paper is supposed to separate. That is the central problem. If BD remains framed in the Abstract, Introduction, and Section III-I as one of three threshold estimators, the natural reviewer response is not "good triangulation" but "why do the estimators fail to converge around the accountant-level band of roughly 0.976 +/- 0.003?" and the manuscript has no persuasive answer beyond "BD is different." The missing bin-width robustness makes that vulnerability worse, not better: with a fixed 0.005 cosine bin width on a very large sample, the present signature-level transition could reflect a real local feature, a histogram-resolution artifact, or both, and running the sweep now creates asymmetric downside risk because instability would directly weaken Method 2 while stability still would not solve the deeper interpretability problem that the transition sits within, not between, modes. By contrast, option (b) aligns the front half of the paper with what the Discussion already correctly says in Sections V-B and V-G: BD/McCrary is informative here as a density-smoothness diagnostic, not as an independent accountant-level threshold setter. That reframing actually sharpens the paper's substantive claim. The coherent story is that accountant-level aggregates are structured enough for KDE and mixture methods to yield convergent thresholds, yet smooth enough that a discontinuity-based method does not identify a sharp density break; this supports "clustered but smoothly mixed" behavior better than the current "three estimators" rhetoric does. A third option the author has not explicitly considered is a hybrid: demote BD in the main text exactly as in option (b), but run a short bin-width sweep and place the results in an appendix or supplement as an audit trail. That would let the authors say, in one sentence, either that the signature-level transition is not robust to binning or that it is bin-stable but still diagnostically located at 0.985 and therefore not used as the accountant-level threshold. In my view that hybrid is the strongest version if time permits; but if the choice is strictly between (a) and (b), I would recommend (b) without hesitation.

paper/codex_partner_redpen_audit_v3_19_0.md

@@ -0,0 +1,43 @@
+# Codex Partner Red-Pen Regression Audit (Paper A v3.19.0)
+
+Scope: focused regression audit of whether the authors' partner red-pen comments on v3.17 have been adequately addressed in the current v3.19.0 manuscript files under `paper/`. This is not a fresh peer review.
+
+## 1. Overall summary
+
+For the 11 lettered red-pen items (a-k), my independent count is **7 RESOLVED / 1 IMPROVED / 0 PARTIAL / 0 UNRESOLVED / 3 N/A**. The two broader theme-level issues are **Citation reality: RESOLVED** and **ZH/EN alignment: N/A**.
+
+My bottom-line assessment is close to Gemini's: the revision substantially addresses the partner's concerns by deleting the most confusing accountant-level GMM / accountant-level BD-McCrary material and by replacing several AI-sounding explanations with more literal, auditable prose. I do not agree with Gemini's fully clean "8 RESOLVED / 3 N/A" verdict, however. The BIC / strict-3-component item is materially improved, but the manuscript still retains "upper bound" wording in the methods and Table VI even though the results correctly call the two-component fit a forced fit. That is a small prose/rationale residue, not a blocking unresolved issue.
+
+## 2. Item-by-item table
+
+| Item | Status | Manuscript section addressing it | Brief justification | Disagreement with Gemini audit |
+|---|---:|---|---|---|
+| Theme 1: Citation reality for refs [5], [16], [21], [22], [25], [27], [37]-[41] | RESOLVED | `paper_a_references_v3.md`; `reference_verification_v3.md` | The current reference list fixes the serious [5] author/title error and includes real, recognizable method references for Hartigan, Burgstahler-Dichev, McCrary, Dempster-Laird-Rubin, and White. The flagged technical references are not hallucinated. Minor citation-polish items from the verification file appear fixed in the current reference list. | No substantive disagreement. One housekeeping note: `reference_verification_v3.md` still describes [5] as a "major problem" in the detailed findings/recommendations because it records the audit history; the actual current reference list is fixed. |
+| Theme 3: ZH/EN alignment gap at end of III-H Calibration Reference | N/A | Entire v3.19.0 manuscript | The dual-language zh-TW/en scaffold that produced the partner's "no English alongside?" concern is gone. The current draft is monolingual English for IEEE submission, so there is no remaining bilingual alignment task. | No disagreement. |
+| (a) A1 stipulation, "do not understand your description" | RESOLVED | Section III-G, `paper_a_methodology_v3.md` | A1 is now stated as a specific cross-year pair-existence assumption: if replication occurs, at least one same-CPA near-identical pair exists in the observed same-CPA pool. The text also states when A1 may fail. This is much clearer than a vague stipulation. | No disagreement. |
+| (h) A1 pair-detectability paragraph red-circled | RESOLVED | Section III-G, `paper_a_methodology_v3.md` | The red-circled assumption is now bounded: it is plausible for high-volume stamping/e-signing, not guaranteed under singletons, multiple templates, or scan noise, and not a within-year uniformity claim. That should answer the partner's concern about over-assumption. | No disagreement. |
+| (b) Conservative structural-similarity wording, "a bit roundabout?" | RESOLVED | Section III-G, `paper_a_methodology_v3.md` | The independent-minimum dHash is now defined directly as the minimum Hamming distance to any same-CPA signature and identified as the statistic used in the classifier and capture-rate analyses. The wording is concise enough for re-read. | No disagreement. |
+| (c) IV-G validation lead-in, "do not understand why you say this" | RESOLVED | Section IV-G, `paper_a_results_v3.md` | The lead-in now explicitly says Section IV-E capture rates are internally circular because Firm A helped set the thresholds, then explains why the three IV-G analyses are threshold-free or threshold-robust. This directly supplies the missing rationale. | No disagreement. |
+| (d) BD/McCrary at accountant level, "cannot understand" | N/A | Removed from current structure | The accountant-level BD/McCrary analysis no longer appears in the live v3.19.0 manuscript. BD/McCrary is now signature-level only and framed as a density-smoothness diagnostic, not an accountant-level threshold device. | No disagreement. |
+| (k) Accountant-level aggregation rationale, "why accountant level total, because component?" | N/A | Removed from current structure | The confusing accountant-level component narrative has been deleted. The paper now avoids translating signature-level outputs into accountant-level mechanism assignments except for auditor-year ranking. | No disagreement. |
+| (e) 92.6% match rate, "do not understand improvement angle" | RESOLVED | Section III-D, `paper_a_methodology_v3.md`; Table III in Section IV-B | The match rate is now a data-processing coverage metric: 168,755 of 182,328 signatures are CPA-matched, and the unmatched 7.4% are excluded because same-CPA best-match statistics are undefined. The old "improvement" angle is gone. | No disagreement. |
+| (f) 0.95 cosine cutoff, "cut-off corresponds to what?" | RESOLVED | Section III-K, `paper_a_methodology_v3.md`; Sections IV-E/F | The text now states that 0.95 corresponds to the whole-sample Firm A P7.5 heuristic: 92.5% of Firm A signatures exceed it and 7.5% fall at or below it. It also distinguishes 0.95 from the calibration-fold P5 = 0.9407 and rounded 0.945 sensitivity cut. | No disagreement. |
+| (g) 139/32 C1/C2 split, "too reliant on weighting factor?" | N/A | Removed from current structure | The C1/C2 accountant-level GMM cluster split is gone from the current manuscript. Residual fold-variance wording no longer invokes the 139/32 split. | No disagreement. |
+| (i) Hartigan rejection-as-bimodality, "so why?" | RESOLVED | Section III-I.1, `paper_a_methodology_v3.md`; Section IV-D.1 | The text now separates the dip test from component counting: it tests unimodality, does not specify a component count, and is used to decide whether a KDE antimode is meaningful. Section IV-D then explains why Firm A's non-rejection and all-CPA rejection matter. | No disagreement. |
+| (j) BIC strict-3-component upper-bound framing, red-circled paragraph | IMPROVED | Section III-I.2/III-I.4, `paper_a_methodology_v3.md`; Section IV-D.3/IV-D.4, `paper_a_results_v3.md` | The results section is much clearer: it labels the 2-component Beta mixture as "A Forced Fit," reports the 3-component BIC preference, and says the Beta/logit disagreement reflects unsupported parametric structure. However, the methods still say the 2-component crossing "should be treated as an upper bound," and Table VI labels one row as "signature-level Beta/KDE upper bound." That residual wording may still prompt "upper bound of what?" from the partner. | I disagree with Gemini's RESOLVED verdict here. The item is not unresolved, but it is only IMPROVED until "upper bound" is either defined in one plain sentence or removed in favor of "forced-fit descriptive reference." |
+
+## 3. Specific pushback on Gemini's RESOLVED verdict
+
+Only item **(j)** needs pushback.
+
+Gemini says the BIC issue is resolved because the results now title the subsection "A Forced Fit" and state that the 2-component structure is not supported. That is true for Section IV-D.3, but not the whole manuscript. Section III-I.2 still says that when BIC prefers three components, "the 2-component crossing should be treated as an upper bound rather than a definitive cut." Section III-I.4 repeats that the 2-component crossing is a forced fit and "should be read as an upper bound," and Table VI contains "signature-level Beta/KDE upper bound."
+
+For a statistically trained reviewer, this may be defensible shorthand. For the partner's original red-pen concern, it is still slightly too abstract. If the authors keep "upper bound," they should define the bound explicitly. Otherwise the safer fix is to remove the term and call these values "forced-fit descriptive references not used operationally."
+
+## 4. Smallest residual set before partner re-read
+
+1. Replace or explain the remaining **"upper bound"** wording in Section III-I.2, Section III-I.4, and Table VI. Suggested direction: "Because the two-component assumption is not supported, we report the crossing only as a forced-fit descriptive reference and do not use it as an operational threshold."
+
+2. Optional housekeeping: update `reference_verification_v3.md` so its detailed [5] entry no longer reads like an active problem after the reference list has been corrected. This is not a manuscript blocker, but it avoids confusion if the partner or a coauthor opens the verification note.
+
+No other partner red-pen issue appears to need substantive revision before re-read.

paper/codex_review_gpt54_v3_3.md

@@ -0,0 +1,130 @@
+# Third-Round Review of Paper A v3.3
+
+**Overall Verdict: Major Revision**
+
+v3.3 is substantially cleaner than v3.2. Most of the round-2 minor issues were genuinely fixed: the anonymization leak is gone, the BD/McCrary wording is now much more careful, the denominator and table-arithmetic errors were corrected, and the manuscript now explicitly distinguishes cosine-conditional from independent-minimum dHash. I do not recommend submission as-is, however, because three non-cosmetic problems remain. First, the central "three-method convergent thresholding" story is still not aligned with the operational classifier: the deployed rules in Section III-L use whole-sample Firm A heuristics (`0.95`, `5`, `15`, `0.837`) rather than the convergent accountant-level thresholds reported in Section IV-E. Second, the held-out Firm A validation section makes an objectively false numerical claim that the held-out rates match the whole-sample rates within the Wilson confidence intervals. Third, the paper relies on interview evidence from Firm A partners as a key calibration pillar but provides no human-subjects/ethics statement, no consent/exemption language, and almost no protocol detail. Those are fixable, but they are still submission-blocking.
+
+**1. v3.2 Findings Follow-up Audit**
+
+| Prior v3.2 finding | Status | v3.3 audit |
+|---|---|---|
+| Three-method convergence overclaim | `FIXED` | The paper now consistently states that the *KDE antimode plus the two mixture-based estimators* converge, while BD/McCrary does not produce an accountant-level transition; see [paper_a_abstract_v3.md](/Volumes/NV2/pdf_recognize/paper/paper_a_abstract_v3.md:11) and [paper_a_conclusion_v3.md](/Volumes/NV2/pdf_recognize/paper/paper_a_conclusion_v3.md:15). |
+| KDE method inconsistency | `FIXED` | The KDE crossover vs KDE antimode distinction is now explicit in [paper_a_methodology_v3.md](/Volumes/NV2/pdf_recognize/paper/paper_a_methodology_v3.md:167), and the Results use the distinction correctly at [paper_a_results_v3.md](/Volumes/NV2/pdf_recognize/paper/paper_a_results_v3.md:29). |
+| Unit-of-analysis clarity | `PARTIALLY-FIXED` | The signature/accountant distinction is much clearer at [paper_a_methodology_v3.md](/Volumes/NV2/pdf_recognize/paper/paper_a_methodology_v3.md:116), but Sections III-L and IV-F/IV-G still mix analysis levels and dHash statistics. The classifier is described with cosine-conditional dHash cutoffs at [paper_a_methodology_v3.md](/Volumes/NV2/pdf_recognize/paper/paper_a_methodology_v3.md:265), while the validation tables report only `dHash_indep` rules at [paper_a_results_v3.md](/Volumes/NV2/pdf_recognize/paper/paper_a_results_v3.md:165) and [paper_a_results_v3.md](/Volumes/NV2/pdf_recognize/paper/paper_a_results_v3.md:221). |
+| Accountant-level interpretation overstated | `FIXED` | The manuscript now consistently frames the accountant-level result as clustered but smoothly mixed, not sharply discrete; see [paper_a_introduction_v3.md](/Volumes/NV2/pdf_recognize/paper/paper_a_introduction_v3.md:59), [paper_a_discussion_v3.md](/Volumes/NV2/pdf_recognize/paper/paper_a_discussion_v3.md:28), and [paper_a_conclusion_v3.md](/Volumes/NV2/pdf_recognize/paper/paper_a_conclusion_v3.md:17). |
+| BD/McCrary rigor | `PARTIALLY-FIXED` | The overclaim is reduced and the limitation sentence is repaired at [paper_a_discussion_v3.md](/Volumes/NV2/pdf_recognize/paper/paper_a_discussion_v3.md:103), but the paper still reports a fixed-bin implementation (`0.005` cosine bins) at [paper_a_methodology_v3.md](/Volumes/NV2/pdf_recognize/paper/paper_a_methodology_v3.md:175) without any reported bin-width sensitivity results or actual McCrary-style density-estimator output. |
+| White 1982 overclaim | `FIXED` | Related Work now uses the narrower pseudo-true-parameter framing at [paper_a_related_work_v3.md](/Volumes/NV2/pdf_recognize/paper/paper_a_related_work_v3.md:72), consistent with Methods at [paper_a_methodology_v3.md](/Volumes/NV2/pdf_recognize/paper/paper_a_methodology_v3.md:192). |
+| Firm A circular validation | `PARTIALLY-FIXED` | The 70/30 CPA-level split is now explicit at [paper_a_results_v3.md](/Volumes/NV2/pdf_recognize/paper/paper_a_results_v3.md:209), but the actual classifier still uses whole-sample Firm A-derived rules at [paper_a_methodology_v3.md](/Volumes/NV2/pdf_recognize/paper/paper_a_methodology_v3.md:268). The manuscript therefore overstates how fully the held-out fold breaks circularity. |
+| `139 + 32` vs `180` discrepancy | `FIXED` | The `171 + 9 = 180` accounting is now internally consistent; see [paper_a_introduction_v3.md](/Volumes/NV2/pdf_recognize/paper/paper_a_introduction_v3.md:54), [paper_a_results_v3.md](/Volumes/NV2/pdf_recognize/paper/paper_a_results_v3.md:122), [paper_a_discussion_v3.md](/Volumes/NV2/pdf_recognize/paper/paper_a_discussion_v3.md:42), and [paper_a_conclusion_v3.md](/Volumes/NV2/pdf_recognize/paper/paper_a_conclusion_v3.md:21). |
+| dHash calibration story internally inconsistent | `PARTIALLY-FIXED` | The distinction between cosine-conditional and independent-minimum dHash is finally stated at [paper_a_methodology_v3.md](/Volumes/NV2/pdf_recognize/paper/paper_a_methodology_v3.md:265), but the Results still do not "report both" as promised at [paper_a_methodology_v3.md](/Volumes/NV2/pdf_recognize/paper/paper_a_methodology_v3.md:267). Tables IX and XI still report only `dHash_indep` rules at [paper_a_results_v3.md](/Volumes/NV2/pdf_recognize/paper/paper_a_results_v3.md:165) and [paper_a_results_v3.md](/Volumes/NV2/pdf_recognize/paper/paper_a_results_v3.md:221). |
+| Section IV-H.3 not threshold-independent | `FIXED` | The paper now correctly labels H.3 as a classifier-based consistency check rather than a threshold-free test; see [paper_a_methodology_v3.md](/Volumes/NV2/pdf_recognize/paper/paper_a_methodology_v3.md:150), [paper_a_results_v3.md](/Volumes/NV2/pdf_recognize/paper/paper_a_results_v3.md:243), and [paper_a_results_v3.md](/Volumes/NV2/pdf_recognize/paper/paper_a_results_v3.md:336). |
+| Table XVI numerical error | `FIXED` | The totals now reconcile: `83,970` single-firm reports plus `384` mixed-firm reports for `84,354` total at [paper_a_results_v3.md](/Volumes/NV2/pdf_recognize/paper/paper_a_results_v3.md:316). |
+| Held-out Firm A denominator shift | `FIXED` | The `178`-CPA held-out denominator is now explicitly explained by two excluded disambiguation-tie CPAs at [paper_a_results_v3.md](/Volumes/NV2/pdf_recognize/paper/paper_a_results_v3.md:210). |
+| Table numbering / cross-reference confusion | `PARTIALLY-FIXED` | The duplicate "Table VIII" phrasing is gone, but numbering still jumps from Table XI to Table XIII; see [paper_a_results_v3.md](/Volumes/NV2/pdf_recognize/paper/paper_a_results_v3.md:214) and [paper_a_results_v3.md](/Volumes/NV2/pdf_recognize/paper/paper_a_results_v3.md:251). |
+| Real firm identities leaked in tables | `FIXED` | The manuscript now consistently uses `Firm A/B/C/D`; see [paper_a_results_v3.md](/Volumes/NV2/pdf_recognize/paper/paper_a_results_v3.md:281) and [paper_a_results_v3.md](/Volumes/NV2/pdf_recognize/paper/paper_a_results_v3.md:322). |
+| Table X mixed unlike units while still reporting precision / F1 | `FIXED` | The paper now explicitly says precision and `F1` are not meaningful here and omits them; see [paper_a_methodology_v3.md](/Volumes/NV2/pdf_recognize/paper/paper_a_methodology_v3.md:242) and [paper_a_results_v3.md](/Volumes/NV2/pdf_recognize/paper/paper_a_results_v3.md:186). |
+| "three independent statistical methods" wording | `FIXED` | The manuscript now uses "methodologically distinct" at [paper_a_abstract_v3.md](/Volumes/NV2/pdf_recognize/paper/paper_a_abstract_v3.md:10) and [paper_a_methodology_v3.md](/Volumes/NV2/pdf_recognize/paper/paper_a_methodology_v3.md:161). |
+| Abstract / conclusion / discussion still implied BD converged | `FIXED` | The relevant sections now explicitly separate the non-transition result from the convergent estimators; see [paper_a_abstract_v3.md](/Volumes/NV2/pdf_recognize/paper/paper_a_abstract_v3.md:11), [paper_a_discussion_v3.md](/Volumes/NV2/pdf_recognize/paper/paper_a_discussion_v3.md:27), and [paper_a_conclusion_v3.md](/Volumes/NV2/pdf_recognize/paper/paper_a_conclusion_v3.md:16). |
+| Stale "discrete behaviour" wording | `FIXED` | The current wording is appropriately narrowed at [paper_a_methodology_v3.md](/Volumes/NV2/pdf_recognize/paper/paper_a_methodology_v3.md:216) and [paper_a_conclusion_v3.md](/Volumes/NV2/pdf_recognize/paper/paper_a_conclusion_v3.md:17). |
+| Related Work still overclaimed White 1982 | `FIXED` | The problematic sentence is gone; see [paper_a_related_work_v3.md](/Volumes/NV2/pdf_recognize/paper/paper_a_related_work_v3.md:72). |
+| Section III-H preview said "two analyses" | `FIXED` | It now correctly says "three analyses" at [paper_a_methodology_v3.md](/Volumes/NV2/pdf_recognize/paper/paper_a_methodology_v3.md:147). |
+| Incorrect limitation sentence about BD/McCrary threshold-setting role | `FIXED` | The limitation is now correctly framed at [paper_a_discussion_v3.md](/Volumes/NV2/pdf_recognize/paper/paper_a_discussion_v3.md:103). |
+
+**2. New Findings in v3.3**
+
+**Blockers**
+
+- The paper still does not document the ethics status of the interview evidence that underwrites the Firm A calibration anchor. The interviews are not incidental; they are used in the Abstract, Introduction, Methods, Discussion, and Conclusion as one of the main justifications for identifying Firm A as replication-dominated; see [paper_a_abstract_v3.md](/Volumes/NV2/pdf_recognize/paper/paper_a_abstract_v3.md:12), [paper_a_introduction_v3.md](/Volumes/NV2/pdf_recognize/paper/paper_a_introduction_v3.md:52), and [paper_a_methodology_v3.md](/Volumes/NV2/pdf_recognize/paper/paper_a_methodology_v3.md:140). There is no statement about IRB/review-board approval, exemption, participant consent, number of interviewees, interview dates, or anonymization protocol. For IEEE Access this is not optional if the paper reports human-subject research.
+
+- The operational classifier is still not the classifier implied by the paper's title and main thresholding narrative. Section III-I says the accountant-level estimates are the threshold reference used in classification at [paper_a_methodology_v3.md](/Volumes/NV2/pdf_recognize/paper/paper_a_methodology_v3.md:210), and Section IV-E says the primary accountant-level interpretation comes from the `0.973 / 0.979 / 0.976` convergence band (with `0.945 / 8.10` as a secondary cross-check) at [paper_a_results_v3.md](/Volumes/NV2/pdf_recognize/paper/paper_a_results_v3.md:148). But the actual five-way classifier in Section III-L uses `0.95`, `0.837`, and dHash cutoffs `5 / 15` from whole-sample Firm A heuristics at [paper_a_methodology_v3.md](/Volumes/NV2/pdf_recognize/paper/paper_a_methodology_v3.md:251) and [paper_a_methodology_v3.md](/Volumes/NV2/pdf_recognize/paper/paper_a_methodology_v3.md:268). As written, the paper demonstrates convergent threshold *analysis*, but deploys a different heuristic classifier.
+
+- The "held-out fold confirms generalization" claim is numerically false as written. The manuscript states that the held-out rates "match the whole-sample rates of Table IX within each rule's Wilson confidence interval" at [paper_a_results_v3.md](/Volumes/NV2/pdf_recognize/paper/paper_a_results_v3.md:230), and repeats the same idea in Discussion at [paper_a_discussion_v3.md](/Volumes/NV2/pdf_recognize/paper/paper_a_discussion_v3.md:44). That is not true for several published rules. Examples: whole-sample `cosine > 0.95 = 92.51%` at [paper_a_results_v3.md](/Volumes/NV2/pdf_recognize/paper/paper_a_results_v3.md:163) is outside the held-out CI `[93.21%, 93.98%]` at [paper_a_results_v3.md](/Volumes/NV2/pdf_recognize/paper/paper_a_results_v3.md:219); whole-sample `dHash_indep ≤ 5 = 84.20%` at [paper_a_results_v3.md](/Volumes/NV2/pdf_recognize/paper/paper_a_results_v3.md:165) is outside `[87.31%, 88.34%]` at [paper_a_results_v3.md](/Volumes/NV2/pdf_recognize/paper/paper_a_results_v3.md:221); whole-sample dual-rule `89.95%` at [paper_a_results_v3.md](/Volumes/NV2/pdf_recognize/paper/paper_a_results_v3.md:168) is outside `[91.09%, 91.97%]` at [paper_a_results_v3.md](/Volumes/NV2/pdf_recognize/paper/paper_a_results_v3.md:225). This needs correction, not softening.
+
+**Major Issues**
+
+- The dHash statistic used by the deployed classifier remains ambiguous. Section III-L says the final classifier retains the *cosine-conditional* dHash cutoffs for continuity at [paper_a_methodology_v3.md](/Volumes/NV2/pdf_recognize/paper/paper_a_methodology_v3.md:267), but Tables IX and XI report only `dHash_indep` rules at [paper_a_results_v3.md](/Volumes/NV2/pdf_recognize/paper/paper_a_results_v3.md:165) and [paper_a_results_v3.md](/Volumes/NV2/pdf_recognize/paper/paper_a_results_v3.md:221). Section III-L also promises that anchor-level analysis reports both cosine-conditional and independent-minimum rates, but the Results do not. This is still a material reproducibility and interpretation gap.
+
+- The paper still overstates what the 70/30 split accomplishes. Section III-K promises that calibration-fold percentiles are derived from the 70% fold only at [paper_a_methodology_v3.md](/Volumes/NV2/pdf_recognize/paper/paper_a_methodology_v3.md:235), but Section III-L then says the classifier uses thresholds inherited from the *whole-sample* Firm A distribution at [paper_a_methodology_v3.md](/Volumes/NV2/pdf_recognize/paper/paper_a_methodology_v3.md:268). That means the held-out fold is not a fully external evaluation for the actual deployed classifier.
+
+- The validation-metric story still overpromises in the Introduction and Impact Statement. The Introduction says the design includes validation using "precision, recall, `F_1`, and equal-error-rate metrics" at [paper_a_introduction_v3.md](/Volumes/NV2/pdf_recognize/paper/paper_a_introduction_v3.md:28), but Methods and Results later state that precision and `F_1` are not meaningful here and that FRR/recall is only valid for the conservative byte-identical subset at [paper_a_methodology_v3.md](/Volumes/NV2/pdf_recognize/paper/paper_a_methodology_v3.md:242) and [paper_a_results_v3.md](/Volumes/NV2/pdf_recognize/paper/paper_a_results_v3.md:203). The Impact Statement is even stronger, claiming the system "distinguishes genuinely hand-signed signatures from reproduced ones" at [paper_a_impact_statement_v3.md](/Volumes/NV2/pdf_recognize/paper/paper_a_impact_statement_v3.md:8), which is not what a five-way confidence classifier with no full ground-truth test set has established.
+
+- The claimed empirical check on the within-auditor-year no-mixing assumption is not actually a check on that assumption. Section III-G says the intra-report consistency analysis "provides an empirical check on the within-auditor-year assumption" at [paper_a_methodology_v3.md](/Volumes/NV2/pdf_recognize/paper/paper_a_methodology_v3.md:127). But Section IV-H.3 measures agreement between *two different signers on the same report* at [paper_a_results_v3.md](/Volumes/NV2/pdf_recognize/paper/paper_a_results_v3.md:312); it does not test whether the *same CPA* mixes signing mechanisms within a fiscal year.
+
+- BD/McCrary is still the weakest statistical component and is not yet reported rigorously enough to sit as an equal methodological peer to the other two methods. The paper specifies a fixed bin width at [paper_a_methodology_v3.md](/Volumes/NV2/pdf_recognize/paper/paper_a_methodology_v3.md:175) and mentions a KDE bandwidth sensitivity check at [paper_a_methodology_v3.md](/Volumes/NV2/pdf_recognize/paper/paper_a_methodology_v3.md:170), but no actual sensitivity results, `Z`-statistics, p-values, or alternate-bin outputs are reported anywhere in Section IV. The narrative conclusions are probably directionally reasonable, but the evidentiary reporting is still thin.
+
+- Reproducibility from the paper alone is still insufficient. Missing or under-specified items include the exact VLM prompt and parsing rules ([paper_a_methodology_v3.md](/Volumes/NV2/pdf_recognize/paper/paper_a_methodology_v3.md:45)), HSV thresholds for red-stamp removal ([paper_a_methodology_v3.md](/Volumes/NV2/pdf_recognize/paper/paper_a_methodology_v3.md:74)), sampling/randomization seeds for the 500-image YOLO annotation set, the 500,000 inter-class pairs, the 50,000 inter-CPA negatives, and the 70/30 Firm A split ([paper_a_results_v3.md](/Volumes/NV2/pdf_recognize/paper/paper_a_results_v3.md:36), [paper_a_results_v3.md](/Volumes/NV2/pdf_recognize/paper/paper_a_results_v3.md:185), [paper_a_results_v3.md](/Volumes/NV2/pdf_recognize/paper/paper_a_results_v3.md:209)), and the initialization/convergence/clipping details for the Beta and logit-GMM fits ([paper_a_methodology_v3.md](/Volumes/NV2/pdf_recognize/paper/paper_a_methodology_v3.md:184), [paper_a_methodology_v3.md](/Volumes/NV2/pdf_recognize/paper/paper_a_methodology_v3.md:191), [paper_a_methodology_v3.md](/Volumes/NV2/pdf_recognize/paper/paper_a_methodology_v3.md:218)).
+
+- Section III-H still contains one misleading sentence about H.1: it says the fixed `0.95` cutoff "is not calibrated to Firm A" at [paper_a_methodology_v3.md](/Volumes/NV2/pdf_recognize/paper/paper_a_methodology_v3.md:148), but Section IV-F explicitly says `0.95` and the dHash percentile rules are anchored to Firm A at [paper_a_results_v3.md](/Volumes/NV2/pdf_recognize/paper/paper_a_results_v3.md:174), and Section III-L says the classifier inherits thresholds from the whole-sample Firm A distribution at [paper_a_methodology_v3.md](/Volumes/NV2/pdf_recognize/paper/paper_a_methodology_v3.md:268). Those statements need to be reconciled.
+
+**Minor Issues**
+
+- The table numbering still skips Table XII; the numbering jumps from Table XI at [paper_a_results_v3.md](/Volumes/NV2/pdf_recognize/paper/paper_a_results_v3.md:214) to Table XIII at [paper_a_results_v3.md](/Volumes/NV2/pdf_recognize/paper/paper_a_results_v3.md:251).
+
+- The label `dHash_indep ≤ 5 (calib-fold median-adjacent)` at [paper_a_results_v3.md](/Volumes/NV2/pdf_recognize/paper/paper_a_results_v3.md:165) is still unclear. If the calibration-fold independent-minimum median is `2`, then `5` is not a transparent "median-adjacent" label.
+
+- The references still need cleanup. At least `[27]` and `[31]`-`[36]` appear unused in the manuscript text, and the Mann-Whitney test is reported at [paper_a_results_v3.md](/Volumes/NV2/pdf_recognize/paper/paper_a_results_v3.md:50) without actually citing `[36]`.
+
+**3. IEEE Access Fit Check**
+
+- **Scope:** Yes. The topic fits IEEE Access well as a multidisciplinary methods paper spanning document forensics, computer vision, and audit-regulation applications.
+
+- **Single-anonymized review:** IEEE Access uses single-anonymized review according to the current reviewer information page. The manuscript's use of `Firm A/B/C/D` is therefore not required for author anonymity, but it is acceptable as an entity-confidentiality choice.
+
+- **Formatting / desk-return risks:** There are three concrete issues.
+  - The abstract is too long for current IEEE journal guidance. The IEEE Author Center says abstracts should be a single paragraph of up to 250 words, whereas the current abstract text at [paper_a_abstract_v3.md](/Volumes/NV2/pdf_recognize/paper/paper_a_abstract_v3.md:5) through [paper_a_abstract_v3.md](/Volumes/NV2/pdf_recognize/paper/paper_a_abstract_v3.md:14) is roughly 368 words by a plain-word count.
+  - The paper includes a standalone `Impact Statement` section at [paper_a_impact_statement_v3.md](/Volumes/NV2/pdf_recognize/paper/paper_a_impact_statement_v3.md:1). That is not a standard IEEE Access Regular Paper section and should be removed or relocated unless the target article type explicitly requires it.
+  - Because the manuscript relies on partner interviews, it also appears to require the human-subject research statement that IEEE journal guidance asks authors to include when applicable.
+
+- **Official sources checked:** [IEEE Access submission guidelines](https://ieeeaccess.ieee.org/authors/submission-guidelines/), [IEEE Author Center article-structure guidance](https://journals.ieeeauthorcenter.ieee.org/create-your-ieee-journal-article/create-the-text-of-your-article/structure-your-article/), and [IEEE Access reviewer information](https://ieeeaccess.ieee.org/wp-content/uploads/2025/09/Reviewer-Information.pdf).
+
+**4. Statistical Rigor Audit**
+
+- The paper's main high-level statistical narrative is now mostly coherent. The "Firm A is replication-dominated but not pure" framing is supported by the combination of the `92.5%` signature-level rate, the `139 / 32` accountant-level split, and the unimodal-long-tail characterization; see [paper_a_introduction_v3.md](/Volumes/NV2/pdf_recognize/paper/paper_a_introduction_v3.md:54), [paper_a_results_v3.md](/Volumes/NV2/pdf_recognize/paper/paper_a_results_v3.md:123), and [paper_a_discussion_v3.md](/Volumes/NV2/pdf_recognize/paper/paper_a_discussion_v3.md:41).
+
+- The Hartigan dip test is now described correctly as a unimodality test, and the paper no longer treats non-rejection as a formal bimodality finding. That said, the text at [paper_a_results_v3.md](/Volumes/NV2/pdf_recognize/paper/paper_a_results_v3.md:71) still moves quickly from "`p = 0.17`" to a substantive "single dominant generative mechanism" reading. That interpretation is plausible, but it is still an inference supported by interviews and ancillary evidence, not something the dip test itself establishes.
+
+- The accountant-level 1D thresholds are statistically described more carefully than before. The `0.973 / 0.979 / 0.976` cosine band is internally consistent across Abstract, Introduction, Results, Discussion, and Conclusion, and the text now correctly treats BD/McCrary non-transition as diagnostic rather than as failed thresholding.
+
+- The main remaining statistical weakness is the disconnect between *where the methods converge* and *what thresholds the classifier actually uses*. If the final classifier remains `0.95 / 5 / 15 / 0.837`, then the three-method convergence analysis is supporting context, not operational threshold-setting. The manuscript needs to say that explicitly or change the classifier accordingly.
+
+- The anchor-based validation is improved, especially because precision and `F_1` were removed and Wilson CIs were added. But the EER remains close to vacuous here: with 310 byte-identical positives all sitting near cosine `1.0`, the reported "`EER ≈ 0`" at [paper_a_results_v3.md](/Volumes/NV2/pdf_recognize/paper/paper_a_results_v3.md:188) is not very informative and should not be treated as a strong biometric-style performance result.
+
+**5. Anonymization Check**
+
+- Within the reviewed manuscript sections, I do **not** see any explicit real firm names or real auditor names. Firms are consistently pseudonymized as `Firm A/B/C/D`; see [paper_a_results_v3.md](/Volumes/NV2/pdf_recognize/paper/paper_a_results_v3.md:281) and [paper_a_results_v3.md](/Volumes/NV2/pdf_recognize/paper/paper_a_results_v3.md:322).
+
+- I also do **not** see author/institution metadata in the reviewed section files. From a single-anonymized IEEE Access standpoint, there is no obvious explicit anonymization leak in the manuscript text provided for review.
+
+- The one caveat is inferential rather than explicit: the combination of interview-based knowledge, Big-4 status, and distinctive cross-firm statistics may allow knowledgeable local readers to guess which firm is Firm A. That is not an explicit leak, but if firm confidentiality matters beyond mere pseudonymization, the authors should be aware of the residual identifiability risk.
+
+**6. Numerical Consistency**
+
+- The major cross-section numbers are now mostly consistent:
+  - `90,282` reports / `182,328` signatures / `758` CPAs are aligned across Abstract, Introduction, Methods, and Conclusion.
+  - Firm A's `171` analyzable CPAs, `9` excluded CPAs, and `139 / 32` accountant-level split are aligned across Introduction, Results, Discussion, and Conclusion.
+  - The partner-ranking `95.9%` top-decile share and the intra-report `89.9%` agreement are aligned between Methods and Results.
+  - Table XVI and Table XVII arithmetic now reconciles.
+
+- The remaining numerical inconsistency is the held-out-validation sentence discussed above. The underlying table counts are internally consistent, but the prose interpretation at [paper_a_results_v3.md](/Volumes/NV2/pdf_recognize/paper/paper_a_results_v3.md:230) and [paper_a_discussion_v3.md](/Volumes/NV2/pdf_recognize/paper/paper_a_discussion_v3.md:44) is not.
+
+- A second consistency problem is metric-level rather than arithmetic: the classifier is described in Section III-L using cosine-conditional dHash cutoffs, while the validation tables are reported in independent-minimum dHash. That numerical comparison is not apples-to-apples until the paper states clearly which statistic drives Table XVII.
+
+**7. Reproducibility**
+
+- The paper is **not yet replicable from the manuscript alone**.
+
+- Missing items that should be added before submission:
+  - Exact VLM prompt, output format, and page-selection parse rule.
+  - YOLO training hyperparameters beyond epoch count and split ratio, plus inference confidence/NMS thresholds.
+  - HSV stamp-removal thresholds.
+  - Exact matching/disambiguation rules for CPA assignment ties.
+  - Random seeds and selection rules for the 500-page annotation sample, the 500,000 inter-class pairs, the 50,000 inter-CPA negatives, and the 70/30 Firm A split.
+  - EM/Beta/logit-GMM initialization, stopping criteria, handling of boundary values for the logit transform, and software/library versions for the mixture fits.
+  - Sensitivity-analysis results for KDE bandwidth and any analogous robustness checks for the BD/McCrary binning choice.
+  - Interview protocol details and the "independent visual inspection" sample size / decision rule.
+
+- I would not describe the current paper as reproducible "from the paper alone" yet. It is closer than v3.2, but it still depends on undocumented implementation choices.
+
+**Bottom Line**
+
+v3.3 is close, and most of the v3.2 cleanup work landed correctly. But before IEEE Access submission, I would require: (1) a clean reconciliation between the three-method threshold story and the actual classifier, (2) correction of the false held-out-validation claim, and (3) an explicit ethics/human-subjects statement plus minimal protocol disclosure for the interview evidence. Once those are fixed, the paper is much closer to minor-revision territory.

paper/codex_review_gpt54_v3_4.md

@@ -0,0 +1,114 @@
+# Fourth-Round Review of Paper A v3.4
+
+**Overall Verdict: Major Revision**
+
+v3.4 is materially better than v3.3. The ethics/interview blocker is genuinely fixed, the classifier-versus-accountant-threshold distinction is much clearer in the prose, Table XII now exists, and the held-out-validation story has been conceptually corrected from the false "within Wilson CI" claim to the right calibration-fold-versus-held-out comparison. I still do not recommend submission as-is, however, because two core problems remain. First, the newly added sensitivity and intra-report analyses do not appear to evaluate the classifier that Section III-L now defines: the paper says the operational five-way classifier uses *cosine-conditional* dHash cutoffs, but the new scripts use `min_dhash_independent` instead. Second, the replacement Table XI has z/p columns that do not consistently match its own reported counts under the script's published two-proportion formula. Those are fixable, but they keep the manuscript in major-revision territory.
+
+**1. v3.3 Blocker Resolution Audit**
+
+| Blocker | Status | Audit |
+|---|---|---|
+| B1. Classifier vs three-method convergence misalignment | `PARTIALLY-RESOLVED` | The prose repair is real. Section III-L now explicitly distinguishes the signature-level operational classifier from the accountant-level convergent reference band at [paper_a_methodology_v3.md](/Volumes/NV2/pdf_recognize/paper/paper_a_methodology_v3.md:251) through [paper_a_methodology_v3.md](/Volumes/NV2/pdf_recognize/paper/paper_a_methodology_v3.md:275), and Section IV-G.3 is added as a sensitivity check at [paper_a_results_v3.md](/Volumes/NV2/pdf_recognize/paper/paper_a_results_v3.md:239) through [paper_a_results_v3.md](/Volumes/NV2/pdf_recognize/paper/paper_a_results_v3.md:262). The remaining problem is that III-L defines the classifier's dHash cutoffs as *cosine-conditional* at [paper_a_methodology_v3.md](/Volumes/NV2/pdf_recognize/paper/paper_a_methodology_v3.md:269) through [paper_a_methodology_v3.md](/Volumes/NV2/pdf_recognize/paper/paper_a_methodology_v3.md:271), but the new sensitivity script loads only `s.min_dhash_independent` at [24_validation_recalibration.py](/Volumes/NV2/pdf_recognize/signature_analysis/24_validation_recalibration.py:83) through [24_validation_recalibration.py](/Volumes/NV2/pdf_recognize/signature_analysis/24_validation_recalibration.py:90) and then claims to "Replicate Section III-L" at [24_validation_recalibration.py](/Volumes/NV2/pdf_recognize/signature_analysis/24_validation_recalibration.py:204) through [24_validation_recalibration.py](/Volumes/NV2/pdf_recognize/signature_analysis/24_validation_recalibration.py:241). So the conceptual alignment is improved, but the new empirical support is still not aligned to the declared classifier. |
+| B2. Held-out validation false within-Wilson-CI claim | `PARTIALLY-RESOLVED` | The false claim itself is removed. Section IV-G.2 now correctly says the calibration fold, not the whole sample, is the right comparison target at [paper_a_results_v3.md](/Volumes/NV2/pdf_recognize/paper/paper_a_results_v3.md:230) through [paper_a_results_v3.md](/Volumes/NV2/pdf_recognize/paper/paper_a_results_v3.md:237), and Discussion mirrors that at [paper_a_discussion_v3.md](/Volumes/NV2/pdf_recognize/paper/paper_a_discussion_v3.md:44). The new script also implements the two-proportion z-test explicitly at [24_validation_recalibration.py](/Volumes/NV2/pdf_recognize/signature_analysis/24_validation_recalibration.py:66) through [24_validation_recalibration.py](/Volumes/NV2/pdf_recognize/signature_analysis/24_validation_recalibration.py:80) and [24_validation_recalibration.py](/Volumes/NV2/pdf_recognize/signature_analysis/24_validation_recalibration.py:175) through [24_validation_recalibration.py](/Volumes/NV2/pdf_recognize/signature_analysis/24_validation_recalibration.py:202). However, several Table XI z/p entries do not match the displayed `k/n` counts under that formula: the `cosine > 0.837` row at [paper_a_results_v3.md](/Volumes/NV2/pdf_recognize/paper/paper_a_results_v3.md:217) implies about `z = +0.41, p = 0.683`, not `+0.31 / 0.756`; the `cosine > 0.9407` row at [paper_a_results_v3.md](/Volumes/NV2/pdf_recognize/paper/paper_a_results_v3.md:220) implies about `z = -3.19, p = 0.0014`, not `-2.83 / 0.005`; and the `dHash_indep <= 15` row at [paper_a_results_v3.md](/Volumes/NV2/pdf_recognize/paper/paper_a_results_v3.md:224) implies about `z = -0.43, p = 0.670`, not `-0.31 / 0.754`. The conceptual blocker is fixed; the replacement inferential table still needs numeric cleanup. |
+| B3. Interview evidence lacks ethics statement | `RESOLVED` | This blocker is fixed. The manuscript now consistently reframes the contextual claim as practitioner / industry-practice knowledge rather than as research interviews; see [paper_a_introduction_v3.md](/Volumes/NV2/pdf_recognize/paper/paper_a_introduction_v3.md:50) through [paper_a_introduction_v3.md](/Volumes/NV2/pdf_recognize/paper/paper_a_introduction_v3.md:54), [paper_a_methodology_v3.md](/Volumes/NV2/pdf_recognize/paper/paper_a_methodology_v3.md:139) through [paper_a_methodology_v3.md](/Volumes/NV2/pdf_recognize/paper/paper_a_methodology_v3.md:140), and [paper_a_methodology_v3.md](/Volumes/NV2/pdf_recognize/paper/paper_a_methodology_v3.md:280) through [paper_a_methodology_v3.md](/Volumes/NV2/pdf_recognize/paper/paper_a_methodology_v3.md:289). I also ran a grep across the nine v3 manuscript files and found no surviving `interview`, `IRB`, or `ethics` strings. The evidentiary burden now sits on paper-internal analyses rather than on undeclared human-subject evidence. |
+
+**2. v3.3 Major-Issues Follow-up**
+
+| Prior major issue | Status | v3.4 audit |
+|---|---|---|
+| dHash classifier ambiguity | `UNFIXED` | III-L now says the classifier uses *cosine-conditional* dHash thresholds at [paper_a_methodology_v3.md](/Volumes/NV2/pdf_recognize/paper/paper_a_methodology_v3.md:269) through [paper_a_methodology_v3.md](/Volumes/NV2/pdf_recognize/paper/paper_a_methodology_v3.md:271), but the Results still report only `dHash_indep` capture rules at [paper_a_results_v3.md](/Volumes/NV2/pdf_recognize/paper/paper_a_results_v3.md:165) through [paper_a_results_v3.md](/Volumes/NV2/pdf_recognize/paper/paper_a_results_v3.md:168) and [paper_a_results_v3.md](/Volumes/NV2/pdf_recognize/paper/paper_a_results_v3.md:221) through [paper_a_results_v3.md](/Volumes/NV2/pdf_recognize/paper/paper_a_results_v3.md:225), despite the promise at [paper_a_methodology_v3.md](/Volumes/NV2/pdf_recognize/paper/paper_a_methodology_v3.md:271) that both statistics would be reported. The new scripts for Table XII and Table XVI also use `min_dhash_independent`, not cosine-conditional dHash, at [24_validation_recalibration.py](/Volumes/NV2/pdf_recognize/signature_analysis/24_validation_recalibration.py:83) through [24_validation_recalibration.py](/Volumes/NV2/pdf_recognize/signature_analysis/24_validation_recalibration.py:90) and [23_intra_report_consistency.py](/Volumes/NV2/pdf_recognize/signature_analysis/23_intra_report_consistency.py:90) through [23_intra_report_consistency.py](/Volumes/NV2/pdf_recognize/signature_analysis/23_intra_report_consistency.py:92). |
+| 70/30 split overstatement | `PARTIALLY-FIXED` | The paper is now more candid that the operational classifier still inherits whole-sample thresholds at [paper_a_methodology_v3.md](/Volumes/NV2/pdf_recognize/paper/paper_a_methodology_v3.md:272) through [paper_a_methodology_v3.md](/Volumes/NV2/pdf_recognize/paper/paper_a_methodology_v3.md:273), and IV-G.2 properly frames the fold comparison at [paper_a_results_v3.md](/Volumes/NV2/pdf_recognize/paper/paper_a_results_v3.md:230) through [paper_a_results_v3.md](/Volumes/NV2/pdf_recognize/paper/paper_a_results_v3.md:237). But the Abstract still says "we break the circularity" at [paper_a_abstract_v3.md](/Volumes/NV2/pdf_recognize/paper/paper_a_abstract_v3.md:12), and the Conclusion repeats that framing at [paper_a_conclusion_v3.md](/Volumes/NV2/pdf_recognize/paper/paper_a_conclusion_v3.md:20), which overstates what the 70/30 split accomplishes for the actual deployed classifier. |
+| Validation-metric story | `PARTIALLY-FIXED` | Methods and Results are substantially improved: precision and `F1` are now explicitly rejected as meaningless here at [paper_a_methodology_v3.md](/Volumes/NV2/pdf_recognize/paper/paper_a_methodology_v3.md:244) through [paper_a_methodology_v3.md](/Volumes/NV2/pdf_recognize/paper/paper_a_methodology_v3.md:246) and [paper_a_results_v3.md](/Volumes/NV2/pdf_recognize/paper/paper_a_results_v3.md:186) through [paper_a_results_v3.md](/Volumes/NV2/pdf_recognize/paper/paper_a_results_v3.md:203). But the Introduction still promises validation with "precision, recall, F1, and equal-error-rate" at [paper_a_introduction_v3.md](/Volumes/NV2/pdf_recognize/paper/paper_a_introduction_v3.md:28), and the Impact Statement still overstates binary discrimination at [paper_a_impact_statement_v3.md](/Volumes/NV2/pdf_recognize/paper/paper_a_impact_statement_v3.md:8). |
+| Within-auditor-year empirical-check confusion | `UNFIXED` | Section III-G still says the intra-report analysis provides an empirical check on the within-auditor-year no-mixing assumption at [paper_a_methodology_v3.md](/Volumes/NV2/pdf_recognize/paper/paper_a_methodology_v3.md:123) through [paper_a_methodology_v3.md](/Volumes/NV2/pdf_recognize/paper/paper_a_methodology_v3.md:127). But Section IV-H.3 still measures agreement between the two different signers on the same report at [paper_a_results_v3.md](/Volumes/NV2/pdf_recognize/paper/paper_a_results_v3.md:343) through [paper_a_results_v3.md](/Volumes/NV2/pdf_recognize/paper/paper_a_results_v3.md:367). That is a cross-partner same-report test, not a same-CPA within-year mixing test. |
+| BD/McCrary rigor | `UNFIXED` | The Methods still mention KDE bandwidth sensitivity at [paper_a_methodology_v3.md](/Volumes/NV2/pdf_recognize/paper/paper_a_methodology_v3.md:173) and define a fixed-bin BD/McCrary procedure at [paper_a_methodology_v3.md](/Volumes/NV2/pdf_recognize/paper/paper_a_methodology_v3.md:177) through [paper_a_methodology_v3.md](/Volumes/NV2/pdf_recognize/paper/paper_a_methodology_v3.md:183), but the Results still give only narrative transition statements at [paper_a_results_v3.md](/Volumes/NV2/pdf_recognize/paper/paper_a_results_v3.md:80) through [paper_a_results_v3.md](/Volumes/NV2/pdf_recognize/paper/paper_a_results_v3.md:83) and [paper_a_results_v3.md](/Volumes/NV2/pdf_recognize/paper/paper_a_results_v3.md:126) through [paper_a_results_v3.md](/Volumes/NV2/pdf_recognize/paper/paper_a_results_v3.md:149), with no alternate-bin analysis, Z-statistics table, p-values, or McCrary-style estimator output. |
+| Reproducibility gaps | `PARTIALLY-FIXED` | There is some improvement at the code level: the new recalibration script exposes the seed and test formulae at [24_validation_recalibration.py](/Volumes/NV2/pdf_recognize/signature_analysis/24_validation_recalibration.py:46), [24_validation_recalibration.py](/Volumes/NV2/pdf_recognize/signature_analysis/24_validation_recalibration.py:128) through [24_validation_recalibration.py](/Volumes/NV2/pdf_recognize/signature_analysis/24_validation_recalibration.py:136), and [24_validation_recalibration.py](/Volumes/NV2/pdf_recognize/signature_analysis/24_validation_recalibration.py:175) through [24_validation_recalibration.py](/Volumes/NV2/pdf_recognize/signature_analysis/24_validation_recalibration.py:202). But from the paper alone the work is still not reproducible: the exact VLM prompt and parse rule remain absent at [paper_a_methodology_v3.md](/Volumes/NV2/pdf_recognize/paper/paper_a_methodology_v3.md:44) through [paper_a_methodology_v3.md](/Volumes/NV2/pdf_recognize/paper/paper_a_methodology_v3.md:49), HSV thresholds remain absent at [paper_a_methodology_v3.md](/Volumes/NV2/pdf_recognize/paper/paper_a_methodology_v3.md:74), visual-inspection sample size/protocol remain absent at [paper_a_methodology_v3.md](/Volumes/NV2/pdf_recognize/paper/paper_a_methodology_v3.md:144) through [paper_a_methodology_v3.md](/Volumes/NV2/pdf_recognize/paper/paper_a_methodology_v3.md:145), and mixture initialization / stopping / boundary handling remain under-specified at [paper_a_methodology_v3.md](/Volumes/NV2/pdf_recognize/paper/paper_a_methodology_v3.md:187) through [paper_a_methodology_v3.md](/Volumes/NV2/pdf_recognize/paper/paper_a_methodology_v3.md:195) and [paper_a_methodology_v3.md](/Volumes/NV2/pdf_recognize/paper/paper_a_methodology_v3.md:221). |
+| Section III-H / IV-F reconciliation | `FIXED` | The manuscript now clearly says the 92.5% Firm A figure is a within-sample consistency check, not the independent validation pillar, at [paper_a_methodology_v3.md](/Volumes/NV2/pdf_recognize/paper/paper_a_methodology_v3.md:155) and [paper_a_results_v3.md](/Volumes/NV2/pdf_recognize/paper/paper_a_results_v3.md:174) through [paper_a_results_v3.md](/Volumes/NV2/pdf_recognize/paper/paper_a_results_v3.md:176). That specific circularity / role-confusion problem is repaired. |
+| "Fixed 0.95 not calibrated to Firm A" inconsistency | `UNFIXED` | III-H still says the fixed `0.95` cutoff "is not calibrated to Firm A" at [paper_a_methodology_v3.md](/Volumes/NV2/pdf_recognize/paper/paper_a_methodology_v3.md:151), but III-L says `0.95` is the whole-sample Firm A P95 heuristic at [paper_a_methodology_v3.md](/Volumes/NV2/pdf_recognize/paper/paper_a_methodology_v3.md:252) and [paper_a_methodology_v3.md](/Volumes/NV2/pdf_recognize/paper/paper_a_methodology_v3.md:272), and IV-F says the same at [paper_a_results_v3.md](/Volumes/NV2/pdf_recognize/paper/paper_a_results_v3.md:174) and [paper_a_results_v3.md](/Volumes/NV2/pdf_recognize/paper/paper_a_results_v3.md:241). This contradiction remains. |
+
+**3. v3.3 Minor-Issues Follow-up**
+
+| Prior minor issue | Status | v3.4 audit |
+|---|---|---|
+| Table XII numbering | `FIXED` | Table XII now exists at [paper_a_results_v3.md](/Volumes/NV2/pdf_recognize/paper/paper_a_results_v3.md:246) through [paper_a_results_v3.md](/Volumes/NV2/pdf_recognize/paper/paper_a_results_v3.md:254), and the numbering now runs XI-XVIII without the previous jump. |
+| `dHash_indep <= 5 (calib-fold median-adjacent)` label | `UNFIXED` | The unclear label remains at [paper_a_results_v3.md](/Volumes/NV2/pdf_recognize/paper/paper_a_results_v3.md:165), even though the same table family now explicitly reports the calibration-fold independent-minimum median as `2` at [paper_a_results_v3.md](/Volumes/NV2/pdf_recognize/paper/paper_a_results_v3.md:227). Calling `5` "median-adjacent" is still opaque. |
+| References [27], [31]-[36] cleanup | `UNFIXED` | These references remain present at [paper_a_references_v3.md](/Volumes/NV2/pdf_recognize/paper/paper_a_references_v3.md:57) through [paper_a_references_v3.md](/Volumes/NV2/pdf_recognize/paper/paper_a_references_v3.md:75), but a citation sweep across the nine manuscript files found no in-text uses of `[27]` or `[31]`-`[36]`. The Mann-Whitney test is still reported at [paper_a_results_v3.md](/Volumes/NV2/pdf_recognize/paper/paper_a_results_v3.md:50) without citing `[36]`. I also do not see uses of `[34]` or `[35]` in the reviewed manuscript text. |
+
+**4. New Findings in v3.4**
+
+**Blockers**
+
+- The new IV-G.3 sensitivity evidence does not appear to use the classifier that III-L now defines. III-L says the operational categories use cosine-conditional dHash cutoffs at [paper_a_methodology_v3.md](/Volumes/NV2/pdf_recognize/paper/paper_a_methodology_v3.md:269) through [paper_a_methodology_v3.md](/Volumes/NV2/pdf_recognize/paper/paper_a_methodology_v3.md:271), and IV-G.3 presents itself as a sensitivity test of that classifier at [paper_a_results_v3.md](/Volumes/NV2/pdf_recognize/paper/paper_a_results_v3.md:239) through [paper_a_results_v3.md](/Volumes/NV2/pdf_recognize/paper/paper_a_results_v3.md:262). But [24_validation_recalibration.py](/Volumes/NV2/pdf_recognize/signature_analysis/24_validation_recalibration.py:83) through [24_validation_recalibration.py](/Volumes/NV2/pdf_recognize/signature_analysis/24_validation_recalibration.py:90) load only `min_dhash_independent`, and the "Replicate Section III-L" classifier at [24_validation_recalibration.py](/Volumes/NV2/pdf_recognize/signature_analysis/24_validation_recalibration.py:212) through [24_validation_recalibration.py](/Volumes/NV2/pdf_recognize/signature_analysis/24_validation_recalibration.py:241) uses that statistic directly. This is currently the most important unresolved issue because the newly added evidence that is meant to support B1 is not evaluating the paper's stated classifier.
+
+**Major Issues**
+
+- Table XI's z/p columns are not consistently arithmetically compatible with the published counts. The formula in [24_validation_recalibration.py](/Volumes/NV2/pdf_recognize/signature_analysis/24_validation_recalibration.py:66) through [24_validation_recalibration.py](/Volumes/NV2/pdf_recognize/signature_analysis/24_validation_recalibration.py:80) is straightforward, but several rows in [paper_a_results_v3.md](/Volumes/NV2/pdf_recognize/paper/paper_a_results_v3.md:217) through [paper_a_results_v3.md](/Volumes/NV2/pdf_recognize/paper/paper_a_results_v3.md:224) do not match their own `k/n` inputs. The qualitative interpretation survives, but a statistical table that does not reproduce from its displayed counts is not submission-ready.
+
+- Table XVI is affected by the same classifier-definition problem as Table XII. The paper says IV-H.3 uses the "dual-descriptor rules of Section III-L" at [paper_a_results_v3.md](/Volumes/NV2/pdf_recognize/paper/paper_a_results_v3.md:347), but [23_intra_report_consistency.py](/Volumes/NV2/pdf_recognize/signature_analysis/23_intra_report_consistency.py:37) through [23_intra_report_consistency.py](/Volumes/NV2/pdf_recognize/signature_analysis/23_intra_report_consistency.py:53) and [23_intra_report_consistency.py](/Volumes/NV2/pdf_recognize/signature_analysis/23_intra_report_consistency.py:90) through [23_intra_report_consistency.py](/Volumes/NV2/pdf_recognize/signature_analysis/23_intra_report_consistency.py:92) classify with `min_dhash_independent`. So the new "fourth pillar" consistency check is not actually tied to the classifier as specified in III-L.
+
+- The four-pillar Firm A validation is ethically cleaner, but not stronger in evidentiary reporting than v3.3. It is stronger on internal consistency because practitioner knowledge is now background-only at [paper_a_methodology_v3.md](/Volumes/NV2/pdf_recognize/paper/paper_a_methodology_v3.md:139) through [paper_a_methodology_v3.md](/Volumes/NV2/pdf_recognize/paper/paper_a_methodology_v3.md:140), and the paper states that the evidence comes from the manuscript's own analyses at [paper_a_methodology_v3.md](/Volumes/NV2/pdf_recognize/paper/paper_a_methodology_v3.md:142) through [paper_a_methodology_v3.md](/Volumes/NV2/pdf_recognize/paper/paper_a_methodology_v3.md:155). But it is not stronger on empirical documentation because the visual-inspection pillar still has no sample size, randomization rule, rater count, or decision protocol at [paper_a_methodology_v3.md](/Volumes/NV2/pdf_recognize/paper/paper_a_methodology_v3.md:144) through [paper_a_methodology_v3.md](/Volumes/NV2/pdf_recognize/paper/paper_a_methodology_v3.md:145). My read is: ethically stronger, scientifically cleaner, but only roughly equal in evidentiary strength unless the visual-inspection protocol is documented.
+
+**Minor Issues**
+
+- III-H says "Two of them are fully threshold-free" at [paper_a_methodology_v3.md](/Volumes/NV2/pdf_recognize/paper/paper_a_methodology_v3.md:150), but item (a) immediately uses a fixed `0.95` cutoff at [paper_a_methodology_v3.md](/Volumes/NV2/pdf_recognize/paper/paper_a_methodology_v3.md:151). The Results intro to Section IV-H is more accurate at [paper_a_results_v3.md](/Volumes/NV2/pdf_recognize/paper/paper_a_results_v3.md:270) through [paper_a_results_v3.md](/Volumes/NV2/pdf_recognize/paper/paper_a_results_v3.md:274). This should be harmonized.
+
+- The Introduction still contains an obsolete metric promise at [paper_a_introduction_v3.md](/Volumes/NV2/pdf_recognize/paper/paper_a_introduction_v3.md:28), and the Impact Statement still reads too strongly for a five-way classifier with no full labeled test set at [paper_a_impact_statement_v3.md](/Volumes/NV2/pdf_recognize/paper/paper_a_impact_statement_v3.md:8). These are not new conceptual flaws, but they are still visible in the current version.
+
+**5. IEEE Access Fit Check**
+
+- **Scope:** Yes. The topic is a plausible IEEE Access Regular Paper fit as a methods paper spanning document forensics, computer vision, and audit/regulatory applications.
+
+- **Abstract length:** Not compliant yet. A local plain-word count of [paper_a_abstract_v3.md](/Volumes/NV2/pdf_recognize/paper/paper_a_abstract_v3.md:5) through [paper_a_abstract_v3.md](/Volumes/NV2/pdf_recognize/paper/paper_a_abstract_v3.md:14) gives about **367 words**. The IEEE Author Center guidance says the abstract should be a single paragraph of up to 250 words. The current abstract is also dense with abbreviations / symbols (`KDE`, `EM`, `BIC`, `GMM`, `~`, `approx`) that IEEE generally prefers authors to avoid in abstracts.
+
+- **Impact Statement section:** The manuscript still includes a standalone Impact Statement at [paper_a_impact_statement_v3.md](/Volumes/NV2/pdf_recognize/paper/paper_a_impact_statement_v3.md:1) through [paper_a_impact_statement_v3.md](/Volumes/NV2/pdf_recognize/paper/paper_a_impact_statement_v3.md:9). **Inference from official IEEE Access / IEEE Author Center sources:** I do not see a Regular Paper requirement for a standalone `Impact Statement` section. Unless an editor specifically requested it, I would remove it or fold its content into the abstract / conclusion / cover letter.
+
+- **Formatting:** I cannot verify final IEEE template conformance from the markdown section files alone. Official IEEE Access guidance requires the journal template and submission of both source and PDF; that should be checked at the generated DOCX / PDF stage, not from these source snippets.
+
+- **Review model / anonymization:** IEEE Access uses **single-anonymized** review. The current pseudonymization of firms is therefore a confidentiality choice, not a review-blinding requirement. Within the nine reviewed section files I do not see author or institution metadata.
+
+- **Official sources checked:**  
+  - IEEE Access submission guidelines: https://ieeeaccess.ieee.org/authors/submission-guidelines/  
+  - IEEE Author Center article-structure guidance: https://journals.ieeeauthorcenter.ieee.org/create-your-ieee-journal-article/create-the-text-of-your-article/structure-your-article/  
+  - IEEE Access reviewer guidelines / reviewer info: https://ieeeaccess.ieee.org/reviewers/reviewer-guidelines/
+
+**6. Statistical Rigor Audit**
+
+- The high-level statistical story is cleaner than in v3.3. The paper now explicitly separates the primary accountant-level 1D convergence (`0.973 / 0.979 / 0.976`) from the secondary 2D-GMM marginal (`0.945`) at [paper_a_results_v3.md](/Volumes/NV2/pdf_recognize/paper/paper_a_results_v3.md:126) through [paper_a_results_v3.md](/Volumes/NV2/pdf_recognize/paper/paper_a_results_v3.md:149), and III-L no longer pretends those accountant-level thresholds are themselves the deployed classifier at [paper_a_methodology_v3.md](/Volumes/NV2/pdf_recognize/paper/paper_a_methodology_v3.md:274).
+
+- The B2 statistical interpretation is substantially improved: IV-G.2 now frames fold differences as heterogeneity rather than as failed generalization at [paper_a_results_v3.md](/Volumes/NV2/pdf_recognize/paper/paper_a_results_v3.md:233) through [paper_a_results_v3.md](/Volumes/NV2/pdf_recognize/paper/paper_a_results_v3.md:237), and Discussion repeats that narrower reading at [paper_a_discussion_v3.md](/Volumes/NV2/pdf_recognize/paper/paper_a_discussion_v3.md:44) through [paper_a_discussion_v3.md](/Volumes/NV2/pdf_recognize/paper/paper_a_discussion_v3.md:45).
+
+- The main remaining statistical weakness is now more specific: the paper's new classifier definition and the paper's new sensitivity evidence are not using the same dHash statistic. That is a model-definition problem, not just a wording problem.
+
+- BD/McCrary remains the least rigorous component. The paper's qualitative interpretation is plausible, but the reporting is still too thin for a method presented as a co-equal thresholding component.
+
+- The anchor-based validation is better framed than before. The manuscript now correctly treats the byte-identical positives as a conservative subset and no longer uses precision / `F1` in the main validation table at [paper_a_results_v3.md](/Volumes/NV2/pdf_recognize/paper/paper_a_results_v3.md:184) through [paper_a_results_v3.md](/Volumes/NV2/pdf_recognize/paper/paper_a_results_v3.md:205).
+
+**7. Anonymization Check**
+
+- Within the nine reviewed v3 manuscript files, I do not see any explicit real firm names or auditor names. The paper consistently uses `Firm A/B/C/D`; see [paper_a_methodology_v3.md](/Volumes/NV2/pdf_recognize/paper/paper_a_methodology_v3.md:287) through [paper_a_methodology_v3.md](/Volumes/NV2/pdf_recognize/paper/paper_a_methodology_v3.md:289) and [paper_a_results_v3.md](/Volumes/NV2/pdf_recognize/paper/paper_a_results_v3.md:353) through [paper_a_results_v3.md](/Volumes/NV2/pdf_recognize/paper/paper_a_results_v3.md:357).
+
+- The new III-M residual-identifiability disclosure at [paper_a_methodology_v3.md](/Volumes/NV2/pdf_recognize/paper/paper_a_methodology_v3.md:287) through [paper_a_methodology_v3.md](/Volumes/NV2/pdf_recognize/paper/paper_a_methodology_v3.md:288) is appropriate. Knowledgeable local readers may still infer Firm A, but the paper now states that risk explicitly.
+
+**8. Numerical Consistency**
+
+- Most of the large headline counts still reconcile across sections: `90,282` reports, `182,328` signatures, `758` CPAs, and the Firm A `171 + 9` accountant split remain internally consistent across [paper_a_abstract_v3.md](/Volumes/NV2/pdf_recognize/paper/paper_a_abstract_v3.md:11) through [paper_a_abstract_v3.md](/Volumes/NV2/pdf_recognize/paper/paper_a_abstract_v3.md:13), [paper_a_introduction_v3.md](/Volumes/NV2/pdf_recognize/paper/paper_a_introduction_v3.md:62) through [paper_a_introduction_v3.md](/Volumes/NV2/pdf_recognize/paper/paper_a_introduction_v3.md:63), [paper_a_results_v3.md](/Volumes/NV2/pdf_recognize/paper/paper_a_results_v3.md:121) through [paper_a_results_v3.md](/Volumes/NV2/pdf_recognize/paper/paper_a_results_v3.md:127), and [paper_a_conclusion_v3.md](/Volumes/NV2/pdf_recognize/paper/paper_a_conclusion_v3.md:19) through [paper_a_conclusion_v3.md](/Volumes/NV2/pdf_recognize/paper/paper_a_conclusion_v3.md:21).
+
+- Table XII arithmetic is internally consistent: both columns sum to `168,740`, and the listed percentages match the counts. Table XVI and Table XVII arithmetic also reconcile. The new numbering XI-XVIII is coherent.
+
+- The important remaining numerical inconsistency is Table XI's inferential columns, not its raw counts or percentages.
+
+**9. Reproducibility**
+
+- The paper is still **not reproducible from the manuscript alone**.
+
+- Missing or under-specified items that should be added before submission:
+  - Exact VLM prompt, parse rule, and failure-handling for page selection at [paper_a_methodology_v3.md](/Volumes/NV2/pdf_recognize/paper/paper_a_methodology_v3.md:44) through [paper_a_methodology_v3.md](/Volumes/NV2/pdf_recognize/paper/paper_a_methodology_v3.md:49).
+  - HSV thresholds for red-stamp removal at [paper_a_methodology_v3.md](/Volumes/NV2/pdf_recognize/paper/paper_a_methodology_v3.md:74).
+  - Random seeds / sampling protocol for the 500-page annotation set, the 50,000 inter-CPA negatives, the 30-signature sanity sample, and the Firm A 70/30 split at [paper_a_methodology_v3.md](/Volumes/NV2/pdf_recognize/paper/paper_a_methodology_v3.md:59), [paper_a_methodology_v3.md](/Volumes/NV2/pdf_recognize/paper/paper_a_methodology_v3.md:232), [paper_a_methodology_v3.md](/Volumes/NV2/pdf_recognize/paper/paper_a_methodology_v3.md:237) through [paper_a_methodology_v3.md](/Volumes/NV2/pdf_recognize/paper/paper_a_methodology_v3.md:239), and [paper_a_methodology_v3.md](/Volumes/NV2/pdf_recognize/paper/paper_a_methodology_v3.md:247).
+  - Visual-inspection sample size, selection rule, and decision protocol at [paper_a_methodology_v3.md](/Volumes/NV2/pdf_recognize/paper/paper_a_methodology_v3.md:144) through [paper_a_methodology_v3.md](/Volumes/NV2/pdf_recognize/paper/paper_a_methodology_v3.md:145).
+  - EM / mixture initialization, stopping criteria, boundary clipping for the logit transform, and software versions for the mixture fits at [paper_a_methodology_v3.md](/Volumes/NV2/pdf_recognize/paper/paper_a_methodology_v3.md:187) through [paper_a_methodology_v3.md](/Volumes/NV2/pdf_recognize/paper/paper_a_methodology_v3.md:195) and [paper_a_methodology_v3.md](/Volumes/NV2/pdf_recognize/paper/paper_a_methodology_v3.md:221).
+
+- The new scripts help the audit, but they also expose that the Results tables are currently not perfectly aligned to the Methods classifier definition. So reproducibility is not only incomplete; it is presently inconsistent in one key place.
+
+**Bottom Line**
+
+v3.4 clears the ethics/interview blocker and substantially improves the classifier-threshold narrative. It is much closer to a submittable paper than v3.3. But I would still require one more round before IEEE Access submission: (1) make Section III-L, Table XII, Table XVI, and the supporting scripts use the same dHash statistic, or explicitly redefine the classifier around `dHash_indep`; (2) recompute and correct the Table XI z/p columns from the displayed counts; (3) remove the remaining overstatements about what the 70/30 split and the validation metrics establish; and (4) cut the abstract to <= 250 words while cleaning the non-standard Impact Statement. If those are repaired cleanly, the paper should move into minor-revision territory.

paper/codex_review_gpt54_v3_5.md

@@ -0,0 +1,165 @@
+# Fifth-Round Review of Paper A v3.5
+
+Audit basis: commit `12f716d`. Line numbers below refer to the current v3.5 markdown and script files.
+
+## 1. Overall Verdict
+
+**Minor Revision**
+
+v3.5 clears the two issues that kept v3.4 in major-revision territory. The classifier definition in Section III-L is now arithmetically aligned with the `dHash_indep` implementation used by the supporting scripts and downstream tables, and Table XI's `z/p` columns now reproduce from the displayed `k/n` counts under the exact two-proportion formula in Script 24. I do not see a core scientific regression in the B1/B2/B3 logic. I would still not submit v3.5 as-is, however, because a short v3.6 cleanup is still warranted: Table IX is not fully synchronized to the current script outputs, "breaks circularity" overclaim language survives in Methods/Results, the export path still hardcodes a double-blind placeholder even though IEEE Access is single-anonymized, and the manuscript still underdocuments BD/McCrary, visual inspection, and several key reproducibility details. This is now a close paper, but not yet the cleanest version to send.
+
+## 2. v3.4 Round-4 Follow-Up Audit
+
+### 2.1 Round-4 Blockers
+
+| Round-4 item | Round-4 status | v3.5 audit | Evidence |
+|---|---|---|---|
+| B1. Classifier vs three-method convergence misalignment | `PARTIALLY-RESOLVED` | `RESOLVED` | Section III-L now defines the operational classifier entirely in `dHash_indep` terms at Methodology L252-L277. The matching downstream tables also use `dHash_indep`: Results L165-L168, L221-L225, L246-L254, and L350-L361. Script 24 likewise loads `min_dhash_independent` and applies it in the Section III-L classifier at Script 24 L86-L99, L157-L168, and L215-L241. |
+| B2. Held-out validation false within-Wilson-CI claim | `PARTIALLY-RESOLVED` | `RESOLVED` | Results L230-L237 now correctly interpret the fold comparison, and the Table XI `z/p` entries at Results L217-L225 reproduce from Script 24's `two_prop_z` formula at Script 24 L69-L83 and L186-L205. |
+| B3. Interview evidence lacks ethics statement | `RESOLVED` | `RESOLVED` | The manuscript still treats practitioner knowledge as background context only and locates evidentiary weight in paper-internal analyses: Introduction L51-L55; Methodology L140-L156 and L282-L291. I found no regression to interview/IRB-style evidentiary claims. |
+
+### 2.2 Round-4 Major and Minor Follow-Up Items
+
+| Round-4 item | Round-4 status | v3.5 audit | Evidence |
+|---|---|---|---|
+| dHash classifier ambiguity | `UNFIXED` | `RESOLVED` | The classifier is now explicitly `dHash_indep`-based throughout III-L, not cosine-conditional: Methodology L254-L277. Results Tables IX, XI, XII, and XVI are written in the same statistic: Results L165-L168, L221-L225, L246-L254, L350-L361. |
+| 70/30 split overstatement | `PARTIALLY-FIXED` | `PARTIALLY-RESOLVED` | The Abstract and Conclusion are repaired: Abstract L5 and Conclusion L19-L21 now use fold-variance language. But the overclaim survives at Methodology L238, Results L171, and the subsection title at Results L207. |
+| Validation-metric story | `PARTIALLY-FIXED` | `RESOLVED` | The Introduction now promises anchor-based capture/FAR reporting rather than precision/F1/EER: Introduction L29-L30. Methods/Results remain aligned on why precision/F1 are not meaningful here: Methodology L245-L246; Results L186-L188. The archived Impact Statement is explicitly excluded from submission and self-warns against overclaim: Impact Statement L1-L12; `export_v3.py` L15-L25. |
+| Within-auditor-year empirical-check confusion | `UNFIXED` | `RESOLVED` | Methodology L123-L128 now explicitly says IV-H.3 is a related but distinct cross-partner same-report homogeneity test, not a same-CPA within-year mixing test. Results L343-L367 matches that framing exactly. |
+| BD/McCrary rigor | `UNFIXED` | `UNRESOLVED` | The paper still gives only narrative BD/McCrary outcomes without a table of `Z` statistics, `p` values, or bin-width robustness: Results L80-L83 and L126-L149. |
+| Reproducibility gaps | `PARTIALLY-FIXED` | `PARTIALLY-RESOLVED` | The scripts expose some seeds and formulas, but the manuscript still omits the exact VLM prompt/parse rule, HSV thresholds, visual-inspection protocol, and EM initialization/stopping details: Methodology L44-L49, L74-L75, L145-L146, L188-L196, L222-L223, L248. |
+| Section III-H / IV-F reconciliation | `FIXED` | `RESOLVED` | The 92.5% Firm A figure is still consistently framed as a within-sample consistency check, not an external validation pillar: Methodology L156-L160; Results L174-L176. |
+| "`0.95` not calibrated to Firm A" inconsistency | `UNFIXED` | `RESOLVED` | III-H now says the `0.95` cutoff is the whole-sample Firm A P95: Methodology L151-L154. III-L repeats that at Methodology L273-L277, and Results uses the same interpretation at L174-L176 and L241-L244. |
+| Table XII numbering | `FIXED` | `RESOLVED` | Numbering remains coherent through XI-XVIII, with Table XII present at Results L246-L254. |
+| `dHash_indep <= 5 (calib-fold median-adjacent)` label | `UNFIXED` | `UNRESOLVED` | The label still appears in Table IX at Results L165. III-L explains the rationale better at Methodology L275, but the table label itself remains opaque. |
+| References `[27]`, `[31]-[36]` cleanup | `UNFIXED` | `RESOLVED` | All seven are now cited in text: `[27]` at Methodology L100; `[31]-[33]` at Introduction L15; `[34]-[35]` at Methodology L44 and L58; `[36]` at Results L50. |
+
+### 2.3 Round-4 New-Issue Audit
+
+| Round-4 new issue | v3.5 audit | Evidence |
+|---|---|---|
+| IV-G.3 sensitivity evidence did not evaluate the stated classifier | `RESOLVED` | III-L now defines the same `dHash_indep` classifier that Script 24 evaluates: Methodology L252-L277; Script 24 L215-L241; Results L239-L262. |
+| Table XI `z/p` columns did not match displayed counts | `RESOLVED` | Results L217-L225 now matches recomputation from Script 24 L69-L83 exactly up to rounding; details in Section 3 below. |
+| Table XVI was affected by the same classifier-definition problem | `RESOLVED` | Table XVI is now aligned because III-L itself is `dHash_indep`-based. Script 23 also uses `min_dhash_independent`: Script 23 L37-L53 and L90-L92. |
+| Visual-inspection pillar still lacked protocol details | `UNRESOLVED` | The claim remains at Methodology L145-L149, but sample size, rater count, and adjudication rule are still absent from the manuscript. |
+| Threshold-free wording in III-H was inaccurate | `RESOLVED` | III-H now correctly says only partner-ranking is fully threshold-free: Methodology L151-L154. Results L270-L274 matches this. |
+| Introduction metric promise / Impact Statement wording still overstated | `RESOLVED` | The Introduction is repaired at L29-L30, and the Impact Statement is archived and excluded from export: Impact Statement L1-L12; `export_v3.py` L15-L25. |
+
+## 3. Verification of the v3.5 Critical Fixes
+
+### 3.1 Table XI Recalculation
+
+I recomputed every Table XI `z/p` pair from the displayed `k/n` counts using the exact two-proportion formula in Script 24 L69-L83. All nine rows now match the manuscript rounding at Results L217-L225.
+
+| Rule | Exact recomputation from displayed `k/n` | Paper value | Audit |
+|---|---|---|---|
+| `cosine > 0.837` | `z = +0.310601`, `p = 0.756104` | `+0.31`, `0.756` | Match |
+| `cosine > 0.9407` | `z = -3.184698`, `p = 0.001449` | `-3.19`, `0.001` | Match |
+| `cosine > 0.945` | `z = -4.541202`, `p = 0.00000559` | `-4.54`, `<0.001` | Match |
+| `cosine > 0.950` | `z = -5.966194`, `p = 0.0000000024` | `-5.97`, `<0.001` | Match |
+| `dHash_indep <= 5` | `z = -14.288642`, `p < 1e-40` | `-14.29`, `<0.001` | Match |
+| `dHash_indep <= 8` | `z = -6.446423`, `p = 1.15e-10` | `-6.45`, `<0.001` | Match |
+| `dHash_indep <= 9` | `z = -5.072930`, `p = 3.92e-07` | `-5.07`, `<0.001` | Match |
+| `dHash_indep <= 15` | `z = -0.313744`, `p = 0.753716` | `-0.31`, `0.754` | Match |
+| `cosine > 0.95 AND dHash_indep <= 8` | `z = -7.603992`, `p = 2.86e-14` | `-7.60`, `<0.001` | Match |
+
+This directly resolves the main round-4 numerical blocker.
+
+### 3.2 Section III-L Uses `dh_indep` Throughout
+
+This fix is real. Section III-L now states at Methodology L254-L255 that all dHash references in the operational classifier are the independent-minimum statistic, and the five categories at L257-L277 are all written with `dHash_indep`. The downstream result tables are consistent with that same statistic:
+
+- Table IX: Results L165-L168.
+- Table XI: Results L221-L225.
+- Table XII: Results L246-L258.
+- Table XVI: Results L347-L367.
+
+Script 24 is now consistent with that choice as well: it loads `min_dhash_independent` at L86-L99 and classifies with it at L215-L241.
+
+### 3.3 "`0.95` is Firm A P95" Is Now Consistent
+
+This inconsistency is fixed across the relevant sections:
+
+- III-H: Methodology L151-L154 states that the `0.95` cutoff is the whole-sample Firm A P95 and that the longitudinal analysis is about stability, not absolute-rate calibration.
+- III-L: Methodology L273-L277 repeats that `0.95` is the whole-sample Firm A P95 heuristic.
+- IV-F / IV-G.3: Results L174-L176 and L241-L244 use the same framing.
+
+I do not see a surviving contradiction of the old "not calibrated to Firm A" type.
+
+## 4. Verification of the v3.5 Major Fixes
+
+- **Abstract length:** The abstract is now one paragraph. A rendered whitespace count after stripping the header/comment gives 247 words, which is nominally under the IEEE 250-word cap. If one counts inline math markers as separate tokens, the count rises above 250, so the abstract is compliant in ordinary rendered form but still too close to the limit for comfort.
+- **"We break the circularity" overclaim:** Removed from the Abstract and Conclusion. The current Abstract L5 and Conclusion L19-L21 use fold-level variance / heterogeneity language instead. However, the same overclaim still survives elsewhere in the paper at Methodology L238 and Results L171 and L207.
+- **Introduction metric language:** Fixed. Introduction L29-L30 now promises per-rule capture/FAR with Wilson intervals and explicitly states why precision/F1 are not meaningful here. The obsolete introduction promise of precision/F1/EER is gone.
+- **III-G / IV-H.3 wording alignment:** Fixed. Methodology L123-L128 and Results L343-L367 now describe the same cross-partner same-report homogeneity test.
+- **III-H threshold-free wording:** Fixed. Methodology L151-L154 and Results L270-L274 now correctly say that only partner-ranking is threshold-free.
+
+## 5. Verification of the v3.5 Minor Fixes
+
+- **Impact Statement exclusion:** Fixed. `export_v3.py` excludes `paper_a_impact_statement_v3.md` from `SECTIONS` at L15-L25, and the archived file itself says it is not part of the IEEE Access submission at Impact Statement L1-L12.
+- **Previously unused references:** Fixed. `[27]`, `[31]`, `[32]`, `[33]`, `[34]`, `[35]`, and `[36]` all now have in-text citations; see the evidence in Section 2.2 above.
+
+## 6. New Findings in v3.5
+
+No core scientific regression is visible in the B1/B2/B3 logic. The remaining new findings are cleanup-level but real:
+
+1. **Table IX is still not fully synchronized to the current script outputs.** Using the displayed counts at Results L160-L168, three percentages are off by `0.01` under standard rounding: `57,131 / 60,448 = 94.51%`, not `94.52%`; `55,916 / 60,448 = 92.50%`, not `92.51%`; and `57,521 / 60,448 = 95.16%`, not `95.17%`. More importantly, Script 24 computes the whole-sample dual rule as `54,370 / 60,448`, not `54,373 / 60,448` (Script 24 L276-L316; generated recalibration report section 3 lines 48-52). This is small, but v3.5 explicitly positions itself as having cleaned exact table arithmetic, so it should be corrected.
+2. **The circularity overclaim is not fully removed paper-wide.** Methodology L238 still says the 70/30 split "break[s] the resulting circularity," Results L171 says the held-out analysis "addresses the circularity," and the IV-G.2 subsection title at Results L207 still says "(breaks calibration-validation circularity)." Those are stronger than the better, narrower interpretation at Results L233-L237, Discussion L44-L45, and Conclusion L20-L21.
+3. **The export path is not submission-ready for IEEE Access single-anonymized review.** `export_v3.py` correctly excludes the Impact Statement, but it still inserts `[Authors removed for double-blind review]` on the title page at L208-L218. If the manuscript were submitted literally from this export path, that would be a packaging error.
+4. **Methodology III-G retains one stale reference to cosine-conditional dHash.** Methodology L131-L132 says cosine-conditional dHash is used "as a diagnostic elsewhere," but no remaining main-text result appears to use it. After the III-L rewrite, this reads as leftover phrasing and should be either deleted or pointed to a real appendix/supplement.
+
+## 7. IEEE Access Submission Readiness Check
+
+- **Scope:** Yes. The topic remains a plausible IEEE Access Regular Paper fit spanning document forensics, computer vision, and audit/regulatory analytics.
+- **Abstract length:** Nominally compliant in rendered form at 247 words, but close enough to the cap that another 5-10 words of trimming would be safer.
+- **Formatting / template:** Not verifiable from the markdown section files alone. The paper is maintained as markdown fragments plus a custom `python-docx` exporter; I did not audit a final IEEE Access template-conformant DOCX/PDF package here.
+- **Review model:** IEEE Access is single-anonymized. The current export path still uses a double-blind placeholder on the title page (`export_v3.py` L208-L218). That must be fixed before submission.
+- **Anonymization:** The manuscript body still consistently uses `Firm A/B/C/D` and does not expose explicit real firm names or author metadata in the reviewed markdown sections. As before, that is a confidentiality choice rather than a review-model requirement.
+- **Ethics / data-source disclosure:** Adequate for this paper's current evidentiary framing. Methodology L282-L291 clearly states the corpus is public MOPS data and that no non-public records or human-subject evidence are used.
+- **Items that could trigger desk return if submitted literally now:** the missing author/affiliation metadata from the current export path, and any unverified IEEE template / metadata nonconformance in the final DOCX/PDF. The remaining scientific issues are reviewer-risk issues rather than obvious desk-return items.
+
+Bottom line on readiness: **not as-is**. The science is close; the packaging and last-round reporting cleanup are not finished.
+
+## 8. Statistical Rigor, Numerical Consistency, and Reproducibility
+
+### Statistical Rigor
+
+- The core statistical story is now coherent. The paper cleanly separates the operational signature-level classifier from the accountant-level convergence band and treats the held-out Firm A split as heterogeneity disclosure rather than a false Wilson-CI "generalization pass": Methodology L252-L277; Results L230-L237; Discussion L44-L45.
+- The anchor-based validation is better framed than in earlier rounds. The byte-identical positives are clearly treated as a conservative subset, and precision/F1 are no longer misused: Methodology L227-L248; Results L184-L205.
+- The main remaining rigor weakness is still BD/McCrary. Because the paper keeps advertising a three-method convergent threshold strategy in the title/abstract/introduction, the absence of explicit BD/McCrary `Z`/`p` reporting and bin-width sensitivity still leaves one of the three methods under-reported.
+- The visual-inspection pillar is still too thinly documented for the rhetorical weight it carries in III-H and the Conclusion.
+
+### Numerical Consistency
+
+- Table XI is now repaired and reproducible from its displayed counts.
+- Table XII, Table XVI, and Table XVII remain arithmetically consistent.
+- Table IX still has the residual percentage/count mismatches noted in Section 6.
+- The biggest numerical issue left is therefore no longer inferential-table arithmetic; it is the smaller but still avoidable transcription drift in Table IX.
+
+### Reproducibility
+
+The paper is still **not reproducible from the manuscript alone**.
+
+The most important under-specified items remain:
+
+- Exact VLM prompt, parse rule, and page-selection failure handling: Methodology L44-L49.
+- HSV thresholds for red-stamp removal: Methodology L74-L75.
+- Randomization / seed rules for the 500-page annotation set, the inter-CPA negative sample, the 30-signature sanity sample, and the Firm A split: Methodology L59-L62 and L232-L248.
+- Visual-inspection protocol details: sample size, rater count, and decision rule are still absent around Methodology L145-L146.
+- EM / mixture initialization count, stopping criteria, logit-boundary clipping, and software versions: Methodology L188-L196 and L222-L223.
+
+The scripts help auditability, but the manuscript still needs a short reproducibility appendix or supplement if the authors want the paper to look fully defensible on first submission.
+
+## 9. What v3.6 Must Change to Clear Review
+
+If the authors want the paper to clear this review and be genuinely submission-ready, v3.6 should do the following:
+
+1. **Re-sync Table IX and mirrored prose to the authoritative script outputs.** Correct the three `0.01` percentage mismatches and the whole-sample dual-rule count (`54,370 / 60,448` if Script 24 is authoritative).
+2. **Remove the surviving circularity overclaim from Methods/Results.** Replace Methodology L238, Results L171, and the IV-G.2 heading at L207 with the softer fold-variance / within-Firm-A heterogeneity framing already used elsewhere.
+3. **Fix the export path for IEEE Access single-anonymized review.** Restore author/affiliation/corresponding-author metadata and audit the real final DOCX/PDF against the IEEE Access template rather than relying on the current double-blind placeholder export.
+4. **Document the visual-inspection protocol.** At minimum: sample size, sampling rule, number of raters, whether review was blinded, and how disagreements were adjudicated.
+5. **Either substantiate BD/McCrary or demote it.** If it stays as one of the three headline methods, add a compact table of `Z` statistics, `p` values, and bin-width robustness. If not, explicitly recast it as a supplementary diagnostic rather than a co-equal threshold estimator.
+6. **Add a short reproducibility appendix or supplement.** Include the VLM prompt/parse rule, HSV thresholds, key seeds/sampling rules, and mixture-model implementation details.
+7. **Clean the stale cosine-conditional dHash sentence at Methodology L131-L132.** After the III-L rewrite, that sentence now looks like leftover terminology.
+
+If those items are addressed cleanly, I would treat the manuscript as submission-ready for IEEE Access.

paper/codex_review_gpt55_v3_18_1.md

@@ -0,0 +1,224 @@
+# Independent Peer Review (Round 16) - Paper A v3.18.1
+
+Reviewer role: independent peer reviewer for IEEE Access Regular Paper.
+Manuscript reviewed: "Replication-Dominated Calibration" - CPA signature analysis, v3.18.1, commit `cb77f481ec2ab4b93b0effbf4c0ee4c89e90d610`.
+Audit basis: manuscript sections under `paper/`, analysis scripts under `signature_analysis/`, generated reports under `/Volumes/NV2/PDF-Processing/signature-analysis/reports/`, and `paper/reference_verification_v3.md`.
+
+## 1. Overall Verdict: Minor Revision
+
+The paper is close to submission-ready and the central empirical story is largely reproducible from the provided scripts: a large Taiwan audit-report corpus; a signature-detection and feature-extraction pipeline; percentile-calibrated dual-descriptor classification; annotation-free validation using byte-identical positives and inter-CPA negatives; and strong Firm A concentration in several benchmark checks. I did not find a surviving "30/30 human rater agreement" claim in the current manuscript.
+
+However, I would not recommend unconditional Accept. Three issues require revision before IEEE Access submission:
+
+1. Several claims are empirically supported but still phrased more strongly than the scripts justify, especially "detects non-hand-signed signatures," "single dominant generative mechanism," and statements that Firm A's industry practice is "widely understood" or majority non-hand-signing. The data support replication-dominated calibration evidence, not a direct observation of signing workflow.
+2. A number of section references are stale after the v3.18 retitling/reframing. The most visible are references to Section IV-F for analyses that now appear under Section IV-G, and Section III-K references "Firm A P5 percentile 0.941" while the reported sensitivity uses 0.945 and calibration-fold P5 is 0.9407.
+3. The empirical audit found no fabricated quantitative core result, but some claims are only partially reproducible from scripts because the generated tables are embedded as manuscript comments and some scripts contain legacy comments or outputs from earlier versions (e.g., EER/precision/F1 code still present in Script 21/19, although the manuscript correctly omits those metrics).
+
+These are Minor rather than Major because the numerical tables I checked generally match the scripts/reports, the prior fabricated rater-agreement problem appears removed, and the manuscript now contains appropriate limitations around annotation-free anchors and signature-level scope.
+
+## 2. Empirical-Claim Audit Table
+
+Status definitions: VERIFIED = matches scripts/reports or reference verification; UNVERIFIABLE = plausible but not independently supported by provided artifacts; SUSPICIOUS = likely true directionally but overphrased or internally inconsistent; FABRICATED = contradicted by provided artifacts or unsupported despite being presented as measured fact. I found no clear fabricated quantitative claim in v3.18.1.
+
+| Claim | Location | Status | Audit basis / notes |
+|---|---:|---|---|
+| 90,282 audit-report PDFs, Taiwan, 2013-2023 | Abstract; III-B; V | VERIFIED | Manuscript dataset summary; pipeline comments. No raw download log audited, but internally consistent across III-B and conclusion. |
+| 86,072 documents with signatures (95.4%); 12 corrupted PDFs excluded; final 86,071 documents | III-B/C/D; Table I/III | VERIFIED | III-C explains 86,072 VLM-positive minus 12 corrupted = 86,071 final. Slight table split is clear enough. |
+| 182,328 extracted signatures | Abstract; III-D; IV-B; conclusion | VERIFIED | Table III and scripts using DB counts; `signature_analysis/21_expanded_validation.py` loads 168,740 post-best-match subset, consistent with matched subset after exclusions. |
+| 758 unique CPAs; >50 accounting firms; 15 document types, 86.4% standard audit reports | III-B/Table I | VERIFIED for 758 and >50; UNVERIFIABLE for 15/86.4 | 758 is repeatedly used in manuscript. I did not find a direct script/report cross-check for the 15 document-type and 86.4% breakdown in the inspected artifacts. |
+| Qwen2.5-VL 32B; first quartile scanning; temperature 0 | III-C | UNVERIFIABLE | Method claim, not contradicted, but no config/output file inspected establishes these exact inference settings. |
+| VLM-YOLO agreement / YOLO detections in 98.8% of VLM-positive documents | Abstract; III-C; IV-B | VERIFIED | Table III: 85,042 / 86,071 = 98.8%. Script provenance not fully traced, but arithmetic and manuscript consistency are correct. |
+| YOLO training set 500 pages, 425/75 split, 100 epochs | III-D; IV-B | VERIFIED with caveat | Method statement; no training logs inspected. The 425/75 split is arithmetically consistent. |
+| YOLO metrics: precision 0.97-0.98, recall 0.95-0.98, mAP@0.50 0.98-0.99, mAP@0.50:0.95 0.85-0.90 | Table II | UNVERIFIABLE | I did not find a training-results artifact in `signature_analysis/`; claim may be true but needs reproducible log/table in supplement. |
+| Detection deployment: 43.1 docs/sec with 8 workers | III-D; Table III | UNVERIFIABLE | Reported in Table III; no script/log inspected verifies runtime. |
+| CPA-matched signatures: 168,755 / 182,328 = 92.6%; unmatched 13,573 = 7.4% | III-D; Table III | VERIFIED | 168,755 + 13,573 = 182,328; percentages correct. |
+| Same-CPA best-match analyses use N = 168,740, 15 fewer than matched count due to singleton CPAs | IV-D.1 | VERIFIED | `signature_analysis/15_hartigan_dip_test.py` and reports use N=168,740; explanation is plausible and internally consistent. |
+| ResNet-50, ImageNet-1K V2, 2048-d embeddings, 224x224 preprocessing, L2 normalization | III-E | VERIFIED | `signature_analysis/10_formal_statistical_analysis.py`, `paper/ablation_backbone_comparison.py`. |
+| All-pairs intra-class N = 41,352,824; inter-class N = 500,000 | Table IV | VERIFIED | `signature_analysis/10_formal_statistical_analysis.py` computes all intra-pairs and samples 500,000 inter-pairs. |
+| Table IV distribution stats: intra mean 0.821, inter mean 0.758, std/median/skew/kurtosis | IV-C/Table IV | VERIFIED | Consistent with formal statistical report logic and Table XVIII ResNet stats; exact JSON not fully quoted here but no contradiction found. |
+| Shapiro-Wilk and K-S reject normality, p < 0.001 | IV-C | VERIFIED with caveat | `signature_analysis/10_formal_statistical_analysis.py` performs tests. Large paired dependence caveat is correctly acknowledged later. |
+| Lognormal best parametric fit by AIC | IV-C | UNVERIFIABLE | Mentioned in manuscript; not confirmed in inspected code excerpt/output. Needs report citation or supplement table. |
+| KDE crossover at 0.837; Cohen's d = 0.669; Mann-Whitney p < 0.001; K-S p < 0.001 | IV-C/Table V | VERIFIED | `signature_analysis/10_formal_statistical_analysis.py` computes these categories; Table XVIII also repeats ResNet crossover/d. |
+| Pairwise p-values unreliable due to non-independence | IV-C | VERIFIED as methodological caveat | Correct; same signature appears in many pairs. |
+| Firm A cosine dip: N=60,448, dip=0.0019, p=0.169, unimodal | IV-D.1/Table V | VERIFIED | `/reports/dip_test/dip_test_results.json`; `signature_analysis/15_hartigan_dip_test.py`. |
+| Firm A dHash dip: N=60,448, dip=0.1051, p<0.001, multimodal | IV-D.1/Table V | VERIFIED | `/reports/dip_test/dip_test_results.json`. |
+| All-CPA cosine dip: N=168,740, dip=0.0035, p<0.001, multimodal | IV-D.1/Table V | VERIFIED | `/reports/dip_test/dip_test_results.json`. |
+| All-CPA dHash dip: N=168,740, dip=0.0468, p<0.001, multimodal | IV-D.1/Table V | VERIFIED | `/reports/dip_test/dip_test_results.json`. |
+| Firm A cosine distribution "reflects a single dominant generative mechanism" | IV-D.1 | SUSPICIOUS | Dip p=0.17 supports failure to reject unimodality, not direct mechanism identification. Rewrite as "consistent with" rather than "reflecting." |
+| BD/McCrary Firm A cosine transition 0.985 at bin 0.005; full 0.985; dHash transition 2 | IV-D.2; Appendix A | VERIFIED | `signature_analysis/25_bd_mccrary_sensitivity.py`; `/reports/bd_sensitivity/bd_sensitivity.json`. |
+| BD transition drift: Firm A cosine 0.987/0.985/0.980/0.975 as bin widens; full dHash 2/10/9 | Appendix A | VERIFIED | `/reports/bd_sensitivity/bd_sensitivity.json`. |
+| BD/McCrary transition lies inside non-hand-signed mode and is not bin-width-stable | IV-D.2; Appendix A | VERIFIED as interpretation | Script supports instability. "Inside mode" is interpretive but reasonable given Firm A high-similarity mass. |
+| Beta mixture: Firm A Delta BIC = 381 preferring K=3; full-sample Delta BIC = 10,175 | IV-D.3; V-B | VERIFIED | `/reports/beta_mixture/beta_mixture_results.json`: -371092.8 vs -371473.9; -787280.4 vs -797455.1. |
+| Firm A forced Beta-2 crossing 0.977; logit-GMM crossing 0.999 | IV-D.3/Table VI | VERIFIED | `/reports/beta_mixture/beta_mixture_results.json`: 0.9774276 and 0.9992143. |
+| Full-sample forced Beta crossing none; logit-GMM 0.980 | IV-D.3/Table VI | VERIFIED | `/reports/beta_mixture/beta_mixture_results.json`. |
+| Operational Firm A P7.5 cosine cut: cos > 0.95; 92.5% above / 7.5% at or below | Abstract; III-H/K; IV-E | VERIFIED | `/reports/pixel_validation/pixel_validation_results.json`: Firm A cosine>0.95 = 0.9251257. |
+| dHash cutoffs <=5, <=8, <=15; Firm A dHash median 2; P75 approx 4; P95 9 | III-K; IV-E/F | VERIFIED | `/reports/validation_recalibration/validation_recalibration.json` and pixel-validation JSON. |
+| Firm A whole-sample capture: cos>0.837 99.93%, cos>0.9407 95.15%, cos>0.945 94.02%, cos>0.95 92.51% | Table IX | VERIFIED mostly | Counts/rates match manuscript except pixel JSON has 0.941 rather than 0.9407 from older run; recalibration JSON supports 0.9407 threshold family. |
+| Firm A whole-sample dHash<=5 84.20%, <=8 95.17%, <=15 99.83%, dual cos>0.95 AND dHash<=8 89.95% | Table IX; abstract | VERIFIED | `/reports/pixel_validation/pixel_validation_results.json`; `/reports/validation_recalibration/validation_recalibration.json`. |
+| 310 byte-identical positives | Abstract; IV-F.1; V-F | VERIFIED | `signature_analysis/19_pixel_identity_validation.py`; `/reports/pixel_validation/pixel_validation_results.json`; `/reports/expanded_validation/expanded_validation_results.json`. |
+| 145 Firm A byte-identical signatures, 50 distinct Firm A partners of 180, 35 cross-year | III-H; V-C; conclusion | VERIFIED with caveat | The manuscript cites this, but the inspected `pixel_validation_results.json` reports only 310 all-sample pixel-identical signatures. I did not inspect an output table listing the 145/50/35 decomposition. Treat as verified only if the supplementary byte-level pair table is included; otherwise demote to UNVERIFIABLE. |
+| 50,000 inter-CPA negative pairs; inter-CPA mean=0.762, P95=0.884, P99=0.913, max=0.988 | IV-F.1 | VERIFIED | `signature_analysis/21_expanded_validation.py`; `/reports/expanded_validation/expanded_validation_results.json`. |
+| Table X FAR at thresholds: 0.837 -> 0.2062; 0.900 -> 0.0233; 0.945 -> 0.0008; 0.950 -> 0.0007; 0.973 -> 0.0003; 0.979 -> 0.0002, Wilson CIs | IV-F.1/Table X | VERIFIED | `/reports/expanded_validation/expanded_validation_results.json`. |
+| Omission of EER/FRR/precision/F1 in Table X because anchor prevalence is arbitrary and byte-identical positives make FRR trivial | III-J; IV-F.1 | VERIFIED methodologically | Correct manuscript correction. Scripts still compute legacy EER/precision/F1 in places; manuscript appropriately omits. |
+| Low-similarity same-CPA negative anchor n=35 | III-J; V-G | VERIFIED | `/reports/pixel_validation/pixel_validation_results.json`. |
+| Firm A 70/30 CPA split: 124 CPAs/45,116 signatures vs 54 CPAs/15,332 signatures | IV-F.2/Table XI | VERIFIED | `/reports/validation_recalibration/validation_recalibration.json`; `signature_analysis/24_validation_recalibration.py`. |
+| 178 Firm A CPAs in split vs 180 registry; two excluded for disambiguation ties | IV-F.2 | UNVERIFIABLE | Plausible and internally consistent, but I did not find a script/report field documenting the two disambiguation ties. |
+| Calibration-fold thresholds: cosine median 0.9862, P1 0.9067, P5 0.9407; dHash median 2, P95 9 | Table XI | VERIFIED | `/reports/validation_recalibration/validation_recalibration.json`; `/reports/expanded_validation/expanded_validation_results.json`. |
+| Table XI fold rates and z-tests | IV-F.2/Table XI | VERIFIED | `/reports/validation_recalibration/validation_recalibration.json`. |
+| Claim: extreme rules agree across folds, operational 85-95% rules differ by 1-5 points, p<0.001 | IV-F.2; conclusion | VERIFIED | Recalibration JSON supports this. |
+| Sensitivity: cos>0.95 vs cos>0.945 reclassifies 8,508 signatures; category counts in Table XII | IV-F.3/Table XII | VERIFIED | `/reports/validation_recalibration/validation_recalibration.json`. |
+| Firm A dual capture shifts from 89.95% to 91.14%, +1.19 pp | IV-F.3 | VERIFIED | Recalibration JSON: 0.89945 vs 0.91138. |
+| Text says "Firm A P5 percentile 0.941" but sensitivity uses 0.945 | III-K | SUSPICIOUS | Calibration-fold P5 is 0.9407; deployed sensitivity cut is 0.945. Revise to avoid "P5 percentile 0.941" vs "0.945 rounded" ambiguity. |
+| Year-by-year Firm A left-tail table, 2013-2023 N/mean/% below 0.95 | IV-G.1/Table XIII | VERIFIED with caveat | Values plausible and internally consistent, but I did not find the specific report output in inspected files. Include generating script/table in supplement. |
+| 2013-2019 mean left-tail 8.26%, 2020-2023 mean 6.96%; lowest 2023 = 3.75% | IV-G.1 | VERIFIED arithmetically from Table XIII | Means computed from unweighted annual percentages. If intended signature-weighted means, disclose. |
+| Partner ranking: 4,629 auditor-years >=5 signatures; Firm A 1,287 baseline 27.8%; top decile 443/462 = 95.9%; top quartile 1,043/1,157 = 90.1%; top half 1,220/2,314 = 52.7% | IV-G.2/Table XIV | VERIFIED | `signature_analysis/22_partner_ranking.py`; `/reports/partner_ranking/partner_ranking_results.json`. |
+| Year-by-year top-decile Firm A share range 88.4%-100% | IV-G.2/Table XV | VERIFIED | `/reports/partner_ranking/partner_ranking_results.json`. |
+| Intra-report corpus: 84,354 two-signer reports; 83,970 single-firm; 384 mixed-firm = 0.46% | IV-G.3 | VERIFIED | `/reports/intra_report/intra_report_results.json` gives same-firm totals plus mixed-firm categories adding to 384. |
+| Intra-report Table XVI: Firm A 30,222 reports, agreement 89.91%; other Big-4 62-67%; 23-28 pp gap | IV-G.3/Table XVI; abstract | VERIFIED | `signature_analysis/23_intra_report_consistency.py`; `/reports/intra_report/intra_report_results.json`. |
+| Firm A both non-hand-signed 26,435/30,222 = 87.5%; both likely hand-signed 4 = 0.01% | IV-G.3 | VERIFIED | `/reports/intra_report/intra_report_results.json`. |
+| Intra-report gap "predicted by firm-wide practice" | IV-G.3 | SUSPICIOUS | Pattern is consistent with firm-wide practice, but not uniquely diagnostic. Use "consistent with" and avoid "sharp discontinuity" unless statistical uncertainty/sensitivity is shown. |
+| Document-level classification cohort 84,386; differs from 85,042 detections by 656 single-signature documents | IV-H/Table XVII | VERIFIED | Legacy PDF verdict report reports total 84,386; explanation internally consistent. |
+| Table XVII document counts: high 29,529; moderate 36,994; style 5,133; uncertain 12,683; likely 47; total 84,386 | IV-H/Table XVII | VERIFIED | Sum = 84,386; consistent with text. |
+| Within 71,656 documents exceeding cosine 0.95: 41.2% high, 51.7% moderate, 7.2% style-only | IV-H | VERIFIED | 29,529 + 36,994 + 5,133 = 71,656; percentages correct. |
+| Abstract says "only 41% exhibit converging structural evidence ... 7% show no structural corroboration" | Abstract/conclusion | VERIFIED with caveat | Correct for documents with cos>0.95, but "only" is rhetoric; moderate 51.7% still has partial structural similarity. |
+| Firm A document capture: 96.9% high/moderate, 0.6% style, 2.5% uncertain, 4/30,226 likely hand-signed | IV-H.1 | VERIFIED | Table XVII Firm A counts sum to 30,226; 22,970+6,311=29,281=96.9%. |
+| Cross-firm dual-descriptor convergence: non-Firm-A CPAs with cos>0.95 have dHash<=5 at 11.3%, Firm A 58.7% | IV-H.2 | UNVERIFIABLE | I did not find a direct output artifact for this exact comparison in inspected scripts/reports. Add reproducible table or script reference. |
+| Ablation Table XVIII: ResNet/VGG/EfficientNet dimensions and stats | IV-I/Table XVIII | VERIFIED with caveat | `paper/ablation_backbone_comparison.py` implements analysis; I did not inspect generated JSON under ablation. |
+| Claim ResNet-50 "best balance" over EfficientNet-B0 despite lower Cohen's d | IV-I; conclusion | VERIFIED as judgment, not a pure metric | The chosen tradeoff is defensible but subjective. Do not overstate as a purely empirical optimum. |
+| Reference verification: [5] fixed to Kao and Wen; [16]/[21]/[22]/[25] corrected/polished | References; reference_verification_v3.md | VERIFIED | Current `paper_a_references_v3.md` reflects the critical [5] correction and most polish recommendations. |
+| "30/30 human rater agreement" | Current manuscript | VERIFIED ABSENT | `rg` found no surviving 30/30/rater agreement claim in manuscript sections. |
+
+## 3. Methodological Rigor
+
+The methodological core is substantially stronger than in earlier described versions. The key positive points are:
+
+- The paper now separates operational calibration from descriptive distributional diagnostics. This is the right move: the signature-level dip/Beta/BD results do not converge to a clean two-mechanism threshold, so a transparent Firm A percentile anchor is more defensible than a forced mixture crossing.
+- The dual-descriptor classifier is methodologically sensible. Cosine captures high-level similarity; independent-minimum dHash adds structural near-duplicate evidence and avoids treating all high-cosine signatures as image reproduction.
+- The pixel-identity positive anchor is valid as a conservative subset, and the manuscript now correctly avoids presenting FRR/EER/precision/F1 against that artificial anchor set as biometric performance.
+- The inter-CPA negative anchor is a meaningful improvement over the n=35 low-similarity same-CPA anchor.
+- The 70/30 Firm A split is a useful disclosure of within-anchor heterogeneity, even though it is not external validation in the ordinary supervised-learning sense.
+
+Remaining rigor concerns:
+
+1. The inference from "Firm A dip p=0.17" to "single dominant generative mechanism" is too strong. A dip-test non-rejection means the data are consistent with unimodality; it does not identify a generative mechanism. The replication-dominated story is supported by the joint evidence, not by the dip result alone.
+2. The Firm A "industry practice is widely understood" claim is background knowledge, not reproducible evidence. It is acceptable as motivation, but not as an evidentiary premise unless the source is documented. The paper says the evidence comes from image analyses, which is good; the wording should keep practitioner knowledge clearly non-load-bearing.
+3. The dHash thresholds are reasonable but still heuristic. The text says the dHash cuts are "on the same reference"; this should specify exactly: whole-sample Firm A distribution, median/P75-ish high band, and style-consistency ceiling at >15.
+4. The BD/McCrary implementation is a custom adjacent-bin diagnostic rather than a standard local-polynomial McCrary density test. The manuscript already frames it as a diagnostic; it should also avoid implying full equivalence to canonical McCrary RDD density testing.
+5. The partner-ranking statistic uses each year's signatures' max similarity to the CPA's full cross-year pool. The paper notes this, but the "auditor-year" label can mislead readers into assuming within-year-only similarity. The untracked `signature_analysis/27_within_year_uniformity.py` suggests this sensitivity is being explored; if not included, the limitation should be more explicit.
+
+## 4. Narrative Discipline
+
+The narrative is much more disciplined than prior-round summaries suggested, but it still needs tightening.
+
+Overclaims / scope creep:
+
+- "Detects non-hand-signed signatures" should usually be "classifies signatures as replication-consistent / non-hand-signed under a calibrated dual-descriptor rule." The system detects image-reuse evidence, not the signing workflow itself.
+- "Undermining individualized attestation" is plausible but legal/regulatory, not empirically established by the pipeline. It is acceptable in the introduction/impact statement if phrased as a concern, not a measured outcome.
+- "From the perspective of the output image the two workflows are equivalent: both reproduce a single stored image so that signatures on different reports from the same partner are identical up to reproduction noise" is too absolute. Multiple templates, role-specific templates, or system upgrades can break the "single stored image" assumption. The methodology later acknowledges multi-template regimes; the introduction/method overview should match that nuance.
+- "This sharp discontinuity ... predicted by firm-wide non-hand-signing practice" should be softened to "consistent with." A cross-firm agreement gap can arise from classifier calibration, firm-specific document-production pipelines, or signer mix.
+- The conclusion says the replication-dominated calibration strategy is "directly generalizable" to settings with a dominant reference subpopulation and byte-level trace. This is plausible, but "directly" is too strong; generalization depends on the presence of analogous anchors and artifact-generation physics.
+
+Scope discipline that works well:
+
+- The paper now repeatedly states that signature-level rates are not partner-level frequencies.
+- The held-out Firm A fold is correctly presented as within-Firm-A sampling variance disclosure rather than external proof.
+- The byte-identical anchor is correctly framed as a conservative subset, not recall ground truth for all positives.
+
+## 5. IEEE Access Fit
+
+IEEE Access fit is good. The work is application-driven, computational, reproducible in spirit, and interdisciplinary across document forensics, audit regulation, and computer vision. The novelty is not in a new neural architecture but in the calibration/validation design for a difficult real-world forensic corpus. That is a reasonable IEEE Access contribution if the manuscript is careful about claims.
+
+Rigor is adequate for a Regular Paper after minor revisions. The main technical limitation is absence of a boundary-focused manual adjudication set, but the paper acknowledges this and offers a coherent annotation-free validation strategy. Reproducibility would improve if the authors bundle the generated JSON/Markdown reports or explicitly map each table to its script/report path.
+
+Clarity is mostly high, but the section-number drift and the 0.941/0.945 wording need cleanup before submission. IEEE Access reviewers will notice stale cross-references.
+
+## 6. Specific Actionable Revisions and Proposed Rewrites
+
+1. Soften mechanism-identification language.
+
+Current:
+"Firm A's per-signature cosine distribution is unimodal (p = 0.17), reflecting a single dominant generative mechanism..."
+
+Proposed:
+"Firm A's per-signature cosine distribution fails to reject unimodality (p = 0.17), a pattern consistent with a dominant high-similarity regime plus a long left tail. We interpret this jointly with the byte-identity, ranking, and intra-report evidence as supporting the replication-dominated calibration framing."
+
+2. Remove overabsolute "single stored image on every report" wording.
+
+Current:
+"both reproduce a single stored image so that signatures on different reports from the same partner are identical up to reproduction noise."
+
+Proposed:
+"both can reproduce one or more stored signature images, producing same-CPA signatures that are identical or near-identical up to reproduction, scanning, compression, and template-variant noise."
+
+3. Clarify practitioner-knowledge status.
+
+Current:
+"industry practice at the firm is widely understood among practitioners..."
+
+Proposed:
+"Practitioner knowledge motivated treating Firm A as a candidate calibration reference, but the evidentiary basis used in this paper is the observable image evidence reported below: byte-identical same-CPA pairs, the Firm A similarity distribution, partner-ranking concentration, and intra-report consistency."
+
+4. Fix section-reference drift.
+
+Examples:
+- III-H says the three complementary analyses are in Section IV-F; in the current manuscript they are in Section IV-G.
+- III-H bullet labels cite IV-F.1/IV-F.2/IV-F.3 for longitudinal, ranking, intra-report; these should be IV-G.1/IV-G.2/IV-G.3.
+- Results IV-F.2 final sentence says "threshold-independent partner-ranking analysis (Section IV-F.2)" but ranking is Section IV-G.2.
+- Methodology III-G says partner-level ranking is Section IV-F.2; update to IV-G.2.
+
+5. Fix the 0.941/0.945 sensitivity wording.
+
+Current:
+"replacing 0.95 with the slightly stricter Firm A P5 percentile 0.941 alters aggregate firm-level capture rates by at most approx 1.2 percentage points"
+
+Proposed:
+"replacing 0.95 with the nearby rounded sensitivity cut 0.945 (motivated by the calibration-fold P5 = 0.9407) shifts whole-Firm-A dual-rule capture by 1.19 percentage points."
+
+6. Add table-to-script provenance.
+
+Add a compact appendix table:
+
+| Manuscript table | Reproduction artifact |
+|---|---|
+| Table V | `signature_analysis/15_hartigan_dip_test.py`; `reports/dip_test/dip_test_results.json` |
+| Table VI | `signature_analysis/17_beta_mixture_em.py`; `reports/beta_mixture/beta_mixture_results.json`; `signature_analysis/25_bd_mccrary_sensitivity.py` |
+| Table X | `signature_analysis/21_expanded_validation.py`; `reports/expanded_validation/expanded_validation_results.json` |
+| Table XI/XII | `signature_analysis/24_validation_recalibration.py`; `reports/validation_recalibration/validation_recalibration.json` |
+| Table XIV/XV | `signature_analysis/22_partner_ranking.py`; `reports/partner_ranking/partner_ranking_results.json` |
+| Table XVI | `signature_analysis/23_intra_report_consistency.py`; `reports/intra_report/intra_report_results.json` |
+
+7. Either document or remove exact unverifiable decomposition claims.
+
+For "145 Firm A signatures across 50 partners of 180, 35 cross-year," include the exact script/report path that generates the decomposition. If no reproducible artifact is packaged, rewrite as:
+"A subset of Firm A byte-identical matches is distributed across many partners; the supplementary byte-identity table reports the exact partner and cross-year counts."
+
+8. Treat "cross-firm dual convergence 11.3% vs 58.7%" as a table or remove it.
+
+This is a useful claim, but I did not find a direct reproduction artifact. Add a small table with counts/denominators and script provenance.
+
+9. Tighten the impact statement.
+
+Current:
+"automatically extracts and analyzes signatures from over 90,000 audit reports..."
+
+This is accurate. But:
+"separate hand-written signatures from reproduced ones" should remain removed/avoided. Use:
+"stratifies signatures by evidence of image reproduction."
+
+10. Clean legacy script comments before supplement release.
+
+Scripts 19 and 21 still contain old comments about EER/FRR/precision/F1 and "interview evidence." Even if the manuscript is corrected, reviewers who inspect code may see these as conceptual residue. Update comments to match the paper's current anchor-based evaluation language.
+
+## 7. Disagreements with Prior Round-7 Gemini Accept Verdict
+
+I disagree with the round-7 Gemini "fully submission-ready / no v3.9 warranted" conclusion, not because the paper is weak, but because that verdict was too trusting of narrative closure.
+
+Specific disagreements:
+
+1. Gemini focused on prior blockers (BD/McCrary reframing, FRR/EER removal, 15-signature footnote) and did not perform a fresh empirical-claim audit. The known missed "30/30 human rater agreement" problem is exactly the kind of issue that survives when reviewers check only the last patch.
+2. Gemini praised the BD/McCrary rewrite as "perfectly calibrated," but the current paper still risks overstating the adjacent-bin diagnostic as a McCrary-style density test. It is now acceptable, but not perfect.
+3. Gemini treated the paper as "fully submission-ready" before the current Firm A replication-dominated framing was fully disciplined. v3.18.1 is better, but still contains overstrong mechanism phrases and practitioner-knowledge language that need tightening.
+4. Gemini did not flag stale cross-references and threshold wording inconsistencies. These are minor, but IEEE reviewers will see them as polish/reproducibility issues.
+5. Gemini's Accept posture likely reflects anchoring on accumulated prior Accept verdicts. The current manuscript should pass after minor revision, but the audit standard should be "can every quantitative and evidentiary claim be traced to an artifact?" not "did the last known blocker get patched?"
+
+Bottom line: I recommend Minor Revision. The empirical core is credible and largely verified, no surviving fabricated rater-agreement claim was found, and the paper fits IEEE Access. The authors should revise the few overstrong claims and improve provenance/cross-reference hygiene before submission.

paper/codex_review_gpt55_v3_18_2.md

@@ -0,0 +1,133 @@
+# Independent Peer Review (Round 17) - Paper A v3.18.2
+
+Reviewer role: independent peer reviewer for IEEE Access Regular Paper.
+Manuscript reviewed: "Replication-Dominated Calibration" - CPA signature analysis, v3.18.2, commit `7990dab` on `yolo-signature-pipeline`.
+Audit basis: manuscript sections under `paper/`, scripts under `signature_analysis/`, prior round-16 review `paper/codex_review_gpt55_v3_18_1.md`, and generated reports under `/Volumes/NV2/PDF-Processing/signature-analysis/reports/`.
+
+## 1. Overall Verdict: Minor Revision
+
+I recommend **Minor Revision**, not unconditional Accept.
+
+The v3.18.2 revision fixes the most important round-16 empirical problem: the cross-firm dual-descriptor convergence claim is no longer the erroneous `11.3%` vs `58.7%` / `5x` statement. The new script `signature_analysis/28_byte_identity_decomposition.py` and JSON artifact reproduce the corrected values: among signatures with cosine `> 0.95`, non-Firm-A has `27,596 / 65,515 = 42.12%` with `dHash_indep <= 5`, while Firm A has `49,388 / 55,921 = 88.32%`, a `~2.1x` gap. The byte-identity decomposition is also now reproducible: `145` Firm A byte-identical signatures, `50` distinct partners, `180` registered Firm A partners, and `35` cross-year matches.
+
+The revision also resolves most stale section references and improves provenance. However, I found three remaining issues that should be corrected before IEEE Access submission:
+
+1. The Appendix B provenance map overclaims: several mapped report artifacts do not exist at the stated paths in the available report tree.
+2. Some mechanism-identification language was softened in Results but remains too strong in Methodology and Discussion, especially "consistent with a single dominant mechanism."
+3. A few exact method/performance claims remain unverifiable from packaged artifacts, especially YOLO validation metrics, VLM prompt/settings, HSV thresholds, runtime, and some extraction/document-type details.
+
+These are Minor because they do not overturn the central empirical findings, but they affect reproducibility and narrative discipline.
+
+## 2. Re-audit of Round-16 Findings
+
+| Round-16 finding | v3.18.2 status | Re-audit notes |
+|---|---|---|
+| Mechanism-identification overclaim from dip-test non-rejection | **PARTIAL** | Results IV-D.1 now correctly says Firm A "fails to reject unimodality." But Methodology III-H still says the distribution is "consistent with a single dominant mechanism (non-hand-signing)," and Discussion V-C says "consistent with a single dominant mechanism plus residual within-firm heterogeneity." A dip-test non-rejection plus left tail does not identify a single mechanism; the joint evidence supports a replication-dominated benchmark, not a mechanism count. |
+| Stale IV-F / IV-G references after retitling | **LARGELY RESOLVED** | I did not find the old round-16 pattern of IV-F references pointing to the new IV-G validation analyses. The current IV-F/IV-G references are mostly correct. Minor remaining issue: Introduction and conclusion still cite byte-identity as Section IV-F.1 although the detailed `145/50/180/35` decomposition itself is not reported in Section IV-F.1, only in III-H/V-C/Appendix B. |
+| Practitioner knowledge as load-bearing evidence | **PARTIAL** | III-H now explicitly says practitioner knowledge is "non-load-bearing," which is good. But Introduction still says Firm A is "widely recognized within the audit profession" and III-H says "widely held within the audit profession" without a citation or source. This is acceptable only as motivation; I would soften or cite. |
+| 0.941 / 0.945 / 0.9407 ambiguity | **RESOLVED** | III-K and IV-F.3 now correctly distinguish the operational 0.95 cut, the nearby rounded sensitivity cut 0.945, and calibration-fold P5 = 0.9407. |
+| Incorrect cross-firm dual-convergence claim | **RESOLVED** | The prior `11.3%` vs `58.7%` / `5x` claim is gone from current manuscript files. The replacement `42.12%` vs `88.32%` / `~2.1x` matches the new JSON artifact. |
+| Byte-identity decomposition was unverifiable | **RESOLVED with packaging caveat** | New script and JSON reproduce `145/50/180/35`. Caveat: the manuscript says reports are under the project's `reports/` tree, but the actual artifact I inspected is under `/Volumes/NV2/PDF-Processing/signature-analysis/reports/...`, not under this repo's `reports/` path. |
+| Legacy EER/FRR/Precision/F1 script comments | **RESOLVED enough** | Scripts 19 and 21 now label EER/FRR/Precision/F1 as legacy / diagnostic-only and state that the manuscript omits them. Some functions still emit those sections if run, but the conceptual warning is explicit. |
+
+## 3. New Empirical-Claim Audit
+
+Status definitions: **VERIFIED** = matches script/report or arithmetic; **PARTIAL** = broadly supported but wording/provenance needs cleanup; **UNVERIFIABLE** = plausible but not traceable in the available artifacts; **SUSPICIOUS** = overphrased or internally inconsistent. I found no new fabricated core result.
+
+| Claim | Status | Audit basis / notes |
+|---|---|---|
+| 90,282 PDFs, 2013-2023, Taiwan | VERIFIED | Consistent across manuscript. Raw scraping log not audited. |
+| 86,072 VLM-positive documents; 12 corrupted PDFs; final 86,071 | VERIFIED | Internally consistent in III-C. |
+| 182,328 extracted signatures; 168,755 CPA-matched; 13,573 unmatched | VERIFIED | Matches manuscript counts and downstream `168,740` after singleton exclusion. |
+| 758 CPAs, >50 firms, 15 document types, 86.4% standard audit reports | PARTIAL | 758/>50 are stable manuscript counts. I did not find a direct packaged JSON for 15 document types / 86.4%. |
+| Qwen2.5-VL 32B, 180 DPI, first-quartile scan, temperature 0 | UNVERIFIABLE | Method claim not contradicted, but prompt/config/log artifact not inspected. |
+| YOLO 500 annotated pages, 425/75 split, 100 epochs | PARTIAL | Method is clear; no training log audited. |
+| YOLO precision 0.97-0.98, recall 0.95-0.98, mAP metrics | UNVERIFIABLE | Table II remains unsupported by a visible training-results artifact. |
+| 43.1 docs/sec with 8 workers | UNVERIFIABLE | Runtime claim still lacks a visible timing log. |
+| Same-CPA best-match N = 168,740, 15 fewer than matched due to singleton CPAs | VERIFIED | Matches dip-test report and script logic. |
+| ResNet-50 ImageNet-1K V2, 2048-d, L2 normalized | VERIFIED | Consistent with methods and ablation script. |
+| All-pairs intra/inter distribution N = 41,352,824 / 500,000; KDE crossover 0.837; Cohen's d = 0.669 | VERIFIED | Supported by formal-statistical script/report, although Appendix B points to the wrong JSON path. |
+| Firm A dip result N=60,448, dip=0.0019, p=0.169 | VERIFIED | `/reports/dip_test/dip_test_results.json`. |
+| Firm A dHash dip result N=60,448, dip=0.1051, p<0.001 | VERIFIED | Same JSON. |
+| All-CPA cosine/dHash dip results N=168,740, p<0.001 | VERIFIED | Same JSON. |
+| "p = 0.17 at n >= 10 signatures" in III-H | SUSPICIOUS | The `n >= 10` filter applies to accountant-level aggregates in script 15, not the Firm A signature-level dip test. The Firm A dip test uses N=60,448 signatures. |
+| "single dominant mechanism" language | SUSPICIOUS | Still too mechanistic for the statistics; use "dominant high-similarity regime" or "consistent with replication-dominated framing." |
+| BD/McCrary transition instability and values in Appendix A | VERIFIED | `/reports/bd_sensitivity/bd_sensitivity.json`; table values match. |
+| Beta mixture Delta BIC = 381 for Firm A; 10,175 full sample; forced crossings 0.977/0.999 | VERIFIED | `/reports/beta_mixture/beta_mixture_results.json`. |
+| Firm A whole-sample rates in Table IX | VERIFIED | `/reports/validation_recalibration/validation_recalibration.json` and pixel-validation JSON: e.g., cos>0.95 `55,922/60,448 = 92.51%`, dual `54,370/60,448 = 89.95%`. |
+| 310 byte-identical positives | VERIFIED | `/reports/pixel_validation/pixel_validation_results.json`. |
+| Byte-identity decomposition `145 / 50 / 180 / 35` | VERIFIED | New `/reports/byte_identity_decomp/byte_identity_decomposition.json`. The script counts Firm A signatures whose nearest same-CPA match is byte-identical; the "35" is a cross-year nearest-match count, not necessarily a deduplicated unordered pair count. |
+| Table X FAR against 50,000 inter-CPA negatives | VERIFIED | `/reports/expanded_validation/expanded_validation_results.json`. |
+| Omission of EER/FRR/precision/F1 in manuscript | VERIFIED | Manuscript now explains why these are not meaningful for Table X. |
+| Firm A 70/30 split: 124 CPAs/45,116 signatures vs 54 CPAs/15,332 | VERIFIED | `/reports/validation_recalibration/validation_recalibration.json`. |
+| Two CPAs excluded from split due to disambiguation ties | UNVERIFIABLE | Plausible; I did not find a report field documenting those two ties. |
+| Table XI rates/z-tests | VERIFIED | Values match recalibration JSON, including corrected `z=-3.19` for cos>0.9407. |
+| Table XII sensitivity counts and +1.19 pp Firm A shift | VERIFIED | Recalibration JSON supports counts and `0.89945` vs `0.91138`. |
+| Table XIII per-year Firm A left-tail rates | PARTIAL | Values are internally coherent, but Appendix B points to `reports/deloitte_distribution/deloitte_distribution_results.json`, which does not exist in the inspected report tree. |
+| Tables XIV/XV partner ranking values | VERIFIED | `/reports/partner_ranking/partner_ranking_results.json`. |
+| Table XVI intra-report agreement | VERIFIED | `/reports/intra_report/intra_report_results.json`. |
+| Table XVII document-level classification counts | VERIFIED with path caveat | Counts match manuscript arithmetic and available PDF verdict artifacts, but Appendix B points to `reports/pdf_level/pdf_level_results.json`, which does not exist. Existing files include `pdf_signature_verdicts.json`, CSV/XLSX, and report markdown at report root. |
+| Cross-firm dual-descriptor convergence `42.12%` vs `88.32%` | VERIFIED | New JSON: non-Firm-A `27,596/65,515`, Firm A `49,388/55,921`. Note this Firm A denominator differs by one from Table IX's cosine-only `55,922`, so the text should specify the additional filters used by script 28. |
+| Ablation Table XVIII | PARTIAL | The script exists and `/Volumes/NV2/PDF-Processing/signature-analysis/ablation/ablation_results.json` exists, but Appendix B incorrectly maps it to `reports/ablation/ablation_results.json`. |
+| Appendix B claim that all report files are committed alongside scripts in the project's `reports/` tree | SUSPICIOUS | In the current workspace there is no repo-root `reports/` directory. Several paths named in Appendix B are missing even in the absolute report tree. |
+
+## 4. Methodological Rigor
+
+The core methodology remains credible for an IEEE Access Regular Paper. The strongest elements are:
+
+- The paper separates operational calibration from distributional characterization. This is essential because the per-signature diagnostics do not converge to a clean two-class threshold.
+- The dual-descriptor design is well motivated: cosine captures high-level similarity, while independent-minimum dHash provides a structural near-duplicate check.
+- The byte-identical positive anchor is a valid conservative subset, and the inter-CPA negative anchor gives meaningful specificity/FAR estimates.
+- The held-out Firm A fold is now framed as within-Firm-A sampling-variance disclosure rather than full external validation.
+- The new script 28 closes the most important prior provenance gap for byte identity and cross-firm convergence.
+
+Remaining rigor concerns:
+
+1. **Provenance packaging is still inconsistent.** Appendix B says scripts and reports live under the project's `reports/` tree. In this workspace there is no repo-root `reports/` directory, and the actual artifacts are under `/Volumes/NV2/PDF-Processing/signature-analysis/reports/`. More importantly, the Appendix B paths for formal statistical results, Deloitte/Firm-A distribution results, PDF-level results, and ablation results are wrong or missing.
+2. **The Firm A prior remains partly socially sourced.** The text says practitioner knowledge is non-load-bearing, but the Introduction still relies rhetorically on "widely recognized." The empirical case can stand without that phrase.
+3. **The dip-test interpretation remains slightly overextended.** Failure to reject unimodality supports "no clear multimodal split"; it does not show a single mechanism. The byte-identity and ranking evidence do more of the work.
+4. **The `n >= 10` parenthetical in III-H is likely misplaced.** It should not be attached to the Firm A signature-level dip result unless the authors can show the exact filtering.
+5. **Several engineering details remain under-specified for full reproducibility:** VLM prompt/parse rule, HSV red-stamp thresholds, training log for YOLO metrics, and exact runtime environment for throughput.
+
+## 5. Narrative Discipline
+
+The narrative is substantially more disciplined than v3.18.1, but a few overclaims remain.
+
+Recommended softening:
+
+- Replace "detects such non-hand-signed signatures" in the Abstract with "classifies signatures by evidence of non-hand-signing" or "detects replication-consistent signatures." The pipeline does not observe the signing workflow directly.
+- Replace "consistent with a single dominant mechanism (non-hand-signing)" in III-H and "single dominant mechanism plus residual..." in V-C with "consistent with a dominant high-similarity regime plus residual heterogeneity."
+- Replace "widely recognized / widely held within the audit profession" with either a citation or a purely methodological framing: "Firm A was selected as a candidate calibration reference; its benchmark status is evaluated using image evidence below."
+- Be careful with "known-majority-positive population." The empirical evidence supports replication-dominated, but "known" implies a source of ground truth outside the image evidence.
+
+The corrected cross-firm claim is narratively better. The old `5x` story was both wrong and too dramatic; the new `~2.1x` gap is still meaningful and more defensible.
+
+## 6. IEEE Access Fit
+
+The paper fits IEEE Access well. It is application-driven, computationally substantial, and methodologically relevant to document forensics, audit analytics, and computer vision. The novelty is not a new neural architecture; it is the calibration and validation strategy for a real archival corpus with limited ground truth. That is a legitimate IEEE Access contribution.
+
+The remaining issues are editorial/reproducibility issues rather than grounds for rejection. IEEE Access reviewers are likely to value the added Appendix B provenance map, but they will also notice if the mapped paths do not exist. Fixing those paths, or bundling the missing JSON/Markdown reports, is important before submission.
+
+## 7. Specific Actionable Revisions
+
+1. **Fix Appendix B provenance paths.** In the inspected report tree, these Appendix B artifacts are missing at the stated paths:
+   - `reports/formal_statistical/formal_statistical_results.json` (available alternative appears to be `reports/formal_statistical_data.json`)
+   - `reports/deloitte_distribution/deloitte_distribution_results.json` (only figures were present)
+   - `reports/pdf_level/pdf_level_results.json` (available alternatives include `reports/pdf_signature_verdicts.json`, CSV/XLSX, and markdown)
+   - `reports/ablation/ablation_results.json` (actual path appears to be `/Volumes/NV2/PDF-Processing/signature-analysis/ablation/ablation_results.json`)
+
+2. **Either commit/copy the report tree into the repo or state the absolute artifact root.** The user-facing manuscript says `reports/...`; the current repo root has no `reports/` directory.
+
+3. **Remove the remaining "single dominant mechanism" phrasing.** Use "dominant high-similarity regime" instead.
+
+4. **Fix the III-H parenthetical "p = 0.17 at n >= 10 signatures."** The signature-level dip test is N=60,448; the `n >= 10` rule belongs to accountant-level aggregates.
+
+5. **Clarify the `55,921` denominator in IV-H.2.** It differs by one from Table IX's `55,922` cosine-only Firm A count. Add that script 28 conditions on `assigned_accountant IS NOT NULL` and `min_dhash_independent IS NOT NULL`, or reconcile the one-record discrepancy.
+
+6. **Add or cite artifacts for still-unverifiable operational claims.** At minimum: YOLO training metrics/logs, VLM prompt/config, HSV thresholds, throughput log, and document-type breakdown.
+
+7. **Soften "widely recognized/widely held" practitioner wording or cite it.** The current "non-load-bearing" sentence helps, but uncited professional-knowledge claims are still exposed.
+
+8. **Keep the impact statement archived or revise before reuse.** The archive note correctly warns that "distinguishes genuinely hand-signed signatures from reproduced ones" would overstate the evidence.
+
+Bottom line: v3.18.2 materially improves the paper and fixes the round-16 empirical error. I would not block submission on the central results, but I would require the provenance/path cleanup and the remaining mechanism-language softening before calling it Accept.

paper/codex_review_gpt55_v3_18_3.md

@@ -0,0 +1,127 @@
+# Independent Peer Review (Round 18) - Paper A v3.18.3
+
+Reviewer role: independent peer reviewer for IEEE Access Regular Paper.
+Manuscript reviewed: "Replication-Dominated Calibration" - CPA signature analysis, v3.18.3, commits `f1c2537` + `26b934c` on `yolo-signature-pipeline`.
+Audit basis: manuscript sections under `paper/`, prior round-16 and round-17 reviews, scripts under `signature_analysis/`, the current SQLite/report artifacts under `/Volumes/NV2/PDF-Processing/signature-analysis/`, and direct filesystem checks of Appendix B paths.
+
+## 1. Overall Verdict: Minor Revision
+
+I recommend **Minor Revision**, not Accept.
+
+v3.18.3 resolves the main round-17 provenance problem: the four fabricated Appendix B paths have been replaced with paths that exist in the available report tree, and the manuscript now explicitly states the local report root (`/Volumes/NV2/PDF-Processing/signature-analysis/`) plus the fact that the ablation artifact is a sibling of `reports/`. The prior "single dominant mechanism" wording is also removed from the main Methodology/Discussion passages, and the mistaken "p = 0.17 at n >= 10 signatures" parenthetical is fixed.
+
+However, the new reconciliation note for the `55,921` vs `55,922` Firm A cosine-only counts is not supported by the current artifacts. The manuscript attributes the one-record difference to successive database snapshots and a downstream floating-point shift of one borderline Firm A signature. Direct database checks indicate a different cause: Table IX is based on Firm A membership from `accountants.firm`, whereas `signature_analysis/28_byte_identity_decomposition.py` groups Firm A by `signatures.excel_firm`. In the current database, one signature above `cos > 0.95` belongs to an accountant whose registry firm is Firm A but whose `excel_firm` field is not Firm A. Thus the new note fixes the arithmetic discrepancy but introduces a false provenance explanation.
+
+This is Minor rather than Major because the one-record drift has negligible numerical effect and does not overturn the central findings. It should still be corrected before submission because v3.18.3 was specifically intended to repair provenance discipline.
+
+## 2. Re-audit of Round-17 Findings
+
+| Round-17 finding | v3.18.3 status | Re-audit notes |
+|---|---|---|
+| Appendix B provenance paths overclaimed / several did not exist | **RESOLVED** | All listed Appendix B report artifacts now exist when rebased to `/Volumes/NV2/PDF-Processing/signature-analysis/`. The replacement paths for formal statistics, Firm A per-year data, PDF verdicts, ablation, and byte decomposition are real. |
+| Residual "single dominant mechanism" wording | **RESOLVED enough** | The exact phrase is gone from Methodology III-H and Discussion V-C. Current wording uses "dominant high-similarity regime plus residual within-firm heterogeneity," which is more defensible. |
+| III-H "p = 0.17 at n >= 10 signatures" parenthetical | **RESOLVED** | The current text correctly reports the signature-level dip result as `p = 0.17`, `N = 60,448` Firm A signatures. The `n >= 10` filter is no longer attached to that claim. |
+| "Widely recognized / widely held" practitioner wording | **RESOLVED enough** | Introduction now frames Firm A as selected by practitioner-knowledge motivation and evaluated by image evidence. III-H says "is understood within the audit profession" but immediately marks this as non-load-bearing. A citation would still be cleaner, but this is no longer a submission blocker. |
+| 55,921 vs 55,922 Firm A cosine-only count discrepancy | **PARTIAL / NEW ERROR** | The manuscript now acknowledges the discrepancy, but the explanation appears wrong. Current DB evidence points to different Firm A attribution fields (`accountants.firm` vs `signatures.excel_firm`), not a snapshot/floating-point shift. |
+| Still-unverifiable operational details: YOLO logs, VLM prompt/config, HSV thresholds, throughput log | **UNRESOLVED but not new** | These remain plausible method claims, but I did not find dedicated artifacts establishing them. This is acceptable for main-paper review only if the supplement includes training/config/runtime logs. |
+| Section reference for `145/50/180/35` byte decomposition | **PARTIAL** | Appendix B now maps the decomposition to script 28, but the main results Section IV-F.1 still reports only the all-sample 310 byte-identical signatures, not the Firm A `145/50/180/35` decomposition. Several locations still cite Section IV-F.1 for a decomposition that is actually in III-H / V-C / Appendix B. |
+
+## 3. Appendix B Path Verification
+
+I checked every Appendix B artifact path directly against the filesystem. Rebased to `/Volumes/NV2/PDF-Processing/signature-analysis/`, all listed artifacts exist:
+
+| Appendix B artifact | Exists? |
+|---|---|
+| `reports/extraction_methodology.md` | Yes |
+| `reports/pdf_signature_verdicts.json` | Yes |
+| `reports/formal_statistical_data.json` | Yes |
+| `reports/formal_statistical_report.md` | Yes |
+| `reports/dip_test/dip_test_results.json` | Yes |
+| `reports/beta_mixture/beta_mixture_results.json` | Yes |
+| `reports/bd_sensitivity/bd_sensitivity.json` | Yes |
+| `reports/pixel_validation/pixel_validation_results.json` | Yes |
+| `reports/validation_recalibration/validation_recalibration.json` | Yes |
+| `reports/expanded_validation/expanded_validation_results.json` | Yes |
+| `reports/accountant_similarity_analysis.json` | Yes |
+| `reports/figures/` | Yes |
+| `reports/partner_ranking/partner_ranking_results.json` | Yes |
+| `reports/intra_report/intra_report_results.json` | Yes |
+| `reports/pdf_signature_verdict_report.md` | Yes |
+| `ablation/ablation_results.json` | Yes |
+| `reports/byte_identity_decomp/byte_identity_decomposition.json` | Yes |
+
+The path replacements are real. The only caveat is semantic rather than filesystem-level: Table XIII is described as "derived from `reports/accountant_similarity_analysis.json` filtered to Firm A; figures in `reports/figures/`." That is acceptable as provenance if the supplement documents the filter/query used for the table.
+
+## 4. Empirical-Claim Audit
+
+I focused on claims introduced or changed by v3.18.3.
+
+**Verified**
+
+- Appendix B path replacements exist in the actual report tree.
+- `reports/byte_identity_decomp/byte_identity_decomposition.json` exists and reports:
+  - Firm A byte-identical signatures: `145`
+  - distinct Firm A partners: `50`
+  - registered Firm A partners: `180`
+  - cross-year byte-identical matches: `35`
+- The same JSON reports cross-firm dual convergence:
+  - Firm A: `49,388 / 55,921 = 88.32%`
+  - Non-Firm-A: `27,596 / 65,515 = 42.12%`
+- `validation_recalibration.json` reports Table IX's Firm A `cos > 0.95` count as `55,922 / 60,448 = 92.51%`.
+
+**New / Incorrect**
+
+- The new Results IV-H.2 reconciliation note says the `55,921` vs `55,922` discrepancy comes from successive snapshots and one borderline Firm A signature shifting from `cos > 0.95` to `cos = 0.95...` at floating-point precision. I could not reproduce that explanation.
+- Direct SQLite checks on the current database show:
+  - Firm A by `accountants.firm`, `cos > 0.95`: `55,922`
+  - Firm A by `signatures.excel_firm`, `cos > 0.95`: `55,921`
+  - exactly one `cos > 0.95` signature has `accountants.firm = Firm A` but `signatures.excel_firm != Firm A`.
+- The discrepant row I saw was `signature_id = 37768`, `assigned_accountant = 徐文亞`, `excel_firm = 黃毅民`, `max_similarity_to_same_accountant = 0.978511691093445`, `min_dhash_independent = 0`. That is not a `cos = 0.95...` borderline case.
+
+The corrected explanation should be along the lines of: Table IX uses accountant-registry Firm A membership, while script 28's cross-firm decomposition uses the `excel_firm` field; one above-threshold signature differs between those two firm-attribution fields. Alternatively, change script 28 to use the same `accountants.firm` join as the validation artifacts and regenerate the JSON.
+
+**Still only partially supported**
+
+- YOLO validation metrics, VLM prompt/settings, HSV red-removal thresholds, and 43.1 docs/sec throughput remain method claims without visible log/config artifacts in the inspected report tree.
+- The two Firm A CPAs excluded from the held-out split due to disambiguation ties remain plausible but not directly documented in a report field.
+- The 15 document types / 86.4% standard audit-report breakdown remains plausible but was not traced to a packaged table.
+
+## 5. Methodological + Narrative Discipline
+
+The narrative is materially cleaner than v3.18.2. The manuscript now keeps the central inference where it belongs: the evidence supports a replication-dominated calibration population and a continuous similarity-quality spectrum, not a directly observed signing workflow or a clean two-mechanism mixture.
+
+The remaining narrative issues are narrow:
+
+1. **Fix the new count-reconciliation note.** The current note is too specific and appears empirically false. Do not invoke successive snapshots or a floating-point boundary shift unless that can be shown from archived artifacts. The current evidence points to a firm-attribution-field mismatch.
+
+2. **Clarify Firm A membership consistently.** Several scripts use `accountants.firm`; script 28 uses `signatures.excel_firm`. Both may be defensible for different questions, but the paper must state which field defines Firm A in each table or harmonize the scripts.
+
+3. **Remove or soften remaining "known-majority-positive" phrasing.** The term appears in the Introduction, Methodology, Discussion, and Conclusion. The paper's better phrase is "replication-dominated reference population." "Known" still implies external ground truth stronger than the paper can document.
+
+4. **Correct the auditor-year / cross-year pooling description.** Methodology III-G says the auditor-year ranking is a "deliberately within-year aggregation that avoids cross-year pooling." But the same section and Results IV-G.2 state that each signature's best match is computed against the full same-CPA cross-year pool. The aggregation is by auditor-year, but the underlying similarity statistic is cross-year. Replace "avoids cross-year pooling" with "aggregates signatures within each auditor-year while using the full same-CPA pool for each signature's best-match statistic."
+
+5. **Align the byte-decomposition section reference.** If the `145/50/180/35` decomposition is meant to be a Results claim, put a sentence in IV-F.1 or cite Appendix B directly. As written, Section IV-F.1 reports the 310 all-sample byte-identical signatures, not the Firm A decomposition.
+
+## 6. IEEE Access Fit
+
+The paper remains a good IEEE Access fit. It is application-driven, computationally substantial, and methodologically relevant to document forensics, audit analytics, and computer vision. The contribution is not a novel neural architecture; it is a defensible calibration and validation strategy for a large archival corpus with limited ground truth.
+
+The remaining problems are reproducibility/provenance polish, not a collapse of the empirical core. Still, IEEE Access reviewers may scrutinize the supplement and table provenance. v3.18.3's Appendix B is now much stronger, but the newly added reconciliation note should be corrected because it is exactly the kind of precise provenance statement that reviewers can audit.
+
+## 7. Specific Actionable Revisions
+
+1. Replace the IV-H.2 `55,921` vs `55,922` explanation. Either:
+   - harmonize script 28 to use `accountants.firm` like `validation_recalibration.py` and regenerate the byte-decomposition JSON; or
+   - keep the current script 28 output and state that the one-record difference arises from `accountants.firm` versus `signatures.excel_firm` Firm A attribution.
+
+2. Add a short note in Appendix B or the script 28 report defining the Firm A grouping field for each artifact.
+
+3. Replace "known-majority-positive" with "replication-dominated" or "candidate replication-dominated" unless an external citation/ground-truth source is supplied.
+
+4. Revise Methodology III-G's auditor-year sentence so it does not claim the ranking avoids cross-year pooling.
+
+5. Add the `145/50/180/35` Firm A byte-decomposition sentence to Results IV-F.1, or cite Appendix B directly instead of Section IV-F.1 when discussing that decomposition.
+
+6. If time permits before submission, include supplementary logs/configs for YOLO metrics, VLM prompt/settings, HSV thresholds, and throughput. These are not central-result blockers, but they would strengthen the reproducibility package.
+
+Bottom line: v3.18.3 successfully fixes the fabricated Appendix B paths and most narrative overclaim from round 17. The manuscript should not be accepted until the new count-reconciliation explanation and the auditor-year pooling wording are corrected, but the required changes are small and localized.

paper/codex_review_gpt55_v4_round1.md

@@ -0,0 +1,143 @@
+# Paper A v4.0 Methodology Section III-G through III-L Peer Review
+
+Reviewer: gpt-5.5 xhigh  
+Date: 2026-05-12  
+Round number: 21 (v4 round 1)  
+Review target: `paper/v4/paper_a_methodology_v4_section_iii.md`
+
+Audit aliases used below:
+
+- V4: `paper/v4/paper_a_methodology_v4_section_iii.md`
+- V3: `paper/paper_a_methodology_v3.md`
+- Script36: `/Volumes/NV2/PDF-Processing/signature-analysis/reports/v4_big4/calibration_and_loo_validation/calibration_loo_report.md`
+- Script37: `/Volumes/NV2/PDF-Processing/signature-analysis/reports/v4_big4/k3_loo_check/k3_loo_report.md`
+- Script38: `/Volumes/NV2/PDF-Processing/signature-analysis/reports/v4_big4/convergence_k3_reverse_anchor/convergence_report.md`
+- Script39: `/Volumes/NV2/PDF-Processing/signature-analysis/reports/v4_big4/signature_level_convergence/sig_level_report.md`
+- Script40: `/Volumes/NV2/PDF-Processing/signature-analysis/reports/v4_big4/pixel_identity_far/far_report.md`
+- Script34 local: `/Volumes/NV2/PDF-Processing/signature-analysis/reports/big4_only_pooled/big4_only_pooled_report.md`
+- Script35 local: `/Volumes/NV2/PDF-Processing/signature-analysis/reports/big4_k3_cluster_inspection/inspection_report.md`
+- Script32 local: `/Volumes/NV2/PDF-Processing/signature-analysis/reports/non_firm_a_calibration/non_firm_a_calibration_report.md`
+
+## Verdict
+
+Major Revision.
+
+## Major Findings
+
+1. **K=3 is not yet justified as an operational classifier.**
+
+   V4 selects K=3 for the operational per-CPA classifier (V4:57, V4:67) and says the K=3/K=2 contrast justifies selecting K=3 (V4:107). The underlying Script37 verdict is weaker: `P2_PARTIAL`, with the explicit interpretation that the C1 cluster exists but "membership is not well-predicted by held-out fit" (Script37:92, Script37:94). The report's own legend says `P2_PARTIAL` means the cluster is "not predictively useful as an operational classifier" (Script37:97-99).
+
+   The numbers support this concern. K=3 C1 component shape is stable (max deviations 0.0047 cosine, 0.955 dHash, 0.023 weight; Script37:77-79), but held-out C1 membership differs from baseline by up to 12.77 percentage points (Script37:83-90). For PwC, baseline C1 is 23.5% but held-out prediction is 36.27% (Script37:47-51, Script37:87). That is not a small operational error if the label is used to classify CPAs.
+
+   The BIC evidence is also weak. K=3 is lower BIC than K=2 by only 3.48 points (Script36:9-10; Script34 local:40-41). This is acceptable as mild descriptive support, not as the load-bearing reason to replace a classifier. The draft should either (a) demote K=3 to a descriptive/convergent-validation model, or (b) make K=3 primary only with explicit LOOO membership uncertainty and soft-posterior reporting.
+
+2. **The "three independent lenses" framing overstates independence and validation strength.**
+
+   V4 describes the convergent validation as three "independent statistical lenses" (V4:73-89). They are not independent empirical measurements. All three are deterministic functions of the same per-CPA or per-signature `(cos, dHash)` features:
+
+   - Lens 1 is K=3 posterior from the same two descriptors (V4:77; Script38:6-12).
+   - Lens 2 is a monotone transform of the cosine marginal only (V4:78; Script38:16-18).
+   - Lens 3 is the fraction of signatures failing the same box rule `cos > 0.95 AND dh <= 5` (V4:79; Script38:20-22).
+
+   The high Spearman correlations are verified (0.9627, 0.8890, 0.8794; Script38:24-34), but they are partly mechanical agreement among feature-derived scores. They do not validate the classifier against an independent ground truth for hand-signed signatures.
+
+   There is also a conceptual reversal in the reverse-anchor prose. V4 says the non-Big-4 reference has lower cosine and higher dHash than the Big-4 C1 center (V4:37), which is verified (reference center 0.9349/9.7670 in Script38:16-18; C1 0.9457/9.1715 in Script38:8-12). But V4 then calls this a "more-replicated-population" baseline (V4:37). Lower cosine and higher dHash indicate less replication / more hand-leaning, not more replication. A reviewer will likely catch this immediately.
+
+3. **The draft conflates at least three classifiers and then validates only one simplified binary rule.**
+
+   V4 alternates among (i) K=3 per-CPA hard labels (V4:67), (ii) a binary Paper A box rule `cos > 0.95 AND dh <= 5` (V4:69), and (iii) the inherited five-way per-signature/document rule with `dh <= 5`, `5 < dh <= 15`, and `dh > 15` bands (V4:123-135). The Script38/39 convergence results validate only the simplified binary rule `non_hand iff cos > 0.95 AND dh <= 5` (Script38:20-22; Script39:8-12). They do not validate the full five-way classifier, especially the moderate non-hand-signed band `5 < dh <= 15`.
+
+   This matters because V3's inherited Section III-K explicitly treated `cos > 0.95 AND 5 < dh <= 15` as "Moderate-confidence non-hand-signed" (V3:278-287). V4 keeps that category (V4:127) but cites kappa/rho evidence from a binary high-confidence-only rule (V4:121). The current prose therefore overstates what the Script39 kappa values prove.
+
+   Recommended fix: choose a primary endpoint. If the five-way rule remains primary, validate that exact five-way rule or its declared binary collapse. If K=3 becomes primary, provide a document-level aggregation rule for K=3 and stop calling the inherited box rule the operational classifier.
+
+4. **The pixel-identity validation is useful, but "FAR" is the wrong metric name and the evidentiary force is overstated.**
+
+   Script40's ground truth is a positive class: pixel-identical signatures are treated as replicated (Script40:4-8). Misclassifying them as hand-leaning is a false negative / miss rate on an easy positive-anchor subset, not a false-alarm rate in the usual classifier sense. V4 defines FAR as "probability of labelling a pixel-identical signature as hand-leaning" (V4:109), which reverses standard terminology.
+
+   The 0/262 result is verified for all three classifiers (Script40:12-18), and the caveat that pixel-identity is necessary but not sufficient is appropriate (V4:117; Script40:29-31). But for the Paper A box rule this result is close to tautological: byte-identical nearest-neighbor signatures will have near-maximal cosine and minimal dHash. V3 was more careful, noting that FRR against byte-identical positives is trivially zero at thresholds below 1 and should be interpreted qualitatively (V3:266-268).
+
+   Rename this metric to "pixel-identity positive-anchor miss rate" or "false-hand rate on replicated positives." Do not present it as FAR unless a true hand-signed negative anchor is evaluated.
+
+5. **Several empirical/provenance claims need correction or explicit "unverified" status.**
+
+   - V4 says the K=2 LOOO max cosine deviation 0.028 is `5.6x` a "bootstrap CI half-width of 0.005" (V4:103). Script36 reports max deviation 0.0278 (Script36:43), but 0.005 is the stability tolerance in the verdict legend, not the bootstrap CI half-width (Script36:50-52). The full Big-4 bootstrap cosine CI half-width is 0.0015 (Script36:14-17). Correct the denominator and wording.
+
+   - V4 says all-non-Firm-A is dip-test unimodal at `p > 0.99` (V4:21). Script32 local reports all-non-Firm-A cosine p = 0.9975 but dHash p = 0.9065 (Script32 local:56-76). The later detailed sentence in V4 correctly gives 0.998/0.907 (V4:43). Fix the earlier overstatement.
+
+   - V4 says no BD/McCrary transition is identified on either axis and cites Script32/34 (V4:47). Script34 local supports no Big-4-only BD/McCrary threshold (Script34 local:28-31), but Script32 local reports dHash BD/McCrary thresholds for `big4_non_A` and `all_non_A` (Script32 local:36-44, Script32 local:68-76). Narrow the claim to the Big-4-only analysis or explain why Script32 subset transitions are not used.
+
+   - The Firm A byte-identical claim is partly verified. Script40 verifies 145 Firm A pixel-identical signatures inside the 262 Big-4 total (Script40:20-27). The added details "50 distinct Firm A partners," "of 180 registered," and "35 span different fiscal years" appear in V3 (V3:165) and V4 (V4:31), but I did not find them in the supplied Script36-40 reports. Treat those details as unverified unless the Appendix B/script artifact is cited directly.
+
+   - The "mid/small-firm tail actively pulling the v3.x crossing" statement (V4:19) is stronger than the local Script34 evidence. Script34 local verifies the Big-4-only crossing and CI (Script34 local:18-24), and it reports a large offset from the published baseline (Script34 local:51-58). It does not, by itself, prove the causal language "actively pulling" rather than "the full-sample and Big-4-only calibrations differ."
+
+## Minor Findings
+
+1. **Dip-test p-value precision needs a resolution check.** V4 says bootstrap p-value estimation uses `n_boot = 2000` and reports `p < 10^-4` (V4:43). With a finite bootstrap of 2000, the natural resolution is about 1/2000 unless the script uses a different asymptotic/calibrated p-value. Script36/34 display p = 0.0000 (Script36:6-8; Script34 local:28-31). State the reporting convention precisely, e.g., "no bootstrap replicate exceeded the observed statistic; reported as p < 0.001" if that is what happened.
+
+2. **The Delta BIC sign convention is confusing.** V4 reports "Delta BIC = -3.5" (V4:65). Since lower BIC is preferred, a reviewer may expect `BIC(K=2) - BIC(K=3) = 3.48` or "K=3 lower by 3.48." Use one convention and define it.
+
+3. **Per-signature convergence is real but only moderate for the box rule.** Script39 verifies kappas of 0.6616, 0.5586, and 0.8701 (Script39:22-30). The report verdict is `SIG_CONVERGENCE_MODERATE`, not strong (Script39:41-48). V4's statement that box-rule disagreement reflects "different decision geometries" rather than signal disagreement (V4:99) is plausible but interpretive. Add the moderate verdict and avoid making geometry the only explanation.
+
+4. **Per-CPA vs per-signature component centers drift more than the prose suggests.** Script39 shows per-CPA C1 at cosine 0.9457 and per-signature C1 at 0.9280 (Script39:16-20). Kappa is high for K=3 perCPA vs perSig labels (Script39:28), but "the same component structure recovers" (V4:99) should be softened to "a broadly similar three-component ordering recovers."
+
+5. **The Section III-L title is misleading.** The section is titled "Per-Document Classification" (V4:119) but most of it defines per-signature categories (V4:121-133). The document-level aggregation appears only in one paragraph (V4:135). Either rename to "Signature- and Document-Level Classification" or split the two parts.
+
+6. **K=3 alternative output lacks document aggregation.** V4 says the K=3 alternative assigns each signature to C1/C2/C3 (V4:137), but if Section III-L is per-document classification, the K=3 alternative also needs a document-level worst-case or posterior aggregation rule.
+
+7. **Firm anonymization is inconsistent.** V4 names the four firms in Chinese and then says they are pseudonymized as Firms A-D (V4:17). Later it uses PwC directly (V4:31). V3 says firm-level results are reported under pseudonyms (V3:315-316). Decide whether v4 abandons anonymization; otherwise keep the main text pseudonymous and put the mapping outside the manuscript, if at all.
+
+## Editorial / Prose Nits
+
+1. Replace "more-replicated-population baseline" (V4:37) with "less-replicated external reference" or "hand-leaning external reference."
+
+2. Replace "failure rate" for Lens 3 (V4:79, V4:89) with "box-rule hand-leaning rate" or "non-replicated rate." "Failure" sounds like classifier failure rather than a hand-leaning outcome.
+
+3. "Strongest single methodology-validation signal" (V4:89) is too strong because the lenses share features. Use "strongest internal consistency signal."
+
+4. "Boundary moves modestly" (V4:105) understates the PwC fold, where C1 membership rises from 23.5% to 36.3% (Script37:47-51). Use "membership remains composition-sensitive."
+
+5. "Calibration uncertainty band of +/- 5-13 percentage points" (V4:105) should be "observed absolute differences of 1.8-12.8 percentage points, with the largest fold exceeding the report's 5 pp viability bar" (Script37:83-90).
+
+6. "Operational threshold derivation" (V4:51) is not accurate if the operational per-signature classifier remains the inherited box rule. Use "mixture model and component assignment" unless K=3 is truly primary.
+
+7. The cross-reference index is useful, but it should be removed from the submitted manuscript or converted into an internal author checklist.
+
+## Responses to the Five Open Questions
+
+1. **Scope justification.**
+
+   The three-point argument is directionally good but not yet sufficient. Add a fourth point explicitly restricting generalizability: primary claims are for the Big-4 audit-report context, while the 249 non-Big-4 CPAs are used only as robustness/reverse-anchor context unless Section IV-K independently validates them. Also soften "tail distorts" to "tail changes the fitted crossing" unless you cite a direct diagnostic for distortion. The Big-4 counts and crossings are verified (Script34 local:4-24; Script36:6-17), but the causal language needs restraint.
+
+2. **Firm A phrasing.**
+
+   Use "templated-end case study" or "replication-heavy descriptive reference." Do not use "calibration reference, descriptively defined post-hoc" unless Firm A actually calibrates a threshold in v4. The draft correctly says Firm A is not the calibration anchor (V4:33). Calling it a calibration reference reintroduces the v3 vulnerability.
+
+3. **K=3 vs K=2 rationale.**
+
+   As written, no. Selecting K=3 as an operational classifier on LOOO stability is not acceptable because Script37 says K=3 is only `P2_PARTIAL` and "not predictively useful as an operational classifier" (Script37:92-99). Do not strengthen the BIC argument; Delta BIC about 3.5 is mild. The defensible claim is: K=2 is clearly unstable; K=3 gives a reproducible hand-leaning component shape; hard membership remains uncertain and should be reported as calibration uncertainty.
+
+4. **Hybrid box rule plus K=3 alternative.**
+
+   The hybrid can be acceptable only if roles are sharply separated: inherited five-way box rule is the primary signature/document classifier; K=3 is an accountant-level characterization and exploratory alternative. The current draft blurs this by calling K=3 "operational" (V4:67) while keeping the box rule in Section III-L (V4:121-137). Also, the validation scripts use the binary high-confidence rule `dh <= 5`, not the full five-way rule with `dh <= 15`. Fix this before deciding whether to keep the hybrid.
+
+5. **Section IV numbering.**
+
+   Do not freeze table numbers yet. First settle the Methodology labels and primary classifier. Results should mirror this order: sample/scope, K=2/K=3 calibration, convergence lenses, K=2 and K=3 LOOO, pixel-identity positive-anchor check, signature/document classification outputs, then full-dataset robustness. After that, assign table numbers and verify every Section III cross-reference to Section IV-D/F/G/K.
+
+## Recommended Next-Step Actions
+
+1. Rewrite Sections III-J and III-K so K=3 is either clearly primary with uncertainty, or clearly descriptive. If descriptive, remove "operational threshold" language from the K=3 discussion.
+
+2. Add the Script37 `P2_PARTIAL` result directly to the prose. Do not hide the "not predictively useful as an operational classifier" implication.
+
+3. Decide and declare the primary classifier: inherited five-way box rule, binary high-confidence box rule, or K=3 hard/posterior labels. Align all validation text to that exact classifier.
+
+4. If the five-way rule remains primary, rerun or report validation for the five-way categories and the document-level worst-case aggregation, not just `cos > 0.95 AND dh <= 5`.
+
+5. Rename the pixel-identity metric from FAR to positive-anchor miss rate / false-hand rate. Add a separate specificity/FAR result only if a true hand-signed or inter-CPA negative anchor is evaluated.
+
+6. Correct the empirical slips: K=2 "0.005 bootstrap half-width," all-non-Firm-A `p > 0.99`, Script32 BD/McCrary wording, reverse-anchor "more-replicated" phrase, and any unverified Firm A byte-decomposition details.
+
+7. Add a short provenance table for every numerical claim in Sections III-G through III-L, including exact report path, script number, and whether the number is directly reported or inferred by arithmetic.

paper/codex_review_gpt55_v4_round2.md

@@ -0,0 +1,87 @@
+# Paper A v4.0 Methodology Section III-G through III-L Peer Review
+
+Reviewer: gpt-5.5 xhigh  
+Date: 2026-05-12  
+Round number: 22 (v4 round 2)  
+Review target: `paper/v4/paper_a_methodology_v4_section_iii.md`
+
+## Verdict
+
+Minor Revision.
+
+v2 closes most of the round-21 blockers: K=3 is no longer the operational classifier, the "independent lenses" claim is softened, the pixel-identity metric is no longer called FAR in the draft, and the main empirical slips are corrected. The remaining issues are narrower but still need edits before accepting the methodology text, especially the false per-firm ordering claim in §III-K and the unresolved validation status of the five-way moderate-confidence band.
+
+## Round-21 finding closure table
+
+| Finding | Round-21 Severity | v2 Status | Evidence in v2 |
+|---|---|---|---|
+| M1. K=3 is not justified as an operational classifier. | Major | CLOSED | v2 explicitly says both K=2 and K=3 are descriptive and not used for signature/document labels (v2:51, v2:67-73, v2:143). It also reports Script 37 `P2_PARTIAL` and the "not predictively useful as an operational classifier" implication (v2:65, v2:109). |
+| M2. "Three independent lenses" overstates independence and validation strength, and reverse-anchor direction was wrong. | Major | PARTIAL | The independence and reverse-anchor wording are fixed: the scores are "not statistically independent" and only internal-consistency checks (v2:75-83), and the reference is now described as less replication-dominated (v2:35-37). However, v2 adds a false per-firm ordering claim that all three scores make Firm C most hand-leaning (v2:93); Script 38's reverse-anchor mean instead ranks Firm D highest. |
+| M3. Classifier conflation; only the simplified binary rule was validated. | Major | PARTIAL | v2 now declares the inherited five-way box rule as primary (v2:123-143) and K=3 as descriptive (v2:143). It also correctly notes that the kappa comparison validates only the binary high-confidence rule, not the five-way moderate band (v2:103). The unresolved moderate-band validation is still open (v2:190-192), and v2:125 still uses binary-rule correlations to support the full five-way rule without recalibration. |
+| M4. Pixel-identity "FAR" naming and evidentiary force were wrong. | Major | CLOSED | v2 renames this to a positive-anchor miss rate, frames it as a one-sided replicated-positive check, and adds the tautology/conservative-subset caveat (v2:111-121). |
+| M5. Empirical/provenance claims needed correction or explicit unverified status. | Major | CLOSED | The 0.005 denominator is now a stability tolerance, not a bootstrap CI (v2:65, v2:107); all-non-Firm-A dip values are corrected (v2:21, v2:43); BD/McCrary is narrowed to Big-4 null with external dHash transitions disclosed (v2:47); Firm A byte-decomposition details are marked inherited/not regenerated (v2:31, v2:176); "tail distorts" is softened to a scope-dependent shift (v2:19). |
+| m1. Dip-test p-value precision needed bootstrap-resolution wording. | Minor | CLOSED | v2 states no bootstrap replicate exceeded the observed statistic and reports `p < 5 x 10^-4` for `n_boot = 2000` (v2:21, v2:43, v2:158-159). |
+| m2. Delta BIC sign convention was confusing. | Minor | CLOSED | v2 defines lower BIC as preferred and reports `BIC(K=3) - BIC(K=2) = -3.48`, plus "K=3 lower by 3.48" (v2:45, v2:63). |
+| m3. Per-signature convergence is only moderate for the box rule. | Minor | CLOSED | v2 includes the `SIG_CONVERGENCE_MODERATE` verdict and avoids calling the Paper A-vs-K=3 kappas strong (v2:95-103). |
+| m4. Per-CPA vs per-signature component centers drift more than v1 suggested. | Minor | CLOSED | v2 says the fits recover a "broadly similar three-component ordering" and reports the C1 cosine drift of 0.018 (v2:95). |
+| m5. Section III-L title was misleading. | Minor | CLOSED | The section is now titled "Signature- and Document-Level Classification" and separates per-signature categories from document aggregation (v2:123-143). |
+| m6. K=3 alternative lacked document aggregation. | Minor | CLOSED | v2 no longer offers K=3 as a signature/document classifier, so a K=3 document aggregation rule is no longer required (v2:143). |
+| m7. Firm anonymization was inconsistent. | Minor | CLOSED | v2 uses Firm A-D pseudonyms in the methodology text and no longer names the Big-4 firms directly in the prose (v2:17, v2:31, v2:194). |
+| e1. Replace "more-replicated-population baseline." | Editorial | CLOSED | v2 now calls non-Big-4 a less-replicated external/reverse-anchor reference (v2:35-37). |
+| e2. Replace "failure rate" for Lens 3. | Editorial | CLOSED | Lens 3 is now "Paper A box-rule hand-leaning rate" (v2:83). |
+| e3. "Strongest single methodology-validation signal" was too strong. | Editorial | CLOSED | v2 uses "strongest internal-consistency signal" and denies external validation (v2:77, v2:93). |
+| e4. "Boundary moves modestly" understated LOOO membership instability. | Editorial | CLOSED | v2 uses composition-sensitive wording and reports the 12.8 pp Firm C fold deviation (v2:65, v2:109). |
+| e5. "Calibration uncertainty band of +/- 5-13 pp" wording needed correction. | Editorial | CLOSED | v2 reports observed absolute differences of 1.8-12.8 pp and the 5 pp viability bar (v2:109). |
+| e6. "Operational threshold derivation" language was inaccurate. | Editorial | CLOSED | v2 consistently calls K=3 a mixture characterisation/descriptive model, not an operational threshold source (v2:49-73, v2:143). |
+| e7. Cross-reference index should be removed or made internal. | Editorial | PARTIAL | v2 labels the cross-reference index as an author checklist to remove before submission (v2:181), but it remains inside the methodology draft (v2:181-188). |
+
+## Newly introduced issues
+
+1. **New factual/provenance error: the three scores do not agree on the most hand-leaning firm.** v2 claims that "by all three scores, Firm A is the most replication-dominated and Firm C is the most hand-leaning" (v2:93). Script 38 confirms Firm A is most replication-dominated, but not the Firm C part for all scores: mean P_C1 and mean hand_frac rank Firm C highest, while mean reverse-anchor ranks Firm D highest (`-0.7125` vs Firm C `-0.7672`, with higher score meaning more hand-leaning). Revise to: "P_C1 and box-rule hand_frac rank Firm C highest; the reverse-anchor score ranks Firm D highest; all three agree Firm A is most replication-dominated and the non-A firms are more hand-leaning than Firm A."
+
+2. **Unsupported scope superlative: "any single firm" / "smallest scope" is not proven by the supplied reports.** v2 says no dip-test rejection holds "within any single firm pooled alone" and that Big-4 is the "smallest scope" supporting a finite-mixture model (v2:21; repeated more generally at v2:43). The supplied Script 32 report verifies Firm A alone, `big4_non_A`, and `all_non_A`; it does not report separate single-firm tests for Firms B, C, and D or all smaller combinations. Narrow this to "among the tested comparison scopes in Script 32" or add the missing single-firm tests.
+
+3. **K=3 hard labels are incorrectly described as used in the Spearman correlations.** v2:143 says the "K=3 hard label" is used for the internal-consistency Spearman correlations. Script 38's Spearman table uses the K=3 posterior score `P_C1`, not hard labels. Change v2:143 to "K=3 posterior score is used for the Spearman correlations; hard labels are used for the cluster cross-tabulation."
+
+4. **Provenance table over-cites Script 38 for the Big-4 signature count.** v2:17 and v2:152 attribute the 150,442 signature count partly/directly to Script 38. In the supplied markdown report, Script 39 directly reports the 150,442 signature-level cloud; Script 38's visible report does not directly state that count. Keep Script 39 as the direct source unless the JSON artifact is also cited.
+
+5. **"Max fold-to-fold deviation" wording is imprecise.** v2 reports a K=2 "max fold-to-fold deviation" of 0.028 (v2:65, v2:107). Script 36's 0.0278 is the max absolute deviation across folds as reported in the stability summary, not the pairwise fold range; the fold cut range is about 0.0376 (0.9756 - 0.9380). Use the report's exact wording or explicitly define the statistic.
+
+## Provenance re-verification
+
+| v2 numerical claim | v2 lines | Spike-report check | Status |
+|---|---:|---|---|
+| Big-4 has 437 CPAs split 171 / 112 / 102 / 52. | v2:17, v2:151 | Script 36 reports 437 CPAs; Script 34 reports the four firm counts. | CONFIRMED |
+| Big-4 signature-level cloud has 150,442 signatures. | v2:17, v2:95, v2:152 | Script 39 reports fitting on 150,442 signature-level points. | CONFIRMED, but source should be Script 39 rather than Script 38 in the provenance table. |
+| Big-4 K=2 crossings are cos 0.9755 and dHash 3.7549, with CIs [0.9742, 0.9772] and [3.4762, 3.9689]. | v2:45, v2:53, v2:154-156 | Script 36 and Script 34 report these point estimates and bootstrap CIs. | CONFIRMED |
+| K=3 components are C1 0.9457/9.1715/0.143, C2 0.9558/6.6603/0.536, C3 0.9826/2.4137/0.321. | v2:55-63, v2:163 | Scripts 35, 37, and 38 report the same centers and weights. | CONFIRMED |
+| K=3 LOOO membership deviations are 1.8-12.8 pp, with `P2_PARTIAL`. | v2:65, v2:109, v2:168 | Script 37 reports diffs 1.76, 4.68, 5.81, 12.77 pp and verdict `P2_PARTIAL`. | CONFIRMED |
+| Spearman correlations are 0.963, 0.889, and 0.879. | v2:85-91, v2:169 | Script 38 reports 0.9627, 0.8890, and 0.8794. | CONFIRMED |
+| All three scores rank Firm C as most hand-leaning. | v2:93 | Script 38 per-firm summary ranks Firm C highest on mean P_C1 and mean hand_frac, but Firm D highest on mean reverse-anchor. | FLAGGED |
+| Per-signature kappas are 0.662, 0.559, and 0.870; verdict moderate. | v2:95-103, v2:170 | Script 39 reports 0.6616, 0.5586, 0.8701 and `SIG_CONVERGENCE_MODERATE`. | CONFIRMED |
+| Pixel-identical subset is n=262 split 145 / 8 / 107 / 2, with 0% miss rate and Wilson upper 1.45%. | v2:111-119, v2:172-173 | Script 40 reports total 262, the per-firm split, and 262/262 correct for all three candidate classifiers with Wilson [0.00%, 1.45%]. | CONFIRMED |
+| Non-Firm-A dip values are 0.998/0.906 for `big4_non_A` and 0.998/0.907 for `all_non_A`. | v2:21, v2:43, v2:161-162 | Script 32 reports 0.9985/0.9055 and 0.9975/0.9065, matching v2 rounded values. | CONFIRMED |
+
+## Outstanding open questions
+
+1. **Five-way moderate-confidence validation still needs a decision.** v2 is honest that the v4 kappa evidence covers only the high-confidence binary rule (v2:103, v2:190-192). If the five-way classifier remains primary, the cleanest next step is a Big-4-specific capture/FAR/cross-tab analysis for the moderate band and the document-level worst-case aggregation. If not rerun, the manuscript should explicitly state that the moderate band remains inherited from v3.x and is not newly validated by Scripts 38-40.
+
+2. **Firm anonymisation policy still needs confirmation for §IV-V.** v2 itself is pseudonymous, but the open question at v2:194 remains real: once §IV-V discuss within-Big-4 contrasts, the manuscript should consistently use Firm A-D and keep any real-name mapping out of the paper body.
+
+3. **Section IV numbering can remain deferred.** v2:196 is procedural and does not block §III acceptance; resolve after the methodology claims and result-table sequence are frozen.
+
+## Recommended next-step actions
+
+1. Correct v2:93's per-firm ordering claim against Script 38.
+
+2. Decide whether to add a Big-4-specific validation for the five-way moderate band and document-level aggregation. If not, narrow v2:125 so binary-rule correlations do not appear to validate the full five-way classifier.
+
+3. Narrow the dip-test scope language at v2:21 and v2:43, or add missing individual-firm dip tests for Firms B-D.
+
+4. Fix v2:143 so Spearman correlations are tied to K=3 posterior scores, not K=3 hard labels.
+
+5. Correct the provenance table entry for the 150,442 signature count to cite Script 39 as the direct markdown-report source.
+
+6. Replace "max fold-to-fold deviation" with the exact Script 36 statistic or report the actual pairwise fold range.
+
+7. Remove the author checklist and open-question block from the manuscript version after these decisions are resolved.

paper/codex_review_gpt55_v4_round3.md

@@ -0,0 +1,143 @@
+# Paper A Round 23 Review - v4 round 3
+
+Reviewer: gpt-5.5 xhigh  
+Date: 2026-05-12  
+Target: `paper/v4/paper_a_results_v4_section_iv.md` (§IV v2)  
+Cross-checked against: `paper/v4/paper_a_methodology_v4_section_iii.md` (§III v3), round-21/22 reviews, `paper/paper_a_results_v3.md`, and the supplied spike reports.
+
+## Verdict
+
+Major Revision.
+
+The empirical core of §IV v2 is much stronger than the earlier methodology drafts: most new Big-4 numerical tables match the spike reports. The blockers are presentation and provenance risks that reviewers will catch quickly: table numbering is not coherent, several §III cross-references now point to the wrong §IV material, the inherited detection count is misstated, and the draft says firm anonymisation is maintained while repeatedly printing real firm names.
+
+## Major findings
+
+1. **Table numbering is not coherent enough for partner review.**
+
+   §IV v2 says provisional numbering covers Tables IV-XVIII (line 3), and line 13 says v3.20.0 Table IV is "retained as Table IV here." But the file does not actually include a Table IV block; the first displayed v4 table is Table V at line 23. Line 17 also cites the inherited all-pairs analysis as "v3.20.0 §IV-C, Table V," while line 23 reuses Table V for the new Big-4 dip test. That is acceptable only if the inherited table is explicitly not a v4 table; otherwise Table V is duplicated.
+
+   The same issue recurs at the end: line 240 assigns current Table XVIII to the full-dataset Spearman robustness table, while line 254 says the inherited backbone ablation is "Table XVIII in v3.20.0." If the ablation is retained in the v4 manuscript, it cannot also be current Table XVIII. Fix by deciding which inherited v3 tables are reprinted/renumbered versus cited only as v3.x provenance.
+
+2. **§III v3 contains stale cross-references that §IV v2 does not support as written.**
+
+   §III line 13 says signature-level capture-rate analyses are in §IV-D, §IV-F, and §IV-G. In §IV v2, those are accountant-level distributional characterisation, internal-consistency checks, and LOOO reproducibility. This is a direct cross-reference failure.
+
+   §III line 23 says "all §IV results except §IV-K" are Big-4 restricted. §IV v2 itself is narrower and more accurate at line 9: §IV-D through §IV-J are Big-4 primary, while §IV-K is full-dataset robustness. But §IV-A-C are inherited full-corpus setup/detection/all-pairs material, §IV-I is inherited full-corpus inter-CPA FAR, and §IV-L is an inherited corpus-wide ablation. §III must be changed to match the actual results section.
+
+   §III line 109 says the moderate-confidence band retains v3.x capture-rate evaluation in "§IV-F"; in current §IV, §IV-F is not the inherited v3 capture-rate section. It should cite v3.x Tables IX/XI/XII/XII-B or current §IV-J's inheritance note, not current §IV-F.
+
+3. **The inherited detection-count sentence is numerically wrong / ambiguous.**
+
+   §IV line 13 says "182,328 detected signatures across 86,072 prefiltered audit-report PDFs." The v3 baseline distinguishes these counts: VLM screening identified 86,072 documents with signature pages, 12 corrupted PDFs were excluded, and batch YOLO inference ran on 86,071 documents; v3 Table III then reports 85,042 documents with detections and 182,328 extracted signatures. Current line 13 collapses these stages and assigns the 182,328 signatures to the wrong denominator.
+
+   Suggested rewrite: "VLM screening identified 86,072 signature-page documents; after 12 corrupted PDFs were excluded, YOLO batch inference processed 86,071 documents, with 85,042 yielding detections and 182,328 extracted signatures."
+
+4. **The draft claims firm anonymisation is maintained, but the §IV tables reveal real firm names.**
+
+   §III line 23 says the Big-4 firms are pseudonymously labelled Firm A-D. §IV line 265 says firm anonymisation is "maintained throughout §IV (Firm A-D used consistently)." That is false: real names appear in the displayed result tables at lines 93-96, 120-123, 132-135, 179-182, 204-207, and 217-220.
+
+   Either remove the parenthetical real names everywhere in §IV or explicitly abandon the pseudonym policy in §III and the close-out checklist. Given prior review history, this should be fixed before partner review.
+
+5. **Some interpretive claims overstate what the spike results prove.**
+
+   The main false one is line 211: it says the non-Firm-A moderate-confidence proportions are "consistent with the §III-K Spearman convergence on the per-CPA hand-leaning ranking." The MC ordering is C (41.44%), B (35.88%), D (29.33%), while Table X's hand-leaning scores rank D above B on all three score summaries and rank D above C on the reverse-anchor score. MC-band occupancy is not a monotone proxy for the per-CPA hand-leaning ranking; D's mass moves heavily into Uncertain instead.
+
+   Line 184 also compares Firm A's signature-level HC rate (81.70%) to its accountant-level C3 rate (82.46%). The numbers are close and the qualitative reading is reasonable, but they are different units. State this as qualitative alignment, not as a like-for-like consistency check.
+
+   Line 43 calls off-Big-4 dHash transitions "consistent with histogram-resolution artefacts." Script 32 verifies varying dHash transitions; it does not by itself prove a bin-width artefact analysis for those accountant-level subsets. "Scope-dependent and not used operationally" is safer.
+
+6. **The moderate-confidence band is honestly disclosed as inherited, but the support language still needs narrowing.**
+
+   §IV line 211 correctly states that Scripts 38-40 do not separately validate the MC band. That is good. But §III line 131 still says the binary-rule internal-consistency checks support continued use of the inherited five-way rule "without recalibration." That is stronger than the evidence: the v4 kappa/Spearman checks cover the binary high-confidence box rule, not the MC band or document-level worst-case aggregation. The defensible wording is: v4 reports Big-4 outputs for the inherited five-way rule; the MC band remains v3-calibrated and not newly validated in Scripts 38-42.
+
+## Minor findings
+
+1. **K=3 LOOO C1 weight drift is rounded away from the report.** §IV line 137 reports max C1 weight deviation as 0.025. Script 37's report says 0.023, and the JSON gives 0.023489. Use 0.023 or 0.0235.
+
+2. **Seed coverage statement stops at Script 41.** §IV line 7 says seeds are fixed across Scripts 32-41, but v2 depends on Script 42 for Tables XV and XV-B. Either include Script 42 if true or say "stochastic v4 spike scripts" rather than implying a complete script range.
+
+3. **Inclusivity of the low-cosine cutoff should match Script 42.** §IV line 17 says cosine `< 0.837` implies Likely-hand-signed; Script 42 defines LH as `cos <= 0.837`. Align §III-L and §IV-C/J exactly.
+
+4. **The "round-22 open question 1, Light scope" process note is not traceable to the round-22 review file.** §IV line 228 may reflect an author decision outside the supplied review, but it should be removed from manuscript prose or backed by an internal note.
+
+5. **The ablation section pointer is wrong.** §IV line 252 says the inherited feature-backbone ablation is from v3.x §IV-H.3, but in `paper/paper_a_results_v3.md` it is §IV-I, beginning at line 461.
+
+6. **Line 73's "component recovery ... across Scripts 35, 37, and 38" can be misread.** Script 37's full-baseline block replicates Script 35, but the LOOO fold components vary by design. Say "the full-fit baseline is reproduced in Scripts 35, 37, and 38" if that is the intended claim.
+
+## Editorial nits
+
+1. Remove the draft note and Phase 3 close-out checklist before submission, or move them to an internal author note.
+
+2. Line 110: "This convergent-checks evidence" should be "These convergence checks" or "This convergence evidence."
+
+3. Line 3: "is finalised" should be "will be finalised" while numbering remains provisional.
+
+4. Standardise "dHash" versus "dh" in tables and prose; the spike reports use `dh`, but the paper body mostly uses dHash.
+
+5. Avoid mixing "replicated," "templated," and "non-hand-signed" as if they are exact synonyms. The paper's caveats rely on preserving those distinctions.
+
+## Provenance verification table
+
+| §IV v2 claim | §IV lines | Source checked | Status |
+|---|---:|---|---|
+| Big-4 primary scope: 437 CPAs and 150,442 signatures with both descriptors. | 9 | Script 36 report lines 6, 32-37; Script 39 report line 12. | Confirmed. |
+| Detection inheritance: 182,328 signatures across 86,072 PDFs. | 13 | v3 results lines 14, 17-25; v3 methodology search hits distinguish 86,072 VLM-positive, 86,071 processed, 85,042 with detections. | Needs correction; denominator conflated. |
+| All-pairs KDE crossover at 0.837. | 17 | v3 results lines 49 and 118; Script 42 rule lines 6-10 uses 0.837. | Confirmed; fix `<` vs `<=` wording. |
+| Big-4 dip-test p-values reported as `< 5 x 10^-4`. | 27, 32 | Script 36 report lines 6-8; Script 34 report lines 28-31; bootstrap resolution stated in §IV line 32. | Confirmed with reporting convention. |
+| Firm A / Big4-non-A / all-non-A dip p-values: 0.992/0.924, 0.998/0.906, 0.998/0.907. | 28-30 | Script 32 report lines 30, 40, 62, 72, 94, 104. | Confirmed after rounding. |
+| BD/McCrary Big-4 null and non-A dHash transitions at 10.8 and 6.6. | 38-41 | Script 34 report lines 28-31; Script 32 report lines 40-41 and 72-73. | Confirmed; artefact interpretation not directly proven. |
+| K=2 components, crossings, bootstrap CIs, and BIC. | 53-63 | Script 34 report lines 23-41; Script 36 report lines 12-28. | Confirmed. |
+| K=3 component centers/weights and BIC lower by 3.48. | 69-73 | Script 35 report lines 6-10; Script 34 report lines 40-49; Script 36 report lines 9-10. | Confirmed. |
+| Spearman correlations 0.9627, 0.8890, 0.8794 and non-Big-4 reference center 0.935/9.77. | 83-87 | Script 38 report lines 16-18 and 24-30. | Confirmed. |
+| Per-firm score summaries in Table X. | 93-98 | Script 38 report lines 43-48. | Confirmed; anonymisation violation. |
+| Cohen kappas 0.662, 0.559, 0.870 and per-signature K=3 centers. | 106-110 | Script 39 report lines 16-28. | Confirmed after rounding. |
+| K=2 LOOO fold rules and all-or-none held-out classifications. | 120-125 | Script 36 report lines 32-44 and JSON stability summary. | Confirmed. |
+| K=3 LOOO C1 fold rates and `P2_PARTIAL`. | 131-137 | Script 37 report lines 16-19, 25-90, 92-99; JSON exact drift values. | Confirmed, except weight drift should be 0.023/0.0235 not 0.025. |
+| Pixel-identity subset n=262, split 145/8/107/2, 0/262 miss rate, Wilson upper 1.45%. | 147-153 | Script 40 report lines 8, 12-18, 22-27. | Confirmed. |
+| Inter-CPA FAR 0.0005 with Wilson [0.0003, 0.0007] inherited from v3. | 157 | v3 results lines 182-190 and 263-275. | Confirmed as inherited, not v4-regenerated. |
+| Five-way per-signature counts and 11 excluded signatures. | 167-173 | Script 42 report lines 14-26. | Confirmed. |
+| Per-firm five-way percentages. | 179-184 | Script 42 report lines 30-44. | Confirmed; line 211 interpretation is not supported. |
+| Document-level overall counts, n=75,233, mixed-firm PDFs n=379. | 188-198 | Script 42 report lines 46-57; JSON `document_level`. | Confirmed. |
+| Single-firm per-document rows. | 204-209 | Script 42 report lines 59-66. | Confirmed. |
+| Full-dataset robustness components, BIC, Spearman rho. | 234-248 | Script 41 report lines 8-31. | Confirmed. |
+| Feature-backbone ablation inherited from v3.x Table XVIII. | 252-254 | v3 results lines 461-475. | Inherited content confirmed, but v3 section pointer and current v4 table numbering collide. |
+
+## Cross-reference checks (§III -> §IV)
+
+| §III v3 claim | §III lines | §IV v2 support | Status |
+|---|---:|---|---|
+| Signature-level capture-rate analyses are in §IV-D/F/G. | 13 | Current §IV-D/F/G are accountant-level dip/mixture, internal consistency, and LOOO. | Fails; stale v3 cross-reference. |
+| All §IV results except §IV-K are Big-4 restricted. | 23 | §IV-A-C, §IV-I, and §IV-L are inherited full-corpus/corpus-wide material. | Fails; narrow to "primary v4 analyses §IV-D-J except inherited §IV-I." |
+| Big-4 scope is 437 CPAs / 150,442 signatures. | 23 | §IV lines 9, 163 and Script 39. | Supported. |
+| Dip-test and BD/McCrary distributional characterisation. | 47-53 | §IV Tables V-VI, lines 23-43. | Supported. |
+| K=2 and K=3 mixture components and mild BIC preference. | 51, 59-73 | §IV Tables VII-VIII, lines 49-73. | Supported. |
+| K=2 unstable and K=3 descriptive only under LOOO. | 71-79, 111-115 | §IV Tables XII-XIII, lines 116-137. | Supported. |
+| Three-score internal consistency and per-firm ranking nuance. | 83-100 | §IV Tables IX-X, lines 79-100. | Supported. |
+| Per-signature K=3 convergence kappas. | 101-109 | §IV Table XI, lines 102-110. | Supported. |
+| Pixel-identity positive-anchor miss rate. | 117-127 | §IV Table XIV, lines 141-153. | Supported. |
+| Five-way signature/document classifier retained as primary; K=3 not used for operational labels. | 131-149 | §IV-J, lines 159-224. | Mostly supported; the MC band remains inherited and current wording should not imply v4 validation. |
+| Moderate-confidence band retains v3.x capture-rate evaluation. | 109, 145, 198 | §IV line 211 cites v3 Tables IX/XI/XII but not XII-B; §III line 109's "§IV-F" is now wrong. | Needs citation cleanup. |
+| Firm anonymisation maintained. | 23 and open question 200 | §IV repeatedly includes real firm names in parentheses. | Fails unless policy changes. |
+
+## Recommended next-step actions
+
+1. Freeze the v4 table scheme before any prose edits: decide whether inherited v3 tables are reprinted as current v4 tables, cited only as v3 tables, or moved to appendix/supplement. Then renumber Tables IV-XVIII and remove Table XV-B if the journal style cannot handle letter suffixes.
+
+2. Fix §III cross-references after the table scheme is frozen, especially §III line 13, §III line 23, and §III lines 109/119/145.
+
+3. Correct §IV line 13's detection denominator and restate the VLM-positive / corrupted-excluded / YOLO-processed / with-detections sequence.
+
+4. Remove all real firm names from §IV or explicitly change the anonymisation policy. Do not leave line 265 claiming anonymisation while tables reveal names.
+
+5. Delete or rewrite line 211's MC-ordering claim. If the MC band remains inherited, present the per-firm MC proportions descriptively only.
+
+6. Narrow the support claim for the five-way rule: Scripts 38-40 validate only the binary high-confidence rule, while Script 42 reports five-way output counts. Either add a Big-4-specific MC/document validation or state plainly that MC/document validation is inherited from v3.x.
+
+7. Fix small numeric/provenance issues: K=3 weight drift 0.023/0.0235, Script 42 seed wording, cutoff inclusivity, v3 ablation section pointer, and the unsupported "round-22 Light scope" process note.
+
+## Phase 4 readiness assessment
+
+Not ready for partner review without Phase 4 revisions.
+
+The spike-script provenance for the new Big-4 result tables is mostly sound, so I do not see a need to rerun the main v4 empirical scripts solely to fix §IV. But the current section would invite reviewer attacks on table identity, stale cross-references, anonymisation, and overinterpretation of the inherited MC band. After those are corrected, §IV should be close to partner-review ready; the only substantive open decision is whether to add a new Big-4-specific validation for the moderate-confidence/document-level rule or keep it explicitly inherited from v3.x.

paper/codex_review_gpt55_v4_round4.md

@@ -0,0 +1,108 @@
+# Paper A Round 24 Review - v4 round 4
+
+Reviewer: gpt-5.5 xhigh  
+Date: 2026-05-12  
+Target: `paper/v4/paper_a_results_v4_section_iv.md` (§IV v3)  
+Paired methodology: `paper/v4/paper_a_methodology_v4_section_iii.md` (§III v4)  
+Rubric: `paper/codex_review_gpt55_v4_round3.md` (6 Major, 6 Minor, 5 Editorial)
+
+## Verdict
+
+Minor Revision.
+
+The round-23 blockers are substantially reduced. The §IV v3 result tables are now mostly provenance-faithful, the inherited-v3 table identity problem is largely resolved, detection counts are corrected, §IV firm rows are pseudonymised, and the moderate-confidence band is now described honestly as inherited rather than newly validated.
+
+I do not recommend Accept yet because several cleanup issues remain visible in the paired §III/§IV package: §III v4 still leaks real firm names despite the pseudonym policy, §III still carries the stale K=3 LOOO weight-drift value of 0.025 where the report and §IV v3 use 0.023, and the internal draft notes/checklists still contain stale round/version/table-numbering language.
+
+## Round-23 Finding Closure Table
+
+| Round-23 finding | Status | v3/v4 evidence |
+|---|---|---|
+| Major 1. Table numbering was incoherent and inherited v3 tables collided with current v4 tables. | PARTIAL | Core collision is fixed: §IV v3 says inherited v3.x tables are cited only as `v3.20.0 Table N` and not renumbered (§IV:3), and detection/all-pairs/ablation are cited as v3.20.0 Tables III/IV/V/XVIII (§IV:13, 19, 256). Residual: the same draft note still says "Tables IV-XVIII" even though the new v4 sequence starts at Table V (§IV:3), and the close-out checklist repeats "Tables IV-XVIII" plus `Table XV-B` (§IV:265). |
+| Major 2. §III v3 contained stale cross-references not supported by §IV v2. | PARTIAL | Main cross-refs are repaired: §III now points signature-level classification to §IV-J and inherited inter-CPA FAR to §IV-I (§III:13), and accurately scopes §IV-D through §IV-J as v4-new Big-4 analyses while excluding §IV-A-C/I/L and full-dataset §IV-K (§III:23). Residual stale/internal references remain: §III says the corresponding FAR evidence comes from "§III-J inherited; Table X" (§III:119), and the open question still proposes adding a moderate-band analysis in current §IV-F even though §IV-F is convergence checks (§III:198; §IV:77-112). |
+| Major 3. Inherited detection-count sentence was numerically wrong / ambiguous. | CLOSED | §IV v3 now distinguishes VLM-positive documents, corrupted exclusions, YOLO-processed documents, detected-document count, and extracted signatures (§IV:13), matching the v3 baseline's Table III sequence (v3:14, 20-22). |
+| Major 4. Draft claimed anonymisation while §IV tables revealed real firm names. | PARTIAL | §IV v3 uses Firm A-D in tables and prose (§IV:91-100, 120-125, 131-137, 179-184, 204-209, 217-222), so the §IV-specific failure is closed. But the paired §III v4 still leaks real names/aliases: "held-out-EY" (§III:71) and "Firms B (KPMG) and D (EY)" (§III:99), contradicting the pseudonym policy in §III:23 and §IV:3. |
+| Major 5. Interpretive claims overstated what the spike results prove. | CLOSED | The off-Big-4 dHash transition language is now scope-dependent rather than an artefact claim (§IV:45). The Firm A HC vs C3 comparison is explicitly qualitative and cross-unit (§IV:186). MC-band ordering is now explicitly descriptive and not treated as Spearman validation (§IV:213). |
+| Major 6. Moderate-confidence band support language needed narrowing. | CLOSED | §III v4 now states that Scripts 38-42 do not separately validate the MC/style/document components and that v4 only supports the binary high-confidence sub-rule (§III:131). §IV v3 repeats this limitation and cites v3.20.0 Tables IX/XI/XII/XII-B as inherited support (§IV:213). |
+| Minor 1. K=3 LOOO C1 weight drift should be 0.023/0.0235, not 0.025. | PARTIAL | §IV v3 is corrected to 0.023 (§IV:139), matching Script 37. §III v4 still says 0.025 in prose and provenance (§III:71, 115, 173). |
+| Minor 2. Seed coverage statement stopped at Script 41 although §IV used Script 42. | CLOSED | §IV v3 now says seeds are fixed across Scripts 32-42 (§IV:7). |
+| Minor 3. Low-cosine cutoff inclusivity should match Script 42 (`cos <= 0.837`). | PARTIAL | §IV v3 is explicit: cosine `<= 0.837` maps to Likely-hand-signed (§IV:19), matching Script 42. §III-L still says "Cosine below" the crossover (§III:143), which is less precise than the inherited rule; make it "at or below 0.837." |
+| Minor 4. "Round-22 open question 1, Light scope" process note was not traceable. | CLOSED | The §IV-K body now describes the full-dataset robustness scope directly, without the round-22 process-note wording (§IV:230). The remaining stale process text is confined to the internal checklist (§IV:260-267). |
+| Minor 5. Ablation section pointer was wrong. | CLOSED | §IV v3 correctly identifies the inherited feature-backbone ablation as v3.20.0 §IV-I and distinguishes v3 Table XVIII from current v4 Table XVIII (§IV:254-256). |
+| Minor 6. "Component recovery across Scripts 35, 37, and 38" could be misread. | CLOSED | §IV v3 now says the full-fit K=3 baseline is reproduced in Scripts 35, 37, and 38, while Script 37 fold components differ by design and are separately reported (§IV:75). |
+| Editorial 1. Remove draft note and Phase 3 close-out checklist before submission. | OPEN | Both files still include internal draft notes and author checklists/open questions (§III:3-9, 187-202; §IV:3, 260-267). §IV's checklist also says the section is being prepared for "codex round 23" even though this is round 24 (§IV:262). |
+| Editorial 2. "This convergent-checks evidence" grammar. | CLOSED | §IV v3 uses "These convergence checks" (§IV:112). |
+| Editorial 3. "is finalised" should be "will be finalised." | CLOSED | §IV v3 uses future/provisional wording (§IV:3, 265). |
+| Editorial 4. Standardise `dHash` versus `dh`. | CLOSED | Manuscript prose/tables consistently use `dHash`; raw spike-script `dh` appears only inside source descriptions or quoted rule names (§III:13, 133-145; §IV:36, 53-63, 167-184). |
+| Editorial 5. Avoid mixing "replicated," "templated," and "non-hand-signed" as exact synonyms. | CLOSED | Current usage mostly preserves distinctions: replicated is used for positive-anchor / C3 contexts (§IV:143-155), non-hand-signed for the operational five-way categories (§IV:167-173), and templated mainly for K=2 fold-rule wording (§IV:120-127). No remaining overclaim depends on treating them as exact synonyms. |
+
+## Newly Introduced Or Remaining Issues
+
+1. **§III v4 still violates the anonymisation policy.** §III says firms are pseudonymously labelled Firm A-D throughout the manuscript (§III:23), but line 71 says "held-out-EY" and line 99 names KPMG and EY. §IV v3 fixed this; §III now needs the same scrub.
+
+2. **§III v4 has a stale K=3 LOOO weight-drift number.** Script 37 reports max C1 weight deviation 0.023, and §IV v3 uses 0.023 (§IV:139). §III still reports 0.025 in two prose locations and the provenance table (§III:71, 115, 173).
+
+3. **Two §III internal references are stale.** The positive-anchor paragraph cites "§III-J inherited; Table X" for inter-CPA FAR (§III:119), but the paired result location is §IV-I and the inherited source is v3.20.0 §IV-F.1/Table X (§IV:157-159). The open question asks whether to add a moderate-band analysis in §IV-F (§III:198), but current §IV-F is the convergence section.
+
+4. **Internal notes are stale enough to confuse a handoff.** §III's draft note says "(2026-05-12, v3)" although the file title is v4 (§III:1, 3). §IV's close-out checklist says "before §IV is sent for codex round 23" even though round 23 has already happened (§IV:262), and item 4 says issues are addressed in "this v2" inside a v3 file (§IV:267).
+
+5. **§III mentions the full-dataset `n = 686` but does not list it in the §III provenance table.** §III:23 states that §IV-K reports a full-dataset cross-check at 686 CPAs; Script 41 directly reports full dataset `N CPAs = 686`. Add that row if the number remains in §III.
+
+6. **The table-numbering note still has a small self-contradiction.** §IV:3 says the new v4 sequence is Table V through Table XVIII, then says "Tables IV-XVIII" remain provisional. Either add a current Table IV, or make all provisional references "Tables V-XVIII" and decide whether `Table XV-B` is acceptable for the target style.
+
+## Cross-Reference Checks (§III v4 <-> §IV v3)
+
+| Claim / linkage | §III v4 line evidence | §IV v3 line evidence | Status |
+|---|---:|---:|---|
+| Big-4 scope and inherited/non-Big-4 exceptions. | §III:23 | §IV:9, 13, 19, 157-159, 230, 254-256 | Supported. |
+| Big-4 sample size: 437 CPAs and 150,442 classified signatures. | §III:23, 157-158 | §IV:9, 15, 165, 175 | Supported. |
+| Dip-test and BD/McCrary accountant-level characterisation. | §III:49-53 | §IV:25-45 | Supported. |
+| K=2/K=3 mixture components and mild BIC preference. | §III:59-69 | §IV:51-75 | Supported. |
+| K=2 unstable; K=3 descriptive, not operational, under LOOO. | §III:71-79, 111-115 | §IV:116-139 | Mostly supported; align §III's 0.025 weight drift to §IV's/report's 0.023. |
+| Three-score internal-consistency correlations and per-firm ranking nuance. | §III:83-99 | §IV:79-102 | Supported, except §III anonymisation leak in line 99. |
+| Per-signature K=3 convergence and binary kappa values. | §III:101-109 | §IV:104-112 | Supported. |
+| Pixel-identity positive-anchor miss rate. | §III:117-127 | §IV:141-155 | Supported, but §III:119 should cite §IV-I/v3 §IV-F.1 for inter-CPA FAR, not "§III-J inherited." |
+| Five-way classifier retained as primary and MC band inherited. | §III:131-149 | §IV:161-213 | Supported; make §III:143 inclusive for `cos <= 0.837`. |
+| K=3 hard label vs K=3 posterior roles. | §III:149 | §IV:215-224 and 81-89 | Supported: hard labels for cluster cross-tab, posterior P(C1) for Spearman. |
+| Full-dataset robustness is light scope only. | §III:23, 31 | §IV:228-252 | Supported, but add provenance for `n = 686` to §III table or remove the number from §III. |
+| Internal author/open-question checklist. | §III:187-202 | §IV:260-267 | Not manuscript-ready; stale references remain. |
+
+## Provenance Re-Verification Of Changed Numerics
+
+| Changed numerical claim | Manuscript line(s) | Source checked | Status |
+|---|---:|---|---|
+| Detection sequence: 86,072 VLM-positive; 12 corrupted; 86,071 YOLO-processed; 85,042 with detections; 182,328 signatures. | §IV:13 | v3 baseline reports 86,071 processed, 85,042 with detections, and 182,328 signatures (v3:14, 20-22). The 86,072/12 sequence is inherited from the v3 narrative already cited in round 23. | Confirmed; round-23 denominator conflation is fixed. |
+| Big-4 signature sample: 150,453 loaded, 150,442 classified, 11 missing descriptors. | §IV:175 | Script 42 reports loaded 150,453, classified 150,442, unclassified 11 (five_way_report:14-16). | Confirmed. |
+| K=2 marginal crossings and bootstrap CIs: cos 0.9755, dHash 3.755, CIs [0.9742, 0.9772] and [3.476, 3.969]. | §IV:62-65; §III:51, 59-60 | Script 36 reports cos point 0.9755 and dHash point 3.7549 with those CIs (calibration_loo_report:14-17). | Confirmed. |
+| K=3 components: C1 0.9457/9.17/0.143; C2 0.9558/6.66/0.536; C3 0.9826/2.41/0.321. | §IV:67-75; §III:61-69 | Scripts 35/37/38 report the same baseline (inspection_report:6-10; k3_loo_report:6-10; convergence_report:8-12). | Confirmed. |
+| K=3 lower than K=2 by 3.48 BIC points. | §IV:75; §III:69 | Script 36 reports K=2 BIC -1108.45 and K=3 BIC -1111.93 (calibration_loo_report:9-10). | Confirmed by arithmetic. |
+| Spearman correlations: 0.9627, 0.8890, 0.8794, with p-values bounded in manuscript. | §IV:81-89; §III:91-99 | Script 38 reports 0.9627 / 3.92e-249, 0.8890 / 1.09e-149, 0.8794 / 2.73e-142 (convergence_report:26-30). | Confirmed. |
+| Per-firm score nuance: Firm C highest on P(C1)=0.3110 and hand_frac=0.7896; Firm D higher on reverse-anchor score -0.7125 vs Firm C -0.7672. | §IV:95-102; §III:99 | Script 38 per-firm summary reports those values (convergence_report:43-48). | Confirmed; §III should anonymise KPMG/EY parentheticals. |
+| K=3 LOOO C1 weight drift is 0.023, not 0.025. | §IV:139; §III:71, 115, 173 | Script 37 reports max C1 weight deviation 0.023 (k3_loo_report:77-79). | §IV confirmed; §III mismatch remains. |
+| Pixel-identical Big-4 subset n=262, split 145/8/107/2, all classifiers 0% miss with Wilson upper 1.45%. | §IV:145-153; §III:117-127 | Script 40 reports total 262, 262/262 correct for all three classifiers, and per-firm split 145/8/107/2 (far_report:8, 12-18, 22-27). | Confirmed. |
+| Five-way per-signature counts: HC 74,593; MC 39,817; HSC 314; UN 35,480; LH 238. | §IV:165-175 | Script 42 reports the same counts and percentages (five_way_report:20-26). | Confirmed. |
+| Per-firm five-way percentages: Firm A 81.70/10.76/0.05/7.42/0.07; Firm B 34.56/35.88/0.29/29.09/0.18; Firm C 23.75/41.44/0.38/34.21/0.22; Firm D 24.51/29.33/0.22/45.65/0.29. | §IV:181-186, 213 | Script 42 reports the same percentages (five_way_report:39-44). | Confirmed; interpretation is now appropriately descriptive. |
+| Document-level counts: n=75,233 PDFs; HC 46,857; MC 19,667; HSC 167; UN 8,524; LH 18; mixed-firm PDFs n=379. | §IV:190-200 | Script 42 reports n=75,233, mixed-firm n=379, and those category counts (five_way_report:46-57). | Confirmed. |
+| Full-dataset robustness: full n=686; component rows; full rho 0.9558; drift 0.0069. | §IV:232-250; §III:23 | Script 41 reports Big-4 n=437, full n=686, component drifts, BICs, rho 0.9558, and drift 0.0069 (fulldataset_report:8-31). | Confirmed; add §III provenance row for n=686. |
+
+## Phase 4 Readiness
+
+Partial.
+
+The empirical tables are close to partner-review ready and I do not see a need to rerun the main v4 scripts for §IV. The remaining issues are mostly manuscript hygiene, pseudonym consistency, and cross-reference/provenance alignment. They are small edits, but they are visible enough that I would not send the paired §III/§IV package to partner review until they are fixed.
+
+## Recommended Next-Step Actions
+
+1. Scrub §III v4 for real firm names/aliases. Replace "held-out-EY" and "Firms B (KPMG) and D (EY)" with Firm A-D language, or explicitly abandon the pseudonym policy everywhere.
+
+2. Align K=3 LOOO weight drift to Script 37 throughout §III: use 0.023 (or 0.0235 if exact precision is preferred), matching §IV:139.
+
+3. Fix the remaining stale cross-references: §III:119 should point to current §IV-I / inherited v3.20.0 §IV-F.1 Table X; §III:198 should not refer to current §IV-F for a possible moderate-band analysis.
+
+4. Make the §III-L low-cosine rule inclusive: Likely hand-signed is `cos <= 0.837`, matching Script 42 and §IV:19.
+
+5. Remove or move internal draft notes, cross-reference indices, open questions, and the §IV Phase 3 close-out checklist before partner review. At minimum, fix stale "v2/v3/round 23" text.
+
+6. Finalise table numbering after deciding whether `Table XV-B` is acceptable. If the current v4 sequence starts at Table V, remove residual "Tables IV-XVIII" wording.
+
+7. Add §III provenance for the full-dataset `n = 686` claim if it remains in §III-G; cite Script 41 / `fulldataset_report.md`.

paper/codex_review_gpt55_v4_round5.md

@@ -0,0 +1,79 @@
+# Paper A Round 25 Review - v4 round 5
+
+Reviewer: gpt-5.5 xhigh  
+Date: 2026-05-12  
+Target: `paper/v4/paper_a_results_v4_section_iv.md` (§IV v3.1 target; file header still says Draft v3)  
+Paired methodology: `paper/v4/paper_a_methodology_v4_section_iii.md` (§III v5)  
+Rubric: `paper/codex_review_gpt55_v4_round4.md` (3 Major-PARTIAL, 2 Minor-PARTIAL, 1 Editorial-OPEN, plus 7 next-step actions)
+
+## Verdict
+
+Minor Revision.
+
+The round-24 empirical and cross-reference residuals have mostly converged. §III v5 now aligns the K=3 LOOO weight drift to 0.023, fixes the §IV-I / v3.20.0 Table X FAR pointer, makes the low-cosine rule inclusive at `cos <= 0.837`, and adds the full-dataset `n = 686` provenance row. §IV v3.1 remains numerically/provenance-faithful.
+
+I do not recommend Accept yet because the partner-facing package still contains internal draft notes/checklists and unresolved table-numbering/version residues. There is also a small anonymisation regression in §III's v5 changelog: the body now uses Firm A-D, but the internal note itself reprints two real firm names (§III:11).
+
+## Round-24 Finding Closure Table
+
+| Round-24 item | v5/v3.1 status | v5/v3.1 line evidence |
+|---|---|---|
+| Major 1. Table numbering was incoherent and inherited v3 tables collided with current v4 tables. | PARTIAL | Core collision remains fixed: §IV says fresh v4 tables are V-XVIII and inherited v3 tables keep `v3.20.0 Table N` (§IV:3); inherited detection/all-pairs/ablation are cited as v3.20.0 Tables III/IV/V/XVIII (§IV:13, 19, 256). Residual remains: the same note still says "Tables IV-XVIII" despite the v4 sequence starting at Table V (§IV:3), and the close-out checklist repeats "Tables IV-XVIII" with `Table XV-B` (§IV:265). |
+| Major 2. §III stale cross-references not supported by §IV. | CLOSED | §III now points signature-level classification to §IV-J and inherited inter-CPA FAR to §IV-I (§III:18), scopes v4-new vs inherited §IV sections accurately (§III:28), cites the FAR evidence as §IV-I / v3.20.0 §IV-F.1 Table X (§III:124), and no longer sends the moderate-band open question to current §IV-F (§III:204). |
+| Major 4. Anonymisation leak in paired §III/§IV package. | PARTIAL | The manuscript body is repaired: §III uses Firm A-D in the score discussion (§III:104), and §IV tables/prose use Firm A-D (§IV:95-98, 181-184, 217-222). However §III's internal v5 changelog reprints real names while saying they were removed (§III:11). This is not a body-table leak, but it keeps the file-level anonymisation cleanup incomplete until draft notes are stripped. |
+| Minor 1. K=3 LOOO C1 weight drift should be 0.023/0.0235, not 0.025. | CLOSED | §III now reports 0.023 in the K=3 LOOO discussion (§III:76, 120) and provenance table (§III:178); §IV reports 0.023 (§IV:139). This matches Script 37 (`k3_loo_report.md`:79). |
+| Minor 3. Low-cosine cutoff inclusivity should match Script 42 (`cos <= 0.837`). | CLOSED | §III-L now defines Likely hand-signed as "Cosine at or below" the crossover with `cos <= 0.837` (§III:148); §IV repeats `cosine <= 0.837 => Likely-hand-signed` and explicitly ties it to Script 42 (§IV:19). |
+| Editorial 1. Remove draft notes and Phase 3 close-out checklist before submission. | OPEN | Internal notes remain in both files: §III has a draft note, cross-reference index, and open questions (§III:3, 193-208); §IV has a draft note and Phase 3 checklist (§IV:3, 260-269). §IV also still identifies itself as Draft v3 / post rounds 21-23 (§IV:1, 3) despite this round targeting v3.1. |
+| Action 1. Scrub §III real firm names/aliases. | PARTIAL | The old body leaks are gone, but §III:11 now quotes two real firm names in the v5 changelog. Replace with "real firm names/aliases" or remove the changelog before partner review. |
+| Action 2. Align K=3 LOOO weight drift to Script 37 throughout §III. | CLOSED | §III:76, §III:120, and §III:178 all use 0.023; §IV:139 matches. |
+| Action 3. Fix stale §III refs: FAR pointer and moderate-band open question. | CLOSED | FAR pointer now cites §IV-I / v3.20.0 §IV-F.1 Table X (§III:124); the moderate-band open question now points to v3.20.0 Tables IX/XI/XII/XII-B and §IV-J, not current §IV-F (§III:204). |
+| Action 4. Make §III-L low-cosine rule inclusive. | CLOSED | §III:148 says `cos <= 0.837`; §IV:19 and Script 42 agree. |
+| Action 5. Remove/move internal notes and fix stale v2/v3/round-23 text. | OPEN | Notes remain (§III:3, 193-208; §IV:3, 260-269). Some stale text is still visible: §IV title and draft note say Draft v3 / post rounds 21-23 (§IV:1, 3), and the checklist says "this v3 of §IV" (§IV:267). |
+| Action 6. Finalise table numbering and remove residual "Tables IV-XVIII" if sequence starts at Table V. | PARTIAL | The current body table sequence is internally usable (V-XVIII with XV-B), but the finalisation note still says Tables IV-XVIII (§IV:3, 265), and §III leaves table numbering open (§III:208). |
+| Action 7. Add §III provenance for full-dataset `n = 686`. | CLOSED | §III now states §IV-K uses `n = 686` (§III:28) and adds a provenance row citing Script 41 / `fulldataset_report.md` (§III:184). §IV reports the same full-dataset count (§IV:230, 247). |
+
+## Newly Introduced Issues
+
+1. **§III v5 changelog reintroduces real firm names.** The body anonymisation fix succeeded, but §III:11 quotes two real names in the internal changelog. If the note is stripped before partner review, this disappears; if the file is circulated as-is, anonymisation is still not clean.
+
+2. **§III empirical-anchor range is stale after the Script 41/42 additions.** §III:14 says empirical anchors reference Scripts 32-40, but the same file now cites Script 41 for full-dataset `n = 686` (§III:184) and references Scripts 38-42 in the classifier-validation caveat (§III:136). §IV's anchor statement already uses Scripts 32-42 (§IV:3). Align §III:14 to Scripts 32-42.
+
+3. **§IV v3.1 is not labelled as v3.1 in the file.** The requested target is §IV v3.1, but the file title and draft note still say v3 / post rounds 21-23 (§IV:1, 3). This is editorial, but it will confuse the Phase 4 handoff.
+
+## Cross-Reference Checks (§III v5 <-> §IV v3.1)
+
+| Linkage | §III v5 evidence | §IV v3.1 evidence | Status |
+|---|---:|---:|---|
+| Big-4 scope and inherited/full-dataset exceptions. | §III:28, 36 | §IV:9, 15, 230, 254-256 | Tight. |
+| K=2/K=3 mixtures are descriptive, not operational. | §III:62, 76-84, 154 | §IV:75, 139, 224 | Tight. |
+| Three-score internal-consistency and per-firm ranking nuance. | §III:88-104 | §IV:79-102 | Tight in body; anonymisation note issue remains outside body (§III:11). |
+| Positive-anchor miss rate and inherited inter-CPA FAR. | §III:122-132, 186 | §IV:143-159 | Tight; the old bad "§III-J inherited; Table X" pointer is gone. |
+| Five-way classifier retained; MC band inherited only. | §III:136-150, 204 | §IV:163, 213 | Tight. |
+| Inclusive LH cutoff at `cos <= 0.837`. | §III:148 | §IV:19 | Tight and matches Script 42. |
+| Full-dataset robustness is light scope only. | §III:28, 184, 204 | §IV:230-252 | Tight. |
+| Internal notes / table-numbering handoff. | §III:193-208 | §IV:260-269 | Not partner-ready; remaining editorial open items are all here. |
+
+## Provenance Spot-Checks Of v5 Changes
+
+| v5 change checked | Manuscript evidence | Spike-report evidence | Status |
+|---|---:|---:|---|
+| K=3 LOOO C1 weight drift is 0.023, not 0.025. | §III:76, 120, 178; §IV:139 | `k3_loo_report.md`:76 lists fold C1 weights; `k3_loo_report.md`:79 reports max C1 weight deviation 0.023. | Confirmed. |
+| Full-dataset `n = 686` provenance row added. | §III:28, 184; §IV:230, 247 | `fulldataset_report.md`:10-13 reports Big-4 437 and full dataset 686; lines 29-31 report full rho 0.9558 and drift 0.0069, matching §IV:246-248. | Confirmed. |
+| Low-cosine Likely-hand-signed rule is inclusive at `cos <= 0.837`. | §III:148; §IV:19 | `five_way_report.md`:6-10 defines HC/MC/HSC/UN/LH and gives `LH : cos <= 0.837`. | Confirmed. |
+| Full-dataset component rows in §IV-K. | §IV:236-240 | `fulldataset_report.md`:19-23 reports the same full component centers, drifts, and BIC values after rounding. | Confirmed. |
+
+## Phase 4 Readiness
+
+Partial.
+
+The empirical content and §III-§IV technical cross-references are ready for Phase 4 technical review. The package is not yet clean enough for partner-facing circulation because the internal notes/checklists remain, §IV still carries v3/round-23 labels, table numbering is still provisional, and §III:11 reprints real firm names inside the changelog.
+
+## Recommended Next-Step Actions
+
+1. Strip or move all internal draft notes, cross-reference indices, open questions, and the §IV Phase 3 checklist before partner review. This also removes the §III:11 anonymisation regression if the changelog is deleted.
+
+2. If any changelog remains, replace the real names in §III:11 with "real firm names/aliases" and update §III:14 from Scripts 32-40 to Scripts 32-42.
+
+3. Finalise §IV table numbering: either make the current v4 sequence explicitly Tables V-XVIII with XV-B accepted, or renumber to remove XV-B; in either case remove residual "Tables IV-XVIII" wording (§IV:3, 265).
+
+4. Update the §IV header/draft note to the actual target version and round status, or remove the draft note entirely (§IV:1, 3, 267).

paper/codex_review_gpt55_v4_round6.md

@@ -0,0 +1,157 @@
+# Paper A Round 26 Review - v4 round 6
+
+Reviewer: gpt-5.5 xhigh  
+Date: 2026-05-12  
+Target: `paper/v4/paper_a_prose_v4_phase4.md` (Phase 4 prose draft v1)  
+Foundation checked: `paper/v4/paper_a_methodology_v4_section_iii.md` (§III v6) and `paper/v4/paper_a_results_v4_section_iv.md` (§IV v3.2)  
+Trajectory checked: rounds 21-25 plus v3.20.0 Abstract / §I / §II / §V / §VI baselines
+
+## Verdict
+
+Major Revision.
+
+The technical core in §III v6 and §IV v3.2 is stable, but the new Phase 4 prose introduces several reviewer-visible regressions. The most important are: (i) the Abstract and Introduction revive the "independent scores" overclaim even though §III/§IV repeatedly say the three scores are not statistically independent; (ii) §I and §V overstate the Big-4 scope evidence by claiming unsupported single-firm and full-dataset dip-test non-rejections; (iii) §II is still a placeholder with `[add citation]`, not a submission-ready related-work section; and (iv) §V-G drops several inherited limitations from v3.20.0.
+
+## Section-By-Section Findings
+
+### Abstract
+
+1. **Major - line 11: "Three independent feature-derived scores" contradicts the converged methodology.** §III-K states that the three scores are "not statistically independent measurements" because all are deterministic functions of the same descriptor means (§III:90), and §IV-F repeats the caveat (§IV:79). The Abstract should say "three feature-derived scores" or "three non-identical feature-derived summaries" and, if space allows, add the shared-feature caveat.
+
+2. **Minor - line 11: "candidate classifiers" can be read as operational-classifier language.** One of the three "candidate classifiers" is the K=3 per-CPA hard label, which §III-J/§III-L explicitly demotes to descriptive characterisation, not operational signature/document classification (§III:64, §III:156). Use "candidate rules/scores" or explicitly reserve "operational classifier" for the inherited five-way box rule.
+
+3. **Minor - line 11: the Abstract passes IEEE Access form but has no margin.** It is one paragraph and `wc -w` counts 247 words, so it satisfies the <=250-word target. Any added caveat will require trimming elsewhere.
+
+4. **Minor - line 11: the Abstract does not name the primary operational output.** The abstract describes the pipeline and the K=3 / convergence / anchor checks, but it does not state that the primary operational output remains the inherited five-way per-signature classifier with worst-case document aggregation (§III-L; §IV-J). This omission makes the K=3 and reverse-anchor checks look more central operationally than §III/§IV allow.
+
+### §I Introduction
+
+1. **Major - line 31: the Big-4 scope claim is overbroad and partly unsupported.** The sentence says "neither any single firm pooled alone nor the broader full-dataset variant rejects unimodality." §III and §IV only report comparison dip tests for Firm A alone, Firms B+C+D pooled, and all non-Firm-A pooled (§III:34, §III:56; §IV:27-34). They explicitly state that single-firm dip tests for Firms B, C, and D were not separately computed (§III:34, §III:56; §IV:34). §IV-K is a light full-dataset K=3 + Spearman robustness check and does not report a full-dataset dip test (§IV:230-252). Rewrite this as "no narrower comparison scope tested in Script 32..." and remove the full-dataset dip-test claim unless a spike report is added.
+
+2. **Major - line 29: the section cross-reference for accountant-level distributional characterisation is wrong.** The prose points to "§III-D" for the Big-4 accountant-level distributional characterisation. In the converged methodology, this material is §III-G through §III-J, especially §III-I and §III-J (§III:18-86). §IV-D/§IV-E are correct.
+
+3. **Major - line 35: the Introduction repeats the "independent feature-derived scores" error.** The next sentence correctly says the scores are not statistically independent, but the opening clause still hands reviewers an avoidable contradiction. This was a central round-21/22 issue and should not reappear in the front matter.
+
+4. **Minor - line 47: contribution 4 again overstates "not at narrower scopes."** The defensible phrase is "not in the narrower comparison scopes tested" because B/C/D single-firm dip tests were not computed.
+
+5. **Minor - line 55: contribution 8 overclaims the full-dataset check.** §IV-K deliberately re-runs only K=3 + Paper A box-rule Spearman convergence at full `n = 686`; it does not re-run LOOO, five-way moderate-band validation, or operational threshold calibration (§IV:230). "Pipeline reproducibility at multiple scopes" should be narrowed to "the K=3 + box-rule rank-convergence check reproduces at the full-CPA scope."
+
+6. **Minor - line 25: the methodological safeguards paragraph uses "external validation" too broadly.** The pixel-identity anchor is a conservative positive-subset check, the inter-CPA FAR is inherited corpus-wide, and LOOO is descriptive composition-sensitivity evidence. The paragraph should avoid implying full external validation of the operational classifier.
+
+### §II Related Work
+
+1. **Major - lines 63-65: §II is not submission-ready prose if inserted as written.** The section says v3.20.0 §II is retained "without substantive change," but the target Phase 4 file is supposed to replace the §II block. As written, it is a meta-summary rather than an actual Related Work section. Either the master manuscript must keep the full v3.20.0 §II text and splice in the LOOO paragraph, or this file must contain the full revised §II.
+
+2. **Major - line 67: unresolved citation placeholder.** "`[add citation]`" is still present. This must be replaced before Phase 5; otherwise a reviewer can attack the only new Related Work content as uncited.
+
+3. **Minor - line 67: "calibration uncertainty band on the operational rule" conflicts with the converged classifier framing.** §III-J says neither K=2 nor K=3 is used as an operational classifier (§III:64), and §III-L reserves operational classification for the inherited five-way box rule (§III:138-156). If the LOOO paragraph is about K=2/K=3 mixture fits, call it a composition-sensitivity or calibration-uncertainty check on the candidate mixture boundary/characterisation, not on "the operational rule."
+
+### §V Discussion
+
+1. **Major - line 81: the prose reifies mechanism labels at the CPA level.** "Some CPAs are templated, some are hand-leaning, some are mixed" is stronger than §III allows. §III-G says a per-CPA mean is a summary statistic, not a claim that all signatures for that CPA share a mechanism (§III:22). Use component-membership wording: "some CPAs' observed signatures place their per-CPA means in the templated, mixed, or hand-leaning regions."
+
+2. **Major - line 81: the within-CPA unimodality explanation is speculative.** The claim that occasional template reuse "produces a unimodal per-signature distribution within the CPA but a multimodal per-CPA distribution across CPAs" is not directly tested in §III/§IV. v3.x tested Firm A and all-CPA signature-level distributions, and v4.0 adds per-signature K=3 consistency (§IV-F), but there is no per-CPA distributional test for individual CPAs.
+
+3. **Major - lines 103-119: limitations are incomplete relative to v3.20.0 and the inherited pipeline.** The v4 limitations keep the Big-4 scope, missing hand-signed ground truth, pixel-identity subset, inherited-rule, A1, K=3 composition, and no-intent caveats. They drop v3 limitations that still apply: ImageNet-pretrained ResNet-50 without signature-domain fine-tuning (v3 §V:90-92), HSV red-stamp removal artifacts (v3 §V:93-95), longitudinal scanning/PDF/compression confounds (v3 §V:97-99), source-exemplar misattribution in max/min pair logic (v3 §V:100-102), and legal/regulatory interpretation limits (v3 §V:108-109). If these are intentionally retired, the draft needs a reason; otherwise they should be restored.
+
+4. **Major - line 107: the scope limitation repeats the unsupported full-dataset dip-test implication.** The sentence says dip-test multimodality is "not available at narrower or broader scopes." §III/§IV do not report full-dataset dip-test results; §IV-K is explicitly a light Spearman robustness check (§IV:230-252). Keep the LOOO broader-scope caveat, but do not claim full-dataset dip-test non-availability without evidence.
+
+5. **Minor - line 79: "v4.0 inherits and confirms" is too strong for the per-signature continuous-spectrum reading.** The exact v3 per-signature diagnostic package is inherited; v4.0's new per-signature evidence is mostly the K=3 consistency check (§IV-F) and five-way output (§IV-J). Safer: "v4.0 inherits this signature-level reading and remains consistent with it."
+
+6. **Minor - line 85: inherited Firm A byte-level details need provenance language.** The 145 Firm A pixel-identical signatures are verified in Script 40, but the "50 distinct partners" and "35 cross-year" details are explicitly inherited from v3 / Script 28 and not regenerated in v4.0 (§III:44, §III:190). The discussion should mark that provenance, especially because the spike reports provided for v4 only verify the 145 count.
+
+7. **Minor - line 87: Firm A does not alone anchor §IV-H.** §IV-H's positive-anchor subset is all Big-4 byte-identical signatures, `n = 262`, split 145 / 8 / 107 / 2 across Firms A-D (§IV:145-153). Firm A is the largest subset and the case-study evidence, but not the whole anchor.
+
+8. **Minor - line 97: "published box rule" is not traceable.** §III/§IV call this the inherited Paper A / v3.x box rule, not a published external rule (§III:96, §III:138; §IV:85-87). Use "inherited box rule" unless there is a publication citation.
+
+9. **Minor - line 97: "produce the same per-CPA ranking" is stronger than the evidence.** The scores are highly correlated, but §III/§IV note a residual non-Firm-A disagreement: reverse-anchor ranks Firm D fractionally above Firm C while P(C1) and box-rule hand-leaning rate rank Firm C highest (§III:106; §IV:102). Say "broadly concordant ranking."
+
+10. **Minor - line 101: "candidate classifiers" again blurs operational status.** K=3 hard labels remain descriptive. This can be fixed together with the Abstract wording.
+
+### §VI Conclusion And Future Work
+
+1. **Major - line 127: "cross-scope pipeline reproducibility" overstates §IV-K.** The full-dataset result verifies only that K=3 P(C1) and Paper A hand-leaning-rate Spearman convergence remains high at `n = 686` with drift `0.0069` (§IV:242-250; full-dataset report:25-31). It does not reproduce the pipeline, the five-way classifier, the moderate-confidence band, LOOO, or operational thresholds at full scope.
+
+2. **Minor - line 129: the future-work audit-quality contrast must stay explicitly descriptive.** "Firm A's 82% templated concentration vs Firm C's 23.5% hand-leaning concentration" comes from K=3 hard-posterior accountant-level assignment (§IV:215-224), whose membership is composition-sensitive (§IV:129-139). The future-work sentence is acceptable if it says these are descriptive component concentrations and that current Paper A provides no audit-quality correlation evidence.
+
+3. **Minor - lines 125-127: the conclusion underplays the actual operational output.** It names the pipeline and methodological checks, but it does not mention the inherited five-way per-signature/document-level classifier that §III-L and §IV-J define as the operational output. This is not a numerical error, but it leaves the operational-vs-descriptive distinction less clear at closure.
+
+## Reviewer-Attack Vulnerabilities Specific To The Prose
+
+1. A reviewer can quote line 11 or line 35 ("independent feature-derived scores") against §III-K/§IV-F's non-independence caveat and argue that the paper exaggerates validation strength.
+
+2. A reviewer can attack the Big-4 scope claim because the prose says "any single firm" and "full-dataset variant" even though B/C/D single-firm dip tests and full-dataset dip tests are not reported.
+
+3. The current §II can be rejected as incomplete because it is a placeholder, not a related-work section, and includes `[add citation]`.
+
+4. "Published box rule" invites a citation challenge. The body only supports "inherited Paper A / v3.x box rule."
+
+5. The discussion sometimes turns descriptive component labels into apparent mechanism claims about CPAs. This conflicts with the §III-G rule that per-CPA means are summaries, not partner-level mechanism assignments.
+
+6. The phrase "candidate classifiers" for K=3 and reverse-anchor checks can be read as walking back the round-21 convergence that K=3 is descriptive and the five-way box rule is operational.
+
+7. The limitations section is vulnerable because it drops inherited limitations that still apply to the pipeline: feature backbone transfer, red-stamp preprocessing, longitudinal document-generation shifts, source-exemplar misattribution, and legal interpretation limits.
+
+8. The full-dataset robustness claim is easy to overread. §IV-K is intentionally "light scope"; calling it pipeline reproducibility or cross-scope operational reproducibility exceeds the evidence.
+
+## Provenance Verification Table
+
+| # | Phase 4 numerical claim | Phase line(s) | Provenance checked | Status |
+|---:|---|---:|---|---|
+| 1 | Abstract is <=250 words | 11 | `sed -n '11p' ... \| wc -w` returned 247 | Confirmed, but close to limit |
+| 2 | 90,282 reports, 182,328 signatures, 758 CPAs | 11, 37, 125 | §IV:7 gives 90,282 PDFs; §IV:13 gives 182,328 extracted signatures; v3 §I:62 gives 758 CPAs | Confirmed with inherited full-corpus CPA source |
+| 3 | Big-4 sub-corpus: 437 CPAs, 150,442 signatures | 11, 37, 125 | §III:30; §IV:9, §IV:15; five-way report:14-15 | Confirmed |
+| 4 | Big-4 dip-test multimodality, `p < 5 x 10^-4` on both axes | 11, 31, 81, 127 | §III:34, §III:56, §III:171-172; §IV:27-34 | Confirmed for Big-4 |
+| 5 | "Neither any single firm pooled alone nor broader full-dataset variant rejects" | 31 | §III:34/56 and §IV:34 say only Firm A alone was tested among single firms; §IV-K has no full-dataset dip test | Not verified / overclaimed |
+| 6 | K=2 crossings `cos*=0.9755`, `dHash*=3.755`, cosine CI half-width 0.0015 | 31 | calibration report:16-17; §III:58, §III:166-170; §IV:60-63 | Confirmed |
+| 7 | K=2 LOOO max cosine-crossing deviation `0.028`, `5.6x` tolerance, Firm A held-out 100% vs non-A 0% | 31, 91 | calibration report:34-44; §III:78, §III:120; §IV:122-127 | Confirmed, with 0.0278 rounded to 0.028 |
+| 8 | K=3 components: C3 `0.983/2.41/0.321`, C2 `0.956/6.66/0.536`, C1 `0.946/9.17/0.143` | 33 | k3 LOOO report:8-10; convergence report:8-12; §III:70-76; §IV:69-75 | Confirmed after rounding |
+| 9 | K=3 C1 LOOO shape drift: cos <=0.005, dHash <=0.96, weight <=0.023 | 11, 33, 93, 127 | k3 LOOO report:77-79; §III:78, §III:122; §IV:139 | Confirmed |
+| 10 | K=3 held-out hard-posterior differences `1.8-12.8 pp` | 33, 93, 117 | k3 LOOO report:83-90; §III:122; §IV:134-139 | Confirmed after rounding |
+| 11 | Three-score Spearman convergence `rho >= 0.879` | 11, 35, 51, 97, 127 | convergence report:28-30; §III:100-104; §IV:83-87 | Confirmed numerically; wording must not say independent |
+| 12 | Per-signature K=3 consistency `Cohen kappa = 0.87` | 97 | §III:108-116; §IV:104-112 | Confirmed |
+| 13 | Pixel-identity subset `n = 262`, all three checks 0% miss, Wilson upper 1.45% | 11, 35, 53, 101, 127 | pixel-identity report:8, 14-16; §III:124-132; §IV:145-153 | Confirmed |
+| 14 | Firm A pixel-identical `145`, plus `50 partners` and `35 cross-year` | 85 | pixel-identity report:24 confirms 145; §III:44 and §III:190 mark 50/35 as inherited from v3 / Script 28, not regenerated in v4 spikes | Partially confirmed; provenance caveat needed |
+| 15 | Inter-CPA FAR `0.0005`, Wilson `[0.0003, 0.0007]` | 53, 101 | §III:188; §IV:157-159; inherited v3.20.0 §IV-F.1 Table X | Confirmed as inherited |
+| 16 | Full-dataset robustness `n = 686`, full rho `0.9558`, drift `0.007` | 11, 55, 107, 127 | full-dataset report:10-13, 25-31; §III:186; §IV:242-250 | Confirmed numerically, but interpretive scope is light |
+| 17 | Firm A `82%/82.5%` templated and Firm C `23.5%` hand-leaning | 85, 129 | convergence report:43-48; §IV:217-224 | Confirmed as descriptive K=3 hard assignment |
+
+## Cross-Reference Checks (Phase 4 <-> §III v6 / §IV v3.2)
+
+| Linkage | Phase 4 evidence | §III / §IV evidence | Status |
+|---|---:|---:|---|
+| Big-4 primary scope and sample size | Lines 11, 31, 37, 107, 125 | §III:30; §IV:9, §IV:15 | Numerically tight, but scope-test wording overbroad |
+| Accountant-level distributional characterisation refs | Line 29 | §III-I/J are the relevant methodology sections (§III:52-86); §IV-D/E correct (§IV:21-75) | Fail: `§III-D` is stale/wrong |
+| K=2 as firm-mass separator, not operational | Lines 31, 91 | §III:78-86, §III:120; §IV:118-127 | Tight |
+| K=3 descriptive only | Lines 33, 49, 93 | §III:64, §III:80-86, §III:156; §IV:75, §IV:139, §IV:224 | Tight, except "candidate classifier" wording |
+| Three-score internal consistency | Lines 11, 35, 51, 97, 127 | §III:90-106; §IV:79-102 | Numerically tight; independence wording fails |
+| Reverse-anchor reference as non-Big-4 | Lines 35, 97 | §III:48-50; §IV:89 | Tight |
+| Pixel-identity positive anchor | Lines 35, 101 | §III:124-134; §IV:141-155 | Tight; Firm A-only anchoring phrase should be narrowed |
+| Inter-CPA negative-anchor FAR | Lines 53, 101 | §III:126, §III:188; §IV:157-159 | Tight as inherited |
+| Five-way classifier primary / MC band inherited | Lines 33, 113 | §III:136-156; §IV:161-224 | Mostly tight; Abstract/Conclusion should name operational output more clearly |
+| Full-dataset robustness | Lines 55, 107, 127 | §IV:228-252 | Numerically tight; "pipeline reproducibility" overclaims light scope |
+| Internal notes and close-out artifacts | Lines 3, 133-142 | Round-25 review kept this open; §III and §IV also retain internal notes | Not partner/Phase-5 ready |
+
+## Phase 5 Readiness
+
+Partial.
+
+The §III/§IV technical foundation would likely survive cross-AI peer review, but the current Phase 4 prose would draw a Major Revision because it reintroduces known overclaims and has an incomplete §II. With the targeted prose repairs below, Phase 5 readiness should move to Yes.
+
+## Recommended Next-Step Actions
+
+1. Replace every "independent feature-derived scores" phrase with "three feature-derived scores" or "three feature-derived summaries," and preserve the shared-feature caveat in Abstract/§I/§V/§VI.
+
+2. Rewrite the Big-4 scope language at lines 31, 47, 81, 107, and 127 to match §III exactly: Big-4 is the smallest scope among the comparison scopes tested; B/C/D single-firm dip tests were not computed; no full-dataset dip-test result is reported.
+
+3. Fix stale cross-references in line 29: use §III-G/I/J/K as appropriate instead of §III-D.
+
+4. Turn §II into a real revised Related Work section: retain the v3.20.0 subsections in the master, splice in the LOOO paragraph, and replace `[add citation]` with a specific cross-validation citation.
+
+5. Rebuild §V-G limitations by merging the v4-specific limitations with still-valid v3 limitations: transferred ResNet-50 features, HSV stamp-removal artifacts, longitudinal scan/PDF confounds, source-exemplar misattribution, and legal/regulatory interpretation.
+
+6. Replace "published box rule" with "inherited Paper A box rule" unless an external publication citation is added.
+
+7. Narrow full-dataset language: say "K=3 + box-rule rank-convergence reproduces at full `n = 686`" rather than "pipeline reproducibility at multiple scopes."
+
+8. Before Phase 5, strip the Phase 4 draft note and close-out checklist (lines 3 and 133-142), and continue the same cleanup for §III/§IV internal notes flagged in round 25.

paper/codex_review_gpt55_v4_round7.md

@@ -0,0 +1,102 @@
+# Paper A Round 27 Review - v4 round 7
+
+Reviewer: gpt-5.5  
+Date: 2026-05-12  
+Target: `paper/v4/paper_a_prose_v4_phase4.md` (Phase 4 prose v2 + abstract trim)  
+Foundation checked: `paper/v4/paper_a_methodology_v4_section_iii.md` (§III v6) and `paper/v4/paper_a_results_v4_section_iv.md` (§IV v3.2)  
+Prior rubric checked: `paper/codex_review_gpt55_v4_round6.md`
+
+## Verdict
+
+Minor Revision.
+
+Phase 4 prose v2 closes the substantive round-26 overclaim cycle. The major technical-prose risks around independent-score language, Big-4 scope, K=3 operational status, full-dataset overread, and restored limitations are now aligned with §III v6 / §IV v3.2.
+
+The remaining issues are packaging / copy-edit blockers, not empirical blockers: §II still marks [42]-[44] as placeholders and the reference list has not been extended past [41]; internal draft notes and the Phase 4 close-out checklist remain; and §V-F still uses "candidate classifiers" for K=3/reverse-anchor checks.
+
+## Round-26 finding closure table
+
+### Major findings
+
+| # | Round-26 finding | v2 status | Round-27 note |
+|---:|---|---|---|
+| M1 | Abstract said "Three independent feature-derived scores" | CLOSED | Abstract now says "Three feature-derived scores" and adds "not statistically independent" (line 11). |
+| M2 | §I overclaimed Big-4 scope by implying any single firm and full-dataset dip-test non-rejection | CLOSED | §I now says "narrower comparison scopes tested" and names only Script 32 scopes (line 31). |
+| M3 | §I stale cross-reference to §III-D | CLOSED | Replaced with §III-G through §III-J plus §IV-D/E (line 29). |
+| M4 | §I repeated independent-score error | CLOSED | §I now states the three scores are not statistically independent and frames convergence as internal consistency (line 35). |
+| M5 | §II not submission-ready if inserted as written | PARTIAL | The v4 addition is real prose, but the file still contains a meta note and depends on master-file splicing of `paper/paper_a_related_work_v3.md` (lines 63-65). |
+| M6 | §II unresolved citation placeholder | OPEN | Body cites Stone/Geisser/Vehtari as [42]-[44], but line 65 says these are placeholders; `paper/paper_a_references_v3.md` stops at [41]. |
+| M7 | §V reified CPA mechanism labels | CLOSED | Wording now says per-CPA means are located in descriptor-plane regions, not that all signatures share a mechanism (line 79). |
+| M8 | §V speculative within-CPA unimodality explanation | CLOSED | The causal claim was removed; v2 only states joint consistency and repeats the summary-statistic caveat (line 79). |
+| M9 | §V limitations incomplete vs v3.20.0 | CLOSED | Restored inherited limitations: ImageNet transfer, HSV artifacts, longitudinal confounds, source-exemplar misattribution, legal/regulatory interpretation (lines 119-127). |
+| M10 | §V scope limitation implied full-dataset dip-test evidence | CLOSED | v2 explicitly says full `n = 686` dip-test marginals and LOOO were not tested (line 105). |
+| M11 | §VI overclaimed "cross-scope pipeline reproducibility" | CLOSED | Conclusion now limits the claim to K=3 + box-rule rank-convergence at full `n = 686` and excludes thresholds/LOOO/five-way/pixel checks (line 135). |
+
+### Minor findings
+
+| # | Round-26 finding | v2 status | Round-27 note |
+|---:|---|---|---|
+| m1 | Abstract "candidate classifiers" blurred operational status | CLOSED | Abstract no longer uses "candidate classifiers"; it names the five-way operational output first (line 11). |
+| m2 | Abstract had no word-count margin | CLOSED | `wc -w` on line 11 returns 243 words, leaving 7 words of margin. |
+| m3 | Abstract omitted primary operational output | CLOSED | Abstract now states the inherited five-way per-signature classifier with worst-case document aggregation (line 11). |
+| m4 | Contribution 4 overclaimed "not at narrower scopes" | CLOSED | Now "narrower comparison scopes tested" (line 47). |
+| m5 | Contribution 8 overclaimed full-dataset check | CLOSED | Now says only K=3 + box-rule rank-convergence reproduces and explicitly excludes other components (line 55). |
+| m6 | Safeguards paragraph used "external validation" too broadly | CLOSED | The paragraph now uses "annotation-free validation against naturally-occurring anchor populations" and does not imply full external validation (line 25). |
+| m7 | §II "calibration uncertainty band on operational rule" conflicted with classifier framing | CLOSED | Rewritten as "composition-sensitivity band on the candidate mixture boundary" and not a sufficiency claim for the five-way classifier (line 65). |
+| m8 | §V "inherits and confirms" too strong for signature-level spectrum | CLOSED | Now "inherits this signature-level reading and remains consistent with it," with no-new-diagnostic caveat (line 77). |
+| m9 | Firm A byte-level details needed provenance language | CLOSED | v2 marks 50 partners / 35 cross-year as inherited from v3.20.0 Script 28 and not regenerated in v4 spikes (line 83). |
+| m10 | Firm A alone did not anchor §IV-H | CLOSED | v2 says the Big-4 byte-identical anchor pools all four firms (line 85). |
+| m11 | "Published box rule" not traceable | CLOSED | Replaced with "inherited Paper A box rule" throughout. |
+| m12 | "Same per-CPA ranking" too strong | CLOSED | v2 now says "broadly concordant" and reports the Firm D/Firm C residual disagreement (line 95). |
+| m13 | §V repeated "candidate classifiers" wording | PARTIAL | Line 99 still says "all three candidate classifiers" for the inherited box rule, K=3 hard label, and reverse-anchor metric. Use "candidate checks" or "candidate scores/rules." |
+| m14 | Future-work audit-quality contrast needed descriptive caveat | CLOSED | Future work now says the Firm A/Firm C contrast is descriptive, not mechanism-level, and not linked to audit-quality outcomes (line 137). |
+| m15 | Conclusion underplayed operational output | CLOSED | Conclusion now names the inherited five-way per-signature classifier and worst-case document aggregation (line 133). |
+
+### Round-26 next-step actions
+
+| # | Action | v2 status | Note |
+|---:|---|---|---|
+| A1 | Replace independent-score language and preserve shared-feature caveat | CLOSED | Done in Abstract, §I, §V, §VI. |
+| A2 | Rewrite Big-4 scope language | CLOSED | Done; no unsupported B/C/D single-firm or full-dataset dip-test claim remains in body prose. |
+| A3 | Fix stale §III-D cross-reference | CLOSED | Done at line 29. |
+| A4 | Turn §II into real revised Related Work and replace `[add citation]` | PARTIAL | The LOOO paragraph is drafted, but references [42]-[44] remain placeholders and absent from the reference list. |
+| A5 | Rebuild §V-G limitations with still-valid v3 limitations | CLOSED | Done at lines 119-127. |
+| A6 | Replace "published box rule" | CLOSED | Done. |
+| A7 | Narrow full-dataset language | CLOSED | Done at lines 55, 105, and 135. |
+| A8 | Strip internal notes/checklists before Phase 5 | OPEN | Draft note and close-out checklist remain (lines 3, 141-150); §III/§IV also retain internal notes/checklists. |
+
+## Newly introduced issues
+
+1. **Minor - §II citation-number gap and placeholder contradiction.** The v2 draft note says §II now has "a real citation," but line 65 says [42]-[44] are placeholders, line 147 still says `[add citation]`, and `paper/paper_a_references_v3.md` stops at [41]. This is the only remaining reviewer-visible blocker if the prose is packaged as manuscript text.
+
+2. **Minor - stale close-out metadata.** The close-out checklist says the abstract is "approximately 235 words" (line 145), but `wc -w` returns 243 words on the abstract paragraph. The author's "244 words" note and the shell count differ by one tokenization unit; both satisfy IEEE Access, but the checklist should be updated or removed.
+
+No newly introduced empirical inconsistency was found.
+
+## Abstract word count verification + key v2 spot checks
+
+Abstract count: `sed -n '11p' paper/v4/paper_a_prose_v4_phase4.md | wc -w` returns **243**. The abstract is one paragraph and under the 250-word IEEE Access target.
+
+Spot-check 1: **Independent-score correction closed.** Lines 11, 35, 95, and 135 now say the scores are feature-derived / shared-input / not statistically independent. This matches §III-K's caveat and §IV-F's framing that the correlations are internal consistency, not external validation.
+
+Spot-check 2: **Big-4 scope and full-dataset correction closed.** Lines 31, 47, 79, 105, and 135 now match §III-G/I and §IV-D/K: Big-4 is the smallest scope among tested comparison scopes; B/C/D single-firm dip tests and full-dataset dip tests were not run; full-dataset evidence is only the light K=3 + box-rule Spearman re-run at `n = 686`.
+
+Spot-check 3: **Operational-vs-descriptive framing closed except line 99 wording.** Lines 11, 33, 55, 111, 133, and 135 reserve operational status for the inherited five-way classifier and keep K=3 descriptive. The only remaining wording leak is line 99's "candidate classifiers."
+
+## Phase 5 readiness
+
+Partial.
+
+Substantively, §III + §IV + Phase 4 prose are converged. Phase 5 should not require new statistical work. It does require one copy-edit/reference pass before packaging: finalize §II citations and references, strip internal notes/checklists, and replace the residual "candidate classifiers" phrase.
+
+## Recommended next-step actions
+
+1. Replace line 99's "all three candidate classifiers" with "all three candidate checks" or "all three candidate scores/rules"; keep K=3 explicitly descriptive.
+
+2. Finalize §II packaging: either splice the full v3.20.0 Related Work body plus the v4 LOOO paragraph into the master, or make this Phase 4 file contain the full §II block. Add real [42]-[44] reference entries and remove the "placeholders" sentence.
+
+3. Strip the Phase 4 draft note and close-out checklist before manuscript assembly; do the same for §III/§IV internal notes and working checklists.
+
+4. Update or remove the stale abstract-count note. The verified shell count is 243 words.
+
+5. After the reference/cross-reference cleanup, run one final manuscript-level lint for unresolved placeholders, duplicate reference numbers, internal notes, and stale section/table references.

paper/export_paper_to_docx.py

@@ -0,0 +1,575 @@
+#!/usr/bin/env python3
+"""
+Export Paper A draft to a single Word document (.docx)
+with IEEE-style formatting, embedded figures, and tables.
+"""
+
+from docx import Document
+from docx.shared import Inches, Pt, RGBColor
+from docx.enum.text import WD_ALIGN_PARAGRAPH
+from docx.enum.table import WD_TABLE_ALIGNMENT
+from pathlib import Path
+import re
+
+# Paths
+PAPER_DIR = Path("/Volumes/NV2/pdf_recognize")
+FIGURE_DIR = Path("/Volumes/NV2/PDF-Processing/signature-analysis/paper_figures")
+OUTPUT_PATH = PAPER_DIR / "Paper_A_IEEE_TAI_Draft.docx"
+
+
+def add_heading(doc, text, level=1):
+    h = doc.add_heading(text, level=level)
+    for run in h.runs:
+        run.font.color.rgb = RGBColor(0, 0, 0)
+    return h
+
+
+def add_para(doc, text, bold=False, italic=False, font_size=10, alignment=None, space_after=6):
+    p = doc.add_paragraph()
+    if alignment:
+        p.alignment = alignment
+    p.paragraph_format.space_after = Pt(space_after)
+    p.paragraph_format.space_before = Pt(0)
+    run = p.add_run(text)
+    run.font.size = Pt(font_size)
+    run.font.name = 'Times New Roman'
+    run.bold = bold
+    run.italic = italic
+    return p
+
+
+def add_table(doc, headers, rows, caption=None):
+    if caption:
+        add_para(doc, caption, bold=True, font_size=9, alignment=WD_ALIGN_PARAGRAPH.CENTER, space_after=4)
+
+    table = doc.add_table(rows=1 + len(rows), cols=len(headers))
+    table.style = 'Table Grid'
+    table.alignment = WD_TABLE_ALIGNMENT.CENTER
+
+    # Header
+    for i, h in enumerate(headers):
+        cell = table.rows[0].cells[i]
+        cell.text = h
+        for p in cell.paragraphs:
+            p.alignment = WD_ALIGN_PARAGRAPH.CENTER
+            for run in p.runs:
+                run.bold = True
+                run.font.size = Pt(8)
+                run.font.name = 'Times New Roman'
+
+    # Data
+    for r_idx, row in enumerate(rows):
+        for c_idx, val in enumerate(row):
+            cell = table.rows[r_idx + 1].cells[c_idx]
+            cell.text = str(val)
+            for p in cell.paragraphs:
+                p.alignment = WD_ALIGN_PARAGRAPH.CENTER
+                for run in p.runs:
+                    run.font.size = Pt(8)
+                    run.font.name = 'Times New Roman'
+
+    doc.add_paragraph()  # spacing
+    return table
+
+
+def add_figure(doc, image_path, caption, width=5.0):
+    if Path(image_path).exists():
+        p = doc.add_paragraph()
+        p.alignment = WD_ALIGN_PARAGRAPH.CENTER
+        run = p.add_run()
+        run.add_picture(str(image_path), width=Inches(width))
+
+        cap = doc.add_paragraph()
+        cap.alignment = WD_ALIGN_PARAGRAPH.CENTER
+        cap.paragraph_format.space_after = Pt(8)
+        run = cap.add_run(caption)
+        run.font.size = Pt(9)
+        run.font.name = 'Times New Roman'
+        run.italic = True
+
+
+def build_document():
+    doc = Document()
+
+    # Set default font
+    style = doc.styles['Normal']
+    font = style.font
+    font.name = 'Times New Roman'
+    font.size = Pt(10)
+
+    # ==================== TITLE ====================
+    add_para(doc, "Automated Detection of Digitally Replicated Signatures\nin Large-Scale Financial Audit Reports",
+             bold=True, font_size=16, alignment=WD_ALIGN_PARAGRAPH.CENTER, space_after=12)
+
+    add_para(doc, "[Authors removed for double-blind review]",
+             italic=True, font_size=10, alignment=WD_ALIGN_PARAGRAPH.CENTER, space_after=4)
+    add_para(doc, "[Affiliations removed for double-blind review]",
+             italic=True, font_size=10, alignment=WD_ALIGN_PARAGRAPH.CENTER, space_after=12)
+
+    # ==================== ABSTRACT ====================
+    add_heading(doc, "Abstract", level=1)
+    abstract_text = (
+        "Regulations in many jurisdictions require Certified Public Accountants (CPAs) to personally sign each audit report they certify. "
+        "However, the digitization of financial reporting makes it trivial to reuse a scanned signature image across multiple reports, "
+        "bypassing this requirement. Unlike signature forgery, where an impostor imitates another person's handwriting, signature replication "
+        "involves a legitimate signer reusing a digital copy of their own genuine signature\u2014a practice that is virtually undetectable through "
+        "manual inspection at scale. We present an end-to-end AI pipeline that automatically detects signature replication in financial audit reports. "
+        "The pipeline employs a Vision-Language Model for signature page identification, YOLOv11 for signature region detection, and ResNet-50 for "
+        "deep feature extraction, followed by a dual-method verification combining cosine similarity with perceptual hashing (pHash). This dual-method "
+        "design distinguishes consistent handwriting style (high feature similarity but divergent perceptual hashes) from digital replication "
+        "(convergent evidence across both methods), resolving an ambiguity that single-metric approaches cannot address. We apply this pipeline to "
+        "90,282 audit reports filed by publicly listed companies in Taiwan over a decade (2013\u20132023), analyzing 182,328 signatures from 758 CPAs. "
+        "Using a known-replication accounting firm as a calibration reference, we establish distribution-free detection thresholds validated against "
+        "empirical ground truth. Our analysis reveals that cosine similarity alone overestimates replication rates by approximately 25-fold, "
+        "underscoring the necessity of multi-method verification. To our knowledge, this is the largest-scale forensic analysis of signature "
+        "authenticity in financial documents."
+    )
+    add_para(doc, abstract_text, font_size=9, space_after=8)
+
+    # ==================== IMPACT STATEMENT ====================
+    add_heading(doc, "Impact Statement", level=1)
+    impact_text = (
+        "Auditor signatures on financial reports are a key safeguard of corporate accountability. When Certified Public Accountants digitally "
+        "copy and paste a single signature image across multiple reports instead of signing each one individually, this safeguard is undermined\u2014"
+        "yet detecting such practices through manual inspection is infeasible at the scale of modern financial markets. We developed an artificial "
+        "intelligence system that automatically extracts and analyzes signatures from over 90,000 audit reports spanning ten years of filings by "
+        "publicly listed companies. By combining deep learning-based visual feature analysis with perceptual hashing, the system distinguishes "
+        "genuinely handwritten signatures from digitally replicated ones. Our analysis reveals that signature replication practices vary substantially "
+        "across accounting firms, with measurable differences between firms known to use digital replication and those that do not. This technology "
+        "can be directly deployed by financial regulators to automate signature authenticity monitoring at national scale."
+    )
+    add_para(doc, impact_text, font_size=9, space_after=8)
+
+    # ==================== I. INTRODUCTION ====================
+    add_heading(doc, "I. Introduction", level=1)
+
+    intro_paras = [
+        "Financial audit reports serve as a critical mechanism for ensuring corporate accountability and investor protection. "
+        "In Taiwan, the Certified Public Accountant Act (\u6703\u8a08\u5e2b\u6cd5 \u00a74) and the Financial Supervisory Commission\u2019s attestation regulations "
+        "(\u67e5\u6838\u7c3d\u8b49\u6838\u6e96\u6e96\u5247 \u00a76) require that certifying CPAs affix their signature or seal (\u7c3d\u540d\u6216\u84cb\u7ae0) to each audit report [1]. "
+        "While the law permits either a handwritten signature or a seal, the CPA\u2019s attestation on each report is intended to represent a deliberate, "
+        "individual act of professional endorsement for that specific audit engagement [2].",
+
+        "The digitization of financial reporting, however, has introduced a practice that challenges this intent. "
+        "As audit reports are now routinely generated, transmitted, and archived as PDF documents, it is technically trivial for a CPA to digitally "
+        "replicate a single scanned signature image and paste it across multiple reports. Although this practice may not violate the literal statutory "
+        "requirement of \u201csignature or seal,\u201d it raises substantive concerns about audit quality: if a CPA\u2019s signature is applied identically across "
+        "hundreds of reports without any variation, does it still represent meaningful attestation of individual professional judgment? "
+        "Unlike traditional signature forgery, where a third party attempts to imitate another person\u2019s handwriting, signature replication involves "
+        "the legitimate signer reusing a digital copy of their own genuine signature. This practice, while potentially widespread, is virtually "
+        "undetectable through manual inspection at scale: regulatory agencies overseeing thousands of publicly listed companies cannot feasibly "
+        "examine each signature for evidence of digital duplication.",
+
+        "The distinction between signature replication and signature forgery is both conceptually and technically important. "
+        "The extensive body of research on offline signature verification [3]\u2013[8] has focused almost exclusively on forgery detection\u2014determining "
+        "whether a questioned signature was produced by its purported author or by an impostor. This framing presupposes that the central threat "
+        "is identity fraud. In our context, identity is not in question; the CPA is indeed the legitimate signer. The question is whether the "
+        "physical act of signing occurred for each individual report, or whether a single signing event was digitally propagated across many reports. "
+        "This replication detection problem is, in one sense, simpler than forgery detection\u2014we need not model the variability of skilled forgers\u2014"
+        "but it requires a different analytical framework, one focused on detecting abnormally high similarity across documents rather than "
+        "distinguishing genuine from forged specimens.",
+
+        "Despite the significance of this problem for audit quality and regulatory oversight, no prior work has addressed signature replication "
+        "detection in financial documents at scale. Woodruff et al. [9] developed an automated pipeline for signature analysis in corporate filings "
+        "for anti-money laundering investigations, but their work focused on author clustering (grouping signatures by signer identity) rather than "
+        "detecting reuse of digital copies. Copy-move forgery detection methods [10], [11] address duplicated regions within or across images, but "
+        "are designed for natural images and do not account for the specific characteristics of scanned document signatures, where legitimate visual "
+        "similarity between a signer\u2019s authentic signatures is expected and must be distinguished from digital duplication. Research on near-duplicate "
+        "image detection using perceptual hashing combined with deep learning [12], [13] provides relevant methodological foundations, but has not "
+        "been applied to document forensics or signature analysis.",
+
+        "In this paper, we present a fully automated, end-to-end pipeline for detecting digitally replicated CPA signatures in audit reports at scale. "
+        "Our approach processes raw PDF documents through six sequential stages: (1) signature page identification using a Vision-Language Model (VLM), "
+        "(2) signature region detection using a trained YOLOv11 object detector, (3) deep feature extraction via a pre-trained ResNet-50 convolutional "
+        "neural network, (4) dual-method similarity verification combining cosine similarity of deep features with perceptual hash (pHash) distance, "
+        "(5) distribution-free threshold calibration using a known-replication reference group, and (6) statistical classification with cross-method validation.",
+
+        "The dual-method verification is central to our contribution. Cosine similarity of deep feature embeddings captures high-level visual style "
+        "similarity\u2014it can identify signatures that share similar stroke patterns and spatial layouts\u2014but cannot distinguish between a CPA who signs "
+        "consistently and one who reuses a digital copy. Perceptual hashing, by contrast, captures structural-level similarity that is sensitive to "
+        "pixel-level correspondence. By requiring convergent evidence from both methods, we can differentiate style consistency (high cosine similarity "
+        "but divergent pHash) from digital replication (high cosine similarity with convergent pHash), resolving an ambiguity that neither method can "
+        "address alone.",
+
+        "A distinctive feature of our approach is the use of a known-replication calibration group for threshold validation. Through domain expertise, "
+        "we identified a major accounting firm (hereafter \u201cFirm A\u201d) whose signatures are known to be digitally replicated across all audit reports. "
+        "This provides an empirical anchor for calibrating detection thresholds: any threshold that fails to classify Firm A\u2019s signatures as replicated "
+        "is demonstrably too conservative, while the distributional characteristics of Firm A\u2019s signatures establish an upper bound on the similarity "
+        "values achievable through replication in real-world scanned documents. This calibration strategy\u2014using a known-positive subpopulation to "
+        "validate detection thresholds\u2014addresses a persistent challenge in document forensics, where ground truth labels are scarce.",
+
+        "We apply this pipeline to 90,282 audit reports filed by publicly listed companies in Taiwan between 2013 and 2023, extracting and analyzing "
+        "182,328 individual CPA signatures from 758 unique accountants. To our knowledge, this represents the largest-scale forensic analysis of "
+        "signature authenticity in financial documents reported in the literature.",
+    ]
+
+    for para in intro_paras:
+        add_para(doc, para)
+
+    # Contributions
+    add_para(doc, "The contributions of this paper are summarized as follows:", space_after=4)
+    contributions = [
+        "Problem formulation: We formally define the signature replication detection problem as distinct from signature forgery detection, "
+        "and argue that it requires a different analytical framework focused on intra-signer similarity distributions rather than "
+        "genuine-versus-forged classification.",
+        "End-to-end pipeline: We present a fully automated pipeline that processes raw PDF audit reports through VLM-based page identification, "
+        "YOLO-based signature detection, deep feature extraction, and dual-method similarity verification, requiring no manual intervention "
+        "after initial model training.",
+        "Dual-method verification: We demonstrate that combining deep feature cosine similarity with perceptual hashing resolves the fundamental "
+        "ambiguity between style consistency and digital replication, supported by an ablation study comparing three feature extraction backbones.",
+        "Calibration methodology: We introduce a threshold calibration approach using a known-replication reference group, providing empirical "
+        "validation in a domain where labeled ground truth is scarce.",
+        "Large-scale empirical analysis: We report findings from the analysis of over 90,000 audit reports spanning a decade, providing the "
+        "first large-scale empirical evidence on signature replication practices in financial reporting.",
+    ]
+    for i, c in enumerate(contributions, 1):
+        p = doc.add_paragraph(style='List Number')
+        run = p.add_run(c)
+        run.font.size = Pt(10)
+        run.font.name = 'Times New Roman'
+
+    add_para(doc, "The remainder of this paper is organized as follows. Section II reviews related work on signature verification, "
+             "document forensics, and perceptual hashing. Section III describes the proposed methodology. Section IV presents experimental "
+             "results including the ablation study and calibration group analysis. Section V discusses the implications and limitations of "
+             "our findings. Section VI concludes with directions for future work.")
+
+    # ==================== II. RELATED WORK ====================
+    add_heading(doc, "II. Related Work", level=1)
+
+    add_heading(doc, "A. Offline Signature Verification", level=2)
+    add_para(doc, "Offline signature verification\u2014determining whether a static signature image is genuine or forged\u2014has been studied "
+             "extensively using deep learning. Bromley et al. [3] introduced the Siamese neural network architecture for signature verification, "
+             "establishing the pairwise comparison paradigm that remains dominant. Dey et al. [4] proposed SigNet, a convolutional Siamese network "
+             "for writer-independent offline verification, demonstrating that deep features learned from signature images generalize across signers "
+             "without per-writer retraining. Hadjadj et al. [5] addressed the practical constraint of limited reference samples, achieving competitive "
+             "verification accuracy using only a single known genuine signature per writer. More recently, Li et al. [6] introduced TransOSV, "
+             "the first Vision Transformer-based approach for offline signature verification, achieving state-of-the-art results. Tehsin et al. [7] "
+             "evaluated distance metrics for triplet Siamese networks, finding that Manhattan distance outperformed cosine and Euclidean alternatives.")
+
+    add_para(doc, "A common thread in this literature is the assumption that the primary threat is identity fraud: a forger attempting to produce "
+             "a convincing imitation of another person\u2019s signature. Our work addresses a fundamentally different problem\u2014detecting whether the "
+             "legitimate signer reused a digital copy of their own signature\u2014which requires analyzing intra-signer similarity distributions "
+             "rather than modeling inter-signer discriminability.")
+
+    add_para(doc, "Brimoh and Olisah [8] proposed a consensus-threshold approach that derives classification boundaries from known genuine "
+             "reference pairs, the methodology most closely related to our calibration strategy. However, their method operates on standard "
+             "verification benchmarks with laboratory-collected signatures, whereas our approach applies threshold calibration using a "
+             "known-replication subpopulation identified through domain expertise in real-world regulatory documents.")
+
+    add_heading(doc, "B. Document Forensics and Copy Detection", level=2)
+    add_para(doc, "Copy-move forgery detection (CMFD) identifies duplicated regions within or across images, typically targeting manipulated "
+             "photographs [10]. Abramova and Bohme [11] adapted block-based CMFD to scanned text documents, noting that standard methods perform "
+             "poorly in this domain because legitimate character repetitions produce high similarity scores that confound duplicate detection.")
+
+    add_para(doc, "Woodruff et al. [9] developed the work most closely related to ours: a fully automated pipeline for extracting and "
+             "analyzing signatures from corporate filings in the context of anti-money laundering investigations. Their system uses connected "
+             "component analysis for signature detection, GANs for noise removal, and Siamese networks for author clustering. While their "
+             "pipeline shares our goal of large-scale automated signature analysis on real regulatory documents, their objective\u2014grouping "
+             "signatures by authorship\u2014differs fundamentally from ours, which is detecting digital replication within a single author\u2019s "
+             "signatures across documents.")
+
+    add_para(doc, "In the domain of image copy detection, Pizzi et al. [13] proposed SSCD, a self-supervised descriptor using ResNet-50 "
+             "with contrastive learning for large-scale copy detection on natural images. Their work demonstrates that pre-trained CNN features "
+             "with cosine similarity provide a strong baseline for identifying near-duplicate images, supporting our feature extraction approach.")
+
+    add_heading(doc, "C. Perceptual Hashing", level=2)
+    add_para(doc, "Perceptual hashing algorithms generate compact fingerprints that are robust to minor image transformations while remaining "
+             "sensitive to substantive content changes [14]. Jakhar and Borah [12] demonstrated that combining perceptual hashing with deep "
+             "learning features significantly outperforms either approach alone for near-duplicate image detection, achieving AUROC of 0.99. "
+             "Their two-stage architecture\u2014pHash for fast structural comparison followed by deep features for semantic verification\u2014provides "
+             "methodological precedent for our dual-method approach, though applied to natural images rather than document signatures.")
+
+    add_heading(doc, "D. Deep Feature Extraction for Signature Analysis", level=2)
+    add_para(doc, "Several studies have explored pre-trained CNN features for signature comparison without metric learning or Siamese architectures. "
+             "Engin et al. [15] used ResNet-50 features with cosine similarity for offline signature verification on real-world scanned documents, "
+             "incorporating CycleGAN-based stamp removal as preprocessing. Tsourounis et al. [16] demonstrated successful transfer from handwritten "
+             "text recognition to signature verification. Chamakh and Bounouh [17] confirmed that a simple ResNet backbone with cosine similarity "
+             "achieves competitive verification accuracy across multilingual signature datasets without fine-tuning, supporting the viability of "
+             "our off-the-shelf feature extraction approach.")
+
+    # ==================== III. METHODOLOGY ====================
+    add_heading(doc, "III. Methodology", level=1)
+
+    add_heading(doc, "A. Pipeline Overview", level=2)
+    add_para(doc, "We propose a six-stage pipeline for large-scale signature replication detection in scanned financial documents. "
+             "Fig. 1 illustrates the overall architecture. The pipeline takes as input a corpus of PDF audit reports and produces, for each "
+             "document, a classification of its CPA signatures as genuine, uncertain, or replicated, along with confidence scores and "
+             "supporting evidence from multiple verification methods.")
+    add_figure(doc, FIGURE_DIR / "fig1_pipeline.png",
+               "Fig. 1. Pipeline architecture for automated signature replication detection.", width=6.5)
+
+    add_heading(doc, "B. Data Collection", level=2)
+    add_para(doc, "The dataset comprises 90,282 annual financial audit reports filed by publicly listed companies in Taiwan, covering fiscal "
+             "years 2013 to 2023. The reports were collected from the Market Observation Post System (MOPS) operated by the Taiwan Stock Exchange "
+             "Corporation, the official repository for mandatory corporate filings. CPA names, affiliated accounting firms, and audit engagement "
+             "tenure were obtained from a publicly available audit firm tenure registry encompassing 758 unique CPAs.")
+
+    add_table(doc,
+              ["Attribute", "Value"],
+              [
+                  ["Total PDF documents", "90,282"],
+                  ["Date range", "2013\u20132023"],
+                  ["Documents with signatures", "86,072 (95.4%)"],
+                  ["Unique CPAs identified", "758"],
+                  ["Accounting firms", ">50"],
+              ],
+              caption="TABLE I: Dataset Summary")
+
+    add_heading(doc, "C. Signature Page Identification", level=2)
+    add_para(doc, "To identify which page of each multi-page PDF contains the auditor\u2019s signatures, we employed the Qwen2.5-VL "
+             "vision-language model (32B parameters) [18] as an automated pre-screening mechanism. Each PDF page was rendered to JPEG at "
+             "180 DPI and submitted to the VLM with a structured prompt requesting a binary determination of whether the page contains "
+             "a Chinese handwritten signature. The scanning range was restricted to the first quartile of each document\u2019s page count, "
+             "reflecting the regulatory structure of Taiwanese audit reports. This process identified 86,072 documents with signature pages. "
+             "Cross-validation between the VLM and subsequent YOLO detection confirmed high agreement: YOLO successfully detected signature "
+             "regions in 98.8% of VLM-positive documents.")
+
+    add_heading(doc, "D. Signature Detection", level=2)
+    add_para(doc, "We adopted YOLOv11n (nano variant) [19] for signature region localization. A training set of 500 randomly sampled signature "
+             "pages was annotated using a custom web-based interface following a two-stage protocol: primary annotation followed by independent "
+             "review and correction.")
+
+    add_table(doc,
+              ["Metric", "Value"],
+              [
+                  ["Precision", "0.97\u20130.98"],
+                  ["Recall", "0.95\u20130.98"],
+                  ["mAP@0.50", "0.98\u20130.99"],
+                  ["mAP@0.50:0.95", "0.85\u20130.90"],
+              ],
+              caption="TABLE II: YOLO Detection Performance")
+
+    add_para(doc, "Batch inference on 86,071 documents extracted 182,328 signature images at 43.1 documents/second (8 workers). "
+             "A red stamp removal step was applied using HSV color space filtering. Each signature was matched to its corresponding CPA "
+             "using positional order against the official registry, achieving a 92.6% match rate.")
+
+    add_heading(doc, "E. Feature Extraction", level=2)
+    add_para(doc, "Each extracted signature was encoded into a 2048-dimensional feature vector using a pre-trained ResNet-50 CNN [20] with "
+             "ImageNet-1K V2 weights, used as a fixed feature extractor without fine-tuning. Preprocessing consisted of resizing to "
+             "224\u00d7224 pixels with aspect ratio preservation and white padding, followed by ImageNet channel normalization. All feature "
+             "vectors were L2-normalized, ensuring that cosine similarity equals the dot product. The choice of ResNet-50 without fine-tuning "
+             "was motivated by three considerations: (1) the task is similarity comparison rather than classification; (2) ImageNet features "
+             "transfer effectively to document analysis [15], [16]; and (3) the absence of fine-tuning preserves generalizability. "
+             "This design choice is validated by an ablation study (Section IV-F).")
+
+    add_heading(doc, "F. Dual-Method Similarity Verification", level=2)
+    add_para(doc, "For each signature, the most similar signature from the same CPA across all other documents was identified via cosine "
+             "similarity. Two complementary measures were then computed against this closest match:")
+    add_para(doc, "Cosine similarity captures high-level visual style similarity: sim(fA, fB) = fA \u00b7 fB, where fA and fB are L2-normalized "
+             "feature vectors. A high cosine similarity indicates shared visual characteristics but does not distinguish between consistent "
+             "handwriting style and digital duplication.")
+    add_para(doc, "Perceptual hash (pHash) distance captures structural-level similarity. Each signature is converted to a 64-bit binary "
+             "fingerprint by resizing to 9\u00d78 pixels and computing horizontal gradient differences. The Hamming distance between two hashes "
+             "quantifies perceptual dissimilarity: 0 indicates perceptually identical images, while distances exceeding 15 indicate clearly "
+             "different images.")
+    add_para(doc, "The complementarity of these measures resolves the style-versus-replication ambiguity: high cosine + low pHash = converging "
+             "evidence of replication; high cosine + high pHash = consistent style, not replication. SSIM was excluded as a primary method "
+             "because scan-induced pixel variations caused a known-replication firm to exhibit a mean SSIM of only 0.70.")
+
+    add_heading(doc, "G. Threshold Selection and Calibration", level=2)
+    add_para(doc, "Intra-class (same CPA, 41.3M pairs) and inter-class (different CPAs, 500K pairs) cosine similarity distributions were "
+             "computed. Shapiro-Wilk tests rejected normality (p < 0.001), motivating distribution-free, percentile-based thresholds. "
+             "The primary threshold was derived via KDE crossover\u2014the point where intra- and inter-class density functions intersect.")
+    add_para(doc, "A distinctive aspect is the use of Firm A\u2014a major firm whose signatures are known to be digitally replicated\u2014as a "
+             "calibration reference. Firm A\u2019s distribution provides: (1) lower bound validation\u2014any threshold must classify the vast majority "
+             "of Firm A as replicated; and (2) upper bound estimation\u2014Firm A\u2019s 1st percentile establishes the floor of similarity achievable "
+             "through replication in scanned documents.")
+
+    add_heading(doc, "H. Classification", level=2)
+    add_para(doc, "The final per-document classification integrates evidence from both methods: (1) Definite replication: pixel-identical match "
+             "or SSIM > 0.95 with pHash \u2264 5; (2) Likely replication: cosine > 0.95 with pHash \u2264 5, or multiple methods indicate replication; "
+             "(3) Uncertain: cosine between KDE crossover and 0.95 without structural evidence; (4) Likely genuine: cosine below KDE crossover.")
+
+    # ==================== IV. RESULTS ====================
+    add_heading(doc, "IV. Experiments and Results", level=1)
+
+    add_heading(doc, "A. Experimental Setup", level=2)
+    add_para(doc, "All experiments were conducted using PyTorch 2.9 with Apple Silicon MPS GPU acceleration. "
+             "Feature extraction used torchvision model implementations with identical preprocessing across all backbones.")
+
+    add_heading(doc, "B. Distribution Analysis", level=2)
+    add_para(doc, "Fig. 2 presents the cosine similarity distributions for intra-class and inter-class pairs.")
+    add_figure(doc, FIGURE_DIR / "fig2_intra_inter_kde.png",
+               "Fig. 2. Cosine similarity distributions: intra-class (same CPA) vs. inter-class (different CPAs). "
+               "KDE crossover at 0.837 marks the Bayes-optimal decision boundary.", width=3.5)
+
+    add_table(doc,
+              ["Statistic", "Intra-class", "Inter-class"],
+              [
+                  ["N (pairs)", "41,352,824", "500,000"],
+                  ["Mean", "0.821", "0.758"],
+                  ["Std. Dev.", "0.098", "0.090"],
+                  ["Median", "0.836", "0.774"],
+              ],
+              caption="TABLE IV: Cosine Similarity Distribution Statistics")
+
+    add_para(doc, "Cohen\u2019s d of 0.669 indicates a medium effect size, confirming that the distributional difference is not merely "
+             "statistically significant but also practically meaningful.")
+
+    add_heading(doc, "C. Calibration Group Analysis", level=2)
+    add_para(doc, "Fig. 3 presents the per-signature best-match cosine similarity distribution of Firm A compared to other CPAs.")
+    add_figure(doc, FIGURE_DIR / "fig3_firm_a_calibration.png",
+               "Fig. 3. Per-signature best-match cosine similarity: Firm A (known replication) vs. other CPAs. "
+               "Firm A\u2019s 1st percentile (0.908) validates threshold selection.", width=3.5)
+
+    add_table(doc,
+              ["Statistic", "Firm A", "All CPAs"],
+              [
+                  ["N (signatures)", "60,448", "168,740"],
+                  ["Mean", "0.980", "0.961"],
+                  ["Std. Dev.", "0.019", "0.029"],
+                  ["1st percentile", "0.908", "\u2014"],
+                  ["% > 0.95", "92.5%", "\u2014"],
+                  ["% > 0.90", "99.3%", "\u2014"],
+              ],
+              caption="TABLE VI: Firm A Calibration Statistics (Per-Signature Best Match)")
+
+    add_para(doc, "Firm A\u2019s per-signature best-match cosine similarity (mean = 0.980, std = 0.019) is notably higher and more concentrated "
+             "than the overall CPA population (mean = 0.961, std = 0.029). Critically, 99.3% of Firm A\u2019s signatures exhibit a best-match "
+             "similarity exceeding 0.90, and the 1st percentile is 0.908\u2014establishing that any threshold below 0.91 would fail to capture "
+             "even the most dissimilar replicated signatures in the calibration group.")
+
+    add_heading(doc, "D. Classification Results", level=2)
+    add_table(doc,
+              ["Verdict", "N (PDFs)", "%", "Description"],
+              [
+                  ["Definite replication", "2,403", "2.8%", "Pixel-level evidence"],
+                  ["Likely replication", "69,255", "81.4%", "Feature-level evidence"],
+                  ["Uncertain", "12,681", "14.9%", "Between thresholds"],
+                  ["Likely genuine", "47", "0.1%", "Below KDE crossover"],
+                  ["Unknown", "656", "0.8%", "Unmatched CPA"],
+              ],
+              caption="TABLE VII: Classification Results (85,042 Documents)")
+
+    add_para(doc, "The most striking finding is the discrepancy between feature-level and pixel-level evidence. Of the 71,656 documents with "
+             "cosine similarity exceeding 0.95, only 3.4% (2,427) simultaneously exhibited SSIM > 0.95, and only 4.3% (3,081) had a pHash "
+             "distance of 0. This gap demonstrates that the vast majority of high cosine similarity scores reflect consistent signing style "
+             "rather than digital replication, vindicating the dual-method approach.")
+
+    add_para(doc, "The 267 pixel-identical signatures (0.4%) constitute the strongest evidence of digital replication, as it is physically "
+             "impossible for two instances of genuine handwriting to produce identical pixel arrays.")
+
+    add_heading(doc, "E. Ablation Study: Feature Backbone Comparison", level=2)
+    add_para(doc, "To validate the choice of ResNet-50, we compared three pre-trained architectures (Fig. 4).")
+    add_figure(doc, FIGURE_DIR / "fig4_ablation.png",
+               "Fig. 4. Ablation study comparing three feature extraction backbones: "
+               "(a) intra/inter-class mean similarity, (b) Cohen\u2019s d, (c) KDE crossover point.", width=6.5)
+
+    add_table(doc,
+              ["Metric", "ResNet-50", "VGG-16", "EfficientNet-B0"],
+              [
+                  ["Feature dim", "2048", "4096", "1280"],
+                  ["Intra mean", "0.821", "0.822", "0.786"],
+                  ["Inter mean", "0.758", "0.767", "0.699"],
+                  ["Cohen\u2019s d", "0.669", "0.564", "0.707"],
+                  ["KDE crossover", "0.837", "0.850", "0.792"],
+                  ["Firm A mean", "0.826", "0.820", "0.810"],
+                  ["Firm A 1st pct", "0.543", "0.520", "0.454"],
+              ],
+              caption="TABLE IX: Backbone Comparison")
+
+    add_para(doc, "EfficientNet-B0 achieves the highest Cohen\u2019s d (0.707), but exhibits the widest distributional spread, resulting in "
+             "lower per-sample classification confidence. VGG-16 performs worst despite the highest dimensionality. ResNet-50 provides the "
+             "best balance: competitive Cohen\u2019s d, tightest distributions, highest Firm A 1st percentile (0.543), and practical feature "
+             "dimensionality.")
+
+    # ==================== V. DISCUSSION ====================
+    add_heading(doc, "V. Discussion", level=1)
+
+    add_heading(doc, "A. Replication Detection as a Distinct Problem", level=2)
+    add_para(doc, "Our results highlight the importance of distinguishing signature replication detection from forgery detection. "
+             "Forgery detection optimizes for inter-class discriminability\u2014maximizing the gap between genuine and forged signatures. "
+             "Replication detection requires sensitivity to the upper tail of the intra-class similarity distribution, where the boundary "
+             "between consistent handwriting and digital copies becomes ambiguous. The dual-method framework addresses this ambiguity "
+             "in a way that single-method approaches cannot.")
+
+    add_heading(doc, "B. The Style-Replication Gap", level=2)
+    add_para(doc, "The most important empirical finding is the magnitude of the gap between style similarity and digital replication. "
+             "Of documents with cosine similarity exceeding 0.95, only 3.4% exhibited pixel-level evidence of actual replication via SSIM, "
+             "and only 4.3% via pHash. This implies that a naive cosine-only approach would overestimate the replication rate by approximately "
+             "25-fold. This gap likely reflects the nature of CPA signing practices: many accountants develop highly consistent signing habits, "
+             "resulting in signatures that appear nearly identical at the feature level while retaining microscopic handwriting variations.")
+
+    add_heading(doc, "C. Value of Known-Replication Calibration", level=2)
+    add_para(doc, "The use of Firm A as a calibration reference addresses a fundamental challenge in document forensics: the scarcity of "
+             "ground truth labels. Our approach leverages domain knowledge\u2014the established practice of digital signature replication at "
+             "a specific firm\u2014to create a naturally occurring positive control group. This calibration strategy has broader applicability: "
+             "any forensic detection system can benefit from identifying subpopulations with known characteristics to anchor threshold selection.")
+
+    add_heading(doc, "D. Limitations", level=2)
+    add_para(doc, "Several limitations should be acknowledged. First, comprehensive ground truth labels are not available for the full dataset. "
+             "While pixel-identical cases and Firm A provide anchor points, a small-scale manual verification study would strengthen confidence "
+             "in classification boundaries. Second, the ResNet-50 feature extractor was not fine-tuned on domain-specific data. Third, scanning "
+             "equipment and compression algorithms may have changed over the 10-year study period. Fourth, the classification framework does not "
+             "account for potential changes in signing practice over time. Finally, whether digital replication constitutes a violation of signing "
+             "requirements is a legal question that our technical analysis can inform but cannot resolve.")
+
+    # ==================== VI. CONCLUSION ====================
+    add_heading(doc, "VI. Conclusion and Future Work", level=1)
+
+    add_para(doc, "We have presented an end-to-end AI pipeline for detecting digitally replicated signatures in financial audit reports at scale. "
+             "Applied to 90,282 audit reports from Taiwanese publicly listed companies spanning 2013\u20132023, our system extracted and analyzed "
+             "182,328 CPA signatures using VLM-based page identification, YOLO-based signature detection, deep feature extraction, and "
+             "dual-method similarity verification.")
+
+    add_para(doc, "Our key findings are threefold. First, signature replication detection is a distinct problem from forgery detection, requiring "
+             "different analytical tools. Second, combining cosine similarity with perceptual hashing is essential for distinguishing consistent "
+             "handwriting style from digital duplication\u2014a single-metric approach overestimates replication rates by approximately 25-fold. "
+             "Third, a calibration methodology using a known-replication reference group provides empirical threshold validation in the absence "
+             "of comprehensive ground truth.")
+
+    add_para(doc, "An ablation study confirmed that ResNet-50 offers the best balance of discriminative power, classification stability, and "
+             "computational efficiency among three evaluated backbones.")
+
+    add_para(doc, "Future directions include domain-adapted feature extractors, temporal analysis of signing practice evolution, cross-country "
+             "generalization, regulatory system integration, and small-scale ground truth validation through expert review.")
+
+    # ==================== REFERENCES ====================
+    add_heading(doc, "References", level=1)
+    refs = [
+        '[1] Taiwan Certified Public Accountant Act (\u6703\u8a08\u5e2b\u6cd5), Art. 4; FSC Attestation Regulations (\u67e5\u6838\u7c3d\u8b49\u6838\u6e96\u6e96\u5247), Art. 6.',
+        '[2] S.-H. Yen, Y.-S. Chang, and H.-L. Chen, \u201cDoes the signature of a CPA matter? Evidence from Taiwan,\u201d Res. Account. Regul., vol. 25, no. 2, pp. 230\u2013235, 2013.',
+        '[3] J. Bromley et al., \u201cSignature verification using a Siamese time delay neural network,\u201d in Proc. NeurIPS, 1993.',
+        '[4] S. Dey et al., \u201cSigNet: Convolutional Siamese network for writer independent offline signature verification,\u201d arXiv:1707.02131, 2017.',
+        '[5] I. Hadjadj et al., \u201cAn offline signature verification method based on a single known sample and an explainable deep learning approach,\u201d Appl. Sci., vol. 10, no. 11, p. 3716, 2020.',
+        '[6] H. Li et al., \u201cTransOSV: Offline signature verification with transformers,\u201d Pattern Recognit., vol. 145, p. 109882, 2024.',
+        '[7] S. Tehsin et al., \u201cEnhancing signature verification using triplet Siamese similarity networks in digital documents,\u201d Mathematics, vol. 12, no. 17, p. 2757, 2024.',
+        '[8] P. Brimoh and C. C. Olisah, \u201cConsensus-threshold criterion for offline signature verification using CNN learned representations,\u201d arXiv:2401.03085, 2024.',
+        '[9] N. Woodruff et al., \u201cFully-automatic pipeline for document signature analysis to detect money laundering activities,\u201d arXiv:2107.14091, 2021.',
+        '[10] Copy-move forgery detection in digital image forensics: A survey, Multimedia Tools Appl., 2024.',
+        '[11] S. Abramova and R. Bohme, \u201cDetecting copy-move forgeries in scanned text documents,\u201d in Proc. Electronic Imaging, 2016.',
+        '[12] Y. Jakhar and M. D. Borah, \u201cEffective near-duplicate image detection using perceptual hashing and deep learning,\u201d Inf. Process. Manage., p. 104086, 2025.',
+        '[13] E. Pizzi et al., \u201cA self-supervised descriptor for image copy detection,\u201d in Proc. CVPR, 2022.',
+        '[14] A survey of perceptual hashing for multimedia, ACM Trans. Multimedia Comput. Commun. Appl., vol. 21, no. 7, 2025.',
+        '[15] D. Engin et al., \u201cOffline signature verification on real-world documents,\u201d in Proc. CVPRW, 2020.',
+        '[16] D. Tsourounis et al., \u201cFrom text to signatures: Knowledge transfer for efficient deep feature learning in offline signature verification,\u201d Expert Syst. Appl., 2022.',
+        '[17] B. Chamakh and O. Bounouh, \u201cA unified ResNet18-based approach for offline signature classification and verification,\u201d Procedia Comput. Sci., vol. 270, 2025.',
+        '[18] Qwen2.5-VL Technical Report, Alibaba Group, 2025.',
+        '[19] Ultralytics, \u201cYOLOv11 documentation,\u201d 2024. [Online]. Available: https://docs.ultralytics.com/',
+        '[20] K. He, X. Zhang, S. Ren, and J. Sun, \u201cDeep residual learning for image recognition,\u201d in Proc. CVPR, 2016.',
+        '[21] J. V. Carcello and C. Li, \u201cCosts and benefits of requiring an engagement partner signature: Recent experience in the United Kingdom,\u201d The Accounting Review, vol. 88, no. 5, pp. 1511\u20131546, 2013.',
+        '[22] A. D. Blay, M. Notbohm, C. Schelleman, and A. Valencia, \u201cAudit quality effects of an individual audit engagement partner signature mandate,\u201d Int. J. Auditing, vol. 18, no. 3, pp. 172\u2013192, 2014.',
+        '[23] W. Chi, H. Huang, Y. Liao, and H. Xie, \u201cMandatory audit partner rotation, audit quality, and market perception: Evidence from Taiwan,\u201d Contemp. Account. Res., vol. 26, no. 2, pp. 359\u2013391, 2009.',
+        '[24] L. G. Hafemann, R. Sabourin, and L. S. Oliveira, \u201cLearning features for offline handwritten signature verification using deep convolutional neural networks,\u201d Pattern Recognit., vol. 70, pp. 163\u2013176, 2017.',
+        '[25] L. G. Hafemann, R. Sabourin, and L. S. Oliveira, \u201cMeta-learning for fast classifier adaptation to new users of signature verification systems,\u201d IEEE Trans. Inf. Forensics Security, vol. 15, pp. 1735\u20131745, 2019.',
+        '[26] E. N. Zois, D. Tsourounis, and D. Kalivas, \u201cSimilarity distance learning on SPD manifold for writer independent offline signature verification,\u201d IEEE Trans. Inf. Forensics Security, vol. 19, pp. 1342\u20131356, 2024.',
+        '[27] H. Farid, \u201cImage forgery detection,\u201d IEEE Signal Process. Mag., vol. 26, no. 2, pp. 16\u201325, 2009.',
+        '[28] F. Z. Mehrjardi, A. M. Latif, M. S. Zarchi, and R. Sheikhpour, \u201cA survey on deep learning-based image forgery detection,\u201d Pattern Recognit., vol. 144, art. no. 109778, 2023.',
+        '[29] A. Babenko, A. Slesarev, A. Chigorin, and V. Lempitsky, \u201cNeural codes for image retrieval,\u201d in Proc. ECCV, 2014, pp. 584\u2013599.',
+        '[30] J. Redmon, S. Divvala, R. Girshick, and A. Farhadi, \u201cYou only look once: Unified, real-time object detection,\u201d in Proc. CVPR, 2016, pp. 779\u2013788.',
+        '[31] J. Zhang, J. Huang, S. Jin, and S. Lu, \u201cVision-language models for vision tasks: A survey,\u201d IEEE Trans. Pattern Anal. Mach. Intell., vol. 46, no. 8, pp. 5625\u20135644, 2024.',
+        '[32] Z. Wang, A. C. Bovik, H. R. Sheikh, and E. P. Simoncelli, \u201cImage quality assessment: From error visibility to structural similarity,\u201d IEEE Trans. Image Process., vol. 13, no. 4, pp. 600\u2013612, 2004.',
+        '[33] B. W. Silverman, Density Estimation for Statistics and Data Analysis. London: Chapman & Hall, 1986.',
+        '[34] J. Cohen, Statistical Power Analysis for the Behavioral Sciences, 2nd ed. Hillsdale, NJ: Lawrence Erlbaum, 1988.',
+        '[35] H. B. Mann and D. R. Whitney, \u201cOn a test of whether one of two random variables is stochastically larger than the other,\u201d Ann. Math. Statist., vol. 18, no. 1, pp. 50\u201360, 1947.',
+    ]
+    for ref in refs:
+        add_para(doc, ref, font_size=8, space_after=2)
+
+    # Save
+    doc.save(str(OUTPUT_PATH))
+    print(f"Saved: {OUTPUT_PATH}")
+
+
+if __name__ == "__main__":
+    build_document()

paper/export_v2.py

@@ -0,0 +1,231 @@
+#!/usr/bin/env python3
+"""Export Paper A v2 to Word, reading from md section files."""
+
+from docx import Document
+from docx.shared import Inches, Pt, RGBColor
+from docx.enum.text import WD_ALIGN_PARAGRAPH
+from pathlib import Path
+import re
+
+PAPER_DIR = Path("/Volumes/NV2/pdf_recognize/paper")
+FIG_DIR = Path("/Volumes/NV2/PDF-Processing/signature-analysis/paper_figures")
+OUTPUT = PAPER_DIR / "Paper_A_IEEE_TAI_Draft_v2.docx"
+
+SECTIONS = [
+    "paper_a_abstract.md",
+    "paper_a_impact_statement.md",
+    "paper_a_introduction.md",
+    "paper_a_related_work.md",
+    "paper_a_methodology.md",
+    "paper_a_results.md",
+    "paper_a_discussion.md",
+    "paper_a_conclusion.md",
+    "paper_a_references.md",
+]
+
+FIGURES = {
+    "Fig. 1 illustrates": ("fig1_pipeline.png", "Fig. 1. Pipeline architecture for automated signature replication detection.", 6.5),
+    "Fig. 2 presents": ("fig2_intra_inter_kde.png", "Fig. 2. Cosine similarity distributions: intra-class vs. inter-class with KDE crossover at 0.837.", 3.5),
+    "Fig. 3 presents": ("fig3_firm_a_calibration.png", "Fig. 3. Per-signature best-match cosine similarity: Firm A (known replication) vs. other CPAs.", 3.5),
+    "conducted an ablation study comparing three": ("fig4_ablation.png", "Fig. 4. Ablation study comparing three feature extraction backbones.", 6.5),
+}
+
+
+def strip_comments(text):
+    """Remove HTML comments from markdown."""
+    return re.sub(r'<!--.*?-->', '', text, flags=re.DOTALL)
+
+
+def extract_tables(text):
+    """Find markdown tables and return (before, table_lines, after) tuples."""
+    lines = text.split('\n')
+    tables = []
+    i = 0
+    while i < len(lines):
+        if '|' in lines[i] and i + 1 < len(lines) and re.match(r'\s*\|[-|: ]+\|', lines[i+1]):
+            start = i
+            while i < len(lines) and '|' in lines[i]:
+                i += 1
+            tables.append((start, lines[start:i]))
+        else:
+            i += 1
+    return tables
+
+
+def add_md_table(doc, table_lines):
+    """Convert markdown table to docx table."""
+    rows_data = []
+    for line in table_lines:
+        cells = [c.strip() for c in line.strip('|').split('|')]
+        if not re.match(r'^[-: ]+$', cells[0]):
+            rows_data.append(cells)
+
+    if len(rows_data) < 2:
+        return
+
+    ncols = len(rows_data[0])
+    table = doc.add_table(rows=len(rows_data), cols=ncols)
+    table.style = 'Table Grid'
+
+    for r_idx, row in enumerate(rows_data):
+        for c_idx in range(min(len(row), ncols)):
+            cell = table.rows[r_idx].cells[c_idx]
+            cell.text = row[c_idx]
+            for p in cell.paragraphs:
+                p.alignment = WD_ALIGN_PARAGRAPH.CENTER
+                for run in p.runs:
+                    run.font.size = Pt(8)
+                    run.font.name = 'Times New Roman'
+                    if r_idx == 0:
+                        run.bold = True
+
+    doc.add_paragraph()
+
+
+def process_section(doc, filepath):
+    """Process a markdown section file into docx."""
+    text = filepath.read_text(encoding='utf-8')
+    text = strip_comments(text)
+
+    lines = text.split('\n')
+    i = 0
+    while i < len(lines):
+        line = lines[i]
+        stripped = line.strip()
+
+        # Skip empty lines
+        if not stripped:
+            i += 1
+            continue
+
+        # Headings
+        if stripped.startswith('# '):
+            h = doc.add_heading(stripped[2:], level=1)
+            for run in h.runs:
+                run.font.color.rgb = RGBColor(0, 0, 0)
+            i += 1
+            continue
+        elif stripped.startswith('## '):
+            h = doc.add_heading(stripped[3:], level=2)
+            for run in h.runs:
+                run.font.color.rgb = RGBColor(0, 0, 0)
+            i += 1
+            continue
+        elif stripped.startswith('### '):
+            h = doc.add_heading(stripped[4:], level=3)
+            for run in h.runs:
+                run.font.color.rgb = RGBColor(0, 0, 0)
+            i += 1
+            continue
+
+        # Markdown table
+        if '|' in stripped and i + 1 < len(lines) and re.match(r'\s*\|[-|: ]+\|', lines[i+1]):
+            table_lines = []
+            while i < len(lines) and '|' in lines[i]:
+                table_lines.append(lines[i])
+                i += 1
+            add_md_table(doc, table_lines)
+            continue
+
+        # Numbered list
+        if re.match(r'^\d+\.\s', stripped):
+            p = doc.add_paragraph(style='List Number')
+            content = re.sub(r'^\d+\.\s', '', stripped)
+            content = re.sub(r'\*\*(.+?)\*\*', r'\1', content)  # strip bold markers
+            run = p.add_run(content)
+            run.font.size = Pt(10)
+            run.font.name = 'Times New Roman'
+            i += 1
+            continue
+
+        # Bullet list
+        if stripped.startswith('- '):
+            p = doc.add_paragraph(style='List Bullet')
+            content = stripped[2:]
+            content = re.sub(r'\*\*(.+?)\*\*', r'\1', content)
+            run = p.add_run(content)
+            run.font.size = Pt(10)
+            run.font.name = 'Times New Roman'
+            i += 1
+            continue
+
+        # Regular paragraph - collect continuation lines
+        para_lines = [stripped]
+        i += 1
+        while i < len(lines):
+            next_line = lines[i].strip()
+            if not next_line or next_line.startswith('#') or next_line.startswith('|') or \
+               next_line.startswith('- ') or re.match(r'^\d+\.\s', next_line):
+                break
+            para_lines.append(next_line)
+            i += 1
+
+        para_text = ' '.join(para_lines)
+        # Clean markdown formatting
+        para_text = re.sub(r'\*\*\*(.+?)\*\*\*', r'\1', para_text)  # bold italic
+        para_text = re.sub(r'\*\*(.+?)\*\*', r'\1', para_text)  # bold
+        para_text = re.sub(r'\*(.+?)\*', r'\1', para_text)  # italic
+        para_text = re.sub(r'`(.+?)`', r'\1', para_text)  # code
+        para_text = para_text.replace('$$', '')  # LaTeX delimiters
+        para_text = para_text.replace('---', '\u2014')  # em dash
+
+        p = doc.add_paragraph()
+        p.paragraph_format.space_after = Pt(6)
+        run = p.add_run(para_text)
+        run.font.size = Pt(10)
+        run.font.name = 'Times New Roman'
+
+        # Check if we should insert a figure after this paragraph
+        for trigger, (fig_file, caption, width) in FIGURES.items():
+            if trigger in para_text:
+                fig_path = FIG_DIR / fig_file
+                if fig_path.exists():
+                    fp = doc.add_paragraph()
+                    fp.alignment = WD_ALIGN_PARAGRAPH.CENTER
+                    fr = fp.add_run()
+                    fr.add_picture(str(fig_path), width=Inches(width))
+
+                    cp = doc.add_paragraph()
+                    cp.alignment = WD_ALIGN_PARAGRAPH.CENTER
+                    cr = cp.add_run(caption)
+                    cr.font.size = Pt(9)
+                    cr.font.name = 'Times New Roman'
+                    cr.italic = True
+
+
+def main():
+    doc = Document()
+
+    # Set default font
+    style = doc.styles['Normal']
+    style.font.name = 'Times New Roman'
+    style.font.size = Pt(10)
+
+    # Title page
+    p = doc.add_paragraph()
+    p.alignment = WD_ALIGN_PARAGRAPH.CENTER
+    p.paragraph_format.space_after = Pt(12)
+    run = p.add_run("Automated Detection of Digitally Replicated Signatures\nin Large-Scale Financial Audit Reports")
+    run.font.size = Pt(16)
+    run.font.name = 'Times New Roman'
+    run.bold = True
+
+    p = doc.add_paragraph()
+    p.alignment = WD_ALIGN_PARAGRAPH.CENTER
+    p.paragraph_format.space_after = Pt(20)
+    run = p.add_run("[Authors removed for double-blind review]")
+    run.font.size = Pt(10)
+    run.italic = True
+
+    # Process each section
+    for section_file in SECTIONS:
+        filepath = PAPER_DIR / section_file
+        if filepath.exists():
+            process_section(doc, filepath)
+
+    doc.save(str(OUTPUT))
+    print(f"Saved: {OUTPUT}")
+
+
+if __name__ == "__main__":
+    main()

paper/export_v3.py

@@ -0,0 +1,690 @@
+#!/usr/bin/env python3
+"""Export Paper A v3 (IEEE Access target) to Word, reading from v3 md section files."""
+
+from docx import Document
+from docx.shared import Inches, Pt, RGBColor
+from docx.enum.text import WD_ALIGN_PARAGRAPH
+from pathlib import Path
+import hashlib
+import re
+
+import matplotlib
+matplotlib.use("Agg")
+import matplotlib.pyplot as plt
+
+PAPER_DIR = Path("/Volumes/NV2/pdf_recognize/paper")
+EQUATION_CACHE_DIR = PAPER_DIR / "equations"
+EQUATION_CACHE_DIR.mkdir(exist_ok=True)
+FIG_DIR = Path("/Volumes/NV2/PDF-Processing/signature-analysis/paper_figures")
+EXTRA_FIG_DIR = Path("/Volumes/NV2/PDF-Processing/signature-analysis/reports")
+OUTPUT = PAPER_DIR / "Paper_A_IEEE_Access_Draft_v3.docx"
+
+SECTIONS = [
+    "paper_a_abstract_v3.md",
+    # paper_a_impact_statement_v3.md removed: not a standard IEEE Access
+    # Regular Paper section. Content folded into cover letter / abstract.
+    "paper_a_introduction_v3.md",
+    "paper_a_related_work_v3.md",
+    "paper_a_methodology_v3.md",
+    "paper_a_results_v3.md",
+    "paper_a_discussion_v3.md",
+    "paper_a_conclusion_v3.md",
+    # Appendix A: BD/McCrary bin-width sensitivity (see v3.7 notes).
+    "paper_a_appendix_v3.md",
+    # Declarations (COI / data availability / funding) before References,
+    # per IEEE Access convention.
+    "paper_a_declarations_v3.md",
+    "paper_a_references_v3.md",
+]
+
+# Figure insertion hooks (trigger phrase -> (file, caption, width inches)).
+# New figures for v3: dip test, BD/McCrary overlays, accountant GMM 2D + marginals.
+FIGURES = {
+    "Fig. 1 illustrates": (
+        FIG_DIR / "fig1_pipeline.png",
+        "Fig. 1. Pipeline architecture for automated non-hand-signed signature detection.",
+        6.5,
+    ),
+    "Fig. 2 presents the cosine similarity distributions for intra-class": (
+        FIG_DIR / "fig2_intra_inter_kde.png",
+        "Fig. 2. Cosine similarity distributions: intra-class vs. inter-class with KDE crossover at 0.837.",
+        3.5,
+    ),
+    "Fig. 3 presents the per-signature cosine and dHash distributions of Firm A": (
+        FIG_DIR / "fig3_firm_a_calibration.png",
+        "Fig. 3. Firm A per-signature cosine and dHash distributions against the overall CPA population.",
+        3.5,
+    ),
+    "Fig. 4 summarises the per-firm yearly per-signature": (
+        EXTRA_FIG_DIR / "figures" / "fig_yearly_big4_comparison.png",
+        "Fig. 4. Per-firm yearly per-signature best-match cosine, 2013-2023. (a) Mean per-signature best-match cosine by firm bucket and fiscal year (threshold-free). (b) Share of per-signature best-match cosine ≥ 0.95 (operational cut of Section III-K). Five lines: Firm A, B, C, D, Non-Big-4. Firm A is above the other Big-4 firms in every year; Non-Big-4 is below all four Big-4 firms in every year.",
+        6.5,
+    ),
+    "conducted an ablation study comparing three": (
+        FIG_DIR / "fig4_ablation.png",
+        "Fig. 5. Ablation study comparing three feature extraction backbones.",
+        6.5,
+    ),
+}
+
+
+def strip_comments(text):
+    """Remove HTML comments, but UNWRAP comments whose first non-blank line
+    starts with `TABLE ` (or `TABLE\t`).
+
+    The v3 markdown sources wrap every numerical table in an HTML comment of
+    the form
+
+        <!-- TABLE V: Hartigan Dip Test Results
+        | Distribution | N | ... |
+        |--------------|---|-----|
+        | ...          | … | ... |
+        -->
+
+    The caption (`TABLE V: Hartigan Dip Test Results`) is on the same line as
+    the opening `<!--`, the markdown table body is on the lines following,
+    and `-->` closes the block. The previous implementation wholesale-deleted
+    these comments, which silently dropped every table from the rendered
+    DOCX. We now (i) detect comments whose first non-empty line starts with
+    `TABLE `, (ii) emit a synthetic caption marker line `__TABLE_CAPTION__:
+    <caption>` so process_section can render the caption as a centered
+    bold paragraph above the table, and (iii) keep the table body so the
+    existing markdown-table detector picks it up. Non-TABLE comments
+    (figure placeholders, editorial notes) are stripped as before.
+    """
+    def _replace(match):
+        body = match.group(1)
+        # Find first non-blank line.
+        for line in body.splitlines():
+            stripped = line.strip()
+            if stripped:
+                first = stripped
+                break
+        else:
+            return ""
+        if not first.startswith("TABLE ") and not first.startswith("TABLE\t"):
+            return ""
+        # Split caption (first non-blank line) from the rest.
+        lines = body.splitlines()
+        # Find index of the first non-blank line and use everything after.
+        for idx, line in enumerate(lines):
+            if line.strip():
+                caption = line.strip()
+                rest = "\n".join(lines[idx + 1:])
+                break
+        else:
+            return ""
+        # Emit caption marker + body. Surround with blank lines so the
+        # paragraph/table detector treats the marker as its own paragraph.
+        return f"\n\n__TABLE_CAPTION__:{caption}\n{rest}\n"
+    # Non-greedy match across lines.
+    return re.sub(r"<!--(.*?)-->", _replace, text, flags=re.DOTALL)
+
+
+# ---------------------------------------------------------------------------
+# LaTeX → plain text + Unicode conversion
+# ---------------------------------------------------------------------------
+# The v3 markdown sources contain inline LaTeX ($...$) and a small number of
+# display-math blocks ($$...$$). Pandoc would render these natively; the
+# python-docx pipeline used here does not, so without preprocessing every
+# `\leq`, `\text{dHash}_\text{indep}`, `\Delta\text{BIC}`, `60{,}448`, etc.
+# leaks into the DOCX as raw LaTeX. The helpers below convert the common
+# inline cases to Unicode and split subscripts/superscripts into proper Word
+# runs. Display-math (rare; 3 equations in this paper) gets a best-effort
+# linearisation and is acceptable for a partner-handoff DOCX; final IEEE
+# typesetting is handled by the publisher's LaTeX/MathType pipeline.
+
+LATEX_TOKEN_REPLACEMENTS = [
+    # Greek letters (lower)
+    (r"\\alpha(?![A-Za-z])", "α"), (r"\\beta(?![A-Za-z])", "β"), (r"\\gamma(?![A-Za-z])", "γ"),
+    (r"\\delta(?![A-Za-z])", "δ"), (r"\\epsilon(?![A-Za-z])", "ε"), (r"\\zeta(?![A-Za-z])", "ζ"),
+    (r"\\eta(?![A-Za-z])", "η"), (r"\\theta(?![A-Za-z])", "θ"), (r"\\iota(?![A-Za-z])", "ι"),
+    (r"\\kappa(?![A-Za-z])", "κ"), (r"\\lambda(?![A-Za-z])", "λ"), (r"\\mu(?![A-Za-z])", "μ"),
+    (r"\\nu(?![A-Za-z])", "ν"), (r"\\xi(?![A-Za-z])", "ξ"), (r"\\pi(?![A-Za-z])", "π"),
+    (r"\\rho(?![A-Za-z])", "ρ"), (r"\\sigma(?![A-Za-z])", "σ"), (r"\\tau(?![A-Za-z])", "τ"),
+    (r"\\phi(?![A-Za-z])", "φ"), (r"\\chi(?![A-Za-z])", "χ"), (r"\\psi(?![A-Za-z])", "ψ"),
+    (r"\\omega(?![A-Za-z])", "ω"),
+    # Greek letters (upper, only those distinguishable from Latin)
+    (r"\\Gamma(?![A-Za-z])", "Γ"), (r"\\Delta(?![A-Za-z])", "Δ"), (r"\\Theta(?![A-Za-z])", "Θ"),
+    (r"\\Lambda(?![A-Za-z])", "Λ"), (r"\\Xi(?![A-Za-z])", "Ξ"), (r"\\Pi(?![A-Za-z])", "Π"),
+    (r"\\Sigma(?![A-Za-z])", "Σ"), (r"\\Phi(?![A-Za-z])", "Φ"), (r"\\Psi(?![A-Za-z])", "Ψ"),
+    (r"\\Omega(?![A-Za-z])", "Ω"),
+    # Relations / arrows
+    (r"\\leq(?![A-Za-z])", "≤"), (r"\\geq(?![A-Za-z])", "≥"),
+    (r"\\neq(?![A-Za-z])", "≠"), (r"\\approx(?![A-Za-z])", "≈"),
+    (r"\\equiv(?![A-Za-z])", "≡"), (r"\\sim(?![A-Za-z])", "~"),
+    (r"\\to(?![A-Za-z])", "→"), (r"\\rightarrow(?![A-Za-z])", "→"),
+    (r"\\leftarrow(?![A-Za-z])", "←"), (r"\\Rightarrow(?![A-Za-z])", "⇒"),
+    (r"\\Leftarrow(?![A-Za-z])", "⇐"),
+    # Binary operators
+    (r"\\times(?![A-Za-z])", "×"), (r"\\cdot(?![A-Za-z])", "·"),
+    (r"\\pm(?![A-Za-z])", "±"), (r"\\mp(?![A-Za-z])", "∓"),
+    (r"\\div(?![A-Za-z])", "÷"),
+    # Misc
+    (r"\\infty(?![A-Za-z])", "∞"), (r"\\partial(?![A-Za-z])", "∂"),
+    (r"\\sum(?![A-Za-z])", "∑"), (r"\\prod(?![A-Za-z])", "∏"),
+    (r"\\int(?![A-Za-z])", "∫"),
+    (r"\\ldots(?![A-Za-z])", "…"), (r"\\dots(?![A-Za-z])", "…"),
+    # Spacing commands (drop or replace with single space)
+    (r"\\,", " "), (r"\\;", " "), (r"\\:", " "),
+    (r"\\!", ""), (r"\\ ", " "),
+    (r"\\quad(?![A-Za-z])", "  "), (r"\\qquad(?![A-Za-z])", "    "),
+    # Escaped punctuation
+    (r"\\%", "%"), (r"\\#", "#"), (r"\\&", "&"),
+    (r"\\\$", "$"), (r"\\_", "_"),
+]
+
+
+def _unwrap_command(text, cmd):
+    """Repeatedly replace `\\cmd{X}` → `X` until stable."""
+    pat = re.compile(r"\\" + cmd + r"\{([^{}]*)\}")
+    prev = None
+    while prev != text:
+        prev = text
+        text = pat.sub(r"\1", text)
+    return text
+
+
+MATH_START = ""  # Private Use Area: XML-safe
+MATH_END = ""
+
+
+def latex_to_unicode(text):
+    """Convert a LaTeX-laced markdown paragraph into plain text.
+
+    Math context is preserved with private-use sentinel characters
+    (MATH_START / MATH_END) so the downstream run-splitter only treats
+    `_X` / `^X` as subscript / superscript inside math regions; in body
+    text underscores in identifiers like `signature_analysis` survive.
+    """
+    if "$" not in text and "\\" not in text:
+        return text
+
+    # 1. Strip display-math delimiters first (keep the inner content for
+    #    best-effort linearisation), wrapping math regions with sentinels.
+    #    Then strip inline math delimiters with the same sentinel wrapping.
+    text = re.sub(r"\$\$([\s\S]+?)\$\$",
+                  lambda m: MATH_START + m.group(1) + MATH_END, text)
+    text = re.sub(r"\$([^$]+?)\$",
+                  lambda m: MATH_START + m.group(1) + MATH_END, text)
+
+    # 2. Replace token-level commands with Unicode glyphs *before* unwrapping
+    #    `\text{...}` and friends, so that `\Delta\text{BIC}` becomes
+    #    `Δ\text{BIC}` (then `ΔBIC`) rather than `\DeltaBIC` which would be
+    #    stripped wholesale by the cleanup pass.
+    for pat, repl in LATEX_TOKEN_REPLACEMENTS:
+        text = re.sub(pat, repl, text)
+
+    # 3. Unwrap formatting / text commands (innermost first via _unwrap loop).
+    for cmd in ("text", "mathbf", "mathit", "mathrm", "mathsf", "mathtt",
+                "operatorname", "emph", "textbf", "textit"):
+        text = _unwrap_command(text, cmd)
+
+    # 4. \frac{a}{b} → (a)/(b); \sqrt{x} → √(x). Apply repeatedly to handle
+    #    one level of nesting; deeper nesting is rare in this paper.
+    for _ in range(3):
+        text = re.sub(
+            r"\\t?frac\{([^{}]+)\}\{([^{}]+)\}",
+            r"(\1)/(\2)",
+            text,
+        )
+    text = re.sub(r"\\sqrt\{([^{}]+)\}", r"√(\1)", text)
+
+    # 5. TeX braces used purely for spacing/grouping: K{=}3 → K=3,
+    #    60{,}448 → 60,448, 10{,}175 → 10,175.
+    text = re.sub(r"\{([=<>+\-,])\}", r"\1", text)
+
+    # 6. Strip any remaining `\cmd{...}` (best effort) and `\cmd ` tokens.
+    text = re.sub(r"\\[a-zA-Z]+\{([^{}]*)\}", r"\1", text)
+    text = re.sub(r"\\[a-zA-Z]+(?![A-Za-z])", "", text)
+
+    # 7. Collapse runs of whitespace introduced by command stripping.
+    text = re.sub(r"[ \t]{2,}", " ", text)
+    return text
+
+
+_SUBSUP_PATTERN = re.compile(
+    r"_\{([^{}]*)\}"     # _{...}
+    r"|\^\{([^{}]*)\}"   # ^{...}
+    r"|_([A-Za-z0-9+\-])"  # _X (single token)
+    r"|\^([A-Za-z0-9+\-])"  # ^X (single token)
+)
+
+
+def _emit_plain(paragraph, text, font_name, font_size, bold, italic):
+    if not text:
+        return
+    run = paragraph.add_run(text)
+    run.font.name = font_name
+    run.font.size = font_size
+    run.bold = bold
+    run.italic = italic
+
+
+def _emit_math(paragraph, text, font_name, font_size, bold, italic):
+    """Emit `text` from a math region: split on `_X` / `_{X}` / `^X` / `^{X}`
+    and render those as Word subscripts / superscripts."""
+    if "_" not in text and "^" not in text:
+        _emit_plain(paragraph, text, font_name, font_size, bold, italic)
+        return
+    pos = 0
+    for m in _SUBSUP_PATTERN.finditer(text):
+        if m.start() > pos:
+            _emit_plain(paragraph, text[pos:m.start()],
+                        font_name, font_size, bold, italic)
+        sub_text = m.group(1) or m.group(3)
+        sup_text = m.group(2) or m.group(4)
+        if sub_text is not None:
+            run = paragraph.add_run(sub_text)
+            run.font.subscript = True
+        else:
+            run = paragraph.add_run(sup_text)
+            run.font.superscript = True
+        run.font.name = font_name
+        run.font.size = font_size
+        run.bold = bold
+        run.italic = italic
+        pos = m.end()
+    if pos < len(text):
+        _emit_plain(paragraph, text[pos:],
+                    font_name, font_size, bold, italic)
+
+
+def add_text_with_subsup(paragraph, text, font_name="Times New Roman",
+                         font_size=Pt(10), bold=False, italic=False):
+    """Add `text` to `paragraph`. Subscript/superscript handling is scoped to
+    math regions delimited by MATH_START / MATH_END sentinels (set up by
+    `latex_to_unicode`). Outside math regions, underscores and carets are
+    preserved literally so identifiers like `signature_analysis` and
+    `paper_a_results_v3.md` survive intact.
+    """
+    if MATH_START not in text:
+        _emit_math(paragraph, text, font_name, font_size, bold, italic) \
+            if False else \
+            _emit_plain(paragraph, text, font_name, font_size, bold, italic)
+        return
+
+    pos = 0
+    while pos < len(text):
+        s = text.find(MATH_START, pos)
+        if s == -1:
+            _emit_plain(paragraph, text[pos:],
+                        font_name, font_size, bold, italic)
+            break
+        if s > pos:
+            _emit_plain(paragraph, text[pos:s],
+                        font_name, font_size, bold, italic)
+        e = text.find(MATH_END, s + 1)
+        if e == -1:
+            # Unterminated math region — emit rest as plain.
+            _emit_plain(paragraph, text[s + 1:],
+                        font_name, font_size, bold, italic)
+            break
+        math_body = text[s + 1:e]
+        _emit_math(paragraph, math_body, font_name, font_size, bold, italic)
+        pos = e + 1
+
+
+# ---------------------------------------------------------------------------
+# Display-equation rendering (matplotlib mathtext → PNG → embedded image)
+# ---------------------------------------------------------------------------
+
+# matplotlib mathtext is a subset of LaTeX. A few common TeX-only macros need
+# to be substituted with mathtext-supported equivalents before parsing.
+_MATHTEXT_SUBS = [
+    (re.compile(r"\\tfrac\b"), r"\\frac"),       # text-frac → frac
+    (re.compile(r"\\dfrac\b"), r"\\frac"),       # display-frac → frac
+    (re.compile(r"\\operatorname\{([^{}]+)\}"),
+     lambda m: r"\mathrm{" + m.group(1) + "}"),  # operatorname → mathrm
+    (re.compile(r"\\,"), " "),                   # thin space
+    (re.compile(r"\\;"), " "),
+    (re.compile(r"\\!"), ""),
+]
+
+
+def _sanitise_for_mathtext(latex: str) -> str:
+    out = latex
+    for pat, repl in _MATHTEXT_SUBS:
+        out = pat.sub(repl, out)
+    return out
+
+
+def render_equation_png(latex: str, fontsize: int = 14) -> Path:
+    """Render a LaTeX math expression to a tightly-cropped PNG using
+    matplotlib mathtext, with content-addressed caching so a re-build only
+    re-renders changed equations. Returns the cached PNG path."""
+    sanitised = _sanitise_for_mathtext(latex.strip())
+    digest = hashlib.sha1(
+        (sanitised + f"|fs{fontsize}").encode("utf-8")).hexdigest()[:16]
+    out_path = EQUATION_CACHE_DIR / f"eq_{digest}.png"
+    if out_path.exists():
+        return out_path
+    fig = plt.figure(figsize=(8, 1.6))
+    fig.text(0.5, 0.5, f"${sanitised}$",
+             fontsize=fontsize, ha="center", va="center")
+    fig.savefig(str(out_path), dpi=220, bbox_inches="tight",
+                pad_inches=0.05)
+    plt.close(fig)
+    return out_path
+
+
+def add_equation_block(doc, latex: str, equation_number: int,
+                       width_inches: float = 4.5):
+    """Insert a centered display equation (rendered as PNG) followed by
+    a right-aligned equation number `(N)`. Width keeps the equation
+    visually proportional within the IEEE Access body column."""
+    img_path = render_equation_png(latex)
+    p = doc.add_paragraph()
+    p.alignment = WD_ALIGN_PARAGRAPH.CENTER
+    p.paragraph_format.space_before = Pt(6)
+    p.paragraph_format.space_after = Pt(6)
+    run = p.add_run()
+    run.add_picture(str(img_path), width=Inches(width_inches))
+    # Equation number on the same paragraph, tab-aligned to the right.
+    num_run = p.add_run(f"\t({equation_number})")
+    num_run.font.name = "Times New Roman"
+    num_run.font.size = Pt(10)
+
+
+def add_md_table(doc, table_lines):
+    rows_data = []
+    for line in table_lines:
+        cells = [c.strip() for c in line.strip("|").split("|")]
+        if not re.match(r"^[-: ]+$", cells[0]):
+            rows_data.append(cells)
+    if len(rows_data) < 2:
+        return
+    ncols = len(rows_data[0])
+    table = doc.add_table(rows=len(rows_data), cols=ncols)
+    table.style = "Table Grid"
+    for r_idx, row in enumerate(rows_data):
+        for c_idx in range(min(len(row), ncols)):
+            cell = table.rows[r_idx].cells[c_idx]
+            raw = row[c_idx]
+            # Strip markdown emphasis markers; convert LaTeX before rendering.
+            raw = re.sub(r"\*\*\*(.+?)\*\*\*", r"\1", raw)
+            raw = re.sub(r"\*\*(.+?)\*\*", r"\1", raw)
+            raw = re.sub(r"\*(.+?)\*", r"\1", raw)
+            raw = re.sub(r"`(.+?)`", r"\1", raw)
+            cell_text = latex_to_unicode(raw)
+            # Replace the default empty paragraph with one we control.
+            cell.text = ""
+            cp = cell.paragraphs[0]
+            cp.alignment = WD_ALIGN_PARAGRAPH.CENTER
+            add_text_with_subsup(
+                cp, cell_text,
+                font_name="Times New Roman",
+                font_size=Pt(8),
+                bold=(r_idx == 0),
+            )
+    doc.add_paragraph()
+
+
+def _insert_figures(doc, para_text):
+    for trigger, (fig_path, caption, width) in FIGURES.items():
+        if trigger in para_text and Path(fig_path).exists():
+            fp = doc.add_paragraph()
+            fp.alignment = WD_ALIGN_PARAGRAPH.CENTER
+            fr = fp.add_run()
+            fr.add_picture(str(fig_path), width=Inches(width))
+            cp = doc.add_paragraph()
+            cp.alignment = WD_ALIGN_PARAGRAPH.CENTER
+            cr = cp.add_run(caption)
+            cr.font.size = Pt(9)
+            cr.font.name = "Times New Roman"
+            cr.italic = True
+
+
+def process_section(doc, filepath, equation_counter=None):
+    """Process one v3 markdown section. `equation_counter` is a single-element
+    list (used as a mutable counter shared across sections) tracking the
+    running display-equation number."""
+    if equation_counter is None:
+        equation_counter = [0]
+    text = filepath.read_text(encoding="utf-8")
+    text = strip_comments(text)
+    lines = text.split("\n")
+    # Defensive blockquote handling: markdown blockquote lines (`> body`) are
+    # not rendered as Word callout blocks here, but stripping the leading
+    # `> ` keeps the body text from leaking the literal `>` and the empty
+    # `>` separator lines into the DOCX.
+    cleaned = []
+    for ln in lines:
+        s = ln.lstrip()
+        if s == ">" or s.startswith("> "):
+            cleaned.append(ln[ln.index(">") + 1:].lstrip() if "> " in ln else "")
+        else:
+            cleaned.append(ln)
+    lines = cleaned
+    i = 0
+    while i < len(lines):
+        line = lines[i]
+        stripped = line.strip()
+        if not stripped:
+            i += 1
+            continue
+        if stripped.startswith("# "):
+            h = doc.add_heading(
+                latex_to_unicode(stripped[2:]).replace(MATH_START, "").replace(MATH_END, ""),
+                level=1)
+            for run in h.runs:
+                run.font.color.rgb = RGBColor(0, 0, 0)
+            i += 1
+            continue
+        if stripped.startswith("## "):
+            h = doc.add_heading(
+                latex_to_unicode(stripped[3:]).replace(MATH_START, "").replace(MATH_END, ""),
+                level=2)
+            for run in h.runs:
+                run.font.color.rgb = RGBColor(0, 0, 0)
+            i += 1
+            continue
+        if stripped.startswith("### "):
+            h = doc.add_heading(
+                latex_to_unicode(stripped[4:]).replace(MATH_START, "").replace(MATH_END, ""),
+                level=3)
+            for run in h.runs:
+                run.font.color.rgb = RGBColor(0, 0, 0)
+            i += 1
+            continue
+        if stripped.startswith("__TABLE_CAPTION__:"):
+            caption_text = stripped[len("__TABLE_CAPTION__:"):].strip()
+            caption_text = latex_to_unicode(caption_text)
+            cp = doc.add_paragraph()
+            cp.alignment = WD_ALIGN_PARAGRAPH.CENTER
+            cp.paragraph_format.space_before = Pt(6)
+            cp.paragraph_format.space_after = Pt(2)
+            add_text_with_subsup(
+                cp, caption_text,
+                font_name="Times New Roman",
+                font_size=Pt(9),
+                bold=True,
+            )
+            i += 1
+            continue
+        if "|" in stripped and i + 1 < len(lines) and re.match(r"\s*\|[-|: ]+\|", lines[i + 1]):
+            table_lines = []
+            while i < len(lines) and "|" in lines[i]:
+                table_lines.append(lines[i])
+                i += 1
+            add_md_table(doc, table_lines)
+            continue
+        # Display math: a line starting with `$$` is treated as a single-line
+        # equation block and rendered as an embedded mathtext PNG with an
+        # auto-incrementing equation number.
+        if stripped.startswith("$$"):
+            # Accumulate until a closing $$ is found (single line in our
+            # corpus, but defensively support multi-line just in case).
+            buf = [stripped]
+            if not (stripped.count("$$") >= 2 and stripped.endswith("$$")):
+                while i + 1 < len(lines):
+                    i += 1
+                    buf.append(lines[i])
+                    if "$$" in lines[i]:
+                        break
+            joined = "\n".join(buf).strip()
+            # Strip the leading and trailing $$ delimiters and any trailing
+            # punctuation (e.g. the `,` that some equation lines end with).
+            inner = joined
+            if inner.startswith("$$"):
+                inner = inner[2:]
+            if inner.endswith("$$"):
+                inner = inner[:-2]
+            inner = inner.rstrip(", ")
+            equation_counter[0] += 1
+            try:
+                add_equation_block(doc, inner, equation_counter[0])
+            except Exception as exc:
+                # Fallback: render as plain centered Times-Roman line so the
+                # build doesn't fail on a single un-renderable equation.
+                p = doc.add_paragraph()
+                p.alignment = WD_ALIGN_PARAGRAPH.CENTER
+                run = p.add_run(f"[equation render failed: {exc}] {inner}")
+                run.font.name = "Times New Roman"
+                run.font.size = Pt(10)
+                run.italic = True
+            i += 1
+            continue
+        if re.match(r"^\d+\.\s", stripped):
+            # Manual numbering: keep the number from the markdown source and
+            # apply a hanging-indent paragraph format. Avoids python-docx's
+            # `style='List Number'` which depends on a properly-set-up
+            # numbering definition that the default Document() lacks.
+            m = re.match(r"^(\d+)\.\s+(.*)$", stripped)
+            num, content = m.group(1), m.group(2)
+            p = doc.add_paragraph()
+            p.paragraph_format.left_indent = Inches(0.4)
+            p.paragraph_format.first_line_indent = Inches(-0.25)
+            p.paragraph_format.space_after = Pt(4)
+            content = re.sub(r"\*\*\*(.+?)\*\*\*", r"\1", content)
+            content = re.sub(r"\*\*(.+?)\*\*", r"\1", content)
+            content = re.sub(r"\*(.+?)\*", r"\1", content)
+            content = re.sub(r"`(.+?)`", r"\1", content)
+            content = latex_to_unicode(content)
+            add_text_with_subsup(p, f"{num}. {content}")
+            i += 1
+            continue
+        if stripped.startswith("- "):
+            # Manual bullets with hanging indent (same rationale as numbered).
+            p = doc.add_paragraph()
+            p.paragraph_format.left_indent = Inches(0.4)
+            p.paragraph_format.first_line_indent = Inches(-0.25)
+            p.paragraph_format.space_after = Pt(4)
+            content = stripped[2:]
+            content = re.sub(r"\*\*\*(.+?)\*\*\*", r"\1", content)
+            content = re.sub(r"\*\*(.+?)\*\*", r"\1", content)
+            content = re.sub(r"\*(.+?)\*", r"\1", content)
+            content = re.sub(r"`(.+?)`", r"\1", content)
+            content = latex_to_unicode(content)
+            add_text_with_subsup(p, f"•  {content}")
+            i += 1
+            continue
+        # Regular paragraph
+        para_lines = [stripped]
+        i += 1
+        while i < len(lines):
+            nxt = lines[i].strip()
+            if (
+                not nxt
+                or nxt.startswith("#")
+                or nxt.startswith("|")
+                or nxt.startswith("- ")
+                or re.match(r"^\d+\.\s", nxt)
+            ):
+                break
+            para_lines.append(nxt)
+            i += 1
+        para_text = " ".join(para_lines)
+        para_text = re.sub(r"\*\*\*(.+?)\*\*\*", r"\1", para_text)
+        para_text = re.sub(r"\*\*(.+?)\*\*", r"\1", para_text)
+        para_text = re.sub(r"\*(.+?)\*", r"\1", para_text)
+        para_text = re.sub(r"`(.+?)`", r"\1", para_text)
+        para_text = para_text.replace("---", "\u2014")
+        para_text = latex_to_unicode(para_text)
+
+        p = doc.add_paragraph()
+        p.paragraph_format.space_after = Pt(6)
+        add_text_with_subsup(p, para_text)
+
+        _insert_figures(doc, para_text)
+
+
+def main():
+    doc = Document()
+    style = doc.styles["Normal"]
+    style.font.name = "Times New Roman"
+    style.font.size = Pt(10)
+
+    # Title page
+    p = doc.add_paragraph()
+    p.alignment = WD_ALIGN_PARAGRAPH.CENTER
+    p.paragraph_format.space_after = Pt(12)
+    run = p.add_run(
+        "Automated Identification of Non-Hand-Signed Auditor Signatures\n"
+        "in Large-Scale Financial Audit Reports:\n"
+        "A Dual-Descriptor Framework with Replication-Dominated Calibration"
+    )
+    run.font.size = Pt(16)
+    run.font.name = "Times New Roman"
+    run.bold = True
+
+    # IEEE Access uses single-anonymized review: author / affiliation
+    # / corresponding-author block must appear on the title page in the
+    # final submission. Fill these placeholders with real metadata
+    # before submitting the generated DOCX.
+    p = doc.add_paragraph()
+    p.alignment = WD_ALIGN_PARAGRAPH.CENTER
+    p.paragraph_format.space_after = Pt(6)
+    run = p.add_run("[AUTHOR NAMES — fill in before submission]")
+    run.font.size = Pt(11)
+
+    p = doc.add_paragraph()
+    p.alignment = WD_ALIGN_PARAGRAPH.CENTER
+    p.paragraph_format.space_after = Pt(6)
+    run = p.add_run("[Affiliations and corresponding-author email — fill in before submission]")
+    run.font.size = Pt(10)
+    run.italic = True
+
+    p = doc.add_paragraph()
+    p.alignment = WD_ALIGN_PARAGRAPH.CENTER
+    p.paragraph_format.space_after = Pt(20)
+    run = p.add_run("Target journal: IEEE Access (Regular Paper, single-anonymized review)")
+    run.font.size = Pt(10)
+    run.italic = True
+
+    equation_counter = [0]
+    for section_file in SECTIONS:
+        filepath = PAPER_DIR / section_file
+        if filepath.exists():
+            process_section(doc, filepath, equation_counter=equation_counter)
+        else:
+            print(f"WARNING: missing section file: {filepath}")
+
+    doc.save(str(OUTPUT))
+    print(f"Saved: {OUTPUT}")
+    _run_linter()
+
+
+def _run_linter():
+    """Run the leak linter on the freshly built DOCX. Non-fatal: prints a
+    summary line. For full output run `python3 paper/lint_paper_v3.py`."""
+    try:
+        import lint_paper_v3  # local module
+    except Exception as exc:  # pragma: no cover
+        print(f"(lint skipped: {exc})")
+        return
+    findings = lint_paper_v3.lint_docx(OUTPUT)
+    errors = sum(1 for f in findings if f.severity == "ERROR")
+    warns = sum(1 for f in findings if f.severity == "WARN")
+    infos = sum(1 for f in findings if f.severity == "INFO")
+    if errors:
+        print(f"\n[lint] {errors} ERROR finding(s) in DOCX — run "
+              f"`python3 paper/lint_paper_v3.py --docx` for details.")
+    elif warns or infos:
+        print(f"[lint] DOCX clean of ERRORs ({warns} WARN, {infos} INFO).")
+    else:
+        print("[lint] DOCX clean.")
+
+
+if __name__ == "__main__":
+    main()

paper/gemini_partner_redpen_audit_v3_19_0.md

@@ -0,0 +1,45 @@
+# Partner Red-Pen Regression Audit (v3.19.0) - Gemini 3.1 Pro
+
+
+### Overall Summary
+The authors have taken a highly rigorous and defensive route to addressing the partner's concerns. The most confusing and convoluted analytical constructs—specifically the accountant-level GMM and accountant-level BD/McCrary tests—have simply been **deleted entirely**. The surviving text has been rewritten to be direct, transparent about limitations, and free of AI-sounding filler. 
+
+Of the 11 specific lettered items (a–k) raised by the partner:
+- **8 are RESOLVED** (rewritten for clarity and precision)
+- **3 are N/A** (the underlying text/analysis was completely removed)
+- **0 are UNRESOLVED, PARTIAL, or IMPROVED**
+
+Additionally, the two overarching thematic items (Citation reality and ZH/EN alignment) are fully RESOLVED or N/A. The smallest residual set of polish required before the partner re-read is **empty**. The manuscript is clean and ready for review.
+
+---
+
+### Detailed Item-by-Item Audit
+
+#### Theme 1: Citation reality (suspected AI hallucinations)
+* **Item**: '輸入?', '有些幻覺像是研究方法', 'BD/McCrary 沒?', '引用?' (Are these hallucinated?)
+* **Status**: **RESOLVED**
+* **Citation**: `@paper/reference_verification_v3.md`, `@paper/paper_a_references_v3.md`
+* **Notes**: The authors conducted a comprehensive `WebFetch` audit of all 41 references. All statistical methods references ([37]-[41]: Hartigan, BD, McCrary, Dempster-Laird-Rubin, White) are 100% real and bibliographically accurate. The audit did catch one genuine error at ref [5] (wrong authors: "I. Hadjadj et al.") which the authors successfully fixed to "H.-H. Kao and C.-Y. Wen" in the current `paper_a_references_v3.md`.
+
+#### Theme 3: ZH/EN alignment gap
+* **Item**: '沒有跟英文嗎?比較' (no English alongside? compare) at end of III-H
+* **Status**: **N/A**
+* **Citation**: Entire manuscript
+* **Notes**: The v3.19.0 draft is now a finalized, monolingual English manuscript prepared for IEEE submission. The dual-language translation scaffolding that caused this misalignment has been removed, rendering the issue moot.
+
+#### Theme 2 & 4: Specific Prose and Numbers (The 11 Lettered Items)
+
+| Item | Partner's Red-Pen Mark | Status | Where it is addressed | Notes / Justification |
+| :--- | :--- | :--- | :--- | :--- |
+| **(a)** & **(h)** | **A1 stipulation, p.16** ('不太懂你的敘述' / entire paragraph red-circled) | **RESOLVED** | Sec III-G (`paper_a_methodology_v3.md`) | The paragraph was completely rewritten. It is no longer roundabout. It explicitly defines A1 as a "cross-year pair-existence property" and clearly lists three concrete conditions where it is *not* guaranteed (e.g., multiple template variants simultaneously, scan-stage noise). |
+| **(b)** | **Conservative structural-similarity, p.16** ('有點繞嗎?' / is it a bit roundabout?) | **RESOLVED** | Sec III-G (`paper_a_methodology_v3.md`) | Reduced to a single, highly literal sentence: "The independent minimum is unconditional on the cosine-nearest pair and is therefore the conservative structural-similarity statistic..." Extremely clear. |
+| **(c)** | **IV-G validation lead-in, p.18** ('不太懂為何陳述?' / don't follow why you say this) | **RESOLVED** | Sec IV-G (`paper_a_results_v3.md`) | The text now explicitly motivates the section: it explains that the prior capture rates are a circular "internal consistency check," so these three new analyses are needed because their "informative quantity does not depend on the threshold's absolute value." |
+| **(d)** & **(k)** | **BD/McCrary at accountant level, p.20** ('看不懂!' / '為何 accountant level 合計, 因為 component?') | **N/A** | *Removed entirely* | The authors deleted the entire accountant-level mixture analysis and accountant-level BD/McCrary test from the paper. Thresholding is now strictly signature-level, completely sidestepping this confusing narrative. |
+| **(e)** | **92.6% match rate, p.13** ('不太懂改善線' / don't follow the improvement angle) | **RESOLVED** | Sec III-D (`paper_a_methodology_v3.md`) | The "improvement angle" has been deleted. The 92.6% is now presented purely descriptively as a data processing metric, explaining that the 7.4% unmatched are "excluded for definitional reasons rather than discarded as noise." |
+| **(f)** | **0.95 cosine cut-off, p.18** ('Cut-off 對應!' / correspondence to what?) | **RESOLVED** | Sec III-K (`paper_a_methodology_v3.md`) | The text directly answers this now: "the cosine cutoff 0.95 corresponds to approximately the whole-sample Firm A P7.5 of the per-signature best-match cosine distribution..." |
+| **(g)** | **139/32 split in C1/C2 clusters, p.18** ('可能太倚加權因子!?' / too reliant on weighting factor?) | **N/A** | *Removed entirely* | Along with the rest of the accountant-level GMM (see item d/k), the C1/C2 cluster analysis and the 139/32 split have been entirely removed from the current draft. |
+| **(i)** | **Hartigan rejection-as-bimodality, p.19** ('?所以為何?' / so why?) | **RESOLVED** | Sec III-I.1 (`paper_a_methodology_v3.md`) | The text no longer falsely equates a dip-test rejection with bimodality. It correctly explains that a significant p-value simply means "more than one peak" and explains it is used only to "decide whether a KDE antimode is well-defined." |
+| **(j)** | **BIC strict-3-component upper-bound framing, p.20** (red-circled paragraph) | **RESOLVED** | Sec IV-D.3 (`paper_a_results_v3.md`) | The text abandons the tortured "upper-bound" framing and bluntly titles the subsection "A Forced Fit." It clearly states that because BIC strongly prefers 3 components, the 2-component parametric structure "is not supported by the data." |
+
+### Smallest Residual Set
+**None.** The authors did not just patch the confusing paragraphs; they systematically dropped the weakest, most complicated statistical claims (accountant-level mixtures) and grounded the remaining text in literal, descriptive language. The paper is safe, highly defensible, and ready to be sent back to the partner.

paper/gemini_review_v3_18_4.md

@@ -0,0 +1,68 @@
+# Independent Peer Review (Round 19) - Paper A v3.18.4
+
+## 1. Overall Verdict: Major Revision
+
+I recommend **Major Revision**. While v3.18.4 resolves the fabricated Appendix B paths and the cross-firm dual-descriptor arithmetic discrepancy, my independent audit found several profound new discrepancies, fabricated rationalizations, and a critical methodological flaw that survived the previous 18 review rounds.
+
+The most severe issues are:
+1. **Fabricated Rationalization for Excluded Documents:** Section IV-H claims 656 documents were excluded because they "carry only a single detected signature, for which no same-CPA pairwise comparison and therefore no best-match cosine / min dHash statistic is available." This fundamentally contradicts the pipeline's core logic (which computes maximum pairwise similarity across the *entire corpus* per CPA, not intra-document) and Section IV-D.1 (which correctly states only 15 signatures belong to singleton CPAs). The 656 documents were actually excluded because they had no CPA-matched signatures at all (`assigned_accountant IS NULL`).
+2. **Fabricated Provenance for Table XIII:** Appendix B claims Table XIII (Firm A per-year cosine distribution) is derived from `reports/accountant_similarity_analysis.json`. However, the generating script (`08_accountant_similarity_analysis.py`) neither extracts nor groups by the `year_month` field. The table's temporal data has no supporting script in the provided pipeline.
+3. **Fabricated Rationalization for Firm A Partners:** Section IV-F.2 claims "two [CPAs were] excluded for disambiguation ties" to explain the 178 vs. 180 Firm A partner split. The actual script `24_validation_recalibration.py` contains no disambiguation logic; it simply takes the set of unique CPAs successfully assigned to Firm A in the database, which happens to be 178.
+4. **Methodological Flaw in Inter-CPA Negative Anchor:** Script `21_expanded_validation.py` claims to generate ~50,000 random inter-CPA pairs for validation. However, the script artificially draws these pairs from a tiny pool of just `n=3,000` randomly selected signatures, rather than the full 168,755 corpus. This severely constrains diversity (reusing the same signatures ~33 times each) and artificially tightens the confidence intervals reported in Table X.
+
+These issues represent severe provenance, narrative, and statistical failures. The paper must undergo a major revision to correct these fabricated rationalizations and ensure the reported numbers and methodologies match the actual execution.
+
+## 2. Empirical-Claim Audit Table
+
+| Claim | Status | Audit basis / notes |
+|---|---|---|
+| 656 single-signature documents excluded because "no same-CPA pairwise comparison" is available | **FABRICATED** | Contradicts cross-document comparison logic and IV-D.1 (only 15 singleton CPAs lack comparison). The real reason is they failed CPA matching entirely. |
+| 178 Firm A CPAs in split vs 180 registry; "two excluded for disambiguation ties" | **FABRICATED** | `24_validation_recalibration.py` simply takes unique accountants with `firm=FIRM_A`. There is no disambiguation logic in the script. |
+| Table XIII (Firm A per-year cosine distribution) | **FABRICATED PROVENANCE** | App. B claims it's derived from `accountant_similarity_analysis.json`, but `08_accountant_similarity_analysis.py` doesn't extract or group by year. |
+| 50,000 inter-CPA negative pairs | **METHODOLOGICALLY FLAWED** | `21_expanded_validation.py` draws 50,000 pairs from a tiny pool of `n=3000` signatures, artificially constraining diversity. |
+| 145/50/180/35 byte-identity decomp | **VERIFIED-AGAINST-ARTIFACT** | Matches `28_byte_identity_decomposition.py`. |
+| Cross-firm convergence 42.12% vs 88.32% | **VERIFIED-AGAINST-ARTIFACT** | Denominators (65,514 and 55,922) reconcile correctly with the updated `accountants.firm` logic. |
+| 90,282 PDFs, 2013-2023, Taiwan | **VERIFIED-IN-TEXT** | Consistent across manuscript. |
+| 86,072 VLM-positive documents; 12 corrupted PDFs; final 86,071 | **VERIFIED-IN-TEXT** | Internally consistent in III-C. |
+| 182,328 extracted signatures; 168,755 CPA-matched; 13,573 unmatched | **VERIFIED-IN-TEXT** | Matches manuscript counts. |
+| 758 CPAs, 15 document types, 86.4% standard audit reports | **UNVERIFIABLE** | Plausible, but no direct packaged JSON verifies the 15/86.4% split. |
+| Qwen2.5-VL 32B, 180 DPI, first-quartile scan, temperature 0 | **UNVERIFIABLE** | No prompt/config/log artifact inspected. |
+| YOLO metrics (precision, recall, mAP) and 43.1 docs/sec throughput | **UNVERIFIABLE** | No training-results or runtime artifact in `signature_analysis/`. |
+| Same-CPA best-match N = 168,740, 15 fewer than matched due to singleton CPAs | **VERIFIED-AGAINST-ARTIFACT** | Matches dip-test report and script logic. |
+| ResNet-50 ImageNet-1K V2, 2048-d, L2 normalized | **VERIFIED-AGAINST-ARTIFACT** | Consistent with methods and ablation script. |
+| All-pairs intra/inter distribution N = 41,352,824 / 500,000; KDE crossover 0.837 | **VERIFIED-AGAINST-ARTIFACT** | Supported by formal-statistical script. |
+| Firm A dip result N=60,448, dip=0.0019, p=0.169 | **VERIFIED-AGAINST-ARTIFACT** | `15_hartigan_dip_test.py`. |
+| Beta mixture Delta BIC = 381 for Firm A; forced crossings 0.977/0.999 | **VERIFIED-AGAINST-ARTIFACT** | `17_beta_mixture_em.py`. |
+
+## 3. Methodological Soundness
+
+While the dual-descriptor design and replication-dominated anchor are fundamentally sound, there is a severe flaw in the inter-CPA negative anchor construction that must be corrected.
+**Flawed Inter-CPA Anchor Generation:** `21_expanded_validation.py` randomly selects just 3,000 feature vectors out of the 168,755 available signatures (via `load_feature_vectors_sample`), and then randomly pairs them to generate 50,000 negative samples. This means that each of the 3,000 signatures is reused in approximately 33 different pairs, artificially deflating the variance and diversity of the negative population. This compromises the tight Wilson 95% confidence intervals on FAR reported in Table X. The script should sample pairs uniformly across the entire 168,755 corpus.
+
+## 4. Narrative Discipline
+
+The manuscript's narrative discipline has improved regarding the removal of the "known-majority-positive" residue. However, the authors have resorted to fabricating rationalizations to explain simple arithmetic gaps:
+- **The 656 Document Exclusion:** Inventing a false methodological limitation ("single signature ... no same-CPA pairwise comparison") to explain a drop in document counts is unacceptable and undermines the paper's credibility, especially when the core methodology explicitly relies on cross-document matching.
+- **The 2 CPAs Exclusion:** Inventing "disambiguation ties" to explain why 178 CPAs are in the Firm A split instead of the registered 180 is similarly dishonest. If the database only successfully matched signatures to 178 Firm A CPAs, the text should state exactly that.
+
+## 5. IEEE Access Fit
+
+The work remains a strong fit for IEEE Access due to its scale and real-world application, provided the provenance and methodological issues are rectified. The journal emphasizes reproducibility, making the fabricated provenance for Table XIII and the statistical flaw in the FAR validation critical blockers for publication.
+
+## 6. Specific Actionable Revisions
+
+1. **Rewrite the 656-document exclusion explanation (Section IV-H):** State that 656 documents were excluded from the per-document classification because none of their extracted signatures could be successfully matched to a registered CPA name, not because single signatures lack cross-document comparison.
+2. **Remove the fabricated "disambiguation ties" claim (Section IV-F.2):** State simply that the 70/30 split was performed over the 178 Firm A CPAs who had successfully matched signatures in the corpus (compared to the 180 in the registry).
+3. **Provide actual script provenance for Table XIII:** Either supply the script that generates the year-by-year left-tail distribution, or remove Table XIII from the manuscript. Do not falsely attribute it to `08_accountant_similarity_analysis.py` (which does not group by year).
+4. **Fix the Inter-CPA Negative Anchor Script:** Modify `21_expanded_validation.py` to sample 50,000 pairs uniformly from the entire 168,755 matched-signature corpus, rather than from a pre-sampled subset of 3,000. Re-run and update Table X.
+5. **(Optional but recommended) Include Unverifiable Logs:** Add YOLO training logs, VLM configuration details, and the 15-document-type breakdown table to the supplementary materials so that claims in Section III-B, III-C, and III-D become verifiable.
+
+## 7. Disagreements with Codex Round-18
+
+I strongly disagree with the Round-18 Codex reviewer's conclusion that the manuscript only required a "Minor Revision." 
+- Codex completely missed that the "656 single-signature documents" explanation in Section IV-H is a fabricated rationalization that fundamentally contradicts the cross-document matching methodology correctly established elsewhere in the paper.
+- Codex blindly accepted the provenance of Table XIII (claiming it was derived from `accountant_similarity_analysis.json`) without checking that the generating script (`08_accountant_similarity_analysis.py`) contains absolutely no temporal (`year_month`) extraction or aggregation logic.
+- Codex missed the completely invented "two CPAs excluded for disambiguation ties" rationalization.
+- Codex missed the statistical flaw in `21_expanded_validation.py` where 50,000 negative pairs are artificially drawn from an overly restricted pool of only 3,000 signatures.
+
+These are significant issues involving empirical honesty and statistical validity that 18 rounds of AI review failed to catch. A Major Revision is strictly required before submission.

paper/gemini_review_v3_19_0.md

@@ -0,0 +1,45 @@
+# Independent Peer Review (Round 20) - Paper A v3.19.0
+
+## 1. Overall Verdict
+**Accept.** The authors have systematically and thoroughly resolved the four major blockers identified in the Round 19 review. The fabricated rationalizations have been entirely stripped out and replaced with honest, database-grounded explanations. The methodological flaw in the inter-CPA negative anchor has been corrected, resulting in statistically valid estimates. The manuscript now exhibits high empirical integrity and is ready for publication.
+
+## 2. Re-audit of Round-19 Findings
+
+| Round-19 finding | v3.19.0 status | Re-audit notes |
+|---|---|---|
+| Fabricated rationalization for 656-document exclusion | **RESOLVED** | The text now correctly explains that these 656 documents were excluded because none of their extracted signatures could be matched to a registered CPA name (`assigned_accountant IS NULL`), directly reflecting the filtering logic observed in `09_pdf_signature_verdict.py` (L44). |
+| Fabricated Table XIII provenance | **RESOLVED** | A new dedicated script (`29_firm_a_yearly_distribution.py`) has been introduced. It extracts and groups by the `year_month` field natively and reproduces the Table XIII data accurately. Appendix B has been updated accordingly. |
+| Fabricated 2-CPA disambiguation ties | **RESOLVED** | The text correctly identifies that the 2 missing Firm A CPAs are singletons (only one signature each). Because their `max_similarity_to_same_accountant` is undefined (NULL), they naturally drop out of the database view queried by `24_validation_recalibration.py` (L75). |
+| Methodological flaw in inter-CPA negative anchor | **RESOLVED** | `21_expanded_validation.py` was rewritten to uniformly sample 50,000 i.i.d. cross-CPA pairs from the full 168,755 matched corpus. The resulting FAR estimates and Wilson CIs in Table X are now statistically valid and methodologically sound. |
+
+## 3. Empirical-Claim Audit Table
+
+| Claim | Status | Audit basis / notes |
+|---|---|---|
+| 656 single-signature documents excluded because `assigned_accountant IS NULL` | **VERIFIED-AGAINST-ARTIFACT** | Matches `09_pdf_signature_verdict.py` filtering logic and accounts precisely for the 85,042 vs 84,386 PDF classification count difference. |
+| 178 Firm A CPAs in fold due to 2 singletons missing best-match statistics | **VERIFIED-AGAINST-ARTIFACT** | Matches SQL logic in `24_validation_recalibration.py` which explicitly requires `max_similarity_to_same_accountant IS NOT NULL`. |
+| Table XIII (Firm A per-year cosine distribution) | **VERIFIED-AGAINST-ARTIFACT** | Generated deterministically by the newly added `29_firm_a_yearly_distribution.py`. |
+| 50,000 inter-CPA negative pairs | **VERIFIED-AGAINST-ARTIFACT** | `21_expanded_validation.py` now explicitly samples uniformly from the `168k` matched corpus rather than a 3,000-row subset. |
+| Inter-CPA cosine stats (mean 0.763, P95 0.886, P99 0.915, max 0.992) | **VERIFIED-AGAINST-ARTIFACT** | Matches updated output logic generated by `21_expanded_validation.py` and cleanly reported in text. |
+| Table X FAR values (e.g. 0.0008 at 0.945, 0.0005 at 0.950) | **VERIFIED-IN-TEXT** | Plausible and updated correctly to reflect the new, unrestricted 50,000-pair draw. |
+| 145/50/180/35 byte-identity decomp | **VERIFIED-IN-TEXT** | Confirmed stable from prior artifact evaluations. |
+| Cross-firm convergence 42.12% vs 88.32% | **VERIFIED-IN-TEXT** | Confirmed stable; denominator math (55,922 Firm A signatures) reconciles natively. |
+| 90,282 PDFs, 2013-2023, Taiwan | **VERIFIED-IN-TEXT** | Consistent across the full manuscript. |
+| 86,072 VLM-positive documents; 12 corrupted PDFs; final 86,071 | **VERIFIED-IN-TEXT** | Consistent across the full manuscript. |
+| 182,328 extracted signatures; 168,755 CPA-matched; 13,573 unmatched | **VERIFIED-IN-TEXT** | Consistent across the full manuscript. |
+| 758 CPAs, 15 document types, 86.4% standard audit reports | **UNVERIFIABLE** | Plausible but no direct structured artifact evaluated. Acceptable as non-critical context. |
+| Qwen2.5-VL 32B, 180 DPI, first-quartile scan, temperature 0 | **UNVERIFIABLE** | Plausible operational config claim; acceptable for main-paper context. |
+| YOLO metrics (precision, recall, mAP) and 43.1 docs/sec throughput | **UNVERIFIABLE** | Plausible claims; acceptable for main-paper text. |
+| Same-CPA best-match N = 168,740, 15 fewer than matched due to singleton CPAs | **VERIFIED-AGAINST-ARTIFACT** | Matches SQL logic correctly excluding NULL best-match statistics. |
+
+## 4. Methodological Soundness
+Outstanding. The authors completely resolved the severe statistical flaw in the negative anchor generation. The new sampling procedure guarantees that the 50,000 negative pairs reflect the true inter-class variance of the full corpus rather than a repetitive subset, properly grounding the FAR Wilson CIs. The dual-descriptor approach, the empirical anchor choice, and the threshold characterization are solid.
+
+## 5. Narrative Discipline
+Excellent. The authors have purged the fabricated rationalizations that undermined previous versions. By plainly stating the mechanical, database-level realities (e.g., singleton records with `max_similarity_to_same_accountant IS NULL` dropping out of SQL views), the narrative is now both empirically honest and technically coherent. 
+
+## 6. IEEE Access Fit
+The manuscript is an excellent fit for IEEE Access. It presents a novel application of deep learning to a large-scale real-world problem, features strong empirical methodologies, and now possesses the rigorous provenance tracking expected of high-quality systems papers. 
+
+## 7. Specific Actionable Revisions
+None required. The manuscript is methodologically sound, narratively disciplined, and ready for publication as-is.

paper/gemini_review_v3_7.md

@@ -0,0 +1,120 @@
+# Independent Peer Review: Paper A (v3.7)
+
+**Target Venue:** IEEE Access (Regular Paper)  
+**Date:** April 21, 2026  
+**Reviewer:** Gemini CLI (6th Round Independent Review)
+
+---
+
+## 1. Overall Verdict
+
+**Verdict: Minor Revision**
+
+**Rationale:**  
+The manuscript presents a methodologically rigorous, highly sophisticated, and large-scale empirical analysis of non-hand-signed auditor signatures. Analyzing over 180,000 signatures from 90,282 audit reports is an impressive feat, and the pipeline architecture combining VLM prescreening, YOLO detection, and ResNet-50 feature extraction is fundamentally sound. The utilization of a "replication-dominated" calibration strategy—validated across both intra-firm consistency metrics and held-out cross-validation folds—represents a significant contribution to document forensics where ground-truth labeling is scarce and expensive. Furthermore, the dual-descriptor approach (using cosine similarity for semantic features and dHash for structural features) effectively resolves the ambiguity between stylistic consistency and mechanical image reproduction. The demotion of the Burgstahler-Dichev / McCrary (BD/McCrary) test to a density-smoothness diagnostic, supported by the new Appendix A, is analytically correct. 
+
+However, approaching this manuscript with a fresh perspective reveals three distinct methodological blind spots that previous review rounds missed. Specifically, the manuscript commits a statistical overclaim regarding the statistical power of the BD/McCrary test at the accountant level, it presents a mathematically tautological False Rejection Rate (FRR) evaluation that borders on reviewer-bait, and it lacks narrative guardrails around its document-level aggregation metrics. Resolving these localized issues will not alter the paper's conclusions but will significantly harden the manuscript against aggressive peer review, making it fully submission-ready for IEEE Access.
+
+---
+
+## 2. Scientific Soundness Audit
+
+### Three-Level Framework Coherence
+The separation of the analysis into signature-level, accountant-level, and auditor-year units is intellectually rigorous and highly defensible. By strictly separating the *pixel-level output quality* (signature level) from the *aggregate behavioral regime* (accountant level), the authors successfully avoid the ecological fallacy of assuming that because an individual practitioner acts in a binary fashion (hand-signing vs. stamping), the aggregate distribution of signature pixels must be neatly bimodal. The evidence compellingly demonstrates that the data forms a continuous quality degradation spectrum at the pixel level.
+
+### Firm A 'Replication-Dominated' Framing
+This is perhaps the strongest conceptual pillar of the paper. Assuming that Firm A acts as a "pure" positive class would inevitably force the thresholding model to interpret the long left tail of the cosine distribution as algorithmic noise or pipeline error. The explicit validation of Firm A as "replication-dominated but not pure"—quantified elegantly by the 139/32 split between high-replication and middle-band clusters in the accountant-level Gaussian Mixture Model (Section IV-E)—logically resolves the 92.5% capture rate without overclaiming. It is a highly defensible stance.
+
+### BD/McCrary Demotion
+Moving the BD/McCrary test from a co-equal threshold estimator to a "density-smoothness diagnostic" is the correct scientific decision. Appendix A empirically demonstrates that the test behaves exactly as one would expect when applied to a large ($N > 60,000$), smooth, heavy-tailed distribution: it detects localized non-linearities caused by histogram binning resolution rather than true mechanistic discontinuities. The theoretical tension is resolved by this demotion.
+
+### Statistical Choices
+The statistical foundations of the paper are appropriate and well-applied:
+*   **Beta/Logit-Gaussian Mixtures:** Fitting Beta mixtures via the EM algorithm is perfectly suited for bounded cosine similarity data $[0,1]$, and the logit-Gaussian cross-check serves as an excellent robustness measure against parametric misspecification.
+*   **Hartigan Dip Test:** The use of the dip test provides a rigorous, non-parametric verification of unimodality/multimodality.
+*   **Wilson Confidence Intervals:** Utilizing Wilson score intervals for the held-out validation metrics (Table XI) correctly models binomial variance, preventing zero-bound confidence interval collapse.
+
+---
+
+## 3. Numerical Consistency Cross-Check
+
+An exhaustive spot-check of the manuscript’s arithmetic, table values, and cited numbers reveals a practically flawless internal consistency. The scripts supporting the pipeline operate exactly as claimed. 
+
+*   **Table VIII:** The reported accountant-level threshold band (KDE antimode: 0.973, Beta-2: 0.979, logit-GMM-2: 0.976) matches the narrative text precisely.
+*   **Table IX:** The proportion of Firm A captures under the dual rule ($54,370 / 60,448 = 89.945\%$) correctly rounds to the reported $89.95\%$.
+*   **Table XI:** The calibration fold's operational dual rule yields $40,335 / 45,116 = 89.402\%$ (reported $89.40\%$), and the held-out fold yields $14,035 / 15,332 = 91.540\%$ (reported $91.54\%$).
+*   **Table XII:** The column sums for $N = 168,740$ match perfectly. Furthermore, the delta column balances precisely to zero ($+2,294 + 6,095 + 119 - 8,508 + 0 = 0$).
+*   **Table XIV:** Top 10% Firm A occupancy is $443 / 462 = 95.88\%$ (reported $95.9\%$), against a baseline of $1,287 / 4,629 = 27.80\%$ (reported $27.8\%$).
+*   **Table XVI:** Firm A's intra-report agreement is correctly calculated as $(26,435 + 734 + 4) / 30,222 = 89.91\%$.
+
+**Minor Narrative Clarification Required:**
+In Table III, total extracted signatures are reported as $182,328$, with $168,755$ successfully matched to CPAs. However, Table V and Table XII utilize $N = 168,740$ signatures for the all-pairs best-match analysis. This delta of $15$ signatures is mathematically implied by CPAs who possess exactly *one* signature in the entire database, rendering a "same-CPA pairwise comparison" impossible. While logically sound to anyone analyzing the pipeline closely, this microscopic $15$-signature discrepancy is exactly the kind of arithmetic artifact that distracts meticulous reviewers. 
+*Recommendation:* Add a one-sentence footnote or parenthetical to Section IV-D explicitly stating this $15$-signature delta is due to single-signature CPAs lacking a pairwise match.
+
+---
+
+## 4. Appendix A Validity
+
+The addition of Appendix A successfully and empirically justifies the main-text demotion of the BD/McCrary test. 
+
+**Strengths:**
+The argument demonstrating that the BD/McCrary transitions drift monotonically with bin width (e.g., Firm A cosine drifting across 0.987 $\rightarrow$ 0.985 $\rightarrow$ 0.980 $\rightarrow$ 0.975) is brilliant. Coupled with the observation that the Z-statistics inflate superlinearly with bin width (from $|Z| \sim 9$ at bin 0.003 to $|Z| \sim 106$ at bin 0.015), the appendix irrefutably proves that the test is interacting with the local curvature of a heavily-populated continuous distribution rather than identifying a discrete, mechanistic boundary. Table A.I is arithmetically consistent with the script's logic.
+
+**Weaknesses:**
+The interpretation paragraph overstates the implications of the accountant-level null finding. It claims that the lack of a transition at the accountant level ($N=686$) is a "robust finding that survives the bin-width sweep." As detailed in Section 6 below, a non-finding surviving a bin-width sweep in a small sample is largely a function of low statistical power, not definitive proof of a smoothly-mixed boundary.
+
+---
+
+## 5. IEEE Access Submission Readiness
+
+The manuscript is in excellent shape for submission to IEEE Access.
+*   **Scope Fit:** High. The paper sits perfectly at the intersection of applied AI, document forensics, and interdisciplinary data science, which is a core demographic for IEEE Access.
+*   **Abstract Length:** The abstract is approximately 234 words, comfortably satisfying the stringent $\leq 250$ word limit requirement.
+*   **Formatting & Structure:** The document adheres to standard IEEE double-column formatting conventions (Roman numeral sections, appropriate table/figure references).
+*   **Anonymization:** Properly handled. Author placeholders, affiliation blocks, and correspondence emails are appropriately bracketed for single-anonymized peer review.
+*   **Desk-Return Risks:** Very low. The inclusion of the ablation study (Table XVIII) and explicit baseline comparisons ensures the paper meets the journal's expectations for methodological validation.
+
+---
+
+## 6. Novel Issues and Methodological Blind Spots
+
+While the previous review rounds improved the manuscript significantly, habituation has allowed three specific narrative and statistical blind spots to persist. These are prime targets for reviewer pushback.
+
+### Issue 1: The Accountant-Level BD/McCrary Null is a Power Artifact, not Proof of Smoothness
+In Section V-B and Appendix A, the authors claim that because the BD/McCrary test yields no significant transition at the accountant level, this "pattern is consistent with a clustered but smoothly mixed accountant-level distribution." Furthermore, Section V-B states that this non-transition is "itself diagnostic of smoothness rather than a failure of the method."
+
+**The Critique:** The McCrary (2008) test relies on local linear regression smoothing. The variance of the estimator scales inversely with $N \cdot h$ (where $h$ is the bin width). With a sample size of only $N=686$ accountants, the test is severely underpowered and lacks the statistical capacity to reject the null of smoothness unless the discontinuity is an absolute, sheer cliff. Asserting that a failure to reject the null affirmatively *proves* the null is true (smoothness) is a fundamental statistical fallacy (Type II error risk). 
+*Impact:* Statistically literate reviewers will immediately flag this as an overclaim. The demotion of the test to a diagnostic is correct, but interpreting the null at $N=686$ as definitive proof of smoothness is flawed.
+
+### Issue 2: Tautological Presentation of FRR and EER (Table X)
+Table X presents a False Rejection Rate (FRR) computed against a "byte-identical" positive anchor. It reports an FRR of $0.000$ for thresholds like 0.95 and 0.973, and subsequently reports an Equal Error Rate (EER) of $\approx 0$ at cosine = 0.990.
+
+**The Critique:** By definition, byte-identical signatures have a cosine similarity asymptotically approaching 1.0 (modulo minor float/cropping artifacts). Evaluating a similarity threshold of 0.95 against inputs that are mathematically defined to score near 1.0 yields a 0% FRR trivially. It is a tautology. While the text in Section V-F attempts to caveat this ("perfect recall against this subset therefore does not generalize"), presenting it as a formal column in Table X with an EER calculation treats it as a standard biometric evaluation. There are no crossing error distributions here to warrant an EER. 
+*Impact:* This is reviewer-bait. Reviewers from the biometric or forensics domains will argue that an EER of 0 is artificially constructed. The true scientific value of Table X is purely the empirical False Acceptance Rate (FAR) derived from the 50,000 inter-CPA negatives. 
+
+### Issue 3: Document-Level Worst-Case Aggregation Narrative
+Section IV-I reports that 35.0% of documents are classified as "High-confidence non-hand-signed" and 43.8% as "Moderate-confidence." This relies on the worst-case rule defined in Section III-L (if one signature on a dual-signed report is stamped, the whole document inherits that label).
+
+**The Critique:** While this "worst-case" aggregation is highly practical for building an operational regulatory auditing tool (flagging the report for review), the narrative in IV-I presents these percentages without reminding the reader that a document might contain a mix of genuine and stamped signatures. Without immediate context, stating that nearly 80% of the market's reports are non-hand-signed invites the ecological fallacy that *both* partners are stamping. 
+*Impact:* A brief narrative safeguard is missing. Section IV-I must briefly cross-reference the intra-report agreement findings (Table XVI) to remind the reader of the composition of these documents, mitigating the risk that the reader misinterprets the document-level severity.
+
+---
+
+## 7. Final Recommendation and v3.8 Action Items
+
+The manuscript is exceptionally strong but requires a few surgical narrative adjustments to remove reviewer-bait and statistical overclaims. I recommend a **Minor Revision** encompassing the following ranked action items.
+
+### BLOCKER (Must Fix for Submission)
+1. **Revise the interpretation of the accountant-level BD/McCrary null.** 
+   *   *Action:* In Section V-B, Section VI (Conclusion), and Appendix A, remove any explicit claims that the null affirmatively proves "smoothly mixed" boundaries. 
+   *   *Replacement Phrasing:* Reframe this finding to acknowledge statistical power. For example: *"We fail to find evidence of a discontinuity at the accountant level. While this is consistent with smoothly mixed clusters, it also reflects the limited statistical power of the BD/McCrary test at smaller sample sizes ($N=686$), reinforcing its role as a diagnostic rather than a definitive estimator."*
+
+### MAJOR (Highly Recommended to Prevent Desk-Reject/Major Revision)
+2. **Reframe Table X to eliminate the tautological FRR/EER presentation.**
+   *   *Action:* Remove the Equal Error Rate (EER) calculation entirely. Add an explicit, prominent table note to Table X stating that FRR is computed against a definitionally extreme subset (byte-identical signatures), making the $0.000$ values an expected mathematical boundary check rather than an empirical discovery of real-world recall. Emphasize that the primary contribution of Table X is the FAR evaluation against the large inter-CPA negative anchor.
+
+### MINOR (Quick Wins for Readability and Precision)
+3. **Contextualize the Document-Level Aggregation (Section IV-I).**
+   *   *Action:* When presenting the 35.0% / 43.8% document-level figures in Section IV-I, explicitly remind the reader of the worst-case aggregation rule. Add a single sentence cross-referencing Table XVI's mixed-report rates to ensure the reader understands the internal composition of these flagged documents.
+4. **Clarify the 15-Signature Delta (Section IV-D / Table XII).**
+   *   *Action:* Add a one-sentence clarification explaining that the delta between the 168,755 CPA-matched signatures (Table III) and the 168,740 signatures analyzed in the all-pairs distributions (Table V/Table XII) consists of CPAs who have exactly one signature in the corpus, making intra-CPA pairwise comparison impossible. This will preempt arithmetic nitpicking by reviewers.

paper/gemini_review_v3_8.md

@@ -0,0 +1,68 @@
+# Independent Peer Review: Paper A (v3.8)
+
+**Target Venue:** IEEE Access (Regular Paper)  
+**Date:** April 21, 2026  
+**Reviewer:** Gemini CLI (7th Round Independent Review)
+
+---
+
+## 1. Overall Verdict
+
+**Verdict: Accept**
+
+**Rationale:**  
+The authors have systematically and thoroughly addressed the three critical methodological and narrative blind spots identified in the Round-6 review. The manuscript is now methodologically robust, empirically expansive, and narratively disciplined. The statistical overclaim regarding the Burgstahler-Dichev / McCrary (BD/McCrary) test's power has been corrected, tempering the prior "proof of smoothness" into a much more defensible "consistent with smoothly mixed clusters" interpretation. The tautological False Rejection Rate (FRR) and Equal Error Rate (EER) evaluations have been successfully excised from Table X, effectively removing a major piece of reviewer-bait. Furthermore, the necessary narrative guardrails surrounding the document-level worst-case aggregation and the 15-signature count discrepancy have been implemented cleanly and precisely. The manuscript is highly polished and fully ready for submission to IEEE Access.
+
+---
+
+## 2. Round-6 Follow-Up Audit
+
+In Round 6, three specific issues were flagged for revision. Below is the audit of their resolution in v3.8.
+
+### A. BD/McCrary Power-Artifact Reframe
+**Status: RESOLVED**
+
+The authors have successfully purged the "null proves smoothness" language and accurately reframed the accountant-level BD/McCrary null finding around its limited statistical power.
+*   **Results IV-D.1:** The text now explicitly states that "at $N = 686$ accountants the BD/McCrary test has limited statistical power, so a non-rejection of the smoothness null does not by itself establish smoothness."
+*   **Results IV-E:** The analysis correctly notes that the lack of a transition is "consistent with---though, at $N = 686$, not sufficient to affirmatively establish---clustered-but-smoothly-mixed accountant-level aggregates."
+*   **Discussion V-B:** The framing is excellent: "the BD null alone cannot affirmatively establish smoothness---only fail to falsify it---and our substantive claim of smoothly-mixed clustering rests on the joint weight of the GMM fit, the dip test, and the BD null rather than on the BD null alone."
+*   **Discussion V-G (Limitations):** A new, dedicated limitation explicitly highlights that the test "cannot reliably detect anything less than a sharp cliff-type density discontinuity" at this sample size.
+*   **Conclusion:** Symmetrically updated to note that the test "cannot affirmatively establish smoothness, but its non-transition is consistent with the smoothly-mixed cluster boundaries."
+*   **Appendix A:** Concludes perfectly that failure to reject the null "constrains the data only to distributions whose between-cluster transitions are gradual *enough* to escape the test's sensitivity at that sample size."
+
+The rewrite is exceptionally clean. It does not feel awkward or bolted-on. By anchoring the smoothly-mixed claim on the *joint weight* of the GMM, the dip test, and the BD null, the authors maintain the strength of their conclusion without committing a Type II error fallacy.
+
+### B. Table X EER/FRR Removal
+**Status: RESOLVED**
+
+The tautological presentation of FRR against the byte-identical positive anchor has been entirely resolved.
+*   **Table X:** The EER row and FRR column have been deleted. The table is now properly framed as an evaluation of False Acceptance Rate (FAR) against the 50,000 inter-CPA negative pairs.
+*   **Table Note:** A clear, unambiguous table note has been added explaining *why* FRR is omitted ("the byte-identical subset has cosine $\approx 1$ by construction, so FRR against that subset is trivially $0$ at every threshold below $1$").
+*   **Methodology III-K & Results IV-G.1:** Both sections now synchronize with this logic, describing the byte-identical set as a "conservative subset" and correctly noting that an EER calculation would be an "arithmetic tautology rather than biometric performance."
+
+This change significantly hardens the paper. By preempting the obvious critique from biometric/forensic reviewers, the authors project statistical maturity.
+
+### C. Section IV-I Narrative Safeguard & 15-Signature Footnote
+**Status: RESOLVED**
+
+Both minor narrative omissions have been addressed exactly as requested.
+*   **Section IV-I Narrative Safeguard:** Right before Table XVII, the authors added a robust clarifying paragraph: "We emphasize that the document-level proportions below reflect the *worst-case aggregation rule*... Document-level rates therefore bound the share of reports in which *at least one* signature is non-hand-signed rather than the share in which *both* are." The explicit cross-reference to the intra-report agreement analysis in Table XVI completely defuses the risk of ecological fallacy.
+*   **15-Signature Footnote:** In Section IV-D, the text now clearly accounts for the discrepancy: "The $N = 168{,}740$ count used in Table V... is $15$ signatures smaller than the $168{,}755$ CPA-matched count reported in Table III: these $15$ signatures belong to CPAs with exactly one signature in the entire corpus, for whom no same-CPA pairwise best-match statistic can be computed..." This effectively closes the arithmetic loop.
+
+---
+
+## 3. New Findings in v3.8
+
+The rewrites in v3.8 are highly successful and introduce no new regressions or inconsistencies. 
+
+The primary concern when hedging a statistical claim is that the resulting language will create tension with other sections of the paper that still rely on the original, stronger claim. The authors avoided this trap brilliantly. By repeatedly stating that the conclusion of "smoothly-mixed clusters" rests on the *convergence* of the Gaussian Mixture Model (GMM) fit, the Hartigan dip test, and the BD/McCrary null—rather than the BD/McCrary null alone—the paper's thesis remains intact and fully supported. 
+
+The only minor artifact of the rewrite is a slight repetitiveness regarding the "$N=686$ limited power" caveat, which appears in IV-D.1, IV-E, V-B, V-G, the Conclusion, and Appendix A. However, in the context of academic publishing where reviewers frequently read sections non-linearly, this repetition is a feature, not a bug. It ensures the caveat is encountered regardless of how a reader approaches the text. The BD/McCrary claim is now perfectly calibrated: it contributes diagnostic value without being overburdened.
+
+---
+
+## 4. Final Submission Readiness
+
+**v3.8 is fully submission-ready.** 
+
+The manuscript requires no further revisions (a v3.9 is not warranted). The paper presents a novel, large-scale, technically sophisticated pipeline that addresses a genuine gap in the document forensics literature. The methodological defenses—particularly the replication-dominated calibration strategy and the convergent threshold framework—are constructed to withstand the most rigorous peer review. The authors should proceed to submit to IEEE Access immediately.

paper/generate_paper_figures.py

@@ -0,0 +1,392 @@
+#!/usr/bin/env python3
+"""
+Generate all figures for Paper A (IEEE TAI submission).
+Outputs to /Volumes/NV2/PDF-Processing/signature-analysis/paper_figures/
+"""
+
+import numpy as np
+import sqlite3
+import json
+import matplotlib
+matplotlib.use('Agg')
+import matplotlib.pyplot as plt
+import matplotlib.patches as mpatches
+from matplotlib.patches import FancyBboxPatch, FancyArrowPatch
+from collections import defaultdict
+from pathlib import Path
+
+# Config
+DB_PATH = '/Volumes/NV2/PDF-Processing/signature-analysis/signature_analysis.db'
+ABLATION_PATH = '/Volumes/NV2/PDF-Processing/signature-analysis/ablation/ablation_results.json'
+OUTPUT_DIR = Path('/Volumes/NV2/PDF-Processing/signature-analysis/paper_figures')
+OUTPUT_DIR.mkdir(parents=True, exist_ok=True)
+
+RANDOM_SEED = 42
+np.random.seed(RANDOM_SEED)
+
+# IEEE formatting
+plt.rcParams.update({
+    'font.family': 'serif',
+    'font.serif': ['Times New Roman', 'DejaVu Serif'],
+    'font.size': 9,
+    'axes.labelsize': 10,
+    'axes.titlesize': 10,
+    'xtick.labelsize': 8,
+    'ytick.labelsize': 8,
+    'legend.fontsize': 8,
+    'figure.dpi': 300,
+    'savefig.dpi': 300,
+    'savefig.bbox': 'tight',
+    'savefig.pad_inches': 0.05,
+})
+
+# IEEE column widths
+COL_WIDTH = 3.5  # single column inches
+FULL_WIDTH = 7.16  # full page width inches
+
+
+def load_signature_data():
+    """Load per-signature best-match similarities and accountant info."""
+    conn = sqlite3.connect(DB_PATH)
+    cur = conn.cursor()
+
+    cur.execute('''
+        SELECT s.assigned_accountant, s.max_similarity_to_same_accountant, a.firm
+        FROM signatures s
+        LEFT JOIN accountants a ON s.assigned_accountant = a.name
+        WHERE s.max_similarity_to_same_accountant IS NOT NULL
+        AND s.assigned_accountant IS NOT NULL
+    ''')
+    rows = cur.fetchall()
+    conn.close()
+
+    data = {
+        'accountants': [r[0] for r in rows],
+        'max_sims': np.array([r[1] for r in rows]),
+        'firms': [r[2] for r in rows],
+    }
+    return data
+
+
+def load_intra_inter_from_features():
+    """Compute intra/inter class distributions from feature vectors."""
+    print("Loading features for intra/inter distributions...")
+    conn = sqlite3.connect(DB_PATH)
+    cur = conn.cursor()
+
+    cur.execute('''
+        SELECT assigned_accountant, feature_vector
+        FROM signatures
+        WHERE feature_vector IS NOT NULL AND assigned_accountant IS NOT NULL
+    ''')
+    rows = cur.fetchall()
+    conn.close()
+
+    acct_groups = defaultdict(list)
+    features_list = []
+    accountants = []
+    for r in rows:
+        feat = np.frombuffer(r[1], dtype=np.float32)
+        idx = len(features_list)
+        features_list.append(feat)
+        accountants.append(r[0])
+        acct_groups[r[0]].append(idx)
+
+    features = np.array(features_list)
+    print(f"  Loaded {len(features)} signatures, {len(acct_groups)} accountants")
+
+    # Intra-class
+    print("  Computing intra-class...")
+    intra_sims = []
+    for acct, indices in acct_groups.items():
+        if len(indices) < 3:
+            continue
+        vecs = features[indices]
+        sim_matrix = vecs @ vecs.T
+        n = len(indices)
+        triu_idx = np.triu_indices(n, k=1)
+        intra_sims.extend(sim_matrix[triu_idx].tolist())
+    intra_sims = np.array(intra_sims)
+    print(f"  Intra-class: {len(intra_sims):,} pairs")
+
+    # Inter-class
+    print("  Computing inter-class...")
+    all_acct_list = list(acct_groups.keys())
+    inter_sims = []
+    for _ in range(500_000):
+        a1, a2 = np.random.choice(len(all_acct_list), 2, replace=False)
+        i1 = np.random.choice(acct_groups[all_acct_list[a1]])
+        i2 = np.random.choice(acct_groups[all_acct_list[a2]])
+        sim = float(features[i1] @ features[i2])
+        inter_sims.append(sim)
+    inter_sims = np.array(inter_sims)
+    print(f"  Inter-class: {len(inter_sims):,} pairs")
+
+    return intra_sims, inter_sims
+
+
+def fig1_pipeline(output_path):
+    """Fig 1: Pipeline architecture diagram."""
+    print("Generating Fig 1: Pipeline...")
+
+    fig, ax = plt.subplots(1, 1, figsize=(FULL_WIDTH, 1.8))
+    ax.set_xlim(0, 10)
+    ax.set_ylim(0, 2)
+    ax.axis('off')
+
+    # Stages
+    stages = [
+        ("90,282\nPDFs", "#E3F2FD"),
+        ("VLM\nPre-screen", "#BBDEFB"),
+        ("YOLO\nDetection", "#90CAF9"),
+        ("ResNet-50\nFeatures", "#64B5F6"),
+        ("Cosine +\npHash", "#42A5F5"),
+        ("Calibration\n& Classify", "#1E88E5"),
+    ]
+
+    annotations = [
+        "86,072 docs",
+        "182,328 sigs",
+        "2048-dim",
+        "Dual verify",
+        "Verdicts",
+    ]
+
+    box_w = 1.3
+    box_h = 1.0
+    gap = 0.38
+    start_x = 0.15
+    y_center = 1.0
+
+    for i, (label, color) in enumerate(stages):
+        x = start_x + i * (box_w + gap)
+        box = FancyBboxPatch(
+            (x, y_center - box_h/2), box_w, box_h,
+            boxstyle="round,pad=0.1",
+            facecolor=color, edgecolor='#1565C0', linewidth=1.2
+        )
+        ax.add_patch(box)
+        ax.text(x + box_w/2, y_center, label,
+                ha='center', va='center', fontsize=8, fontweight='bold',
+                color='#0D47A1' if i < 3 else 'white')
+
+        # Arrow + annotation
+        if i < len(stages) - 1:
+            arrow_x = x + box_w + 0.02
+            ax.annotate('', xy=(arrow_x + gap - 0.04, y_center),
+                       xytext=(arrow_x, y_center),
+                       arrowprops=dict(arrowstyle='->', color='#1565C0', lw=1.5))
+            ax.text(arrow_x + gap/2, y_center - 0.62, annotations[i],
+                   ha='center', va='top', fontsize=6.5, color='#555555', style='italic')
+
+    plt.savefig(output_path, format='png')
+    plt.savefig(output_path.with_suffix('.pdf'), format='pdf')
+    plt.close()
+    print(f"  Saved: {output_path}")
+
+
+def fig2_intra_inter_kde(intra_sims, inter_sims, output_path):
+    """Fig 2: Intra vs Inter class cosine similarity distributions."""
+    print("Generating Fig 2: Intra vs Inter KDE...")
+    from scipy.stats import gaussian_kde
+
+    fig, ax = plt.subplots(1, 1, figsize=(COL_WIDTH, 2.5))
+
+    x_grid = np.linspace(0.3, 1.0, 500)
+
+    kde_intra = gaussian_kde(intra_sims, bw_method=0.02)
+    kde_inter = gaussian_kde(inter_sims, bw_method=0.02)
+
+    y_intra = kde_intra(x_grid)
+    y_inter = kde_inter(x_grid)
+
+    ax.fill_between(x_grid, y_intra, alpha=0.3, color='#E53935', label='Intra-class (same CPA)')
+    ax.fill_between(x_grid, y_inter, alpha=0.3, color='#1E88E5', label='Inter-class (diff. CPA)')
+    ax.plot(x_grid, y_intra, color='#C62828', linewidth=1.5)
+    ax.plot(x_grid, y_inter, color='#1565C0', linewidth=1.5)
+
+    # Find crossover
+    diff = y_intra - y_inter
+    sign_changes = np.where(np.diff(np.sign(diff)))[0]
+    crossovers = x_grid[sign_changes]
+    valid = crossovers[(crossovers > 0.5) & (crossovers < 1.0)]
+    if len(valid) > 0:
+        xover = valid[-1]
+        ax.axvline(x=xover, color='#4CAF50', linestyle='--', linewidth=1.2, alpha=0.8)
+        ax.text(xover + 0.01, ax.get_ylim()[1] * 0.85, f'KDE crossover\n= {xover:.3f}',
+                fontsize=7, color='#2E7D32', va='top')
+
+    ax.set_xlabel('Cosine Similarity')
+    ax.set_ylabel('Density')
+    ax.legend(loc='upper left', framealpha=0.9)
+    ax.set_xlim(0.35, 1.0)
+    ax.spines['top'].set_visible(False)
+    ax.spines['right'].set_visible(False)
+
+    plt.tight_layout()
+    plt.savefig(output_path, format='png')
+    plt.savefig(output_path.with_suffix('.pdf'), format='pdf')
+    plt.close()
+    print(f"  Saved: {output_path}")
+
+
+def fig3_firm_a_calibration(data, output_path):
+    """Fig 3: Firm A calibration - per-signature best match distribution."""
+    print("Generating Fig 3: Firm A Calibration...")
+    from scipy.stats import gaussian_kde
+
+    firm_a_mask = np.array([f == '勤業眾信聯合' for f in data['firms']])
+    non_firm_a_mask = ~firm_a_mask
+
+    firm_a_sims = data['max_sims'][firm_a_mask]
+    others_sims = data['max_sims'][non_firm_a_mask]
+
+    fig, ax = plt.subplots(1, 1, figsize=(COL_WIDTH, 2.5))
+
+    x_grid = np.linspace(0.5, 1.0, 500)
+
+    kde_a = gaussian_kde(firm_a_sims, bw_method=0.015)
+    kde_others = gaussian_kde(others_sims, bw_method=0.015)
+
+    y_a = kde_a(x_grid)
+    y_others = kde_others(x_grid)
+
+    ax.fill_between(x_grid, y_a, alpha=0.35, color='#E53935',
+                    label=f'Firm A (known replication, n={len(firm_a_sims):,})')
+    ax.fill_between(x_grid, y_others, alpha=0.25, color='#78909C',
+                    label=f'Other CPAs (n={len(others_sims):,})')
+    ax.plot(x_grid, y_a, color='#C62828', linewidth=1.5)
+    ax.plot(x_grid, y_others, color='#546E7A', linewidth=1.5)
+
+    # Mark key statistics
+    p1 = np.percentile(firm_a_sims, 1)
+    ax.axvline(x=p1, color='#E53935', linestyle=':', linewidth=1, alpha=0.7)
+    ax.text(p1 - 0.01, ax.get_ylim()[1] * 0.5 if ax.get_ylim()[1] > 0 else 10,
+            f'Firm A\n1st pct\n= {p1:.3f}', fontsize=6.5, color='#C62828',
+            ha='right', va='center')
+
+    mean_a = firm_a_sims.mean()
+    ax.axvline(x=mean_a, color='#E53935', linestyle='--', linewidth=1, alpha=0.7)
+
+    ax.set_xlabel('Per-Signature Best-Match Cosine Similarity')
+    ax.set_ylabel('Density')
+    ax.legend(loc='upper left', framealpha=0.9, fontsize=7)
+    ax.set_xlim(0.5, 1.005)
+    ax.spines['top'].set_visible(False)
+    ax.spines['right'].set_visible(False)
+
+    plt.tight_layout()
+    plt.savefig(output_path, format='png')
+    plt.savefig(output_path.with_suffix('.pdf'), format='pdf')
+    plt.close()
+    print(f"  Saved: {output_path}")
+
+
+def fig4_ablation(output_path):
+    """Fig 4: Ablation backbone comparison."""
+    print("Generating Fig 4: Ablation...")
+
+    with open(ABLATION_PATH) as f:
+        results = json.load(f)
+
+    backbones = ['ResNet-50\n(2048-d)', 'VGG-16\n(4096-d)', 'EfficientNet-B0\n(1280-d)']
+    backbone_keys = ['resnet50', 'vgg16', 'efficientnet_b0']
+    results_map = {r['backbone']: r for r in results}
+
+    fig, axes = plt.subplots(1, 3, figsize=(FULL_WIDTH, 2.2))
+
+    colors = ['#1E88E5', '#FFA726', '#66BB6A']
+
+    # Panel (a): Intra/Inter means with error bars
+    ax = axes[0]
+    x = np.arange(len(backbones))
+    width = 0.35
+
+    intra_means = [results_map[k]['intra']['mean'] for k in backbone_keys]
+    intra_stds = [results_map[k]['intra']['std'] for k in backbone_keys]
+    inter_means = [results_map[k]['inter']['mean'] for k in backbone_keys]
+    inter_stds = [results_map[k]['inter']['std'] for k in backbone_keys]
+
+    bars1 = ax.bar(x - width/2, intra_means, width, yerr=intra_stds,
+                   color='#E53935', alpha=0.7, label='Intra', capsize=3, error_kw={'linewidth': 0.8})
+    bars2 = ax.bar(x + width/2, inter_means, width, yerr=inter_stds,
+                   color='#1E88E5', alpha=0.7, label='Inter', capsize=3, error_kw={'linewidth': 0.8})
+
+    ax.set_ylabel('Cosine Similarity')
+    ax.set_xticks(x)
+    ax.set_xticklabels(backbones, fontsize=7)
+    ax.legend(fontsize=7)
+    ax.set_ylim(0.5, 1.0)
+    ax.set_title('(a) Mean Similarity', fontsize=9)
+    ax.spines['top'].set_visible(False)
+    ax.spines['right'].set_visible(False)
+
+    # Panel (b): Cohen's d
+    ax = axes[1]
+    cohens_ds = [results_map[k]['cohens_d'] for k in backbone_keys]
+    bars = ax.bar(x, cohens_ds, 0.5, color=colors, alpha=0.8, edgecolor='#333', linewidth=0.5)
+    ax.set_ylabel("Cohen's d")
+    ax.set_xticks(x)
+    ax.set_xticklabels(backbones, fontsize=7)
+    ax.set_ylim(0, 0.9)
+    ax.set_title("(b) Cohen's d", fontsize=9)
+    ax.spines['top'].set_visible(False)
+    ax.spines['right'].set_visible(False)
+
+    # Add value labels
+    for bar, val in zip(bars, cohens_ds):
+        ax.text(bar.get_x() + bar.get_width()/2, bar.get_height() + 0.02,
+                f'{val:.3f}', ha='center', va='bottom', fontsize=7, fontweight='bold')
+
+    # Panel (c): KDE crossover
+    ax = axes[2]
+    crossovers = [results_map[k]['kde_crossover'] for k in backbone_keys]
+    bars = ax.bar(x, crossovers, 0.5, color=colors, alpha=0.8, edgecolor='#333', linewidth=0.5)
+    ax.set_ylabel('KDE Crossover')
+    ax.set_xticks(x)
+    ax.set_xticklabels(backbones, fontsize=7)
+    ax.set_ylim(0.7, 0.9)
+    ax.set_title('(c) KDE Crossover', fontsize=9)
+    ax.spines['top'].set_visible(False)
+    ax.spines['right'].set_visible(False)
+
+    for bar, val in zip(bars, crossovers):
+        ax.text(bar.get_x() + bar.get_width()/2, bar.get_height() + 0.005,
+                f'{val:.3f}', ha='center', va='bottom', fontsize=7, fontweight='bold')
+
+    plt.tight_layout()
+    plt.savefig(output_path, format='png')
+    plt.savefig(output_path.with_suffix('.pdf'), format='pdf')
+    plt.close()
+    print(f"  Saved: {output_path}")
+
+
+def main():
+    print("=" * 60)
+    print("Generating Paper Figures")
+    print("=" * 60)
+
+    # Fig 1: Pipeline (no data needed)
+    fig1_pipeline(OUTPUT_DIR / 'fig1_pipeline.png')
+
+    # Fig 4: Ablation (uses pre-computed JSON)
+    fig4_ablation(OUTPUT_DIR / 'fig4_ablation.png')
+
+    # Load data for Fig 2 & 3
+    data = load_signature_data()
+    print(f"Loaded {len(data['max_sims']):,} signatures")
+
+    # Fig 3: Firm A calibration (uses per-signature best match from DB)
+    fig3_firm_a_calibration(data, OUTPUT_DIR / 'fig3_firm_a_calibration.png')
+
+    # Fig 2: Intra vs Inter (needs full feature vectors)
+    intra_sims, inter_sims = load_intra_inter_from_features()
+    fig2_intra_inter_kde(intra_sims, inter_sims, OUTPUT_DIR / 'fig2_intra_inter_kde.png')
+
+    print("\n" + "=" * 60)
+    print("All figures saved to:", OUTPUT_DIR)
+    print("=" * 60)
+
+
+if __name__ == "__main__":
+    main()

paper/generate_recalibrated_report.py

@@ -0,0 +1,413 @@
+#!/usr/bin/env python3
+"""
+Generate complete PDF-level Excel report with Firm A-calibrated dual-method classification.
+Output: One row per PDF with identification, CPA info, detection stats,
+        cosine similarity, dHash distance, and new dual-method verdicts.
+"""
+
+import sqlite3
+import numpy as np
+import openpyxl
+from openpyxl.styles import Font, PatternFill, Alignment, Border, Side
+from collections import defaultdict
+from pathlib import Path
+from datetime import datetime
+
+DB_PATH = '/Volumes/NV2/PDF-Processing/signature-analysis/signature_analysis.db'
+OUTPUT_DIR = Path('/Volumes/NV2/PDF-Processing/signature-analysis/recalibrated')
+OUTPUT_DIR.mkdir(parents=True, exist_ok=True)
+OUTPUT_PATH = OUTPUT_DIR / 'pdf_level_recalibrated_report.xlsx'
+
+FIRM_A = '勤業眾信聯合'
+KDE_CROSSOVER = 0.837
+COSINE_HIGH = 0.95
+PHASH_HIGH_CONF = 5
+PHASH_MOD_CONF = 15
+
+
+def load_all_data():
+    """Load all signature data grouped by PDF."""
+    conn = sqlite3.connect(DB_PATH)
+    cur = conn.cursor()
+
+    # Get all signatures with their stats
+    cur.execute('''
+        SELECT s.signature_id, s.image_filename, s.assigned_accountant,
+               s.max_similarity_to_same_accountant,
+               s.phash_distance_to_closest,
+               s.ssim_to_closest,
+               s.signature_verdict,
+               a.firm, a.risk_level, a.mean_similarity, a.ratio_gt_95,
+               a.signature_count
+        FROM signatures s
+        LEFT JOIN accountants a ON s.assigned_accountant = a.name
+        WHERE s.assigned_accountant IS NOT NULL
+    ''')
+    rows = cur.fetchall()
+
+    # Get PDF metadata from the master index or derive from filenames
+    # Also get YOLO detection info
+    cur.execute('''
+        SELECT s.image_filename,
+               s.detection_confidence
+        FROM signatures s
+    ''')
+    detection_rows = cur.fetchall()
+    detection_conf = {r[0]: r[1] for r in detection_rows}
+
+    conn.close()
+
+    # Group by PDF
+    pdf_data = defaultdict(lambda: {
+        'signatures': [],
+        'accountants': set(),
+        'firms': set(),
+    })
+
+    for r in rows:
+        sig_id, filename, accountant, cosine, phash, ssim, verdict, \
+            firm, risk, mean_sim, ratio95, sig_count = r
+
+        # Extract PDF key from filename
+        # Format: {company}_{year}_{type}_page{N}_sig{M}.png or similar
+        parts = filename.rsplit('_sig', 1)
+        pdf_key = parts[0] if len(parts) > 1 else filename.rsplit('.', 1)[0]
+        page_parts = pdf_key.rsplit('_page', 1)
+        pdf_key = page_parts[0] if len(page_parts) > 1 else pdf_key
+
+        pdf_data[pdf_key]['signatures'].append({
+            'sig_id': sig_id,
+            'filename': filename,
+            'accountant': accountant,
+            'cosine': cosine,
+            'phash': phash,
+            'ssim': ssim,
+            'old_verdict': verdict,
+            'firm': firm,
+            'risk_level': risk,
+            'acct_mean_sim': mean_sim,
+            'acct_ratio_95': ratio95,
+            'acct_sig_count': sig_count,
+            'detection_conf': detection_conf.get(filename),
+        })
+        if accountant:
+            pdf_data[pdf_key]['accountants'].add(accountant)
+        if firm:
+            pdf_data[pdf_key]['firms'].add(firm)
+
+    print(f"Loaded {sum(len(v['signatures']) for v in pdf_data.values()):,} signatures across {len(pdf_data):,} PDFs")
+    return pdf_data
+
+
+def classify_dual_method(max_cosine, min_phash):
+    """New dual-method classification with Firm A-calibrated thresholds."""
+    if max_cosine is None:
+        return 'unknown', 'none'
+
+    if max_cosine > COSINE_HIGH:
+        if min_phash is not None and min_phash <= PHASH_HIGH_CONF:
+            return 'high_confidence_replication', 'high'
+        elif min_phash is not None and min_phash <= PHASH_MOD_CONF:
+            return 'moderate_confidence_replication', 'medium'
+        else:
+            return 'high_style_consistency', 'low'
+    elif max_cosine > KDE_CROSSOVER:
+        return 'uncertain', 'low'
+    else:
+        return 'likely_genuine', 'medium'
+
+
+def build_report(pdf_data):
+    """Build Excel report."""
+    wb = openpyxl.Workbook()
+    ws = wb.active
+    ws.title = "PDF-Level Report"
+
+    # Define columns
+    columns = [
+        # Group A: PDF Identification (Blue)
+        ('pdf_key', 'PDF Key'),
+        ('n_signatures', '# Signatures'),
+
+        # Group B: CPA Info (Green)
+        ('accountant_1', 'CPA 1 Name'),
+        ('accountant_2', 'CPA 2 Name'),
+        ('firm_1', 'Firm 1'),
+        ('firm_2', 'Firm 2'),
+        ('is_firm_a', 'Is Firm A'),
+
+        # Group C: Detection (Yellow)
+        ('avg_detection_conf', 'Avg Detection Conf'),
+
+        # Group D: Cosine Similarity - Sig 1 (Red)
+        ('sig1_cosine', 'Sig1 Max Cosine'),
+        ('sig1_cosine_verdict', 'Sig1 Cosine Verdict'),
+        ('sig1_acct_mean', 'Sig1 CPA Mean Sim'),
+        ('sig1_acct_ratio95', 'Sig1 CPA >0.95 Ratio'),
+        ('sig1_acct_count', 'Sig1 CPA Sig Count'),
+
+        # Group E: Cosine Similarity - Sig 2 (Purple)
+        ('sig2_cosine', 'Sig2 Max Cosine'),
+        ('sig2_cosine_verdict', 'Sig2 Cosine Verdict'),
+        ('sig2_acct_mean', 'Sig2 CPA Mean Sim'),
+        ('sig2_acct_ratio95', 'Sig2 CPA >0.95 Ratio'),
+        ('sig2_acct_count', 'Sig2 CPA Sig Count'),
+
+        # Group F: dHash Distance (Orange)
+        ('min_phash', 'Min dHash Distance'),
+        ('max_phash', 'Max dHash Distance'),
+        ('avg_phash', 'Avg dHash Distance'),
+        ('sig1_phash', 'Sig1 dHash Distance'),
+        ('sig2_phash', 'Sig2 dHash Distance'),
+
+        # Group G: SSIM (for reference only) (Gray)
+        ('max_ssim', 'Max SSIM'),
+        ('avg_ssim', 'Avg SSIM'),
+
+        # Group H: Dual-Method Classification (Dark Blue)
+        ('dual_verdict', 'Dual-Method Verdict'),
+        ('dual_confidence', 'Confidence Level'),
+        ('max_cosine', 'PDF Max Cosine'),
+        ('pdf_min_phash', 'PDF Min dHash'),
+
+        # Group I: CPA Risk (Teal)
+        ('sig1_risk', 'Sig1 CPA Risk Level'),
+        ('sig2_risk', 'Sig2 CPA Risk Level'),
+    ]
+
+    col_keys = [c[0] for c in columns]
+    col_names = [c[1] for c in columns]
+
+    # Header styles
+    header_fill = PatternFill(start_color='1F4E79', end_color='1F4E79', fill_type='solid')
+    header_font = Font(name='Arial', size=9, bold=True, color='FFFFFF')
+    data_font = Font(name='Arial', size=9)
+    thin_border = Border(
+        left=Side(style='thin'),
+        right=Side(style='thin'),
+        top=Side(style='thin'),
+        bottom=Side(style='thin'),
+    )
+
+    # Group colors
+    group_colors = {
+        'A': 'D6E4F0',  # Blue - PDF ID
+        'B': 'D9E2D0',  # Green - CPA
+        'C': 'FFF2CC',  # Yellow - Detection
+        'D': 'F4CCCC',  # Red - Cosine Sig1
+        'E': 'E1D5E7',  # Purple - Cosine Sig2
+        'F': 'FFE0B2',  # Orange - dHash
+        'G': 'E0E0E0',  # Gray - SSIM
+        'H': 'B3D4FC',  # Dark Blue - Dual method
+        'I': 'B2DFDB',  # Teal - Risk
+    }
+
+    group_ranges = {
+        'A': (0, 2), 'B': (2, 7), 'C': (7, 8),
+        'D': (8, 13), 'E': (13, 18), 'F': (18, 23),
+        'G': (23, 25), 'H': (25, 29), 'I': (29, 31),
+    }
+
+    # Write header
+    for col_idx, name in enumerate(col_names, 1):
+        cell = ws.cell(row=1, column=col_idx, value=name)
+        cell.font = header_font
+        cell.fill = header_fill
+        cell.alignment = Alignment(horizontal='center', wrap_text=True)
+        cell.border = thin_border
+
+    # Process PDFs
+    row_idx = 2
+    verdict_counts = defaultdict(int)
+    firm_a_counts = defaultdict(int)
+
+    for pdf_key, pdata in sorted(pdf_data.items()):
+        sigs = pdata['signatures']
+        if not sigs:
+            continue
+
+        # Sort signatures by position (sig1, sig2)
+        sigs_sorted = sorted(sigs, key=lambda s: s['filename'])
+        sig1 = sigs_sorted[0] if len(sigs_sorted) > 0 else None
+        sig2 = sigs_sorted[1] if len(sigs_sorted) > 1 else None
+
+        # Compute PDF-level aggregates
+        cosines = [s['cosine'] for s in sigs if s['cosine'] is not None]
+        phashes = [s['phash'] for s in sigs if s['phash'] is not None]
+        ssims = [s['ssim'] for s in sigs if s['ssim'] is not None]
+        confs = [s['detection_conf'] for s in sigs if s['detection_conf'] is not None]
+
+        max_cosine = max(cosines) if cosines else None
+        min_phash = min(phashes) if phashes else None
+        max_phash = max(phashes) if phashes else None
+        avg_phash = np.mean(phashes) if phashes else None
+        max_ssim = max(ssims) if ssims else None
+        avg_ssim = np.mean(ssims) if ssims else None
+        avg_conf = np.mean(confs) if confs else None
+
+        is_firm_a = FIRM_A in pdata['firms']
+
+        # Dual-method classification
+        verdict, confidence = classify_dual_method(max_cosine, min_phash)
+        verdict_counts[verdict] += 1
+        if is_firm_a:
+            firm_a_counts[verdict] += 1
+
+        # Cosine verdicts per signature
+        def cosine_verdict(cos):
+            if cos is None: return None
+            if cos > COSINE_HIGH: return 'high'
+            if cos > KDE_CROSSOVER: return 'uncertain'
+            return 'low'
+
+        # Build row
+        row_data = {
+            'pdf_key': pdf_key,
+            'n_signatures': len(sigs),
+            'accountant_1': sig1['accountant'] if sig1 else None,
+            'accountant_2': sig2['accountant'] if sig2 else None,
+            'firm_1': sig1['firm'] if sig1 else None,
+            'firm_2': sig2['firm'] if sig2 else None,
+            'is_firm_a': 'Yes' if is_firm_a else 'No',
+            'avg_detection_conf': round(avg_conf, 4) if avg_conf else None,
+            'sig1_cosine': round(sig1['cosine'], 4) if sig1 and sig1['cosine'] else None,
+            'sig1_cosine_verdict': cosine_verdict(sig1['cosine']) if sig1 else None,
+            'sig1_acct_mean': round(sig1['acct_mean_sim'], 4) if sig1 and sig1['acct_mean_sim'] else None,
+            'sig1_acct_ratio95': round(sig1['acct_ratio_95'], 4) if sig1 and sig1['acct_ratio_95'] else None,
+            'sig1_acct_count': sig1['acct_sig_count'] if sig1 else None,
+            'sig2_cosine': round(sig2['cosine'], 4) if sig2 and sig2['cosine'] else None,
+            'sig2_cosine_verdict': cosine_verdict(sig2['cosine']) if sig2 else None,
+            'sig2_acct_mean': round(sig2['acct_mean_sim'], 4) if sig2 and sig2['acct_mean_sim'] else None,
+            'sig2_acct_ratio95': round(sig2['acct_ratio_95'], 4) if sig2 and sig2['acct_ratio_95'] else None,
+            'sig2_acct_count': sig2['acct_sig_count'] if sig2 else None,
+            'min_phash': min_phash,
+            'max_phash': max_phash,
+            'avg_phash': round(avg_phash, 2) if avg_phash is not None else None,
+            'sig1_phash': sig1['phash'] if sig1 else None,
+            'sig2_phash': sig2['phash'] if sig2 else None,
+            'max_ssim': round(max_ssim, 4) if max_ssim is not None else None,
+            'avg_ssim': round(avg_ssim, 4) if avg_ssim is not None else None,
+            'dual_verdict': verdict,
+            'dual_confidence': confidence,
+            'max_cosine': round(max_cosine, 4) if max_cosine is not None else None,
+            'pdf_min_phash': min_phash,
+            'sig1_risk': sig1['risk_level'] if sig1 else None,
+            'sig2_risk': sig2['risk_level'] if sig2 else None,
+        }
+
+        for col_idx, key in enumerate(col_keys, 1):
+            val = row_data.get(key)
+            cell = ws.cell(row=row_idx, column=col_idx, value=val)
+            cell.font = data_font
+            cell.border = thin_border
+
+            # Color by group
+            for group, (start, end) in group_ranges.items():
+                if start <= col_idx - 1 < end:
+                    cell.fill = PatternFill(start_color=group_colors[group],
+                                           end_color=group_colors[group],
+                                           fill_type='solid')
+                    break
+
+            # Highlight Firm A rows
+            if is_firm_a and col_idx == 7:
+                cell.font = Font(name='Arial', size=9, bold=True, color='CC0000')
+
+            # Color verdicts
+            if key == 'dual_verdict':
+                colors = {
+                    'high_confidence_replication': 'FF0000',
+                    'moderate_confidence_replication': 'FF6600',
+                    'high_style_consistency': '009900',
+                    'uncertain': 'FF9900',
+                    'likely_genuine': '006600',
+                }
+                if val in colors:
+                    cell.font = Font(name='Arial', size=9, bold=True, color=colors[val])
+
+        row_idx += 1
+
+    # Auto-width
+    for col_idx in range(1, len(col_keys) + 1):
+        ws.column_dimensions[openpyxl.utils.get_column_letter(col_idx)].width = 15
+
+    # Freeze header
+    ws.freeze_panes = 'A2'
+    ws.auto_filter.ref = f"A1:{openpyxl.utils.get_column_letter(len(col_keys))}{row_idx-1}"
+
+    # === Summary Sheet ===
+    ws2 = wb.create_sheet("Summary")
+    ws2.cell(row=1, column=1, value="Dual-Method Classification Summary").font = Font(size=14, bold=True)
+    ws2.cell(row=2, column=1, value=f"Generated: {datetime.now().strftime('%Y-%m-%d %H:%M')}")
+    ws2.cell(row=3, column=1, value=f"Calibration: Firm A (dHash median=5, p95=15)")
+
+    ws2.cell(row=5, column=1, value="Verdict").font = Font(bold=True)
+    ws2.cell(row=5, column=2, value="Count").font = Font(bold=True)
+    ws2.cell(row=5, column=3, value="%").font = Font(bold=True)
+    ws2.cell(row=5, column=4, value="Firm A").font = Font(bold=True)
+    ws2.cell(row=5, column=5, value="Firm A %").font = Font(bold=True)
+
+    total = sum(verdict_counts.values())
+    fa_total = sum(firm_a_counts.values())
+    order = ['high_confidence_replication', 'moderate_confidence_replication',
+             'high_style_consistency', 'uncertain', 'likely_genuine', 'unknown']
+
+    for i, v in enumerate(order):
+        n = verdict_counts.get(v, 0)
+        fa = firm_a_counts.get(v, 0)
+        ws2.cell(row=6+i, column=1, value=v)
+        ws2.cell(row=6+i, column=2, value=n)
+        ws2.cell(row=6+i, column=3, value=f"{100*n/total:.1f}%" if total > 0 else "0%")
+        ws2.cell(row=6+i, column=4, value=fa)
+        ws2.cell(row=6+i, column=5, value=f"{100*fa/fa_total:.1f}%" if fa_total > 0 else "0%")
+
+    ws2.cell(row=6+len(order), column=1, value="Total").font = Font(bold=True)
+    ws2.cell(row=6+len(order), column=2, value=total)
+    ws2.cell(row=6+len(order), column=4, value=fa_total)
+
+    # Thresholds
+    ws2.cell(row=15, column=1, value="Thresholds Used").font = Font(size=12, bold=True)
+    ws2.cell(row=16, column=1, value="Cosine high threshold")
+    ws2.cell(row=16, column=2, value=COSINE_HIGH)
+    ws2.cell(row=17, column=1, value="KDE crossover")
+    ws2.cell(row=17, column=2, value=KDE_CROSSOVER)
+    ws2.cell(row=18, column=1, value="dHash high-confidence (Firm A median)")
+    ws2.cell(row=18, column=2, value=PHASH_HIGH_CONF)
+    ws2.cell(row=19, column=1, value="dHash moderate-confidence (Firm A p95)")
+    ws2.cell(row=19, column=2, value=PHASH_MOD_CONF)
+
+    for col in range(1, 6):
+        ws2.column_dimensions[openpyxl.utils.get_column_letter(col)].width = 30
+
+    # Save
+    wb.save(str(OUTPUT_PATH))
+    print(f"\nSaved: {OUTPUT_PATH}")
+    print(f"Total PDFs: {total:,}")
+    print(f"Firm A PDFs: {fa_total:,}")
+
+    # Print summary
+    print(f"\n{'Verdict':<35} {'Count':>8} {'%':>7}  | {'Firm A':>8} {'%':>7}")
+    print("-" * 70)
+    for v in order:
+        n = verdict_counts.get(v, 0)
+        fa = firm_a_counts.get(v, 0)
+        if n > 0:
+            print(f"  {v:<33} {n:>8,} {100*n/total:>6.1f}%  | {fa:>8,} {100*fa/fa_total:>6.1f}%"
+                  if fa_total > 0 else f"  {v:<33} {n:>8,} {100*n/total:>6.1f}%")
+    print("-" * 70)
+    print(f"  {'Total':<33} {total:>8,}         | {fa_total:>8,}")
+
+
+def main():
+    print("=" * 60)
+    print("Generating Recalibrated PDF-Level Report")
+    print(f"Calibration: Firm A ({FIRM_A})")
+    print(f"Method: Dual (Cosine + dHash)")
+    print("=" * 60)
+
+    pdf_data = load_all_data()
+    build_report(pdf_data)
+
+
+if __name__ == "__main__":
+    main()

paper/lint_paper_v3.py

@@ -0,0 +1,399 @@
+#!/usr/bin/env python3
+"""Paper A v3 markdown / DOCX leak linter.
+
+Runs two pass:
+
+  Source pass — scans the v3 markdown sources for syntax patterns that the
+  python-docx export pipeline does NOT render natively. Each finding is a
+  file:line:severity:message tuple. Severity is ERROR (will leak literal
+  syntax into Word), WARN (sometimes leaks), or INFO (style nits).
+
+  DOCX pass — opens the rendered DOCX and scans every paragraph and table
+  cell for known leak signatures. This is the authoritative check: even
+  if the source pass is clean, the DOCX pass tells you what your partner
+  will actually see. The DOCX pass currently checks for:
+
+    - leftover LaTeX commands (`\\cmd`)
+    - unstripped `$` math delimiters
+    - pandoc footnote markers (`[^name]`)
+    - markdown blockquote markers (lines starting with `> `)
+    - TeX brace tricks (`{=}`, `{,}`)
+    - PUA sentinels (`\\uE000`, `\\uE001`) leaking from the math-region
+      run-splitter
+    - the synthetic table-caption marker `__TABLE_CAPTION__:` if it ever
+      survives processing
+
+Exit code:
+  0  clean
+  1  WARN-level findings only (ship-able after review)
+  2  ERROR-level findings (do NOT ship)
+
+Usage:
+  python3 paper/lint_paper_v3.py           # both passes
+  python3 paper/lint_paper_v3.py --source  # source-side only
+  python3 paper/lint_paper_v3.py --docx    # DOCX-side only
+
+Designed to be run after `python3 export_v3.py` and before copying the
+DOCX to ~/Downloads.
+"""
+
+from __future__ import annotations
+
+import argparse
+import re
+import sys
+from dataclasses import dataclass
+from pathlib import Path
+
+PAPER_DIR = Path(__file__).resolve().parent
+DOCX_PATH = PAPER_DIR / "Paper_A_IEEE_Access_Draft_v3.docx"
+
+V3_SOURCES = [
+    "paper_a_abstract_v3.md",
+    "paper_a_introduction_v3.md",
+    "paper_a_related_work_v3.md",
+    "paper_a_methodology_v3.md",
+    "paper_a_results_v3.md",
+    "paper_a_discussion_v3.md",
+    "paper_a_conclusion_v3.md",
+    "paper_a_appendix_v3.md",
+    "paper_a_declarations_v3.md",
+    "paper_a_references_v3.md",
+]
+
+
+# ---------------------------------------------------------------------------
+# Finding model + ANSI colour helpers
+# ---------------------------------------------------------------------------
+
+SEVERITY_RANK = {"ERROR": 2, "WARN": 1, "INFO": 0}
+COLOR = {
+    "ERROR": "\033[31m",  # red
+    "WARN":  "\033[33m",  # yellow
+    "INFO":  "\033[36m",  # cyan
+    "RESET": "\033[0m",
+    "BOLD":  "\033[1m",
+}
+
+
+@dataclass
+class Finding:
+    severity: str
+    rule: str
+    location: str  # "file:line" or "DOCX:para 42" / "DOCX:table 6 row 3 col 2"
+    message: str
+    snippet: str = ""
+
+    def render(self, use_color: bool = True) -> str:
+        col = COLOR[self.severity] if use_color else ""
+        rst = COLOR["RESET"] if use_color else ""
+        bold = COLOR["BOLD"] if use_color else ""
+        head = f"{col}[{self.severity}]{rst} {bold}{self.rule}{rst} @ {self.location}"
+        body = f"\n    {self.message}"
+        snip = f"\n    > {self.snippet}" if self.snippet else ""
+        return head + body + snip
+
+
+# ---------------------------------------------------------------------------
+# Source-side rules
+# ---------------------------------------------------------------------------
+
+# Each rule: (pattern, severity, rule_id, message, predicate)
+# predicate(match, line) → bool: returns True to keep the finding (lets us
+# suppress matches that are inside HTML comments or fenced code blocks).
+
+def _outside_table_comment(match: re.Match, line: str, in_comment: bool, in_table: bool) -> bool:
+    """Suppress findings inside HTML comments (where they're allowed) or
+    inside markdown table rows (where they survive intact via add_md_table)."""
+    return not in_comment and not in_table
+
+
+def _always(match: re.Match, line: str, in_comment: bool, in_table: bool) -> bool:
+    return True
+
+
+SOURCE_RULES = [
+    # Pandoc footnote markers — leak as raw text in the DOCX.
+    (re.compile(r"\[\^[A-Za-z0-9_-]+\]"),
+     "ERROR", "pandoc-footnote",
+     "Pandoc-style footnote `[^name]` does not render in DOCX. "
+     "Inline the explanation as a parenthetical instead.",
+     _outside_table_comment),
+
+    # Markdown blockquote `> body` lines — exporter strips them defensively
+    # now, but flag for awareness so authors don't rely on them rendering.
+    (re.compile(r"^>\s"),
+     "WARN", "blockquote",
+     "Markdown blockquote `> ...` is stripped to plain paragraph in DOCX "
+     "(no quote-block formatting). If you intended a callout, use bold "
+     "lead-in instead.",
+     _always),
+
+    # Display-math fences `$$...$$` (only when the line itself starts with
+    # `$$`) — exporter does best-effort linearisation, but the result is
+    # ugly. Inline the equation as plain prose where possible.
+    (re.compile(r"^\$\$.+?\$\$\s*$|^\$\$\s*$"),
+     "WARN", "display-math",
+     "Display math `$$...$$` renders as a best-effort plain-text "
+     "linearisation in DOCX (no MathType/equation rendering). Consider "
+     "replacing with a numbered equation image or inline prose.",
+     _always),
+
+    # Inline math containing `\frac{...{...}...}` — nested braces in a
+    # frac argument are not handled by the exporter's regex.
+    (re.compile(r"\\t?frac\{[^{}]*\{[^{}]*\}[^{}]*\}\{|\\t?frac\{[^{}]+\}\{[^{}]*\{"),
+     "WARN", "nested-frac",
+     "Nested-brace `\\frac{...}{...}` may not linearise cleanly. Verify "
+     "the rendered DOCX paragraph or rewrite the math inline.",
+     _outside_table_comment),
+
+    # Setext-style headers (=== / ---) under a line of text — not handled.
+    (re.compile(r"^=+\s*$|^-{3,}\s*$"),
+     "INFO", "setext-header",
+     "Setext-style header (=== / ---) is not handled by the exporter; "
+     "use ATX (#, ##, ###) instead.",
+     _always),
+
+    # Pandoc fenced div `:::` — not handled.
+    (re.compile(r"^:::"),
+     "ERROR", "pandoc-fenced-div",
+     "Pandoc fenced div `:::` is not handled by the exporter and would "
+     "leak into the DOCX as plain text.",
+     _always),
+
+    # Pandoc bracketed-attribute spans `[text]{.class}` — not handled.
+    (re.compile(r"\][\{][^}]*[\}]"),
+     "WARN", "pandoc-attribute-span",
+     "Pandoc attribute span `[text]{.class}` is not parsed by the exporter "
+     "and the brace block will leak.",
+     _outside_table_comment),
+
+    # File paths in body text — Appendix B is the canonical home for
+    # script→artifact references.
+    (re.compile(r"`signature_analysis/\d+_[a-z_]+\.py`"),
+     "INFO", "script-path-in-body",
+     "Verbose script path in body text. Consider replacing with "
+     "'(reproduction artifact in Appendix B)' for body-prose tightness.",
+     _outside_table_comment),
+
+    # `reports/...json` paths in body text — same rationale.
+    (re.compile(r"`reports/[a-z_]+/[a-z_]+\.(?:json|md)`"),
+     "INFO", "report-path-in-body",
+     "Verbose report-artifact path in body text. Consider replacing with "
+     "'(see Appendix B provenance map)'.",
+     _outside_table_comment),
+
+    # Bare HTML comments that are NOT TABLE/FIGURE markers may indicate
+    # editorial residue. Stripped wholesale by exporter, so harmless, but
+    # worth visibility.
+    (re.compile(r"^<!--\s*$|^<!-- (?!TABLE |FIGURE )"),
+     "INFO", "html-comment",
+     "HTML comment block (non-TABLE) — stripped from DOCX. Keep for "
+     "editorial notes or remove for tidiness.",
+     _always),
+]
+
+
+def lint_sources() -> list[Finding]:
+    findings: list[Finding] = []
+    for src in V3_SOURCES:
+        path = PAPER_DIR / src
+        if not path.exists():
+            continue
+        in_comment = False
+        in_table = False
+        for line_no, line in enumerate(path.read_text(encoding="utf-8").splitlines(), 1):
+            # Track HTML-comment context (multi-line aware).
+            if "<!--" in line:
+                in_comment = True
+            stripped = line.strip()
+            if stripped.startswith("|") and stripped.endswith("|"):
+                in_table = True
+            else:
+                in_table = False
+            for pat, sev, rule, msg, predicate in SOURCE_RULES:
+                for m in pat.finditer(line):
+                    if not predicate(m, line, in_comment, in_table):
+                        continue
+                    findings.append(Finding(
+                        severity=sev,
+                        rule=rule,
+                        location=f"{src}:{line_no}",
+                        message=msg,
+                        snippet=line.rstrip()[:120],
+                    ))
+            if "-->" in line:
+                in_comment = False
+    return findings
+
+
+# ---------------------------------------------------------------------------
+# DOCX-side rules
+# ---------------------------------------------------------------------------
+
+DOCX_LEAK_PATTERNS = [
+    # (pattern, severity, rule_id, message)
+    (re.compile(r"\\[a-zA-Z]+(?:\{[^{}]*\})?"),
+     "ERROR", "leftover-latex-cmd",
+     "LaTeX command `\\cmd` leaked into DOCX. Either add a token rule to "
+     "`latex_to_unicode` in `export_v3.py` or rewrite the source as plain text."),
+
+    (re.compile(r"(?<!\\)\$[^$\s][^$]*\$"),
+     "ERROR", "unstripped-dollar-math",
+     "Inline math `$...$` was not stripped. The math-context handler in "
+     "`latex_to_unicode` should have wrapped the content with PUA sentinels."),
+
+    (re.compile(r"\[\^[A-Za-z0-9_-]+\]"),
+     "ERROR", "pandoc-footnote-leak",
+     "Pandoc footnote marker leaked into DOCX. Inline the footnote body "
+     "as a parenthetical at the source."),
+
+    (re.compile(r"^>\s"),
+     "ERROR", "blockquote-leak",
+     "Markdown blockquote `> ...` leaked literal `>` into DOCX. The "
+     "exporter pre-pass should strip these — check `process_section`."),
+
+    (re.compile(r"\{[,=<>+\-]\}"),
+     "ERROR", "tex-brace-trick",
+     "TeX brace-trick `{=}` / `{,}` leaked. Should be stripped by "
+     "`latex_to_unicode`."),
+
+    (re.compile(r"[]"),
+     "ERROR", "pua-sentinel-leak",
+     "Math-region PUA sentinel (\\uE000 / \\uE001) leaked. A render path "
+     "is bypassing `add_text_with_subsup`; check headings / list items / "
+     "title-page paragraphs."),
+
+    (re.compile(r"__TABLE_CAPTION__"),
+     "ERROR", "table-caption-marker-leak",
+     "Synthetic `__TABLE_CAPTION__:` marker leaked. The marker is meant "
+     "to be consumed by `process_section` and rendered as a centered "
+     "bold caption paragraph."),
+
+    (re.compile(r"signature[a-z]+analysis/\d+[a-z_]+\.py"),
+     "ERROR", "underscore-eaten-path",
+     "Underscores eaten from a script path (e.g., "
+     "`signatureanalysis/28byteidentitydecomposition.py`). The "
+     "math-context-scoped subscript handler in `add_text_with_subsup` "
+     "should leave underscores intact in plain text."),
+
+    (re.compile(r"\b(\w+_\w+)+\b", flags=re.UNICODE),
+     "INFO", "underscore-identifier",
+     "Underscored identifier in body text (e.g., a code symbol or path). "
+     "Verify it renders with underscores intact, not as subscripts."),
+]
+
+
+def lint_docx(docx_path: Path = DOCX_PATH) -> list[Finding]:
+    try:
+        from docx import Document
+    except ImportError:
+        return [Finding("ERROR", "missing-dep",
+                        "lint:docx",
+                        "python-docx is not installed; cannot run DOCX pass.")]
+
+    if not docx_path.exists():
+        return [Finding("ERROR", "missing-docx",
+                        str(docx_path),
+                        "Built DOCX not found. Run `python3 export_v3.py` first.")]
+
+    doc = Document(str(docx_path))
+    findings: list[Finding] = []
+    seen_signatures = set()  # dedupe identical leaks across paragraphs
+
+    def scan(text: str, location: str):
+        for pat, sev, rule, msg in DOCX_LEAK_PATTERNS:
+            for m in pat.finditer(text):
+                # Skip the INFO-level identifier rule unless it looks like
+                # an obvious math residue (e.g., dHash_indep or N_a).
+                if rule == "underscore-identifier":
+                    sample = m.group(0)
+                    # Only complain about identifiers that look like math
+                    # residue: short, underscore-separated single-char tokens.
+                    parts = sample.split("_")
+                    if not all(len(p) <= 4 for p in parts):
+                        continue
+                    if not all(p.isalnum() and not p.isdigit() for p in parts):
+                        continue
+                key = (rule, m.group(0))
+                if key in seen_signatures:
+                    continue
+                seen_signatures.add(key)
+                findings.append(Finding(
+                    severity=sev,
+                    rule=rule,
+                    location=location,
+                    message=msg,
+                    snippet=text[max(0, m.start() - 30):m.end() + 30].replace("\n", " ")[:140],
+                ))
+
+    for i, p in enumerate(doc.paragraphs):
+        if p.text:
+            scan(p.text, f"DOCX:para {i}")
+    for ti, t in enumerate(doc.tables):
+        for ri, row in enumerate(t.rows):
+            for ci, cell in enumerate(row.cells):
+                if cell.text:
+                    scan(cell.text, f"DOCX:table {ti + 1} row {ri} col {ci}")
+
+    return findings
+
+
+# ---------------------------------------------------------------------------
+# Reporter
+# ---------------------------------------------------------------------------
+
+def summarise(findings: list[Finding], use_color: bool = True) -> int:
+    def c(key: str) -> str:
+        return COLOR[key] if use_color else ""
+
+    if not findings:
+        print(f"{c('BOLD')}{c('INFO')}clean — no leaks detected{c('RESET')}")
+        return 0
+    counts = {"ERROR": 0, "WARN": 0, "INFO": 0}
+    findings.sort(key=lambda f: (-SEVERITY_RANK[f.severity], f.location))
+    for f in findings:
+        counts[f.severity] += 1
+        print(f.render(use_color))
+        print()
+    print(f"{c('BOLD')}summary{c('RESET')}: "
+          f"{c('ERROR')}{counts['ERROR']} ERROR{c('RESET')}  "
+          f"{c('WARN')}{counts['WARN']} WARN{c('RESET')}  "
+          f"{c('INFO')}{counts['INFO']} INFO{c('RESET')}")
+    if counts["ERROR"]:
+        return 2
+    if counts["WARN"]:
+        return 1
+    return 0
+
+
+def main():
+    ap = argparse.ArgumentParser(
+        description="Lint Paper A v3 markdown sources and rendered DOCX for "
+                    "syntax-leak issues.",
+    )
+    ap.add_argument("--source", action="store_true",
+                    help="run only the markdown source pass")
+    ap.add_argument("--docx", action="store_true",
+                    help="run only the rendered DOCX pass")
+    ap.add_argument("--no-color", action="store_true",
+                    help="disable ANSI colour output")
+    args = ap.parse_args()
+
+    use_color = sys.stdout.isatty() and not args.no_color
+    findings: list[Finding] = []
+    if args.source or not (args.source or args.docx):
+        print(f"{COLOR['BOLD'] if use_color else ''}--- source pass "
+              f"({len(V3_SOURCES)} files) ---{COLOR['RESET'] if use_color else ''}")
+        findings.extend(lint_sources())
+    if args.docx or not (args.source or args.docx):
+        print(f"{COLOR['BOLD'] if use_color else ''}\n--- docx pass "
+              f"({DOCX_PATH.name}) ---{COLOR['RESET'] if use_color else ''}")
+        findings.extend(lint_docx())
+
+    print()
+    sys.exit(summarise(findings, use_color))
+
+
+if __name__ == "__main__":
+    main()

paper/opus_final_review_v3_9.md

@@ -0,0 +1,246 @@
+# Paper A v3.9 — Final Independent Peer Review (Opus 4.7)
+
+**Reviewer:** Claude Opus 4.7 (1M context), independent round 9
+**Date:** 2026-04-21
+**Commit reviewed:** 85cfefe
+**Target venue:** IEEE Access (Regular Paper)
+**Prior rounds reviewed:** codex v3.3 / v3.4 / v3.5 / v3.8 (Minor Revision each), Gemini v3.7 (Accept), Gemini v3.8 (Accept), codex v3.8 (Minor Revision)
+
+---
+
+## 1. Overall verdict
+
+**Minor Revision.** I dissent from the Gemini-3.1-Pro round-7 Accept verdict and align with codex round-8's Minor judgment, but for a *different* set of issues that both codex and Gemini missed. The v3.9 edits to Table XV and to the two explicit cross-reference breakages did land cleanly and close codex's round-8 findings. However, in the same revision cycle the paper accumulated an **internally contradicted BD/McCrary accountant-level claim**: multiple locations in the main text (Section IV-D.1, Section IV-E Table VIII note, Section V-B, Conclusion) assert flatly that BD/McCrary "does not produce a significant transition" at the accountant level and that the null "persists across the Appendix-A bin-width sweep," yet Appendix A Table A.I itself documents (i) an accountant-level cosine transition at bin-width 0.005 with $z_{\text{below}}=-3.23$, $z_{\text{above}}=+5.18$ (clearly |Z|>1.96) and (ii) an accountant-level dHash transition at bin-width 1.0 with $z_{\text{below}}=-2.00$, $z_{\text{above}}=+3.24$. Appendix A acknowledges the latter marginally; the main text denies both. The substantive argument of the paper (smoothly-mixed accountant aggregates) is *not* threatened because (a) the transition at bin 0.005 is outside the convergence band anyway and (b) the dHash transition is exactly at the |Z|=1.96 boundary, but the **paper-to-appendix internal contradiction is a reviewer-facing red flag that a competent accountant-statistics reviewer will catch instantly**. This must be fixed before submission. All other issues I found are clean cosmetic/clarity items. The paper is otherwise ready.
+
+---
+
+## 2. v3.8 → v3.9 delta verification
+
+I re-verified both round-8 fixes against their authoritative sources.
+
+**Fix 1: Table XV per-year Firm A baseline-share column.** Verified directly against `reports/partner_ranking/partner_ranking_report.md` (generated 2026-04-21 01:55:27, paper commit same day). All 11 yearly values match exactly: 2013 32.4%, 2014 27.8%, 2015 27.7%, 2016 26.2%, 2017 27.2%, 2018 26.5%, 2019 27.0%, 2020 27.7%, 2021 28.7%, 2022 28.3%, 2023 27.4%. The fix is complete and correct. Codex's numerical-impossibility argument (97/324 floor = 29.9% > prior 26.2%) no longer applies. (results_v3.md lines 331–341)
+
+**Fix 2: Cross-reference corrections.**
+* "Section IV-F" → "Section IV-J" for the ablation study: methodology_v3.md line 87 correctly reads `(Section IV-J)`, and results_v3.md line 412 defines `## J. Ablation Study: Feature Backbone Comparison`. Verified.
+* Table XVIII note "Tables IV/VI" → "Table XIII": results_v3.md lines 429–432 now refer to Table XIII for the best-match mean comparison. Verified.
+
+**No regressions detected in the v3.8→v3.9 edits themselves.** I re-validated the full section/sub-section reference map (III-A…III-M, IV-A…IV-J, IV-D.1/2, IV-G.1/2/3/4, IV-H.1/2/3, IV-I.1/2, V-A…V-G, VI) and every textual `Section X-Y(.Z)` reference resolves to an existing target. All 41 references [1]–[41] are cited in the body.
+
+---
+
+## 3. Numerical audit findings (spot-check against scripts)
+
+I verified 19 numerical claims against authoritative reports under `reports/`. All pass.
+
+| # | Paper claim | Source | Verified |
+|---|-------------|--------|----------|
+| 1 | Table IX whole-Firm-A cos>0.837 = 99.93% (60,408/60,448) | validation_recalibration.json whole_firm_a | ✓ |
+| 2 | Table IX cos>0.9407 = 95.15% (57,518/60,448) | same | ✓ (57518/60448=95.1529%) |
+| 3 | Table IX cos>0.95 = 92.51% (55,922/60,448) | same | ✓ |
+| 4 | Table IX cos>0.973 = 79.45% (48,028/60,448) | same | ✓ |
+| 5 | Table IX dual cos>0.95 AND dh≤8 = 89.95% (54,370/60,448) | same | ✓ |
+| 6 | Table XI calib cos>0.9407 = 94.99%, z=-3.19, p=0.0014 | validation_recalibration.json generalization_tests | ✓ |
+| 7 | Table XI held-out cos>0.9407 = 95.63% (14,662/15,332) | same | ✓ (rate 0.9563) |
+| 8 | Table V Firm A cos dip=0.0019, p=0.169 | dip_test_report.md | ✓ |
+| 9 | Table V Firm A dHash dip=0.1051, p<0.001 | same | ✓ |
+| 10 | Table V all-CPA 168,740 cos dip=0.0035 | same | ✓ |
+| 11 | Table VIII accountant KDE antimode cos=0.973 | accountant_three_methods_report.md | ✓ (0.9726) |
+| 12 | Table VIII accountant Beta-2 cos=0.979 | same | ✓ (0.9788) |
+| 13 | Table VIII accountant logit-GMM cos=0.976 | same | ✓ (0.9759) |
+| 14 | Table VIII accountant 2D-GMM marginal cos=0.945 | same | ✓ (0.9450) |
+| 15 | Table X FAR at 0.837=0.2062, CI [0.2027, 0.2098] | expanded_validation_report.md | ✓ |
+| 16 | Table X FAR at 0.973=0.0003 | same | ✓ |
+| 17 | Table XIV Firm A baseline 27.8% (1287/4629) | partner_ranking_report.md | ✓ |
+| 18 | 3.5× top-10% concentration ratio (95.9/27.8) | arithmetic | ✓ (3.45→3.5×) |
+| 19 | Table XVI Firm A intra-report 89.91% agreement | (26435+734+0+4)/30222 | ✓ (89.91%) |
+
+**Minor numerical imprecision (cosmetic, not blocker).** Results §IV-I.1 says "The absence of any meaningful 'likely hand-signed' rate (4 of 30,000+ Firm A documents, 0.01%) implies…" The true value is 4/30,226 = **0.013%**. Rounding 0.013% to "0.01%" is unusual; "0.013%" or "~0.01%" would be more accurate. (results_v3.md line 404)
+
+**Subtle inconsistency between two scripts (NOT paper's fault, flag-only).** `expanded_validation_report.md` records held-out `cos>0.9407` as k=14,664 (95.64%), while `validation_recalibration.json` records k=14,662 (95.63%). The paper cites the latter (authoritative), so the paper is internally self-consistent. The drift is in the underlying Script 22/24 pair and may be worth reconciling in the reproducibility package (the paper names only Script 24 in its captions, which is correct).
+
+---
+
+## 4. Cross-reference audit findings
+
+I enumerated every `Section X-Y(.Z)` and `Table [roman]` reference in the submission files and checked resolution.
+
+* All 32 distinct section references resolve. No dangling targets.
+* All 18 tables (I–XVIII plus A.I) defined are used at least once **except** Table XII, which is defined (results §IV-G.3) but the only textual mentions of "Table XII" are in the aggregation sentence at results line 59 ("downstream all-pairs analyses (Tables XII, XVIII)"), not at the point where Table XII is first presented.
+  * **Issue (MINOR):** results_v3.md §IV-G.3 (lines 245–268) introduces Table XII as "the Classifier Sensitivity … table" without any in-text `Table XII` numeral reference. A reader looking for the anchor will find it only in the earlier cross-reference at line 59, which is confusing. Add an explicit "Table XII reports …" or "… (Table XII) …" at line 252. This is exactly the sort of orphaned-table issue that IEEE Access copyediting catches.
+
+* **Issue (MINOR clarity — not broken, but misleading):** results_v3.md line 59 characterises Tables XII and XVIII as "downstream all-pairs analyses" that share the 168,740 count. Table XII is the per-signature classifier output (168,740) — not all-pairs — and Table XVIII's all-pairs intra-class stats are over 41.35M all-CPA pairs or 16M Firm-A-only pairs, not 168,740. The 15-signature exclusion described in line 59 does affect the 168,740 signature set (which is the unit in Tables V, XII, and Firm-A rows of XIII), but labelling them "all-pairs analyses" is a misnomer. Recommend: replace "(Tables XII, XVIII)" with "(Tables V, XII, and the Firm-A per-signature statistics of Tables XIII and XVIII)" or simply "(all same-CPA per-signature best-match analyses)".
+
+* Figures 1–4 are referenced; captions are elsewhere in the export pipeline and I did not audit PNG files. No textual figure-reference is broken.
+
+---
+
+## 5. Arithmetic audit findings
+
+I recomputed every `X%`, `k of N`, `k/n` and ratio I could find. Results:
+
+| Claim | Computed | Paper | Status |
+|-------|----------|-------|--------|
+| 182,328 / 86,071 docs avg | 2.118 | — | — |
+| 182,328 / 85,042 with-detections | 2.144 | "2.14 sigs/doc" | ✓ (docs-with-detections denominator) |
+| 85,042 / 86,071 | 98.80% | "98.8%" | ✓ |
+| 168,755 / 182,328 | 92.55% | "92.6%" | ✓ |
+| 85,042 − 84,386 | 656 | "656 documents" | ✓ |
+| 29,529 + 36,994 + 5,133 + 12,683 + 47 | 84,386 | ✓ | ✓ |
+| 29,529 / 84,386 | 35.00% | "35.0%" | ✓ |
+| 22,970 / 30,226 | 75.99% | "76.0%" | ✓ |
+| (22,970+6,311) / 30,226 | 96.87% | "96.9%" | ✓ |
+| 26,435 / 30,222 | 87.47% | "87.5%" | ✓ |
+| (26,435+734+0+4) / 30,222 | 89.91% | "89.91%" | ✓ |
+| 4 / 30,226 | 0.0132% | "0.01%" | **△ should be 0.013%** |
+| 141 + 361 + 184 | 686 | GMM total | ✓ |
+| 0.21 + 0.51 + 0.28 | 1.00 | GMM weights | ✓ |
+| 139 / 171 | 81.3% | "81%" | ✓ |
+| 32 / 171 | 18.7% | "19%" (§V-C) | ✓ |
+| 29,529 / 71,656 | 41.21% | "41.2%" | ✓ |
+| 36,994 / 71,656 | 51.63% | "51.7%" | ✓ |
+| 5,133 / 71,656 | 7.16% | "7.2%" | ✓ |
+| 95.9 / 27.8 | 3.45 | "3.5×" | ✓ |
+| 90.1 / 27.8 | 3.24 | "3.2×" | ✓ |
+| 139+32 = 171; 141-139 | 2 | non-Firm-A in C1 | ✓ |
+| cos>0.95: 92.51%, below: 7.49% | "92.5% / 7.5%" | ✓ | ✓ |
+| Abstract word count | 244 | ≤250 | ✓ |
+
+**One non-blocking integrity note.** Intro line 54: "92.5% of Firm A signatures exceed cosine 0.95 but 7.5% fall below". This is the *whole-sample* Firm A rate (55,922/60,448 = 92.51%). Methodology §III-H line 147 and §V-C line 42 reuse the same 92.5% / 7.5% split. **Consistent** across locations.
+
+---
+
+## 6. Narrative / consistency findings
+
+### 6.1 BD/McCrary accountant-level claim — **main-text vs Appendix A contradiction (MAJOR)**
+
+This is the principal finding of my round. Three locations in the main text state or imply that BD/McCrary produces *no* significant accountant-level transition and that this null persists across the bin-width sweep:
+
+1. **results_v3.md §IV-D.1, lines 85–86:** "At the accountant level the test does not produce a significant transition in either the cosine-mean or the dHash-mean distribution, and this null persists across the Appendix-A bin-width sweep."
+
+2. **results_v3.md §IV-E Table VIII row (line 145):** `| Accountant-level, BD/McCrary transition (diagnostic; null across Appendix A) | no transition | no transition |`
+
+3. **results_v3.md §IV-E line 130, line 152; discussion_v3.md §V-B line 27; conclusion_v3.md line 16:** variants of "BD/McCrary finds no significant transition at the accountant level".
+
+But `reports/bd_sensitivity/bd_sensitivity.md` (and Appendix A Table A.I lines 23–28) actually report:
+
+* Accountant cosine bin 0.005: transition at 0.9800 with $z_{\text{below}}=-3.23$, $z_{\text{above}}=+5.18$ — **both exceed |1.96|, 1 significant transition.**
+* Accountant cosine bin 0.002: no transition; bin 0.010: no transition.
+* Accountant dHash bin 1.0: transition at 3.0 with $z_{\text{below}}=-2.00$, $z_{\text{above}}=+3.24$ — **|Z|=2.00 just above critical, 1 marginal transition.**
+* Accountant dHash bin 0.2: no transition; bin 0.5: no transition.
+
+Appendix A itself (line 36) acknowledges the dHash marginal transition ("the one marginal transition it does produce … sits exactly at the critical value for α = 0.05") but is **silent about the bin-0.005 cosine transition at 0.980**, even though the $|Z|$ values ($-3.23$ / $+5.18$) are well past the 1.96 cutoff and the accountant-level cosine convergence band the paper anchors its primary threshold to is $[0.973, 0.979]$ — i.e., the BD/McCrary transition at 0.980 sits **directly at the upper edge of that convergence band**, not outside it.
+
+**Substantive implication.** The paper's "smoothly-mixed cluster" narrative is not falsified by this — two of three cosine bin widths and two of three dHash bin widths do produce no transition, and one can still argue the pattern is "largely absent." But the paper currently claims something stronger than the data supports, namely that the null is unqualified at the accountant level. A reviewer who reads Appendix A Table A.I against Section IV-D.1 will see the contradiction within 30 seconds.
+
+**Fix.** Either (a) soften the main-text language to "the BD/McCrary accountant-level test rejects the smoothness null in only one of three cosine bin widths and one of three dHash bin widths; the pattern is largely but not uniformly null" (matching Appendix A's own hedging), or (b) additionally note in Appendix A the bin-0.005 cosine transition and explain why it does not disturb the substantive reading (e.g., sits at the band edge, $Z$ inflates with bin width as documented, consistent with a mild histogram-resolution artifact). Option (b) is stronger. **Either way the four locations in §IV-D.1 / Table VIII / §IV-E / §V-B / conclusion must be brought into alignment with Appendix A.**
+
+### 6.2 Related Work line 67 — stale BD/McCrary framing (MINOR)
+
+related_work_v3.md line 67: "The BD/McCrary pairing is well suited to detecting the boundary between two generative mechanisms (non-hand-signed vs. hand-signed) under minimal distributional assumptions."
+
+The rest of the paper (Methodology §III-I.3, Results §IV-D.1, Appendix A) has **demoted** BD/McCrary from a threshold estimator to a density-smoothness diagnostic precisely because it does *not* cleanly detect that boundary (transitions sit inside the non-hand-signed mode, not between modes). Related Work's enthusiastic framing is residue from the v3.6-and-earlier framing and should be softened to something like "BD/McCrary provides a local-density-discontinuity diagnostic that is informative about distributional smoothness under minimal assumptions." This is a related-work-intent question only; the downstream text handles the nuance correctly.
+
+### 6.3 "0.01%" vs "0.013%" (MINOR)
+
+results_v3.md §IV-I.1 line 404: "4 of 30,000+ Firm A documents, 0.01%". True value 0.013%; reviewers who recompute will flag. Replace with "0.013%" or "roughly 0.01%".
+
+### 6.4 No substantive abstract-vs-body contradictions detected
+
+I cross-checked the abstract's quantitative claims (threshold convergence within ∼0.006 at cosine ≈0.975, FAR ≤ 0.001 at accountant-level thresholds, 310 byte-identical positives, ∼50,000-pair inter-CPA negative anchor, 182,328 signatures / 90,282 reports / 758 CPAs / 2013–2023) against the body and all match.
+
+### 6.5 No terminology drift detected
+
+`dHash` / `dHash_indep` / `independent minimum dHash` are defined in §III-G and used consistently; the operational classifier §III-L is explicit that it uses the independent-minimum variant; Tables IX/XI/XII/XVI all use that variant. Previous reviewers correctly flagged this; v3.9 is clean.
+
+---
+
+## 7. Novel issues no prior reviewer caught
+
+Beyond item **6.1 (BD/McCrary main-vs-appendix contradiction)**, which is the primary novel finding, I identified:
+
+### 7.1 Orphaned Table XII first reference
+
+Table XII is defined inside §IV-G.3 (results line 252) but the sub-section opens at line 245 without an in-text `Table XII` reference. The only textual `Table XII` string in the paper is in the line-59 aggregation sentence. A first-reader following the narrative has no numeric pointer to the table at the point of presentation. No prior reviewer flagged this. Fix: insert "Table XII presents the five-way output under each cut." before line 252 `<!-- TABLE XII: ... -->` comment, or similar.
+
+### 7.2 Section IV-E wording ambiguity around "the two-component GMM"
+
+results_v3.md line 131: "For completeness we also report the two-dimensional two-component GMM's marginal crossings at cosine = 0.945 and dHash = 8.10".
+
+This is ambiguous because §IV-E has *already* selected $K^*=3$ on BIC at line 103. The 2-component 2D fit here is an additional, separately-fit 2-comp 2D GMM reported for cross-check only. A reader can reasonably wonder whether this is the same fit at $K=3$ (it is not) or a parallel $K=2$ fit used only for the marginal crossings (it is). Fix: replace "the two-dimensional two-component GMM" with "a separately fit two-component 2D GMM (reported for cross-check of the 1D accountant-level crossings)".
+
+### 7.3 Subtle overclaim in `Methodology §III-H line 156`
+
+methodology_v3.md line 156: "We emphasize that the 92.5% figure is a within-sample consistency check rather than an independent validation of Firm A's status; the validation role is played by the visual inspection, the accountant-level mixture, the three complementary analyses above, and the held-out Firm A fold described in Section III-K."
+
+However, as results §IV-G.2 cautions, the 70/30 held-out fold's operational rules differ between folds by 1–5 pp with $p<0.001$. The held-out fold therefore confirms the *qualitative* replication-dominated framing but does **not** provide clean quantitative validation. Calling it part of "the validation role" is slightly stronger than the results section is willing to say. Fix: replace "held-out Firm A fold" with "held-out Firm A fold (which confirms the qualitative replication-dominated framing; fold-level rate differences are disclosed in Section IV-G.2)".
+
+### 7.4 Abstract's "visual inspection and accountant-level mixture evidence"
+
+abstract_v3.md line 5: "… visual inspection and accountant-level mixture evidence supporting majority non-hand-signing and a minority of hand-signers". This omits the partner-level ranking analysis (§IV-H.2), which is the only **threshold-free** piece of evidence and is the strongest of the four. Including it in the one-sentence evidence summary would sharpen the abstract. Non-blocking: the abstract is already at 244/250 words.
+
+### 7.5 `Section III-I.4` never referenced
+
+methodology_v3.md defines subsections III-I.1 (KDE), III-I.2 (Beta mixture EM), III-I.3 (BD/McCrary), III-I.4 (Convergent Validation), III-I.5 (Accountant-Level Application). Only III-I.3 and III-I.5 are referenced in text. III-I.4's substantive content (level-shift framing) is summarised in §IV-E and §V-B; the standalone subsection could be folded into III-I.5 or III-I.1, or a forward-reference could be added. Non-blocking, but IEEE Access copyediting may flag a subsection with no cross-reference.
+
+### 7.6 BD/McCrary-as-threshold-estimator trace in Conclusion
+
+conclusion_v3.md line 14: "Third, we introduced a convergent threshold framework combining two methodologically distinct estimators … together with a Burgstahler-Dichev / McCrary density-smoothness diagnostic."
+
+This is fine — diagnostic, not estimator — and matches methodology §III-I.3 framing. But it contrasts with introduction_v3.md line 43–44 which still reads "(5) threshold determination using two methodologically distinct estimators … complemented by a Burgstahler-Dichev / McCrary density-smoothness diagnostic …". Self-consistent. I verified there is no stale "three-method threshold" residue. v3.9 is clean on this.
+
+---
+
+## 8. Final recommendation — v3.10 action items
+
+### BLOCKER (must fix before submission)
+
+**B1. BD/McCrary accountant-level claim contradicts Appendix A.** (See §6.1.)
+* File: `paper_a_results_v3.md`, §IV-D.1, lines 85–86.
+* Change: "At the accountant level the test does not produce a significant transition in either the cosine-mean or the dHash-mean distribution, and this null persists across the Appendix-A bin-width sweep."
+* Replace with: "At the accountant level the BD/McCrary null is not rejected in two of three cosine bin widths (0.002 and 0.010) and two of three dHash bin widths (0.2 and 0.5); the one cosine transition (at bin width 0.005) sits at cosine 0.980 — at the upper edge of the convergence band of our two threshold estimators (Section IV-E) — and the one dHash transition (at bin width 1.0) has $|Z|$ at the 1.96 critical value. We read this pattern as *largely* null and report it as consistent with, rather than affirmative proof of, clustered-but-smoothly-mixed accountant-level aggregates (Appendix A)."
+* File: `paper_a_results_v3.md`, §IV-E Table VIII row (line 145). Change `null across Appendix A` to `largely null; 1/3 cos and 1/3 dHash bin widths exhibit a marginal transition (Appendix A)`.
+* File: `paper_a_discussion_v3.md` §V-B line 27 and `paper_a_conclusion_v3.md` line 16 — apply matching softening.
+
+### MAJOR (strongly recommended before submission)
+
+**M1. Related Work BD/McCrary framing stale.** (See §6.2.)
+* File: `paper_a_related_work_v3.md` line 67.
+* Soften "is well suited to detecting the boundary between two generative mechanisms" to "provides a local-density-discontinuity diagnostic that is informative about distributional smoothness".
+
+**M2. Orphaned Table XII first reference.** (See §7.1.)
+* File: `paper_a_results_v3.md` line 252, immediately before the `<!-- TABLE XII: … -->` comment.
+* Insert: "Table XII reports the five-way classifier output under both operational cuts."
+
+### MINOR (nice-to-have)
+
+**m1.** results_v3.md line 404: replace "0.01%" with "0.013%".
+
+**m2.** results_v3.md line 131: replace "the two-dimensional two-component GMM" with "a separately fit two-component 2D GMM (reported for cross-check of the 1D accountant-level crossings)".
+
+**m3.** results_v3.md line 59: replace "(Tables XII, XVIII)" with "(all same-CPA per-signature best-match analyses, including Tables V, XII, and XVIII)" to remove the "all-pairs" misnomer.
+
+**m4.** methodology_v3.md line 156: replace "the held-out Firm A fold described in Section III-K" with "the held-out Firm A fold (which confirms the qualitative replication-dominated framing; fold-level rate differences are disclosed in Section IV-G.2)".
+
+**m5.** abstract_v3.md (optional, non-blocking): consider inserting "the threshold-free partner-ranking analysis," before "and a minority of hand-signers" if word budget allows.
+
+**m6.** methodology_v3.md §III-I.4 never cross-referenced (§7.5). Either add one forward reference or fold into §III-I.1/5. Non-blocking.
+
+### Submission-readiness summary
+
+With **B1** addressed the paper is submission-ready. **M1** and **M2** are strongly recommended but would not by themselves be grounds for rejection. All **m1–m6** items are cosmetic.
+
+### IEEE Access compliance check
+
+* Abstract word count: 244 / 250 ✓
+* Impact statement correctly removed from submission via export_v3.py SECTIONS list ✓
+* Single-anonymized: "Firm A / B / C / D" pseudonyms used consistently, residual identifiability disclosed (methodology §III-M) ✓
+* Reference formatting: IEEE numbered, sequential by first appearance, 41 entries, all cited ✓
+* No author/institution information in v3 section files ✓
+* Figures 1–4 referenced; Table A.I defined in appendix with consistent IEEE prefix ✓
+* Appendix A correctly titled "Appendix A. BD/McCrary Bin-Width Sensitivity" and appears after Conclusion in the assembly order ✓
+
+**Reviewer's bottom line.** The paper is well-crafted, numerically rigorous, and has survived eight prior review rounds. v3.9 closed both codex round-8 items cleanly. The one residual issue I identified (**B1**) is a paper-vs-appendix contradiction that any careful round-10 reviewer will catch. It is fixable in 20 minutes by softening four sentences. After that fix the paper is ready for IEEE Access submission.
+
+---
+
+*End of review.*

paper/paper_a_abstract.md

@@ -0,0 +1,16 @@
+# Abstract
+
+<!-- 150-250 words -->
+
+Regulations in many jurisdictions require Certified Public Accountants (CPAs) to attest to each audit report they certify, typically by affixing a signature or seal.
+However, the digitization of financial reporting makes it straightforward to reuse a scanned signature image across multiple reports, potentially undermining the intent of individualized attestation.
+Unlike signature forgery, where an impostor imitates another person's handwriting, signature replication involves a legitimate signer reusing a digital copy of their own genuine signature---a practice that is difficult to detect through manual inspection at scale.
+We present an end-to-end AI pipeline that automatically detects signature replication in financial audit reports.
+The pipeline employs a Vision-Language Model for signature page identification, YOLOv11 for signature region detection, and ResNet-50 for deep feature extraction, followed by a dual-method verification combining cosine similarity with difference hashing (dHash).
+This dual-method design distinguishes consistent handwriting style (high feature similarity but divergent perceptual hashes) from digital replication (convergent evidence across both methods), addressing an ambiguity that single-metric approaches cannot resolve.
+We apply this pipeline to 90,282 audit reports filed by publicly listed companies in Taiwan over a decade (2013--2023), analyzing 182,328 signatures from 758 CPAs.
+Using an accounting firm independently identified as employing digital replication as a calibration reference, we establish empirically grounded detection thresholds.
+Our analysis reveals that among documents with high feature-level similarity (cosine > 0.95), the structural verification layer stratifies them into distinct populations: 41% with converging replication evidence, 52% with partial structural similarity, and 7% with no structural corroboration despite near-identical features---demonstrating that single-metric approaches conflate style consistency with digital duplication.
+To our knowledge, this represents the largest-scale analysis of signature authenticity in financial audit documents to date.
+
+<!-- Word count: ~220 -->

paper/paper_a_abstract_v3.md

@@ -0,0 +1,7 @@
+# Abstract
+
+<!-- IEEE Access target: <= 250 words, single paragraph -->
+
+Regulations require Certified Public Accountants (CPAs) to attest to each audit report by affixing a signature, but digitization makes reusing a stored signature image across reports---through administrative stamping or firm-level electronic signing---technically trivial and visually invisible to report users, undermining individualized attestation. We build an end-to-end pipeline that detects such *non-hand-signed* signatures at scale: a Vision-Language Model identifies signature pages, a YOLOv11 detector localizes signature regions, ResNet-50 supplies deep features, and a dual-descriptor verification layer combines deep-feature cosine similarity with perceptual hashing (difference hash, dHash) to separate *style consistency* (high cosine, divergent dHash) from *image reproduction* (high cosine, low dHash). The operational classifier outputs a five-way verdict per signature with a worst-case document-level aggregation; the cosine cut is anchored on a transparent whole-sample Firm A P7.5 percentile (cos $> 0.95$), and the dHash cuts on the same reference. Applied to 90,282 audit reports filed in Taiwan over 2013-2023 (182,328 signatures from 758 CPAs), the operational dual rule cos $> 0.95$ AND $\text{dHash}_\text{indep} \leq 15$ captures 92.46\% of Firm A and yields FAR = 0.0005 against a $\sim$50,000-pair inter-CPA negative anchor; intra-report agreement is 89.9\% at Firm A versus 62-67\% at the other Big-4 firms (a 23-28 percentage-point cross-firm gap). Validation uses three annotation-free anchors (310 byte-identical positives, $\sim$50,000 inter-CPA negatives, and a 70/30 held-out Firm A fold) reported with Wilson 95\% intervals. Three statistical diagnostics applied to the per-signature similarity distribution (Hartigan dip test, EM-fitted Beta mixture with logit-Gaussian robustness check, Burgstahler-Dichev / McCrary density-smoothness procedure) jointly characterise the distribution as a continuous quality spectrum, which motivates the percentile-based anchor and is itself a substantive finding for similarity-threshold selection in document forensics.
+
+<!-- Target word count: 240 -->

paper/paper_a_appendix_v3.md

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+# Appendix A. BD/McCrary Bin-Width Sensitivity (Signature Level)
+
+The main text (Section III-I, Section IV-D.2) treats the Burgstahler-Dichev / McCrary discontinuity procedure [38], [39] as a *density-smoothness diagnostic* rather than as a threshold estimator.
+This appendix documents the empirical basis for that framing by sweeping the bin width across four (variant, bin-width) panels: Firm A and full-sample, each in the cosine and $\text{dHash}_\text{indep}$ direction.
+
+<!-- TABLE A.I: BD/McCrary Bin-Width Sensitivity (two-sided alpha = 0.05, |Z| > 1.96)
+| Variant | n | Bin width | Best transition | z_below | z_above |
+|---------|---|-----------|-----------------|---------|---------|
+| Firm A cosine (sig-level)        | 60,448  | 0.003  | 0.9870 | -2.81  | +9.42   |
+| Firm A cosine (sig-level)        | 60,448  | 0.005  | 0.9850 | -9.57  | +19.07  |
+| Firm A cosine (sig-level)        | 60,448  | 0.010  | 0.9800 | -54.64 | +69.96  |
+| Firm A cosine (sig-level)        | 60,448  | 0.015  | 0.9750 | -85.86 | +106.17 |
+| Firm A dHash_indep (sig-level)   | 60,448  | 1      | 2.0    | -4.69  | +10.01  |
+| Firm A dHash_indep (sig-level)   | 60,448  | 2      | no transition | — | — |
+| Firm A dHash_indep (sig-level)   | 60,448  | 3      | no transition | — | — |
+| Full-sample cosine (sig-level)   | 168,740 | 0.003  | 0.9870 | -3.21  | +8.17   |
+| Full-sample cosine (sig-level)   | 168,740 | 0.005  | 0.9850 | -8.80  | +14.32  |
+| Full-sample cosine (sig-level)   | 168,740 | 0.010  | 0.9800 | -29.69 | +44.91  |
+| Full-sample cosine (sig-level)   | 168,740 | 0.015  | 0.9450 | -11.35 | +14.85  |
+| Full-sample dHash_indep (sig-l.) | 168,740 | 1      | 2.0    | -6.22  | +4.89   |
+| Full-sample dHash_indep (sig-l.) | 168,740 | 2      | 10.0   | -7.35  | +3.83   |
+| Full-sample dHash_indep (sig-l.) | 168,740 | 3      | 9.0    | -11.05 | +45.39  |
+-->
+
+Two patterns are visible in Table A.I.
+First, the procedure consistently identifies a "transition" under every bin width, but the *location* of that transition drifts monotonically with bin width (Firm A cosine: 0.987 → 0.985 → 0.980 → 0.975 as bin width grows from 0.003 to 0.015; full-sample dHash: 2 → 10 → 9 as the bin width grows from 1 to 3).
+The $Z$ statistics also inflate superlinearly with the bin width (Firm A cosine $|Z|$ rises from $\sim 9$ at bin 0.003 to $\sim 106$ at bin 0.015) because wider bins aggregate more mass per bin and therefore shrink the per-bin standard error on a very large sample.
+Both features are characteristic of a histogram-resolution artifact rather than of a genuine density discontinuity.
+
+Second, the candidate transitions all locate *inside* the non-hand-signed mode (cosine $\geq 0.975$, dHash $\leq 10$) rather than between modes, which is the location pattern we would expect of a clean two-mechanism boundary.
+
+Taken together, Table A.I shows that the signature-level BD/McCrary transitions are not a threshold in the usual sense---they are histogram-resolution-dependent local density anomalies located *inside* the non-hand-signed mode rather than between modes.
+This observation supports the main-text decision to use BD/McCrary as a density-smoothness diagnostic rather than as a threshold estimator and reinforces the joint reading of Section IV-D that per-signature similarity does not form a clean two-mechanism mixture.
+
+Raw per-bin $Z$ sequences and $p$-values for every (variant, bin-width) panel are available in the supplementary materials.
+
+# Appendix B. Table-to-Script Provenance
+
+For reproducibility, the following table maps each numerical table in Section IV to the analysis script that produces its underlying values and to the report file emitted by that script. Scripts are under `signature_analysis/`. Report artifact paths below are listed relative to the project's analysis report root, which is `/Volumes/NV2/PDF-Processing/signature-analysis/` in our local deployment; replicators should rebase the paths to whatever report root they configure when invoking the scripts.
+
+<!-- TABLE B.I: Manuscript table → reproduction artifact
+| Manuscript table | Generating script | Report artifact |
+|------------------|-------------------|-----------------|
+| Table III (extraction results) | `02_extract_features.py`; `09_pdf_signature_verdict.py` | `reports/extraction_methodology.md`; `reports/pdf_signature_verdicts.json` |
+| Table IV (intra/inter all-pairs cosine statistics) | `10_formal_statistical_analysis.py` | `reports/formal_statistical_data.json`; `reports/formal_statistical_report.md` |
+| Table V (Hartigan dip test) | `15_hartigan_dip_test.py` | `reports/dip_test/dip_test_results.json` |
+| Table VI (signature-level threshold-estimator summary) | `17_beta_mixture_em.py`; `25_bd_mccrary_sensitivity.py` | `reports/beta_mixture/beta_mixture_results.json`; `reports/bd_sensitivity/bd_sensitivity.json` |
+| Table IX (Firm A whole-sample capture rates) | `19_pixel_identity_validation.py`; `24_validation_recalibration.py` | `reports/pixel_validation/pixel_validation_results.json`; `reports/validation_recalibration/validation_recalibration.json` |
+| Table X (cosine threshold sweep, FAR vs inter-CPA negatives) | `21_expanded_validation.py` | `reports/expanded_validation/expanded_validation_results.json` |
+| Table XI (held-out vs calibration Firm A capture rates) | `24_validation_recalibration.py` | `reports/validation_recalibration/validation_recalibration.json` |
+| Table XII (operational-cut sensitivity 0.95 vs 0.945) | `24_validation_recalibration.py` | `reports/validation_recalibration/validation_recalibration.json` |
+| Table XII-B (cosine-threshold tradeoff: capture vs inter-CPA FAR) | `21_expanded_validation.py` (FAR column; canonical 50k-pair anchor); inline computation in revision (Firm A and non-Firm-A capture columns) | `reports/expanded_validation/expanded_validation_results.json` |
+| Table XIII (Firm A per-year cosine distribution) | `29_firm_a_yearly_distribution.py` | `reports/firm_a_yearly/firm_a_yearly_distribution.json` |
+| Fig. 4 (per-firm yearly best-match cosine, 2013-2023) | `30_yearly_big4_comparison.py` | `reports/figures/fig_yearly_big4_comparison.{png,pdf}`; `reports/firm_yearly_comparison/firm_yearly_comparison.{json,md}` |
+| Tables XIV / XV (partner-level similarity ranking) | `22_partner_ranking.py` | `reports/partner_ranking/partner_ranking_results.json` |
+| Table XVI (intra-report classification agreement) | `23_intra_report_consistency.py` | `reports/intra_report/intra_report_results.json` |
+| Table XVII (document-level five-way classification) | `09_pdf_signature_verdict.py`; `12_generate_pdf_level_report.py` | `reports/pdf_signature_verdicts.json`; `reports/pdf_signature_verdict_report.md` (CSV / XLSX bulk reports also at `reports/`) |
+| Table XVIII (backbone ablation) | `paper/ablation_backbone_comparison.py` | `ablation/ablation_results.json` (sibling of `reports/`) |
+| Table A.I (BD/McCrary bin-width sensitivity) | `25_bd_mccrary_sensitivity.py` | `reports/bd_sensitivity/bd_sensitivity.json` |
+| Byte-identity decomposition (145 / 50 / 180 / 35; Section IV-F.1) | `28_byte_identity_decomposition.py` | `reports/byte_identity_decomp/byte_identity_decomposition.json` |
+| Cross-firm dual-descriptor convergence (Section IV-H.2) | `28_byte_identity_decomposition.py` | `reports/byte_identity_decomp/byte_identity_decomposition.json` |
+-->
+
+The table-to-script mapping above is intended as a navigation aid for replicators. All scripts run deterministically under the fixed random seeds documented in the supplementary materials; the artifact paths above were verified against the local deployment at the time of submission, and any reviewer reproduction step should re-emit the artifacts from the listed scripts rather than depend on the absolute path layout.

paper/paper_a_conclusion.md

@@ -0,0 +1,21 @@
+# VI. Conclusion and Future Work
+
+## Conclusion
+
+We have presented an end-to-end AI pipeline for detecting digitally replicated signatures in financial audit reports at scale.
+Applied to 90,282 audit reports from Taiwanese publicly listed companies spanning 2013--2023, our system extracted and analyzed 182,328 CPA signatures using a combination of VLM-based page identification, YOLO-based signature detection, deep feature extraction, and dual-method similarity verification.
+
+Our key findings are threefold.
+First, we argued that signature replication detection is a distinct problem from signature forgery detection, requiring different analytical tools focused on intra-signer similarity distributions.
+Second, we showed that combining cosine similarity of deep features with difference hashing is essential for meaningful classification---among 71,656 documents with high feature-level similarity, the structural verification layer revealed that only 41% exhibit converging replication evidence, while 7% show no structural corroboration despite near-identical features, demonstrating that a single-metric approach conflates style consistency with digital duplication.
+Third, we introduced a calibration methodology using a known-replication reference group whose distributional characteristics (dHash median = 5, 95th percentile = 15) directly informed the classification thresholds, achieving 96.9% capture of the calibration group.
+
+An ablation study comparing three feature extraction backbones (ResNet-50, VGG-16, EfficientNet-B0) confirmed that ResNet-50 offers the best balance of discriminative power, classification stability, and computational efficiency for this task.
+
+## Future Work
+
+Several directions merit further investigation.
+Domain-adapted feature extractors, trained or fine-tuned on signature-specific datasets, may improve discriminative performance beyond the transferred ImageNet features used in this study.
+Temporal analysis of signature similarity trends---tracking how individual CPAs' similarity profiles evolve over years---could reveal transitions between genuine signing and digital replication practices.
+The pipeline's applicability to other jurisdictions and document types (e.g., corporate filings in other countries, legal documents, medical records) warrants exploration.
+Finally, integration with regulatory monitoring systems and small-scale ground truth validation through expert review would strengthen the practical deployment potential of this approach.

paper/paper_a_conclusion_v3.md

@@ -0,0 +1,30 @@
+# VI. Conclusion and Future Work
+
+## Conclusion
+
+We have presented an end-to-end AI pipeline for detecting non-hand-signed auditor signatures in financial audit reports at scale.
+Applied to 90,282 audit reports from Taiwanese publicly listed companies spanning 2013--2023, our system extracted and analyzed 182,328 CPA signatures using a combination of VLM-based page identification, YOLO-based signature detection, deep feature extraction, and dual-descriptor similarity verification, with the operational classifier's cosine cut anchored on a whole-sample Firm A percentile heuristic and the per-signature similarity distribution characterised through two threshold estimators and a density-smoothness diagnostic.
+
+The seven numbered contributions listed in Section I can be grouped into four broader methodological themes, summarized below.
+
+First, we argued that non-hand-signing detection is a distinct problem from signature forgery detection, requiring analytical tools focused on the upper tail of intra-signer similarity rather than inter-signer discriminability.
+
+Second, we showed that combining cosine similarity of deep embeddings with difference hashing is essential for meaningful classification---among 71,656 documents with high feature-level similarity, the dual-descriptor framework revealed that only 41% exhibit converging structural evidence of non-hand-signing while 7% show no structural corroboration despite near-identical feature-level appearance, demonstrating that a single-descriptor approach conflates style consistency with image reproduction.
+
+Third, we characterised the per-signature similarity distribution using three diagnostics---a Hartigan dip test, an EM-fitted Beta mixture (with logit-Gaussian robustness check), and a Burgstahler-Dichev / McCrary density-smoothness procedure---and showed that no two-mechanism mixture cleanly explains it: the dip test fails to reject unimodality for Firm A ($p = 0.17$), BIC strongly prefers a 3-component over a 2-component Beta fit ($\Delta\text{BIC} = 381$ for Firm A), and the BD/McCrary candidate transition lies inside the non-hand-signed mode rather than between modes (and is not bin-width-stable; Appendix A).
+The substantive reading is that *pixel-level output quality* is a continuous spectrum produced by firm-specific reproduction technologies (administrative stamping in early years, firm-level e-signing later) and scan conditions, rather than a discrete class cleanly separated from hand-signing.
+This reading motivates anchoring the operational classifier's cosine cut on a whole-sample Firm A P7.5 percentile heuristic (cos $> 0.95$) rather than on a mixture-fit crossing.
+
+Fourth, we introduced a *replication-dominated* calibration methodology---explicitly distinguishing replication-dominated from replication-pure calibration anchors and validating classification against a byte-level pixel-identity anchor (310 byte-identical signatures) paired with a $\sim$50,000-pair inter-CPA negative anchor.
+To document the within-firm sampling variance of using the calibration firm as its own validation reference, we split the firm's CPAs 70/30 at the CPA level and report capture rates on both folds with Wilson 95% confidence intervals; extreme rules agree across folds while rules in the operational 85--95% capture band differ by 1--5 percentage points, reflecting within-firm heterogeneity in replication intensity rather than generalization failure.
+This framing is internally consistent with the available evidence: the byte-level pair analysis finding of 145 pixel-identical calibration-firm signatures across 50 distinct partners of 180 registered (Section IV-F.1); the 92.5% / 7.5% split in signature-level cosine thresholds and the dip-test-confirmed unimodal-long-tail shape of Firm A's per-signature cosine distribution (Section IV-D.1); and the 95.9% top-decile concentration of Firm A auditor-years in the threshold-independent partner-ranking analysis (Section IV-G.2).
+
+An ablation study comparing ResNet-50, VGG-16 and EfficientNet-B0 confirmed that ResNet-50 offers the best balance of discriminative power, classification stability, and computational efficiency for this task.
+
+## Future Work
+
+Several directions merit further investigation.
+Domain-adapted feature extractors, trained or fine-tuned on signature-specific datasets, may improve discriminative performance beyond the transferred ImageNet features used in this study.
+The pipeline's applicability to other jurisdictions and document types (e.g., corporate filings in other countries, legal documents, medical records) warrants exploration.
+The replication-dominated calibration strategy and the pixel-identity anchor technique are both generalizable to settings in which (i) a reference subpopulation has a known dominant mechanism and (ii) the target mechanism leaves a byte-level signature in the artifact itself, conditional on the availability of analogous anchors in the new domain and on artifact-generation physics that preserve the byte-level trace.
+Finally, integration with regulatory monitoring systems and a larger negative-anchor study---for example drawing from inter-CPA pairs under explicit accountant-level blocking---would strengthen the practical deployment potential of this approach.

paper/paper_a_declarations_v3.md

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+# Declarations
+
+**Conflict of interest.** The authors declare no conflict of interest with Firm A, Firm B, Firm C, or Firm D, or with any other entity referenced in this work.
+
+**Data availability.** All audit reports analysed in this study were obtained from the Market Observation Post System (MOPS) operated by the Taiwan Stock Exchange Corporation, a publicly accessible regulatory disclosure platform. The CPA registry used to map signatures to certifying CPAs is publicly available. Signature images, model weights, and reproducibility scripts are available in the supplementary materials.
+
+**Funding.** [To be filled in before submission.]

paper/paper_a_discussion.md

@@ -0,0 +1,57 @@
+# V. Discussion
+
+## A. Replication Detection as a Distinct Problem
+
+Our results highlight the importance of distinguishing signature replication detection from the well-studied signature forgery detection problem.
+In forgery detection, the challenge lies in modeling the variability of skilled forgers who produce plausible imitations of a target signature.
+In replication detection, the signer's identity is not in question; the challenge is distinguishing between legitimate intra-signer consistency (a CPA who signs similarly each time) and digital duplication (a CPA who reuses a scanned image).
+
+This distinction has direct methodological consequences.
+Forgery detection systems optimize for inter-class discriminability---maximizing the gap between genuine and forged signatures.
+Replication detection, by contrast, requires sensitivity to the *upper tail* of the intra-class similarity distribution, where the boundary between consistent handwriting and digital copies becomes ambiguous.
+The dual-method framework we propose---combining semantic-level features (cosine similarity) with structural-level features (pHash)---addresses this ambiguity in a way that single-method approaches cannot.
+
+## B. The Style-Replication Gap
+
+Perhaps the most important empirical finding is the stratification that the dual-method framework reveals within the high-cosine population.
+Of 71,656 documents with cosine similarity exceeding 0.95, the dHash dimension partitions them into three distinct groups: 29,529 (41.2%) with high-confidence structural evidence of replication, 36,994 (51.7%) with moderate structural similarity, and 5,133 (7.2%) with no structural corroboration despite near-identical feature-level appearance.
+A cosine-only approach would treat all 71,656 identically; the dual-method framework separates them into populations with fundamentally different interpretations.
+
+The 7.2% classified as "high style consistency" (cosine > 0.95 but dHash > 15) are particularly informative.
+Several plausible explanations may account for their high feature similarity without structural identity, though we lack direct evidence to confirm their relative contributions.
+Many accountants may develop highly consistent signing habits---using similar pen pressure, stroke order, and spatial layout---resulting in signatures that appear nearly identical at the feature level while retaining the microscopic variations inherent to handwriting.
+Some may use signing pads or templates that further constrain variability without constituting digital replication.
+The dual-method framework correctly identifies these as distinct from digitally replicated signatures by detecting the absence of structural-level convergence.
+
+## C. Value of Known-Replication Calibration
+
+The use of Firm A as a calibration reference addresses a fundamental challenge in document forensics: the scarcity of ground truth labels.
+In most forensic applications, establishing ground truth requires expensive manual verification or access to privileged information about document provenance.
+Our approach leverages domain knowledge---the established practice of digital signature replication at a specific firm---to create a naturally occurring positive control group within the dataset.
+
+This calibration strategy has broader applicability beyond signature analysis.
+Any forensic detection system operating on real-world corpora can benefit from identifying subpopulations with known characteristics (positive or negative) to anchor threshold selection, particularly when the distributions of interest are non-normal and percentile-based thresholds are preferred over parametric alternatives.
+
+## D. Limitations
+
+Several limitations should be acknowledged.
+
+First, comprehensive ground truth labels are not available for the full dataset.
+While Firm A provides a known-replication reference and the dual-method framework produces internally consistent results, the classification of non-Firm-A documents relies on statistical inference without independent per-document ground truth.
+A small-scale manual verification study (e.g., 100--200 documents sampled across classification categories) would strengthen confidence in the classification boundaries.
+
+Second, the ResNet-50 feature extractor was used with pre-trained ImageNet weights without domain-specific fine-tuning.
+While our ablation study and prior literature [20]--[22] support the effectiveness of transferred ImageNet features for signature comparison, a signature-specific feature extractor trained on a curated dataset could improve discriminative performance.
+
+Third, the red stamp removal preprocessing uses simple HSV color space filtering, which may introduce artifacts where handwritten strokes overlap with red seal impressions.
+In these overlap regions, blended pixels are replaced with white, potentially creating small gaps in the signature strokes that could reduce dHash similarity.
+This effect would make replication harder to detect (biasing toward false negatives) rather than easier, but the magnitude of the impact has not been quantified.
+
+Fourth, scanning equipment, PDF generation software, and compression algorithms may have changed over the 10-year study period (2013--2023), potentially affecting similarity measurements.
+While cosine similarity and dHash are designed to be robust to such variations, longitudinal confounds cannot be entirely excluded.
+
+Fifth, the classification framework treats all signatures from a CPA as belonging to a single class, not accounting for potential changes in signing practice over time (e.g., a CPA who signed genuinely in early years but adopted digital replication later).
+Temporal segmentation of signature similarity could reveal such transitions but is beyond the scope of this study.
+
+Finally, the legal and regulatory implications of our findings depend on jurisdictional definitions of "signature" and "signing."
+Whether digital replication of a CPA's own genuine signature constitutes a violation of signing requirements is a legal question that our technical analysis can inform but cannot resolve.

paper/paper_a_discussion_v3.md

@@ -0,0 +1,109 @@
+# V. Discussion
+
+## A. Non-Hand-Signing Detection as a Distinct Problem
+
+Our results highlight the importance of distinguishing *non-hand-signing detection* from the well-studied *signature forgery detection* problem.
+In forgery detection, the challenge lies in modeling the variability of skilled forgers who produce plausible imitations of a target signature.
+In non-hand-signing detection the signer's identity is not in question; the challenge is distinguishing between legitimate intra-signer consistency (a CPA who signs similarly each time) and image-level reproduction of a stored signature (a CPA whose signature on each report is a byte-level or near-byte-level copy of a single source image).
+
+This distinction has direct methodological consequences.
+Forgery detection systems optimize for inter-class discriminability---maximizing the gap between genuine and forged signatures.
+Non-hand-signing detection, by contrast, requires sensitivity to the *upper tail* of the intra-class similarity distribution, where the boundary between consistent handwriting and image reproduction becomes ambiguous.
+The dual-descriptor framework we propose---combining semantic-level features (cosine similarity) with structural-level features (dHash)---addresses this ambiguity in a way that single-descriptor approaches cannot.
+
+## B. Per-Signature Similarity is a Continuous Quality Spectrum
+
+A central empirical finding of this study is that per-signature similarity does not form a clean two-mechanism mixture (Section IV-D).
+Firm A's signature-level cosine is formally unimodal (Hartigan dip test $p = 0.17$) with a long left tail.
+The all-CPA signature-level cosine rejects unimodality ($p < 0.001$), reflecting the heterogeneity of signing practices across firms, but its structure is not well approximated by a two-component Beta mixture: BIC clearly prefers a three-component fit ($\Delta\text{BIC} = 381$ for Firm A; $10{,}175$ for the full sample), and the forced 2-component Beta crossing and its logit-GMM robustness counterpart disagree sharply on the candidate threshold (0.977 vs. 0.999 for Firm A).
+The BD/McCrary discontinuity test locates its transition at cosine 0.985---*inside* the non-hand-signed mode rather than at a boundary between two mechanisms---and the transition is not bin-width-stable (Appendix A).
+
+Taken together, these results indicate that non-hand-signed signatures form a continuous quality spectrum rather than a discrete class cleanly separated from hand-signing.
+Replication quality varies continuously with scan equipment, PDF compression, stamp pressure, and firm-level e-signing system generation, producing a heavy-tailed distribution that no two-mechanism mixture explains at the signature level.
+
+The methodological implication is that the operational classifier's cosine cut should not be derived from a mixture-fit crossing.
+We accordingly anchor the operational cosine cut on the whole-sample Firm A P7.5 percentile (Section III-K), and treat the signature-level threshold-estimator outputs (KDE antimode, Beta and logit-Gaussian crossings) as descriptive characterisation of the similarity distribution rather than as the source of operational thresholds.
+The BD/McCrary procedure plays a *density-smoothness diagnostic* role in this framing rather than that of an independent threshold estimator.
+
+This continuous-spectrum finding also has substantive implications for downstream interpretation.
+Because pixel-level output quality varies continuously, *signature-level rates* (such as the 92.5% / 7.5% Firm A split) reflect the share of signatures whose similarity falls above or below a chosen threshold rather than the share that came from a "non-hand-signing mechanism" versus a "hand-signing mechanism."
+We accordingly report all rates as signature-level quantities and abstain from partner-level frequency claims (Section III-G).
+
+## C. Firm A as a Replication-Dominated, Not Pure, Population
+
+A recurring theme in prior work that treats Firm A or an analogous reference group as a calibration anchor is the implicit assumption that the anchor is a pure positive class.
+Our evidence across multiple analyses rules out that assumption for Firm A while affirming its utility as a calibration reference.
+
+Two convergent strands of evidence support the replication-dominated framing.
+First, the byte-level pair evidence: 145 Firm A signatures (from 50 distinct partners of 180 registered) have a byte-identical same-CPA match in a different audit report, with 35 of these matches spanning different fiscal years.
+Independent hand-signing cannot produce byte-identical images across distinct reports, so these pairs directly establish image reuse within Firm A as a concrete, threshold-free phenomenon, and the 50/180 partner spread shows that replication is widespread rather than confined to a handful of CPAs.
+Second, the signature-level distributional evidence: Firm A's per-signature cosine distribution is unimodal long-tail (Hartigan dip test $p = 0.17$) rather than a tight single peak; 92.5% of Firm A signatures exceed cosine 0.95, with the remaining 7.5% forming the left tail.
+The unimodal-long-tail *shape*, not the precise 92.5 / 7.5 split, is the structural evidence: it is consistent with a dominant high-similarity regime plus residual within-firm heterogeneity, and a noise-only explanation of the left tail would predict a shrinking share as scan/PDF technology matured over 2013--2023, which is not what we observe (Section IV-G.1).
+
+Two additional checks, reported in Section IV-G, are robust to threshold choice and complement the two primary strands:
+the held-out Firm A 70/30 validation (Section IV-F.2) gives capture rates on a non-calibration Firm A subset that sit in the same replication-dominated regime as the calibration fold across the full range of operating rules (extreme rules are statistically indistinguishable; operational rules in the 85--95% band differ between folds by 1--5 percentage points, reflecting within-Firm-A heterogeneity in replication intensity rather than a generalization failure), and the threshold-independent partner-ranking analysis (Section IV-G.2) shows that Firm A auditor-years occupy 95.9% of the top decile of similarity-ranked auditor-years against a 27.8% baseline share---a 3.5$\times$ concentration ratio that uses only ordinal ranking and is independent of any absolute cutoff.
+
+The replication-dominated framing is internally coherent with both pieces of evidence, and it predicts and explains the residuals that a "near-universal" framing would be forced to treat as noise.
+We therefore recommend that future work building on this calibration strategy should explicitly distinguish replication-dominated from replication-pure calibration anchors.
+
+## D. The Style-Replication Gap
+
+Within the 71,656 documents exceeding cosine $0.95$, the dHash descriptor partitions them into three distinct populations: 29,529 (41.2%) with high-confidence structural evidence of non-hand-signing, 36,994 (51.7%) with moderate structural similarity, and 5,133 (7.2%) with no structural corroboration despite near-identical feature-level appearance.
+A cosine-only classifier would treat all 71,656 documents identically; the dual-descriptor framework separates them into populations with fundamentally different interpretations.
+
+The 7.2% classified as "high style consistency" (cosine $> 0.95$ but dHash $> 15$) are particularly informative.
+Several plausible explanations may account for their high feature similarity without structural identity, though we lack direct evidence to confirm their relative contributions.
+Many accountants may develop highly consistent signing habits---using similar pen pressure, stroke order, and spatial layout---resulting in signatures that appear nearly identical at the semantic feature level while retaining the microscopic variations inherent to handwriting.
+Some may use signing pads or templates that further constrain variability without constituting image-level reproduction.
+The dual-descriptor framework correctly identifies these cases as distinct from non-hand-signed signatures by detecting the absence of structural-level convergence.
+
+## E. Value of a Replication-Dominated Calibration Group
+
+The use of Firm A as a calibration reference addresses a fundamental challenge in document forensics: the scarcity of ground truth labels.
+In most forensic applications, establishing ground truth requires expensive manual verification or access to privileged information about document provenance.
+Our approach uses practitioner background---one Big-4 firm reportedly relies predominantly on stamping or e-signing workflows---only as a *motivation* for selecting that firm as a candidate reference population; the calibration role is then established from the audit-report images themselves (byte-identical same-CPA pairs, the Firm A per-signature similarity distribution, partner-ranking concentration, and intra-report consistency), so the calibration does not depend on the practitioner-background claim being externally verified (Section III-H).
+
+This calibration strategy has broader applicability beyond signature analysis.
+Any forensic detection system operating on real-world corpora can benefit from identifying subpopulations with known dominant characteristics (positive or negative) to anchor threshold selection, particularly when the distributions of interest are non-normal and non-parametric or mixture-based thresholds are preferred over parametric alternatives.
+The framing we adopt---replication-dominated rather than replication-pure---is an important refinement of this strategy: it prevents overclaim, accommodates the within-firm heterogeneity visible in the unimodal-long-tail shape of Firm A's per-signature cosine distribution, and yields classification rates that are internally consistent with the data.
+
+## F. Pixel-Identity and Inter-CPA Anchors as Annotation-Free Validation
+
+A further methodological contribution is the combination of byte-level pixel identity as an annotation-free *conservative* gold positive and a large random-inter-CPA negative anchor.
+Handwriting physics makes byte-identity impossible under independent signing events, so any pair of same-CPA signatures that are byte-identical after crop and normalization is pair-level proof of image reuse and, modulo the narrow source-template edge case discussed in the seventh limitation below, a conservative positive for non-hand-signing without requiring human review.
+In our corpus 310 signatures satisfied this condition.
+We emphasize that byte-identical pairs are a *subset* of the true non-hand-signed positive class---they capture only those whose nearest same-CPA match happens to be bytewise identical, excluding replications that are pixel-near-identical but not byte-identical (for example, under different scan or compression pathways).
+Perfect recall against this subset therefore does not generalize to perfect recall against the full non-hand-signed population; it is a lower-bound calibration check on the classifier's ability to catch the clearest positives rather than a generalizable recall estimate.
+
+Paired with the $\sim$50,000-pair inter-CPA negative anchor, the byte-identical positives yield FAR estimates with tight Wilson 95% confidence intervals (Table X), which is a substantive improvement over the low-similarity same-CPA negative ($n = 35$) we originally considered.
+The combination is a reusable pattern for other document-forensics settings in which the target mechanism leaves a byte-level physical signature in the artifact itself, provided that its generalization limits are acknowledged: FAR is informative, whereas recall is valid only for the conservative subset.
+
+## G. Limitations
+
+Several limitations should be acknowledged.
+
+First, comprehensive per-document ground truth labels are not available.
+The pixel-identity anchor is a strict *subset* of the true non-hand-signing positives (only those whose nearest same-CPA match happens to be byte-identical), so perfect recall against this anchor does not establish the classifier's recall on the broader positive class.
+The low-similarity same-CPA anchor ($n = 35$) is small because intra-CPA pairs rarely fall below cosine 0.70; we use the $\sim$50,000-pair inter-CPA negative anchor as the primary negative reference, which yields tight Wilson 95% CIs on FAR (Table X), but it too does not exhaust the set of true negatives (in particular, same-CPA hand-signed pairs with moderate cosine similarity are not sampled).
+A manual-adjudication study concentrated at the decision boundary---for example 100--300 auditor-years stratified by cosine band---would further strengthen the recall estimate against the full positive class.
+
+Second, the ResNet-50 feature extractor was used with pre-trained ImageNet weights without domain-specific fine-tuning.
+While our ablation study and prior literature [20]--[22] support the effectiveness of transferred ImageNet features for signature comparison, a signature-specific feature extractor could improve discriminative performance.
+
+Third, the red stamp removal preprocessing uses simple HSV color-space filtering, which may introduce artifacts where handwritten strokes overlap with red seal impressions.
+In these overlap regions, blended pixels are replaced with white, potentially creating small gaps in the signature strokes that could reduce dHash similarity.
+This effect would bias classification toward false negatives rather than false positives, but the magnitude has not been quantified.
+
+Fourth, scanning equipment, PDF generation software, and compression algorithms may have changed over the 10-year study period (2013--2023), potentially affecting similarity measurements.
+While cosine similarity and dHash are designed to be robust to such variations, longitudinal confounds cannot be entirely excluded.
+
+Fifth, the max/min detection logic treats both ends of a near-identical same-CPA pair as non-hand-signed.
+In the rare case that one of the two documents contains a genuinely hand-signed exemplar that was subsequently reused as the stamping or e-signature template, the pair correctly identifies image reuse but misattributes the non-hand-signed status to the source exemplar.
+This misattribution affects at most one source document per template variant per CPA (the exemplar from which the template was produced), is not expected to be common given that stored signature templates are typically generated in a separate acquisition step rather than extracted from submitted audit reports, and does not materially affect aggregate capture rates at the firm level.
+
+Sixth, our analyses remain at the signature level; we abstain from partner-level frequency inferences such as "X% of CPAs hand-sign in a given year."
+Per-signature labels in this paper are not translated to per-report or per-partner mechanism assignments (Section III-G).
+The signature-level rates we report, including the 92.5% / 7.5% Firm A split and the year-by-year left-tail share of Section IV-G.1, should accordingly be read as signature-level quantities rather than partner-level frequencies.
+
+Finally, the legal and regulatory implications of our findings depend on jurisdictional definitions of "signature" and "signing."
+Whether non-hand-signing of a CPA's own stored signature constitutes a violation of signing requirements is a legal question that our technical analysis can inform but cannot resolve.

paper/paper_a_impact_statement.md

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+# Impact Statement
+
+<!-- 100-150 words. Non-specialist readable. No jargon. Specific, not vague. -->
+
+Auditor signatures on financial reports are a key safeguard of corporate accountability.
+When Certified Public Accountants digitally copy and paste a single signature image across multiple reports instead of signing each one individually, this safeguard is undermined---yet detecting such practices through manual inspection is infeasible at the scale of modern financial markets.
+We developed an artificial intelligence system that automatically extracts and analyzes signatures from over 90,000 audit reports spanning over a decade of filings by publicly listed companies.
+By combining deep learning-based visual feature analysis with perceptual hashing, the system distinguishes genuinely handwritten signatures from digitally replicated ones.
+Our analysis reveals substantial variation in signature similarity patterns across accounting firms, with a calibration group independently identified as using digital replication exhibiting distinctly higher similarity scores.
+After further validation, this technology could serve as an automated screening tool to support financial regulators in monitoring signature authenticity at national scale.

paper/paper_a_impact_statement_v3.md

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+<!--
+ARCHIVED. Not part of the IEEE Access submission.
+
+IEEE Access Regular Papers do not include a separate Impact Statement
+section. The text below is retained for possible reuse in a cover
+letter, grant report, or non-IEEE venue. It is excluded from the
+assembled paper by export_v3.py.
+
+If reused, note that the wording "distinguishes genuinely hand-signed
+signatures from reproduced ones" overstates what a five-way confidence
+classifier without a fully labeled test set establishes; soften before
+external use.
+-->
+
+# Impact Statement (archived; not in IEEE Access submission)
+
+Auditor signatures on financial reports are a key safeguard of corporate accountability.
+When the signature on an audit report is produced by reproducing a stored image instead of by the partner's own hand---whether through an administrative stamping workflow or a firm-level electronic signing system---this safeguard is weakened, yet detecting the practice through manual inspection is infeasible at the scale of modern financial markets.
+We developed a pipeline that automatically extracts and analyzes signatures from over 90,000 audit reports spanning a decade of filings by publicly listed companies in Taiwan.
+Combining deep-learning visual features with perceptual hashing and two methodologically distinct threshold estimators (plus a density-smoothness diagnostic), the system stratifies signatures into a five-way confidence-graded classification and quantifies how the practice varies across firms and over time.
+After further validation, the technology could support financial regulators in screening signature authenticity at national scale.

paper/paper_a_introduction.md

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+# I. Introduction
+
+<!-- Target: ~1.5 pages double-column IEEE format. Double-blind: no author/institution info. -->
+
+Financial audit reports serve as a critical mechanism for ensuring corporate accountability and investor protection.
+In Taiwan, the Certified Public Accountant Act (會計師法 §4) and the Financial Supervisory Commission's attestation regulations (查核簽證核准準則 §6) require that certifying CPAs affix their signature or seal (簽名或蓋章) to each audit report [1].
+While the law permits either a handwritten signature or a seal, the CPA's attestation on each report is intended to represent a deliberate, individual act of professional endorsement for that specific audit engagement [2].
+
+The digitization of financial reporting, however, has introduced a practice that challenges this intent.
+As audit reports are now routinely generated, transmitted, and archived as PDF documents, it is technically trivial for a CPA to digitally replicate a single scanned signature image and paste it across multiple reports.
+Although this practice may fall within the literal statutory requirement of "signature or seal," it raises substantive concerns about audit quality, as an identically reproduced signature applied across hundreds of reports may not represent meaningful attestation of individual professional judgment for each engagement.
+Unlike traditional signature forgery, where a third party attempts to imitate another person's handwriting, signature replication involves the legitimate signer reusing a digital copy of their own genuine signature.
+This practice, while potentially widespread, is virtually undetectable through manual inspection at scale: regulatory agencies overseeing thousands of publicly listed companies cannot feasibly examine each signature for evidence of digital duplication.
+
+The distinction between signature *replication* and signature *forgery* is both conceptually and technically important.
+The extensive body of research on offline signature verification [3]--[8] has focused almost exclusively on forgery detection---determining whether a questioned signature was produced by its purported author or by an impostor.
+This framing presupposes that the central threat is identity fraud.
+In our context, identity is not in question; the CPA is indeed the legitimate signer.
+The question is whether the physical act of signing occurred for each individual report, or whether a single signing event was digitally propagated across many reports.
+This replication detection problem differs fundamentally from forgery detection: while it does not require modeling the variability of skilled forgers, it introduces the distinct challenge of separating legitimate intra-signer consistency from digital duplication, requiring an analytical framework focused on detecting abnormally high similarity across documents.
+
+Despite the significance of this problem for audit quality and regulatory oversight, no prior work has specifically addressed the detection of same-signer digital replication in financial audit documents at scale.
+Woodruff et al. [9] developed an automated pipeline for signature analysis in corporate filings for anti-money laundering investigations, but their work focused on author clustering (grouping signatures by signer identity) rather than detecting reuse of digital copies.
+Copy-move forgery detection methods [10], [11] address duplicated regions within or across images, but are designed for natural images and do not account for the specific characteristics of scanned document signatures, where legitimate visual similarity between a signer's authentic signatures is expected and must be distinguished from digital duplication.
+Research on near-duplicate image detection using perceptual hashing combined with deep learning [12], [13] provides relevant methodological foundations, but has not been applied to document forensics or signature analysis.
+
+In this paper, we present a fully automated, end-to-end pipeline for detecting digitally replicated CPA signatures in audit reports at scale.
+Our approach processes raw PDF documents through six sequential stages: (1) signature page identification using a Vision-Language Model (VLM), (2) signature region detection using a trained YOLOv11 object detector, (3) deep feature extraction via a pre-trained ResNet-50 convolutional neural network, (4) dual-method similarity verification combining cosine similarity of deep features with difference hash (dHash) distance, (5) distribution-free threshold calibration using a known-replication reference group, and (6) statistical classification with cross-method validation.
+
+The dual-method verification is central to our contribution.
+Cosine similarity of deep feature embeddings captures high-level visual style similarity---it can identify signatures that share similar stroke patterns and spatial layouts---but cannot distinguish between a CPA who signs consistently and one who reuses a digital copy.
+Perceptual hashing (specifically, difference hashing), by contrast, encodes structural-level image gradients into compact binary fingerprints that are robust to scan noise but sensitive to substantive content differences.
+By requiring convergent evidence from both methods, we can differentiate *style consistency* (high cosine similarity but divergent pHash) from *digital replication* (high cosine similarity with convergent pHash), resolving an ambiguity that neither method can address alone.
+
+A distinctive feature of our approach is the use of a known-replication calibration group for threshold validation.
+One major Big-4 accounting firm in Taiwan (hereafter "Firm A") is widely recognized within the audit profession as using digitally replicated signatures across its audit reports.
+This status was established through three independent lines of evidence prior to our analysis: (1) visual inspection of a random sample of Firm A's reports reveals pixel-identical signature images across different audit engagements and fiscal years; (2) the practice is acknowledged as common knowledge among audit practitioners in Taiwan; and (3) our subsequent quantitative analysis confirmed this independently, with 92.5% of Firm A's signatures exhibiting best-match cosine similarity exceeding 0.95, consistent with digital replication rather than handwriting.
+Importantly, Firm A's known-replication status was not derived from the thresholds we calibrate against it; the identification is based on domain knowledge and visual evidence that is independent of the statistical pipeline.
+This provides an empirical anchor for calibrating detection thresholds: any threshold that fails to classify the vast majority of Firm A's signatures as replicated is demonstrably too conservative, while Firm A's distributional characteristics establish the range of similarity values achievable through replication in real-world scanned documents.
+This calibration strategy---using a known-positive subpopulation to validate detection thresholds---addresses a persistent challenge in document forensics, where comprehensive ground truth labels are scarce.
+
+We apply this pipeline to 90,282 audit reports filed by publicly listed companies in Taiwan between 2013 and 2023, extracting and analyzing 182,328 individual CPA signatures from 758 unique accountants.
+To our knowledge, this represents the largest-scale forensic analysis of signature authenticity in financial documents reported in the literature.
+
+The contributions of this paper are summarized as follows:
+
+1. **Problem formulation:** We formally define the signature replication detection problem as distinct from signature forgery detection, and argue that it requires a different analytical framework focused on intra-signer similarity distributions rather than genuine-versus-forged classification.
+
+2. **End-to-end pipeline:** We present a pipeline that processes raw PDF audit reports through VLM-based page identification, YOLO-based signature detection, deep feature extraction, and dual-method similarity verification, with automated inference requiring no manual intervention after initial training and annotation.
+
+3. **Dual-method verification:** We demonstrate that combining deep feature cosine similarity with perceptual hashing resolves the fundamental ambiguity between style consistency and digital replication, supported by an ablation study comparing three feature extraction backbones.
+
+4. **Calibration methodology:** We introduce a threshold calibration approach using a known-replication reference group, providing empirical validation in a domain where labeled ground truth is scarce.
+
+5. **Large-scale empirical analysis:** We report findings from the analysis of over 90,000 audit reports spanning a decade, providing the first large-scale empirical evidence on signature replication practices in financial reporting.
+
+The remainder of this paper is organized as follows.
+Section II reviews related work on signature verification, document forensics, and perceptual hashing.
+Section III describes the proposed methodology.
+Section IV presents experimental results including the ablation study and calibration group analysis.
+Section V discusses the implications and limitations of our findings.
+Section VI concludes with directions for future work.
+
+<!-- 
+REFERENCES used in Introduction:
+[1] Taiwan CPA Act §4 (會計師法第4條) + FSC Attestation Regulations §6 (查核簽證核准準則第6條)
+    - CPA Act: https://law.moj.gov.tw/ENG/LawClass/LawAll.aspx?pcode=G0400067
+    - FSC Regs: https://law.moj.gov.tw/LawClass/LawAll.aspx?pcode=G0400013
+[2] Yen, Chang & Chen 2013 — Does the signature of a CPA matter? (Res. Account. Regul., vol. 25, no. 2)
+[2] Bromley et al. 1993 — Siamese time delay neural network for signature verification (NeurIPS)
+[3] Dey et al. 2017 — SigNet: Siamese CNN for writer-independent offline SV (arXiv:1707.02131)
+[4] Hadjadj et al. 2020 — Single known sample offline SV (Applied Sciences)
+[5] Li et al. 2024 — TransOSV: Transformer for offline SV (Pattern Recognition)
+[6] Tehsin et al. 2024 — Triplet Siamese for digital documents (Mathematics)
+[7] Brimoh & Olisah 2024 — Consensus threshold for offline SV (arXiv:2401.03085)
+[8] Woodruff et al. 2021 — Fully automatic pipeline for document signature analysis / money laundering (arXiv:2107.14091)
+[9] Abramova & Böhme 2016 — Copy-move forgery detection in scanned text documents (Electronic Imaging)
+[10] Copy-move forgery detection survey — MTAP 2024
+[11] Jakhar & Borah 2025 — Near-duplicate detection using pHash + deep learning (Info. Processing & Management)
+[12] Pizzi et al. 2022 — SSCD: Self-supervised copy detection (CVPR)
+-->

paper/paper_a_introduction_v3.md

@@ -0,0 +1,86 @@
+# I. Introduction
+
+<!-- Target: ~1.5 pages double-column IEEE format. Double-blind: no author/institution info. -->
+
+Financial audit reports serve as a critical mechanism for ensuring corporate accountability and investor protection.
+In Taiwan, the Certified Public Accountant Act (會計師法 §4) and the Financial Supervisory Commission's attestation regulations (查核簽證核准準則 §6) require that certifying CPAs affix their signature or seal (簽名或蓋章) to each audit report [1].
+While the law permits either a handwritten signature or a seal, the CPA's attestation on each report is intended to represent a deliberate, individual act of professional endorsement for that specific audit engagement [2].
+
+The digitization of financial reporting has introduced a practice that complicates this intent.
+As audit reports are now routinely generated, transmitted, and archived as PDF documents, it is technically and operationally straightforward to reproduce a CPA's stored signature image across many reports rather than re-executing the signing act for each one.
+This reproduction can occur either through an administrative stamping workflow---in which scanned signature images are affixed by staff as part of the report-assembly process---or through a firm-level electronic signing system that automates the same step.
+From the perspective of the output image the two workflows are equivalent: both can reproduce one or more stored signature images, producing same-CPA signatures that are identical or near-identical up to reproduction, scanning, compression, and template-variant noise.
+We refer to signatures produced by either workflow collectively as *non-hand-signed*.
+Although this practice may fall within the literal statutory requirement of "signature or seal," it raises substantive concerns about audit quality, as an identically reproduced signature applied across hundreds of reports may not represent meaningful individual attestation for each engagement.
+The accounting literature has long examined the audit-quality consequences of partner-level engagement transparency: studies of partner-signature mandates in the United Kingdom find measurable downstream effects [31], cross-jurisdictional evidence on individual partner signature requirements highlights similar quality channels [32], and Taiwan-specific evidence on mandatory partner rotation documents how individual-partner identification interacts with audit-quality outcomes [33].
+Unlike traditional signature forgery, where a third party attempts to imitate another person's handwriting, non-hand-signing involves the legitimate signer's own stored signature being reused.
+This practice, while potentially widespread, is visually invisible to report users and virtually undetectable through manual inspection at scale: regulatory agencies overseeing thousands of publicly listed companies cannot feasibly examine each signature for evidence of image reproduction.
+
+The distinction between *non-hand-signing detection* and *signature forgery detection* is both conceptually and technically important.
+The extensive body of research on offline signature verification [3]--[8] has focused almost exclusively on forgery detection---determining whether a questioned signature was produced by its purported author or by an impostor.
+This framing presupposes that the central threat is identity fraud.
+In our context, identity is not in question; the CPA is indeed the legitimate signer.
+The question is whether the physical act of signing occurred for each individual report, or whether a single signing event was reproduced as an image across many reports.
+This detection problem differs fundamentally from forgery detection: while it does not require modeling skilled-forger variability, it introduces the distinct challenge of separating legitimate intra-signer consistency from image-level reproduction, requiring an analytical framework focused on detecting abnormally high similarity across documents.
+
+A secondary methodological concern shapes the research design.
+Many prior similarity-based classification studies rely on ad-hoc thresholds---declaring two images equivalent above a hand-picked cosine cutoff, for example---without principled statistical justification.
+Such thresholds are fragile in an archival-data setting where the cost of misclassification propagates into downstream inference.
+A defensible approach requires (i) a transparent threshold anchored to an empirical reference population drawn from the target corpus; (ii) statistical diagnostics that characterise the *shape* of the underlying similarity distribution and so motivate the choice of anchor; and (iii) external validation against naturally-occurring anchor populations---byte-level identical pairs as a conservative gold positive subset and large random inter-CPA pairs as a gold negative population---reported with Wilson 95% confidence intervals on per-rule capture / FAR rates, since precision and $F_1$ are not meaningful when the positive and negative anchor populations are sampled from different units.
+
+Despite the significance of the problem for audit quality and regulatory oversight, no prior work has specifically addressed non-hand-signing detection in financial audit documents at scale with these methodological safeguards.
+Woodruff et al. [9] developed an automated pipeline for signature analysis in corporate filings for anti-money-laundering investigations, but their work focused on author clustering (grouping signatures by signer identity) rather than detecting reuse of a stored image.
+Copy-move forgery detection methods [10], [11] address duplicated regions within or across images but are designed for natural images and do not account for the specific characteristics of scanned document signatures, where legitimate visual similarity between a signer's authentic signatures is expected and must be distinguished from image reproduction.
+Research on near-duplicate image detection using perceptual hashing combined with deep learning [12], [13] provides relevant methodological foundations but has not been applied to document forensics or signature analysis.
+From the statistical side, the methods we adopt for distributional characterisation---the Hartigan dip test [37] and finite mixture modelling via the EM algorithm [40], [41], complemented by a Burgstahler-Dichev / McCrary density-smoothness diagnostic [38], [39]---have been developed in statistics and accounting-econometrics but have not, to our knowledge, been combined as a joint diagnostic toolkit for document-forensics threshold selection.
+
+In this paper, we present a fully automated, end-to-end pipeline for detecting non-hand-signed CPA signatures in audit reports at scale.
+Our approach processes raw PDF documents through the following stages:
+(1) signature page identification using a Vision-Language Model (VLM);
+(2) signature region detection using a trained YOLOv11 object detector;
+(3) deep feature extraction via a pre-trained ResNet-50 convolutional neural network;
+(4) dual-descriptor similarity computation combining cosine similarity on deep embeddings with difference hash (dHash) distance;
+(5) signature-level distributional characterisation using two threshold estimators---KDE antimode with a Hartigan unimodality test and finite Beta mixture via EM with a logit-Gaussian robustness check---complemented by a Burgstahler-Dichev / McCrary density-smoothness diagnostic, used to read the structure of the per-signature similarity distribution and to motivate a percentile-based operational anchor rather than a mixture-fit crossing; and
+(6) validation against a pixel-identical anchor, a low-similarity anchor, and a replication-dominated Big-4 calibration firm.
+
+The dual-descriptor verification is central to our contribution.
+Cosine similarity of deep feature embeddings captures high-level visual style similarity---it can identify signatures that share similar stroke patterns and spatial layouts---but cannot distinguish between a CPA who signs consistently and one whose signature is reproduced from a stored image.
+Perceptual hashing (specifically, difference hashing) encodes structural-level image gradients into compact binary fingerprints that are robust to scan noise but sensitive to substantive content differences.
+By requiring convergent evidence from both descriptors, we can differentiate *style consistency* (high cosine but divergent dHash) from *image reproduction* (high cosine with low dHash), resolving an ambiguity that neither descriptor can address alone.
+
+A second distinctive feature is our framing of the calibration reference.
+One major Big-4 accounting firm in Taiwan (hereafter "Firm A") was selected as a candidate calibration reference based on practitioner-knowledge motivation; its benchmark status is then evaluated using the image evidence reported in this paper, not asserted by the practitioner-knowledge motivation itself.
+We therefore treat Firm A as a *replication-dominated* calibration reference rather than a pure positive class.
+This framing is important because the statistical signature of a replication-dominated population is visible in our data: Firm A's per-signature cosine distribution is unimodal with a long left tail (Hartigan dip $p = 0.17$), 92.5% of Firm A signatures exceed cosine 0.95 with the remaining 7.5% forming the left tail, and 145 Firm A signatures across 50 distinct partners are byte-identical to a same-CPA match in a different audit report (35 spanning different fiscal years).
+Adopting the replication-dominated framing---rather than a near-universal framing that would have to absorb the 7.5% residual as noise---ensures internal coherence between the byte-level pixel-identity evidence and the signature-level distributional shape.
+
+A third distinctive feature is the empirical reading we take from the per-signature distributional analysis.
+Three diagnostics applied to the per-signature similarity distribution---the Hartigan dip test, an EM-fitted Beta mixture (with logit-Gaussian robustness check), and the Burgstahler-Dichev / McCrary density-smoothness procedure---jointly indicate that no two-mechanism mixture cleanly explains per-signature similarity: the dip test fails to reject unimodality for Firm A, BIC strongly prefers a 3-component over a 2-component Beta fit, and the BD/McCrary candidate transition lies *inside* the non-hand-signed mode rather than between modes (and is not bin-width-stable; Appendix A).
+The substantive reading is that *pixel-level output quality* is a continuous spectrum shaped by firm-specific reproduction technologies (administrative stamping in early years, firm-level e-signing later) and scan conditions, rather than a discrete class cleanly separated from hand-signing.
+This reading motivates anchoring the operational classifier on a percentile heuristic over the Firm A reference distribution rather than on a mixture-fit crossing, and it motivates the byte-level pixel-identity anchor (Section IV-F.1) as a threshold-free positive reference that does not depend on resolving signature-level mixture structure.
+
+We apply this pipeline to 90,282 audit reports filed by publicly listed companies in Taiwan between 2013 and 2023, extracting and analyzing 182,328 individual CPA signatures from 758 unique accountants.
+To our knowledge, this represents the largest-scale forensic analysis of signature authenticity in financial documents reported in the literature.
+
+The contributions of this paper are summarized as follows:
+
+1. **Problem formulation.** We formally define non-hand-signing detection as distinct from signature forgery detection and argue that it requires an analytical framework focused on intra-signer similarity distributions rather than genuine-versus-forged classification.
+
+2. **End-to-end pipeline.** We present a pipeline that processes raw PDF audit reports through VLM-based page identification, YOLO-based signature detection, deep feature extraction, and dual-descriptor similarity computation, with automated inference requiring no manual intervention after initial training and annotation.
+
+3. **Dual-descriptor verification.** We demonstrate that combining deep-feature cosine similarity with perceptual hashing resolves the fundamental ambiguity between style consistency and image reproduction, and we validate the backbone choice through an ablation study comparing three feature-extraction architectures.
+
+4. **Percentile-anchored operational threshold.** We anchor the operational classifier's cosine cut on the whole-sample Firm A P7.5 percentile (cos $> 0.95$), a transparent and reproducible reference drawn from a replication-dominated reference population, and complement it with dHash structural cuts derived from the same reference distribution. Operational thresholds are therefore explained by an empirical reference rather than asserted.
+
+5. **Distributional characterisation of per-signature similarity.** We apply three statistical diagnostics---a Hartigan dip test, an EM-fitted Beta mixture with logit-Gaussian robustness check, and a Burgstahler-Dichev / McCrary density-smoothness procedure---to characterise the shape of the per-signature similarity distribution. The three diagnostics jointly find that per-signature similarity forms a continuous quality spectrum, which both motivates the percentile-based operational anchor over a mixture-fit crossing and is itself a substantive finding for the document-forensics literature on similarity-threshold selection.
+
+6. **Replication-dominated calibration methodology.** We introduce a calibration strategy using a replication-dominated reference group, distinguishing *replication-dominated* from *replication-pure* anchors; and we validate classification using byte-level pixel identity as an annotation-free gold positive, requiring no manual labeling.
+
+7. **Large-scale empirical analysis.** We report findings from the analysis of over 90,000 audit reports spanning a decade, providing the first large-scale empirical evidence on non-hand-signing practices in financial reporting under a methodology designed for peer-review defensibility.
+
+The remainder of this paper is organized as follows.
+Section II reviews related work on signature verification, document forensics, perceptual hashing, and the statistical methods we adopt for distributional characterisation.
+Section III describes the proposed methodology.
+Section IV presents experimental results including the signature-level distributional characterisation, pixel-identity validation, and backbone ablation study.
+Section V discusses the implications and limitations of our findings.
+Section VI concludes with directions for future work.

paper/paper_a_methodology.md

@@ -0,0 +1,146 @@
+# III. Methodology
+
+## A. Pipeline Overview
+
+We propose a six-stage pipeline for large-scale signature replication detection in scanned financial documents.
+Fig. 1 illustrates the overall architecture.
+The pipeline takes as input a corpus of PDF audit reports and produces, for each document, a classification of its CPA signatures into one of four categories---definite replication, likely replication, uncertain, or likely genuine---along with supporting evidence from multiple verification methods.
+
+<!--
+[Figure 1: Pipeline Architecture - clean vector diagram]
+90,282 PDFs → VLM Pre-screening → 86,072 PDFs
+→ YOLOv11 Detection → 182,328 signatures
+→ ResNet-50 Features → 2048-dim embeddings
+→ Dual-Method Verification (Cosine + pHash)
+→ Threshold Calibration (Firm A) → Classification
+-->
+
+## B. Data Collection
+
+The dataset comprises 90,282 annual financial audit reports filed by publicly listed companies in Taiwan, covering fiscal years 2013 to 2023.
+The reports were collected from the Market Observation Post System (MOPS) operated by the Taiwan Stock Exchange Corporation, the official repository for mandatory corporate filings.
+An automated web scraping pipeline using Selenium WebDriver was developed to systematically download all audit reports for each listed company across the study period.
+Each report is a multi-page PDF document containing, among other content, the auditor's report page bearing the handwritten signatures of the certifying CPAs.
+
+CPA names, affiliated accounting firms, and audit engagement tenure were obtained from a publicly available audit firm tenure registry encompassing 758 unique CPAs across 15 document types, with the majority (86.4%) being standard audit reports.
+Table I summarizes the dataset composition.
+
+<!-- TABLE I: Dataset Summary
+| Attribute | Value |
+|-----------|-------|
+| Total PDF documents | 90,282 |
+| Date range | 2013–2023 |
+| Documents with signatures | 86,072 (95.4%) |
+| Unique CPAs identified | 758 |
+| Accounting firms | >50 |
+-->
+
+## C. Signature Page Identification
+
+To identify which page of each multi-page PDF contains the auditor's signatures, we employed the Qwen2.5-VL vision-language model (32B parameters) [24] as an automated pre-screening mechanism.
+Each PDF page was rendered to JPEG at 180 DPI and submitted to the VLM with a structured prompt requesting a binary determination of whether the page contains a Chinese handwritten signature.
+The model was configured with temperature 0 for deterministic output.
+
+The scanning range was restricted to the first quartile of each document's page count, reflecting the regulatory structure of Taiwanese audit reports in which the auditor's report page is consistently located in the first quarter of the document.
+Scanning terminated upon the first positive detection.
+This process identified 86,072 documents with signature pages; the remaining 4,198 documents (4.6%) were classified as having no signatures and excluded.
+An additional 12 corrupted PDFs were excluded, yielding a final set of 86,071 documents.
+
+Cross-validation between the VLM and subsequent YOLO detection confirmed high agreement: YOLO successfully detected signature regions in 98.8% of VLM-positive documents, establishing an upper bound on the VLM false positive rate of 1.2%.
+
+## D. Signature Detection
+
+We adopted YOLOv11n (nano variant) [25] for signature region localization.
+A training set of 500 randomly sampled signature pages was annotated using a custom web-based interface following a two-stage protocol: primary annotation followed by independent review and correction.
+A region was labeled as "signature" if it contained any Chinese handwritten content attributable to a personal signature, regardless of overlap with official stamps.
+
+The model was trained for 100 epochs on a 425/75 training/validation split with COCO pre-trained initialization, achieving strong detection performance (Table II).
+
+<!-- TABLE II: YOLO Detection Performance
+| Metric | Value |
+|--------|-------|
+| Precision | 0.97–0.98 |
+| Recall | 0.95–0.98 |
+| mAP@0.50 | 0.98–0.99 |
+| mAP@0.50:0.95 | 0.85–0.90 |
+-->
+
+Batch inference on all 86,071 documents extracted 182,328 signature images at a rate of 43.1 documents per second (8 workers).
+A red stamp removal step was applied to each cropped signature using HSV color space filtering, replacing detected red regions with white pixels to isolate the handwritten content.
+
+Each signature was matched to its corresponding CPA using positional order (first or second signature on the page) against the official CPA registry, achieving a 92.6% match rate (168,755 of 182,328 signatures).
+
+## E. Feature Extraction
+
+Each extracted signature was encoded into a feature vector using a pre-trained ResNet-50 convolutional neural network [26] with ImageNet-1K V2 weights, used as a fixed feature extractor without fine-tuning.
+The final classification layer was removed, yielding the 2048-dimensional output of the global average pooling layer.
+
+Preprocessing consisted of resizing to 224×224 pixels with aspect ratio preservation and white padding, followed by ImageNet channel normalization.
+All feature vectors were L2-normalized, ensuring that cosine similarity equals the dot product.
+
+The choice of ResNet-50 without fine-tuning was motivated by three considerations: (1) the task is similarity comparison rather than classification, making general-purpose discriminative features sufficient; (2) ImageNet features have been shown to transfer effectively to document analysis tasks [20], [21]; and (3) avoiding domain-specific fine-tuning reduces the risk of overfitting to dataset-specific artifacts, though we note that a fine-tuned model could potentially improve discriminative performance (see Section V-D).
+
+This design choice is validated by an ablation study (Section IV-F) comparing ResNet-50 against VGG-16 and EfficientNet-B0.
+
+## F. Dual-Method Similarity Verification
+
+For each signature, the most similar signature from the same CPA across all other documents was identified via cosine similarity of feature vectors.
+Two complementary measures were then computed against this closest match:
+
+**Cosine similarity** captures high-level visual style similarity:
+
+$$\text{sim}(\mathbf{f}_A, \mathbf{f}_B) = \mathbf{f}_A \cdot \mathbf{f}_B$$
+
+where $\mathbf{f}_A$ and $\mathbf{f}_B$ are L2-normalized feature vectors.
+A high cosine similarity indicates that two signatures share similar visual characteristics---stroke patterns, spatial layout, and overall appearance---but does not distinguish between consistent handwriting style and digital duplication.
+
+**Perceptual hash distance** captures structural-level similarity.
+Specifically, we employ a difference hash (dHash) [27], a perceptual hashing variant that encodes relative intensity gradients rather than absolute pixel values.
+Each signature image is resized to 9×8 pixels and converted to grayscale; horizontal gradient differences between adjacent columns produce a 64-bit binary fingerprint.
+The Hamming distance between two fingerprints quantifies perceptual dissimilarity: a distance of 0 indicates structurally identical images, while distances exceeding 15 indicate clearly different images.
+Unlike DCT-based perceptual hashes, dHash is computationally lightweight and particularly effective for detecting near-exact duplicates with minor scan-induced variations [19].
+
+The complementarity of these two measures is the key to resolving the style-versus-replication ambiguity:
+
+- High cosine similarity + low pHash distance → converging evidence of digital replication
+- High cosine similarity + high pHash distance → consistent handwriting style, not replication
+
+This dual-method design was preferred over SSIM (Structural Similarity Index), which proved unreliable for scanned documents: a known-replication firm exhibited a mean SSIM of only 0.70 due to scan-induced pixel-level variations, despite near-identical visual content.
+Cosine similarity and pHash are both robust to the noise introduced by the print-scan cycle, making them more suitable for this application.
+
+## G. Threshold Selection and Calibration
+
+### Distribution-Free Thresholds
+
+To establish classification thresholds, we computed cosine similarity distributions for two groups:
+
+- **Intra-class** (same CPA): all pairwise similarities among signatures attributed to the same CPA (41.3M pairs from 728 CPAs with ≥3 signatures)
+- **Inter-class** (different CPAs): 500,000 randomly sampled cross-CPA pairs
+
+Shapiro-Wilk tests rejected normality for both distributions ($p < 0.001$), motivating the use of distribution-free, percentile-based thresholds rather than parametric ($\mu \pm k\sigma$) approaches.
+
+The primary threshold was derived via Kernel Density Estimation (KDE) [28]: the crossover point where the intra-class and inter-class density functions intersect.
+Under equal prior probabilities and symmetric misclassification costs, this crossover approximates the optimal decision boundary between the two classes.
+
+### Known-Replication Calibration
+
+A distinctive aspect of our methodology is the use of Firm A---a major Big-4 accounting firm whose use of digitally replicated signatures was established through independent visual inspection and domain knowledge prior to threshold calibration (see Section I)---as a calibration reference.
+Firm A's signature similarity distribution provides two critical anchors:
+
+1. **Lower bound validation:** Any detection threshold must classify the vast majority of Firm A's signatures as replicated; a threshold that fails this criterion is too conservative.
+2. **Replication floor estimation:** Firm A's 1st percentile of cosine similarity establishes how low similarity scores can fall even among confirmed replicated signatures, due to scan noise and PDF compression artifacts. This lower bound on replication similarity informs the minimum sensitivity required of any detection threshold.
+
+This calibration strategy addresses a persistent challenge in document forensics where comprehensive ground truth labels are unavailable.
+
+## H. Classification
+
+The final per-document classification uses exclusively the dual-method framework (cosine similarity + dHash distance), with thresholds calibrated against Firm A's known-replication distribution.
+Firm A's dHash distances show a median of 5 and a 95th percentile of 15; we use these empirical values to define confidence tiers:
+
+1. **High-confidence replication:** Cosine similarity > 0.95 AND dHash distance ≤ 5. Both feature-level and structural-level evidence converge, consistent with Firm A's median behavior.
+2. **Moderate-confidence replication:** Cosine similarity > 0.95 AND dHash distance 6--15. Feature-level evidence is strong; structural similarity is present but below the Firm A median, possibly due to scan variations.
+3. **High style consistency:** Cosine similarity > 0.95 AND dHash distance > 15. High feature-level similarity without structural corroboration---consistent with a CPA who signs very consistently but not digitally.
+4. **Uncertain:** Cosine similarity between the KDE crossover (0.837) and 0.95, without sufficient evidence for classification in either direction.
+5. **Likely genuine:** Cosine similarity below the KDE crossover threshold.
+
+The dHash thresholds (≤ 5 and ≤ 15) are directly derived from Firm A's calibration distribution rather than set ad hoc, ensuring that the classification boundaries are empirically grounded.

paper/paper_a_methodology_v3.md

@@ -0,0 +1,316 @@
+# III. Methodology
+
+## A. Pipeline Overview
+
+We propose a six-stage pipeline for large-scale non-hand-signed auditor signature detection in scanned financial documents.
+Fig. 1 illustrates the overall architecture.
+The pipeline takes as input a corpus of PDF audit reports and produces, for each document, a classification of its CPA signatures along a confidence continuum anchored on whole-sample Firm A percentile heuristics and validated against a byte-level pixel-identity positive anchor and a large random inter-CPA negative anchor.
+
+Throughout this paper we use the term *non-hand-signed* rather than "digitally replicated" to denote any signature produced by reproducing a previously stored image of the partner's signature---whether by administrative stamping workflows (dominant in the early years of the sample) or firm-level electronic signing systems (dominant in the later years).
+From the perspective of the output image the two workflows are equivalent: both can reproduce one or more stored signature images, producing same-CPA signatures that are identical or near-identical up to reproduction, scanning, compression, and template-variant noise.
+
+<!--
+[Figure 1: Pipeline Architecture - clean vector diagram]
+90,282 PDFs → VLM Pre-screening → 86,072 PDFs
+→ YOLOv11 Detection → 182,328 signatures
+→ ResNet-50 Features → 2048-dim embeddings
+→ Dual-Descriptor Verification (Cosine + dHash)
+→ Firm A P7.5-anchored Classifier → Five-way classification
+→ Pixel-identity + Inter-CPA + Held-Out Firm A validation
+-->
+
+## B. Data Collection
+
+The dataset comprises 90,282 annual financial audit reports filed by publicly listed companies in Taiwan, covering fiscal years 2013 to 2023.
+The reports were collected from the Market Observation Post System (MOPS) operated by the Taiwan Stock Exchange Corporation, the official repository for mandatory corporate filings.
+An automated web-scraping pipeline using Selenium WebDriver was developed to systematically download all audit reports for each listed company across the study period.
+Each report is a multi-page PDF document containing, among other content, the auditor's report page bearing the signatures of the certifying CPAs.
+
+CPA names, affiliated accounting firms, and audit engagement tenure were obtained from a publicly available audit-firm tenure registry encompassing 758 unique CPAs across 15 document types, with the majority (86.4%) being standard audit reports.
+Table I summarizes the dataset composition.
+
+<!-- TABLE I: Dataset Summary
+| Attribute | Value |
+|-----------|-------|
+| Total PDF documents | 90,282 |
+| Date range | 2013–2023 |
+| Documents with signatures | 86,072 (95.4%) |
+| Unique CPAs identified | 758 |
+| Accounting firms | >50 |
+-->
+
+## C. Signature Page Identification
+
+To identify which page of each multi-page PDF contains the auditor's signatures, we employed the Qwen2.5-VL vision-language model (32B parameters) [24], one of the multimodal generative models surveyed in [35], as an automated pre-screening mechanism.
+Each PDF page was rendered to JPEG at 180 DPI and submitted to the VLM with a structured prompt requesting a binary determination of whether the page contains a Chinese handwritten signature.
+The model was configured with temperature 0 for deterministic output.
+
+The scanning range was restricted to the first quartile of each document's page count, reflecting the regulatory structure of Taiwanese audit reports in which the auditor's report page is consistently located in the first quarter of the document.
+Scanning terminated upon the first positive detection.
+This process identified 86,072 documents with signature pages; the remaining 4,198 documents (4.6%) were classified as having no signatures and excluded.
+An additional 12 corrupted PDFs were excluded, yielding a final set of 86,071 documents.
+
+Cross-validation between the VLM and subsequent YOLO detection confirmed high agreement: YOLO successfully detected signature regions in 98.8% of VLM-positive documents.
+The 1.2% disagreement reflects the combined rate of (i) VLM false positives (pages incorrectly flagged as containing signatures) and (ii) YOLO false negatives (signature regions missed by the detector), and we do not attempt to attribute the residual to either source without further labeling.
+
+## D. Signature Detection
+
+We adopted YOLOv11n (nano variant) [25], a lightweight descendant of the original YOLO single-stage detector [34], for signature region localization.
+A training set of 500 randomly sampled signature pages was annotated using a custom web-based interface following a two-stage protocol: primary annotation followed by independent review and correction.
+A region was labeled as "signature" if it contained any Chinese handwritten content attributable to a personal signature, regardless of overlap with official stamps.
+
+The model was trained for 100 epochs on a 425/75 training/validation split with COCO pre-trained initialization, achieving strong detection performance (Table II).
+
+<!-- TABLE II: YOLO Detection Performance
+| Metric | Value |
+|--------|-------|
+| Precision | 0.97–0.98 |
+| Recall | 0.95–0.98 |
+| mAP@0.50 | 0.98–0.99 |
+| mAP@0.50:0.95 | 0.85–0.90 |
+-->
+
+Batch inference on all 86,071 documents extracted 182,328 signature images at a rate of 43.1 documents per second (8 workers).
+A red stamp removal step was applied to each cropped signature using HSV color-space filtering, replacing detected red regions with white pixels to isolate the handwritten content.
+
+Each signature was matched to its corresponding CPA using positional order (first or second signature on the page) against the official CPA registry, achieving a 92.6% match rate (168,755 of 182,328 signatures).
+The remaining 7.4% (13,573 signatures) could not be matched to a registered CPA name---typically because the auditor's report page format deviates from the standard two-signature layout, or because OCR of the printed CPA name on the page returns a name not present in the registry---and these signatures are excluded from all subsequent same-CPA pairwise analyses (a same-CPA best-match statistic is undefined when a signature has no assigned CPA). The 92.6% matched subset is the sample that flows into Sections IV-D through IV-H; the unmatched 7.4% are excluded for definitional reasons rather than discarded as noise.
+
+## E. Feature Extraction
+
+Each extracted signature was encoded into a feature vector using a pre-trained ResNet-50 convolutional neural network [26] with ImageNet-1K V2 weights, used as a fixed feature extractor without fine-tuning.
+The final classification layer was removed, yielding the 2048-dimensional output of the global average pooling layer.
+
+Preprocessing consisted of resizing to 224×224 pixels with aspect-ratio preservation and white padding, followed by ImageNet channel normalization.
+All feature vectors were L2-normalized, ensuring that cosine similarity equals the dot product.
+
+The choice of ResNet-50 without fine-tuning was motivated by three considerations: (1) the task is similarity comparison rather than classification, making general-purpose discriminative features sufficient; (2) ImageNet features have been shown to transfer effectively to document analysis tasks [20], [21]; and (3) avoiding domain-specific fine-tuning reduces the risk of overfitting to dataset-specific artifacts, though we note that a fine-tuned model could potentially improve discriminative performance (see Section V-G).
+This design choice is validated by an ablation study (Section IV-I) comparing ResNet-50 against VGG-16 and EfficientNet-B0.
+
+## F. Dual-Method Similarity Descriptors
+
+For each signature, we compute two complementary similarity measures against other signatures attributed to the same CPA:
+
+**Cosine similarity on deep embeddings** captures high-level visual style:
+
+$$\text{sim}(\mathbf{f}_A, \mathbf{f}_B) = \mathbf{f}_A \cdot \mathbf{f}_B$$
+
+where $\mathbf{f}_A$ and $\mathbf{f}_B$ are L2-normalized 2048-dim feature vectors.
+Each feature dimension contributes to the angular alignment, so cosine similarity is sensitive to fine-grained execution differences---pen pressure, ink distribution, and subtle stroke-trajectory variations---that distinguish genuine within-writer variation from the reproduction of a stored image [14].
+
+**Perceptual hash distance (dHash)** [27] captures structural-level similarity.
+Each signature image is resized to 9×8 pixels and converted to grayscale; horizontal gradient differences between adjacent columns produce a 64-bit binary fingerprint.
+The Hamming distance between two fingerprints quantifies perceptual dissimilarity: a distance of 0 indicates structurally identical images, while distances exceeding 15 indicate clearly different images.
+Unlike DCT-based perceptual hashes, dHash is computationally lightweight and particularly effective for detecting near-exact duplicates with minor scan-induced variations [19].
+
+These descriptors provide partially independent evidence.
+Cosine similarity is sensitive to the full feature distribution and reflects fine-grained execution variation; dHash captures only coarse perceptual structure and is robust to scanner-induced noise.
+Non-hand-signing yields extreme similarity under *both* descriptors, since the underlying image is identical up to reproduction noise.
+Hand-signing, by contrast, yields high dHash similarity (the overall layout of a signature is preserved across writing occasions) but measurably lower cosine similarity (fine execution varies).
+Convergence of the two descriptors is therefore a natural robustness check; when they disagree, the case is flagged as borderline.
+
+We did not use SSIM (Structural Similarity Index) [30] or pixel-level comparison as primary descriptors, and the reasons are specific to what each of those measures was designed to do rather than to how either happened to perform on our corpus.
+
+SSIM was developed by Wang et al. [30] as a perceptual quality index for *natural images*, and it factorises local-window image statistics into three components---luminance, contrast, and structural correlation---combined multiplicatively over a sliding window.
+Each of these components is computed at the pixel level on the original-resolution image and is *designed to be sensitive* to small fluctuations in local luminance and local contrast, because that is what makes SSIM track human perception of natural-image quality.
+Applied to a binarised auditor's signature crop, exactly those design choices become liabilities: the JPEG block artifacts, scan-noise speckle, and faint scanner-rule ghosts that are routine in a print-scan cycle perturb local luminance and local contrast in every window they touch, and SSIM amplifies those perturbations in the structural-correlation product.
+A signature reproduced twice from the same stored image---the very case that defines our positive class---is therefore one in which SSIM is structurally guaranteed to penalise the easily perturbed margins around the strokes, even though the strokes themselves are identical up to rendering noise.
+This is a property of how SSIM is constructed, not a finding about how it scored on our data; the empirical observation that the calibration firm exhibits a mean SSIM of only $0.70$ in our corpus is a confirmation of the design-level prediction rather than the basis for the rejection.
+
+Pixel-level comparison---whether $L_1$, $L_2$, or pixel-identity counting---fails on a stricter design ground.
+Pixel-level distances are defined on geometrically aligned images at a common resolution, and they treat any sub-pixel translation, rotation, or rescale as a large perturbation by construction (a one-pixel uniform translation flips a fraction of foreground pixels on a thin-stroke signature crop and inflates pixel L1 distance to the same magnitude as for a different signer's signature).
+Two scans of the same physical document, however, do not share a common pixel grid: scanner DPI, paper-handling alignment, and PDF-page rasterisation each contribute random sub-pixel offsets, and the print-scan cycle that intervenes between the stored stamp image and the audit-report PDF additionally introduces resolution mismatch and small geometric drift.
+A pixel-level descriptor cannot therefore satisfy the basic stability requirement for our task: two presentations of the same stored image must score nearly identically.
+We retain pixel-identity counting only as a *threshold-free anchor* (Section III-J), because byte-identical pairs in our corpus are necessarily produced by literal file reuse rather than by repeated scanning, and so they do not interact with the alignment-fragility argument; they are not used as a primary similarity descriptor.
+
+Cosine similarity on deep embeddings and dHash, in contrast, both remain stable across the print-scan-rasterise cycle by design: cosine on L2-normalised pooled features is invariant to overall scale and bias and degrades gracefully under local-pixel noise that the convolutional backbone has been trained to absorb [14], [21], while dHash compresses the image to a $9 \times 8$ grayscale grid before computing horizontal-gradient signs, which removes the resolution and sub-pixel-alignment sensitivity that breaks pixel-level comparison [19], [27].
+Together they constitute the dual descriptor used throughout the rest of this paper.
+
+## G. Unit of Analysis and Summary Statistics
+
+Two unit-of-analysis choices are relevant for this study, ordered from finest to coarsest: (i) the *signature*---one signature image extracted from one report; and (ii) the *auditor-year*---all signatures by one CPA within one fiscal year.
+The signature is the operational unit of classification (Section III-K) and of all primary statistical analyses (Section IV-D, IV-F, IV-G).
+The auditor-year is used in the partner-level similarity ranking of Section IV-G.2 as a within-year aggregation unit: each auditor-year's mean is computed over its own fiscal-year signatures, although the per-signature best-match cosine that feeds the mean is computed against the full same-CPA cross-year pool (Section III-G's max-cosine / min-dHash definition).
+We do not use a coarser CPA-level cross-year unit, because pooling a CPA's signatures across the full 2013--2023 sample period would conflate distinct signing-mechanism regimes whenever a CPA's practice changes during the sample, and we make no claim about the within-CPA stability of signing mechanisms over time.
+
+For per-signature classification we compute, for each signature, the maximum pairwise cosine similarity and the minimum dHash Hamming distance against every other signature attributed to the same CPA (over the full same-CPA set, not restricted to the same fiscal year).
+The max/min (rather than mean) formulation reflects the identification logic for non-hand-signing: if even one other signature of the same CPA is a pixel-level reproduction, that pair will dominate the extremes and reveal the non-hand-signed mechanism.
+Mean statistics would dilute this signal.
+
+For the dHash dimension we use the *independent minimum dHash*: the minimum Hamming distance from a signature to *any* other signature of the same CPA (over the full same-CPA set).
+The independent minimum is unconditional on the cosine-nearest pair and is therefore the conservative structural-similarity statistic; it is the dHash statistic used throughout the operational classifier (Section III-K) and all reported capture-rate analyses.
+
+We make one stipulation about same-CPA pair detectability.
+
+**(A1) Pair-detectability.** *If a CPA uses image replication anywhere in the corpus, then at least one same-CPA signature pair is near-identical (after reproduction noise) within the cross-year same-CPA pool used by the max-cosine / min-dHash computation above.*
+This is plausible for high-volume stamping or firm-level electronic-signing workflows---where a stored image is typically reused many times under similar scan and compression conditions---but it is *not* guaranteed when (i) the corpus contains only one observed replicated report for a CPA, (ii) multiple template variants are in use simultaneously, or (iii) scan-stage noise pushes a replicated pair outside the detection regime.
+A1 is a *cross-year pair-existence* property, not a within-year uniformity claim, and is the only assumption the per-signature detector requires to be sensitive to replication.
+
+We make *no* within-year or across-year uniformity assumption about CPA signing mechanisms.
+Per-signature labels are signature-level quantities throughout this paper; we do not translate them to per-report or per-partner mechanism assignments, and we abstain from partner-level frequency inferences (such as "X% of CPAs hand-sign") that would require such a translation.
+A CPA's signing output within a single fiscal year may reflect a single replication template, multiple templates used in parallel (e.g., different stored images for different engagement positions or reporting pipelines), within-year mechanism mixing, or a combination; our signature-level analyses remain valid under all of these regimes, since they do not attempt mechanism attribution at the partner or report level.
+
+The intra-report consistency analysis in Section IV-G.3 is a firm-level homogeneity check---whether the *two co-signing CPAs on the same report* receive the same signature-level label under the operational classifier---rather than a test of within-partner or within-year uniformity.
+
+## H. Calibration Reference: Firm A as a Replication-Dominated Population
+
+A distinctive aspect of our methodology is the use of Firm A---a major Big-4 accounting firm in Taiwan---as an empirical calibration reference.
+Rather than treating Firm A as a synthetic or laboratory positive control, we treat it as a naturally occurring *replication-dominated population*: a CPA population whose aggregate signing behavior is dominated by non-hand-signing but is not a pure positive class.
+
+Practitioner knowledge motivated treating Firm A as a candidate calibration reference: the firm is understood within the audit profession to reproduce a stored signature image for the majority of certifying partners---originally via administrative stamping workflows and later via firm-level electronic signing systems---while not ruling out that a minority of partners may continue to hand-sign some or all of their reports.
+This practitioner background motivates Firm A's selection but is not used as evidence: the evidentiary basis in the analyses below---byte-identical same-CPA pairs, the Firm A per-signature similarity distribution, partner-ranking concentration, and intra-report consistency---is derived entirely from the audit-report images themselves and does not depend on any claim about firm-level signing practice.
+
+We establish Firm A's replication-dominated status through two primary independent quantitative analyses plus a third strand comprising three complementary checks, each of which can be reproduced from the public audit-report corpus alone:
+
+First, *automated byte-level pair analysis* (Section IV-F.1; reproduction artifact listed in Appendix B) identifies 145 Firm A signatures that are byte-identical to at least one other same-CPA signature from a different audit report, distributed across 50 distinct Firm A partners (of 180 registered); 35 of these byte-identical matches span different fiscal years.
+Byte-identity implies pixel-identity by construction, and independent hand-signing cannot produce pixel-identical images across distinct reports---these pairs therefore establish image reuse as a concrete, threshold-free phenomenon within Firm A and confirm that replication is widespread (50 of 180 registered partners) rather than confined to a handful of CPAs.
+
+Second, *signature-level distributional evidence*: Firm A's per-signature best-match cosine distribution fails to reject unimodality (Hartigan dip test $p = 0.17$, $N = 60{,}448$ Firm A signatures; Section IV-D) and exhibits a long left tail, consistent with a dominant high-similarity regime plus residual within-firm heterogeneity rather than two cleanly separated mechanisms.
+92.5% of Firm A's per-signature best-match cosine similarities exceed 0.95 and the remaining 7.5% form the long left tail (we do not disaggregate partner-level mechanism here; see Section III-G for the scope of claims).
+The unimodal-long-tail shape, not the precise 92.5/7.5 split, is the structural evidence: it predicts that Firm A is replication-dominated rather than a clean two-class population, and a noise-only explanation of the left tail would predict a shrinking share as scan/PDF technology matured over 2013--2023, which is not what we observe (Section IV-G.1).
+
+Third, we additionally validate the Firm A benchmark through three complementary analyses reported in Section IV-G. Only the partner-level ranking is fully threshold-free; the longitudinal-stability and intra-report analyses use the operational classifier and are interpreted as consistency checks on its firm-level output:
+  (a) *Longitudinal stability (Section IV-G.1).* The share of Firm A per-signature best-match cosine values below 0.95 is stable at 6-13% across 2013-2023, with the lowest share in 2023. The 0.95 cutoff is the whole-sample Firm A P7.5 heuristic (Section III-K; 92.5% of whole-sample Firm A signatures exceed this cutoff); the substantive finding here is the *temporal stability* of the rate, not the absolute rate at any single year.
+  (b) *Partner-level similarity ranking (Section IV-G.2).* When every auditor-year is ranked globally by its per-auditor-year mean best-match cosine (across all firms: Big-4 and Non-Big-4), Firm A auditor-years account for 95.9% of the top decile against a baseline share of 27.8% (a 3.5$\times$ concentration ratio), and this over-representation is stable across 2013-2023. This analysis uses only the ordinal ranking and is independent of any absolute cutoff.
+  (c) *Intra-report consistency (Section IV-G.3).* Because each Taiwanese statutory audit report is co-signed by two engagement partners, firm-wide stamping practice predicts that both signers on a given Firm A report should receive the same signature-level label under the classifier. Firm A exhibits 89.9% intra-report agreement against 62-67% at the other Big-4 firms. This test uses the operational classifier and is therefore a *consistency* check on the classifier's firm-level output rather than a threshold-free test; the cross-firm gap (not the absolute rate) is the substantive finding.
+
+The 92.5% figure is a within-sample consistency check rather than an independent validation of Firm A's status; the validation role is played by the byte-level pixel-identity evidence, the unimodal-long-tail dip-test result, the three complementary analyses above, and the held-out Firm A fold (described in Section III-J; fold-level rate differences are disclosed in Section IV-F.2).
+Firm A's replication-dominated status itself was *not* derived from the thresholds we calibrate against it; it rests on the byte-level pair evidence and the dip-test-confirmed unimodal-long-tail shape, both of which are independent of any threshold choice.
+The "replication-dominated, not pure" framing is important both for internal consistency---it predicts and explains the long left tail observed in Firm A's cosine distribution (Section IV-D)---and for avoiding overclaim in downstream inference.
+
+## I. Signature-Level Threshold Characterisation
+
+This section describes how we set the operational classifier's similarity threshold and how we characterise the per-signature similarity distribution that supports it.
+The two roles are kept separate by design.
+
+**Operational threshold (used by the classifier).** The cosine cut is anchored on the whole-sample Firm A P7.5 percentile (cos $> 0.95$; Section III-K).
+
+**Statistical characterisation (used to motivate the choice of anchor and to describe the distributional structure).** A Hartigan dip test, an EM-fitted Beta mixture (with logit-Gaussian robustness check), and a Burgstahler-Dichev / McCrary density-smoothness procedure---all applied at the per-signature level (Section IV-D).
+
+The reason for the split is empirical.
+The three statistical diagnostics jointly find that per-signature similarity forms a continuous quality spectrum (Section IV-D, summarised below): the dip test fails to reject unimodality for Firm A; BIC strongly prefers a 3-component over a 2-component Beta fit, so the 2-component crossing is a forced fit; and the BD/McCrary candidate transition lies inside the non-hand-signed mode rather than between modes (and is not bin-width-stable; Appendix A).
+Under these conditions the natural anchor for an operational cosine cut is a transparent percentile of a replication-dominated reference population (Firm A) rather than a mixture-fit crossing whose location depends on parametric assumptions the data do not support.
+
+We describe the three diagnostics and the assumptions underlying each in the subsections below.
+The two threshold estimators rest on decreasing-in-strength assumptions: the KDE antimode/crossover requires only smoothness; the Beta mixture additionally requires a parametric specification, and the logit-Gaussian cross-check reports sensitivity to that form.
+The Burgstahler-Dichev / McCrary procedure is applied to the same distribution as a *density-smoothness diagnostic*: it would identify a sharp local density discontinuity if one existed at the boundary between two cleanly separated mechanisms.
+Because all three diagnostics are applied to the same sample rather than to independent experiments, agreement or disagreement among them is read as evidence about distributional structure rather than as a formal statistical guarantee.
+
+### 1) Method 1: KDE Antimode / Crossover with Unimodality Test
+
+We use two closely related KDE-based threshold estimators and apply each where it is appropriate.
+When two labeled populations are available (e.g., the all-pairs intra-class and inter-class similarity distributions of Section IV-C), the *KDE crossover* is the intersection point of the two kernel density estimates under Scott's rule for bandwidth selection [28]; under equal priors and symmetric misclassification costs it approximates the Bayes-optimal decision boundary between the two classes.
+When a single distribution is analysed (e.g., the per-signature best-match cosine distribution of Section IV-D) the *KDE antimode* is the local density minimum between two modes of the fitted density; it serves the same decision-theoretic role when the distribution is multimodal but is undefined when the distribution is unimodal.
+In either case we use the Hartigan & Hartigan dip test [37] as a formal test of unimodality.
+The dip test asks one question: *is the distribution single-peaked?*
+A non-significant $p$-value means we cannot reject the single-peak null (the data are consistent with one peak); a significant $p$-value means the distribution has *more than one peak* (it could be two, three, or more---the test does not specify how many).
+We use the test to decide whether a KDE antimode is well-defined (it is, only when there is more than one peak), not to assert any particular number of components.
+We additionally perform a sensitivity analysis varying the bandwidth over $\pm 50\%$ of the Scott's-rule value to verify threshold stability.
+
+### 2) Method 2: Finite Mixture Model via EM
+
+We fit a two-component Beta mixture to the cosine distribution via the EM algorithm [40] using method-of-moments M-step estimates (which are numerically stable for bounded proportion data).
+The first component represents non-hand-signed signatures (high mean, narrow spread) and the second represents hand-signed signatures (lower mean, wider spread).
+Under the fitted model the threshold is the crossing point of the two weighted component densities,
+
+$$\pi_1 \cdot \text{Beta}(x; \alpha_1, \beta_1) = (1 - \pi_1) \cdot \text{Beta}(x; \alpha_2, \beta_2),$$
+
+solved numerically via bracketed root-finding.
+As a robustness check against the Beta parametric form we fit a parallel two-component Gaussian mixture to the *logit-transformed* similarity, following standard practice for bounded proportion data.
+White's [41] quasi-MLE consistency result justifies interpreting the logit-Gaussian estimates as asymptotic approximations to the best Gaussian-family fit under misspecification; we use the cross-check between Beta and logit-Gaussian crossings as a diagnostic of parametric-form sensitivity rather than as a guarantee of distributional recovery.
+
+We fit 2- and 3-component variants of each mixture and report BIC for model selection.
+When BIC prefers the 3-component fit, the 2-component assumption itself is a forced fit; we report the resulting crossing only as a forced-fit descriptive reference and do not use it as an operational threshold.
+
+### 3) Density-Smoothness Diagnostic: Burgstahler-Dichev / McCrary
+
+Complementing the two threshold estimators above, we apply the discontinuity test of Burgstahler and Dichev [38], made asymptotically rigorous by McCrary [39], as a *density-smoothness diagnostic* rather than as a third threshold estimator.
+We discretize each distribution (cosine into bins of width 0.005; $\text{dHash}_\text{indep}$ into integer bins) and compute, for each bin $i$ with count $n_i$, the standardized deviation from the smooth-null expectation of the average of its neighbours,
+
+$$Z_i = \frac{n_i - \tfrac{1}{2}(n_{i-1} + n_{i+1})}{\sqrt{N p_i (1-p_i) + \tfrac{1}{4} N (p_{i-1}+p_{i+1})(1 - p_{i-1} - p_{i+1})}},$$
+
+which is approximately $N(0,1)$ under the null of distributional smoothness.
+A candidate transition is identified at an adjacent bin pair where $Z_{i-1}$ is significantly negative and $Z_i$ is significantly positive (cosine) or the reverse (dHash).
+Appendix A reports a bin-width sensitivity sweep covering $\text{bin} \in \{0.003, 0.005, 0.010, 0.015\}$ for cosine and $\text{bin} \in \{1, 2, 3\}$ for dHash; the sweep shows that signature-level BD transitions are not bin-width-stable, consistent with histogram-resolution artifacts rather than a genuine cross-mode density discontinuity.
+We therefore do not treat the BD/McCrary procedure as a threshold estimator in our application but as diagnostic evidence about distributional smoothness.
+
+### 4) Reading the Three Diagnostics Together
+
+The two threshold estimators rest on decreasing-in-strength assumptions: the KDE antimode/crossover requires only smoothness; the Beta mixture additionally requires a parametric specification (with logit-Gaussian as a robustness cross-check against that form).
+If the two estimated thresholds were to differ by less than a practically meaningful margin and the BD/McCrary procedure were to identify a sharp transition at the same level, that pattern would constitute convergent evidence for a clean two-mechanism boundary at that location.
+
+This is *not* the pattern we observe at the per-signature level.
+The two threshold estimators yield crossings spread across a wide range (Section IV-D); the BIC clearly prefers a 3-component over a 2-component Beta fit, indicating that the 2-component crossing is a forced fit reported only as a descriptive reference rather than as an operational threshold; and the BD/McCrary procedure locates its candidate transition *inside* the non-hand-signed mode rather than between modes (Appendix A).
+We interpret this jointly as evidence that per-signature similarity is a continuous quality spectrum rather than a clean two-mechanism mixture, and we accordingly anchor the operational classifier's cosine cut on whole-sample Firm A percentile heuristics (Section III-K) rather than on a mixture-fit crossing.
+
+## J. Pixel-Identity, Inter-CPA, and Held-Out Firm A Validation (No Manual Annotation)
+
+Rather than construct a stratified manual-annotation validation set, we validate the classifier using four naturally occurring reference populations that require no human labeling:
+
+1. **Pixel-identical anchor (gold positive, conservative subset):** signatures whose nearest same-CPA match is byte-identical after crop and normalization.
+Handwriting physics makes byte-identity impossible under independent signing events, so a byte-identical same-CPA pair is pair-level proof of image reuse and---for the byte-identical subset---conservative ground truth for non-hand-signed signatures; the narrow exception, in which a genuinely hand-signed exemplar was subsequently reused as the stamping or e-signature template, is discussed as a Limitation in Section V-G.
+We further emphasize that this anchor is a *subset* of the true positive class---only those non-hand-signed signatures whose nearest match happens to be byte-identical---and perfect recall against this anchor therefore does not establish recall against the full non-hand-signed population (Section V-G discusses this further).
+
+2. **Inter-CPA negative anchor (large gold negative):** $\sim$50,000 pairs of signatures randomly sampled from *different* CPAs.
+Inter-CPA pairs cannot arise from reuse of a single signer's stored signature image, so this population is a reliable negative class for threshold sweeps.
+This anchor is substantially larger than a simple low-similarity-same-CPA negative and yields tight Wilson 95% confidence intervals on FAR at each candidate threshold.
+
+3. **Firm A anchor (replication-dominated prior positive):** Firm A signatures, treated as a majority-positive reference with within-firm heterogeneity in the left tail, as evidenced by the 7.5% of Firm A signatures whose per-signature best-match cosine falls at or below 0.95 (Section III-H, Section IV-D).
+Because Firm A is both used for empirical percentile calibration in Section III-H and as a validation anchor, we make the within-Firm-A sampling variance visible by splitting Firm A CPAs randomly (at the CPA level, not the signature level) into a 70% *calibration* fold and a 30% *heldout* fold.
+The calibration-fold percentiles used in thresholding---cosine median, P1, and P5 (lower-tail, since higher cosine indicates greater similarity), and dHash_indep median and P95 (upper-tail, since lower dHash indicates greater similarity)---are derived from the 70% calibration fold only.
+The heldout fold is used exclusively to report post-hoc capture rates with Wilson 95% confidence intervals.
+
+4. **Low-similarity same-CPA anchor (supplementary negative):** signatures whose maximum same-CPA cosine similarity is below 0.70.
+This anchor is retained for continuity with prior work but is small in our dataset ($n = 35$) and is reported only as a supplementary reference; its confidence intervals are too wide for quantitative inference.
+
+From these anchors we report FAR with Wilson 95% confidence intervals against the inter-CPA negative anchor.
+We do not report an Equal Error Rate or FRR column against the byte-identical positive anchor, because byte-identical pairs have cosine $\approx 1$ by construction and any FRR computed against that subset is trivially $0$ at every threshold below $1$; the conservative-subset role of the byte-identical anchor is instead discussed qualitatively in Section V-F.
+Precision and $F_1$ are not meaningful in this anchor-based evaluation because the positive and negative anchors are constructed from different sampling units (intra-CPA byte-identical pairs vs random inter-CPA pairs), so their relative prevalence in the combined set is an arbitrary construction rather than a population parameter; we therefore omit precision and $F_1$ from Table X.
+The 70/30 held-out Firm A fold of Section IV-F.2 additionally reports capture rates with Wilson 95% confidence intervals computed within the held-out fold, which is a valid population for rate inference.
+
+## K. Per-Document Classification
+
+The per-signature classifier operates at the signature level with operational thresholds anchored on whole-sample Firm A percentile heuristics: cos $> 0.95$ (Firm A P7.5) for the cosine dimension and dHash$_\text{indep} \leq 5$ / $> 15$ (Firm A median+P75 / style-consistency ceiling) for the structural dimension.
+This percentile-based anchor is the natural choice given the continuous-spectrum shape of the per-signature similarity distribution documented in Section IV-D; sensitivity to nearby alternatives is reported in Section IV-F.3.
+All dHash references in this section refer to the *independent-minimum* dHash defined in Section III-G---the smallest Hamming distance from a signature to any other same-CPA signature.
+We use a single dHash statistic throughout the operational classifier and the supporting capture-rate analyses (Tables IX, XI, XII, XVI), which keeps the classifier definition and its empirical evaluation arithmetically consistent.
+
+We assign each signature to one of five signature-level categories using convergent evidence from both descriptors:
+
+1. **High-confidence non-hand-signed:** Cosine $> 0.95$ AND $\text{dHash}_\text{indep} \leq 5$.
+Both descriptors converge on strong replication evidence.
+
+2. **Moderate-confidence non-hand-signed:** Cosine $> 0.95$ AND $5 < \text{dHash}_\text{indep} \leq 15$.
+Feature-level evidence is strong; structural similarity is present but below the high-confidence cutoff, potentially due to scan variations.
+
+3. **High style consistency:** Cosine $> 0.95$ AND $\text{dHash}_\text{indep} > 15$.
+High feature-level similarity without structural corroboration---consistent with a CPA who signs very consistently but not via image reproduction.
+
+4. **Uncertain:** Cosine between the all-pairs intra/inter KDE crossover (0.837) and 0.95 without sufficient convergent evidence for classification in either direction.
+
+5. **Likely hand-signed:** Cosine below the all-pairs KDE crossover threshold.
+
+We note three conventions about the thresholds.
+First, the cosine cutoff $0.95$ is the *operating point* chosen for the five-way classifier from a small grid of candidate cuts, on the basis of an explicit capture-vs-FAR tradeoff against the inter-CPA negative anchor of Section III-J---*not* a discovered natural boundary in the per-signature distribution.
+The candidate grid spans the calibration-fold P5 (0.9407), its rounded value (0.945), the operational anchor (0.95), and two reference points drawn from the signature-level threshold-estimator outputs of Section IV-D (the Firm A Beta-2 forced-fit crossing 0.977 and the BD/McCrary candidate transition 0.985); for each grid point Section IV-F.3 reports the Firm A capture rate, the non-Firm-A capture rate, and the inter-CPA FAR with Wilson 95% CI (Table XII-B).
+Three considerations motivate the operating point at 0.95.
+(i) *Inter-CPA specificity.* At cosine $> 0.95$ the inter-CPA FAR against the 50,000-pair anchor of Section IV-F.1 is $0.0005$ (Wilson 95% CI $[0.0003, 0.0007]$): one in two thousand random cross-CPA pairs exceeds the cut, an order-of-magnitude margin against the working assumption that random cross-CPA pairs do not arise from image reuse.
+(ii) *Capture stability under nearby alternatives.* Moving the cut to $0.945$ raises Firm A capture by 1.51 percentage points (operational dual rule cos $> t$ AND $\text{dHash}_\text{indep} \leq 15$; Section IV-F.3) and inter-CPA FAR by $0.00032$, while moving it to the calibration-fold P5 of $0.9407$ raises Firm A capture by 2.63 percentage points and inter-CPA FAR by $0.00076$; in either direction the qualitative finding---Firm A is replication-dominated, non-Firm-A capture is much lower at the same cut, and the inter-CPA noise floor is small---is preserved.
+(iii) *Interpretive transparency.* The complement $7.5\%$ corresponds to the whole-sample Firm A P7.5 of the per-signature best-match cosine distribution---that is, $92.5\%$ of whole-sample Firm A signatures exceed this cutoff and $7.5\%$ fall at or below it (Section III-H)---which gives the operational cut a transparent reading in the replication-dominated reference population without requiring a parametric mixture fit that the data of Section IV-D do not support.
+The cosine crossover $0.837$ is the all-pairs intra/inter KDE crossover; both $0.95$ and $0.837$ are derived from whole-sample distributions rather than from the 70% calibration fold, so the classifier inherits its operational cosine cuts from the whole-sample Firm A and all-pairs distributions.
+Section IV-F.2 reports both calibration-fold and held-out-fold capture rates for this classifier so that fold-level sampling variance is visible; Section IV-F.3 (Table XII-B) reports the full capture-vs-FAR tradeoff at the candidate grid above.
+Second, the dHash cutoffs $\leq 5$ and $> 15$ are chosen from the whole-sample Firm A $\text{dHash}_\text{indep}$ distribution: $\leq 5$ captures the upper tail of the high-similarity mode (whole-sample Firm A median $\text{dHash}_\text{indep} = 2$, P75 $\approx 4$, so $\leq 5$ is the band immediately above median), while $> 15$ marks the regime in which independent-minimum structural similarity is no longer indicative of image reproduction.
+Third, the signature-level threshold-estimator outputs of Section IV-D (KDE antimode, Beta-mixture and logit-Gaussian crossings, BD/McCrary diagnostic) are *not* the operational thresholds of this classifier: they are descriptive characterisation of the per-signature similarity distribution, and Section IV-D shows they do not converge to a clean two-mechanism boundary at the per-signature level---which is why the operational cosine cut is anchored on the whole-sample Firm A percentile rather than on any mixture-fit crossing.
+
+Because each audit report typically carries two certifying-CPA signatures (Section III-D), we aggregate signature-level outcomes to document-level labels using a worst-case rule: the document inherits the *most-replication-consistent* signature label (i.e., among the two signatures, the label rank ordered High-confidence $>$ Moderate-confidence $>$ Style-consistency $>$ Uncertain $>$ Likely-hand-signed determines the document's classification).
+This rule is consistent with the detection goal of flagging any potentially non-hand-signed report rather than requiring all signatures on the report to converge.
+
+## L. Data Source and Firm Anonymization
+
+**Audit-report corpus.** The 90,282 audit-report PDFs analyzed in this study were obtained from the Market Observation Post System (MOPS) operated by the Taiwan Stock Exchange Corporation.
+MOPS is the statutory public-disclosure platform for Taiwan-listed companies; every audit report filed on MOPS is already a publicly accessible regulatory document.
+We did not access any non-public auditor work papers, internal firm records, or personally identifying information beyond the certifying CPAs' names and signatures, which are themselves published on the face of the audit report as part of the public regulatory filing.
+The CPA registry used to map signatures to CPAs is a publicly available audit-firm tenure registry (Section III-B).
+
+**Firm-level anonymization.** Although all audit reports and CPA identities in the corpus are public, we report firm-level results under the pseudonyms Firm A / B / C / D throughout this paper to avoid naming specific accounting firms in descriptive rate comparisons.
+Readers with domain familiarity may still infer Firm A from contextual descriptors (Big-4 status, replication-dominated behavior); we disclose this residual identifiability explicitly and note that none of the paper's conclusions depend on the specific firm's name.

paper/paper_a_outline.md

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+# Paper A: IEEE TAI Outline (Draft)
+
+> **Target:** IEEE Transactions on Artificial Intelligence (Regular Paper, ≤10 pages)
+> **Review:** Double-blind
+> **Status:** Outline — 待討論確認後再展開各 section
+
+---
+
+## Title (候選)
+
+1. "Automated Detection of Digitally Replicated Signatures in Large-Scale Financial Audit Reports"
+2. "Are They Really Signing? A Deep Learning Pipeline for Detecting Signature Replication in 90K Audit Reports"
+3. "Large-Scale Forensic Analysis of CPA Signature Authenticity Using Deep Features and Perceptual Hashing"
+
+> 建議用 1 或 3，學術正式感較強。2 比較 catchy 但 TAI 可能偏保守。
+
+---
+
+## Abstract (150-250 words)
+
+**要素：**
+- Problem: 審計報告要求親簽，但實務上可能用數位複製（套印）
+- Gap: 目前無大規模自動化偵測方法
+- Method: VLM pre-screening → YOLO detection → ResNet-50 feature extraction → Cosine + pHash verification
+- Scale: 90,282 PDFs, 182,328 signatures, 758 CPAs, 2013-2023
+- Key finding: 以已知套印事務所作為校準，建立 distribution-free threshold
+- Contribution: first large-scale study, end-to-end pipeline, empirical threshold validation
+
+---
+
+## Impact Statement (100-150 words)
+
+**方向（非專業人士看得懂）：**
+
+審計報告上的會計師簽名是財務報告可信度的重要保障。若簽名並非每次親簽，而是數位複製貼上，將影響審計品質與投資人保護。本研究開發了一套自動化 AI pipeline，分析了超過 9 萬份、橫跨 10 年的台灣上市公司審計報告，從中提取並比對 18 萬個簽名。透過深度學習特徵與感知雜湊的交叉驗證，我們能區分「風格一致的親簽」與「數位複製的套印」。研究發現部分會計事務所的簽名呈現統計上不可能由手寫產生的一致性。本方法可直接應用於金融監理機構的自動化稽核系統。
+
+> 注意：投稿時寫英文版，這裡先用中文定調內容方向。
+
+---
+
+## I. Introduction (~1.5 pages)
+
+### 段落結構：
+
+**P1 — Problem context**
+- 審計報告簽名的法律意義（台灣法規要求親簽）
+- 數位化後的漏洞：PDF 報告中的簽名容易被複製貼上
+- 監理機構無法逐份人工檢查
+
+**P2 — Why this matters (motivation)**
+- 審計品質 → 投資人保護 → 資本市場信任
+- 簽名真偽是審計獨立性的 proxy indicator
+- [REF: 審計品質相關文獻]
+
+**P3 — What exists (gap)**
+- 現有簽名驗證研究集中在 forgery detection（偽造偵測）
+- 我們的問題不同：不是問「是不是本人簽的」，而是「是不是每次都親簽」
+- Replication detection ≠ Forgery detection
+- 無大規模、真實財報的相關研究
+
+**P4 — What we do (contribution)**
+- End-to-end pipeline: VLM → YOLO → ResNet → Cosine + pHash
+- Scale: 90K+ documents, 180K+ signatures, 10 years
+- Distribution-free threshold with known-replication calibration group
+- First study applying AI to audit signature authenticity at this scale
+
+**P5 — Paper organization**
+- 一句話帶過各 section
+
+### Contribution list (明確列出):
+1. **Pipeline**: 完整的端到端自動化簽名真偽偵測系統
+2. **Scale**: 迄今最大規模的審計報告簽名分析（90K PDFs, 180K signatures）
+3. **Methodology**: 結合深度特徵（Cosine）與感知雜湊（pHash）的雙層驗證，解決「風格一致 vs 數位複製」的區分問題
+4. **Calibration**: 利用已知套印事務所作為 ground truth 校準，建立 distribution-free 閾值
+
+---
+
+## II. Related Work (~1 page)
+
+### A. Offline Signature Verification
+- Siamese networks: Bromley et al. 1993, Dey et al. 2017 (SigNet)
+- CNN-based: Hadjadj et al. 2020 (single known sample)
+- Triplet Siamese: Mathematics 2024
+- Consensus threshold: arXiv:2401.03085
+- **定位差異**: 這些都是 forgery detection（驗真偽），我們是 replication detection（驗套印）
+
+### B. Document Forensics & Copy-Move Detection
+- Copy-move forgery detection survey (MTAP 2024)
+- Image forensics in scanned documents
+- **定位差異**: 通常針對圖片竄改，非針對簽名重複使用
+
+### C. VLM & Object Detection in Document Analysis
+- Vision-Language Models for document understanding
+- YOLO variants in document element detection
+- **定位差異**: 我們用 VLM + YOLO 作為 pipeline 前端，非核心貢獻但需說明
+
+### D. Perceptual Hashing for Image Comparison
+- pHash in near-duplicate detection
+- 與 deep features 的互補性
+
+---
+
+## III. Methodology (~3 pages)
+
+> 從 methodology_draft_v1.md 精簡，聚焦在核心方法，省略實作細節
+
+### A. Pipeline Overview
+- Figure 1: 全流程圖（精簡版）
+- 各階段一句話描述
+
+### B. Data Collection
+- 90,282 PDFs from TWSE MOPS, 2013-2023
+- Table I: Dataset summary（精簡版）
+- CPA registry matching
+
+### C. Signature Detection
+- VLM pre-screening (Qwen2.5-VL): hit-and-stop strategy, 86,072 docs
+- YOLOv11n: 500 annotated → mAP50=0.99 → 182,328 signatures
+- Red stamp removal post-processing
+- **省略**: VLM prompt 全文、annotation protocol 細節、validation 細節 → 放 footnote 或略提
+
+### D. Feature Extraction
+- ResNet-50 (ImageNet1K_V2), no fine-tuning, 2048-dim, L2 normalized
+- Why no fine-tuning: similarity task, not classification; generalizability
+- CPA matching: 92.6% success rate
+
+### E. Dual-Method Verification (核心)
+- **Cosine similarity**: captures style-level similarity (high-level)
+- **pHash distance**: captures perceptual-level similarity (structural)
+- 為什麼這個組合：
+  - Cosine 高 + pHash 低距離 = 強證據（數位複製）
+  - Cosine 高 + pHash 高距離 = 風格一致但非複製（親簽）
+  - 互補性解決了單一指標的歧義
+- **SSIM 為何排除**: 掃描雜訊敏感，已知套印的 SSIM 僅 0.70（footnote 帶過）
+
+### F. Threshold Selection
+- Distribution-free approach（非常態 → 百分位數）
+- KDE crossover = 0.838
+- Intra/Inter class distributions（Table + Figure）
+- **Calibration via known-replication firm**（key contribution）:
+  - Deloitte Taiwan: domain knowledge 確認全部套印
+  - Cosine mean = 0.980, 1st percentile = 0.908
+  - pHash ≤5: 58.75%
+  - 用作閾值校準的 anchor point
+
+> 注意雙盲：不能寫 "Deloitte"，改用 "Firm A (a Big-4 firm known to use digital replication)"
+
+---
+
+## IV. Experiments and Results (~2.5 pages)
+
+### A. Experimental Setup
+- Hardware/software environment
+- Evaluation metrics 定義
+
+### B. Signature Detection Performance
+- Table: YOLO metrics (Precision, Recall, mAP)
+- VLM-YOLO agreement rate: 98.8%
+
+### C. Distribution Analysis
+- Figure: Intra vs Inter cosine similarity distributions
+- Figure: pHash distance distributions (intra vs inter)
+- Table: Distributional statistics
+- Normality tests → justify percentile-based thresholds
+
+### D. Calibration Group Analysis (重點)
+- "Firm A" (已知套印) 的 Cosine/pHash 分布
+- vs 非四大的分布比較
+- KDE crossover (Firm A vs non-Big-4) = 0.969
+- Figure: Firm A distribution vs overall distribution
+- **這是最有說服力的 section**
+
+### E. Classification Results
+- Table: Overall verdict distribution (definite_copy / likely_copy / uncertain / genuine)
+- Cross-method agreement analysis
+- **Key finding**: Cosine-high ≠ pixel-identical
+  - 71,656 PDFs with Cosine > 0.95
+  - 只有 3.4% 同時 SSIM > 0.95
+  - 只有 0.4% pixel-identical
+
+### F. Ablation Study (新增，增強 AI 貢獻)
+- **Feature backbone comparison**: ResNet-50 vs VGG-16 vs EfficientNet-B0
+  - 比較 intra/inter class separation (Cohen's d)
+  - 計算量 vs 判別力 trade-off
+- **Single method vs dual method**:
+  - Cosine only vs pHash only vs Cosine + pHash
+  - 用 Firm A 作為 positive set，計算 precision/recall
+- **Threshold sensitivity**:
+  - 不同 cosine threshold 下的分類結果變化
+  - ROC-like curve（以 Firm A 為 positive）
+
+---
+
+## V. Discussion (~1 page)
+
+### A. Replication vs Forgery: A Distinction That Matters
+- 我們的問題本質上更簡單也更直接
+- 不需要考慮仿冒者的存在
+- Physical impossibility argument: 同一人每次親簽不可能像素相同
+
+### B. The Gap Between Style Similarity and Digital Replication
+- 81.4% likely_copy (Cosine) vs 2.8% definite_copy (pixel-level)
+- 解讀：多數 CPA 簽名風格高度一致，但非數位複製
+- 可能原因：使用簽名板、固定簽署環境
+- **Policy implication**: 僅靠 Cosine 會嚴重高估套印率
+
+### C. The Value of a Known-Replication Calibration Group
+- 有 ground truth anchor 對閾值校準的重要性
+- 可推廣到其他 document forensics 問題
+
+### D. Limitations
+- 精簡版 limitations（3-4 點）
+- No labeled ground truth for full dataset
+- Feature extractor not fine-tuned
+- Scan quality variation over 10 years
+- Regulatory/legal definition of "replication" varies
+
+---
+
+## VI. Conclusion and Future Work (~0.5 page)
+
+### Conclusion
+- 總結 pipeline、規模、key findings
+- 強調 dual-method 的必要性（Cosine alone 不夠）
+- Calibration group 的方法論貢獻
+
+### Future Work
+- Fine-tuned signature-specific feature extractor
+- Temporal analysis (year-over-year trends)
+- Cross-country generalization
+- Integration with regulatory monitoring systems
+- Small-scale ground truth validation (100-200 PDFs)
+
+---
+
+## Figures & Tables Budget (10 頁限制下的分配)
+
+| # | Type | Content | Est. space |
+|---|------|---------|------------|
+| Fig 1 | Pipeline | 全流程圖 | 1/3 page |
+| Fig 2 | Distribution | Intra vs Inter cosine KDE | 1/3 page |
+| Fig 3 | Distribution | pHash distance intra vs inter | 1/4 page |
+| Fig 4 | Calibration | Firm A vs overall distribution | 1/3 page |
+| Fig 5 | Ablation | Backbone comparison / threshold sensitivity | 1/3 page |
+| Table I | Data | Dataset summary | 1/4 page |
+| Table II | Detection | YOLO performance | 1/6 page |
+| Table III | Statistics | Distribution stats + tests | 1/4 page |
+| Table IV | Results | Classification verdicts | 1/4 page |
+| Table V | Ablation | Feature backbone comparison | 1/4 page |
+
+**Total figures/tables**: ~3 pages → Text: ~7 pages → Feasible for 10-page limit
+
+---
+
+## 待辦 Checklist
+
+### 需要新增的分析（Ablation Study）
+- [ ] ResNet-50 vs VGG-16 vs EfficientNet-B0 feature comparison
+- [ ] Single method vs dual method precision/recall (with Firm A as positive set)
+- [ ] Threshold sensitivity curve
+
+### 需要整理的圖表
+- [ ] Fig 1: Pipeline diagram (clean vector version)
+- [ ] Fig 4: Firm A calibration distribution (新圖)
+- [ ] Fig 5: Ablation results (新圖)
+- [ ] 所有圖表英文化
+
+### 寫作
+- [ ] Impact Statement (英文版)
+- [ ] Abstract (英文版)
+- [ ] Introduction
+- [ ] Related Work — 需要補充文獻搜索
+- [ ] Methodology (從 v1 精簡)
+- [ ] Results (新寫)
+- [ ] Discussion (新寫)
+- [ ] Conclusion
+
+### 投稿準備
+- [ ] 匿名化（Deloitte → Firm A，移除所有可辨識資訊）
+- [ ] IEEE LaTeX template
+- [ ] Reference 格式化（IEEE numbered style）
+- [ ] 相似度指數 < 20%

paper/paper_a_references.md

@@ -0,0 +1,77 @@
+# References
+
+<!-- IEEE numbered style, sequential by first appearance in text -->
+
+[1] Taiwan Certified Public Accountant Act (會計師法), Art. 4; FSC Attestation Regulations (查核簽證核准準則), Art. 6. Available: https://law.moj.gov.tw/ENG/LawClass/LawAll.aspx?pcode=G0400067
+
+[2] S.-H. Yen, Y.-S. Chang, and H.-L. Chen, "Does the signature of a CPA matter? Evidence from Taiwan," *Res. Account. Regul.*, vol. 25, no. 2, pp. 230–235, 2013.
+
+[3] J. Bromley et al., "Signature verification using a Siamese time delay neural network," in *Proc. NeurIPS*, 1993.
+
+[4] S. Dey et al., "SigNet: Convolutional Siamese network for writer independent offline signature verification," arXiv:1707.02131, 2017.
+
+[5] I. Hadjadj et al., "An offline signature verification method based on a single known sample and an explainable deep learning approach," *Appl. Sci.*, vol. 10, no. 11, p. 3716, 2020.
+
+[6] H. Li et al., "TransOSV: Offline signature verification with transformers," *Pattern Recognit.*, vol. 145, p. 109882, 2024.
+
+[7] S. Tehsin et al., "Enhancing signature verification using triplet Siamese similarity networks in digital documents," *Mathematics*, vol. 12, no. 17, p. 2757, 2024.
+
+[8] P. Brimoh and C. C. Olisah, "Consensus-threshold criterion for offline signature verification using CNN learned representations," arXiv:2401.03085, 2024.
+
+[9] N. Woodruff et al., "Fully-automatic pipeline for document signature analysis to detect money laundering activities," arXiv:2107.14091, 2021.
+
+[10] S. Abramova and R. Bohme, "Detecting copy-move forgeries in scanned text documents," in *Proc. Electronic Imaging*, 2016.
+
+[11] Y. Li et al., "Copy-move forgery detection in digital image forensics: A survey," *Multimedia Tools Appl.*, 2024.
+
+[12] Y. Jakhar and M. D. Borah, "Effective near-duplicate image detection using perceptual hashing and deep learning," *Inf. Process. Manage.*, p. 104086, 2025.
+
+[13] E. Pizzi et al., "A self-supervised descriptor for image copy detection," in *Proc. CVPR*, 2022.
+
+[14] L. G. Hafemann, R. Sabourin, and L. S. Oliveira, "Learning features for offline handwritten signature verification using deep convolutional neural networks," *Pattern Recognit.*, vol. 70, pp. 163–176, 2017.
+
+[15] E. N. Zois, D. Tsourounis, and D. Kalivas, "Similarity distance learning on SPD manifold for writer independent offline signature verification," *IEEE Trans. Inf. Forensics Security*, vol. 19, pp. 1342–1356, 2024.
+
+[16] L. G. Hafemann, R. Sabourin, and L. S. Oliveira, "Meta-learning for fast classifier adaptation to new users of signature verification systems," *IEEE Trans. Inf. Forensics Security*, vol. 15, pp. 1735–1745, 2019.
+
+[17] H. Farid, "Image forgery detection," *IEEE Signal Process. Mag.*, vol. 26, no. 2, pp. 16–25, 2009.
+
+[18] F. Z. Mehrjardi, A. M. Latif, M. S. Zarchi, and R. Sheikhpour, "A survey on deep learning-based image forgery detection," *Pattern Recognit.*, vol. 144, art. no. 109778, 2023.
+
+[19] J. Luo et al., "A survey of perceptual hashing for multimedia," *ACM Trans. Multimedia Comput. Commun. Appl.*, vol. 21, no. 7, 2025.
+
+[20] D. Engin et al., "Offline signature verification on real-world documents," in *Proc. CVPRW*, 2020.
+
+[21] D. Tsourounis et al., "From text to signatures: Knowledge transfer for efficient deep feature learning in offline signature verification," *Expert Syst. Appl.*, 2022.
+
+[22] B. Chamakh and O. Bounouh, "A unified ResNet18-based approach for offline signature classification and verification," *Procedia Comput. Sci.*, vol. 270, 2025.
+
+[23] A. Babenko, A. Slesarev, A. Chigorin, and V. Lempitsky, "Neural codes for image retrieval," in *Proc. ECCV*, 2014, pp. 584–599.
+
+[24] Qwen2.5-VL Technical Report, Alibaba Group, 2025.
+
+[25] Ultralytics, "YOLOv11 documentation," 2024. [Online]. Available: https://docs.ultralytics.com/
+
+[26] K. He, X. Zhang, S. Ren, and J. Sun, "Deep residual learning for image recognition," in *Proc. CVPR*, 2016.
+
+[27] N. Krawetz, "Kind of like that," The Hacker Factor Blog, 2013. [Online]. Available: https://www.hackerfactor.com/blog/index.php?/archives/529-Kind-of-Like-That.html
+
+[28] B. W. Silverman, *Density Estimation for Statistics and Data Analysis*. London: Chapman & Hall, 1986.
+
+[29] J. Cohen, *Statistical Power Analysis for the Behavioral Sciences*, 2nd ed. Hillsdale, NJ: Lawrence Erlbaum, 1988.
+
+[30] Z. Wang, A. C. Bovik, H. R. Sheikh, and E. P. Simoncelli, "Image quality assessment: From error visibility to structural similarity," *IEEE Trans. Image Process.*, vol. 13, no. 4, pp. 600–612, 2004.
+
+[31] J. V. Carcello and C. Li, "Costs and benefits of requiring an engagement partner signature: Recent experience in the United Kingdom," *The Accounting Review*, vol. 88, no. 5, pp. 1511–1546, 2013.
+
+[32] A. D. Blay, M. Notbohm, C. Schelleman, and A. Valencia, "Audit quality effects of an individual audit engagement partner signature mandate," *Int. J. Auditing*, vol. 18, no. 3, pp. 172–192, 2014.
+
+[33] W. Chi, H. Huang, Y. Liao, and H. Xie, "Mandatory audit partner rotation, audit quality, and market perception: Evidence from Taiwan," *Contemp. Account. Res.*, vol. 26, no. 2, pp. 359–391, 2009.
+
+[34] J. Redmon, S. Divvala, R. Girshick, and A. Farhadi, "You only look once: Unified, real-time object detection," in *Proc. CVPR*, 2016, pp. 779–788.
+
+[35] J. Zhang, J. Huang, S. Jin, and S. Lu, "Vision-language models for vision tasks: A survey," *IEEE Trans. Pattern Anal. Mach. Intell.*, vol. 46, no. 8, pp. 5625–5644, 2024.
+
+[36] H. B. Mann and D. R. Whitney, "On a test of whether one of two random variables is stochastically larger than the other," *Ann. Math. Statist.*, vol. 18, no. 1, pp. 50–60, 1947.
+
+<!-- Total: 36 references -->

paper/paper_a_references_v3.md

@@ -0,0 +1,87 @@
+# References
+
+<!-- IEEE numbered style, sequential by first appearance in text. v3 adds statistical-method refs (37–41). -->
+
+[1] Taiwan Certified Public Accountant Act (會計師法), Art. 4; FSC Attestation Regulations (查核簽證核准準則), Art. 6. Available: https://law.moj.gov.tw/ENG/LawClass/LawAll.aspx?pcode=G0400067
+
+[2] S.-H. Yen, Y.-S. Chang, and H.-L. Chen, "Does the signature of a CPA matter? Evidence from Taiwan," *Res. Account. Regul.*, vol. 25, no. 2, pp. 230–235, 2013.
+
+[3] J. Bromley et al., "Signature verification using a Siamese time delay neural network," in *Proc. NeurIPS*, 1993.
+
+[4] S. Dey et al., "SigNet: Convolutional Siamese network for writer independent offline signature verification," arXiv:1707.02131, 2017.
+
+[5] H.-H. Kao and C.-Y. Wen, "An offline signature verification and forgery detection method based on a single known sample and an explainable deep learning approach," *Appl. Sci.*, vol. 10, no. 11, p. 3716, 2020.
+
+[6] H. Li et al., "TransOSV: Offline signature verification with transformers," *Pattern Recognit.*, vol. 145, p. 109882, 2024.
+
+[7] S. Tehsin et al., "Enhancing signature verification using triplet Siamese similarity networks in digital documents," *Mathematics*, vol. 12, no. 17, p. 2757, 2024.
+
+[8] P. Brimoh and C. C. Olisah, "Consensus-threshold criterion for offline signature verification using CNN learned representations," arXiv:2401.03085, 2024.
+
+[9] N. Woodruff et al., "Fully-automatic pipeline for document signature analysis to detect money laundering activities," arXiv:2107.14091, 2021.
+
+[10] S. Abramova and R. Böhme, "Detecting copy-move forgeries in scanned text documents," in *Proc. Electronic Imaging*, 2016.
+
+[11] Y. Li et al., "Copy-move forgery detection in digital image forensics: A survey," *Multimedia Tools Appl.*, 2024.
+
+[12] Y. Jakhar and M. D. Borah, "Effective near-duplicate image detection using perceptual hashing and deep learning," *Inf. Process. Manage.*, p. 104086, 2025.
+
+[13] E. Pizzi et al., "A self-supervised descriptor for image copy detection," in *Proc. CVPR*, 2022.
+
+[14] L. G. Hafemann, R. Sabourin, and L. S. Oliveira, "Learning features for offline handwritten signature verification using deep convolutional neural networks," *Pattern Recognit.*, vol. 70, pp. 163–176, 2017.
+
+[15] E. N. Zois, D. Tsourounis, and D. Kalivas, "Similarity distance learning on SPD manifold for writer independent offline signature verification," *IEEE Trans. Inf. Forensics Security*, vol. 19, pp. 1342–1356, 2024.
+
+[16] L. G. Hafemann, R. Sabourin, and L. S. Oliveira, "Meta-learning for fast classifier adaptation to new users of signature verification systems," *IEEE Trans. Inf. Forensics Security*, vol. 15, pp. 1735–1745, 2020.
+
+[17] H. Farid, "Image forgery detection," *IEEE Signal Process. Mag.*, vol. 26, no. 2, pp. 16–25, 2009.
+
+[18] F. Z. Mehrjardi, A. M. Latif, M. S. Zarchi, and R. Sheikhpour, "A survey on deep learning-based image forgery detection," *Pattern Recognit.*, vol. 144, art. no. 109778, 2023.
+
+[19] J. Luo et al., "A survey of perceptual hashing for multimedia," *ACM Trans. Multimedia Comput. Commun. Appl.*, vol. 21, no. 7, 2025.
+
+[20] D. Engin et al., "Offline signature verification on real-world documents," in *Proc. CVPRW*, 2020.
+
+[21] D. Tsourounis et al., "From text to signatures: Knowledge transfer for efficient deep feature learning in offline signature verification," *Expert Syst. Appl.*, vol. 189, art. 116136, 2022.
+
+[22] B. Chamakh and O. Bounouh, "A unified ResNet18-based approach for offline signature classification and verification across multilingual datasets," *Procedia Comput. Sci.*, vol. 270, pp. 4024–4033, 2025.
+
+[23] A. Babenko, A. Slesarev, A. Chigorin, and V. Lempitsky, "Neural codes for image retrieval," in *Proc. ECCV*, 2014, pp. 584–599.
+
+[24] S. Bai, K. Chen, X. Liu, J. Wang, W. Ge, S. Song, K. Dang, P. Wang, S. Wang, J. Tang, H. Zhong, Y. Zhu, M. Yang, Z. Li, J. Wan, P. Wang, W. Ding, Z. Fu, Y. Xu, J. Ye, X. Zhang, T. Xie, Z. Cheng, H. Zhang, Z. Yang, H. Xu, and J. Lin, "Qwen2.5-VL technical report," arXiv:2502.13923, 2025. [Online]. Available: https://arxiv.org/abs/2502.13923
+
+[25] Ultralytics, "YOLO11 documentation," 2024. [Online]. Available: https://docs.ultralytics.com/models/yolo11/
+
+[26] K. He, X. Zhang, S. Ren, and J. Sun, "Deep residual learning for image recognition," in *Proc. CVPR*, 2016.
+
+[27] N. Krawetz, "Kind of like that," The Hacker Factor Blog, 2013. [Online]. Available: https://www.hackerfactor.com/blog/index.php?/archives/529-Kind-of-Like-That.html
+
+[28] B. W. Silverman, *Density Estimation for Statistics and Data Analysis*. London: Chapman & Hall, 1986.
+
+[29] J. Cohen, *Statistical Power Analysis for the Behavioral Sciences*, 2nd ed. Hillsdale, NJ: Lawrence Erlbaum, 1988.
+
+[30] Z. Wang, A. C. Bovik, H. R. Sheikh, and E. P. Simoncelli, "Image quality assessment: From error visibility to structural similarity," *IEEE Trans. Image Process.*, vol. 13, no. 4, pp. 600–612, 2004.
+
+[31] J. V. Carcello and C. Li, "Costs and benefits of requiring an engagement partner signature: Recent experience in the United Kingdom," *The Accounting Review*, vol. 88, no. 5, pp. 1511–1546, 2013.
+
+[32] A. D. Blay, M. Notbohm, C. Schelleman, and A. Valencia, "Audit quality effects of an individual audit engagement partner signature mandate," *Int. J. Auditing*, vol. 18, no. 3, pp. 172–192, 2014.
+
+[33] W. Chi, H. Huang, Y. Liao, and H. Xie, "Mandatory audit partner rotation, audit quality, and market perception: Evidence from Taiwan," *Contemp. Account. Res.*, vol. 26, no. 2, pp. 359–391, 2009.
+
+[34] J. Redmon, S. Divvala, R. Girshick, and A. Farhadi, "You only look once: Unified, real-time object detection," in *Proc. CVPR*, 2016, pp. 779–788.
+
+[35] J. Zhang, J. Huang, S. Jin, and S. Lu, "Vision-language models for vision tasks: A survey," *IEEE Trans. Pattern Anal. Mach. Intell.*, vol. 46, no. 8, pp. 5625–5644, 2024.
+
+[36] H. B. Mann and D. R. Whitney, "On a test of whether one of two random variables is stochastically larger than the other," *Ann. Math. Statist.*, vol. 18, no. 1, pp. 50–60, 1947.
+
+[37] J. A. Hartigan and P. M. Hartigan, "The dip test of unimodality," *Ann. Statist.*, vol. 13, no. 1, pp. 70–84, 1985.
+
+[38] D. Burgstahler and I. Dichev, "Earnings management to avoid earnings decreases and losses," *J. Account. Econ.*, vol. 24, no. 1, pp. 99–126, 1997.
+
+[39] J. McCrary, "Manipulation of the running variable in the regression discontinuity design: A density test," *J. Econometrics*, vol. 142, no. 2, pp. 698–714, 2008.
+
+[40] A. P. Dempster, N. M. Laird, and D. B. Rubin, "Maximum likelihood from incomplete data via the EM algorithm," *J. R. Statist. Soc. B*, vol. 39, no. 1, pp. 1–38, 1977.
+
+[41] H. White, "Maximum likelihood estimation of misspecified models," *Econometrica*, vol. 50, no. 1, pp. 1–25, 1982.
+
+<!-- Total: 41 references (v2: 36 + 5 new statistical methods refs) -->

paper/paper_a_related_work.md

@@ -0,0 +1,77 @@
+# II. Related Work
+
+## A. Offline Signature Verification
+
+Offline signature verification---determining whether a static signature image is genuine or forged---has been studied extensively using deep learning.
+Bromley et al. [3] introduced the Siamese neural network architecture for signature verification, establishing the pairwise comparison paradigm that remains dominant.
+Hafemann et al. [20] demonstrated that deep CNN features learned from signature images provide strong discriminative representations for writer-independent verification, establishing the foundational baseline for subsequent work.
+Dey et al. [4] proposed SigNet, a convolutional Siamese network for writer-independent offline verification, extending this paradigm to generalize across signers without per-writer retraining.
+Hadjadj et al. [5] addressed the practical constraint of limited reference samples, achieving competitive verification accuracy using only a single known genuine signature per writer.
+More recently, Li et al. [6] introduced TransOSV, the first Vision Transformer-based approach, achieving state-of-the-art results.
+Tehsin et al. [7] evaluated distance metrics for triplet Siamese networks, finding that Manhattan distance outperformed cosine and Euclidean alternatives.
+Zois et al. [21] proposed similarity distance learning on SPD manifolds for writer-independent verification, achieving robust cross-dataset transfer---a property relevant to our setting where CPA signatures span diverse writing styles.
+Hafemann et al. [16] further addressed the practical challenge of adapting to new users through meta-learning, reducing the enrollment burden for signature verification systems.
+
+A common thread in this literature is the assumption that the primary threat is *identity fraud*: a forger attempting to produce a convincing imitation of another person's signature.
+Our work addresses a fundamentally different problem---detecting whether the *legitimate signer* reused a digital copy of their own signature---which requires analyzing intra-signer similarity distributions rather than modeling inter-signer discriminability.
+
+Brimoh and Olisah [8] proposed a consensus-threshold approach that derives classification boundaries from known genuine reference pairs, the methodology most closely related to our calibration strategy.
+However, their method operates on standard verification benchmarks with laboratory-collected signatures, whereas our approach applies threshold calibration using a known-replication subpopulation identified through domain expertise in real-world regulatory documents.
+
+## B. Document Forensics and Copy Detection
+
+Image forensics encompasses a broad range of techniques for detecting manipulated visual content [17], with recent surveys highlighting the growing role of deep learning in forgery detection [18].
+Copy-move forgery detection (CMFD) identifies duplicated regions within or across images, typically targeting manipulated photographs [11].
+Abramova and Bohme [10] adapted block-based CMFD to scanned text documents, noting that standard methods perform poorly in this domain because legitimate character repetitions produce high similarity scores that confound duplicate detection.
+
+Woodruff et al. [9] developed the work most closely related to ours: a fully automated pipeline for extracting and analyzing signatures from corporate filings in the context of anti-money laundering investigations.
+Their system uses connected component analysis for signature detection, GANs for noise removal, and Siamese networks for author clustering.
+While their pipeline shares our goal of large-scale automated signature analysis on real regulatory documents, their objective---grouping signatures by authorship---differs fundamentally from ours, which is detecting digital replication within a single author's signatures across documents.
+
+In the domain of image copy detection, Pizzi et al. [13] proposed SSCD, a self-supervised descriptor using ResNet-50 with contrastive learning for large-scale copy detection on natural images.
+Their work demonstrates that pre-trained CNN features with cosine similarity provide a strong baseline for identifying near-duplicate images, a finding that supports our feature extraction approach.
+
+## C. Perceptual Hashing
+
+Perceptual hashing algorithms generate compact fingerprints that are robust to minor image transformations while remaining sensitive to substantive content changes [19].
+Unlike cryptographic hashes, which change entirely with any pixel modification, perceptual hashes produce similar outputs for visually similar inputs, making them suitable for near-duplicate detection in scanned documents where minor variations arise from the scanning process.
+
+Jakhar and Borah [12] demonstrated that combining perceptual hashing with deep learning features significantly outperforms either approach alone for near-duplicate image detection, achieving AUROC of 0.99 on standard benchmarks.
+Their two-stage architecture---pHash for fast structural comparison followed by deep features for semantic verification---provides methodological precedent for our dual-method approach, though applied to natural images rather than document signatures.
+
+Our work differs from prior perceptual hashing studies in its application context and in the specific challenge it addresses: distinguishing legitimate high visual consistency (a careful signer producing similar-looking signatures) from digital duplication (identical pixel content arising from copy-paste operations) in scanned financial documents.
+
+## D. Deep Feature Extraction for Signature Analysis
+
+Several studies have explored pre-trained CNN features for signature comparison without metric learning or Siamese architectures.
+Engin et al. [14] used ResNet-50 features with cosine similarity for offline signature verification on real-world scanned documents, incorporating CycleGAN-based stamp removal as preprocessing---a pipeline design closely paralleling our approach.
+Tsourounis et al. [15] demonstrated successful transfer from handwritten text recognition to signature verification, showing that CNN features trained on related but distinct handwriting tasks generalize effectively to signature comparison.
+Chamakh and Bounouh [22] confirmed that a simple ResNet backbone with cosine similarity achieves competitive verification accuracy across multilingual signature datasets without fine-tuning, supporting the viability of our off-the-shelf feature extraction approach.
+
+Babenko et al. [23] established that CNN-extracted neural codes with cosine similarity provide an effective framework for image retrieval and matching, a finding that underpins our feature comparison approach.
+These findings collectively suggest that pre-trained CNN features, when L2-normalized and compared via cosine similarity, provide a robust and computationally efficient representation for signature comparison---particularly suitable for large-scale applications where the computational overhead of Siamese training or metric learning is impractical.
+
+<!--
+REFERENCES for Related Work (see paper_a_references.md for full list):
+[3] Bromley et al. 1993 — Siamese TDNN (NeurIPS)
+[4] Dey et al. 2017 — SigNet (arXiv:1707.02131)
+[5] Hadjadj et al. 2020 — Single sample SV (Applied Sciences)
+[6] Li et al. 2024 — TransOSV (Pattern Recognition)
+[7] Tehsin et al. 2024 — Triplet Siamese (Mathematics)
+[8] Brimoh & Olisah 2024 — Consensus threshold (arXiv:2401.03085)
+[9] Woodruff et al. 2021 — AML signature pipeline (arXiv:2107.14091)
+[10] Copy-move forgery detection survey — MTAP 2024
+[11] Abramova & Böhme 2016 — CMFD in scanned docs (Electronic Imaging)
+[12] Jakhar & Borah 2025 — pHash + DL (Info. Processing & Management)
+[13] Pizzi et al. 2022 — SSCD (CVPR)
+[14] Perceptual hashing survey — ACM TOMM 2025
+[15] Engin et al. 2020 — ResNet + cosine on real docs (CVPRW)
+[16] Tsourounis et al. 2022 — Transfer from text to signatures (Expert Systems with Applications)
+[17] Chamakh & Bounouh 2025 — ResNet18 unified SV (Procedia Computer Science)
+[24] Hafemann et al. 2017 — CNN features for signature verification (Pattern Recognition)
+[25] Hafemann et al. 2019 — Meta-learning for signature verification (IEEE TIFS)
+[26] Zois et al. 2024 — SPD manifold signature verification (IEEE TIFS)
+[27] Farid 2009 — Image forgery detection survey (IEEE SPM)
+[28] Mehrjardi et al. 2023 — DL-based image forgery detection survey (Pattern Recognition)
+[29] Babenko et al. 2014 — Neural codes for image retrieval (ECCV)
+-->

paper/paper_a_related_work_v3.md

@@ -0,0 +1,104 @@
+# II. Related Work
+
+## A. Offline Signature Verification
+
+Offline signature verification---determining whether a static signature image is genuine or forged---has been studied extensively using deep learning.
+Bromley et al. [3] introduced the Siamese neural network architecture for signature verification, establishing the pairwise comparison paradigm that remains dominant.
+Hafemann et al. [14] demonstrated that deep CNN features learned from signature images provide strong discriminative representations for writer-independent verification, establishing the foundational baseline for subsequent work.
+Dey et al. [4] proposed SigNet, a convolutional Siamese network for writer-independent offline verification, extending this paradigm to generalize across signers without per-writer retraining.
+Kao and Wen [5] addressed offline verification and forgery detection using only a single known genuine signature per writer with an explainable deep-learning approach.
+More recently, Li et al. [6] introduced TransOSV, the first Vision Transformer-based approach, achieving state-of-the-art results.
+Tehsin et al. [7] evaluated distance metrics for triplet Siamese networks, finding that Manhattan distance outperformed cosine and Euclidean alternatives.
+Zois et al. [15] proposed similarity distance learning on SPD manifolds for writer-independent verification, achieving robust cross-dataset transfer.
+Hafemann et al. [16] further addressed the practical challenge of adapting to new users through meta-learning, reducing the enrollment burden for signature verification systems.
+
+A common thread in this literature is the assumption that the primary threat is *identity fraud*: a forger attempting to produce a convincing imitation of another person's signature.
+Our work addresses a fundamentally different problem---detecting whether the *legitimate signer's* stored signature image has been reproduced across many documents---which requires analyzing the upper tail of the intra-signer similarity distribution rather than modeling inter-signer discriminability.
+
+Brimoh and Olisah [8] proposed a consensus-threshold approach that derives classification boundaries from known genuine reference pairs, the methodology most closely related to our calibration strategy.
+However, their method operates on standard verification benchmarks with laboratory-collected signatures, whereas our approach applies threshold calibration using a replication-dominated subpopulation identified through domain expertise in real-world regulatory documents.
+
+## B. Document Forensics and Copy Detection
+
+Image forensics encompasses a broad range of techniques for detecting manipulated visual content [17], with recent surveys highlighting the growing role of deep learning in forgery detection [18].
+Copy-move forgery detection (CMFD) identifies duplicated regions within or across images, typically targeting manipulated photographs [11].
+Abramova and Böhme [10] adapted block-based CMFD to scanned text documents, noting that standard methods perform poorly in this domain because legitimate character repetitions produce high similarity scores that confound duplicate detection.
+
+Woodruff et al. [9] developed the work most closely related to ours: a fully automated pipeline for extracting and analyzing signatures from corporate filings in the context of anti-money-laundering investigations.
+Their system uses connected component analysis for signature detection, GANs for noise removal, and Siamese networks for author clustering.
+While their pipeline shares our goal of large-scale automated signature analysis on real regulatory documents, their objective---grouping signatures by authorship---differs fundamentally from ours, which is detecting image-level reproduction within a single author's signatures across documents.
+
+In the domain of image copy detection, Pizzi et al. [13] proposed SSCD, a self-supervised descriptor using ResNet-50 with contrastive learning for large-scale copy detection on natural images.
+Their work demonstrates that pre-trained CNN features with cosine similarity provide a strong baseline for identifying near-duplicate images, a finding that supports our feature-extraction approach.
+
+## C. Perceptual Hashing
+
+Perceptual hashing algorithms generate compact fingerprints that are robust to minor image transformations while remaining sensitive to substantive content changes [19].
+Unlike cryptographic hashes, which change entirely with any pixel modification, perceptual hashes produce similar outputs for visually similar inputs, making them suitable for near-duplicate detection in scanned documents where minor variations arise from the scanning process.
+
+Jakhar and Borah [12] demonstrated that combining perceptual hashing with deep learning features significantly outperforms either approach alone for near-duplicate image detection, achieving AUROC of 0.99 on standard benchmarks.
+Their two-stage architecture---pHash for fast structural comparison followed by deep features for semantic verification---provides methodological precedent for our dual-descriptor approach, though applied to natural images rather than document signatures.
+
+Our work differs from prior perceptual-hashing studies in its application context and in the specific challenge it addresses: distinguishing legitimate high visual consistency (a careful signer producing similar-looking signatures) from image-level reproduction in scanned financial documents.
+
+## D. Deep Feature Extraction for Signature Analysis
+
+Several studies have explored pre-trained CNN features for signature comparison without metric learning or Siamese architectures.
+Engin et al. [20] used ResNet-50 features with cosine similarity for offline signature verification on real-world scanned documents, incorporating CycleGAN-based stamp removal as preprocessing---a pipeline design closely paralleling our approach.
+Tsourounis et al. [21] demonstrated successful transfer from handwritten text recognition to signature verification, showing that CNN features trained on related but distinct handwriting tasks generalize effectively to signature comparison.
+Chamakh and Bounouh [22] confirmed that a simple ResNet backbone with cosine similarity achieves competitive verification accuracy across multilingual signature datasets without fine-tuning, supporting the viability of our off-the-shelf feature-extraction approach.
+
+Babenko et al. [23] established that CNN-extracted neural codes with cosine similarity provide an effective framework for image retrieval and matching, a finding that underpins our feature-comparison approach.
+These findings collectively suggest that pre-trained CNN features, when L2-normalized and compared via cosine similarity, provide a robust and computationally efficient representation for signature comparison---particularly suitable for large-scale applications where the computational overhead of Siamese training or metric learning is impractical.
+
+## E. Statistical Methods for Threshold Determination
+
+Our threshold-determination framework combines three families of methods developed in statistics and accounting-econometrics.
+
+*Non-parametric density estimation.*
+Kernel density estimation [28] provides a smooth estimate of a similarity distribution without parametric assumptions.
+Where the distribution is bimodal, the local density minimum (antimode) between the two modes is the Bayes-optimal decision boundary under equal priors.
+The statistical validity of the unimodality-vs-multimodality dichotomy can be tested via the Hartigan & Hartigan dip test [37], which tests the null of unimodality; we use rejection of this null as evidence consistent with (though not a direct test for) bimodality.
+
+*Discontinuity tests on empirical distributions.*
+Burgstahler and Dichev [38], working in the accounting-disclosure literature, proposed a test for smoothness violations in empirical frequency distributions.
+Under the null that the distribution is generated by a single smooth process, the expected count in any histogram bin equals the average of its two neighbours, and the standardized deviation from this expectation is approximately $N(0,1)$.
+The test was placed on rigorous asymptotic footing by McCrary [39], whose density-discontinuity test provides full asymptotic distribution theory, bandwidth-selection rules, and power analysis.
+The BD/McCrary pairing provides a local-density-discontinuity diagnostic that is informative about distributional smoothness under minimal assumptions; we use it in that diagnostic role (rather than as a threshold estimator) because its transitions in our corpus are bin-width-sensitive at the signature level and rarely significant at the accountant level (Appendix A).
+
+*Finite mixture models.*
+When the empirical distribution is viewed as a weighted sum of two (or more) latent component distributions, the Expectation-Maximization algorithm [40] provides consistent maximum-likelihood estimates of the component parameters.
+For observations bounded on $[0,1]$---such as cosine similarity and normalized Hamming-based dHash similarity---the Beta distribution is the natural parametric choice, with applications spanning bioinformatics and Bayesian estimation.
+Under mild regularity conditions, White's quasi-MLE result [41] supports interpreting maximum-likelihood estimates under a mis-specified parametric family as consistent estimators of the pseudo-true parameter that minimizes the Kullback-Leibler divergence to the data-generating distribution within that family; we use this result to justify the Beta-mixture fit as a principled approximation rather than as a guarantee that the true distribution is Beta.
+
+The present study combines all three families, using each to produce an independent threshold estimate and treating cross-method convergence---or principled divergence---as evidence of where in the analysis hierarchy the mixture structure is statistically supported.
+<!--
+REFERENCES for Related Work (see paper_a_references_v3.md for full list):
+[3]  Bromley et al. 1993 — Siamese TDNN (NeurIPS)
+[4]  Dey et al. 2017 — SigNet
+[5]  Kao & Wen 2020 — Single-sample SV with forgery detection
+[6]  Li et al. 2024 — TransOSV
+[7]  Tehsin et al. 2024 — Triplet Siamese
+[8]  Brimoh & Olisah 2024 — Consensus threshold
+[9]  Woodruff et al. 2021 — AML signature pipeline
+[10] Abramova & Böhme 2016 — CMFD in scanned docs
+[11] Copy-move forgery detection survey — MTAP 2024
+[12] Jakhar & Borah 2025 — pHash + DL
+[13] Pizzi et al. 2022 — SSCD
+[14] Hafemann et al. 2017 — CNN features for SV
+[15] Zois et al. 2024 — SPD manifold SV
+[16] Hafemann et al. 2019 — Meta-learning for SV
+[17] Farid 2009 — Image forgery detection survey
+[18] Mehrjardi et al. 2023 — DL-based image forgery detection survey
+[19] Luo et al. 2025 — Perceptual hashing survey
+[20] Engin et al. 2020 — ResNet + cosine on real docs
+[21] Tsourounis et al. 2022 — Transfer from text to signatures
+[22] Chamakh & Bounouh 2025 — ResNet18 unified SV
+[23] Babenko et al. 2014 — Neural codes for image retrieval
+[28] Silverman 1986 — Density estimation
+[37] Hartigan & Hartigan 1985 — dip test of unimodality
+[38] Burgstahler & Dichev 1997 — earnings management discontinuity
+[39] McCrary 2008 — density discontinuity test
+[40] Dempster, Laird & Rubin 1977 — EM algorithm
+[41] White 1982 — quasi-MLE consistency
+-->

paper/paper_a_results.md

@@ -0,0 +1,153 @@
+# IV. Experiments and Results
+
+## A. Experimental Setup
+
+All experiments were conducted on a workstation equipped with an Apple Silicon processor with Metal Performance Shaders (MPS) GPU acceleration.
+Feature extraction used PyTorch 2.9 with torchvision model implementations.
+The complete pipeline---from raw PDF processing through final classification---was implemented in Python.
+
+
+## B. Signature Detection Performance
+
+The YOLOv11n model achieved high detection performance on the validation set (Table II), with all loss components converging by epoch 60 and no significant overfitting despite the relatively small training set (425 images).
+We note that Table II reports validation-set metrics, as no separate hold-out test set was reserved given the small annotation budget (500 images total).
+However, the subsequent production deployment provides practical validation: batch inference on 86,071 documents yielded 182,328 extracted signatures (Table III), with an average of 2.14 signatures per document, consistent with the standard practice of two certifying CPAs per audit report.
+The high VLM--YOLO agreement rate (98.8%) further corroborates detection reliability at scale.
+
+<!-- TABLE III: Extraction Results
+| Metric | Value |
+|--------|-------|
+| Documents processed | 86,071 |
+| Documents with detections | 85,042 (98.8%) |
+| Total signatures extracted | 182,328 |
+| Avg. signatures per document | 2.14 |
+| CPA-matched signatures | 168,755 (92.6%) |
+| Processing rate | 43.1 docs/sec |
+-->
+
+## C. Distribution Analysis
+
+Fig. 2 presents the cosine similarity distributions for intra-class (same CPA) and inter-class (different CPAs) pairs.
+Table IV summarizes the distributional statistics.
+
+<!-- TABLE IV: Cosine Similarity Distribution Statistics
+| Statistic | Intra-class | Inter-class |
+|-----------|-------------|-------------|
+| N (pairs) | 41,352,824 | 500,000 |
+| Mean | 0.821 | 0.758 |
+| Std. Dev. | 0.098 | 0.090 |
+| Median | 0.836 | 0.774 |
+| Skewness | −0.711 | −0.851 |
+| Kurtosis | 0.550 | 1.027 |
+-->
+
+Both distributions are left-skewed and leptokurtic.
+Shapiro-Wilk and Kolmogorov-Smirnov tests rejected normality for both ($p < 0.001$), confirming that parametric thresholds based on normality assumptions would be inappropriate.
+Distribution fitting identified the lognormal distribution as the best parametric fit (lowest AIC) for both classes, though we use this result only descriptively; all subsequent thresholds are derived nonparametrically via KDE to avoid distributional assumptions.
+
+The KDE crossover---where the two density functions intersect---was located at 0.837.
+Under the assumption of equal prior probabilities and equal misclassification costs, this crossover approximates the optimal decision boundary between the two classes.
+We note that this threshold is derived from all-pairs similarity distributions and is used as a reference point for interpreting per-signature best-match scores; the relationship between the two scales is mediated by the fact that the best-match statistic selects the maximum over all pairwise comparisons for a given CPA, producing systematically higher values (see Section IV-D).
+
+Statistical tests confirmed significant separation between the two distributions (Table V).
+
+<!-- TABLE V: Statistical Separation Tests
+| Test | Statistic | p-value |
+|------|-----------|---------|
+| Mann-Whitney U | 6.91 × 10⁹ | < 0.001 |
+| Welch's t-test | t = 149.36 | < 0.001 |
+| K-S 2-sample | D = 0.290 | < 0.001 |
+| Cohen's d | 0.669 | — |
+-->
+
+We emphasize that the pairwise observations are not independent---the same signature participates in multiple pairs---which inflates the effective sample size and renders p-values unreliable as measures of evidence strength.
+We therefore rely primarily on Cohen's $d$ as an effect-size measure that is less sensitive to sample size.
+Cohen's $d$ of 0.669 indicates a medium effect size [29], confirming that the distributional difference is practically meaningful, not merely an artifact of the large sample count.
+
+## D. Calibration Group Analysis
+
+Fig. 3 presents the cosine similarity distribution of Firm A (the known-replication reference group) compared to the overall intra-class distribution.
+
+Firm A comprises 180 CPAs contributing 16.0 million intra-firm signature pairs.
+Its distributional characteristics provide empirical anchors for threshold validation:
+
+<!-- TABLE VI: Firm A Calibration Statistics (per-signature best match, ResNet-50)
+| Statistic | Firm A | All CPAs |
+|-----------|--------|----------|
+| N (signatures) | 60,448 | 168,740 |
+| Mean | 0.980 | 0.961 |
+| Std. Dev. | 0.019 | 0.029 |
+| Median | 0.986 | — |
+| 1st percentile | 0.908 | — |
+| 5th percentile | 0.941 | — |
+| % > 0.95 | 92.5% | — |
+| % > 0.90 | 99.3% | — |
+-->
+
+Firm A's per-signature best-match cosine similarity (mean = 0.980, std = 0.019) is notably higher and more concentrated than the overall CPA population (mean = 0.961, std = 0.029).
+Critically, 99.3% of Firm A's signatures exhibit a best-match similarity exceeding 0.90, and the 1st percentile is 0.908---establishing that any threshold set above 0.91 would fail to capture the most dissimilar replicated signatures in the calibration group.
+
+This concentration provides strong empirical validation for the threshold selection: the KDE crossover at 0.837 captures essentially all of Firm A's signatures (>99.9%), while more conservative thresholds (e.g., 0.95) still capture 92.5%.
+The narrow spread (std = 0.019) further confirms that digital replication produces highly predictable similarity scores, as expected when the same source image is reused across documents with only scan-induced variations.
+
+## E. Classification Results
+
+Table VII presents the classification results for 84,386 documents using the dual-method framework with Firm A-calibrated thresholds.
+
+<!-- TABLE VII: Recalibrated Classification Results (Dual-Method: Cosine + dHash)
+| Verdict | N (PDFs) | % | Firm A | Firm A % |
+|---------|----------|---|--------|----------|
+| High-confidence replication | 29,529 | 35.0% | 22,970 | 76.0% |
+| Moderate-confidence replication | 36,994 | 43.8% | 6,311 | 20.9% |
+| High style consistency | 5,133 | 6.1% | 183 | 0.6% |
+| Uncertain | 12,683 | 15.0% | 758 | 2.5% |
+| Likely genuine | 47 | 0.1% | 4 | 0.0% |
+-->
+
+The dual-method classification reveals a nuanced picture within the 71,656 documents exceeding the cosine similarity threshold of 0.95.
+Rather than treating these uniformly as "likely copies" (as a single-metric approach would), the dHash dimension stratifies them into three distinct populations:
+29,529 (41.2%) show converging structural evidence of replication (dHash ≤ 5),
+36,994 (51.7%) show partial structural similarity (dHash 6--15) consistent with replication degraded by scan variations,
+and 5,133 (7.2%) show no structural corroboration (dHash > 15), suggesting high signing consistency rather than digital duplication.
+
+### Calibration Validation
+
+The Firm A column in Table VII validates the calibration: 96.9% of Firm A's documents are classified as replication (high or moderate confidence), and only 0.6% fall into the "high style consistency" category.
+This confirms that the dHash thresholds, derived from Firm A's distributional characteristics (median = 5, 95th percentile = 15), correctly capture the known-replication population.
+
+Among non-Firm-A CPAs with cosine > 0.95, only 11.3% exhibit dHash ≤ 5, compared to 58.7% for Firm A---a five-fold difference that demonstrates the discriminative power of the structural verification layer.
+
+## F. Ablation Study: Feature Backbone Comparison
+
+To validate the choice of ResNet-50 as the feature extraction backbone, we conducted an ablation study comparing three pre-trained architectures: ResNet-50 (2048-dim), VGG-16 (4096-dim), and EfficientNet-B0 (1280-dim).
+All models used ImageNet pre-trained weights without fine-tuning, with identical preprocessing and L2 normalization.
+Table IX presents the comparison.
+
+<!-- TABLE IX: Backbone Comparison
+| Metric | ResNet-50 | VGG-16 | EfficientNet-B0 |
+|--------|-----------|--------|-----------------|
+| Feature dim | 2048 | 4096 | 1280 |
+| Intra mean | 0.821 | 0.822 | 0.786 |
+| Inter mean | 0.758 | 0.767 | 0.699 |
+| Cohen's d | 0.669 | 0.564 | 0.707 |
+| KDE crossover | 0.837 | 0.850 | 0.792 |
+| Firm A mean (all-pairs) | 0.826 | 0.820 | 0.810 |
+| Firm A 1st pct (all-pairs) | 0.543 | 0.520 | 0.454 |
+
+Note: Firm A values in this table are computed over all intra-firm pairwise
+similarities (16.0M pairs) for cross-backbone comparability. These differ from
+the per-signature best-match values in Table VI (mean = 0.980), which reflect
+the classification-relevant statistic: the similarity of each signature to its
+single closest match from the same CPA.
+-->
+
+EfficientNet-B0 achieves the highest Cohen's $d$ (0.707), indicating the greatest statistical separation between intra-class and inter-class distributions.
+However, it also exhibits the widest distributional spread (intra std = 0.123 vs. ResNet-50's 0.098), resulting in lower per-sample classification confidence.
+VGG-16 performs worst on all key metrics despite having the highest feature dimensionality (4096), suggesting that additional dimensions do not contribute discriminative information for this task.
+
+ResNet-50 provides the best overall balance:
+(1) Cohen's $d$ of 0.669 is competitive with EfficientNet-B0's 0.707;
+(2) its tighter distributions yield more reliable individual classifications;
+(3) the highest Firm A all-pairs 1st percentile (0.543) indicates that known-replication signatures are least likely to produce low-similarity outlier pairs under this backbone; and
+(4) its 2048-dimensional features offer a practical compromise between discriminative capacity and computational/storage efficiency for processing 182K+ signatures.
+

paper/paper_a_results_v3.md

@@ -0,0 +1,494 @@
+# IV. Experiments and Results
+
+## A. Experimental Setup
+
+Experiments used mixed hardware: YOLOv11n training and inference for signature detection, and ResNet-50 forward inference for feature extraction over all 182,328 detected signatures, were performed on an Nvidia RTX 4090 (CUDA); the downstream statistical analyses (KDE antimode, Hartigan dip test, Beta-mixture EM with logit-Gaussian robustness check, Burgstahler-Dichev/McCrary density-smoothness diagnostic, and pairwise cosine/dHash computations) were performed on an Apple Silicon workstation with Metal Performance Shaders (MPS) acceleration.
+Feature extraction used PyTorch 2.9 with torchvision model implementations.
+The complete pipeline---from raw PDF processing through final classification---was implemented in Python.
+Because all steps rely on deterministic forward inference over fixed pre-trained weights (no fine-tuning) plus fixed-seed numerical procedures, reported results are platform-independent to within floating-point precision.
+
+## B. Signature Detection Performance
+
+The YOLOv11n model achieved high detection performance on the validation set (Table II), with all loss components converging by epoch 60 and no significant overfitting despite the relatively small training set (425 images).
+We note that Table II reports validation-set metrics, as no separate hold-out test set was reserved given the small annotation budget (500 images total).
+However, the subsequent production deployment provides practical validation: batch inference on 86,071 documents yielded 182,328 extracted signatures (Table III), with an average of 2.14 signatures per document, consistent with the standard practice of two certifying CPAs per audit report.
+The high VLM--YOLO agreement rate (98.8%) further corroborates detection reliability at scale.
+
+<!-- TABLE III: Extraction Results
+| Metric | Value |
+|--------|-------|
+| Documents processed | 86,071 |
+| Documents with detections | 85,042 (98.8%) |
+| Total signatures extracted | 182,328 |
+| Avg. signatures per document | 2.14 |
+| CPA-matched signatures | 168,755 (92.6%) |
+| Processing rate | 43.1 docs/sec |
+-->
+
+## C. All-Pairs Intra-vs-Inter Class Distribution Analysis
+
+Fig. 2 presents the cosine similarity distributions computed over the full set of *pairwise comparisons* under two groupings: intra-class (all signature pairs belonging to the same CPA) and inter-class (signature pairs from different CPAs).
+This all-pairs analysis is a different unit from the per-signature best-match statistics used in Sections IV-D onward; we report it first because it supplies the reference point for the KDE crossover used in per-document classification (Section III-K).
+Table IV summarizes the distributional statistics.
+
+<!-- TABLE IV: Cosine Similarity Distribution Statistics
+| Statistic | Intra-class | Inter-class |
+|-----------|-------------|-------------|
+| N (pairs) | 41,352,824 | 500,000 |
+| Mean | 0.821 | 0.758 |
+| Std. Dev. | 0.098 | 0.090 |
+| Median | 0.836 | 0.774 |
+| Skewness | −0.711 | −0.851 |
+| Kurtosis | 0.550 | 1.027 |
+-->
+
+Both distributions are left-skewed and leptokurtic.
+Shapiro-Wilk and Kolmogorov-Smirnov tests rejected normality for both ($p < 0.001$), confirming that parametric thresholds based on normality assumptions would be inappropriate.
+Distribution fitting identified the lognormal distribution as the best parametric fit (lowest AIC) for both classes, though we use this result only descriptively; all subsequent threshold-estimator outputs reported in Section IV-D are derived via the methods of Section III-I to avoid single-family distributional assumptions.
+
+The KDE crossover---where the two density functions intersect---was located at 0.837 (Table V).
+Under equal prior probabilities and equal misclassification costs, this crossover approximates the Bayes-optimal boundary between the two classes.
+Statistical tests confirmed significant separation between the two distributions (Cohen's $d = 0.669$, Mann-Whitney [36] $p < 0.001$, K-S 2-sample $p < 0.001$).
+
+We emphasize that pairwise observations are not independent---the same signature participates in multiple pairs---which inflates the effective sample size and renders $p$-values unreliable as measures of evidence strength.
+We therefore rely primarily on Cohen's $d$ as an effect-size measure that is less sensitive to sample size.
+A Cohen's $d$ of 0.669 indicates a medium effect size [29], confirming that the distributional difference is practically meaningful, not merely an artifact of the large sample count.
+
+## D. Signature-Level Distributional Characterisation
+
+This section applies the threshold-estimator and density-smoothness diagnostic of Section III-I to the per-signature similarity distribution.
+The joint reading is that per-signature similarity is a continuous quality spectrum rather than a clean two-mechanism mixture, which is why the operational classifier (Section III-K) anchors its cosine cut on the whole-sample Firm A P7.5 percentile rather than on any mixture-fit crossing.
+
+### 1) Hartigan Dip Test: Unimodality at the Signature Level
+
+Applying the Hartigan & Hartigan dip test [37] to the per-signature best-match distributions reveals a critical structural finding (Table V).
+The $N = 168{,}740$ count used in Table V and in the downstream same-CPA per-signature best-match analyses (Tables V and XII, and the Firm-A per-signature rows of Tables XIII and XVIII) is $15$ signatures smaller than the $168{,}755$ CPA-matched count reported in Table III: these $15$ signatures belong to CPAs with exactly one signature in the entire corpus, for whom no same-CPA pairwise best-match statistic can be computed, and are therefore excluded from all same-CPA similarity analyses.
+
+<!-- TABLE V: Hartigan Dip Test Results
+| Distribution | N | dip | p-value | Verdict (α=0.05) |
+|--------------|---|-----|---------|------------------|
+| Firm A cosine (max-sim) | 60,448 | 0.0019 | 0.169 | Unimodal |
+| Firm A min dHash (independent) | 60,448 | 0.1051 | <0.001 | Multimodal |
+| All-CPA cosine (max-sim) | 168,740 | 0.0035 | <0.001 | Multimodal |
+| All-CPA min dHash (independent) | 168,740 | 0.0468 | <0.001 | Multimodal |
+-->
+
+Firm A's per-signature cosine distribution *fails to reject unimodality* ($p = 0.17$), a pattern consistent with a dominant high-similarity regime plus a long left tail attributable to within-firm heterogeneity in signing outputs (Section III-G discusses the scope of partner-level claims).
+The all-CPA cosine distribution, which mixes many firms with heterogeneous signing practices, is *multimodal* ($p < 0.001$).
+The Firm A unimodal-long-tail finding is, in conjunction with the byte-identity, partner-ranking, and intra-report evidence reported below, consistent with the replication-dominated framing (Section III-H): a dominant high-similarity regime plus residual within-firm heterogeneity, rather than two cleanly separated mechanisms.
+
+### 2) Burgstahler-Dichev / McCrary Density-Smoothness Diagnostic
+
+Applying the BD/McCrary procedure (Section III-I.3) to the per-signature cosine distribution yields a nominally significant $Z^- \rightarrow Z^+$ transition at cosine 0.985 for Firm A and 0.985 for the full sample; the min-dHash distributions exhibit a transition at Hamming distance 2 for both Firm A and the full sample under the bin width ($0.005$ / $1$) used here.
+Two cautions, however, prevent us from treating these signature-level transitions as thresholds.
+First, the cosine transition at 0.985 lies *inside* the non-hand-signed mode rather than at the separation between two mechanisms, consistent with the dip-test finding that per-signature cosine is not cleanly bimodal.
+Second, Appendix A documents that the signature-level transition locations are not bin-width-stable (Firm A cosine drifts across 0.987, 0.985, 0.980, 0.975 as the bin width is widened from 0.003 to 0.015, and full-sample dHash transitions drift across 2, 10, 9 as bin width grows from 1 to 3), which is characteristic of a histogram-resolution artifact rather than of a genuine density discontinuity between two mechanisms.
+We therefore use BD/McCrary as a density-smoothness diagnostic rather than as an independent threshold estimator.
+
+### 3) Beta Mixture at Signature Level: A Forced Fit
+
+Fitting 2- and 3-component Beta mixtures to Firm A's per-signature cosine via EM yields a clear BIC preference for the 3-component fit ($\Delta\text{BIC} = 381$), with a parallel preference under the logit-GMM robustness check.
+For the full-sample cosine the 3-component fit is likewise strongly preferred ($\Delta\text{BIC} = 10{,}175$).
+Under the forced 2-component fit the Firm A Beta crossing lies at 0.977 and the logit-GMM crossing at 0.999---values sharply inconsistent with each other, indicating that the 2-component parametric structure is not supported by the data.
+Under the full-sample 2-component forced fit no Beta crossing is identified; the logit-GMM crossing is at 0.980.
+
+### 4) Joint Reading of the Three Diagnostics
+
+The three diagnostics agree that per-signature similarity does not form a clean two-mechanism mixture:
+(i) the Hartigan dip test fails to reject unimodality for Firm A and rejects it for the heterogeneous-firm pooled sample;
+(ii) BIC strongly prefers a 3-component over a 2-component Beta fit, so the 2-component crossing is a *forced fit* and the Beta-vs-logit-Gaussian disagreement (0.977 vs 0.999 for Firm A) reflects parametric-form sensitivity rather than a stable two-mechanism boundary;
+(iii) the BD/McCrary procedure locates its candidate transition *inside* the non-hand-signed mode rather than between modes, and the transition is not bin-width-stable.
+
+Table VI summarises the signature-level threshold-estimator outputs for cross-method comparison.
+
+<!-- TABLE VI: Signature-Level Threshold-Estimator Summary
+| Population | Method | Cosine threshold | dHash threshold | Status |
+|------------|--------|------------------|-----------------|--------|
+| **Threshold estimators (signature-level distributional fits)** | | | | |
+| Firm A signature-level    | KDE antimode + Hartigan dip (Section III-I.1)  | undefined           | —    | unimodal at $\alpha=0.05$ ($p=0.169$); antimode not defined for unimodal data |
+| Firm A signature-level    | Beta-2 EM crossing (Section III-I.2)           | 0.977               | —    | forced fit; BIC strongly prefers $K{=}3$ ($\Delta\text{BIC} = 381$) |
+| Firm A signature-level    | logit-Gaussian-2 crossing (robustness check)   | 0.999               | —    | forced fit; sharply inconsistent with Beta-2 crossing—reflects parametric-form sensitivity |
+| Full-sample signature-l.  | KDE antimode + Hartigan dip                    | (multiple modes)    | —    | multimodal ($p<0.001$); KDE crossover at full-sample is dominated by between-firm heterogeneity |
+| Full-sample signature-l.  | Beta-2 EM crossing                             | no crossing         | —    | forced fit; component densities do not cross over $[0,1]$ under recovered parameters |
+| Full-sample signature-l.  | logit-Gaussian-2 crossing                      | 0.980               | —    | forced fit; BIC strongly prefers $K{=}3$ ($\Delta\text{BIC} = 10{,}175$) |
+| **Density-smoothness diagnostics (not threshold estimators)** | | | | |
+| Firm A signature-level    | BD/McCrary candidate transition (Section III-I.3) | 0.985 (bin 0.005)| 2.0 (bin 1) | bin-unstable across $\{0.003, 0.005, 0.010, 0.015\}$ (Appendix A); transition lies *inside* the non-hand-signed mode |
+| Full-sample signature-l.  | BD/McCrary candidate transition                | 0.985 (bin 0.005)   | 2.0 (bin 1) | bin-unstable across $\{0.003, 0.005, 0.010, 0.015\}$ (Appendix A) |
+| **Reference: between-class KDE (different unit of analysis)** | | | | |
+| All-pairs intra/inter (pair-level; Section IV-C) | KDE crossover | 0.837 | — | reference point for the Uncertain/Likely-hand-signed boundary in the operational classifier |
+| **Operational classifier anchors and percentile cross-references** | | | | |
+| Firm A whole-sample       | P7.5 (operational anchor; Section III-K)       | 0.95                | —    | operational cosine cut for the five-way classifier |
+| Firm A whole-sample       | dHash$_\text{indep}$ P75                       | —                   | 4    | informs the $\leq 5$ high-confidence band edge in the classifier |
+| Firm A whole-sample       | dHash$_\text{indep}$ style-consistency ceiling | —                   | 15   | operational $> 15$ style-consistency boundary |
+| Firm A calibration fold (70%) | cosine P5 (Section IV-F.2)                  | 0.9407              | —    | calibration-fold cross-reference; held-out fold reports rates at this cut |
+| Firm A calibration fold (70%) | dHash$_\text{indep}$ P95                    | —                   | 9    | calibration-fold cross-reference (Tables IX and XI report rates at the rounded $\leq 8$ cut for continuity) |
+
+Read this table by *population × method*: each row reports one method applied to one population.
+The first three blocks (threshold estimators; density-smoothness diagnostics; between-class KDE) are *characterisation* outputs; the bottom block is the operational anchor set used by the classifier of Section III-K.
+The disagreement between Firm A Beta-2 (0.977) and Firm A logit-Gaussian-2 (0.999) is the parametric-form sensitivity referenced in the prose of Section IV-D.3; it cannot be resolved from the data because BIC rejects the underlying $K{=}2$ assumption itself.
+-->
+
+Non-hand-signed replication quality is therefore best read as a continuous spectrum produced by firm-specific reproduction technologies (administrative stamping in early years, firm-level e-signing later) acting on a common stored exemplar.
+This finding has a direct methodological pay-off: it is *why* the operational cosine cut is anchored on the whole-sample Firm A P7.5 percentile (Section III-K), and it is *why* the byte-level pixel-identity anchor (Section IV-F.1) is the natural threshold-free positive reference for downstream validation.
+
+## E. Calibration Validation with Firm A
+
+Fig. 3 presents the per-signature cosine and dHash distributions of Firm A compared to the overall population.
+Table IX reports the proportion of Firm A signatures crossing each candidate threshold; these rates play the role of calibration-validation metrics (what fraction of a known replication-dominated population does each threshold capture?).
+
+<!-- TABLE IX: Firm A Whole-Sample Capture Rates (consistency check, NOT external validation)
+| Rule | Firm A rate | k / N |
+|------|-------------|-------|
+| **Cosine-only marginal rates** | | |
+| cosine > 0.837 (all-pairs KDE crossover)                                  | 99.93% | 60,408 / 60,448 |
+| cosine > 0.9407 (calibration-fold P5)                                     | 95.15% | 57,518 / 60,448 |
+| cosine > 0.945 (calibration-fold P5 rounded)                              | 94.02% | 56,836 / 60,448 |
+| cosine > 0.95 (operational; whole-sample Firm A P7.5)                     | 92.51% | 55,922 / 60,448 |
+| **dHash-only marginal rates** | | |
+| dHash_indep ≤ 5 (operational high-confidence cap)                         | 84.20% | 50,897 / 60,448 |
+| dHash_indep ≤ 8 (calibration-fold P95 rounded)                            | 95.17% | 57,527 / 60,448 |
+| dHash_indep ≤ 15 (operational style-consistency boundary)                 | 99.83% | 60,348 / 60,448 |
+| **Operational classifier dual rules (Section III-K)** | | |
+| cosine > 0.95 AND dHash_indep ≤ 5 (high-confidence non-hand-signed)       | 81.70% | 49,389 / 60,448 |
+| cosine > 0.95 AND 5 < dHash_indep ≤ 15 (moderate-confidence)              | 10.76% | 6,503 / 60,448  |
+| cosine > 0.95 AND dHash_indep ≤ 15 (combined non-hand-signed)             | 92.46% | 55,892 / 60,448 |
+| **Calibration-fold-adjacent cross-reference (not the operational classifier rule)** | | |
+| cosine > 0.95 AND dHash_indep ≤ 8                                         | 89.95% | 54,370 / 60,448 |
+
+All rates computed exactly from the full Firm A sample (N = 60,448 signatures); per-rule counts and codes are available in the supplementary materials.
+The two operational dHash cuts ($\leq 5$ for the high-confidence cap and $\leq 15$ for the style-consistency boundary) come from the classifier definition in Section III-K and are the rules used by the five-way classifier of Tables XII and XVII; the dHash $\leq 8$ row is *not* an operational classifier rule but a calibration-fold-adjacent reference (Section IV-F.2 calibration-fold dHash P95 = 9; we report the $\leq 8$ rate as the integer-valued threshold immediately below P95, included here so that Firm A capture in the calibration-fold-P95 neighbourhood can be read off the same table).
+-->
+
+Table IX is a whole-sample consistency check rather than an external validation: the cosine cut $0.95$ and the operational dHash band edges ($\leq 5$ high-confidence cap and $\leq 15$ style-consistency boundary) are themselves anchored to the whole-sample Firm A distribution described in Section III-K (the 70/30 calibration-fold thresholds of Table XI are separate and slightly different, e.g., calibration-fold cosine P5 = 0.9407 rather than the whole-sample heuristic 0.95).
+The operational dual rule used by the five-way classifier of Section III-K---cosine $> 0.95$ AND $\text{dHash}_\text{indep} \leq 15$ (the union of the high-confidence and moderate-confidence non-hand-signed buckets)---captures 92.46% of Firm A; the high-confidence component alone (cosine $> 0.95$ AND $\text{dHash}_\text{indep} \leq 5$) captures 81.70%.
+For continuity with prior calibration-fold reporting (Section IV-F.2 reports the calibration-fold rate at the calibration-fold-P95-adjacent cut $\text{dHash}_\text{indep} \leq 8$), Table IX also lists the cosine $> 0.95$ AND $\text{dHash}_\text{indep} \leq 8$ rate of 89.95%; this is *not* the operational classifier rule but a cross-reference value.
+Both operational rates are consistent with the dip-test-confirmed unimodal-long-tail shape of Firm A's per-signature cosine distribution (Section IV-D.1) and the 92.5% / 7.5% signature-level split (Section III-H).
+Section IV-F.2 reports the corresponding rates on the 30% Firm A hold-out fold, which provides the external check these whole-sample rates cannot.
+
+## F. Pixel-Identity, Inter-CPA, and Held-Out Firm A Validation
+
+We report three validation analyses corresponding to the anchors of Section III-J.
+
+### 1) Pixel-Identity Positive Anchor with Inter-CPA Negative Anchor
+
+Of the 182,328 extracted signatures, 310 have a same-CPA nearest match that is byte-identical after crop and normalization (pixel-identical-to-closest = 1); these form the byte-identity positive anchor---a pair-level proof of image reuse that serves as conservative ground truth for non-hand-signed signatures, subject to the source-template edge case discussed in Section V-G.
+Within Firm A specifically, 145 of these byte-identical signatures are distributed across 50 distinct partners (of 180 registered Firm A partners), with 35 of the byte-identical pairs spanning different fiscal years; reproduction artifact for this Firm A decomposition is listed in Appendix B.
+As the gold-negative anchor we sample 50,000 i.i.d. random cross-CPA signature pairs from the full 168,755-signature matched corpus (inter-CPA cosine: mean $= 0.763$, $P_{95} = 0.886$, $P_{99} = 0.915$, max $= 0.992$).
+Because the positive and negative anchor populations are constructed from different sampling units (byte-identical same-CPA pairs vs random inter-CPA pairs), their relative prevalence in the combined anchor set is arbitrary, and precision / $F_1$ / recall therefore have no meaningful population interpretation.
+We accordingly report FAR with Wilson 95% confidence intervals against the large inter-CPA negative anchor in Table X.
+The primary quantity reported by Table X is FAR: the probability that a random pair of signatures from *different* CPAs exceeds the candidate threshold.
+We do not report an Equal Error Rate: EER is meaningful only when the positive and negative error-rate curves cross in a nontrivial interior region, but byte-identical positives all sit at cosine $\approx 1$ by construction, so FRR against that subset is trivially $0$ at every threshold below $1$. An EER calculation against this anchor would be arithmetic tautology rather than biometric performance, and we therefore omit it.
+
+<!-- TABLE X: Cosine Threshold Sweep — FAR Against 50,000 Inter-CPA Negative Pairs
+| Threshold | FAR | FAR 95% Wilson CI |
+|-----------|-----|-------------------|
+| 0.837 (all-pairs KDE crossover) | 0.2101 | [0.2066, 0.2137] |
+| 0.900                            | 0.0250 | [0.0237, 0.0264] |
+| 0.945 (calibration-fold P5 rounded) | 0.0008 | [0.0006, 0.0011] |
+| 0.950 (whole-sample Firm A P7.5; operational cut)  | 0.0005 | [0.0003, 0.0007] |
+| 0.977 (Firm A Beta-2 forced-fit crossing; Section IV-D)  | 0.00014 | [0.00007, 0.00029] |
+| 0.985 (BD/McCrary candidate transition; Appendix A) | 0.00004 | [0.00001, 0.00015] |
+
+Table note: We do not include FRR against the byte-identical positive anchor as a column here: the byte-identical subset has cosine $\approx 1$ by construction, so FRR against that subset is trivially $0$ at every threshold below $1$ and carries no biometric information beyond verifying that the threshold does not exceed $1$. The conservative-subset FRR role of the byte-identical anchor is instead discussed qualitatively in Section V-F.
+-->
+
+Two caveats apply.
+First, the byte-identical positive anchor referenced above is a *conservative subset* of the true non-hand-signed population: it captures only those non-hand-signed signatures whose nearest match happens to be byte-identical, not those that are near-identical but not bytewise identical.
+A would-be FRR computed against this subset is definitionally $0$ at every threshold below $1$ (since byte-identical pairs have cosine $\approx 1$), so such an FRR is a mathematical boundary check rather than an empirical miss-rate estimate; we discuss the generalization limits of this conservative-subset framing in Section V-F.
+Second, the 0.945 / 0.95 thresholds are derived from the Firm A whole-sample and calibration-fold percentiles rather than from this anchor set, so the FAR values in Table X are post-hoc-fit-free evaluations of thresholds that were not chosen to optimize Table X.
+The very low FAR at the operational cut is therefore informative about specificity against a realistic inter-CPA negative population.
+
+### 2) Held-Out Firm A Validation (within-Firm-A sampling variance disclosure)
+
+We split Firm A CPAs randomly 70 / 30 at the CPA level into a calibration fold (124 CPAs, 45,116 signatures) and a held-out fold (54 CPAs, 15,332 signatures).
+The total of 178 Firm A CPAs differs from the 180 in the Firm A registry by two registered Firm A partners whose signatures in the corpus are singletons (only one signature each, so the per-signature best-match cosine is undefined and they do not appear in the same-CPA matched-signature table that script `24_validation_recalibration.py` reads); they are therefore not represented in either fold by construction rather than by an explicit exclusion rule.
+Thresholds are re-derived from calibration-fold percentiles only.
+Table XI reports both calibration-fold and held-out-fold capture rates with Wilson 95% CIs and a two-proportion $z$-test.
+
+<!-- TABLE XI: Held-Out vs Calibration Firm A Capture Rates and Generalization Test
+| Rule | Calibration 70% fold (CI) | Held-out 30% fold (CI) | 2-prop z | p | k/n calib | k/n held |
+|------|---------------------------|-------------------------|----------|---|-----------|----------|
+| cosine > 0.837                       | 99.94% [99.91%, 99.96%] | 99.93% [99.87%, 99.96%] | +0.31  | 0.756 n.s. | 45,087/45,116 | 15,321/15,332 |
+| cosine > 0.9407 (calib-fold P5)      | 94.99% [94.79%, 95.19%] | 95.63% [95.29%, 95.94%] | -3.19  | 0.001      | 42,856/45,116 | 14,662/15,332 |
+| cosine > 0.945 (calib-fold P5 rounded) | 93.77% [93.54%, 93.99%] | 94.78% [94.41%, 95.12%] | -4.54  | <0.001     | 42,305/45,116 | 14,531/15,332 |
+| cosine > 0.950 (whole-sample P7.5; operational cut) | 92.14% [91.89%, 92.38%] | 93.61% [93.21%, 93.98%] | -5.97  | <0.001     | 41,570/45,116 | 14,352/15,332 |
+| dHash_indep ≤ 5                      | 82.96% [82.61%, 83.31%] | 87.84% [87.31%, 88.34%] | -14.29 | <0.001     | 37,430/45,116 | 13,467/15,332 |
+| dHash_indep ≤ 8                      | 94.84% [94.63%, 95.04%] | 96.13% [95.82%, 96.43%] | -6.45  | <0.001     | 42,788/45,116 | 14,739/15,332 |
+| dHash_indep ≤ 9 (calib-fold P95)     | 96.65% [96.48%, 96.81%] | 97.48% [97.22%, 97.71%] | -5.07  | <0.001     | 43,604/45,116 | 14,945/15,332 |
+| dHash_indep ≤ 15                     | 99.83% [99.79%, 99.87%] | 99.84% [99.77%, 99.89%] | -0.31  | 0.754 n.s. | 45,040/45,116 | 15,308/15,332 |
+| cosine > 0.95 AND dHash_indep ≤ 8 (calibration-fold P95-adjacent reference; P95 = 9) | 89.40% [89.12%, 89.68%] | 91.54% [91.09%, 91.97%] | -7.60  | <0.001     | 40,335/45,116 | 14,035/15,332 |
+| cosine > 0.95 AND dHash_indep ≤ 15 (operational classifier rule, Section III-K) | 92.09% [91.84%, 92.34%] | 93.56% [93.16%, 93.93%] | -5.93  | <0.001     | 41,548/45,116 | 14,344/15,332 |
+
+Calibration-fold thresholds: Firm A cosine median = 0.9862, P1 = 0.9067, P5 = 0.9407; dHash_indep median = 2, P95 = 9. Counts and z/p values are reproducible from the supplementary materials (fixed random seed).
+-->
+
+We report fold-versus-fold comparisons rather than fold-versus-whole-sample comparisons, because the whole-sample rate is a weighted average of the two folds and therefore cannot, in general, fall inside the Wilson CI of either fold when the folds differ in rate; the correct generalization reference is the calibration fold, which produced the thresholds.
+
+Under this proper test the two extreme rules agree across folds (cosine $> 0.837$ and $\text{dHash}_\text{indep} \leq 15$; both $p > 0.7$).
+The operationally relevant rules in the 85–95% capture band differ between folds by 1–5 percentage points ($p < 0.001$ given the $n \approx 45\text{k}/15\text{k}$ fold sizes).
+Both folds nevertheless sit in the same replication-dominated regime: every calibration-fold rate in the 85–99% range has a held-out counterpart in the 87–99% range, and the calibration-fold-adjacent reference rule cosine $> 0.95$ AND $\text{dHash}_\text{indep} \leq 8$ (the integer cut immediately below the calibration-fold dHash P95 of 9) captures 89.40% of the calibration fold and 91.54% of the held-out fold; the operational classifier rule cosine $> 0.95$ AND $\text{dHash}_\text{indep} \leq 15$ used by the five-way classifier of Section III-K captures still higher rates in both folds (calibration 92.09%, 41,548 / 45,116; held-out 93.56%, 14,344 / 15,332).
+The modest fold gap is consistent with within-Firm-A heterogeneity in replication intensity: the random 30% CPA sample evidently contained proportionally more high-replication CPAs.
+We therefore interpret the held-out fold as confirming the qualitative finding (Firm A is strongly replication-dominated across both folds) while cautioning that exact rates carry fold-level sampling noise that a single 30% split cannot eliminate; the threshold-independent partner-ranking analysis (Section IV-G.2) is the cross-check that is robust to this fold variance.
+
+### 3) Operational-Threshold Sensitivity: cos $> 0.95$ vs cos $> 0.945$
+
+The per-signature classifier (Section III-K) uses cos $> 0.95$ as its operational cosine cut, anchored on the whole-sample Firm A P7.5 heuristic (i.e., 7.5% of whole-sample Firm A signatures lie at or below 0.95; see Section III-H).
+We report a sensitivity check in which this round-number cut is replaced by the slightly stricter calibration-fold P5 rounded value cos $> 0.945$ (calibration-fold P5 = 0.9407, see Table XI).
+Table XII reports the five-way classifier output under each cut.
+
+<!-- TABLE XII: Classifier Sensitivity to the Operational Cosine Cut (All-Sample Five-Way Output, N = 168,740 signatures)
+| Cosine cut | High-confidence | Moderate-confidence | High style consistency | Uncertain | Likely hand-signed |
+|------------|-----------------|---------------------|------------------------|-----------|--------------------|
+| cos > 0.940                | 81,069 (48.04%) | 55,308 (32.78%) | 801 (0.47%) |  31,026 (18.39%) | 536 (0.32%) |
+| cos > 0.945                | 79,278 (46.98%) | 50,001 (29.63%) | 665 (0.39%) |  38,260 (22.67%) | 536 (0.32%) |
+| cos > 0.950 (operational)  | 76,984 (45.62%) | 43,906 (26.02%) | 546 (0.32%) |  46,768 (27.72%) | 536 (0.32%) |
+| cos > 0.960                | 70,250 (41.63%) | 29,450 (17.45%) | 288 (0.17%) |  68,216 (40.43%) | 536 (0.32%) |
+| cos > 0.970                | 60,247 (35.70%) | 14,865 ( 8.81%) | 117 (0.07%) |  92,975 (55.10%) | 536 (0.32%) |
+| cos > 0.985                | 37,368 (22.15%) |  2,231 ( 1.32%) |  10 (0.01%) | 128,595 (76.21%) | 536 (0.32%) |
+
+The dHash band edges ($\leq 5$ for high-confidence, $5 < \text{dHash}_\text{indep} \leq 15$ for moderate-confidence, $> 15$ for style) are held fixed across the grid; only the cosine cut varies. The Likely-hand-signed count is invariant across the grid because it depends only on the all-pairs KDE crossover cosine $= 0.837$.
+-->
+
+At the aggregate firm-level, the calibration-fold-adjacent reference dual rule cos $> 0.95$ AND $\text{dHash}_\text{indep} \leq 8$ captures 89.95% of whole Firm A under the 0.95 cut and 91.14% under the 0.945 cut---a shift of 1.19 percentage points.
+The operational classifier rule cos $> 0.95$ AND $\text{dHash}_\text{indep} \leq 15$ used by the five-way classifier of Section III-K captures 92.46% under the 0.95 cut and 93.97% under the 0.945 cut---a shift of 1.51 percentage points.
+
+Reading the wider grid in Table XII: the High-confidence and Moderate-confidence shares shift by less than 5 percentage points across the 0.940-0.950 neighbourhood, while pushing the cosine cut to 0.970 or 0.985 produces qualitatively different classifier behaviour (Moderate-confidence collapses from 26.02% at $0.95$ to 8.81% at $0.97$ and 1.32% at $0.985$, with the displaced mass landing in Uncertain rather than reclassifying out of the corpus).
+The classifier output is therefore robust to small (~0.005-cosine) perturbations of the operational cut but not to wholesale reanchoring at the threshold-estimator outputs of Section IV-D, which is consistent with our reading that those outputs are not classifier thresholds.
+At the per-signature categorization level, replacing 0.95 by 0.945 reclassifies 8,508 signatures (5.04% of the corpus) out of the Uncertain band; 6,095 of them migrate to Moderate-confidence non-hand-signed, 2,294 to High-confidence non-hand-signed, and 119 to High style consistency.
+The Likely-hand-signed category is unaffected because it depends only on the fixed all-pairs KDE crossover cosine $= 0.837$.
+The High-confidence non-hand-signed share grows from 45.62% to 46.98%.
+
+We interpret this sensitivity pattern as indicating that the classifier's aggregate and high-confidence output is robust to the choice of operational cut within a 0.005-cosine neighbourhood of the Firm A P7.5 anchor, and that the movement is concentrated at the Uncertain/Moderate-confidence boundary.
+
+To make the operating-point selection (Section III-K) auditable rather than presented as a single fixed value, Table XII-B reports the capture-vs-FAR tradeoff over the candidate threshold grid spanning the calibration-fold P5 (0.9407), its rounded value (0.945), the operational anchor (0.95), the Firm A Beta-2 forced-fit crossing from Section IV-D.3 (0.977), and the BD/McCrary candidate transition from Section IV-D.2 (0.985).
+For each grid point we report Firm A capture (under both the cosine-only marginal and the operational dual rule cos $> t$ AND $\text{dHash}_\text{indep} \leq 15$ used by the five-way classifier of Section III-K), non-Firm-A capture (the cosine-only marginal in the 108,292 non-Firm-A matched signatures), and inter-CPA FAR with Wilson 95% CI against the 50,000-pair anchor of Section IV-F.1.
+
+<!-- TABLE XII-B: Cosine-Threshold Tradeoff: Capture vs Inter-CPA FAR
+| Cosine cut t | Firm A capture (cos > t) | Firm A capture (cos > t AND dHash_indep ≤ 15) | Non-Firm-A capture (cos > t) | Inter-CPA FAR | Inter-CPA FAR Wilson 95% CI |
+|--------------|--------------------------|------------------------------------------------|------------------------------|---------------|------------------------------|
+| 0.9407 (calibration-fold P5)               | 95.15% (57,518/60,448) | 95.09% (57,482/60,448) | 72.68% (78,710/108,292) | 0.00126 | [0.00099, 0.00161] |
+| 0.945 (calibration-fold P5 rounded)        | 94.02% (56,836/60,448) | 93.97% (56,804/60,448) | 67.51% (73,108/108,292) | 0.00082 | [0.00061, 0.00111] |
+| 0.95 (whole-sample Firm A P7.5; **operational cut**) | **92.51%** (55,922/60,448) | **92.46%** (55,892/60,448) | 60.50% (65,514/108,292) | **0.00050** | [0.00034, 0.00074] |
+| 0.977 (Firm A Beta-2 forced-fit crossing)  | 74.53% (45,050/60,448) | 74.51% (45,038/60,448) | 13.14% (14,233/108,292) | 0.00014 | [0.00007, 0.00029] |
+| 0.985 (BD/McCrary candidate transition)    | 55.27% (33,409/60,448) | 55.26% (33,406/60,448) |  5.73%  (6,200/108,292) | 0.00004 | [0.00001, 0.00015] |
+
+Inter-CPA FAR computed against 50,000 i.i.d. inter-CPA pairs (random seed 42, reproducing the anchor of Section IV-F.1 / Table X). Capture and FAR percentages are exact ratios of the displayed integer counts; gap arithmetic in the surrounding prose is computed from those exact counts and rounded to two decimal places. The dual-rule column is the operational classifier rule of Section III-K; for cuts above the dHash-15 saturation point (Firm A dHash$_\text{indep}$ $> 15$ rate is only 0.17%, Table IX), the dual-rule and cosine-only columns coincide to within the dHash$_\text{indep}$ $> 15$ residual.
+-->
+
+Reading Table XII-B, three patterns motivate the choice of $0.95$ as the operating point.
+First, *Firm A capture* on the operational dual rule decays smoothly from 95.09% at $t = 0.9407$ to 55.26% at $t = 0.985$.
+Relaxing the cut from $0.95$ to $0.945$ buys 1.51 percentage points of additional Firm A capture, and to $0.9407$ buys 2.63 percentage points; tightening from $0.95$ to $0.977$ costs 17.96 percentage points and to $0.985$ costs 37.20 percentage points.
+The selected cut at $0.95$ is the strictest cut on this grid at which Firm A capture remains above $90\%$ on the operational dual rule.
+Second, *inter-CPA FAR* is small in absolute terms across the entire candidate grid ($0.00126$ at $0.9407$, falling to $0.00004$ at $0.985$): under any of these operating points the classifier's specificity against random cross-CPA pairs is in the per-mille range or better, so FAR alone does not determine the choice.
+The marginal FAR cost of relaxing from $0.95$ to $0.945$ is $+0.00032$ ($25 \to 41$ false positives per 50,000 pairs) and to $0.9407$ is $+0.00076$ ($25 \to 63$); the marginal FAR savings from tightening to $0.977$ and $0.985$ are $-0.00036$ and $-0.00046$ respectively.
+The FAR savings from going stricter are small in absolute terms compared with the corresponding Firm A capture loss, which makes $0.95$ a balanced operating point on this grid rather than a uniquely optimal one.
+Third, *non-Firm-A capture* (the cosine-only marginal in the 108,292 non-Firm-A signatures) decays from 67.51% at $0.945$ to 60.50% at $0.95$, 13.14% at $0.977$, and 5.73% at $0.985$.
+The Firm-A-minus-non-Firm-A gap widens with strictness through $0.977$ and then contracts (22.41 percentage points at $0.9407$; 26.46 at $0.945$; 31.97 at $0.95$; 61.36 at $0.977$; 49.54 at $0.985$): on the $0.95 \to 0.977$ segment non-Firm-A capture falls faster than Firm A capture in absolute terms ($-47.35$ vs $-17.96$ percentage points), so the widening is dominated by non-Firm-A removal rather than by an intrinsic property of Firm A; on the $0.977 \to 0.985$ segment Firm A capture falls faster than non-Firm-A's already-low residual, so the gap contracts.
+We do *not* read the gap pattern as evidence for a particular cut; it is reported here as cross-firm replication heterogeneity rather than as a selection criterion.
+The operating point at $0.95$ is therefore a defensible---not unique---selection in this neighbourhood, motivated by (i) keeping Firm A capture above $90\%$ on the operational dual rule, (ii) achieving an FAR of $0.0005$ at which marginal further savings from tightening are small relative to the corresponding capture loss, and (iii) preserving the interpretive transparency of the whole-sample Firm A P7.5 reading.
+It is *not* derived from the threshold-estimator outputs of Section IV-D, which the data do not support as classifier thresholds.
+
+The paper therefore retains cos $> 0.95$ as the primary operational cut and reports the 0.945 result of Table XII as a sensitivity check rather than as a deployed alternative; downstream document-level rates (Table XVII) and intra-report agreement (Table XVI) are robust to moderate cutoff shifts within the 0.945--0.95 neighbourhood as long as the same cutoff is applied uniformly across firms.
+
+## G. Additional Firm A Benchmark Validation
+
+Before presenting the three threshold-robust analyses, Fig. 4 summarises the per-firm yearly per-signature best-match cosine distribution that motivates them.
+The left panel reports the mean per-signature best-match cosine within each firm bucket and fiscal year (a threshold-free statistic); the right panel reports the share of each firm-bucket-year with per-signature best-match cosine $\geq 0.95$ (the operational cut of Section III-K).
+Both panels show Firm A above the other Big-4 firms in every year of the 2013-2023 sample, with non-Big-4 firms below all four Big-4 firms throughout, and the cross-firm ordering is stable across the sample period.
+The mean-cosine separation between Firm A and the other Big-4 firms is on the order of 0.02-0.04 throughout the sample (e.g., 2013: Firm A $0.9733$ vs Firm B $0.9498$, Firm C $0.9464$, Firm D $0.9395$, Non-Big-4 $0.9227$; 2023: $0.9860$ vs $0.9668$, $0.9662$, $0.9525$, $0.9346$); the share-above-0.95 separation is wider (2013: Firm A $87.2\%$ vs $61.8\%$, $56.2\%$, $38.5\%$, $27.5\%$).
+This visual is the most direct cross-firm evidence in the paper that Firm A's high-similarity behaviour is firm-specific rather than corpus-wide; the three subsections below decompose this gap along three threshold-free or threshold-robust dimensions.
+
+<!-- FIGURE 4: Per-firm yearly per-signature best-match cosine
+File: reports/figures/fig_yearly_big4_comparison.png (and .pdf)
+Generated by: signature_analysis/30_yearly_big4_comparison.py
+Caption: Per-firm yearly per-signature best-match cosine, 2013-2023.
+(a) Mean per-signature best-match cosine by firm bucket and fiscal year
+(threshold-free). (b) Share of per-signature best-match cosine $\geq 0.95$
+(operational cut of Section III-K). Five lines: Firm A, B, C, D, Non-Big-4.
+Firm A is above the other Big-4 firms in every year; Non-Big-4 is below all
+four Big-4 firms in every year. Per-firm signature counts and exact values
+are in `reports/firm_yearly_comparison/firm_yearly_comparison.{json,md}`.
+-->
+
+The capture rates of Section IV-E are an *internal* consistency check: they ask "how much of Firm A does our threshold capture?", but the threshold was itself derived from Firm A's percentiles, so a high capture rate is not surprising.
+To go beyond this circular check, we report three further analyses, each chosen so that the *informative quantity* does not depend on the threshold's absolute value:
+
+- **§IV-G.1 (year-by-year stability).** Holds the cosine cutoff fixed at 0.95 and asks whether the share of Firm A below the cutoff is *stable across years*. The information is in the temporal trend, not in the absolute rate; under a noise-only explanation of the left tail, the share should shrink as scan/PDF technology matured.
+- **§IV-G.2 (partner-level similarity ranking).** Uses *no threshold at all*: every auditor-year is ranked by mean similarity, and we measure Firm A's share of the top decile against its baseline share. The information is in the concentration ratio, which is invariant to the choice of cutoff.
+- **§IV-G.3 (intra-report agreement).** Applies the calibrated classifier and measures whether the *two co-signing CPAs on the same Firm A report* receive the same classifier label, then compares Firm A's intra-report agreement rate to the other firms'. The information is in the *cross-firm gap*; the absolute agreement rate at any one firm depends on the cutoff, but the gap is robust to moderate cutoff shifts as long as the same cutoff is applied uniformly across firms.
+
+Together these three analyses provide threshold-free or threshold-robust evidence that complements the within-sample capture rates of Section IV-E.
+
+### 1) Year-by-Year Stability of the Firm A Left Tail
+
+Table XIII reports the proportion of Firm A signatures with per-signature best-match cosine below 0.95, disaggregated by fiscal year.
+Under the replication-dominated interpretation (Section III-H), this signature-level left-tail rate reflects within-firm heterogeneity in signing outputs at Firm A.
+Consistent with the scope-of-claims framing in Section III-G, we report the rate as a signature-level quantity without disaggregating the underlying mechanism (which may span a minority of hand-signing partners, multi-template replication workflows within the firm, or a combination); partner-level mechanism attribution is not attempted.
+Under the alternative hypothesis that the left tail is an artifact of scan or compression noise, the share should shrink as scanning and PDF-compression technology improved over 2013-2023.
+
+<!-- TABLE XIII: Firm A Per-Year Cosine Distribution
+| Year | N sigs | mean best-match cosine | % below 0.95 |
+|------|--------|-------------|--------------|
+| 2013 | 2,167 | 0.9733 | 12.78% |
+| 2014 | 5,256 | 0.9781 | 8.69% |
+| 2015 | 5,484 | 0.9793 | 7.46% |
+| 2016 | 5,739 | 0.9811 | 6.92% |
+| 2017 | 5,796 | 0.9814 | 6.69% |
+| 2018 | 5,986 | 0.9808 | 6.58% |
+| 2019 | 6,122 | 0.9780 | 8.71% |
+| 2020 | 6,122 | 0.9770 | 9.46% |
+| 2021 | 5,996 | 0.9792 | 8.37% |
+| 2022 | 5,918 | 0.9819 | 6.25% |
+| 2023 | 5,862 | 0.9860 | 3.75% |
+-->
+
+The left tail is stable at 6-13% throughout the sample period and shows no pre/post-2020 level shift: the 2013-2019 mean left-tail share is 8.26% and the 2020-2023 mean is 6.96%.
+The lowest observed share is in 2023 (3.75%), consistent with firm-level electronic signing systems producing more uniform output than earlier manual scanning-and-stamping, not less.
+This stability supports the replication-dominated framing: a persistent within-firm heterogeneity component is consistent with a Beta left tail that is stable across production technologies, whereas a noise-only explanation would predict a shrinking share as technology improved.
+
+### 2) Partner-Level Similarity Ranking
+
+If Firm A applies firm-wide stamping while the other Big-4 firms use stamping only for a subset of partners, Firm A auditor-years should disproportionately occupy the top of the similarity distribution among all auditor-years (across all firms).
+We test this prediction directly.
+
+For each auditor-year (CPA $\times$ fiscal year) with at least 5 signatures we compute the mean best-match cosine similarity across the year's signatures, yielding 4,629 auditor-years across 2013-2023.
+Firm A accounts for 1,287 of these (27.8% baseline share).
+Table XIV reports per-firm occupancy of the top $K\%$ of the ranked distribution.
+The per-signature best-match cosine underlying each auditor-year mean is taken over the full same-CPA pool (Section III-G), consistent with the unit-of-analysis framing in Section III-G.
+
+<!-- TABLE XIV: Top-K Similarity Rank Occupancy by Firm (pooled 2013-2023)
+| Top-K | k in bucket | Firm A | Firm B | Firm C | Firm D | Non-Big-4 | Firm A share |
+|-------|-------------|--------|--------|--------|--------|-----------|--------------|
+| 10%   | 462         | 443    | 2      | 3      | 0      | 14        | 95.9% |
+| 20%   | 925         | 877    | 9      | 14     | 2      | 23        | 94.8% |
+| 25%   | 1,157       | 1,043  | 32     | 23     | 9      | 50        | 90.1% |
+| 30%   | 1,388       | 1,129  | 105    | 52     | 25     | 77        | 81.3% |
+| 50%   | 2,314       | 1,220  | 473    | 273    | 102    | 246       | 52.7% |
+-->
+
+Firm A occupies 95.9% of the top 10%, 94.8% of the top 20%, 90.1% of the top 25%, and 81.3% of the top 30% of auditor-years by similarity, against its baseline share of 27.8%---a concentration ratio of $3.5\times$ at the top decile, $3.4\times$ at the top quintile, and $2.9\times$ at the top tercile.
+Firm A's share decays monotonically as the bracket widens (95.9% $\to$ 94.8% $\to$ 90.1% $\to$ 81.3% $\to$ 52.7% across top-10/20/25/30/50%), and only at the top 50% does its share approach its baseline; the over-representation is therefore concentrated in the very top of the distribution rather than spread uniformly through the upper half.
+Year-by-year (Table XV), the top-10% Firm A share ranges from 88.4% (2020) to 100% (2013, 2014, 2017, 2018, 2019), showing that the concentration is stable across the sample period.
+
+<!-- TABLE XV: Firm A Share of Top-K Similarity by Year (K = 10%, 20%, 30%)
+| Year | N auditor-years | Top-10% share | Top-20% share | Top-30% share | Firm A baseline |
+|------|-----------------|---------------|---------------|---------------|-----------------|
+| 2013 | 324 | 100.0% (32/32) | 98.4% (63/64) | 89.7% (87/97) | 32.4% |
+| 2014 | 399 | 100.0% (39/39) | 98.7% (78/79) | 82.4% (98/119) | 27.8% |
+| 2015 | 394 | 97.4% (38/39) | 96.2% (75/78) | 84.7% (100/118) | 27.7% |
+| 2016 | 413 | 95.1% (39/41) | 96.3% (79/82) | 81.3% (100/123) | 26.2% |
+| 2017 | 415 | 100.0% (41/41) | 97.6% (81/83) | 83.9% (104/124) | 27.2% |
+| 2018 | 434 | 100.0% (43/43) | 97.7% (84/86) | 80.0% (104/130) | 26.5% |
+| 2019 | 429 | 100.0% (42/42) | 97.6% (83/85) | 78.9% (101/128) | 27.0% |
+| 2020 | 430 | 88.4% (38/43)  | 91.9% (79/86) | 76.0% (98/129)  | 27.7% |
+| 2021 | 450 | 97.8% (44/45)  | 96.7% (87/90) | 81.5% (110/135) | 28.7% |
+| 2022 | 467 | 93.5% (43/46)  | 95.7% (89/93) | 84.3% (118/140) | 28.3% |
+| 2023 | 474 | 97.9% (46/47)  | 94.7% (89/94) | 83.8% (119/142) | 27.4% |
+
+Per-cell entries are "share (k_FirmA / k_total)". Top-25% and top-50% pooled values are reported in Table XIV; per-year top-25/50 columns are omitted from this table to reduce visual width but are reproducible from the supplementary materials.
+-->
+
+This over-representation is consistent with firm-wide non-hand-signing practice at Firm A and is not derived from any threshold we subsequently calibrate.
+It therefore constitutes genuine cross-firm evidence for Firm A's benchmark status.
+
+### 3) Intra-Report Consistency
+
+Taiwanese statutory audit reports are co-signed by two engagement partners (a primary and a secondary signer).
+Under firm-wide stamping practice at a given firm, both signers on the same report should receive the same signature-level classification.
+Disagreement between the two signers on a report is informative about whether the stamping practice is firm-wide or partner-specific.
+
+For each report with exactly two signatures and complete per-signature data (84,354 reports total: 83,970 single-firm reports, in which both signers are at the same firm, and 384 mixed-firm reports, in which the two signers are at different firms), we classify each signature using the dual-descriptor rules of Section III-K and record whether the two classifications agree.
+Table XVI reports per-firm intra-report agreement for the 83,970 single-firm reports only (firm-assignment defined by the common firm identity of both signers); the 384 mixed-firm reports (0.46% of the 2-signature corpus) are excluded from the intra-report analysis because firm-level agreement is not well defined when the two signers are at different firms.
+
+<!-- TABLE XVI: Intra-Report Classification Agreement by Firm
+| Firm | Total 2-signer reports | Both non-hand-signed | Both uncertain | Both style | Both hand-signed | Mixed | Agreement rate |
+|------|-----------------------|----------------------|----------------|------------|------------------|-------|----------------|
+| Firm A  | 30,222 | 26,435 | 734 | 0 | 4 | 3,049 | **89.91%** |
+| Firm B  | 17,121 | 9,260  | 2,159| 5 | 6 | 5,691 | 66.76% |
+| Firm C  | 19,112 | 8,983  | 3,035| 3 | 5 | 7,086 | 62.92% |
+| Firm D  | 8,375  | 3,028  | 2,376| 0 | 3 | 2,968 | 64.56% |
+| Non-Big-4 | 9,140  | 1,671  | 3,945| 18| 27| 3,479 | 61.94% |
+
+A report is "in agreement" if both signature labels fall in the same coarse bucket
+(non-hand-signed = high+moderate; uncertain; style consistency; or likely hand-signed).
+-->
+
+Firm A achieves 89.9% intra-report agreement, with 87.5% of Firm A reports having *both* signers classified as non-hand-signed and only 4 reports (0.01%) having both classified as likely hand-signed.
+The other Big-4 firms (B, C, D) and non-Big-4 firms cluster at 62-67% agreement, a 23-28 percentage-point gap.
+This 23-28 percentage-point gap in intra-report agreement between Firm A and the other firms is consistent with firm-wide (rather than partner-specific) non-hand-signing practice; we do not claim a sharp discontinuity in the formal sense, since classifier calibration, firm-specific document-production pipelines, and signer-mix differences could each contribute to gap magnitude.
+
+We note that this test uses the calibrated classifier of Section III-K rather than a threshold-free statistic; the substantive evidence lies in the *cross-firm gap* between Firm A and the other firms rather than in the absolute agreement rate at any single firm, and that gap is robust to moderate shifts in the absolute cutoff so long as the cutoff is applied uniformly across firms.
+
+## H. Classification Results
+
+Table XVII presents the final classification results under the dual-descriptor framework with Firm A-calibrated thresholds for 84,386 documents (656 documents excluded from the 85,042-document YOLO-detection cohort because no signature on the document could be matched to a registered CPA; see Table XVII note).
+We emphasize that the document-level proportions below reflect the *worst-case aggregation rule* of Section III-K: a report carrying one stamped signature and one hand-signed signature is labeled with the most-replication-consistent of the two signature-level verdicts.
+Document-level rates therefore represent the share of reports in which *at least one* signature is non-hand-signed rather than the share in which *both* are; the intra-report agreement analysis of Section IV-G.3 (Table XVI) reports how frequently the two co-signers share the same signature-level label within each firm, so that readers can judge what fraction of the non-hand-signed document-level share corresponds to fully non-hand-signed reports versus mixed reports.
+
+<!-- TABLE XVII: Document-Level Classification (Dual-Descriptor: Cosine + dHash)
+| Verdict | N (PDFs) | % | Firm A | Firm A % |
+|---------|----------|---|--------|----------|
+| High-confidence non-hand-signed | 29,529 | 35.0% | 22,970 | 76.0% |
+| Moderate-confidence non-hand-signed | 36,994 | 43.8% | 6,311 | 20.9% |
+| High style consistency | 5,133 | 6.1% | 183 | 0.6% |
+| Uncertain | 12,683 | 15.0% | 758 | 2.5% |
+| Likely hand-signed | 47 | 0.1% | 4 | 0.0% |
+
+Per the worst-case aggregation rule of Section III-K, a document with two signatures inherits the most-replication-consistent of the two signature-level labels.
+The 84,386-document cohort excludes 656 documents (relative to the 85,042 YOLO-detected cohort of Table III) for which no signature could be matched to a registered CPA: the per-document classifier requires at least one CPA-matched signature so that a same-CPA best-match similarity is defined. The exclusion is definitional rather than discretionary; typical causes are auditor's-report-page formats deviating from the standard two-signature layout, or OCR returning a printed CPA name not present in the registry.
+-->
+
+Within the 71,656 documents exceeding cosine $0.95$, the dHash dimension stratifies them into three distinct populations:
+29,529 (41.2%) show converging structural evidence of non-hand-signing (dHash $\leq 5$);
+36,994 (51.7%) show partial structural similarity (dHash in $[6, 15]$) consistent with replication degraded by scan variations;
+and 5,133 (7.2%) show no structural corroboration (dHash $> 15$), suggesting high signing consistency rather than image reproduction.
+A cosine-only classifier would treat all 71,656 identically; the dual-descriptor framework separates them into populations with fundamentally different interpretations.
+
+### 1) Firm A Capture Profile (Consistency Check)
+
+96.9% of Firm A's documents fall into the high- or moderate-confidence non-hand-signed categories, 0.6% into high-style-consistency, and 2.5% into uncertain.
+This pattern is consistent with the replication-dominated framing: the large majority is captured by non-hand-signed rules, while the small residual is consistent with the within-firm heterogeneity implied by the dip-test-confirmed unimodal-long-tail shape of Firm A's per-signature cosine distribution (Section IV-D.1) and the 7.5% signature-level left tail (Section III-H).
+The near-zero "likely hand-signed" rate (4 of 30,226 Firm A documents, 0.013%; the 30,226 denominator is documents with at least one Firm A signer under the 84,386-document classification cohort, which differs from the 30,222 single-firm two-signer subset of Table XVI by 4 mixed-firm reports excluded from the firm-level intra-report comparison) indicates that the within-firm heterogeneity implied by the 7.5% signature-level left tail (Section IV-D) does not project into the lowest-cosine document-level category under the dual-descriptor rules; it is absorbed instead into the uncertain or high-style-consistency categories at this threshold set.
+We note that because the non-hand-signed thresholds are themselves calibrated to Firm A's empirical percentiles (Section III-H), these rates are an internal consistency check rather than an external validation; the held-out Firm A validation of Section IV-F.2 is the corresponding external check.
+
+### 2) Cross-Firm Comparison of Dual-Descriptor Convergence
+
+Among the 65,514 non-Firm-A signatures with per-signature best-match cosine $> 0.95$, 42.12% have $\text{dHash}_\text{indep} \leq 5$, compared to 88.32% of the 55,922 Firm A signatures meeting the same cosine condition---a $\sim 2.1\times$ difference that the structural-verification layer makes visible.
+The Firm A denominator (55,922) matches Table IX exactly: both Table IX and the cross-firm decomposition define Firm A membership via the CPA registry (`accountants.firm`), and the cross-firm analysis additionally requires a non-null independent-min dHash record, which all 55,922 Firm A cosine-eligible signatures have in the current database.
+This cross-firm gap is consistent with firm-wide non-hand-signing practice at Firm A versus partner-specific or per-engagement replication at other firms; it complements the partner-level ranking (Section IV-G.2) and intra-report consistency (Section IV-G.3) findings.
+Reproduction artifact for these counts is listed in Appendix B.
+
+## I. Ablation Study: Feature Backbone Comparison
+
+To validate the choice of ResNet-50 as the feature extraction backbone, we conducted an ablation study comparing three pre-trained architectures: ResNet-50 (2048-dim), VGG-16 (4096-dim), and EfficientNet-B0 (1280-dim).
+All models used ImageNet pre-trained weights without fine-tuning, with identical preprocessing and L2 normalization.
+Table XVIII presents the comparison.
+
+<!-- TABLE XVIII: Backbone Comparison
+| Metric | ResNet-50 | VGG-16 | EfficientNet-B0 |
+|--------|-----------|--------|-----------------|
+| Feature dim | 2048 | 4096 | 1280 |
+| Intra mean | 0.821 | 0.822 | 0.786 |
+| Inter mean | 0.758 | 0.767 | 0.699 |
+| Cohen's d | 0.669 | 0.564 | 0.707 |
+| KDE crossover | 0.837 | 0.850 | 0.792 |
+| Firm A mean (all-pairs) | 0.826 | 0.820 | 0.810 |
+| Firm A 1st pct (all-pairs) | 0.543 | 0.520 | 0.454 |
+
+Note: Firm A values in this table are computed over all intra-firm pairwise
+similarities (16.0M pairs) for cross-backbone comparability. These differ from
+the per-signature best-match statistic used in Section IV-D and visualized in
+Table XIII (whole-sample Firm A best-match mean $\approx 0.980$), which reflects
+the classification-relevant quantity: the similarity of each signature to its
+single closest match from the same CPA.
+-->
+
+EfficientNet-B0 achieves the highest Cohen's $d$ (0.707), indicating the greatest statistical separation between intra-class and inter-class distributions.
+However, it also exhibits the widest distributional spread (intra std $= 0.123$ vs. ResNet-50's $0.098$), resulting in lower per-sample classification confidence.
+VGG-16 performs worst on all key metrics despite having the highest feature dimensionality (4096), suggesting that additional dimensions do not contribute discriminative information for this task.
+
+ResNet-50 provides the best overall balance:
+(1) Cohen's $d$ of 0.669 is competitive with EfficientNet-B0's 0.707;
+(2) its tighter distributions yield more reliable individual classifications;
+(3) the highest Firm A all-pairs 1st percentile (0.543) indicates that known-replication signatures are least likely to produce low-similarity outlier pairs under this backbone; and
+(4) its 2048-dimensional features offer a practical compromise between discriminative capacity and computational/storage efficiency for processing 182K+ signatures.

paper/recalibrate_classification.py

@@ -0,0 +1,305 @@
+#!/usr/bin/env python3
+"""
+Recalibrate classification using Firm A as ground truth.
+Dual-method only: Cosine + dHash (drops SSIM and pixel-identical).
+
+Approach:
+1. Load per-signature best-match cosine + pHash from DB
+2. Use Firm A (勤業眾信聯合) as known-positive calibration set
+3. Analyze 2D distribution (cosine × pHash) for Firm A vs others
+4. Determine calibrated thresholds
+5. Reclassify all PDFs
+6. Output new Table VII
+"""
+
+import sqlite3
+import numpy as np
+from collections import defaultdict
+from pathlib import Path
+import json
+
+DB_PATH = '/Volumes/NV2/PDF-Processing/signature-analysis/signature_analysis.db'
+OUTPUT_DIR = Path('/Volumes/NV2/PDF-Processing/signature-analysis/recalibrated')
+OUTPUT_DIR.mkdir(parents=True, exist_ok=True)
+
+FIRM_A = '勤業眾信聯合'
+KDE_CROSSOVER = 0.837  # from intra/inter analysis
+
+
+def load_data():
+    """Load per-signature data with cosine and pHash."""
+    conn = sqlite3.connect(DB_PATH)
+    cur = conn.cursor()
+
+    cur.execute('''
+        SELECT s.signature_id, s.image_filename, s.assigned_accountant,
+               s.max_similarity_to_same_accountant,
+               s.phash_distance_to_closest,
+               a.firm
+        FROM signatures s
+        LEFT JOIN accountants a ON s.assigned_accountant = a.name
+        WHERE s.assigned_accountant IS NOT NULL
+        AND s.max_similarity_to_same_accountant IS NOT NULL
+    ''')
+    rows = cur.fetchall()
+    conn.close()
+
+    data = []
+    for r in rows:
+        data.append({
+            'sig_id': r[0],
+            'filename': r[1],
+            'accountant': r[2],
+            'cosine': r[3],
+            'phash': r[4],  # may be None
+            'firm': r[5],
+        })
+    print(f"Loaded {len(data):,} signatures")
+    return data
+
+
+def analyze_firm_a(data):
+    """Analyze Firm A's dual-method distribution to calibrate thresholds."""
+    firm_a = [d for d in data if d['firm'] == FIRM_A]
+    others = [d for d in data if d['firm'] != FIRM_A]
+
+    print(f"\n{'='*60}")
+    print(f"FIRM A CALIBRATION ANALYSIS")
+    print(f"{'='*60}")
+    print(f"Firm A signatures: {len(firm_a):,}")
+    print(f"Other signatures:  {len(others):,}")
+
+    # Firm A cosine distribution
+    fa_cosine = np.array([d['cosine'] for d in firm_a])
+    ot_cosine = np.array([d['cosine'] for d in others])
+
+    print(f"\n--- Cosine Similarity ---")
+    print(f"Firm A:  mean={fa_cosine.mean():.4f}, std={fa_cosine.std():.4f}, "
+          f"p1={np.percentile(fa_cosine,1):.4f}, p5={np.percentile(fa_cosine,5):.4f}")
+    print(f"Others:  mean={ot_cosine.mean():.4f}, std={ot_cosine.std():.4f}")
+
+    # Firm A pHash distribution (only where available)
+    fa_phash = [d['phash'] for d in firm_a if d['phash'] is not None]
+    ot_phash = [d['phash'] for d in others if d['phash'] is not None]
+
+    print(f"\n--- pHash (dHash) Distance ---")
+    print(f"Firm A with pHash: {len(fa_phash):,}")
+    print(f"Others with pHash: {len(ot_phash):,}")
+
+    if fa_phash:
+        fa_ph = np.array(fa_phash)
+        print(f"Firm A:  mean={fa_ph.mean():.2f}, median={np.median(fa_ph):.0f}, "
+              f"p95={np.percentile(fa_ph,95):.0f}")
+        print(f"  pHash=0:  {(fa_ph==0).sum():,} ({100*(fa_ph==0).mean():.1f}%)")
+        print(f"  pHash<=2: {(fa_ph<=2).sum():,} ({100*(fa_ph<=2).mean():.1f}%)")
+        print(f"  pHash<=5: {(fa_ph<=5).sum():,} ({100*(fa_ph<=5).mean():.1f}%)")
+        print(f"  pHash<=10:{(fa_ph<=10).sum():,} ({100*(fa_ph<=10).mean():.1f}%)")
+        print(f"  pHash<=15:{(fa_ph<=15).sum():,} ({100*(fa_ph<=15).mean():.1f}%)")
+        print(f"  pHash>15: {(fa_ph>15).sum():,} ({100*(fa_ph>15).mean():.1f}%)")
+
+    if ot_phash:
+        ot_ph = np.array(ot_phash)
+        print(f"\nOthers:  mean={ot_ph.mean():.2f}, median={np.median(ot_ph):.0f}")
+        print(f"  pHash=0:  {(ot_ph==0).sum():,} ({100*(ot_ph==0).mean():.1f}%)")
+        print(f"  pHash<=5: {(ot_ph<=5).sum():,} ({100*(ot_ph<=5).mean():.1f}%)")
+        print(f"  pHash<=10:{(ot_ph<=10).sum():,} ({100*(ot_ph<=10).mean():.1f}%)")
+        print(f"  pHash>15: {(ot_ph>15).sum():,} ({100*(ot_ph>15).mean():.1f}%)")
+
+    # 2D analysis: cosine × pHash for Firm A
+    print(f"\n--- 2D Analysis: Cosine × pHash (Firm A) ---")
+    fa_both = [(d['cosine'], d['phash']) for d in firm_a if d['phash'] is not None]
+    if fa_both:
+        cosines, phashes = zip(*fa_both)
+        cosines = np.array(cosines)
+        phashes = np.array(phashes)
+
+        # Cross-tabulate
+        for cos_thresh in [0.95, 0.90, KDE_CROSSOVER]:
+            for ph_thresh in [5, 10, 15]:
+                match = ((cosines > cos_thresh) & (phashes <= ph_thresh)).sum()
+                total = len(cosines)
+                print(f"  Cosine>{cos_thresh:.3f} AND pHash<={ph_thresh}: "
+                      f"{match:,}/{total:,} ({100*match/total:.1f}%)")
+
+    # Same for others (high cosine subset)
+    print(f"\n--- 2D Analysis: Cosine × pHash (Others, cosine > 0.95 only) ---")
+    ot_both_high = [(d['cosine'], d['phash']) for d in others
+                    if d['phash'] is not None and d['cosine'] > 0.95]
+    if ot_both_high:
+        cosines_o, phashes_o = zip(*ot_both_high)
+        phashes_o = np.array(phashes_o)
+        print(f"  N (others with cosine>0.95 and pHash): {len(ot_both_high):,}")
+        for ph_thresh in [5, 10, 15]:
+            match = (phashes_o <= ph_thresh).sum()
+            print(f"  pHash<={ph_thresh}: {match:,}/{len(phashes_o):,} ({100*match/len(phashes_o):.1f}%)")
+
+    return fa_phash, ot_phash
+
+
+def reclassify_pdfs(data):
+    """
+    Reclassify all PDFs using calibrated dual-method thresholds.
+
+    New classification (cosine + dHash only):
+    1. High-confidence replication: cosine > 0.95 AND pHash ≤ 5
+    2. Moderate-confidence replication: cosine > 0.95 AND pHash 6-15
+    3. High style consistency: cosine > 0.95 AND (pHash > 15 OR pHash unavailable)
+    4. Uncertain: cosine between KDE_CROSSOVER and 0.95
+    5. Likely genuine: cosine < KDE_CROSSOVER
+    """
+    # Group signatures by PDF (derive PDF from filename pattern)
+    # Filename format: {company}_{year}_{type}_sig{N}.png or similar
+    # We need to group by source PDF
+    conn = sqlite3.connect(DB_PATH)
+    cur = conn.cursor()
+
+    # Get PDF-level data
+    cur.execute('''
+        SELECT s.signature_id, s.image_filename, s.assigned_accountant,
+               s.max_similarity_to_same_accountant,
+               s.phash_distance_to_closest,
+               a.firm
+        FROM signatures s
+        LEFT JOIN accountants a ON s.assigned_accountant = a.name
+        WHERE s.assigned_accountant IS NOT NULL
+        AND s.max_similarity_to_same_accountant IS NOT NULL
+    ''')
+    rows = cur.fetchall()
+
+    # Group by PDF: extract PDF identifier from filename
+    # Signature filenames are like: {pdfname}_page{N}_sig{M}.png
+    pdf_sigs = defaultdict(list)
+    for r in rows:
+        sig_id, filename, accountant, cosine, phash, firm = r
+        # Extract PDF name (everything before _page or _sig)
+        parts = filename.rsplit('_sig', 1)
+        pdf_key = parts[0] if len(parts) > 1 else filename.rsplit('.', 1)[0]
+        # Further strip _page part
+        page_parts = pdf_key.rsplit('_page', 1)
+        pdf_key = page_parts[0] if len(page_parts) > 1 else pdf_key
+
+        pdf_sigs[pdf_key].append({
+            'cosine': cosine,
+            'phash': phash,
+            'firm': firm,
+            'accountant': accountant,
+        })
+
+    conn.close()
+
+    print(f"\n{'='*60}")
+    print(f"RECLASSIFICATION (Dual-Method: Cosine + dHash)")
+    print(f"{'='*60}")
+    print(f"Total PDFs: {len(pdf_sigs):,}")
+
+    # Classify each PDF based on its signatures
+    verdicts = defaultdict(int)
+    firm_a_verdicts = defaultdict(int)
+    details = []
+
+    for pdf_key, sigs in pdf_sigs.items():
+        # Use the signature with the highest cosine as the representative
+        best_sig = max(sigs, key=lambda s: s['cosine'])
+        cosine = best_sig['cosine']
+        phash = best_sig['phash']
+        is_firm_a = best_sig['firm'] == FIRM_A
+
+        # Also check if ANY signature in this PDF has low pHash
+        min_phash = None
+        for s in sigs:
+            if s['phash'] is not None:
+                if min_phash is None or s['phash'] < min_phash:
+                    min_phash = s['phash']
+
+        # Classification
+        if cosine > 0.95 and min_phash is not None and min_phash <= 5:
+            verdict = 'high_confidence_replication'
+        elif cosine > 0.95 and min_phash is not None and min_phash <= 15:
+            verdict = 'moderate_confidence_replication'
+        elif cosine > 0.95:
+            verdict = 'high_style_consistency'
+        elif cosine > KDE_CROSSOVER:
+            verdict = 'uncertain'
+        else:
+            verdict = 'likely_genuine'
+
+        verdicts[verdict] += 1
+        if is_firm_a:
+            firm_a_verdicts[verdict] += 1
+
+        details.append({
+            'pdf': pdf_key,
+            'cosine': cosine,
+            'min_phash': min_phash,
+            'verdict': verdict,
+            'is_firm_a': is_firm_a,
+        })
+
+    total = sum(verdicts.values())
+    firm_a_total = sum(firm_a_verdicts.values())
+
+    # Print results
+    print(f"\n--- New Classification Results ---")
+    print(f"{'Verdict':<35} {'Count':>8} {'%':>7}  |  {'Firm A':>8} {'%':>7}")
+    print("-" * 75)
+
+    order = ['high_confidence_replication', 'moderate_confidence_replication',
+             'high_style_consistency', 'uncertain', 'likely_genuine']
+    labels = {
+        'high_confidence_replication': 'High-conf. replication',
+        'moderate_confidence_replication': 'Moderate-conf. replication',
+        'high_style_consistency': 'High style consistency',
+        'uncertain': 'Uncertain',
+        'likely_genuine': 'Likely genuine',
+    }
+
+    for v in order:
+        n = verdicts.get(v, 0)
+        fa = firm_a_verdicts.get(v, 0)
+        pct = 100 * n / total if total > 0 else 0
+        fa_pct = 100 * fa / firm_a_total if firm_a_total > 0 else 0
+        print(f"  {labels.get(v, v):<33} {n:>8,} {pct:>6.1f}%  |  {fa:>8,} {fa_pct:>6.1f}%")
+
+    print("-" * 75)
+    print(f"  {'Total':<33} {total:>8,} {'100.0%':>7}  |  {firm_a_total:>8,} {'100.0%':>7}")
+
+    # Precision/Recall using Firm A as positive set
+    print(f"\n--- Firm A Capture Rate (Calibration Validation) ---")
+    fa_replication = firm_a_verdicts.get('high_confidence_replication', 0) + \
+                     firm_a_verdicts.get('moderate_confidence_replication', 0)
+    print(f"  Firm A classified as replication (high+moderate): {fa_replication:,}/{firm_a_total:,} "
+          f"({100*fa_replication/firm_a_total:.1f}%)")
+
+    fa_high = firm_a_verdicts.get('high_confidence_replication', 0)
+    print(f"  Firm A classified as high-confidence: {fa_high:,}/{firm_a_total:,} "
+          f"({100*fa_high/firm_a_total:.1f}%)")
+
+    # Save results
+    results = {
+        'classification': {v: verdicts.get(v, 0) for v in order},
+        'firm_a': {v: firm_a_verdicts.get(v, 0) for v in order},
+        'total_pdfs': total,
+        'firm_a_pdfs': firm_a_total,
+        'thresholds': {
+            'cosine_high': 0.95,
+            'kde_crossover': KDE_CROSSOVER,
+            'phash_high_confidence': 5,
+            'phash_moderate_confidence': 15,
+        },
+    }
+
+    with open(OUTPUT_DIR / 'recalibrated_results.json', 'w') as f:
+        json.dump(results, f, indent=2)
+
+    print(f"\nResults saved: {OUTPUT_DIR / 'recalibrated_results.json'}")
+    return results
+
+
+def main():
+    data = load_data()
+    analyze_firm_a(data)
+    results = reclassify_pdfs(data)
+
+
+if __name__ == "__main__":
+    main()

paper/reference_verification_v3.md

@@ -0,0 +1,226 @@
+# Reference Verification — Paper A v3 (41 refs)
+
+Date: 2026-04-27 (initial audit); v3.18 reference list updated to incorporate every fix recorded below.
+
+Method: WebSearch + WebFetch verification of each citation against authoritative sources (publisher pages, DOIs, arXiv, IEEE Xplore, Project Euclid, etc.).
+
+## Summary (audit history)
+- Verified correct on first audit: 35/41
+- Minor discrepancies (typos, page numbers, year on early-access vs. issue): 5/41 — all fixed in v3.18
+- MAJOR PROBLEMS (wrong author): 1/41 — `[5]` Hadjadj et al. → Kao and Wen, fixed in v3.18
+
+The current `paper_a_references_v3.md` reflects every correction listed below. The detailed findings are retained as an audit trail; the live reference list no longer carries any of the recorded errors.
+
+The single major problem at the time of the audit was **[5]**, where the paper at the cited venue/article number is real, but the cited authors ("Hadjadj et al.") were wrong — the actual authors are Kao and Wen. None of the statistical-method refs [37]–[41] flagged by the partner are fabricated; all five are bibliographically correct.
+
+## Detailed findings
+
+### [1] Taiwan CPA Act + FSC Attestation Regulations
+**Status:** ✅ VERIFIED
+**Notes:** The URL https://law.moj.gov.tw/ENG/LawClass/LawAll.aspx?pcode=G0400067 resolves to the official Republic of China (Taiwan) "Certified Public Accountant Act" page (Laws & Regulations Database, Financial Supervisory Commission).
+**Evidence:** WebFetch returned the CPA Act page with 8 chapters; latest amendment 2018-01-31. Article 4 and the FSC Attestation Regulations (查核簽證核准準則) are part of the official regulatory framework.
+
+### [2] S.-H. Yen, Y.-S. Chang, H.-L. Chen, "Does the signature of a CPA matter? Evidence from Taiwan," Res. Account. Regul., 25(2), 230–235, 2013.
+**Status:** ✅ VERIFIED
+**Evidence:** ScienceDirect listing (https://www.sciencedirect.com/science/article/abs/pii/S1052045713000234) confirms authors Sin-Hui Yen, Yu-Shan Chang, Hui-Ling Chen; Research in Accounting Regulation 25(2):230–235, 2013.
+
+### [3] J. Bromley et al., "Signature verification using a Siamese time delay neural network," Proc. NeurIPS, 1993.
+**Status:** ✅ VERIFIED
+**Notes:** Authors are Bromley, Bentz, Bottou, Guyon, LeCun, Moore, Säckinger, Shah; pages 737–744 of NIPS 6 (1993). Citation as "Bromley et al." in NeurIPS 1993 is correct.
+**Evidence:** https://proceedings.neurips.cc/paper/1993/hash/288cc0ff022877bd3df94bc9360b9c5d-Abstract.html
+
+### [4] S. Dey et al., "SigNet: Convolutional Siamese network for writer independent offline signature verification," arXiv:1707.02131, 2017.
+**Status:** ✅ VERIFIED
+**Evidence:** arXiv 1707.02131 resolves to exactly this title; authors Sounak Dey, Anjan Dutta, J.I. Toledo, Suman K. Ghosh, Josep Llados, Umapada Pal; submitted July 2017.
+
+### [5] I. Hadjadj et al., "An offline signature verification method based on a single known sample and an explainable deep learning approach," Appl. Sci., 10(11), 3716, 2020.
+**Status:** ❌ MAJOR PROBLEM (wrong authors)
+**Notes:** The paper at Applied Sciences vol. 10, issue 11, article 3716 (DOI 10.3390/app10113716) is real, but the actual authors are **Hsin-Hsiung Kao and Che-Yen Wen**, NOT "Hadjadj et al." The full title in the journal is also "An Offline Signature Verification **and Forgery Detection** Method Based on a Single Known Sample and an Explainable Deep Learning Approach" — the v3 reference omits "and Forgery Detection."
+**Evidence:** MDPI listing (https://www.mdpi.com/2076-3417/10/11/3716) and Semantic Scholar both list authors as Kao and Wen, published 27 May 2020. There is a separate researcher I. Hadjadj who works on signature verification with co-authors Gattal/Djeddi/Ayad/Siddiqi/Abass on textural-descriptor methods, but that work is published elsewhere — not in Appl. Sci. 10(11):3716.
+**Recommendation:** Replace authors with "H.-H. Kao and C.-Y. Wen" and use correct title.
+
+### [6] H. Li et al., "TransOSV: Offline signature verification with transformers," Pattern Recognit., 145, 109882, 2024.
+**Status:** ✅ VERIFIED
+**Notes:** Authors Huan Li, Ping Wei, Zeyu Ma, Changkai Li, Nanning Zheng. PR vol. 145, art. 109882, January 2024.
+**Evidence:** ScienceDirect S0031320323005800.
+
+### [7] S. Tehsin et al., "Enhancing signature verification using triplet Siamese similarity networks in digital documents," Mathematics, 12(17), 2757, 2024.
+**Status:** ✅ VERIFIED
+**Notes:** Authors Sara Tehsin, Ali Hassan, Farhan Riaz, Inzamam Mashood Nasir, Norma Latif Fitriyani, Muhammad Syafrudin. DOI 10.3390/math12172757.
+**Evidence:** https://www.mdpi.com/2227-7390/12/17/2757
+
+### [8] P. Brimoh and C. C. Olisah, "Consensus-threshold criterion for offline signature verification using CNN learned representations," arXiv:2401.03085, 2024.
+**Status:** ✅ VERIFIED
+**Notes:** Full title is "...using **Convolutional Neural Network** Learned Representations" (the v3 ref says "CNN" — acceptable abbreviation).
+**Evidence:** https://arxiv.org/abs/2401.03085 — authors Paul Brimoh and Chollette C. Olisah.
+
+### [9] N. Woodruff et al., "Fully-automatic pipeline for document signature analysis to detect money laundering activities," arXiv:2107.14091, 2021.
+**Status:** ✅ VERIFIED
+**Evidence:** arXiv 2107.14091 — authors Nikhil Woodruff, Amir Enshaei, Bashar Awwad Shiekh Hasan; submitted 29 July 2021.
+
+### [10] S. Abramova and R. Böhme, "Detecting copy-move forgeries in scanned text documents," Proc. Electronic Imaging, 2016.
+**Status:** ✅ VERIFIED
+**Notes:** Published in IS&T Electronic Imaging: Media Watermarking, Security, and Forensics 2016, pp. 1–10 (article 4 in session 8). Authors Svetlana Abramova and Rainer Böhme.
+**Evidence:** https://library.imaging.org/ei/articles/28/8/art00004 ; Semantic Scholar entry confirms title and authors.
+
+### [11] Y. Li et al., "Copy-move forgery detection in digital image forensics: A survey," Multimedia Tools Appl., 2024.
+**Status:** ✅ VERIFIED
+**Notes:** Published in Multimedia Tools and Applications, 2024, DOI 10.1007/s11042-024-18399-2.
+**Evidence:** https://link.springer.com/article/10.1007/s11042-024-18399-2
+
+### [12] Y. Jakhar and M. D. Borah, "Effective near-duplicate image detection using perceptual hashing and deep learning," Inf. Process. Manage., 104086, 2025.
+**Status:** ✅ VERIFIED
+**Notes:** Authors Yash Jakhar and Malaya Dutta Borah; Information Processing & Management 62(4):104086, July 2025; DOI 10.1016/j.ipm.2025.104086.
+**Evidence:** https://www.sciencedirect.com/science/article/abs/pii/S0306457325000287
+
+### [13] E. Pizzi et al., "A self-supervised descriptor for image copy detection," Proc. CVPR, 2022.
+**Status:** ✅ VERIFIED
+**Notes:** Authors Ed Pizzi, Sreya Dutta Roy, Sugosh Nagavara Ravindra, Priya Goyal, Matthijs Douze; CVPR 2022.
+**Evidence:** https://openaccess.thecvf.com/content/CVPR2022/html/Pizzi_A_Self-Supervised_Descriptor_for_Image_Copy_Detection_CVPR_2022_paper.html ; arXiv 2202.10261.
+
+### [14] L. G. Hafemann, R. Sabourin, L. S. Oliveira, "Learning features for offline handwritten signature verification using deep convolutional neural networks," Pattern Recognit., 70, 163–176, 2017.
+**Status:** ✅ VERIFIED
+**Evidence:** ScienceDirect S0031320317302017; PR 70:163–176, 2017; arXiv 1705.05787.
+
+### [15] E. N. Zois, D. Tsourounis, D. Kalivas, "Similarity distance learning on SPD manifold for writer independent offline signature verification," IEEE Trans. Inf. Forensics Security, 19, 1342–1356, 2024.
+**Status:** ✅ VERIFIED
+**Evidence:** IEEE Xplore document 10319735; TIFS vol. 19, pp. 1342–1356, 2024.
+
+### [16] L. G. Hafemann, R. Sabourin, L. S. Oliveira, "Meta-learning for fast classifier adaptation to new users of signature verification systems," IEEE Trans. Inf. Forensics Security, 15, 1735–1745, 2019.
+**Status:** ⚠️ MINOR
+**Notes:** Volume and pages (15, 1735–1745) are correct. Year is technically 2020 for the journal issue (DOI 10.1109/TIFS.2019.2949425; early-access October 2019, issue volume 15 published 2020). The "2019" in the v3 reference reflects the online/early-access date but is inconsistent with TIFS's volume-15 2020 issue convention.
+**Evidence:** arXiv 1910.08060; ÉTS espace listing confirms TIFS 15:1735–1745, 2020.
+**Recommendation:** Change year to 2020 for IEEE Access editorial consistency, or accept as-is (both forms appear in the literature).
+
+### [17] H. Farid, "Image forgery detection," IEEE Signal Process. Mag., 26(2), 16–25, 2009.
+**Status:** ✅ VERIFIED
+**Notes:** The paper's actual title (in some indexes) is given as "A Survey of Image Forgery Detection," but the IEEE Xplore canonical title is "Image Forgery Detection." Vol. 26, no. 2, pp. 16–25, March 2009.
+**Evidence:** https://pages.cs.wisc.edu/~dyer/cs534/papers/farid-sigproc09.pdf (PDF header confirms IEEE SPM, March 2009, p. 16).
+
+### [18] F. Z. Mehrjardi, A. M. Latif, M. S. Zarchi, R. Sheikhpour, "A survey on deep learning-based image forgery detection," Pattern Recognit., 144, 109778, 2023.
+**Status:** ✅ VERIFIED
+**Evidence:** ScienceDirect S0031320323004764; PR vol. 144 art. 109778, December 2023.
+
+### [19] J. Luo et al., "A survey of perceptual hashing for multimedia," ACM Trans. Multimedia Comput. Commun. Appl., 21(7), 2025.
+**Status:** ✅ VERIFIED
+**Notes:** Published April 2025, DOI 10.1145/3727880.
+**Evidence:** https://dl.acm.org/doi/10.1145/3727880
+
+### [20] D. Engin et al., "Offline signature verification on real-world documents," Proc. CVPRW, 2020.
+**Status:** ✅ VERIFIED
+**Notes:** Authors Deniz Engin, Alperen Kantarci, Secil Arslan, Hazim Kemel Ekenel; CVPR 2020 Biometrics Workshop.
+**Evidence:** https://openaccess.thecvf.com/content_CVPRW_2020/html/w48/Engin_Offline_Signature_Verification_on_Real-World_Documents_CVPRW_2020_paper.html
+
+### [21] D. Tsourounis et al., "From text to signatures: Knowledge transfer for efficient deep feature learning in offline signature verification," Expert Syst. Appl., 2022.
+**Status:** ⚠️ MINOR
+**Notes:** Citation lacks volume/article number. Full record: Expert Systems with Applications, vol. 189, art. 116136, 2022. Authors Tsourounis, Theodorakopoulos, Zois, Economou.
+**Evidence:** ScienceDirect S0957417421014652.
+**Recommendation:** Add ", vol. 189, art. 116136" for IEEE-style completeness.
+
+### [22] B. Chamakh and O. Bounouh, "A unified ResNet18-based approach for offline signature classification and verification," Procedia Comput. Sci., 270, 2025.
+**Status:** ⚠️ MINOR
+**Notes:** Full title in publisher record is "A Unified ResNet18-Based Approach for Offline Signature Classification and Verification **Across Multilingual Datasets**." Procedia CS vol. 270, pp. 4024–4033, 2025 (KES 2025).
+**Evidence:** ScienceDirect S1877050925032004.
+**Recommendation:** Either keep short title or add "Across Multilingual Datasets" for accuracy; add page range.
+
+### [23] A. Babenko, A. Slesarev, A. Chigorin, V. Lempitsky, "Neural codes for image retrieval," Proc. ECCV, 2014, pp. 584–599.
+**Status:** ✅ VERIFIED
+**Evidence:** Springer LNCS 8689, ECCV 2014 Part I, pp. 584–599; arXiv 1404.1777.
+
+### [24] S. Bai et al., "Qwen2.5-VL technical report," arXiv:2502.13923, 2025.
+**Status:** ✅ VERIFIED
+**Evidence:** arXiv 2502.13923; lead author Shuai Bai, Qwen Team Alibaba; submitted 19 Feb 2025. URL https://arxiv.org/abs/2502.13923 resolves correctly.
+
+### [25] Ultralytics, "YOLOv11 documentation," 2024.
+**Status:** ⚠️ MINOR
+**Notes:** Ultralytics names the model **"YOLO11"** (no "v"), released 10 Sept 2024. The cited URL https://docs.ultralytics.com/ is the docs root and resolves; the model-specific page is https://docs.ultralytics.com/models/yolo11/.
+**Recommendation:** Rename to "YOLO11" to match official Ultralytics terminology, or note that "YOLOv11" is informal.
+
+### [26] K. He, X. Zhang, S. Ren, J. Sun, "Deep residual learning for image recognition," Proc. CVPR, 2016.
+**Status:** ✅ VERIFIED
+**Evidence:** CVF Open Access; CVPR 2016 pp. 770–778.
+
+### [27] N. Krawetz, "Kind of like that," The Hacker Factor Blog, 2013.
+**Status:** ⚠️ MINOR
+**Notes:** Blog post is real (the canonical dHash explanation). The cited URL https://www.hackerfactor.com/blog/index.php?/archives/529-Kind-of-Like-That.html is the historical permalink; the active URL form returned by Google is https://www.hackerfactor.com/blog/?/archives/529-Kind-of-Like-That.html. Both 403'd in our WebFetch test (likely User-Agent block on the blog), but the post is widely cited and references confirm it exists. Year is 2013 per blog archive.
+**Recommendation:** Verify the URL still resolves in a browser; both index.php and bare forms are accepted by the blog historically.
+
+### [28] B. W. Silverman, Density Estimation for Statistics and Data Analysis. London: Chapman & Hall, 1986.
+**Status:** ✅ VERIFIED
+**Evidence:** Routledge/Taylor&Francis catalog; ISBN 0412246201; Chapman & Hall, London, 1986.
+
+### [29] J. Cohen, Statistical Power Analysis for the Behavioral Sciences, 2nd ed. Hillsdale, NJ: Lawrence Erlbaum, 1988.
+**Status:** ✅ VERIFIED
+**Evidence:** Routledge listing ISBN 9780805802832; Lawrence Erlbaum Associates, 2nd ed., 1988.
+
+### [30] Z. Wang, A. C. Bovik, H. R. Sheikh, E. P. Simoncelli, "Image quality assessment: From error visibility to structural similarity," IEEE Trans. Image Process., 13(4), 600–612, 2004.
+**Status:** ✅ VERIFIED
+**Evidence:** IEEE Xplore document 1284395; vol. 13, no. 4, pp. 600–612, April 2004.
+
+### [31] J. V. Carcello and C. Li, "Costs and benefits of requiring an engagement partner signature: Recent experience in the United Kingdom," The Accounting Review, 88(5), 1511–1546, 2013.
+**Status:** ✅ VERIFIED
+**Evidence:** SSRN abstract 2225427; The Accounting Review 88(5):1511–1546, September 2013.
+
+### [32] A. D. Blay, M. Notbohm, C. Schelleman, A. Valencia, "Audit quality effects of an individual audit engagement partner signature mandate," Int. J. Auditing, 18(3), 172–192, 2014.
+**Status:** ✅ VERIFIED
+**Evidence:** Wiley DOI 10.1111/ijau.12022; IJA 18(3):172–192, 2014.
+
+### [33] W. Chi, H. Huang, Y. Liao, H. Xie, "Mandatory audit partner rotation, audit quality, and market perception: Evidence from Taiwan," Contemp. Account. Res., 26(2), 359–391, 2009.
+**Status:** ✅ VERIFIED
+**Evidence:** Wiley DOI 10.1506/car.26.2.2; CAR 26(2):359–391, 2009.
+
+### [34] J. Redmon, S. Divvala, R. Girshick, A. Farhadi, "You only look once: Unified, real-time object detection," Proc. CVPR, 2016, pp. 779–788.
+**Status:** ✅ VERIFIED
+**Evidence:** CVF Open Access; CVPR 2016 pp. 779–788.
+
+### [35] J. Zhang, J. Huang, S. Jin, S. Lu, "Vision-language models for vision tasks: A survey," IEEE Trans. Pattern Anal. Mach. Intell., 46(8), 5625–5644, 2024.
+**Status:** ✅ VERIFIED
+**Evidence:** IEEE Xplore document 10445007; DOI 10.1109/TPAMI.2024.3369699; TPAMI 46(8):5625–5644, August 2024.
+
+### [36] H. B. Mann and D. R. Whitney, "On a test of whether one of two random variables is stochastically larger than the other," Ann. Math. Statist., 18(1), 50–60, 1947.
+**Status:** ✅ VERIFIED
+**Evidence:** Project Euclid DOI 10.1214/aoms/1177730491; AMS 18(1):50–60, March 1947.
+
+### [37] J. A. Hartigan and P. M. Hartigan, "The dip test of unimodality," Ann. Statist., 13(1), 70–84, 1985.
+**Status:** ✅ VERIFIED
+**Notes:** **Partner-flagged ref — confirmed real and bibliographically correct.** Annals of Statistics 13(1):70–84, March 1985.
+**Evidence:** Project Euclid https://projecteuclid.org/journals/annals-of-statistics/volume-13/issue-1/The-Dip-Test-of-Unimodality/10.1214/aos/1176346577.full
+
+### [38] D. Burgstahler and I. Dichev, "Earnings management to avoid earnings decreases and losses," J. Account. Econ., 24(1), 99–126, 1997.
+**Status:** ✅ VERIFIED
+**Notes:** **Partner-flagged ref — confirmed real and bibliographically correct.** Seminal earnings-management paper.
+**Evidence:** ScienceDirect S0165410197000177; JAE 24(1):99–126, December 1997.
+
+### [39] J. McCrary, "Manipulation of the running variable in the regression discontinuity design: A density test," J. Econometrics, 142(2), 698–714, 2008.
+**Status:** ✅ VERIFIED
+**Notes:** **Partner-flagged ref — confirmed real and bibliographically correct.** Foundational RDD density-manipulation test (>1750 citations).
+**Evidence:** ScienceDirect S0304407607001133; JoE 142(2):698–714, February 2008.
+
+### [40] A. P. Dempster, N. M. Laird, D. B. Rubin, "Maximum likelihood from incomplete data via the EM algorithm," J. R. Statist. Soc. B, 39(1), 1–38, 1977.
+**Status:** ✅ VERIFIED
+**Notes:** **Partner-flagged ref — confirmed real and bibliographically correct.** Canonical EM algorithm paper, presented to RSS Research Section 8 Dec 1976.
+**Evidence:** Wiley DOI 10.1111/j.2517-6161.1977.tb01600.x; JRSS B 39(1):1–38, 1977.
+
+### [41] H. White, "Maximum likelihood estimation of misspecified models," Econometrica, 50(1), 1–25, 1982.
+**Status:** ⚠️ MINOR
+**Notes:** **Partner-flagged ref — confirmed real, but page numbers slightly off.** Some sources list pp. 1–25, others pp. 1–26. The Econometric Society's official record (and JSTOR 1912526) lists pages 1–25; Emerald and a few other indices list 1–26 (likely including a typo-correction footnote). The v3 reference's "1–25" matches the Econometric Society canonical listing.
+**Evidence:** https://www.econometricsociety.org/publications/econometrica/1982/01/01/maximum-likelihood-estimation-misspecified-models ; JSTOR 1912526. Authors and venue exact.
+**Recommendation:** No fix needed; "1–25" is the canonical page range.
+
+## Recommendations
+
+**Critical fixes (must fix before submission):**
+
+1. **[5]** Replace authors and title:
+   - Current: `I. Hadjadj et al., "An offline signature verification method based on a single known sample and an explainable deep learning approach," Appl. Sci., vol. 10, no. 11, p. 3716, 2020.`
+   - Corrected: `H.-H. Kao and C.-Y. Wen, "An offline signature verification and forgery detection method based on a single known sample and an explainable deep learning approach," Appl. Sci., vol. 10, no. 11, p. 3716, 2020.`
+
+**Recommended polish (style/completeness):**
+
+2. **[16]** Year is 2020 in TIFS volume 15; consider changing 2019 → 2020 (or leave as 2019 if matching the early-access date is preferred — both are defensible).
+3. **[21]** Add volume and article number: `Expert Syst. Appl., vol. 189, art. 116136, 2022.`
+4. **[22]** Add page range: `Procedia Comput. Sci., vol. 270, pp. 4024–4033, 2025.` Optionally restore full subtitle "Across Multilingual Datasets."
+5. **[25]** Use Ultralytics' official name "YOLO11" (no "v") if matching their branding; current "YOLOv11" is widely used colloquially but not the canonical name.
+6. **[27]** Verify URL renders in a browser; both `blog/index.php?/archives/...` and `blog/?/archives/...` forms have historically resolved on hackerfactor.com.
+
+**No fix needed:** All five partner-flagged statistical-method references [37]–[41] are real, correctly attributed, and bibliographically accurate. The partner's suspicion that they might be AI hallucinations is unfounded — Hartigan & Hartigan (1985), Burgstahler & Dichev (1997), McCrary (2008), Dempster-Laird-Rubin (1977), and White (1982) are all foundational, heavily-cited works in their respective fields.

paper/renumber_citations.py

@@ -0,0 +1,195 @@
+#!/usr/bin/env python3
+"""
+Renumber all in-text citations to sequential order by first appearance.
+Also rewrites references.md with the final numbering.
+"""
+import re
+from pathlib import Path
+
+PAPER_DIR = Path("/Volumes/NV2/pdf_recognize/paper")
+
+# === FINAL NUMBERING (by order of first appearance in paper) ===
+# Format: new_number: (short_key, full_citation)
+FINAL_REFS = {
+    1:  ("cpa_act", 'Taiwan Certified Public Accountant Act (會計師法), Art. 4; FSC Attestation Regulations (查核簽證核准準則), Art. 6. Available: https://law.moj.gov.tw/ENG/LawClass/LawAll.aspx?pcode=G0400067'),
+    2:  ("yen2013", 'S.-H. Yen, Y.-S. Chang, and H.-L. Chen, "Does the signature of a CPA matter? Evidence from Taiwan," *Res. Account. Regul.*, vol. 25, no. 2, pp. 230–235, 2013.'),
+    3:  ("bromley1993", 'J. Bromley et al., "Signature verification using a Siamese time delay neural network," in *Proc. NeurIPS*, 1993.'),
+    4:  ("dey2017", 'S. Dey et al., "SigNet: Convolutional Siamese network for writer independent offline signature verification," arXiv:1707.02131, 2017.'),
+    5:  ("hadjadj2020", 'I. Hadjadj et al., "An offline signature verification method based on a single known sample and an explainable deep learning approach," *Appl. Sci.*, vol. 10, no. 11, p. 3716, 2020.'),
+    6:  ("li2024", 'H. Li et al., "TransOSV: Offline signature verification with transformers," *Pattern Recognit.*, vol. 145, p. 109882, 2024.'),
+    7:  ("tehsin2024", 'S. Tehsin et al., "Enhancing signature verification using triplet Siamese similarity networks in digital documents," *Mathematics*, vol. 12, no. 17, p. 2757, 2024.'),
+    8:  ("brimoh2024", 'P. Brimoh and C. C. Olisah, "Consensus-threshold criterion for offline signature verification using CNN learned representations," arXiv:2401.03085, 2024.'),
+    9:  ("woodruff2021", 'N. Woodruff et al., "Fully-automatic pipeline for document signature analysis to detect money laundering activities," arXiv:2107.14091, 2021.'),
+    10: ("abramova2016", 'S. Abramova and R. Bohme, "Detecting copy-move forgeries in scanned text documents," in *Proc. Electronic Imaging*, 2016.'),
+    11: ("cmfd_survey", 'Y. Li et al., "Copy-move forgery detection in digital image forensics: A survey," *Multimedia Tools Appl.*, 2024.'),
+    12: ("jakhar2025", 'Y. Jakhar and M. D. Borah, "Effective near-duplicate image detection using perceptual hashing and deep learning," *Inf. Process. Manage.*, p. 104086, 2025.'),
+    13: ("pizzi2022", 'E. Pizzi et al., "A self-supervised descriptor for image copy detection," in *Proc. CVPR*, 2022.'),
+    14: ("hafemann2017", 'L. G. Hafemann, R. Sabourin, and L. S. Oliveira, "Learning features for offline handwritten signature verification using deep convolutional neural networks," *Pattern Recognit.*, vol. 70, pp. 163–176, 2017.'),
+    15: ("zois2024", 'E. N. Zois, D. Tsourounis, and D. Kalivas, "Similarity distance learning on SPD manifold for writer independent offline signature verification," *IEEE Trans. Inf. Forensics Security*, vol. 19, pp. 1342–1356, 2024.'),
+    16: ("hafemann2019", 'L. G. Hafemann, R. Sabourin, and L. S. Oliveira, "Meta-learning for fast classifier adaptation to new users of signature verification systems," *IEEE Trans. Inf. Forensics Security*, vol. 15, pp. 1735–1745, 2019.'),
+    17: ("farid2009", 'H. Farid, "Image forgery detection," *IEEE Signal Process. Mag.*, vol. 26, no. 2, pp. 16–25, 2009.'),
+    18: ("mehrjardi2023", 'F. Z. Mehrjardi, A. M. Latif, M. S. Zarchi, and R. Sheikhpour, "A survey on deep learning-based image forgery detection," *Pattern Recognit.*, vol. 144, art. no. 109778, 2023.'),
+    19: ("phash_survey", 'J. Luo et al., "A survey of perceptual hashing for multimedia," *ACM Trans. Multimedia Comput. Commun. Appl.*, vol. 21, no. 7, 2025.'),
+    20: ("engin2020", 'D. Engin et al., "Offline signature verification on real-world documents," in *Proc. CVPRW*, 2020.'),
+    21: ("tsourounis2022", 'D. Tsourounis et al., "From text to signatures: Knowledge transfer for efficient deep feature learning in offline signature verification," *Expert Syst. Appl.*, 2022.'),
+    22: ("chamakh2025", 'B. Chamakh and O. Bounouh, "A unified ResNet18-based approach for offline signature classification and verification," *Procedia Comput. Sci.*, vol. 270, 2025.'),
+    23: ("babenko2014", 'A. Babenko, A. Slesarev, A. Chigorin, and V. Lempitsky, "Neural codes for image retrieval," in *Proc. ECCV*, 2014, pp. 584–599.'),
+    24: ("qwen2025", 'Qwen2.5-VL Technical Report, Alibaba Group, 2025.'),
+    25: ("yolov11", 'Ultralytics, "YOLOv11 documentation," 2024. [Online]. Available: https://docs.ultralytics.com/'),
+    26: ("he2016", 'K. He, X. Zhang, S. Ren, and J. Sun, "Deep residual learning for image recognition," in *Proc. CVPR*, 2016.'),
+    27: ("krawetz2013", 'N. Krawetz, "Kind of like that," The Hacker Factor Blog, 2013. [Online]. Available: https://www.hackerfactor.com/blog/index.php?/archives/529-Kind-of-Like-That.html'),
+    28: ("silverman1986", 'B. W. Silverman, *Density Estimation for Statistics and Data Analysis*. London: Chapman & Hall, 1986.'),
+    29: ("cohen1988", 'J. Cohen, *Statistical Power Analysis for the Behavioral Sciences*, 2nd ed. Hillsdale, NJ: Lawrence Erlbaum, 1988.'),
+    30: ("wang2004", 'Z. Wang, A. C. Bovik, H. R. Sheikh, and E. P. Simoncelli, "Image quality assessment: From error visibility to structural similarity," *IEEE Trans. Image Process.*, vol. 13, no. 4, pp. 600–612, 2004.'),
+    31: ("carcello2013", 'J. V. Carcello and C. Li, "Costs and benefits of requiring an engagement partner signature: Recent experience in the United Kingdom," *The Accounting Review*, vol. 88, no. 5, pp. 1511–1546, 2013.'),
+    32: ("blay2014", 'A. D. Blay, M. Notbohm, C. Schelleman, and A. Valencia, "Audit quality effects of an individual audit engagement partner signature mandate," *Int. J. Auditing*, vol. 18, no. 3, pp. 172–192, 2014.'),
+    33: ("chi2009", 'W. Chi, H. Huang, Y. Liao, and H. Xie, "Mandatory audit partner rotation, audit quality, and market perception: Evidence from Taiwan," *Contemp. Account. Res.*, vol. 26, no. 2, pp. 359–391, 2009.'),
+    34: ("redmon2016", 'J. Redmon, S. Divvala, R. Girshick, and A. Farhadi, "You only look once: Unified, real-time object detection," in *Proc. CVPR*, 2016, pp. 779–788.'),
+    35: ("vlm_survey", 'J. Zhang, J. Huang, S. Jin, and S. Lu, "Vision-language models for vision tasks: A survey," *IEEE Trans. Pattern Anal. Mach. Intell.*, vol. 46, no. 8, pp. 5625–5644, 2024.'),
+    36: ("mann1947", 'H. B. Mann and D. R. Whitney, "On a test of whether one of two random variables is stochastically larger than the other," *Ann. Math. Statist.*, vol. 18, no. 1, pp. 50–60, 1947.'),
+}
+
+# === LINE-SPECIFIC REPLACEMENTS PER FILE ===
+# Each entry: (unique_context_string, old_text, new_text)
+
+INTRO_FIXES = [
+    # Line 16: SV range should start at [3] not [2] (since [2] is Yen)
+    ("offline signature verification [2]--[7]",
+     "offline signature verification [2]--[7]",
+     "offline signature verification [3]--[8]"),
+    # Line 23: Woodruff
+    ("Woodruff et al. [8]",
+     "Woodruff et al. [8]",
+     "Woodruff et al. [9]"),
+    # Line 24: CMFD refs
+    ("Copy-move forgery detection methods [9], [10]",
+     "methods [9], [10]",
+     "methods [10], [11]"),
+    # Line 25: pHash+DL refs
+    ("perceptual hashing combined with deep learning [11], [12]",
+     "deep learning [11], [12]",
+     "deep learning [12], [13]"),
+    # Line 28: pHash -> dHash in pipeline description
+    ("perceptual hash (pHash) distance",
+     "perceptual hash (pHash) distance",
+     "difference hash (dHash) distance"),
+]
+
+RW_FIXES = [
+    # Line 7: Hafemann 2017
+    ("Hafemann et al. [24]", "et al. [24]", "et al. [14]"),
+    # Line 12: Zois
+    ("Zois et al. [26]", "et al. [26]", "et al. [15]"),
+    # Line 13: Hafemann 2019
+    ("Hafemann et al. [25]", "et al. [25]", "et al. [16]"),
+    # Line 18: Brimoh (wrongly [7], should be [8])
+    ("Brimoh and Olisah [7]", "Olisah [7]", "Olisah [8]"),
+    # Line 23: Farid
+    ("manipulated visual content [27]", "content [27]", "content [17]"),
+    # Line 23: Mehrjardi
+    ("forgery detection [28]", "detection [28]", "detection [18]"),
+    # Line 24: CMFD survey
+    ("manipulated photographs [10]", "photographs [10]", "photographs [11]"),
+    # Line 25: Abramova (was [11], should be [10])
+    ("Abramova and Bohme [11]", "Bohme [11]", "Bohme [10]"),
+    # Line 27: Woodruff (was [8], should be [9])
+    ("Woodruff et al. [8]", "et al. [8]", "et al. [9]"),
+    # Line 31: Pizzi (was [12], should be [13])
+    ("Pizzi et al. [12]", "et al. [12]", "et al. [13]"),
+    # Line 36: pHash survey (was [13], should be [19])
+    ("substantive content changes [13]", "changes [13]", "changes [19]"),
+    # Line 39: Jakhar (was [11], should be [12])
+    ("Jakhar and Borah [11]", "Borah [11]", "Borah [12]"),
+    # Line 47: Engin (was [14], should be [20])
+    ("Engin et al. [14]", "et al. [14]", "et al. [20]"),
+    # Line 48: Tsourounis (was [15], should be [21])
+    ("Tsourounis et al. [15]", "et al. [15]", "et al. [21]"),
+    # Line 49: Chamakh (was [16], should be [22])
+    ("Chamakh and Bounouh [16]", "Bounouh [16]", "Bounouh [22]"),
+    # Line 51: Babenko (was [29], should be [23])
+    ("Babenko et al. [29]", "et al. [29]", "et al. [23]"),
+]
+
+METH_FIXES = [
+    # Line 40: Qwen (was [17], should be [24])
+    ("parameters) [17]", ") [17]", ") [24]"),
+    # Line 53: YOLO (was [18], should be [25])
+    ("(nano variant) [18]", "variant) [18]", "variant) [25]"),
+    # Line 75: ResNet (was [19], should be [26])
+    ("neural network [19]", "network [19]", "network [26]"),
+    # Line 81: Engin, Tsourounis (was [14], [15], should be [20], [21])
+    ("document analysis tasks [14], [15]",
+     "tasks [14], [15]",
+     "tasks [20], [21]"),
+    # Line 98: Krawetz dHash (was [36], should be [27])
+    ("(dHash) [36]", ") [36]", ") [27]"),
+    # Line 101: pHash survey ref (was [14], should be [19])
+    ("scan-induced variations [14]",
+     "variations [14]",
+     "variations [19]"),
+    # Line 122: Silverman KDE (was [33], should be [28])
+    ("(KDE) [33]", ") [33]", ") [28]"),
+]
+
+RESULTS_FIXES = [
+    # Cohen's d citation (was [34], should be [29])
+    ("effect size [34]", "size [34]", "size [29]"),
+]
+
+DISCUSSION_FIXES = [
+    # Engin/Tsourounis/Chamakh range (was [14]--[16], should be [20]--[22])
+    ("prior literature [14]--[16]",
+     "literature [14]--[16]",
+     "literature [20]--[22]"),
+]
+
+
+def apply_fixes(filepath, fixes):
+    text = filepath.read_text(encoding='utf-8')
+    changes = 0
+    for context, old, new in fixes:
+        if context in text:
+            text = text.replace(old, new, 1)
+            changes += 1
+        else:
+            print(f"  WARNING: context not found in {filepath.name}: {context[:60]}...")
+    filepath.write_text(text, encoding='utf-8')
+    print(f"  {filepath.name}: {changes} fixes applied")
+    return changes
+
+
+def rewrite_references():
+    """Rewrite references.md with final sequential numbering."""
+    lines = ["# References\n\n"]
+    lines.append("<!-- IEEE numbered style, sequential by first appearance in text -->\n\n")
+
+    for num, (key, citation) in sorted(FINAL_REFS.items()):
+        lines.append(f"[{num}] {citation}\n\n")
+
+    lines.append(f"<!-- Total: {len(FINAL_REFS)} references -->\n")
+
+    ref_path = PAPER_DIR / "paper_a_references.md"
+    ref_path.write_text("".join(lines), encoding='utf-8')
+    print(f"  paper_a_references.md: rewritten with {len(FINAL_REFS)} references")
+
+
+def main():
+    print("Renumbering citations...\n")
+
+    total = 0
+    total += apply_fixes(PAPER_DIR / "paper_a_introduction.md", INTRO_FIXES)
+    total += apply_fixes(PAPER_DIR / "paper_a_related_work.md", RW_FIXES)
+    total += apply_fixes(PAPER_DIR / "paper_a_methodology.md", METH_FIXES)
+    total += apply_fixes(PAPER_DIR / "paper_a_results.md", RESULTS_FIXES)
+    total += apply_fixes(PAPER_DIR / "paper_a_discussion.md", DISCUSSION_FIXES)
+
+    print(f"\nTotal fixes: {total}")
+
+    print("\nRewriting references.md...")
+    rewrite_references()
+
+    print("\nDone! Verify with: grep -n '\\[.*\\]' paper/paper_a_*.md")
+
+
+if __name__ == "__main__":
+    main()

paper/v4/paper_a_methodology_v4_section_iii.md

@@ -0,0 +1,447 @@
+# Section III. Methodology — v4.0 Draft v7 (post codex rounds 21–34)
+
+> **Draft note (2026-05-13, v7; internal — remove before submission).** This file replaces the §III-G through §III-M block of `paper/paper_a_methodology_v3.md` (v3.20.0). Sub-sections III-A through III-F (Pipeline / Data Collection / Page Identification / Detection / Feature Extraction / Dual-Method Descriptors) are unchanged from v3.20.0 and not reproduced here. The §III-G through §III-M block has been substantially restructured between v6 and v7 (2026-05-13): codex round-29 demolished the distributional path to thresholds (Scripts 39b–39e prove (cos, dHash) multimodality is composition + integer artefact); v4.0 pivots to anchor-based multi-level inter-CPA coincidence-rate calibration (Scripts 40b, 43, 44, 45, 46); §III-I is rewritten as the no-natural-threshold diagnostic; §III-J is recast as a firm-compositional descriptive partition (not three mechanism clusters); §III-L is a new major sub-section on anchor-based threshold calibration; §III-M is a new sub-section on validation strategy and limitations under the unsupervised setting. Prior internal draft notes (v2–v6 changelog) have been moved to `paper/v4/CHANGELOG.md`.
+>
+> Empirical anchors throughout reference Scripts 32–46 on branch `paper-a-v4-big4`; a curated provenance table appears at the end of this section listing the principal numerical claims with their script and report path.
+
+## G. Unit of Analysis and Scope
+
+We analyse signatures at two units of resolution. The **signature** — one signature image extracted from one report — is the operational unit of classification (§III-L) and of the signature-level analyses in §IV (notably §IV-J for the five-way per-signature category counts and the inherited inter-CPA negative-anchor coincidence-rate analysis referenced in §IV-I; reported under prior "FAR" terminology in v3.x). The **accountant** — one CPA aggregated over all of their signatures in the corpus — is the unit of mixture-model characterisation (§III-J), of per-CPA internal-consistency analysis (§III-K), and of the leave-one-firm-out reproducibility check (§III-K). At the accountant level we compute, for each CPA with $n_{\text{sig}} \geq 10$ signatures, the per-CPA mean of the per-signature best-match cosine ($\overline{\text{cos}}_a$) and the per-CPA mean of the independent-minimum dHash ($\overline{\text{dHash}}_a$). The minimum threshold of 10 signatures per CPA is required for the per-CPA mean to be a stable summary; CPAs below this threshold are excluded from the accountant-level analyses but remain in the per-signature analyses.
+
+We make no within-year or across-year uniformity assumption about CPA signing mechanisms. Per-signature labels are signature-level quantities throughout this paper; we do not translate them to per-report or per-partner mechanism assignments, and we abstain from partner-level frequency inferences (such as "X% of CPAs hand-sign") that would require such a translation. A CPA's per-CPA mean is a *summary statistic* of their observed signatures, not a claim that all of their signatures share a single mechanism.
+
+We adopt one stipulation about same-CPA pair detectability:
+
+> **(A1) Pair-detectability.** *If a CPA uses image replication anywhere in the corpus, then at least one same-CPA signature pair is near-identical (after reproduction noise) within the cross-year same-CPA pool used by the max-cosine / min-dHash computation.*
+
+A1 is plausible for high-volume stamping or firm-level electronic signing workflows but is not guaranteed when (i) the corpus contains only one observed replicated report for a CPA, (ii) multiple template variants are used in parallel, or (iii) scan-stage noise pushes a replicated pair outside the detection regime. A1 is the only assumption the per-signature detector requires to be sensitive to replication.
+
+**Scope: the Big-4 sub-corpus.** v4.0's primary analyses (§III-I, §III-J, §III-K, §III-L, and the v4-new analyses in §IV-D through §IV-J) are restricted to the four largest accounting firms in Taiwan, pseudonymously labelled Firm A through Firm D throughout the manuscript. §IV-A through §IV-C, §IV-I (inter-CPA negative-anchor coincidence rate), and §IV-L (feature-backbone ablation) report inherited corpus-wide v3.x material that v4.0 does not re-scope to Big-4. §IV-K reports a deliberately narrow full-dataset cross-check at $n = 686$ CPAs. The Big-4 sub-corpus comprises 437 CPAs (171 / 112 / 102 / 52 across Firms A through D) with $n_{\text{sig}} \geq 10$ — the threshold for accountant-level analyses (Scripts 36, 38) — totalling 150,442 Big-4 signatures with both pre-computed descriptors available. Restricting the v4-new analyses to Big-4 is a methodological choice driven by four considerations:
+
+1. **Leave-one-firm-out fold feasibility.** §III-K reports leave-one-firm-out (LOOO) cross-validation of the Big-4 K=3 fit. The Big-4 sub-corpus permits a four-fold LOOO at the firm level (one fold per Big-4 firm). No analogous firm-level fold is available outside Big-4 because mid/small firms have CPA counts of $O(1)$–$O(30)$ per firm.
+
+2. **Firm A as templated-end case study.** Firm A is empirically the firm whose CPAs are most concentrated in the high-cosine, low-dHash corner of the descriptor plane (§III-J K=3 component cross-tab; v3.x byte-level pair analysis referenced in §III-H). v4.0 retains Firm A within the Big-4 scope as a descriptive case study of the templated end, rather than treating Firm A as the calibration anchor for thresholds (the v3.x role of Firm A).
+
+3. **Within-firm cross-CPA collision structure analysis.** §III-L.4 reports a Big-4 cross-firm hit-matrix analysis (Script 44) that quantifies the within-firm cross-CPA template-like collision pattern. The four-firm setting affords the cleanest signal for this analysis; replicating the same matrix structure on the heterogeneous mid/small-firm tail is left as future work.
+
+4. **Restricted generalisability claim.** v4.0's primary claims are scoped to the Big-4 audit-report context; we do not assert that the same descriptive mixture structure or operational alert behaviour extends to mid/small firms. The 249 non-Big-4 CPAs enter only (a) as an external reference population in §III-H's reverse-anchor internal-consistency check, (b) as a robustness comparison in §IV-K, and (c) as a corroborating-population check on the dHash discrete-mass-point artefact in §III-I.4 (Script 39c). Generalisation beyond Big-4 is left as future work.
+
+We earlier (v4.0 first draft) listed "statistical multimodality at the accountant level" among the scope justifications, on the basis that the Hartigan dip test rejects unimodality on the Big-4 accountant-level marginals. §III-I.4 reports diagnostics (Scripts 39b–39e) that explain the rejection as a joint effect of between-firm composition shift and dHash integer mass points, not as evidence of within-population continuous bimodality. We therefore no longer list dip-test multimodality among the Big-4 scope rationales; the K=3 mixture is retained as a descriptive partition (§III-J), not as inferential evidence for two mechanism modes.
+
+**Sample-size reconciliation.** Two Big-4 signature counts appear in this section and §IV: $n = 150{,}442$ for analyses using the pre-computed per-signature descriptors $\text{cos}_s$ (`max_similarity_to_same_accountant`) and $\text{dHash}_s$ (`min_dhash_independent`), and $n = 150{,}453$ for analyses recomputing pair-level metrics directly from the stored feature and dHash byte vectors (Scripts 40b, 43, 44). The $11$-signature difference reflects descriptor-completion status: $11$ signatures have feature vectors and dHash byte vectors stored but lack the pre-computed extrema. The $11$ signatures are negligible at population scale and do not affect any reported coincidence rate within $0.01$ percentage point. The CPA counts $468$ (all Big-4 CPAs with both vectors stored) and $437$ (Big-4 CPAs with $n_{\text{sig}} \geq 10$ for accountant-level stability) likewise reflect a single uniform exclusion rule rather than analysis-specific subsetting.
+
+## H. Reference Populations
+
+v4.0 distinguishes two reference populations in its calibration, replacing v3.x's single-anchor framing.
+
+**Internal reference: Firm A as the templated-end case study.** Firm A is empirically the firm whose CPAs are most concentrated in the high-cosine, low-dHash corner of the Big-4 descriptor plane. In the Big-4 K=3 descriptive partition (§III-J; Scripts 35, 38), Firm A accounts for 0% of the C1 component (low-cos / high-dHash corner; cos $\approx 0.946$, dHash $\approx 9.17$, weight $\approx 0.143$), 17.5% of the C2 component (central region), and 82.5% of the C3 component (high-cos / low-dHash corner); the opposite pattern holds at Firm C (Script 35: 23.5% C1, 75.5% C2, 1.0% C3, hereafter referred to as "the Firm whose CPAs are most concentrated in C1"). The byte-level pair analysis reported in v3.x §IV-F.1 identifies 145 Firm A pixel-identical signatures at the signature level (Script 40 verifies the 145/262 split among Big-4 pixel-identical signatures); the additional details that v3.x attributes to this analysis (50 distinct Firm A partners of 180 registered; 35 byte-identical matches spanning different fiscal years) are inherited from the Script 28 / Appendix B byte-decomposition output and were not regenerated in the v4.0 spike scripts. We retain those v3.x details by reference and mark them in the provenance table as "inherited from v3 §IV-F.1 / Script 28."
+
+In v4.0, Firm A is *not* the calibration anchor for the operational threshold. Firm A enters the Big-4 mixture on equal footing with Firms B through D; the K=3 components are derived from the joint Big-4 distribution (§III-J), not from Firm A alone. Firm A's role in the methodology is descriptive: it is the Big-4 firm whose CPAs are most concentrated in the high-cosine, low-dHash corner of the descriptor plane, and the byte-level pair evidence above provides the firm-level signature-reuse evidence that anchors §III-K's pixel-identity positive-anchor miss rate.
+
+**External reference: non-Big-4 as the reverse-anchor reference for internal-consistency checking.** The 249 non-Big-4 CPAs ($n_{\text{sig}} \geq 10$, drawn from $\sim$30 mid- and small-firms) constitute a population strictly outside the Big-4 target. Their per-CPA $(\overline{\text{cos}}_a, \overline{\text{dHash}}_a)$ distribution defines a 2D Gaussian reference (fit by Minimum Covariance Determinant with support fraction 0.85 for robustness; Script 38). This reference is used in §III-K's reverse-anchor internal-consistency check: each Big-4 CPA's location relative to the reference centre, measured as the marginal cosine cumulative-distribution-function value under the reference, is one of three feature-derived scores that v4.0 uses as a cross-check on the inherited per-signature classifier. The reverse-anchor reference is *not* a positive or negative anchor for threshold derivation — its role is to provide a strictly out-of-target benchmark against which the within-Big-4 mixture-derived ranking can be internally cross-checked.
+
+The reverse-anchor reference centre is at $\overline{\text{cos}} = 0.935$, $\overline{\text{dHash}} = 9.77$ (Script 38). The reference sits at a lower cosine and higher dHash than the Big-4 K=3 low-cos / high-dHash component (cos $= 0.946$, dHash $= 9.17$; §III-J); compared to the Big-4 high-cos / low-dHash component (cos $= 0.983$, dHash $= 2.41$; §III-J) the reference is markedly less replication-dominated. The reverse-anchor metric for a given Big-4 CPA is the percentile of $\overline{\text{cos}}_a$ within the reference marginal cosine distribution, sign-flipped so that lower percentile (further into the left tail of the reference) corresponds to a Big-4 CPA whose mean cosine sits further from the templated end of the descriptor plane. This is a "deviation in the less-replication-dominated descriptor-position direction" measure, not a "deviation toward the templated descriptor-position" measure; the reference is the less-replication-dominated population.
+
+## I. Distributional Diagnostics: Why the Composition Path Does Not Yield a Natural Threshold
+
+This section characterises the joint distribution of accountant-level descriptor means $(\overline{\text{cos}}_a, \overline{\text{dHash}}_a)$ across the 437 Big-4 CPAs of §III-G and tests whether the distribution provides distributional support — in the form of within-population bimodality — for the operational thresholds inherited from v3.x. We apply four diagnostic procedures in turn: a univariate unimodality test on each accountant-level marginal; a 2D Gaussian mixture fit (developed in §III-J); a density-smoothness diagnostic; and a composition decomposition that distinguishes within-population multimodality from between-firm location-shift artefacts (the v4-new diagnostic battery). The four diagnostics jointly imply that the operational thresholds are *not* anchored by distributional bimodality: §III-L develops an anchor-based calibration framework that does not require this assumption.
+
+**1. Hartigan dip test on each accountant-level marginal.** We apply the Hartigan & Hartigan dip test [37] to each of the two marginal distributions $\{\overline{\text{cos}}_a\}_{a=1}^{437}$ and $\{\overline{\text{dHash}}_a\}_{a=1}^{437}$, with bootstrap-based $p$-value estimation ($n_{\text{boot}} = 2000$). In both cases no bootstrap replicate exceeded the observed dip statistic, so the empirical $p$-value is bounded above by $5 \times 10^{-4}$; we report this in tables as $p < 5 \times 10^{-4}$ rather than $p = 0$ to reflect the bootstrap resolution (Script 34). For comparison, no rejection of unimodality holds in the comparison scopes tested in Script 32: Firm A pooled alone ($p_{\text{cos}} = 0.992$, $p_{\text{dHash}} = 0.924$, $n = 171$); Firms B + C + D pooled ($p_{\text{cos}} = 0.998$, $p_{\text{dHash}} = 0.906$, $n = 266$); all non-Firm-A CPAs pooled ($p_{\text{cos}} = 0.998$, $p_{\text{dHash}} = 0.907$, $n = 515$). Single-firm dip tests for Firms B, C, and D were not separately computed; the comparison scopes above sufficed to establish that no narrower-than-Big-4 *tested* scope at the accountant level rejected unimodality. The accountant-level Big-4 rejection is a descriptive observation; §III-I.4 below shows that the rejection is fully explained by between-firm location-shift effects rather than within-population bimodality.
+
+**2. K=2 / K=3 Gaussian mixture fits (descriptive partition).** A 2-component 2D Gaussian Mixture Model (full covariance, $n_{\text{init}} = 15$, fixed seed 42; Script 34) recovers components at $(\overline{\text{cos}}, \overline{\text{dHash}}) = (0.954, 7.14)$, weight $0.689$, and $(0.983, 2.41)$, weight $0.311$. The marginal crossings of the K=2 fit are $\overline{\text{cos}}^* = 0.9755$ and $\overline{\text{dHash}}^* = 3.755$, with bootstrap 95% confidence intervals $[0.9742, 0.9772]$ and $[3.48, 3.97]$ over $n_{\text{boot}} = 500$ resamples. The 3-component fit (§III-J) is BIC-preferred — using the convention that lower BIC is preferred, $\text{BIC}(K{=}3) - \text{BIC}(K{=}2) = -3.48$ (Script 36). The $\Delta$BIC magnitude is small in absolute terms; we do not treat $\Delta\text{BIC} = 3.5$ alone as decisive evidence for K=3 as a population mixture. Following §III-I.4 we treat both K=2 and K=3 fits as *descriptive partitions* of the joint Big-4 distribution that reflect firm-composition structure (Firm A vs others; §III-J) rather than as inferential evidence for two or three latent population modes.
+
+**3. Burgstahler-Dichev / McCrary density-smoothness diagnostic.** We apply the discontinuity test of [38, 39] as a *density-smoothness diagnostic* (rather than as a threshold estimator) on each accountant-level marginal axis (cosine in bins of $0.002$, dHash in integer bins). At the Big-4 scope, the diagnostic identifies no significant transition on either marginal at $\alpha = 0.05$ (Script 34). Outside Big-4, the diagnostic does flag dHash transitions in some subsets (Script 32: `big4_non_A` dHash transition at $10.8$; `all_non_A` dHash transition at $6.6$; pre-2018 and post-2020 time-stratified variants also exhibit one or more dHash transitions), but no cosine transition is identified in any subset. The Big-4-scope null on both axes is consistent with §III-I.4 below: under the composition decomposition the Big-4 marginals are unimodal once between-firm and integer-tie confounds are removed, so a local-discontinuity test correctly fails to flag a within-population transition.
+
+**4. Composition decomposition (Scripts 39b–39e).** §III-I.1 establishes that the accountant-level marginals reject unimodality at the Big-4 sub-corpus. The remaining question is whether the rejection reflects (a) genuine within-population bimodality at the signature or accountant level, (b) between-firm location-shift artefacts (firms with different mean descriptor positions pool to a multi-peaked distribution), or (c) integer mass-point artefacts on the integer-valued dHash axis (the dHash dip statistic is sensitive to spikes at integer values). We apply four diagnostics that decompose the rejection into these candidate sources:
+
+*Within-firm signature-level dip (Scripts 39b, 39c).* Repeating the dip test at the signature level inside each individual Big-4 firm (Script 39b) and inside each individual non-Big-4 firm with $\geq 500$ signatures (Script 39c) yields a consistent picture. The cosine marginal *fails* to reject unimodality in every single firm tested — all four Big-4 firms ($p_{\text{cos}} \in \{0.176, 0.991, 0.551, 0.976\}$ for Firms A through D; Script 39b) and ten non-Big-4 firms with $\geq 500$ signatures ($p_{\text{cos}} \in [0.59, 0.99]$; Script 39c). The raw dHash marginal *does* reject unimodality in every firm tested ($p < 5 \times 10^{-4}$ in all $14$ firms), but the raw dHash values are integer-valued in $\{0, 1, \ldots, 64\}$, leaving open the possibility of an integer-tie artefact.
+
+*Integer-jitter robustness (Scripts 39d, 39e).* Adding independent uniform jitter $\sim \mathrm{U}[-0.5, +0.5]$ to break exact dHash ties and re-running the dip test on the perturbed signature cloud (5 seeds, $n_{\text{boot}} = 2000$; Script 39d) eliminates the dHash within-firm rejection in every Big-4 firm tested (Firm A jittered $p_{\text{median}} = 0.999$; B $0.996$; C $0.999$; D $0.9995$; $0$/$5$ seeds reject at $\alpha = 0.05$ in any firm). All ten non-Big-4 firms similarly fail to reject after jitter ($p \in [0.71, 1.00]$). The pooled-Big-4 dHash dip *does* survive jitter alone ($p_{\text{median}} = 0$, $5$/$5$ seeds reject), but Firm A's mean dHash ($2.73$) is substantially below Firms B/C/D's ($6.46$, $7.39$, $7.21$) — a between-firm location shift. Script 39e applies a 2 \times 2 factorial correction (firm-mean centring $\times$ integer jitter) on the Big-4 pooled dHash:
+
+| Condition | Firm-mean centred | Integer jitter | Median dip $p$ |  Reject at $\alpha = 0.05$ |
+|---|---|---|---|---|
+| 1 raw | — | — | $< 5 \times 10^{-4}$ | $5/5$ |
+| 2 centred only | $\checkmark$ | — | $< 5 \times 10^{-4}$ | $5/5$ |
+| 3 jittered only | — | $\checkmark$ | $< 5 \times 10^{-4}$ | $5/5$ |
+| 4 centred and jittered | $\checkmark$ | $\checkmark$ | $\mathbf{0.35}$ | $\mathbf{0/5}$ |
+
+Removing *both* the between-firm location shift *and* the integer mass points eliminates the Big-4 dHash rejection. The Big-4 pooled dHash multimodality is therefore fully attributable to firm-composition contrast (primarily Firm A's mean $\text{dHash} = 2.73$ versus Firms B/C/D $\approx 6.5$–$7.4$) and integer-density artefacts, with no residual continuous within-firm bimodality.
+
+*Cosine analogue.* The cosine axis exhibits the same pattern. Codex-verified read-only spike on the Big-4 pooled signature cloud yields signature-level cosine dip $p < 5 \times 10^{-4}$ on the raw data, but $p = 0.597$ after firm-mean centring; accountant-level cosine $p = 1.0$ after firm-mean centring. The cosine multimodality is therefore between-firm composition-driven, not within-population bimodality.
+
+*Integer-histogram valleys (Script 39d).* A genuine within-firm dHash antimode would appear as a strict local minimum in the count histogram with deep relative depth. Within each of the four Big-4 firms, the dHash histogram on bins $0$–$20$ exhibits no strict local minimum; the Big-4 pooled histogram exhibits one shallow valley at $\text{dHash} = 4$ with relative depth $0.021$ (a $2.1\%$ count drop). No valley near the inherited $\text{dHash} = 5$ operational boundary appears within any individual firm. The hypothesised dHash antimode near $\text{dHash} \approx 5$ is not empirically supported by the histogram analysis.
+
+**5. Conclusion: no natural threshold from the descriptor distribution.** §III-I.4 jointly establishes that (a) the Big-4 accountant-level dip rejection is fully attributable to between-firm composition and integer mass-point artefacts; (b) within any individual firm, the descriptor marginals at the signature level are unimodal once integer ties are broken; and (c) no integer-histogram valley near the inherited $\text{dHash} = 5$ operational boundary exists within any firm. The descriptor distributions therefore do not contain a within-population bimodal antimode that could anchor an operational threshold. The K=2 / K=3 mixture fits of §III-I.2 and §III-J are retained as *descriptive partitions* that reflect firm-composition contrast, not as inferential evidence for two or three population modes. §III-L develops the v4.0 anchor-based threshold calibration framework, which derives operational rates from inter-CPA pair-level negative-anchor coincidences rather than from a distributional antimode.
+
+## J. K=3 as a Descriptive Partition of Firm-Composition Contrast
+
+This section develops the K=2 and K=3 Gaussian mixture fits to the Big-4 accountant-level distribution and clarifies their role. **Both fits are descriptive partitions of the joint Big-4 distribution; they reflect firm-composition contrast — primarily Firm A versus Firms B, C, D — rather than within-population mechanism modes.** §III-I.4 demonstrates that the apparent multimodality of the accountant-level marginals is fully explained by between-firm location shifts and integer mass-point artefacts, leaving no residual evidence for two or three latent within-population mechanism classes. Neither mixture is used to assign signature-level or document-level labels in the v4.0 primary analysis. The operational classifier of §III-L is calibrated via inter-CPA negative-anchor coincidence rates, not via mixture-derived antimodes.
+
+**K=2 fit.** Two components at $(\overline{\text{cos}}, \overline{\text{dHash}}) = (0.954, 7.14)$ (weight $0.689$) and $(0.983, 2.41)$ (weight $0.311$) (Script 34). $\text{BIC}(K{=}2) = -1108.45$. Marginal crossings: $\overline{\text{cos}}^* = 0.9755$, $\overline{\text{dHash}}^* = 3.755$. We refer to the components by index rather than by mechanism labels, since §III-I.4 establishes that the K=2 separation is firm-compositional rather than mechanistic.
+
+**K=3 fit.** Three components, sorted by ascending cosine mean (Script 35; Script 38 reproduces):
+
+| Component | $\overline{\text{cos}}$ | $\overline{\text{dHash}}$ | weight | descriptive position |
+|---|---|---|---|---|
+| C1 | 0.9457 | 9.17 | 0.143 | low-cos / high-dHash corner |
+| C2 | 0.9558 | 6.66 | 0.536 | central region |
+| C3 | 0.9826 | 2.41 | 0.321 | high-cos / low-dHash corner |
+
+$\text{BIC}(K{=}3) = -1111.93$, lower than $K{=}2$ by $3.48$ (mild numerical preference for K=3 under standard BIC interpretation, but not by itself decisive). The "descriptive position" column replaces v3.x's "hand-leaning / mixed / replicated" mechanism labels: §III-I.4 establishes that the cosine and dHash axes both lack within-population bimodality, so component centres are best interpreted as locations in a continuous descriptor space rather than as latent mechanism modes.
+
+**Per-firm component composition (Script 35 firm × cluster cross-tab).** The K=3 partition is dominated by firm membership:
+
+- Firm A: $0\%$ C1, $17.5\%$ C2, $82.5\%$ C3
+- Firm B: $8.9\%$ C1, $\sim 78\%$ C2, $\sim 13\%$ C3
+- Firm C: $23.5\%$ C1, $75.5\%$ C2, $1.0\%$ C3
+- Firm D: $11.5\%$ C1, $\sim 84\%$ C2, $\sim 4.5\%$ C3
+
+Firm A accounts for $141$ of the $143$ C3-assigned CPAs; Firm C accounts for $24$ of the $40$ C1-assigned CPAs. The K=3 partition is therefore well-described as a firm-compositional decomposition: C3 is essentially "Firm A and any non-Firm-A CPA whose mean descriptors happen to land in the high-cos / low-dHash corner"; C1 is essentially "non-Firm-A CPAs whose mean descriptors land in the low-cos / high-dHash corner." The composition contrast that K=3 captures at the accountant level reappears at the deployment level in the cross-firm hit matrix of §III-L.4 (Script 44): nearly all (98%) of the inter-CPA-anchor hits for a Firm A source signature have a Firm A candidate, and the same within-firm concentration holds for Firms B, C, D individually. The K=3 partition and the cross-firm hit matrix therefore describe the same underlying firm-compositional structure at two different units of analysis.
+
+**Leave-one-firm-out stability (Scripts 36, 37).** Leave-one-firm-out cross-validation shows that K=2 is unstable across folds: holding Firm A out gives a fold rule cos $> 0.938$ AND dHash $\leq 8.79$, while holding any single non-Firm-A Big-4 firm out gives a fold rule near cos $> 0.975$ AND dHash $\leq 3.76$ (Script 36). The maximum absolute deviation of the four fold cosine crossings from their across-fold mean is $0.028$ (the corresponding pairwise across-fold range is $0.0376$, from $0.9380$ for the held-out-Firm-A fold to $0.9756$ for the held-out-Firm-D fold; Script 36 stability summary). The $0.028$ value is $5.6\times$ the report's $0.005$ across-fold stability tolerance. K=3 in contrast has a *reproducible component shape*: across the four folds the C1 cosine mean varies by at most $0.005$, the C1 dHash mean by at most $0.96$, and the C1 weight by at most $0.023$ (Script 37). K=3 hard-posterior membership for the held-out firm is composition-sensitive — for Firm C the held-out C1 rate is $36.3\%$ vs the full-Big-4 baseline of $23.5\%$, an absolute difference of $12.8$ pp; for Firm A the held-out C1 rate is $4.7\%$ vs baseline $0.0\%$; the report's own legend classifies this pattern as `P2_PARTIAL` ("the C1 cluster exists but membership is not well-predicted by the held-out fit"). We accordingly do not use K=3 hard-posterior membership as an operational label.
+
+We take the joint K=2 / K=3 LOOO evidence as supporting the following descriptive claims, all of which are used in §III-K and §V but none of which underwrites the v4.0 operational classifier:
+
+- The Big-4 K=2 marginal crossing $(0.975, 3.76)$ is essentially a firm-mass separator between Firm A and Firms B + C + D, not a within-Big-4 mechanism boundary.
+- The Big-4 K=3 mixture exhibits a reproducible three-component component shape across LOOO folds at the descriptor-position level, with C1 reproducibly located at $\overline{\text{cos}} \approx 0.946$, $\overline{\text{dHash}} \approx 9.17$.
+- Hard-posterior K=3 membership is composition-sensitive across folds (max absolute deviation $12.8$ pp); K=3 is therefore not used to assign operational labels to CPAs in v4.0.
+
+The operational signature-level classifier of §III-L is calibrated against inter-CPA pair-level negative-anchor coincidence rates, not against mixture-derived antimodes. Cross-checks between the inherited five-way box rule and the K=3 partition appear in §III-K.
+
+## K. Convergent Internal-Consistency Checks
+
+The descriptive partition of §III-J is supported by three feature-derived per-CPA scores and a hard-ground-truth subset analysis. We caution at the outset that the three scores are **not statistically independent measurements** — all three are deterministic functions of the same per-CPA descriptor means $(\overline{\text{cos}}_a, \overline{\text{dHash}}_a)$ — so their high pairwise rank correlations are partly a mechanical consequence of shared inputs. Per §III-I.4, none of the three scores has a within-population bimodality interpretation; they are firm-compositional position scores at the accountant level. The checks below therefore document **internal consistency among feature-derived ranks**, not external validation against an independent hand-signed ground truth (which the corpus does not provide).
+
+**1. Three feature-derived per-CPA scores (Script 38).** For each Big-4 CPA we compute:
+
+- **Score 1 (K=3 posterior on the low-cos / high-dHash component):** $P(\text{C1})$ from the K=3 fit of §III-J. Per §III-J this is a firm-compositional position score on the (cos, dHash) plane (not a probability of any latent "hand-signing mechanism") — a function of both descriptor means.
+- **Score 2 (reverse-anchor cosine percentile):** the marginal cosine CDF value of $\overline{\text{cos}}_a$ under the non-Big-4 reference Gaussian of §III-H, sign-flipped so that lower percentile (further into the reference's left tail) corresponds to a Big-4 CPA whose mean cosine sits further from the templated end. This is a function of $\overline{\text{cos}}_a$ alone.
+- **Score 3 (inherited binary high-confidence box rule rate):** the per-CPA fraction of signatures that do **not** satisfy the inherited binary high-confidence box rule (cos $> 0.95$ AND dHash $\leq 5$). This is a per-signature-aggregated function of the same descriptors.
+
+Pairwise Spearman rank correlations among the three scores, $n = 437$ Big-4 CPAs (Script 38):
+
+| Pair | Spearman $\rho$ | $p$-value |
+|---|---|---|
+| Score 1 vs Score 3 | $+0.963$ | $< 10^{-248}$ |
+| Score 2 vs Score 3 | $+0.889$ | $< 10^{-149}$ |
+| Score 1 vs Score 2 | $+0.879$ | $< 10^{-142}$ |
+
+We read this as the strongest internal-consistency signal in v4.0: three different summarisations of the same descriptor pair agree on the per-CPA descriptor-position ranking with $\rho > 0.87$. The three scores agree on placing Firm A as the most replication-dominated descriptor position and the three non-Firm-A Big-4 firms further from the templated end, but they do not all rank the non-Firm-A firms identically: the K=3 posterior P(C1) and the box-rule less-replication-dominated rate (Scores 1 and 3) place Firm C at the less-replication-dominated end of Big-4 (mean P(C1) $= 0.311$; mean box-rule less-replication-dominated rate $= 0.790$), while the reverse-anchor cosine percentile (Score 2) places Firm D fractionally higher than Firm C (mean reverse-anchor score $-0.7125$ vs Firm C $-0.7672$, with higher value indicating deeper into the reference left tail). The mean values for Firms B and D sit between Firms A and C on Scores 1 and 3 (Script 38 per-firm summary). We do not claim this constitutes external validation of any operational classifier; the inherited box rule is calibrated separately (§III-L), and the convergence above shows that a mixture-derived score and a reverse-anchor score concur with the box rule's per-CPA-aggregated outputs on the directional ordering, with a modest disagreement at the less-replication-dominated end between the three non-A Big-4 firms.
+
+**2. Per-signature consistency (Script 39).** Per-CPA aggregation could in principle reflect averaging across within-CPA heterogeneity rather than coherent within-CPA behaviour. We test this by repeating the K=3 fit at the signature level — fitting a fresh K=3 GMM to the 150,442 Big-4 signature-level $(\text{cos}, \text{dHash}_{\text{indep}})$ points (Script 39) — and comparing labels. The per-CPA and per-signature K=3 fits recover a broadly similar three-component ordering; per-CPA C1 is at $\overline{\text{cos}} = 0.946$, $\overline{\text{dHash}} = 9.17$ vs per-signature C1 at $\overline{\text{cos}} = 0.928$, $\overline{\text{dHash}} = 9.75$ (an absolute cosine drift of $0.018$). Cohen $\kappa$ on the binary collapse (replicated vs not-replicated):
+
+| Pair | Cohen $\kappa$ |
+|---|---|
+| Paper A binary high-confidence box rule vs per-CPA K=3 hard label | $0.662$ |
+| Paper A binary high-confidence box rule vs per-signature K=3 hard label | $0.559$ |
+| Per-CPA K=3 vs per-signature K=3 | $0.870$ |
+
+The Script 39 report verdict is `SIG_CONVERGENCE_MODERATE`. The $\kappa = 0.870$ between per-CPA-fit and per-signature-fit K=3 binary labels indicates that per-CPA aggregation does not collapse the broad three-component ordering. The lower $\kappa = 0.56\text{–}0.66$ between the binary box rule and either K=3 fit is consistent with two factors: different decision geometries (rectangular box vs Gaussian-mixture posterior boundary), and the fact that the binary box rule is a strict subset of the inherited five-way rule. We note that this comparison validates only the binary high-confidence rule (cos $> 0.95$ AND dHash $\leq 5$); §III-K does not directly validate the five-way rule's `5 < \text{dHash} \leq 15` moderate-confidence band, which retains its v3.20.0 calibration and capture-rate evaluation (v3.20.0 Tables IX, XI, XII, XII-B; documented as inherited in §IV-J).
+
+**3. Leave-one-firm-out reproducibility (Scripts 36, 37).** Discussed in §III-J above. We summarise the joint result for cross-reference:
+
+- *K=2 LOOO is unstable.* The maximum absolute deviation of the four fold cosine crossings from their across-fold mean is $0.028$, against the report's $0.005$ across-fold stability tolerance (Script 36; pairwise fold range $0.0376$, from $0.9380$ to $0.9756$). When Firm A is held out, the fold rule classifies $171/171$ of held-out Firm A CPAs as templated; when any non-Firm-A Big-4 firm is held out, the fold rule classifies $0$ of the held-out firm's CPAs as templated. This pattern indicates the K=2 boundary is essentially a Firm-A-vs-others separator rather than a within-Big-4 mechanism boundary.
+
+- *K=3 LOOO is partially stable.* The C1 (low-cos / high-dHash) component shape is reproducible across folds: max deviation from the full-Big-4 baseline is $0.005$ in cosine, $0.96$ in dHash, and $0.023$ in mixture weight (Script 37). Hard-posterior membership remains composition-sensitive — observed absolute differences are $1.8$–$12.8$ pp across the four folds, with the Firm C fold exceeding the report's $5$ pp viability bar; the report's own verdict is `P2_PARTIAL` ("K=3 is not predictively useful as an operational classifier"). We accordingly do not use K=3 hard-posterior membership as an operational label.
+
+**4. Positive-anchor miss rate on byte-identical signatures (Script 40).** The corpus provides one hard ground-truth subset: signatures whose nearest same-CPA match is byte-identical after crop and normalisation. Independent hand-signing cannot produce pixel-identical images, so byte-identical signatures are conservative-subset ground truth for the *replicated* class. The Big-4 byte-identical subset comprises $n = 262$ signatures ($145 / 8 / 107 / 2$ across Firms A through D; Script 40).
+
+We report each candidate classifier's *positive-anchor miss rate* — the fraction of byte-identical signatures classified as belonging to the less-replication-dominated descriptor positions. This is a one-sided check against a conservative positive subset, **not a paired specificity metric in the usual two-class sense**; we do not report a paired negative-anchor metric here because no signature-level hand-signed ground truth exists. The corresponding signature-level inter-CPA negative-anchor ICCR evidence is developed in §III-L.1 (Big-4 sample) and the v3.x §IV-I corpus-wide version (reported under prior "FAR" terminology):
+
+| Candidate classifier | Pixel-identity miss rate (Wilson 95% CI) |
+|---|---|
+| Inherited Paper A binary high-confidence box rule (cos $> 0.95$ AND dHash $\leq 5$) | $0\%$ $[0\%, 1.45\%]$ |
+| K=3 per-CPA hard label (C3 high-cos / low-dHash corner; descriptive only) | $0\%$ $[0\%, 1.45\%]$ |
+| Reverse-anchor with prevalence-calibrated cut | $0\%$ $[0\%, 1.45\%]$ |
+
+All three candidate scores correctly assign every byte-identical signature to the replicated class. We caution that for the inherited box rule this result is close to tautological: byte-identical nearest-neighbour signatures have cosine $\approx 1$ and dHash $\approx 0$ by construction, so any threshold strictly below cos $= 1$ and strictly above dHash $= 0$ will capture them; v3.x discussed this conservative-subset caveat at length (v3 §III-J item 1, V-F). The positive-anchor miss rate is therefore a necessary check (a classifier that *failed* this check would be disqualified), not a sufficient validation of the classifier's behaviour on the non-byte-identical replicated population. The reverse-anchor cut here is chosen by prevalence calibration against the inherited box rule's overall replicated rate ($49.58\%$ of Big-4 signatures; Script 40); this is a documented v4.0 limitation since no signature-level hand-signed ground truth exists to permit direct ROC optimisation.
+
+## L. Anchor-Based Threshold Calibration and Operational Classifier
+
+§III-I.4 established that the descriptor distributions do not contain a within-population bimodal antimode that could anchor an operational threshold; the K=3 mixture of §III-J is a descriptive firm-compositional partition, not a mechanism-cluster model. This section develops v4.0's anchor-based threshold calibration: the operational thresholds inherited from v3.x are characterised by their inter-CPA pair-level negative-anchor coincidence behaviour and their pool-normalised per-signature and per-document alert behaviour, at multiple units of analysis. Throughout this section we report **inter-CPA coincidence rates** rather than "False Acceptance Rates"; we explain the terminological choice in §III-L.0.
+
+### L.0. Calibration methodology
+
+**Operational classifier (inherited from v3.20.0 §III-K, retained unchanged).** Each Big-4 signature is assigned to one of five categories using the per-signature descriptor pair $(\text{cos}_s, \text{dHash}_s)$ where $\text{cos}_s$ is the maximum cosine similarity to another signature by the same CPA and $\text{dHash}_s$ is the minimum independent dHash to another signature by the same CPA:
+
+1. **High-confidence non-hand-signed (HC):** Cosine $> 0.95$ AND $\text{dHash}_{\text{indep}} \leq 5$. Both descriptors converge on strong replication evidence.
+2. **Moderate-confidence non-hand-signed (MC):** Cosine $> 0.95$ AND $5 < \text{dHash}_{\text{indep}} \leq 15$. Feature-level evidence is strong; structural similarity is present but below the high-confidence cutoff.
+3. **High style consistency (HSC):** Cosine $> 0.95$ AND $\text{dHash}_{\text{indep}} > 15$. High feature-level similarity without structural corroboration — consistent with a CPA who signs very consistently but not via image reproduction.
+4. **Uncertain (UN):** Cosine between the all-pairs intra/inter KDE crossover ($0.837$) and $0.95$.
+5. **Likely hand-signed (LH):** Cosine $\leq 0.837$.
+
+The thresholds ($\text{cos} = 0.95$ as the cosine operating point, $\text{cos} = 0.837$ as the all-pairs KDE crossover, $\text{dHash} = 5$ and $15$ as structural-similarity sub-band cutoffs) are inherited from v3.x §III-K and retain their v3.x calibration provenance. Document-level labels are aggregated via the v3.x worst-case rule: each audit report inherits the most-replication-consistent category among its certifying-CPA signatures (rank order HC > MC > HSC > UN > LH).
+
+**Why retained without v4.0 recalibration.** The inherited thresholds preserve continuity with v3.x reporting and with the existing literature. §III-I.4 establishes that a v4.0 recalibration cannot be anchored on distributional antimodes (no within-population bimodality exists); §III-L.1 confirms that the cosine threshold's specificity behaviour at the inter-CPA pair level (the v3.x calibration anchor) is reproducible on the v4 spike sample, and §III-L.1 newly characterises the structural-dimension threshold $\text{dHash} \leq 5$'s pair-level coincidence behaviour. Sub-band thresholds ($\text{dHash} = 15$, $\text{cos} = 0.837$) retain v3.x's inherited calibration; v4.0 does not provide independent calibration for those sub-bands.
+
+**Three units of analysis.** We report inter-CPA negative-anchor coincidence behaviour at three units, each addressing a different operational question:
+
+- *Per comparison.* For a randomly drawn pair of signatures from different CPAs, what fraction satisfies the rule (cos $>$ cos\_threshold and / or dHash $\leq$ dHash\_threshold)? This is the unit at which v3.x §IV-I characterised the cosine threshold's specificity behaviour and at which threshold-derivation in biometric verification is conventionally calibrated. We report it for both the cosine and dHash dimensions, marginally and jointly (§III-L.1).
+- *Per signature pool.* For a Big-4 source signature $s$ with same-CPA pool of size $n_{\text{pool}}(s)$, what is the probability that the deployed rule fires *under the counterfactual* of replacing the source's same-CPA pool with $n_{\text{pool}}(s)$ random non-same-CPA candidates? This addresses the standard concern that a per-pair rate computed on independent pairs is not the deployed-rule rate at the per-signature classifier level: the deployed rule takes max-cosine and min-dHash over a pool of size $n_{\text{pool}}(s)$, so its effective coincidence rate is approximately $1 - (1 - p_{\text{pair}})^{n_{\text{pool}}}$ in the independence limit (§III-L.2).
+- *Per document.* For an audit report aggregated via the worst-case rule, what fraction of documents have at least one signature whose deployed pool-normalised rule fires under the same inter-CPA candidate-replacement counterfactual? This is the operational alarm-rate unit (§III-L.3).
+
+**Any-pair vs same-pair semantics.** The deployed rule uses independent extrema: a signature satisfies the HC rule if $\max_{\text{pool}} \text{cos} > 0.95$ AND $\min_{\text{pool}} \text{dHash} \leq 5$, *not* if a single candidate in the pool satisfies both. We refer to this as the **any-pair** rule. A stricter alternative — the **same-pair** rule — requires a single candidate to satisfy both inequalities; the deployed v3/v4 rule is any-pair, but we report same-pair as a stricter alternative classifier where useful (§III-L.2, §III-L.4).
+
+**Terminological note on "FAR".** The v3.x and biometric-verification literature speak of "False Acceptance Rate" (FAR) for a per-pair rate computed on independent inter-CPA pairs. We adopt **inter-CPA coincidence rate (ICCR)** as the v4.0 metric name and *do not* use "FAR" in the manuscript prose, for two reasons: (a) FAR has a specific biometric-verification meaning that requires ground-truth negative labels (which the corpus does not provide at the signature level); (b) §III-L.4 shows that the inter-CPA negative-anchor assumption — that inter-CPA pairs are negative — is partially violated by within-firm cross-CPA template-like collision structures. Reading "inter-CPA coincidence rate" as a *specificity proxy* under an explicitly disclosed assumption is faithful to the evidence; reading it as a true biometric FAR would overstate the evidence. We retain the v3.x numerical results (which are quantitatively reproduced in §III-L.1) under the new terminology.
+
+### L.1. Per-comparison inter-CPA coincidence rate (Script 40b)
+
+We sample $5 \times 10^5$ inter-CPA pairs uniformly at random from Big-4 signatures, computing for each pair the cosine similarity (feature dot product) and Hamming distance between the dHash byte vectors. Marginal and joint rates at threshold $k$ are reported with Wilson 95% confidence intervals (Script 40b).
+
+| Threshold | Per-comparison inter-CPA coincidence rate | 95% Wilson CI |
+|---|---|---|
+| Cosine $> 0.95$ | $0.00060$ | $[0.00053, 0.00067]$ |
+| Cosine $> 0.945$ (v3.x published "natural threshold") | $0.00081$ | $[0.00073, 0.00089]$ |
+| Cosine $> 0.97$ | $0.00024$ | $[0.00020, 0.00029]$ |
+| Cosine $> 0.98$ | $0.00009$ | $[0.00007, 0.00012]$ |
+| dHash $\leq 5$ | $0.00129$ | $[0.00120, 0.00140]$ |
+| dHash $\leq 4$ | $0.00050$ | $[0.00044, 0.00057]$ |
+| dHash $\leq 3$ | $0.00019$ | $[0.00015, 0.00023]$ |
+| dHash $\leq 2$ | $0.00006$ | $[0.00004, 0.00008]$ |
+| Joint: cos $> 0.95$ AND dHash $\leq 5$ | $0.00014$ | (any-pair semantics) |
+| Joint: cos $> 0.95$ AND dHash $\leq 4$ | $0.00011$ | (any-pair semantics) |
+
+The cosine row at $\text{cos} > 0.95$ replicates the v3.x §IV-I Table X result (v3.x reported the per-comparison rate as $0.0005$ under prior "FAR" terminology from a similarly-sized inter-CPA negative anchor; the v4 spike on a $5 \times 10^5$-pair sample yields $0.00060$, within the v3.x reported precision). The dHash and joint rows are v4-new: v3.x calibration did not provide an inter-CPA pair-level coincidence rate for the structural dimension or the joint rule.
+
+The all-firms-scope sample yields slightly lower per-comparison coincidence rates (cos $> 0.95$: $0.00031$; dHash $\leq 5$: $0.00073$; joint: $0.00007$); the all-firms sample weights small CPAs more heavily under CPA-uniform pair sampling, so we treat the Big-4 sample as the primary calibration scope and report all-firms as a corroborating-scope robustness check.
+
+**Conditional inter-CPA coincidence rate.** A natural follow-up question is whether the dHash dimension provides marginal specificity beyond the cosine gate. For pairs with cos $> 0.95$, the conditional rate of dHash $\leq 5$ is $0.234$ (Wilson 95% CI $[0.190, 0.285]$; $70$ of $299$ pairs in the Big-4 sample). At cos $> 0.95$, dHash provides $\sim 4.3\times$ further per-comparison specificity (joint $0.00014$ vs cos-only $0.00060$).
+
+The per-comparison rate is a useful *specificity-proxy calibration* for the deployed rule's pair-level behaviour. It does *not* directly translate to the deployed-rule specificity at the per-signature classifier level, because the deployed classifier takes extrema over a same-CPA pool of size $n_{\text{pool}}$. The pool-normalised inter-CPA alert rate is reported in §III-L.2.
+
+### L.2. Pool-normalised inter-CPA alert rate (Script 43)
+
+The deployed rule uses $\max_{\text{pool}} \text{cos}$ and $\min_{\text{pool}} \text{dHash}$ over the same-CPA pool of size $n_{\text{pool}}(s)$ for each signature $s$. A per-comparison rate is therefore not the rate at which the deployed classifier fires per signature. To compute the per-signature inter-CPA-equivalent rate, for each Big-4 source signature $s$ we simulate one realisation of an inter-CPA candidate pool of the same size $n_{\text{pool}}(s)$, drawn uniformly from non-same-CPA signatures across all firms, compute the deployed extrema and rule indicator, and aggregate (Script 43; $n_{\text{sig}} = 150{,}453$ vector-complete in this analysis; CPA-block bootstrap 95% CIs reported below).
+
+**Headline rates (deployed any-pair rule, HC = cos $> 0.95$ AND dHash $\leq 5$).** Wilson 95% CIs on the point estimate, CPA-block bootstrap 95% CI on $n_{\text{boot}} = 1000$ replicates:
+
+| Rule semantics | Per-signature ICCR | Wilson 95% CI | CPA-bootstrap 95% CI |
+|---|---|---|---|
+| Any-pair (deployed) | $0.1102$ | $[0.1086, 0.1118]$ | $[0.0908, 0.1330]$ |
+| Same-pair (stricter alternative) | $0.0827$ | $[0.0813, 0.0841]$ | $[0.0668, 0.1021]$ |
+
+Per-firm any-pair rates (no bootstrap; descriptive):
+
+| Firm | $n_{\text{sig}}$ | Any-pair ICCR | Same-pair ICCR |
+|---|---|---|---|
+| Firm A | $60{,}450$ | $0.2594$ | $0.2018$ |
+| Firm B | $34{,}254$ | $0.0147$ | $0.0023$ |
+| Firm C | $38{,}616$ | $0.0053$ | $0.0019$ |
+| Firm D | $17{,}133$ | $0.0110$ | $0.0051$ |
+
+**Pool-size decile dependence.** The deployed rule's pool-normalised rate is monotonically (broadly) increasing in $n_{\text{pool}}$, consistent with the $1 - (1 - p_{\text{pair}})^{n_{\text{pool}}}$ form expected under inter-CPA independence (Script 43 decile table). Decile 1 (smallest pools, $n_{\text{pool}} \in [0, 201]$): any-pair ICCR $= 0.0249$. Decile 10 (largest, $n_{\text{pool}} \in [846, 1115]$): any-pair ICCR $= 0.1905$. The trend is broadly monotonic with two minor non-monotone reversals (decile 5 and decile 9 dip below their predecessors).
+
+**Threshold sensitivity at per-signature unit.** Tightening the HC rule from $\text{dHash} \leq 5$ to $\text{dHash} \leq 3$ (same-pair) reduces the per-signature ICCR from $0.0827$ to $0.0449$ (Big-4 pooled); tightening to $\text{dHash} \leq 4$ gives $0.0639$ (same-pair). Stakeholders requiring a per-signature ICCR of $\leq 0.05$ at HC can adopt dHash $\leq 3$ same-pair as a stricter operating point; at $\leq 0.10$ the inherited HC any-pair rule with $\text{dHash} \leq 5$ at $0.1102$ is within tolerance.
+
+### L.3. Document-level inter-CPA proxy alert rate (Script 45)
+
+The deployed worst-case aggregation classifies each document by the most-replication-consistent category among its constituent signatures (§III-L.0). Three operationally meaningful document-level alarm definitions are reported, each as the fraction of documents whose worst-case signature category falls in the alarm set under the same inter-CPA candidate-pool counterfactual as §III-L.2 (Script 45; $n_{\text{docs}} = 75{,}233$ Big-4 documents):
+
+| Alarm definition | Alarm set | Document-level ICCR | Wilson 95% CI |
+|---|---|---|---|
+| D1 | HC only | $0.1797$ | $[0.1770, 0.1825]$ |
+| D2 | HC + MC ("any non-hand-signed verdict") | $0.3375$ | $[0.3342, 0.3409]$ |
+| D3 | HC + MC + HSC | $0.3384$ | $[0.3351, 0.3418]$ |
+
+Per-firm D2 document-level rates:
+
+| Firm | $n_{\text{docs}}$ | D2 (HC + MC) ICCR |
+|---|---|---|
+| Firm A | $30{,}226$ | $0.6201$ |
+| Firm B | $17{,}127$ | $0.1600$ |
+| Firm C | $19{,}501$ | $0.1635$ |
+| Firm D | $8{,}379$ | $0.0863$ |
+
+The document-level D2 rate of $33.75\%$ pooled over Big-4 is the most operationally relevant alarm-rate metric: it is the fraction of audit documents that would carry at least one signature flagged HC or MC under the counterfactual of inter-CPA candidate-pool replacement. The non-trivial per-document inter-CPA alarm rate (and its concentration in Firm A at $62\%$) motivates the positioning of the operational system as a **screening framework with human-in-the-loop review**, not as an autonomous forensic classifier (§III-M).
+
+### L.4. Firm heterogeneity (Script 44)
+
+§III-L.2 and §III-L.3 report large per-firm variation in the deployed rule's pool-normalised behaviour: Firm A's any-pair per-signature ICCR is $0.2594$, an order of magnitude larger than Firm B's $0.0147$, Firm C's $0.0053$, Firm D's $0.0110$. A natural alternative explanation is the pool-size confound: Firm A's median pool size ($\sim 285$) is larger than other firms', and pool size monotonically (broadly) increases the per-signature rate (§III-L.2 decile trend). We test the firm-vs-pool confound with a logistic regression of the per-signature hit indicator (any-pair HC) on firm dummies (Firm A = reference) and centred log pool size (Script 44):
+
+| Term | Odds ratio (vs Firm A) | Direction | Magnitude |
+|---|---|---|---|
+| Firm B | $0.053$ | $< 1$ | $\sim 19\times$ lower odds than Firm A |
+| Firm C | $0.010$ | $< 1$ | $\sim 100\times$ lower odds than Firm A |
+| Firm D | $0.027$ | $< 1$ | $\sim 37\times$ lower odds than Firm A |
+| log(pool size, centred) | $4.01$ | $> 1$ | $\sim 4\times$ higher odds per unit log pool size |
+
+The Firm B/C/D odds ratios are very small after controlling for pool size, indicating that firm membership accounts for a large multiplicative effect on the per-signature rate that is *not* explained by pool size alone. (We report odds ratios rather than $z$-scores because per-signature observations are clustered by CPA and firm, and naive standard errors would be inflated by within-cluster correlation; a cluster-robust standard error analysis is left as a robustness check.)
+
+The per-decile per-firm breakdown (Script 44) confirms the pattern: within every pool-size decile, Firms B/C/D have rates of $0.0006$–$0.0358$, while Firm A's rate ranges $0.0541$–$0.5958$ across deciles. The firm gap is large within matched pool sizes, not driven by pool composition.
+
+**Cross-firm hit matrix.** Among Big-4 source signatures whose any-pair rule fires under the inter-CPA candidate-pool counterfactual, the candidate firm of the max-cosine partner is distributed as follows (Script 44):
+
+| Source firm | Firm A candidate | Firm B | Firm C | Firm D | non-Big-4 | hits |
+|---|---|---|---|---|---|---|
+| Firm A | $14{,}447$ | $95$ | $44$ | $19$ | $17$ | $14{,}622$ |
+| Firm B | $92$ | $371$ | $8$ | $4$ | $9$ | $484$ |
+| Firm C | $16$ | $7$ | $149$ | $5$ | $1$ | $178$ |
+| Firm D | $22$ | $2$ | $6$ | $106$ | $1$ | $137$ |
+
+For the same-pair joint event (a single candidate satisfying both $\text{cos} > 0.95$ and $\text{dHash} \leq 5$), the candidate firm is even more strongly concentrated within the source firm: Firm A source $\to$ Firm A candidate in $11{,}314$ of $11{,}319$ same-pair hits ($99.96\%$); Firm B source $\to$ Firm B candidate in $85$ of $87$ ($97.7\%$); Firm C source $\to$ Firm C candidate in $54$ of $55$ ($98.2\%$); Firm D source $\to$ Firm D candidate in $64$ of $66$ ($97.0\%$).
+
+**Interpretation.** The cross-firm hit matrix shows that nearly all inter-CPA collisions under the deployed rule originate from candidates within the source firm (different CPA, same firm). This pattern is consistent with — but not by itself diagnostic of — firm-specific template, stamp, or document-production reuse: within-firm scanning workflows, common form templates, and shared report-generation infrastructure could produce visually similar signature crops across different CPAs within the same firm. The byte-level evidence of v3.x §IV-F.1 (Firm A's $145$ pixel-identical signatures across $\sim 50$ distinct certifying partners) provides direct evidence that firm-level template reuse does occur at Firm A; the broader inter-CPA collision pattern in §III-L.4 is consistent with that mechanism extending in milder form to Firms B/C/D. We report this as "inter-CPA collision concentration is within-firm" — a descriptive observation about deployed-rule behaviour — and refrain from inferring that the within-firm hits constitute deliberate or systematic template sharing.
+
+This connects back to §III-J: the K=3 firm-composition contrast at the accountant level (Firm A dominating C3; Firm C dominating C1) reappears at the deployment level in the cross-firm hit matrix, where nearly all collisions are within-firm. The K=3 partition and the cross-firm hit matrix describe the same underlying firm-compositional structure at two different units of analysis.
+
+### L.5. Alert-rate sensitivity around inherited thresholds (Script 46)
+
+To test whether the inherited cosine threshold $0.95$ and dHash threshold $5$ coincide with a low-gradient (plateau-stable) region of the deployed-rule alert-rate surface — which would be weak distributional evidence that the inherited thresholds are stable operating points — we sweep each threshold across a range and report the per-signature alert rate on actual observed Big-4 same-CPA pools (not inter-CPA-replaced pools), comparing the local gradient at the inherited threshold to the median gradient across the sweep (Script 46).
+
+At the inherited HC operating point cos $> 0.95$ AND dHash $\leq 5$, the local gradient of the per-signature alert rate is substantially larger than the median gradient across the sweep (cosine: ratio $\approx 25\times$ at the $0.95$ point relative to median; dHash: ratio $\approx 3.8\times$ at the $5$ point relative to median; both Script 46). Reading these ratios descriptively, the inherited HC threshold is *locally sensitive* rather than plateau-stable: small threshold perturbations materially change the deployed alert rate (cosine sweep at dHash $\leq 5$ yields rates of $0.5091$ at cos $> 0.945$ vs $0.4789$ at cos $> 0.955$, a $3.0$ pp swing across a $0.01$ cosine perturbation; dHash sweep at cos $> 0.95$ yields rates of $0.4207$ at dHash $\leq 4$ vs $0.5639$ at dHash $\leq 6$, a $14.3$ pp swing across a single integer step). The local-gradient-to-median-gradient ratios are descriptive diagnostics, not formal plateau tests; the primary evidence for "no within-population bimodal antimode at these thresholds" comes from §III-I.4's composition decomposition, not from §III-L.5.
+
+The MC/HSC boundary at dHash $= 15$, by contrast, *is* in a low-gradient region (ratio $\approx 0.08$ to the median); the plateau-like behaviour around dHash $= 15$ is corroborating evidence that the high-end structural threshold lies in a regime where the rule's alert rate is approximately saturated, consistent with the high-dHash tail behaviour expected once near-identical pairs have been exhausted. The §III-L.5 non-plateau / local-sensitivity finding therefore applies specifically to the HC cutoff (cos $= 0.95$, dHash $= 5$); the MC/HSC sub-band boundary at dHash $= 15$ exhibits the opposite behaviour and is plateau-like.
+
+We interpret the inherited HC thresholds as **specificity-anchored operating points** chosen for the specificity-vs-alert-yield tradeoff (§III-L.1), *not* as distributional antimodes. Stakeholders requiring different operating points on the tradeoff curve can derive thresholds by inverting the per-comparison or pool-normalised ICCR curves (§III-L.1, §III-L.2) at their preferred specificity target.
+
+### L.6. Observed deployed alert rate on actual same-CPA pools
+
+The pool-normalised inter-CPA rates of §III-L.2 and §III-L.3 use the counterfactual of replacing the source signature's same-CPA pool with random non-same-CPA candidates. The **observed deployed alert rate** uses the source's actual same-CPA pool, i.e., the rate at which the deployed rule fires on the real corpus. For Big-4, the inherited HC any-pair rule fires on $49.58\%$ of signatures and $62.28\%$ of documents (Script 46; Script 42 reproduces the per-signature rate at $49.58\%$).
+
+The per-signature observed-deployed rate is $\sim 4.5\times$ the pool-normalised inter-CPA rate ($0.4958$ vs $0.1102$); the per-document observed-deployed rate is $\sim 3.5\times$ the pool-normalised inter-CPA D1 (HC) rate ($0.6228$ vs $0.1797$). We refer to this multiplicative gap as the **deployed-rate excess over the inter-CPA proxy**:
+
+- Per-signature: $0.4958 - 0.1102 = 0.3856$ ($38.6$ pp excess)
+- Per-document HC: $0.6228 - 0.1797 = 0.4431$ ($44.3$ pp excess)
+
+We *do not* interpret the deployed-rate excess as a presumed true-positive rate; the inferential limits of this interpretation are developed in §III-M. The deployed-rate excess is best read as a *same-CPA repeatability signal* — a quantity that exceeds what random inter-CPA candidate replacement would produce — rather than as an estimate of true replication prevalence.
+
+### L.7. K=3 not used as classifier
+
+The K=3 mixture of §III-J is reported in §IV as an accountant-level descriptive summary alongside the per-signature five-way classifier. We do not assign signature-level or document-level labels from the K=3 mixture in any v4.0 result table; the K=3 hard label is used only for the accountant-level firm × cluster cross-tabulation (§III-J; Script 35), and the K=3 *posterior* P(C1) is used (as the continuous Score 1) in the internal-consistency Spearman correlations of §III-K. The operational classifier of §III-L.0 is the inherited v3.x five-way box rule; the calibration evidence in §III-L.1 through §III-L.6 characterises its multi-level coincidence behaviour against the inter-CPA negative anchor.
+
+## M. Validation Strategy and Limitations under Unsupervised Setting
+
+The v4.0 corpus lacks signature-level ground-truth replication labels: no signature is annotated as definitively hand-signed or definitively templated. The conservative positive anchor (pixel-identical same-CPA signatures; §III-K.4 and v3.x §IV-F.1) is by construction near $\text{cos} = 1$ and $\text{dHash} = 0$, providing a tautological capture-check rather than a sensitivity estimate for the non-byte-identical replicated class. The corpus therefore does not admit standard supervised classifier validation: we cannot report False Rejection Rate, sensitivity, recall, Equal Error Rate, ROC-AUC, or precision against ground truth.
+
+In place of supervised validation, v4.0 adopts a **multi-tool collection of partial-evidence diagnostics**, each with an explicitly disclosed assumption:
+
+| Tool | What it measures | Untested assumption |
+|---|---|---|
+| Per-comparison inter-CPA coincidence rate (§III-L.1; Script 40b) | Pair-level specificity proxy under a random-pair negative anchor | Inter-CPA pairs are negative (i.e., not template-related); partially violated by within-firm sharing (§III-L.4) |
+| Pool-normalised per-signature ICCR (§III-L.2; Script 43) | Deployed-rule specificity proxy at per-signature unit, accounting for pool size | Same as above + that pool replacement preserves the negative-anchor property |
+| Document-level ICCR (§III-L.3; Script 45) | Operational alarm rate proxy at per-document unit under three alarm definitions | Same as above |
+| Firm-heterogeneity logistic regression (§III-L.4; Script 44) | Multiplicative effect of firm membership on per-signature rate, controlling for pool size | Per-signature observations are clustered by CPA/firm; naïve standard errors inflated; cluster-robust analysis is a future check |
+| Cross-firm hit matrix (§III-L.4; Script 44) | Concentration of inter-CPA collisions within source firm | None — direct descriptive observation |
+| Alert-rate sensitivity sweep (§III-L.5; Script 46) | Local sensitivity of deployed rule to threshold perturbation | Gradient comparison is descriptive, not a formal plateau test |
+| Convergent score Spearman ranking (§III-K.1; Script 38) | Internal-consistency of three feature-derived per-CPA scores | Scores share underlying inputs and are not statistically independent |
+| Pixel-identical conservative positive capture (§III-K.4; v3.x; Script 40) | Trivial sanity check on the conservative positive anchor | Anchor is tautologically captured by any reasonable threshold |
+| LOOO firm-level reproducibility (§III-K.3; Scripts 36, 37) | Algorithmic stability of K=2 / K=3 partition across firm folds | Stability is necessary but not sufficient for classification validity |
+
+No single tool in this collection provides ground-truth validation. Their conjunction constitutes the unsupervised validation ceiling that the v4.0 corpus admits.
+
+**What v4.0 does not claim.** We do not claim a validated forensic detector or an autonomous classification system. We do not report False Rejection Rate, sensitivity, recall, EER, ROC-AUC, precision, or positive predictive value against ground truth, because no ground truth exists at the signature level. We do not interpret the deployed-rate excess of §III-L.6 as a presumed true-positive rate: that interpretation would require assuming that the within-firm same-CPA pool's collision rate equals the inter-CPA proxy rate in the absence of replication (i.e., that genuine same-CPA hand-signing would produce a collision rate no higher than random inter-CPA pairs). Two factors make the assumption unsafe: (a) a CPA who signs consistently can produce stylistically similar signatures across years that exceed inter-CPA similarity at the cosine axis; (b) within-firm template sharing (§III-L.4 cross-firm hit matrix; v3.x byte-level evidence of Firm A's pixel-identical signatures across partners) places a substantial inter-CPA collision floor that itself reflects template-like reuse rather than independent inter-CPA random matching. We do not infer that the within-firm collision concentration of §III-L.4 constitutes deliberate template sharing; we describe it as "inter-CPA collision concentration is within-firm" and treat the mechanism as an open empirical question.
+
+**What v4.0 does claim.** The deployed signature-replication screening rule is characterised at three units of analysis (per-comparison, per-signature pool, per-document) against an inter-CPA negative-anchor coincidence-rate calibration. The per-comparison rates ($\leq 0.0006$ at cos $> 0.95$; $\leq 0.0013$ at dHash $\leq 5$; $\leq 0.00014$ jointly) are specificity-proxy-anchored operating points consistent with biometric-verification convention, with the proxy nature recorded in §III-L.0 and §III-M. The per-signature and per-document rates ($0.11$ and $0.34$ respectively under the deployed any-pair HC + MC alarm) are operationally meaningful **alarm-yield** indicators rather than true error rates. Per-firm rates show substantial heterogeneity (Firm A's per-document HC + MC alarm at $0.62$ vs Firm B/C/D at $0.09$–$0.16$), driven by firm-level rather than pool-size effects, and concentrated in within-firm cross-CPA candidate matching. The framework is positioned as a **specificity-proxy-anchored screening tool with human-in-the-loop review**, not as a validated forensic classifier.
+
+**Specificity-alert-yield tradeoff.** Because sensitivity is unobservable, stakeholders cannot derive an operating point by optimising a ROC criterion. Instead, the specificity-proxy-anchored framework offers a *specificity-alert-yield tradeoff*: tighter operating points (e.g., cos $> 0.98$ AND dHash $\leq 3$) reduce both per-comparison ICCR (to $\approx 5 \times 10^{-5}$; §III-L.1 inversion) and per-signature alert yield (to $\approx 0.05$; §III-L.2), with an unknown effect on actual replication-detection recall. Tighter operating points are not necessarily preferable: any tightening reduces the alert rate but may also miss true replicated signatures whose noise has pushed them outside the tighter envelope. The deployment decision depends on the relative cost of manual review (per alarm) and missed-replication risk (per false negative) — neither directly observable from corpus data.
+
+---
+
+## Provenance table for key numerical claims in §III-G through §III-L
+
+The table below lists the principal numerical claims and their data-source scripts. The table is curated for primary results; supporting numbers used illustratively in prose (e.g., all-firms-scope corroborating rates, per-decile fold values, illustrative threshold-inversion examples) are documented in the corresponding spike-script JSON outputs at `reports/v4_big4/*/` and are not individually tabled here.
+
+| Claim | Value | Source | Notes |
+|---|---|---|---|
+| Big-4 CPA count, $n_{\text{sig}} \geq 10$ | $437$ ($171/112/102/52$) | Script 36 sample sizes; Script 38 per-firm summary | direct |
+| Big-4 signature count (descriptor-complete) | $150{,}442$ | Script 39 / 39b / 39d / 39e / 45 / 46 | analyses using pre-computed descriptors |
+| Big-4 signature count (vector-complete) | $150{,}453$ | Script 40b / 43 / 44 | analyses recomputing from feature + dHash vectors |
+| Non-Big-4 reference CPA count | $249$ | Script 38 reference population | direct |
+| Big-4 K=2 marginal crossings $(0.9755, 3.755)$ | direct | Script 34; Script 36 §A | direct |
+| Bootstrap 95% CI cosine $[0.9742, 0.9772]$ | direct | Script 34; Script 36 §A | $n_{\text{boot}} = 500$ |
+| Bootstrap 95% CI dHash $[3.48, 3.97]$ | direct | Script 34; Script 36 §A | $n_{\text{boot}} = 500$ |
+| Bootstrap CI half-width $0.0015$ (cos) | direct | Script 36 (mean of CI half-widths) | direct |
+| Dip-test Big-4 cosine $p < 5 \times 10^{-4}$ | direct | Script 34 reports $p = 0.0000$; we bound by bootstrap resolution $n_{\text{boot}} = 2000$ | reporting convention |
+| Dip-test Big-4 dHash $p < 5 \times 10^{-4}$ | direct | Script 34 | reporting convention |
+| Dip-test Firm A $(p_{\text{cos}} = 0.992, p_{\text{dHash}} = 0.924)$ | direct | Script 32 §`firm_A` | direct |
+| Dip-test `big4_non_A` $(0.998, 0.906)$ | direct | Script 32 §`big4_non_A` | direct |
+| Dip-test `all_non_A` $(0.998, 0.907)$ | direct | Script 32 §`all_non_A` | direct |
+| K=3 component centers / weights | $(0.9457, 9.17, 0.143)$ / $(0.9558, 6.66, 0.536)$ / $(0.9826, 2.41, 0.321)$ | Script 35 / Script 38 | direct |
+| $\Delta\text{BIC}(K{=}3, K{=}2) = -3.48$ | direct | Script 34 (BIC K=2 = $-1108.45$; Script 36 reports BIC K=3 = $-1111.93$) | direct (arithmetic) |
+| K=2 LOOO max cosine deviation $0.028$ | direct | Script 36 stability summary | direct |
+| K=2 LOOO Firm A held-out $171/171$ replicated | direct | Script 36 fold table | direct |
+| K=3 C1 component shape drift (cos $0.005$, dHash $0.96$, weight $0.023$) | direct | Script 37 stability summary | direct |
+| K=3 LOOO held-out C1 absolute differences $1.8$–$12.8$ pp | direct | Script 37 held-out prediction check | direct |
+| Three-score pairwise Spearman ($0.963$, $0.889$, $0.879$) | direct | Script 38 correlations | direct |
+| Per-CPA / per-signature K=3 Cohen $\kappa$ ($0.662$, $0.559$, $0.870$) | direct | Script 39 kappa table | direct |
+| Per-CPA / per-signature K=3 C1 center drift $0.018$ (cosine) | derived | $\lvert 0.9457 - 0.9280 \rvert$; Script 39 components | direct |
+| Pixel-identity Big-4 subset $n = 262$ ($145/8/107/2$) | direct | Script 40 sample | direct |
+| Full-dataset accountant count $n = 686$ | direct | Script 41 (`fulldataset_report.md`) | direct |
+| Positive-anchor miss rate $0\%$ on $n = 262$ (Wilson upper $1.45\%$) | direct | Script 40 results table | direct |
+| Inter-CPA cos $> 0.95$ ICCR $0.0005$ (Wilson 95% $[0.0003, 0.0007]$) | inherited | v3 §IV-F.1 / Table X | v3 reported this as "FAR"; v4.0 reframes as inter-CPA coincidence rate per §III-L.0 |
+| Firm A byte-identical $145$ pixel-identical signatures in Big-4 subset | direct | Script 40 sample breakdown | direct |
+| Firm A byte-identical "50 distinct partners of 180; 35 cross-year" | inherited | v3 §IV-F.1 / Script 28 / Appendix B byte-decomposition output | **inherited from v3; not regenerated in v4.0 spike scripts** |
+| Big-4 K=3 per-firm C1 hard-assignment ($0\%$ / $8.9\%$ / $23.5\%$ / $11.5\%$) | direct | Script 35 firm × cluster cross-tab | direct |
+| **Composition decomposition (§III-I.4):** | | | |
+| Within-firm signature-level dip $p_{\text{cos}}$ Big-4 (A/B/C/D) | $0.176 / 0.991 / 0.551 / 0.976$ | Script 39b per-firm | direct, $n_{\text{boot}} = 2000$ |
+| Within-firm signature-level dip $p_{\text{cos}}$ non-Big-4 (10 firms, range) | $[0.59, 0.99]$ | Script 39c per-firm | direct, firms with $\geq 500$ signatures |
+| Within-firm jittered-dHash dip $p$ Big-4 (5 seeds, median) A/B/C/D | $0.999 / 0.996 / 0.999 / 0.9995$ | Script 39d multi-seed | uniform jitter $[-0.5, +0.5]$ |
+| Within-firm jittered-dHash dip $p$ non-Big-4 (5 seeds, range across 10 firms) | $[0.71, 1.00]$ | Script 39d / 39c | uniform jitter $[-0.5, +0.5]$ |
+| Big-4 pooled dHash dip $p$ raw / jittered (seed median) | $< 5 \times 10^{-4}$ / $< 5 \times 10^{-4}$ | Script 39d | jitter alone does not eliminate Big-4 pooled rejection |
+| Big-4 pooled dHash dip $p$ firm-centred + jittered (5-seed median) | $0.35$ | Script 39e 2×2 factorial | both corrections eliminate rejection ($0/5$ seeds at $\alpha = 0.05$) |
+| Big-4 firm-centred signature-level cos dip $p$ | $0.597$ | codex round-30 verification on Script 43 substrate | independent verification |
+| Big-4 firm-centred accountant-level cos\_mean dip $p$ | $1.0$ | codex round-30 verification | independent verification |
+| Per-firm Big-4 dHash mean (A/B/C/D) | $2.73 / 6.46 / 7.39 / 7.21$ | Script 39e per-firm summary | direct |
+| Big-4 integer-histogram valley near $\text{dHash} \approx 5$ within any firm | none in any of A/B/C/D | Script 39d valley analysis | bins $0$–$20$ |
+| **Anchor-based calibration (§III-L.1):** | | | |
+| Per-comparison ICCR cos $> 0.95$ Big-4 | $0.00060$ (Wilson 95% $[0.00053, 0.00067]$) | Script 40b | $5 \times 10^5$ inter-CPA pairs, Big-4 scope |
+| Per-comparison ICCR cos $> 0.945$ Big-4 | $0.00081$ (Wilson 95% $[0.00073, 0.00089]$) | Script 40b | direct |
+| Per-comparison ICCR cos $> 0.97$ / cos $> 0.98$ Big-4 | $0.00024$ / $0.00009$ | Script 40b | direct |
+| Per-comparison ICCR dHash $\leq 5$ Big-4 | $0.00129$ (Wilson 95% $[0.00120, 0.00140]$) | Script 40b | direct, v4 new |
+| Per-comparison ICCR dHash $\leq 4 / 3 / 2$ Big-4 | $0.00050 / 0.00019 / 0.00006$ | Script 40b | direct |
+| Per-comparison joint ICCR cos $> 0.95$ AND dHash $\leq 5$ Big-4 | $0.00014$ | Script 40b | any-pair semantics |
+| Per-comparison joint ICCR cos $> 0.95$ AND dHash $\leq 4$ Big-4 | $0.00011$ | Script 40b | any-pair semantics |
+| Conditional ICCR dHash $\leq 5$ given cos $> 0.95$ Big-4 | $0.234$ (Wilson 95% $[0.190, 0.285]$) | Script 40b | $70 / 299$ pairs |
+| All-firms per-comparison joint ICCR | $0.00007$ | Script 40b | corroborating scope |
+| **Pool-normalised per-signature alert rate (§III-L.2):** | | | |
+| Per-signature any-pair ICCR HC Big-4 | $0.1102$ (Wilson 95% $[0.1086, 0.1118]$; CPA-bootstrap 95% $[0.0908, 0.1330]$) | Script 43 | $n_{\text{sig}} = 150{,}453$ (vector-complete) |
+| Per-signature same-pair ICCR HC Big-4 | $0.0827$ (Wilson 95% $[0.0813, 0.0841]$; CPA-bootstrap 95% $[0.0668, 0.1021]$) | Script 43 | stricter alternative |
+| Per-firm any-pair ICCR HC (A/B/C/D) | $0.2594 / 0.0147 / 0.0053 / 0.0110$ | Script 43 per-firm | direct |
+| Per-firm same-pair ICCR HC (A/B/C/D) | $0.2018 / 0.0023 / 0.0019 / 0.0051$ | Script 43 per-firm | direct |
+| Pool-size decile 1 / decile 10 any-pair ICCR | $0.0249 / 0.1905$ | Script 43 decile table | broadly monotone with two minor reversals |
+| Per-signature tighter ICCR cos $> 0.95$ AND dHash $\leq 3$ same-pair Big-4 | $0.0449$ | Script 43 | optional stricter operating point |
+| **Document-level alert rate (§III-L.3):** | | | |
+| Document-level ICCR D1 (HC only) Big-4 | $0.1797$ (Wilson 95% $[0.1770, 0.1825]$) | Script 45 | $n_{\text{docs}} = 75{,}233$ |
+| Document-level ICCR D2 (HC + MC) Big-4 | $0.3375$ (Wilson 95% $[0.3342, 0.3409]$) | Script 45 | operational alarm definition |
+| Document-level ICCR D3 (HC + MC + HSC) Big-4 | $0.3384$ (Wilson 95% $[0.3351, 0.3418]$) | Script 45 | descriptive |
+| Per-firm document-level D2 ICCR (A/B/C/D) | $0.6201 / 0.1600 / 0.1635 / 0.0863$ | Script 45 per-firm | direct |
+| **Firm-heterogeneity logistic regression (§III-L.4):** | | | |
+| Logistic OR (Firm B / C / D vs A) | $0.053 / 0.010 / 0.027$ | Script 44 regression | controlling for log pool size; reference $=$ Firm A |
+| Logistic OR log(pool size, centred) | $4.01$ | Script 44 regression | pool-size effect after firm adjustment |
+| Cross-firm hit matrix Firm A source $\to$ Firm A candidate (any-pair) | $14{,}447 / 14{,}622$ | Script 44 cross-firm matrix | $98.8\%$ within-firm |
+| Cross-firm hit matrix same-pair within-firm rate (A/B/C/D) | $99.96\% / 97.7\% / 98.2\% / 97.0\%$ | Script 44 same-pair section | direct |
+| **Threshold-sensitivity (§III-L.5):** | | | |
+| Local / median gradient ratio cos $= 0.95$ | $\approx 25\times$ | Script 46 plateau diagnostic | descriptive, not formal plateau test |
+| Local / median gradient ratio dHash $= 5$ | $\approx 3.8\times$ | Script 46 plateau diagnostic | descriptive |
+| Local / median gradient ratio dHash $= 15$ | $\approx 0.08$ | Script 46 plateau diagnostic | MC/HSC boundary plateau-like |
+| **Observed deployed alert rate (§III-L.6):** | | | |
+| Per-signature observed-deployed HC rate Big-4 | $0.4958$ | Script 46 / Script 42 | actual same-CPA pools |
+| Per-document observed-deployed HC rate Big-4 | $0.6228$ | Script 46 | actual same-CPA pools |
+| Deployed-rate excess over inter-CPA proxy (per-sig HC) | $0.3856$ pp | derived | $0.4958 - 0.1102$ |
+| Deployed-rate excess over inter-CPA proxy (per-doc HC) | $0.4431$ pp | derived | $0.6228 - 0.1797$ |
+| **Sample-size reconciliation:** | | | |
+| Big-4 signatures with pre-computed descriptors | $150{,}442$ | Script 39 / 39b / 39d / 39e / 45 / 46 | descriptor-complete subset |
+| Big-4 signatures with feature + dHash vectors stored | $150{,}453$ | Script 40b / 43 / 44 | vector-complete subset |
+| Difference between the two counts | $11$ signatures | direct (descriptor-completion lag) | negligible at population scale |
+| Big-4 CPAs all (any signature count) | $468$ | Script 40b / 43 / 44 | direct |
+| Big-4 CPAs with $n_{\text{sig}} \geq 10$ for accountant-level stability | $437$ | Scripts 36 / 38 / 39 | accountant-level analysis threshold |
+
+---
+
+## Cross-reference index (author working checklist; remove before submission)
+
+- **Big-4 sub-corpus definition** (§III-G) — 437 CPAs / $n_{\text{sig}} \geq 10$ at accountant-level, 468 CPAs / 150,442–150,453 signatures at signature-level (sample-size reconciliation in §III-G).
+- **Reference populations** (§III-H) — Firm A as templated-end case study; non-Big-4 ($n = 249$) as reverse-anchor reference (less-replicated population).
+- **Distributional diagnostics + composition decomposition** (§III-I) — Big-4 accountant-level dip-test rejection ($p < 5 \times 10^{-4}$); §III-I.4's 2×2 factorial decomposition (firm centring × integer jitter) shows the rejection is fully explained by between-firm location shift + integer mass-point artefacts; **no within-population bimodality and no natural threshold**.
+- **K=3 as descriptive firm-compositional partition** (§III-J) — C1/C2/C3 are descriptive positions on the descriptor plane reflecting Firm A vs others composition; not mechanism clusters; not used as operational classifier.
+- **Convergent internal-consistency** (§III-K) — three feature-derived scores ($\rho \geq 0.879$, not independent measurements); per-signature K=3 ($\kappa = 0.87$ vs per-CPA fit); K=2 LOOO unstable, K=3 LOOO partial; pixel-identity miss rate $0\%$ on $n = 262$.
+- **Anchor-based threshold calibration + operational classifier** (§III-L) — inherited five-way rule retained; characterised by inter-CPA negative-anchor coincidence rates at per-comparison (§III-L.1: cos $> 0.95$ at $0.0006$, dHash $\leq 5$ at $0.0013$, joint at $0.00014$), per-signature pool (§III-L.2: $0.11$ any-pair HC), per-document (§III-L.3: HC $0.18$; HC+MC $0.34$); firm heterogeneity (§III-L.4) decisive after pool-size adjustment; within-firm cross-CPA collision concentration $\geq 97\%$; threshold-sensitivity analysis (§III-L.5) confirms HC threshold is locally sensitive, not plateau-stable; deployed-rate excess over proxy (§III-L.6) $\approx 38$ pp per-signature and $\approx 44$ pp per-document.
+- **Validation strategy and limitations** (§III-M) — multi-tool diagnostic collection (9 tools, each with disclosed untested assumption); positioning as anchor-calibrated screening framework with human-in-the-loop review, not as validated forensic detector; no FRR / sensitivity / EER / ROC-AUC reportable.
+
+## Open questions remaining for partner / reviewer
+
+1. **Five-way rule validation against the moderate-confidence band.** §III-K's $\kappa$ evidence covers only the binary high-confidence rule (cos $> 0.95$ AND dHash $\leq 5$). The moderate-confidence band (cos $> 0.95$ AND $5 < \text{dHash} \leq 15$) inherits its v3.x calibration and capture-rate evidence (v3.20.0 Tables IX, XI, XII, XII-B). Is this inheritance sufficient (Big-4 per-firm MC proportions are reported descriptively in §IV-J's Table XV), or should v4.0 add a Big-4-specific MC-band capture-rate analysis as an additional sub-section?
+
+2. **Anonymisation of within-Big-4 firm contrasts.** §III-H states that Firm C is the firm most concentrated in C1 hand-leaning at $23.5\%$ (Script 35). The within-Big-4 ordering by hand-leaning concentration is informative for the §V discussion. v3.x reports under pseudonyms throughout. Confirm that we maintain pseudonyms consistently in §IV–V even when discussing the specific Firm C / Firm B / Firm D hand-leaning rates.
+
+3. **Section IV table numbering.** Defer until §III final accepted by partner / reviewer; results numbering should mirror §III flow (sample/scope → mixture characterisation → convergent checks → LOOO → pixel-identity → signature/document classification → full-dataset robustness).

paper/v4/paper_a_prose_v4_phase4.md

@@ -0,0 +1,162 @@
+# Paper A v4.0 Phase 4 Prose Draft v3 (post codex rounds 26–34)
+
+> **Draft note (2026-05-13, Phase 4 v3; internal — remove before submission).** This file replaces the v3.20.0 Abstract, §I Introduction, §II Related Work, §V Discussion, and §VI Conclusion blocks with the v4.0 prose. The methodology and results sections (§III v7 and §IV v3.2 on this branch) are the technical foundation; Phase 4 prose aligns the narrative with the post-codex-round-34 framing. v3 (2026-05-13) reflects the major restructuring driven by codex rounds 29–34: distributional path to thresholds demolished (Scripts 39b–39e); anchor-based multi-level inter-CPA coincidence-rate calibration adopted (Scripts 40b, 43, 44, 45, 46); K=3 demoted to descriptive firm-compositional partition; "FAR" terminology replaced by "inter-CPA coincidence rate (ICCR)" throughout; nine-tool unsupervised validation strategy disclosed; positioning as anchor-calibrated screening framework with human-in-the-loop review (not validated forensic detector). Empirical anchors cite Scripts 32–46 on branch `paper-a-v4-big4`. Prior Phase 4 v2 changelog has been moved to `paper/v4/CHANGELOG.md`.
+
+---
+
+# Abstract
+
+> *IEEE Access target: <= 250 words, single paragraph.*
+
+Regulations require Certified Public Accountants (CPAs) to attest each audit report with a signature, but digitization makes reusing a stored signature image across reports — through administrative stamping or firm-level electronic signing — technically trivial and visually invisible, undermining individualized attestation. We build an end-to-end pipeline detecting such *non-hand-signed* signatures at scale: a Vision-Language Model identifies signature pages, YOLOv11 localizes signatures, ResNet-50 supplies deep features, and a dual-descriptor layer combines cosine similarity with an independent-minimum perceptual hash (dHash) to separate *style consistency* from *image reproduction*. Applied to 90,282 Taiwan audit reports (2013–2023), the pipeline yields 182,328 signatures from 758 CPAs; primary analyses are scoped to the Big-4 sub-corpus (437 CPAs; 150,442 signatures). Distributional diagnostics show that the apparent multimodality of the descriptor distribution dissolves under joint firm-mean centring and integer-tie jitter ($p$ rises to $0.35$), so no within-population bimodal antimode anchors the operational thresholds. We instead adopt an anchor-based inter-CPA coincidence-rate (ICCR) calibration at three units: per-comparison ($0.0006$ at cos$>0.95$; $0.0013$ at dHash$\leq 5$; $0.00014$ jointly), pool-normalised per-signature ($0.11$ under the deployed any-pair high-confidence rule), and per-document ($0.34$ for the operational HC+MC alarm). Firm heterogeneity is decisive: Firm A's per-document HC+MC alarm rate is $0.62$ versus $0.09$–$0.16$ at Firms B/C/D after pool-size adjustment, with $98$–$100\%$ of inter-CPA collisions concentrated within the source firm — consistent with firm-level template-like reuse. We position the system as a specificity-proxy-anchored screening framework with human-in-the-loop review, not as a validated forensic detector; no calibrated error rates are reportable without signature-level ground truth.
+
+---
+
+# I. Introduction
+
+> *Target: ~1.5 pages double-column IEEE format. Double-blind: no author/institution info.*
+
+Financial audit reports serve as a critical mechanism for ensuring corporate accountability and investor protection. In Taiwan, the Certified Public Accountant Act (會計師法 §4) and the Financial Supervisory Commission's attestation regulations (查核簽證核准準則 §6) require certifying CPAs to affix their signature or seal (簽名或蓋章) to each audit report [1]. While the law permits either a handwritten signature or a seal, the CPA's attestation on each report is intended to represent a deliberate, individual act of professional endorsement for that specific audit engagement [2].
+
+The digitization of financial reporting has introduced a practice that complicates this intent. As audit reports are now routinely generated, transmitted, and archived as PDF documents, it is technically and operationally straightforward to reproduce a CPA's stored signature image across many reports rather than re-executing the signing act for each one. This reproduction can occur either through an administrative stamping workflow — in which scanned signature images are affixed by staff as part of the report-assembly process — or through a firm-level electronic signing system that automates the same step. We refer to signatures produced by either workflow collectively as *non-hand-signed*. Although this practice may fall within the literal statutory requirement of "signature or seal," it raises substantive concerns about audit quality, as an identically reproduced signature applied across hundreds of reports may not represent meaningful individual attestation for each engagement. The accounting literature has examined the audit-quality consequences of partner-level engagement transparency: studies of partner-signature mandates in the United Kingdom find measurable downstream effects [31], cross-jurisdictional evidence on individual partner signature requirements highlights similar quality channels [32], and Taiwan-specific evidence on mandatory partner rotation documents how individual-partner identification interacts with audit-quality outcomes [33]. Unlike traditional signature forgery, where a third party attempts to imitate another person's handwriting, non-hand-signing involves the legitimate signer's own stored signature being reused, and is visually invisible to report users at scale.
+
+The distinction between *non-hand-signing detection* and *signature forgery detection* is conceptually and technically important. The extensive body of research on offline signature verification [3]–[8] focuses almost exclusively on forgery detection — determining whether a questioned signature was produced by its purported author. In our context, identity is not in question; the CPA is indeed the legitimate signer. The question is whether the physical act of signing occurred for each individual report, or whether a single signing event was reproduced as an image across many reports. This detection problem differs fundamentally from forgery detection: while it does not require modeling skilled-forger variability, it introduces the distinct challenge of separating legitimate intra-signer consistency from image-level reproduction.
+
+A methodological concern shapes the research design. Many prior similarity-based classification studies rely on ad-hoc thresholds — declaring two images equivalent above a hand-picked cosine cutoff, for example — without principled statistical justification. Such thresholds are fragile in an archival-data setting. A defensible approach requires (i) explicit calibration of the operational thresholds against measurable negative-anchor evidence; (ii) diagnostic procedures that test whether the descriptor distribution itself supports a within-population threshold, including formal decomposition of apparent multimodality into between-group composition and integer-tie artefacts; (iii) annotation-free reporting of operational alarm rates at multiple analysis units (per-comparison, per-signature pool, per-document) with Wilson 95% confidence intervals; (iv) per-firm stratification of the reported rates to surface heterogeneity that aggregate metrics conceal; and (v) explicit disclosure of the unsupervised setting's limits — in particular, the inability to estimate true error rates without signature-level ground-truth labels.
+
+Despite the significance of the problem for audit quality and regulatory oversight, no prior work has specifically addressed non-hand-signing detection in financial audit documents at scale with these methodological safeguards. Woodruff et al. [9] developed an automated pipeline for signature analysis in corporate filings for anti-money-laundering investigations, but their work focused on author clustering rather than detecting image reuse. Copy-move forgery detection methods [10], [11] address duplicated regions within or across images but are designed for natural images and do not account for the specific characteristics of scanned document signatures. Research on near-duplicate image detection using perceptual hashing combined with deep learning [12], [13] provides relevant methodological foundations but has not been applied to document forensics or signature analysis. From the statistical side, the methods we adopt for distributional characterisation — the Hartigan dip test [37] and finite mixture modelling via the EM algorithm [40], [41], complemented by a Burgstahler-Dichev / McCrary density-smoothness diagnostic [38], [39] — have been developed in statistics and accounting-econometrics but have not been combined as a joint diagnostic toolkit for document-forensics threshold characterisation.
+
+In this paper we present a fully automated, end-to-end pipeline for detecting non-hand-signed CPA signatures in audit reports at scale, together with a multi-tool validation framework that explicitly discloses the unsupervised setting's limits. The pipeline processes raw PDF documents through (1) signature page identification with a Vision-Language Model; (2) signature region detection with a trained YOLOv11 object detector; (3) deep feature extraction via a pre-trained ResNet-50; (4) dual-descriptor similarity (cosine + independent-minimum dHash); (5) anchor-based threshold calibration at three units of analysis (per-comparison, pool-normalised per-signature, per-document) against an inter-CPA negative-anchor coincidence-rate proxy (§III-L); (6) firm-stratified per-rule reporting and a within-firm cross-CPA hit-matrix analysis (§III-L.4); (7) a composition decomposition that establishes the absence of a within-population bimodal antimode in the descriptor distributions (§III-I.4); and (8) a multi-tool unsupervised validation strategy with disclosed assumption-violation analysis (§III-M).
+
+The methodological reframing relative to earlier versions of this work is central to our v4.0 contribution. Earlier work in this lineage adopted a distributional path to thresholds — fitting accountant-level finite-mixture models and treating their marginal crossings as data-derived "natural" thresholds. v4.0 reports a composition decomposition diagnostic (§III-I.4) that overturns this reading: the apparent multimodality of the Big-4 accountant-level distribution is fully explained by between-firm location-shift effects (Firm A's mean dHash of $2.73$ versus Firms B/C/D's $6.46$, $7.39$, $7.21$) and integer mass-point artefacts on the integer-valued dHash axis. Once both confounds are removed (firm-mean centring plus uniform integer jitter), the Big-4 pooled dHash dip test yields $p_{\text{median}} = 0.35$ across five jitter seeds, eliminating the rejection. Within-firm signature-level cosine and jittered-dHash dip tests fail to reject in every individual Big-4 firm and in every individual mid/small firm with $\geq 500$ signatures (10 firms tested in Script 39c). The descriptor distributions therefore contain no within-population bimodal antimode that could anchor an operational threshold.
+
+In place of distributional anchoring, v4.0 adopts an anchor-based inter-CPA coincidence-rate (ICCR) calibration. At the per-comparison unit, the inherited cos$>0.95$ operating point yields ICCR $= 0.00060$ on a $5 \times 10^5$-pair Big-4 sample (replicating v3.x's reported per-comparison rate of $0.0005$ under prior "FAR" terminology); the dHash$\leq 5$ structural cutoff yields ICCR $= 0.00129$ (v4 new); the joint rule cos$>0.95$ AND dHash$\leq 5$ yields joint ICCR $= 0.00014$ (any-pair semantics, matching the deployed extrema rule). At the pool-normalised per-signature unit, the same rule's effective coincidence rate is materially higher because the deployed classifier takes max-cosine and min-dHash over a same-CPA pool: pooled Big-4 any-pair ICCR is $0.1102$ (Wilson 95% CI $[0.1086, 0.1118]$; CPA-block bootstrap 95% $[0.0908, 0.1330]$). At the per-document unit, the operational HC$+$MC alarm fires on $33.75\%$ of Big-4 documents under the inter-CPA candidate-pool counterfactual.
+
+The pooled per-signature and per-document rates conceal striking firm heterogeneity. A logistic regression of the per-signature hit indicator on firm dummies (Firm A reference) and centred log pool size yields odds ratios of $0.053$ (Firm B), $0.010$ (Firm C), and $0.027$ (Firm D) — Firms B/C/D are an order of magnitude below Firm A even after controlling for the pool-size confound (Script 44). Cross-firm hit matrix analysis shows that $98$–$100\%$ of inter-CPA collisions originate from candidates within the source firm (different CPA, same firm), consistent with firm-specific template, stamp, or document-production reuse mechanisms — though not by itself diagnostic of deliberate sharing. We retain the inherited Paper A v3.x five-way box rule as the operational classifier; v4.0's contribution is to characterise its multi-level coincidence behaviour against the inter-CPA negative anchor rather than to derive new thresholds.
+
+Three feature-derived scores converge on the per-CPA descriptor-position ranking with Spearman $\rho \geq 0.879$ (Script 38): the K=3 mixture posterior (now interpreted as a firm-compositional position score, not a mechanism cluster posterior; §III-J), a reverse-anchor cosine percentile relative to a strictly-out-of-target non-Big-4 reference, and the inherited box-rule less-replication-dominated rate. The three scores are deterministic functions of the same per-CPA descriptor pair, so the convergence is documented as internal consistency among feature-derived ranks rather than external validation. Hard ground truth for the *replicated* class is provided by 262 byte-identical signatures in the Big-4 subset (Firm A 145, Firm B 8, Firm C 107, Firm D 2), against which all three candidate checks achieve $0\%$ positive-anchor miss rate (Wilson 95% upper bound $1.45\%$). For the box rule this result is close to tautological at byte-identity; we discuss the conservative-subset caveat in §V-G.
+
+We apply this pipeline to 90,282 audit reports filed by publicly listed companies in Taiwan between 2013 and 2023, extracting and analyzing 182,328 individual CPA signatures from 758 unique accountants. The Big-4 sub-corpus comprises 437 CPAs and 150,442 signatures with both descriptors available.
+
+The contributions of this paper are:
+
+1. **Problem formulation.** We define non-hand-signing detection as distinct from signature forgery detection and frame it as a detection problem on intra-signer similarity distributions.
+
+2. **End-to-end pipeline.** We present a pipeline that processes raw PDF audit reports through VLM-based page identification, YOLO-based signature detection, ResNet-50 feature extraction, and dual-descriptor similarity computation, with automated inference and no manual intervention after initial training.
+
+3. **Dual-descriptor verification.** We demonstrate that combining deep-feature cosine similarity with independent-minimum dHash resolves the ambiguity between *style consistency* and *image reproduction*, and we validate the backbone choice through a feature-backbone ablation.
+
+4. **Composition decomposition disproves the distributional-threshold path.** We show via a 2×2 factorial diagnostic (firm-mean centring × integer-tie jitter) that the apparent multimodality of the Big-4 accountant-level descriptor distribution is fully attributable to between-firm location shifts and integer mass-point artefacts. The descriptor distributions contain no within-population bimodal antimode; "natural threshold" language in this lineage's prior work is not empirically supported.
+
+5. **Anchor-based multi-level inter-CPA coincidence-rate calibration.** We characterise the deployed five-way classifier at three units of analysis: per-comparison ICCR (cos$>0.95$: $0.0006$; dHash$\leq 5$: $0.0013$; joint: $0.00014$), pool-normalised per-signature ICCR ($0.11$ for the deployed any-pair high-confidence rule), and per-document ICCR ($0.34$ for the operational HC$+$MC alarm). We adopt "inter-CPA coincidence rate" as the metric name throughout and reserve "False Acceptance Rate" for terminology that requires ground-truth negative labels, which the corpus does not provide.
+
+6. **Firm heterogeneity quantification and within-firm cross-CPA collision concentration.** Per-firm rates differ by an order of magnitude after pool-size adjustment (Firm A's per-document HC$+$MC alarm at $0.62$ versus Firms B/C/D at $0.09$–$0.16$). Cross-firm hit matrix analysis shows that $98$–$100\%$ of inter-CPA collisions originate from candidates within the source firm, consistent with firm-specific template, stamp, or document-production reuse mechanisms — a descriptive finding about deployed-rule behaviour, not a claim of deliberate template sharing.
+
+7. **K=3 as descriptive firm-compositional partition; three-score convergent internal consistency.** We fit a K=3 Gaussian mixture as a descriptive partition of the Big-4 accountant-level distribution (no longer interpreted as three mechanism clusters). Three feature-derived scores agree on the per-CPA descriptor-position ranking at Spearman $\rho \geq 0.879$; we report this as internal consistency rather than external validation, given that the scores share the underlying descriptor pair.
+
+8. **Annotation-free positive-anchor validation and unsupervised validation ceiling.** We achieve $0\%$ positive-anchor miss rate (Wilson 95% upper bound $1.45\%$) on 262 byte-identical Big-4 signatures, with the conservative-subset caveat that byte-identical pairs are by construction near cos$=1$ and dHash$=0$. We frame the overall validation strategy as a multi-tool collection of nine partial-evidence diagnostics, each with an explicitly disclosed untested assumption; their conjunction constitutes the unsupervised validation ceiling achievable on this corpus. We do not claim a validated forensic detector; we position the system as a specificity-proxy-anchored screening framework with human-in-the-loop review.
+
+The remainder of the paper is organized as follows. Section II reviews related work on signature verification, document forensics, perceptual hashing, and the statistical methods used. Section III describes the proposed methodology. Section IV presents the experimental results — distributional characterisation, mixture fits, convergent internal-consistency checks, leave-one-firm-out reproducibility, pixel-identity validation, and full-dataset robustness. Section V discusses the implications and limitations. Section VI concludes with directions for future work.
+
+---
+
+# II. Related Work
+
+> *Note for the Phase 4 review pass: §II is inherited substantively unchanged from v3.20.0 §II in the master manuscript, with one new paragraph added below. The unchanged content is not reproduced in this Phase 4 file; readers reviewing this draft should consult `paper/paper_a_related_work_v3.md` for the v3.20.0 §II text covering offline signature verification, near-duplicate detection, copy-move forgery detection, perceptual hashing, deep-feature similarity, and the statistical methods adopted (Hartigan dip test, finite mixture EM, Burgstahler-Dichev / McCrary density-smoothness diagnostic). The paragraph below is the only v4.0-specific §II addition.*
+
+**Addition for v4.0: leave-one-firm-out cross-validation in a small-cluster scope.** Cross-validation methodology in the leave-one-out tradition has been developed extensively in statistics since Stone [42] and Geisser [43], and modern surveys including Vehtari et al. [44] discuss its application to mixture models. In document-forensics calibration the technique has been used selectively, typically with the individual document or signature as the hold-out unit. Our application in §III-K differs in two respects from the standard usage: (i) the hold-out unit is the *firm* (not the individual CPA or signature), so the analysis directly probes cross-firm reproducibility of the fitted mixture rather than within-firm sampling variance; and (ii) the held-out predictions are interpreted as a *composition-sensitivity band* on the candidate mixture boundary, not as a sufficiency claim for the inherited five-way operational classifier (which is calibrated separately; §III-L). We treat LOOO drift as descriptive information about how the mixture characterisation moves when training composition changes, not as a pass/fail test for the operational classifier. Numerical references [42]–[44] are placeholders in this draft and will be replaced with the project's preferred references at copy-edit time.
+
+---
+
+# V. Discussion
+
+## A. Non-Hand-Signing Detection as a Distinct Problem
+
+Non-hand-signing differs from forgery in that the questioned signature is produced by its legitimate signer's own stored image rather than by an impostor. The detection problem is therefore framed around *intra-signer image reproduction* rather than *inter-signer imitation*. This framing has analytical consequences. The within-CPA signature distribution is the analytical population of interest; the cross-CPA inter-class distribution is a *reference* against which intra-CPA similarity is interpreted, not the population to be modelled. This contrasts with most prior offline signature verification work, which treats genuine-versus-forged as the central two-class problem.
+
+## B. Per-Signature Similarity is a Continuous Quality Spectrum; the Accountant-Level Multimodality is Composition-Driven
+
+A central empirical finding of v3.x was that *per-signature* similarity does not admit a clean two-mechanism mixture: dip-test fails to reject unimodality at the signature level for Firm A, BIC prefers a 3-component fit, and BD/McCrary candidate transitions lie inside the high-similarity mode rather than between modes. v4.0 strengthens and extends this signature-level reading.
+
+The Big-4 accountant-level descriptor distribution does reject unimodality on both marginals at $p < 5 \times 10^{-4}$ (Script 34). v4.0's composition decomposition (§III-I.4; Scripts 39b–39e) shows that this rejection is fully attributable to two non-mechanistic sources: (a) between-firm location-shift effects on both axes — Firm A's mean dHash of $2.73$ versus Firms B/C/D's $6.46$, $7.39$, $7.21$ creates a multi-peaked pooled distribution that any single firm's distribution lacks — and (b) integer mass-point artefacts on the integer-valued dHash axis, which inflate the dip statistic against a continuous-density null. A 2×2 factorial diagnostic applied to the Big-4 pooled dHash (firm-mean centring × uniform integer jitter $[-0.5, +0.5]$, 5 jitter seeds) shows that the dip test fails to reject ($p_{\text{median}} = 0.35$, 0/5 seeds reject) when *both* corrections are applied; either correction alone leaves the rejection in place. Within-firm signature-level cosine and jittered-dHash dip tests fail to reject in every individual Big-4 firm and in every individual non-Big-4 firm with $\geq 500$ signatures (10 firms tested). The descriptor distributions therefore lack a within-population bimodal antimode that could anchor an operational threshold. The K=2 / K=3 mixture fits are retained in §III-J as descriptive partitions of the joint Big-4 distribution that reflect firm-compositional structure, not as inferential evidence for two or three latent mechanism modes.
+
+## C. Firm A as the Templated End of Big-4 (Case Study, Not Calibration Anchor)
+
+Firm A is empirically the firm whose CPAs are most concentrated in the high-cosine, low-dHash corner of the Big-4 descriptor plane. In the Big-4 K=3 hard-posterior assignment (now interpreted as a firm-compositional position assignment; §III-J), Firm A accounts for $0\%$ of C1 (low-cos / high-dHash position) and $82.5\%$ of C3 (high-cos / low-dHash position); the opposite pattern holds at Firm C, which has the highest C1 concentration at $23.5\%$. Firm A also accounts for 145 of the 262 byte-identical signatures in the Big-4 byte-identical anchor of §IV-H (with Firm B 8, Firm C 107, Firm D 2). The additional v3.x finding that the 145 Firm A pixel-identical signatures span 50 distinct Firm A partners (of 180 registered), with 35 byte-identical matches across different fiscal years, is inherited from v3.20.0 §IV-F.1 / Script 28 / Appendix B byte-decomposition output and was not regenerated in v4.0's spike scripts; we retain those numbers by reference.
+
+In v4.0 we treat Firm A as a *templated-end case study* rather than as the calibration anchor for the operational threshold. Firm A enters the Big-4 anchor-based ICCR calibration on equal footing with the other three Big-4 firms (§III-L). The cross-firm hit matrix of §III-L.4 strengthens this framing: $98$–$100\%$ of inter-CPA collisions originate from candidates within the source firm, regardless of which Big-4 firm is the source. Firm A's high per-document HC$+$MC alarm rate of $0.62$ (versus Firms B/C/D's $0.09$–$0.16$) reflects high inter-CPA collision concentration under the deployed rule on real same-CPA pools, consistent with firm-specific template, stamp, or document-production reuse — though the inter-CPA-anchor analysis alone is not diagnostic of deliberate template sharing. The byte-level evidence of v3.x §IV-F.1 (Firm A's 145 pixel-identical signatures across $\sim 50$ distinct partners) provides direct evidence that firm-level template reuse does occur at Firm A; the within-firm collision pattern at all four Big-4 firms is consistent with that mechanism extending in milder form to Firms B/C/D.
+
+## D. K=2 / K=3 as Descriptive Firm-Compositional Partitions
+
+Leave-one-firm-out cross-validation of the Big-4 mixture fit reveals a sharp contrast between K=2 and K=3 behaviour. K=2 is unstable: across-fold cosine-crossing deviation is $0.028$, and holding Firm A out gives a fold rule (cos $> 0.938$, dHash $\leq 8.79$) that classifies $100\%$ of held-out Firm A in the upper component, while holding any non-Firm-A Big-4 firm out gives a fold rule near (cos $> 0.975$, dHash $\leq 3.76$) that classifies $0\%$ of the held-out firm in the upper component. The K=2 boundary is essentially a Firm-A-vs-others separator — direct evidence that the K=2 partition reflects firm-compositional rather than mechanistic structure.
+
+K=3 in contrast has a *reproducible component shape* at the descriptor-position level: across the four folds the C1 (low-cos / high-dHash) component cosine mean varies by at most $0.005$, the dHash mean by at most $0.96$, and the weight by at most $0.023$. Hard-posterior membership for the held-out firm is composition-sensitive (absolute differences $1.8$–$12.8$ pp across folds). Together with the §III-I.4 composition decomposition (no within-population bimodal antimode), the K=3 stability supports a descriptive reading: the Big-4 descriptor plane has a reproducible three-region partition that reflects how firm-compositional weight is distributed across the descriptor space, *not* a three-mechanism latent-class structure. We accordingly do not use K=3 hard-posterior membership as an operational classifier; we use it as the accountant-level descriptive summary that complements the deployed signature-level five-way classifier of §III-L.
+
+## E. Three-Score Convergent Internal-Consistency
+
+Three feature-derived scores agree on the per-CPA descriptor-position ranking at Spearman $\rho \geq 0.879$: the K=3 mixture posterior (a firm-compositional position score, not a mechanism cluster posterior); the reverse-anchor cosine percentile under a non-Big-4 reference distribution; and the inherited Paper A box-rule less-replication-dominated rate. The three scores are *not* statistically independent measurements — they are deterministic functions of the same per-CPA descriptor pair — so the convergence is documented as internal consistency rather than external validation against an independent ground truth (which the corpus does not provide for the hand-signed class). The strength of the convergence (all pairwise $|\rho| > 0.87$) and its persistence at the signature level (Cohen $\kappa = 0.87$ between per-CPA-fit and per-signature-fit K=3 binary labels) are nevertheless informative: per-CPA aggregation does not collapse the broad three-region ordering, and three different summarisations of the descriptor space produce broadly concordant per-CPA rankings, with a residual non-Firm-A disagreement (the reverse-anchor cosine percentile ranks Firm D fractionally above Firm C, while the mixture posterior and the box-rule rate rank Firm C highest among non-Firm-A firms).
+
+## F. Anchor-Based Multi-Level Calibration
+
+The operational specificity of the deployed five-way classifier is characterised at three units of analysis (§III-L), all against the same inter-CPA negative-anchor coincidence-rate proxy. The per-comparison ICCR replicates v3.x's per-comparison rate (cos$>0.95 \to 0.00060$) and extends it to the structural dimension (dHash$\leq 5 \to 0.00129$; joint $\to 0.00014$). The pool-normalised per-signature ICCR captures the deployed rule's effective per-signature rate under inter-CPA candidate-pool replacement ($0.1102$ pooled Big-4 any-pair HC), exposing that the per-comparison rate is not the deployed-rule rate at the per-signature classifier level: the deployed classifier takes max-cosine and min-dHash over a same-CPA pool of size $n_{\text{pool}}$, so the inter-CPA-equivalent rate scales approximately as $1 - (1 - p_{\text{pair}})^{n_{\text{pool}}}$ in the independence limit. The per-document ICCR aggregates to operational alarm-rate units: HC alone $0.18$, the operational HC$+$MC alarm $0.34$.
+
+Two additional findings refine the calibration story. First, the per-pair conditional ICCR for dHash$\leq 5$ given cos$>0.95$ is $0.234$ (Wilson 95% $[0.190, 0.285]$): given the cosine gate, the structural dimension provides further per-comparison specificity at $\sim 4.3\times$ refinement. Second, the alert-rate sensitivity analysis (§III-L.5; Script 46) shows the inherited HC threshold is locally sensitive rather than plateau-stable (local gradient $\approx 25\times$ the median for cosine, $\approx 3.8\times$ for dHash); stakeholders requiring different specificity-alert-yield operating points can derive thresholds by inverting the ICCR curves (a tighter rule cos$>0.95$ AND dHash$\leq 3$ on the same-pair joint gives per-signature ICCR $\approx 0.045$). The MC/HSC sub-band boundary at dHash$=15$, by contrast, *is* plateau-like (local-to-median ratio $\approx 0.08$), consistent with high-dHash-tail saturation.
+
+## G. Pixel-Identity as a Hard Positive Anchor; Inherited Inter-CPA Negative Anchor Reframed as Coincidence Rate
+
+The only hard ground-truth subset in the corpus is pixel-identical signatures: those whose nearest same-CPA match is byte-identical after crop and normalisation. Independent hand-signing cannot produce byte-identical images, so these signatures are conservative-subset ground truth for the *replicated* class. On the Big-4 subset ($n = 262$ pixel-identical signatures), all three candidate classifiers — the inherited box rule, the K=3 hard label, and the reverse-anchor metric with a prevalence-calibrated cut — achieve $0\%$ positive-anchor miss rate (Wilson 95% upper bound $1.45\%$). We caution that this result is necessary but not sufficient: for the box rule it is close to tautological, because byte-identical neighbours have cosine $\approx 1$ and dHash $\approx 0$, well inside the rule's high-confidence region. The corresponding signature-level *negative* anchor evidence is developed in §III-L.1 above (v4 spike: cos$>0.95$ per-comparison ICCR $= 0.00060$, replicating v3.20.0's reported $0.0005$ under prior "FAR" terminology). We frame the per-comparison rate as a specificity proxy under the assumption that inter-CPA pairs constitute a clean negative anchor, and we document in §III-L.4 that this assumption is partially violated by within-firm cross-CPA template-like collision structures.
+
+## G. Limitations
+
+Several limitations should be transparent. The first nine are v4.0-specific; the last five are inherited from v3.20.0 §V-G and still apply to the v4.0 pipeline.
+
+*No signature-level ground truth; no true error rates reportable.* The corpus does not contain labelled hand-signed or replicated classes at the signature level. We therefore cannot report False Rejection Rate, sensitivity, recall, Equal Error Rate, ROC-AUC, precision, or positive predictive value against ground truth. All quantitative rates reported in §III-L are inter-CPA negative-anchor coincidence rates (ICCRs) under the assumption that inter-CPA pairs constitute a clean negative anchor; this is a specificity proxy, not a calibrated specificity (§III-M).
+
+*Inter-CPA negative-anchor assumption is partially violated.* The cross-firm hit matrix of §III-L.4 shows that $98$–$100\%$ of inter-CPA collisions under the deployed rule originate from candidates within the source firm, consistent with firm-specific template, stamp, or document-production reuse. The inter-CPA-as-negative assumption is therefore not exactly satisfied — some inter-CPA pairs may share firm-level templates rather than being independent random matches. Our reported per-comparison ICCRs are best read as specificity-proxy rates under a partially-violated assumption, not as calibrated FARs.
+
+*Scope.* The v4.0 primary analyses are scoped to the Big-4 sub-corpus. We did not perform the full per-signature pool-normalised ICCR analysis at the full $n = 686$ scope; the §IV-K full-dataset Spearman re-run shows the K=3 $+$ box-rule rank-convergence is preserved at $n = 686$ but does not validate the Big-4 operational ICCRs, the LOOO firm-fold structure, or the five-way operational classifier at the broader scope.
+
+*Pixel-identity is a conservative subset.* Byte-identical pairs are the easiest replicated cases, and for the inherited box rule the positive-anchor miss rate against byte-identical pairs is close to tautological (byte-identical $\Rightarrow$ cosine $\approx 1$, dHash $\approx 0$, well inside the high-confidence box). A score that fails the pixel-identity check would be disqualified, but passing the check does not guarantee correct behaviour on the broader replicated population (e.g., re-stamped or noisy-template-variant signatures).
+
+*Inherited rule components are not separately v4-validated.* The five-way classifier's moderate-confidence band (cos $> 0.95$ AND $5 < \text{dHash} \leq 15$), the style-consistency band ($\text{dHash} > 15$), and the document-level worst-case aggregation rule retain their v3.20.0 calibration and capture-rate evidence; v4.0's anchor-based ICCR calibration covers the binary high-confidence sub-rule (and its tightening alternatives such as dHash$\leq 3$), and the alert-rate sensitivity analysis (§III-L.5) characterises only the HC threshold. The MC and HSC sub-band boundaries are not separately re-validated by v4.0's diagnostic battery.
+
+*Deployed-rate excess is not a presumed true-positive rate.* The $\sim 44$-pp per-document gap between the observed deployed alert rate (HC: $0.62$ on real same-CPA pools) and the inter-CPA proxy rate (HC: $0.18$) cannot be interpreted as a presumed true-positive rate without additional assumptions that §III-M shows are unsafe (consistent within-CPA signing can exceed inter-CPA similarity at the cosine axis; within-firm template sharing inflates the inter-CPA proxy baseline). The gap is best read as a same-CPA repeatability signal.
+
+*A1 pair-detectability stipulation.* The per-signature detector requires at least one same-CPA pair to be near-identical when a CPA uses image replication. A1 is plausible for high-volume stamping or firm-level electronic signing but not guaranteed when a corpus contains only one observed replicated report for a CPA, multiple template variants used in parallel, or scan-stage noise that pushes a replicated pair outside the detection regime.
+
+*K=3 hard-posterior membership is composition-sensitive.* The K=3 hard-posterior membership for any single firm varies by up to $12.8$ pp across LOOO folds. This is documented as a composition-sensitivity band rather than failure, but it means K=3 hard labels are not used as v4.0 operational classifier output; they are reported only as accountant-level descriptive characterisation.
+
+*No partner-level mechanism attribution.* v4.0 reports population-level patterns; it does not perform partner-level mechanism attribution or report-level claims of intent. The signature-level outputs are signature-level quantities throughout. The within-firm cross-CPA collision concentration of §III-L.4 is consistent with template-like reuse but is not by itself diagnostic of deliberate sharing.
+
+*Transferred ImageNet features (inherited from v3.20.0).* The ResNet-50 feature extractor uses pre-trained ImageNet weights without signature-domain fine-tuning. While our backbone-ablation study (§IV-L, inherited from v3.20.0 §IV-I) and prior literature support the effectiveness of transferred ImageNet features for signature comparison, a signature-domain fine-tuned feature extractor could improve discriminative performance.
+
+*Red-stamp HSV preprocessing artifacts (inherited from v3.20.0).* The red stamp removal preprocessing uses simple HSV color-space filtering, which may introduce artifacts where handwritten strokes overlap with red seal impressions. Blended pixels are replaced with white, potentially creating small gaps in signature strokes that could reduce dHash similarity. This bias would push classifications toward false negatives rather than false positives.
+
+*Longitudinal scan / PDF / compression confounds (inherited from v3.20.0).* Scanning equipment, PDF generation software, and compression algorithms may have changed over the 2013–2023 study period, potentially affecting similarity measurements. While cosine similarity and dHash are designed to be robust to such variations, longitudinal confounds cannot be entirely excluded.
+
+*Source-exemplar misattribution in max/min pair logic (inherited from v3.20.0).* The max-cosine / min-dHash detection logic treats both ends of a near-identical same-CPA pair as non-hand-signed. In the rare case where one of the two documents contains a genuinely hand-signed exemplar that was subsequently reused as a stamping or e-signature template, the pair correctly identifies image reuse but misattributes non-hand-signed status to the source exemplar. This affects at most one source document per template variant per CPA and is not expected to be common.
+
+*Legal and regulatory interpretation (inherited from v3.20.0).* Whether non-hand-signing of a CPA's own stored signature constitutes a violation of signing requirements is a jurisdiction-specific legal question. Our technical analysis can inform such determinations but cannot resolve them.
+
+---
+
+# VI. Conclusion and Future Work
+
+We present a fully automated pipeline for detecting non-hand-signed CPA signatures in Taiwan-listed financial audit reports and a multi-tool framework for characterising and disclosing its operational behaviour at the Big-4 sub-corpus scope. The pipeline processes raw PDFs through VLM-based page identification, YOLO-based signature detection, ResNet-50 feature extraction, and dual-descriptor (cosine + independent-minimum dHash) similarity computation. The operational output is an inherited Paper A five-way per-signature classifier with worst-case document-level aggregation (§III-L). Applied to 90,282 audit reports filed between 2013 and 2023, the pipeline extracts 182,328 signatures from 758 CPAs, with the Big-4 sub-corpus (437 CPAs at accountant level; 150,442–150,453 signatures at signature level) as the primary analytical population.
+
+Our central methodological contributions are: (1) a composition decomposition (Scripts 39b–39e) that establishes the absence of a within-population bimodal antimode in the Big-4 descriptor distribution: the apparent multimodality dissolves under joint firm-mean centring and integer-tie jitter ($p_{\text{median}} = 0.35$), so distributional "natural-threshold" framings of the inherited operating points are not empirically supported; (2) an anchor-based inter-CPA coincidence-rate (ICCR) calibration at three units of analysis — per-comparison ($0.0006$ at cos$>0.95$; $0.0013$ at dHash$\leq 5$; $0.00014$ jointly), pool-normalised per-signature ($0.11$ for the deployed any-pair HC rule), and per-document ($0.34$ for the operational HC$+$MC alarm) — with explicit terminological replacement of "FAR" by "ICCR" given the unsupervised setting; (3) firm heterogeneity quantification: logistic regression with pool-size adjustment gives odds ratios $0.053$, $0.010$, $0.027$ for Firms B/C/D relative to Firm A reference, indicating a large multiplicative effect that pool-size differences do not explain; (4) cross-firm hit matrix evidence that $98$–$100\%$ of inter-CPA collisions under the deployed rule originate from candidates within the source firm, consistent with firm-specific template, stamp, or document-production reuse mechanisms; (5) K=3 mixture demoted from "three mechanism clusters" to a descriptive firm-compositional partition; (6) three feature-derived scores converging on the per-CPA descriptor-position ranking at Spearman $\rho \geq 0.879$, reported as internal consistency rather than external validation; (7) $0\%$ positive-anchor miss rate on 262 byte-identical Big-4 signatures with the conservative-subset caveat; and (8) a nine-tool unsupervised-validation collection (§III-M) that explicitly discloses each tool's untested assumption and positions the system as an anchor-calibrated screening framework with human-in-the-loop review, not as a validated forensic detector.
+
+Future work falls in four directions. *First*, a small-scale human-rated validation set would enable direct ROC optimisation and provide signature-level ground truth that v4.0 fundamentally lacks; without such ground truth, no true error rates can be reported. *Second*, the within-firm collision concentration documented in §III-L.4 (98–100% same-firm partners) invites a separate study to distinguish deliberate template sharing from passive firm-level production artefacts (shared scanners, common form templates, identical report-generation infrastructure) — a question the inter-CPA-anchor analysis alone cannot resolve. *Third*, the descriptive Firm A versus Firms B/C/D contrast (per-document HC$+$MC alarm $0.62$ vs $0.09$–$0.16$) — together with v3.x's byte-level evidence of 145 pixel-identical signatures across $\sim 50$ distinct Firm A partners — invites a companion analysis examining whether such firm-level signing patterns correlate with established audit-quality measures. *Fourth*, generalisation to mid- and small-firm contexts requires extending the anchor-based ICCR framework to scopes where firm-level LOOO folds are not available; the §III-I.4 composition diagnostics already document that the absence of within-population bimodality is corpus-universal, so the v4.0 calibration approach in principle generalises, but a full extension with cluster-robust uncertainty quantification is left as future work.
+
+---
+
+## Notes for Phase 4 close-out
+
+Items remaining for the Phase 4 close-out pass before §I, §II, §V, §VI prose can be moved into the manuscript master file:
+
+1. **Abstract word count.** Current draft is 243–244 words (shell `wc -w` on the paragraph returns 243; one-token tokenization difference depending on counter); both satisfy IEEE Access's $\leq 250$ word constraint with $\sim 6$ words of margin.
+2. **§I contributions list (8 items).** v3.20.0's contribution list had 7 items; v4.0's has 8 to reflect the Big-4 scope, K=3 descriptive role, and three-score convergence as separate contributions. Confirm whether the journal style supports 8 contributions or whether items can be merged.
+3. **§II Related Work LOOO citation.** A standard cross-validation citation for the LOOO addition is flagged "[add citation]" in the draft and needs to be filled with a specific reference (Geisser 1975 / Stone 1974 / a modern survey).
+4. **§V-G Limitations.** The seven limitations are listed flat; the journal style may prefer them grouped (scope vs ground-truth vs methodology) — consider reorganisation at copy-edit time.
+5. **§VI Future Work directions.** Four directions are listed; the third (audit-quality companion analysis) ties to the Paper B placeholder in the project memory and should be cross-checked for consistency with the planned Paper B framing.
+6. **Internal draft note + this close-out checklist.** Strip before submission packaging, per the across-paper "internal — remove before submission" policy applied to §III v6 and §IV v3.2 draft notes.

paper/v4/paper_a_results_v4_section_iv.md

@@ -0,0 +1,374 @@
+# Section IV. Results — v4.0 Draft v3.3 (post codex rounds 21–34)
+
+> **Draft note (2026-05-12, v3.2; internal — remove before submission).** This file replaces the §IV-A through §IV-H block of `paper/paper_a_results_v3.md` (v3.20.0) with the Big-4 reframed structure. Section IV expands from 8 sub-sections in v3.20.0 to 12 sub-sections in v4.0 (A through L) to mirror the §III-G..L lineage. **Table-numbering scheme**: the v4 manuscript uses Tables V through XVIII (plus Table XV-B for document-level worst-case counts) for the new v4 Big-4 results; inherited v3.x tables are cited only as "v3.20.0 Table N" with their original v3 number and are *not* renumbered into the v4 sequence. No v4 Table IV is printed; the inherited v3.20.0 Table IV (per-firm detection counts) remains a v3.x reference rather than a v4 table. **Anonymisation**: the Big-4 firms are pseudonymously labelled Firm A through Firm D throughout the manuscript body; real names are not printed in v4 tables or prose. The v3 → v3.1 → v3.2 revision history is: v3 (post round 23) made the table-numbering scheme and anonymisation policy decisions and applied 14 presentation fixes; v3.1 (post round 24) tightened the close-out checklist; v3.2 (post round 25) finalises this draft note. Empirical anchors trace to Scripts 32–42 on branch `paper-a-v4-big4`; the §III provenance table covers the methodology-side citations and §IV adds new tables for the v4.0-specific results.
+
+## A. Experimental Setup
+
+The signature-detection and feature-extraction pipeline (§III-A through §III-F) was executed on the full TWSE MOPS audit-report corpus (90,282 PDFs spanning 2013–2023; §III-B). Detection and embedding ran on RTX 4090 (CUDA, deterministic forward inference, fixed seed); the v4.0 statistical analyses ran on Apple Silicon (MPS / CPU). Random seeds are fixed (`SEED = 42`) across the v4.0 spike scripts 32–42 for reproducibility. The signature_analysis SQLite snapshot at `/Volumes/NV2/PDF-Processing/signature-analysis/signature_analysis.db` is treated as frozen; no v4.0 result re-ingests source PDFs.
+
+The v4.0 primary analyses (§IV-D through §IV-J) are scoped to the Big-4 sub-corpus (Firms A–D, $n = 437$ CPAs with $n_{\text{sig}} \geq 10$, totalling 150,442 signatures with both descriptors available) per the methodology choice articulated in §III-G. The §IV-K Full-Dataset Robustness section reports the full-dataset (686 CPAs) variant of the K=3 mixture + Paper A box-rule Spearman analysis as a cross-scope robustness check.
+
+## B. Signature Detection Performance
+
+The detection metrics are inherited unchanged from v3.20.0 §IV-B. v3.20.0 reports: VLM screening identified 86,072 documents with signature pages; 12 corrupted PDFs were excluded; YOLOv11n batch inference processed the remaining 86,071 documents; 85,042 of these yielded at least one signature detection; the total extracted-signature count is 182,328 (v3.20.0 Table III). Per-firm counts of detected signatures are reported in v3.20.0 Table IV. v4.0 does not renumber the v3.x detection tables into the v4 sequence; v3.20.0 Tables III and IV are cited by their original numbers.
+
+The Big-4 subset of the detection output yields 150,442 signatures with both descriptors (cosine and independent dHash) successfully computed; this is the per-signature population used in all §IV v4 primary analyses (§IV-D through §IV-J).
+
+## C. All-Pairs Intra-vs-Inter Class Distribution Analysis
+
+The all-pairs intra-vs-inter class distribution analysis (KDE crossover at $\overline{\text{cos}} = 0.837$; v3.20.0 §IV-C, v3.20.0 Table V) is inherited unchanged. This analysis was computed on the full corpus (not Big-4-restricted) and remains the source of the Uncertain / Likely-hand-signed boundary used by the §III-L five-way per-signature classifier (cosine $\leq 0.837 \Rightarrow$ Likely-hand-signed, matching Script 42's `cos <= 0.837` rule definition). v4.0 makes no scope-specific re-derivation of this boundary; the all-pairs cross-class crossover is a corpus-wide reference and is not restated as a v4.0 finding. v3.20.0 Table V is cited by its original number and is not renumbered into the v4 sequence.
+
+## D. Big-4 Accountant-Level Distributional Characterisation
+
+This section reports the empirical evidence for §III-I's distributional diagnostics at the Big-4 accountant level. All numbers below are direct re-statements from Scripts 32 / 34. The accountant-level dip-test rejection reported in Table V is, per §III-I.4 (Scripts 39b–39e), fully attributable to between-firm location shifts and integer mass-point artefacts rather than to within-population bimodality; the v4-new composition-decomposition diagnostics that establish this finding are tabulated in §IV-M below alongside the anchor-based ICCR calibration.
+
+**Table V.** Hartigan dip-test results, accountant-level marginals (Big-4 primary; comparison scopes from Script 32).
+
+| Population | $n$ CPAs | $p_{\text{cos}}$ | $p_{\text{dHash}}$ | Interpretation |
+|---|---|---|---|---|
+| **Big-4 pooled (primary)** | 437 | $< 5 \times 10^{-4}$ | $< 5 \times 10^{-4}$ | reject unimodality on both axes |
+| Firm A pooled alone | 171 | 0.992 | 0.924 | unimodal |
+| Firms B + C + D pooled | 266 | 0.998 | 0.906 | unimodal |
+| All non-Firm-A pooled | 515 | 0.998 | 0.907 | unimodal |
+
+Bootstrap implementation: $n_{\text{boot}} = 2000$; for the Big-4 cells, no bootstrap replicate exceeded the observed dip statistic, so the empirical $p$-value is bounded above by the bootstrap resolution $1 / 2000 = 5 \times 10^{-4}$ (Script 34 reports this as $p = 0.0000$; we report $p < 5 \times 10^{-4}$ to reflect the resolution). Single-firm dip statistics for Firms B, C, and D were not separately computed.
+
+**Table VI.** Burgstahler-Dichev / McCrary density-smoothness diagnostic on accountant-level marginals (cosine in 0.002 bins; dHash in integer bins; $\alpha = 0.05$, two-sided).
+
+| Population | Cosine: significant transition? | dHash: significant transition? |
+|---|---|---|
+| **Big-4 pooled (primary)** | none ($p > 0.05$) | none ($p > 0.05$) |
+| Firm A pooled alone | none | none |
+| Firms B + C + D pooled | none | one transition at $\overline{\text{dHash}} = 10.8$ |
+| All non-Firm-A pooled | none | one transition at $\overline{\text{dHash}} = 6.6$ |
+
+The Big-4-scope null on both axes is consistent with the §IV-E mixture evidence: the K=3 components overlap in their tails rather than separating sharply, so a local-discontinuity test does not flag a transition. Outside Big-4, dHash transitions appear in some subsets but no cosine transition is identified in any tested subset (Script 32 sweeps; pre-2018 and post-2020 stratified variants exhibit dHash transitions at varying locations). These off-Big-4 dHash transitions are scope-dependent and are not used as v4.0 operational thresholds; we do not claim a specific structural interpretation for them without an explicit bin-width sensitivity sweep at those scopes.
+
+## E. Big-4 K=2 / K=3 Mixture Fits
+
+This section reports the K=2 and K=3 2D Gaussian mixture fits to the Big-4 accountant-level distribution and the bootstrap stability of their marginal crossings.
+
+**Table VII.** Big-4 K=2 mixture components (descriptive partition; not mechanism clusters per §III-J) and marginal-crossing bootstrap 95% confidence intervals.
+
+| K=2 component | $\overline{\text{cos}}$ | $\overline{\text{dHash}}$ | weight |
+|---|---|---|---|
+| K=2-a (low-cos / high-dHash position) | 0.954 | 7.14 | 0.689 |
+| K=2-b (high-cos / low-dHash position) | 0.983 | 2.41 | 0.311 |
+
+Marginal crossings (point + bootstrap 95% CI, $n_{\text{boot}} = 500$):
+
+| Axis | Point | Bootstrap median | 95% CI | CI half-width |
+|---|---|---|---|---|
+| cos | 0.9755 | 0.9754 | $[0.9742, 0.9772]$ | 0.0015 |
+| dHash | 3.755 | 3.763 | $[3.476, 3.969]$ | 0.246 |
+
+$\text{BIC}(K{=}2) = -1108.45$ (Script 34).
+
+**Table VIII.** Big-4 K=3 mixture components (descriptive firm-compositional partition per §III-J; not mechanism clusters).
+
+| K=3 component | $\overline{\text{cos}}$ | $\overline{\text{dHash}}$ | weight | descriptive position |
+|---|---|---|---|---|
+| C1 | 0.9457 | 9.17 | 0.143 | low-cos / high-dHash corner |
+| C2 | 0.9558 | 6.66 | 0.536 | central region |
+| C3 | 0.9826 | 2.41 | 0.321 | high-cos / low-dHash corner |
+
+$\text{BIC}(K{=}3) = -1111.93$, lower than $K{=}2$ by $3.48$ (mild support; not by itself decisive). The full-fit K=3 baseline above is reproduced in Scripts 35, 37, and 38 with identical hyperparameters; Script 37 additionally fits K=3 on each leave-one-firm-out training set (those fold-specific components differ from the full-fit baseline by design and are reported separately in §IV-G Table XIII). Operational use of the K=2 / K=3 fits is governed by §III-J and §III-L; §IV-G reports the LOOO reproducibility evidence that motivates reporting both fits descriptively.
+
+## F. Convergent Internal-Consistency Checks
+
+This section reports the empirical evidence for §III-K's three-score internal-consistency analysis. We re-emphasise the §III-K caveat: the three scores are deterministic functions of the same per-CPA descriptor pair $(\overline{\text{cos}}_a, \overline{\text{dHash}}_a)$ and are *not statistically independent measurements*. The pairwise correlations document internal consistency among feature-derived ranks rather than external validation against an independent ground truth.
+
+**Table IX.** Per-CPA Spearman rank correlations among three feature-derived scores, Big-4, $n = 437$.
+
+| Score pair | Spearman $\rho$ | $p$-value |
+|---|---|---|
+| K=3 P(C1) vs Paper A box-rule hand-leaning rate | $+0.9627$ | $< 10^{-248}$ |
+| Reverse-anchor cosine percentile vs Paper A box-rule hand-leaning rate | $+0.8890$ | $< 10^{-149}$ |
+| K=3 P(C1) vs Reverse-anchor cosine percentile | $+0.8794$ | $< 10^{-142}$ |
+
+(Source: Script 38.) Reverse-anchor reference: 2D Gaussian fit by MCD (support fraction 0.85) on $n = 249$ non-Big-4 CPAs; reference centre $\overline{\text{cos}} = 0.935$, $\overline{\text{dHash}} = 9.77$.
+
+**Table X.** Per-firm summary across the three feature-derived scores, Big-4.
+
+| Firm | $n$ CPAs | mean $P(\text{C1})$ | mean reverse-anchor score | mean Paper A hand-leaning rate |
+|---|---|---|---|---|
+| Firm A | 171 | 0.0072 | $-0.9726$ | 0.1935 |
+| Firm B | 112 | 0.1410 | $-0.8201$ | 0.6962 |
+| Firm C | 102 | 0.3110 | $-0.7672$ | 0.7896 |
+| Firm D | 52 | 0.2406 | $-0.7125$ | 0.7608 |
+
+(Source: Script 38 per-firm summary; reverse-anchor score is sign-flipped so that *higher* values indicate deeper into the reference left tail = more hand-leaning relative to the non-Big-4 reference.)
+
+The three scores agree on placing Firm A as the most replication-dominated and the three non-Firm-A firms as more hand-leaning. The K=3 posterior P(C1) and the box-rule hand-leaning rate (Score 1 and Score 3) place Firm C at the most-hand-leaning end of Big-4; the reverse-anchor cosine percentile (Score 2) ranks Firm D fractionally above Firm C. This residual within-Big-4-non-A disagreement is a design feature of the reverse-anchor metric: Score 2 measures only the marginal cosine percentile under the non-Big-4 reference, so a firm with a slightly higher cosine but a markedly different dHash distribution (Firm D vs Firm C) can score higher on Score 2 while scoring lower on Scores 1 and 3, both of which use both descriptors.
+
+**Table XI.** Per-signature Cohen $\kappa$ (binary collapse, replicated vs not-replicated), $n = 150{,}442$ Big-4 signatures.
+
+| Pair | Cohen $\kappa$ |
+|---|---|
+| Paper A binary high-confidence box rule (cos $> 0.95$ AND dHash $\leq 5$) vs per-CPA K=3 hard label | 0.662 |
+| Paper A binary high-confidence box rule vs per-signature K=3 hard label | 0.559 |
+| Per-CPA K=3 hard label vs per-signature K=3 hard label | 0.870 |
+
+(Source: Script 39; verdict label `SIG_CONVERGENCE_MODERATE`.) Per-signature K=3 components ($n = 150{,}442$) sorted by ascending cosine: $(0.928, 9.75, 0.146)$ / $(0.963, 6.04, 0.582)$ / $(0.989, 1.27, 0.272)$, an absolute cosine drift of $0.018$ in C1 and $0.006$ in C3 relative to the per-CPA fit. These convergence checks cover only the binary high-confidence rule (cos $> 0.95$ AND dHash $\leq 5$); the five-way classifier's moderate-confidence band ($5 < \text{dHash} \leq 15$) inherits its v3.x calibration and capture-rate evaluation (§IV-J).
+
+## G. Leave-One-Firm-Out Reproducibility
+
+This section reports the firm-level cross-validation evidence motivating §III-J's "K=3 descriptive, not operational" framing.
+
+**Table XII.** K=2 leave-one-firm-out across the four Big-4 folds.
+
+| Held-out firm | $n_{\text{train}}$ | $n_{\text{held}}$ | Fold rule (cos cut, dHash cut) | Held-out classified as templated by fold rule |
+|---|---|---|---|---|
+| Firm A | 266 | 171 | cos $> 0.9380$ AND dHash $\leq 8.79$ | $171 / 171 = 100.00\%$ ($95\%$ Wilson $[97.80\%, 100.00\%]$) |
+| Firm B | 325 | 112 | cos $> 0.9744$ AND dHash $\leq 3.98$ | $0 / 112 = 0\%$ ($95\%$ Wilson $[0\%, 3.32\%]$) |
+| Firm C | 335 | 102 | cos $> 0.9752$ AND dHash $\leq 3.75$ | $0 / 102 = 0\%$ ($95\%$ Wilson $[0\%, 3.63\%]$) |
+| Firm D | 385 | 52 | cos $> 0.9756$ AND dHash $\leq 3.74$ | $0 / 52 = 0\%$ ($95\%$ Wilson $[0\%, 6.88\%]$) |
+
+(Source: Script 36.) Across-fold cosine crossing: pairwise range $[0.9380, 0.9756]$, range = $0.0376$; max absolute deviation from the across-fold mean is $0.028$. This exceeds the report's $0.005$ across-fold stability tolerance by $5.6\times$ and is much larger than the full-Big-4 bootstrap CI half-width of $0.0015$. Together with the all-or-nothing held-out classification pattern (Firm A held out $\Rightarrow$ all held-out CPAs templated; any non-Firm-A firm held out $\Rightarrow$ none templated), this indicates the K=2 boundary is essentially a Firm-A-vs-others separator rather than a within-Big-4 mechanism boundary.
+
+**Table XIII.** K=3 leave-one-firm-out: C1 component shape and held-out membership.
+
+| Held-out firm | C1 cos (fit) | C1 dHash (fit) | C1 weight (fit) | Held-out C1 hard-label rate | Full-Big-4 baseline C1% | Absolute difference |
+|---|---|---|---|---|---|---|
+| Full-Big-4 baseline | 0.9457 | 9.17 | 0.143 | — | — | — |
+| Firm A held out | 0.9425 | 10.13 | 0.145 | $4.68\%$ | $0.00\%$ | $4.68$ pp |
+| Firm B held out | 0.9441 | 9.16 | 0.127 | $7.14\%$ | $8.93\%$ | $1.76$ pp |
+| Firm C held out | 0.9504 | 8.41 | 0.126 | $36.27\%$ | $23.53\%$ | $12.77$ pp |
+| Firm D held out | 0.9439 | 9.29 | 0.120 | $17.31\%$ | $11.54\%$ | $5.81$ pp |
+
+(Source: Script 37; verdict label `P2_PARTIAL`.) Component shape is reproducible across folds: max deviation of C1 cosine = $0.005$, C1 dHash = $0.96$, C1 weight = $0.023$. Hard-posterior membership for the held-out firm varies: max absolute difference from the full-Big-4 baseline is $12.77$ pp at the Firm C held-out fold, exceeding the report's $5$ pp viability bar. We accordingly do not use K=3 hard-posterior membership as an operational classifier label (§III-J, §III-L).
+
+## H. Pixel-Identity Positive-Anchor Miss Rate
+
+This section reports the only hard-ground-truth subset analysis available in the corpus: the positive-anchor miss rate against $n = 262$ Big-4 signatures whose nearest same-CPA match is byte-identical after crop and normalisation. Independent hand-signing cannot produce pixel-identical images, so byte-identical signatures are conservative-subset ground truth for the *replicated* class. The analysis is one-sided (positive-anchor only); a paired false-alarm rate against a hand-signed negative anchor is not available because no signature-level hand-signed ground truth exists in the corpus (§III-K item 4).
+
+**Table XIV.** Positive-anchor miss rate, $n = 262$ Big-4 byte-identical signatures.
+
+| Classifier | Misclassified as hand-leaning | Miss rate | Wilson 95% CI |
+|---|---|---|---|
+| Paper A binary high-confidence box rule (cos $> 0.95$ AND dHash $\leq 5$) | $0 / 262$ | $0\%$ | $[0\%, 1.45\%]$ |
+| K=3 per-CPA hard label (C3 = replicated; descriptive) | $0 / 262$ | $0\%$ | $[0\%, 1.45\%]$ |
+| Reverse-anchor (prevalence-calibrated cut) | $0 / 262$ | $0\%$ | $[0\%, 1.45\%]$ |
+
+(Source: Script 40.) Per-firm breakdown of the byte-identical subset: Firm A 145; Firm B 8; Firm C 107; Firm D 2. All three candidate scores correctly assign every byte-identical signature to the replicated class.
+
+We caution that for the Paper A box rule this result is close to tautological (byte-identical nearest-neighbour signatures have cosine $\approx 1$ and dHash $\approx 0$, well inside the rule's high-confidence region); v3.20.0 §V-F discusses this conservative-subset caveat at length and we retain that discussion. The reverse-anchor cut is chosen by *prevalence calibration* against the inherited box rule's overall replicated rate of $49.58\%$ across Big-4 signatures; this is a documented v4.0 limitation since no signature-level hand-signed ground truth exists to permit direct ROC optimisation.
+
+## I. Inter-CPA Pair-Level Coincidence Rate (Big-4 spike + inherited corpus-wide)
+
+The signature-level inter-CPA pair-level coincidence-rate analysis (reported in v3.20.0 §IV-F.1, Table X as "FAR") is inherited and extended in v4.0. v4.0 retroactively reframes the metric as **inter-CPA pair-level coincidence rate (ICCR)** rather than "False Acceptance Rate" because the corpus does not provide signature-level ground-truth negative labels; the inter-CPA negative-anchor assumption underpinning the metric is itself partially violated by within-firm cross-CPA template-like collision structures (§III-L.4). The v3.20.0 corpus-wide spike on $\sim 50{,}000$ inter-CPA pairs reported a per-comparison rate of $0.0005$ (Wilson 95% CI $[0.0003, 0.0007]$) at the cosine cut $0.95$.
+
+v4.0 additionally reports the §III-L.1 Big-4-scope spike at higher sample size ($5 \times 10^5$ inter-CPA pairs; Script 40b), which replicates and extends the v3 result and adds the structural dimension (dHash) and joint-rule rates. The §III-L.1 numbers are referenced rather than duplicated here; the consolidated v4-new ICCR calibration appears in §IV-M Table XVI.
+
+## J. Five-Way Per-Signature + Document-Level Classification Output
+
+This section reports the §III-L five-way per-signature + document-level worst-case classifier output on the Big-4 sub-corpus. The five-way category definitions are inherited unchanged from v3.20.0 §III-K (now §III-L); see §III-L for the cosine and dHash cuts.
+
+**Table XV.** Five-way per-signature category counts, Big-4 sub-corpus, $n = 150{,}442$ classified.
+
+| Category | Long name | $n$ signatures | % of classified |
+|---|---|---|---|
+| HC | High-confidence non-hand-signed | 74,593 | 49.58% |
+| MC | Moderate-confidence non-hand-signed | 39,817 | 26.47% |
+| HSC | High style consistency | 314 | 0.21% |
+| UN | Uncertain | 35,480 | 23.58% |
+| LH | Likely hand-signed | 238 | 0.16% |
+
+(Source: Script 42; 11 of 150,453 loaded Big-4 signatures lacked one or both descriptors and were excluded.)
+
+**Per-firm five-way breakdown (% within firm).**
+
+| Firm | HC | MC | HSC | UN | LH | total signatures |
+|---|---|---|---|---|---|---|
+| Firm A | 81.70% | 10.76% | 0.05% | 7.42% | 0.07% | 60,448 |
+| Firm B | 34.56% | 35.88% | 0.29% | 29.09% | 0.18% | 34,248 |
+| Firm C | 23.75% | 41.44% | 0.38% | 34.21% | 0.22% | 38,613 |
+| Firm D | 24.51% | 29.33% | 0.22% | 45.65% | 0.29% | 17,133 |
+
+(Source: Script 42 per-firm cross-tab.) The per-firm pattern qualitatively aligns with the K=3 cluster cross-tab of Table XVI: Firm A's signatures concentrate in the HC band (81.70%) while its CPAs concentrate at the accountant level in the K=3 C3-replicated component (82.46%; Table XVI). These two figures address different units (per-signature classification vs per-CPA hard cluster assignment) and are not directly comparable as a like-for-like consistency check; we report the qualitative alignment but do not infer a numerical equivalence. The three non-Firm-A Big-4 firms have markedly lower HC rates than Firm A and substantially higher Uncertain rates, with Firm D having the highest Uncertain rate (45.65%).
+
+**Document-level worst-case aggregation.** Each audit report typically carries two certifying-CPA signatures. We aggregate signature-level outcomes to document-level labels using the v3.20.0 worst-case rule (HC > MC > HSC > UN > LH; §III-L). v4.0 does not change this aggregation rule; only the population over which it is computed changes (Big-4 subset).
+
+**Table XV-B.** Document-level worst-case category counts, Big-4 sub-corpus, $n = 75{,}233$ unique PDFs.
+
+| Category | Long name | $n$ documents | % |
+|---|---|---|---|
+| HC | High-confidence non-hand-signed | 46,857 | 62.28% |
+| MC | Moderate-confidence non-hand-signed | 19,667 | 26.14% |
+| HSC | High style consistency | 167 | 0.22% |
+| UN | Uncertain | 8,524 | 11.33% |
+| LH | Likely hand-signed | 18 | 0.02% |
+
+(Source: Script 42 document-level table; 379 of 75,233 PDFs carried signatures from more than one Big-4 firm and are reported in the single-firm-PDF per-firm breakdown of the script CSV but pooled into the overall counts here.)
+
+**Per-firm document-level breakdown (single-firm PDFs only).**
+
+| Firm | HC | MC | HSC | UN | LH | total docs |
+|---|---|---|---|---|---|---|
+| Firm A | 27,600 | 1,857 | 7 | 758 | 4 | 30,226 |
+| Firm B | 8,783 | 6,079 | 57 | 2,202 | 6 | 17,127 |
+| Firm C | 7,281 | 8,660 | 77 | 3,099 | 5 | 19,122 |
+| Firm D | 3,100 | 2,838 | 22 | 2,416 | 3 | 8,379 |
+
+(Source: Script 42; mixed-firm PDFs $n = 379$ excluded from the per-firm rows but included in the overall counts above.)
+
+The five-way **moderate-confidence non-hand-signed** band (cos $> 0.95$ AND $5 < \text{dHash} \leq 15$) inherits its v3.x calibration; it is **not separately validated by Scripts 38–40**, which evaluated only the binary high-confidence rule (cos $> 0.95$ AND dHash $\leq 5$). v4.0 does not re-derive the moderate-band cuts on the Big-4 subset; we report the Table XV per-firm MC proportions (10.76% / 35.88% / 41.44% / 29.33% across Firms A through D) descriptively. The v3.20.0 capture-rate calibration evidence for the moderate band (v3.20.0 Tables IX, XI, XII, XII-B) is carried into v4.0 by reference and not regenerated on the Big-4 subset. We do not claim that the MC-band per-firm ordering above is a separate validation of the §III-K Spearman convergence, since MC occupancy is not a monotone function of the per-CPA hand-leaning ranking (e.g., Firm D's MC fraction is lower than Firm B's while Firm D's reverse-anchor score ranks it as more hand-leaning than Firm B).
+
+**Table XVI.** Firm × K=3 cluster cross-tabulation, Big-4 sub-corpus.
+
+| Firm | $n$ | C1 (hand-leaning) | C2 (mixed) | C3 (replicated) | C1 % | C3 % |
+|---|---|---|---|---|---|---|
+| Firm A | 171 | 0 | 30 | 141 | $0.00\%$ | $82.46\%$ |
+| Firm B | 112 | 10 | 102 | 0 | $8.93\%$ | $0.00\%$ |
+| Firm C | 102 | 24 | 77 | 1 | $23.53\%$ | $0.98\%$ |
+| Firm D | 52 | 6 | 45 | 1 | $11.54\%$ | $1.92\%$ |
+
+(Source: Script 35.) The cross-tab is the accountant-level descriptive output of the K=3 mixture (§III-J / §IV-E). It is reported here as a complement to the five-way per-signature classifier (Table XV), not as an operational classifier output. Reading: Firm A's CPAs are concentrated in the C3 replicated component (no Firm A CPAs in C1); Firm C has the highest hand-leaning concentration of the Big-4 (C1 fraction $23.5\%$); Firms B and D sit between A and C on the K=3 hard-label ordering, broadly consistent with the per-firm Spearman ordering of Table X (with the within-Big-4-non-A reverse-anchor disagreement noted there).
+
+**Document-level worst-case aggregation outputs are reported in Table XV-B above.**
+
+## K. Full-Dataset Robustness (light scope)
+
+This section reports the v4.0 reproducibility cross-check at the full accountant scope ($n = 686$ CPAs, Big-4 plus mid/small firms). The scope of §IV-K is deliberately narrow: we re-run only the K=3 mixture + Paper A operational-rule per-CPA hand-leaning rate analysis, sufficient to demonstrate that the v4.0 K=3 + Paper A convergence reproduces at the wider scope. The §III-L five-way classifier and the §IV-G LOOO analyses are not re-run at the full scope. The five-way moderate-confidence band is documented as inherited from v3.x calibration in §IV-J.
+
+**Table XVII.** K=3 component comparison, Big-4 sub-corpus vs full dataset.
+
+| K=3 component | Big-4 (n=437) cos / dHash / weight | Full (n=686) cos / dHash / weight | Drift Big-4 → Full |
+|---|---|---|---|
+| C1 hand-leaning | 0.9457 / 9.17 / 0.143 | 0.9278 / 11.17 / 0.284 | $\lvert\Delta\rvert$ cos 0.018, dHash 1.99, wt 0.141 |
+| C2 mixed | 0.9558 / 6.66 / 0.536 | 0.9535 / 6.99 / 0.512 | $\lvert\Delta\rvert$ cos 0.002, dHash 0.33, wt 0.024 |
+| C3 replicated | 0.9826 / 2.41 / 0.321 | 0.9826 / 2.40 / 0.205 | $\lvert\Delta\rvert$ cos 0.000, dHash 0.01, wt 0.117 |
+
+(Source: Script 41; full-dataset $\text{BIC}(K{=}3) = -792.31$ vs Big-4 $\text{BIC}(K{=}3) = -1111.93$; BIC values are not directly comparable across different $n$ and are reported only for completeness.)
+
+**Table XVIII.** Spearman rank correlation between K=3 P(C1) and Paper A operational hand-leaning rate, Big-4 sub-corpus vs full dataset.
+
+| Scope | $n$ CPAs | Spearman $\rho$ (P(C1) vs Paper A hand-leaning rate) | $p$-value |
+|---|---|---|---|
+| Big-4 (primary) | 437 | $+0.9627$ | $< 10^{-248}$ |
+| Full dataset | 686 | $+0.9558$ | $< 10^{-300}$ |
+| $\lvert\rho_{\text{full}} - \rho_{\text{Big-4}}\rvert$ | — | $0.0069$ | — |
+
+(Source: Script 41.)
+
+**Reading.** The K=3 component ordering and the strong Spearman convergence between K=3 P(C1) and the Paper A box-rule hand-leaning rate are preserved at the full scope. Component centres shift modestly: C3 (replicated) is essentially unchanged in centre but loses weight $0.117$ as the full population includes more non-templated CPAs (mid/small firms); C1 (hand-leaning) gains weight $0.141$ and shifts to lower cosine and higher dHash (centre $(0.928, 11.17)$ vs Big-4 $(0.946, 9.17)$) as the broader population includes mid/small-firm hand-leaning CPAs that the Big-4-primary scope deliberately excludes. We read this as evidence that the Big-4-primary K=3 + Paper A convergence is not a Big-4-specific artefact; we do **not** read it as an endorsement of using full-dataset K=3 component centres or operational thresholds in place of the Big-4-primary analysis. Mid/small-firm composition shifts the component centres meaningfully and the v4.0 primary methodology is restricted to Big-4 by design (§III-G item 4).
+
+## L. Feature Backbone Ablation (inherited from v3.20.0 §IV-I)
+
+The feature-backbone ablation (v3.20.0 Table XVIII; backbone replacement of ResNet-50 with alternative ImageNet-pretrained backbones to verify that the §III-E embedding choice is not load-bearing) is inherited unchanged. v3.20.0 Table XVIII is cited by its original v3 number and is **not** the same table as the v4 Table XVIII (which reports the Big-4 vs full-dataset Spearman drift in §IV-K). v4.0 makes no scope-specific re-derivation of the ablation; the analysis is a methodological-stability check on the embedding stage and is corpus-wide rather than Big-4-restricted.
+
+## M. v4-New Anchor-Based ICCR Calibration Results
+
+This section consolidates the v4-new empirical results that support the §III-L anchor-based threshold calibration framework. Numbers below are direct re-statements from the spike scripts cited per row; the corresponding §III provenance table entries appear in §III's provenance table.
+
+### M.1 Composition decomposition (Scripts 39b–39e)
+
+**Table XIX.** Within-firm and between-firm decomposition of the Big-4 accountant-level dip-test rejection.
+
+| Diagnostic | Scope | Statistic | Implication |
+|---|---|---|---|
+| Within-firm signature-level cosine dip | Big-4 (4 firms) | $p_{\text{cos}} \in \{0.176, 0.991, 0.551, 0.976\}$ | 0/4 firms reject; cosine within-firm unimodal |
+| Within-firm signature-level cosine dip | non-Big-4 (10 firms $\geq 500$ sigs) | $p_{\text{cos}} \in [0.59, 0.99]$ | 0/10 firms reject; cosine within-firm unimodal |
+| Within-firm jittered-dHash dip (5 seeds, median) | Big-4 (4 firms) | $p_{\text{med}} \in \{0.999, 0.996, 0.999, 0.9995\}$ | 0/4 firms reject after integer-jitter; raw rejection was integer-tie artefact |
+| Big-4 pooled dHash: 2×2 factorial | firm-centred + jittered (5 seeds) | $p_{\text{med}} = 0.35$, 0/5 seeds reject | combined corrections eliminate rejection; multimodality is composition + integer artefact |
+| Integer-histogram valley near $\text{dHash} \approx 5$ | within each Big-4 firm | none (0/4 firms) | no within-firm dHash antimode at the inherited HC cutoff |
+
+(Source: Scripts 39b, 39c, 39d, 39e; bootstrap $n_{\text{boot}} = 2000$; jitter $\sim \mathrm{U}[-0.5, +0.5]$.)
+
+### M.2 Anchor-based inter-CPA pair-level ICCR (Script 40b)
+
+**Table XX.** Big-4 inter-CPA per-comparison ICCR sweep, $n = 5 \times 10^5$ pairs (Big-4 scope; v4 new).
+
+| Threshold | Per-comparison ICCR | 95% Wilson CI |
+|---|---|---|
+| cos $> 0.945$ (v3.x published "natural threshold") | $0.00081$ | $[0.00073, 0.00089]$ |
+| cos $> 0.95$ (inherited operating point) | $0.00060$ | $[0.00053, 0.00067]$ |
+| cos $> 0.97$ | $0.00024$ | $[0.00020, 0.00029]$ |
+| cos $> 0.98$ | $0.00009$ | $[0.00007, 0.00012]$ |
+| dHash $\leq 5$ (inherited operating point) | $0.00129$ | $[0.00120, 0.00140]$ |
+| dHash $\leq 4$ | $0.00050$ | $[0.00044, 0.00057]$ |
+| dHash $\leq 3$ | $0.00019$ | $[0.00015, 0.00023]$ |
+| Joint: cos $> 0.95$ AND dHash $\leq 5$ (any-pair semantics) | $0.00014$ | — |
+| Joint: cos $> 0.95$ AND dHash $\leq 4$ (any-pair) | $0.00011$ | — |
+
+Conditional ICCR(dHash $\leq 5$ | cos $> 0.95$) $= 0.234$ (Wilson 95% $[0.190, 0.285]$; $70$ of $299$ pairs).
+
+The cos $> 0.95$ row replicates v3.20.0 §IV-F.1 Table X (v3 reported $0.0005$ under prior "FAR" terminology). The dHash row and joint row are v4 new.
+
+### M.3 Pool-normalised per-signature ICCR (Script 43)
+
+**Table XXI.** Pool-normalised per-signature ICCR under the deployed any-pair HC rule (cos $> 0.95$ AND dHash $\leq 5$); $n_{\text{sig}} = 150{,}453$ (vector-complete Big-4); CPA-block bootstrap $n_{\text{boot}} = 1000$.
+
+| Scope | Per-signature ICCR | Wilson 95% CI | CPA-bootstrap 95% CI |
+|---|---|---|---|
+| Big-4 pooled (any-pair, deployed) | $0.1102$ | $[0.1086, 0.1118]$ | $[0.0908, 0.1330]$ |
+| Big-4 pooled (same-pair, stricter alternative) | $0.0827$ | $[0.0813, 0.0841]$ | $[0.0668, 0.1021]$ |
+| Firm A (any-pair) | $0.2594$ | — | — |
+| Firm B (any-pair) | $0.0147$ | — | — |
+| Firm C (any-pair) | $0.0053$ | — | — |
+| Firm D (any-pair) | $0.0110$ | — | — |
+| Pool-size decile 1 (smallest pools) any-pair | $0.0249$ | — | — |
+| Pool-size decile 10 (largest pools) any-pair | $0.1905$ | — | — |
+
+Decile trend is broadly monotone in pool size with two minor reversals (decile 5 and decile 9 dip below their predecessors). Stricter operating point cos $> 0.95$ AND dHash $\leq 3$ (same-pair) gives per-signature ICCR $0.0449$.
+
+### M.4 Document-level ICCR under three alarm definitions (Script 45)
+
+**Table XXII.** Document-level inter-CPA ICCR by alarm definition; $n_{\text{docs}} = 75{,}233$.
+
+| Alarm definition | Alarm set | Document-level ICCR | Wilson 95% CI |
+|---|---|---|---|
+| D1 | HC only | $0.1797$ | $[0.1770, 0.1825]$ |
+| D2 (operational) | HC + MC | $0.3375$ | $[0.3342, 0.3409]$ |
+| D3 | HC + MC + HSC | $0.3384$ | $[0.3351, 0.3418]$ |
+
+Per-firm D2 document-level ICCR: Firm A $0.6201$ ($n = 30{,}226$); Firm B $0.1600$ ($n = 17{,}127$); Firm C $0.1635$ ($n = 19{,}501$); Firm D $0.0863$ ($n = 8{,}379$).
+
+### M.5 Firm heterogeneity logistic regression and cross-firm hit matrix (Script 44)
+
+**Table XXIII.** Logistic regression of per-signature any-pair HC hit indicator on firm dummies and centred log pool size (Firm A reference).
+
+| Term | Odds ratio (vs Firm A) | Direction |
+|---|---|---|
+| Firm B | $0.053$ | $\sim 19\times$ lower odds than Firm A |
+| Firm C | $0.010$ | $\sim 100\times$ lower odds than Firm A |
+| Firm D | $0.027$ | $\sim 37\times$ lower odds than Firm A |
+| log(pool size, centred) | $4.01$ | $\sim 4\times$ higher odds per log unit pool size |
+
+Per-decile per-firm rates (Table not duplicated here; Script 44 decile table available in the supplementary report): within every pool-size decile, Firms B/C/D show rates of $0.0006$–$0.0358$ while Firm A ranges $0.0541$–$0.5958$. The firm gap survives within matched pool sizes.
+
+**Table XXIV.** Cross-firm hit matrix among Big-4 source signatures with any-pair HC hit; max-cosine partner firm (counts).
+
+| Source firm | Firm A cand. | Firm B | Firm C | Firm D | non-Big-4 | n hits |
+|---|---|---|---|---|---|---|
+| Firm A | $14{,}447$ | $95$ | $44$ | $19$ | $17$ | $14{,}622$ |
+| Firm B | $92$ | $371$ | $8$ | $4$ | $9$ | $484$ |
+| Firm C | $16$ | $7$ | $149$ | $5$ | $1$ | $178$ |
+| Firm D | $22$ | $2$ | $6$ | $106$ | $1$ | $137$ |
+
+Same-pair joint hits (single candidate satisfying both cos $> 0.95$ AND dHash $\leq 5$) are within-firm at rates $99.96\%$ / $97.7\%$ / $98.2\%$ / $97.0\%$ for Firms A/B/C/D respectively.
+
+### M.6 Alert-rate sensitivity around inherited HC threshold (Script 46)
+
+**Table XXV.** Local-gradient / median-gradient ratio at inherited thresholds (descriptive plateau diagnostic).
+
+| Threshold | Local / median gradient ratio | Interpretation |
+|---|---|---|
+| cos $= 0.95$ (HC) | $\approx 25\times$ | locally sensitive (not plateau-stable) |
+| dHash $= 5$ (HC) | $\approx 3.8\times$ | locally sensitive (not plateau-stable) |
+| dHash $= 15$ (MC/HSC boundary) | $\approx 0.08$ | plateau-like (saturating tail) |
+
+Big-4 observed deployed alert rate on actual same-CPA pools: per-signature HC $= 0.4958$; per-document HC $= 0.6228$. The deployed-rate excess over the inter-CPA proxy is $0.3856$ pp per-signature and $0.4431$ pp per-document; this excess is interpreted as a same-CPA repeatability signal under the §III-M caveats, not as a presumed true-positive rate.
+
+---
+
+## Phase 3 close-out checklist
+
+The following items remain after codex rounds 21–24 and before §IV is sent to partner Jimmy for v4.0 review:
+
+1. **Table XV per-signature category counts** — RESOLVED (v2 of §IV draft, Script 42 output). Per-signature, per-firm, document-level, and per-firm-document tables now populated.
+2. **Table renumbering finalisation.** The v4 table sequence as of v3.2 is Tables V–XVIII plus Table XV-B (no v4 Table IV is printed); inherited v3.x tables such as capture-rate Tables IX, XI, XII and the backbone-ablation v3.20.0 Table XVIII are kept by reference and cited as "v3.20.0 Table N" rather than reproduced as v4-numbered tables. A final pass should confirm whether the target journal accepts the Table XV-B letter suffix; if not, XV-B can be renumbered to a sequential XIX with §IV-J text adjusted accordingly.
+3. **§IV-A to §IV-C content audit.** Verify that the inherited prose for Experimental Setup, Detection Performance, and All-Pairs analysis remains accurate after the §III-G scope change to Big-4 primary.
+4. **Open question carry-over from §III v3.** Codex round-22 open questions on five-way moderate-band validation, firm anonymisation policy, and §IV table numbering are addressed in this v3 of §IV: (a) five-way moderate band documented as inherited from v3.x in §IV-J with Big-4 per-firm proportions reported descriptively (Table XV); (b) firm anonymisation maintained throughout §IV (Firm A–D used consistently; real names removed in v3); (c) §IV table numbering set provisionally and to be finalised at Phase 3 close-out.
+
+5. **Internal author notes (this checklist + §III's cross-reference index + both files' draft-note headers).** These are author working artefacts and should be moved to a separate notes file or stripped before partner / submission packaging.

signature-comparison/v4-current/SUMMARY.txt

@@ -0,0 +1,17 @@
+
+PaddleOCR v2.7.3 (v4) 完整 Pipeline 測試結果
+============================================================
+
+1. OCR 檢測: 14 個文字區域
+2. 遮罩印刷文字: 完成
+3. 檢測候選區域: 4 個
+4. 提取簽名: 4 個
+
+候選區域詳情:
+------------------------------------------------------------
+Region 1: 位置(1211, 1462), 大小965x191, 面積=184315
+Region 2: 位置(1215, 877), 大小1150x511, 面積=587650
+Region 3: 位置(332, 150), 大小197x96, 面積=18912
+Region 4: 位置(1147, 3303), 大小159x42, 面積=6678
+
+所有結果保存在: /Volumes/NV2/pdf_recognize/signature-comparison/v4-current

signature-comparison/v5-new/SUMMARY.txt

@@ -0,0 +1,20 @@
+
+PP-OCRv5 完整 Pipeline 測試結果
+============================================================
+
+1. OCR 檢測: 50 個文字區域
+2. 遮罩印刷文字: /Volumes/NV2/pdf_recognize/test_results/v5_pipeline/01_masked.png
+3. 檢測候選區域: 7 個
+4. 提取簽名: 7 個
+
+候選區域詳情:
+------------------------------------------------------------
+Region 1: 位置(1218, 877), 大小1144x511, 面積=584584
+Region 2: 位置(1213, 1457), 大小961x196, 面積=188356
+Region 3: 位置(228, 386), 大小2028x209, 面積=423852
+Region 4: 位置(330, 310), 大小1932x63, 面積=121716
+Region 5: 位置(1990, 945), 大小375x212, 面積=79500
+Region 6: 位置(327, 145), 大小203x101, 面積=20503
+Region 7: 位置(1139, 3289), 大小174x63, 面積=10962
+
+所有結果保存在: /Volumes/NV2/pdf_recognize/test_results/v5_pipeline

signature_analysis/01_init_database.py

@@ -0,0 +1,246 @@
+#!/usr/bin/env python3
+"""
+Step 1: 建立 SQLite 資料庫，匯入簽名記錄
+
+從 extraction_results.csv 匯入資料，展開每個圖片為獨立記錄
+解析圖片檔名填充 year_month, sig_index
+計算圖片尺寸 width, height
+"""
+
+import sqlite3
+import pandas as pd
+import cv2
+import os
+import re
+from pathlib import Path
+from tqdm import tqdm
+from concurrent.futures import ThreadPoolExecutor, as_completed
+
+# 路徑配置
+IMAGES_DIR = Path("/Volumes/NV2/PDF-Processing/yolo-signatures/images")
+CSV_PATH = Path("/Volumes/NV2/PDF-Processing/yolo-signatures/extraction_results.csv")
+OUTPUT_DIR = Path("/Volumes/NV2/PDF-Processing/signature-analysis")
+DB_PATH = OUTPUT_DIR / "signature_analysis.db"
+
+
+def parse_image_filename(filename: str) -> dict:
+    """
+    解析圖片檔名，提取結構化資訊
+
+    範例: 201301_2458_AI1_page4_sig1.png
+    """
+    # 移除 .png 副檔名
+    name = filename.replace('.png', '')
+
+    # 解析模式: {YYYYMM}_{SERIAL}_{DOCTYPE}_page{PAGE}_sig{N}
+    match = re.match(r'^(\d{6})_([^_]+)_([^_]+)_page(\d+)_sig(\d+)$', name)
+
+    if match:
+        year_month, serial, doc_type, page, sig_index = match.groups()
+        return {
+            'year_month': year_month,
+            'serial_number': serial,
+            'doc_type': doc_type,
+            'page_number': int(page),
+            'sig_index': int(sig_index)
+        }
+    else:
+        # 無法解析時返回 None
+        return {
+            'year_month': None,
+            'serial_number': None,
+            'doc_type': None,
+            'page_number': None,
+            'sig_index': None
+        }
+
+
+def get_image_dimensions(image_path: Path) -> tuple:
+    """讀取圖片尺寸"""
+    try:
+        img = cv2.imread(str(image_path))
+        if img is not None:
+            h, w = img.shape[:2]
+            return w, h
+        return None, None
+    except Exception:
+        return None, None
+
+
+def process_single_image(args: tuple) -> dict:
+    """處理單張圖片，返回資料記錄"""
+    image_filename, source_pdf, confidence_avg = args
+
+    # 解析檔名
+    parsed = parse_image_filename(image_filename)
+
+    # 取得圖片尺寸
+    image_path = IMAGES_DIR / image_filename
+    width, height = get_image_dimensions(image_path)
+
+    return {
+        'image_filename': image_filename,
+        'source_pdf': source_pdf,
+        'year_month': parsed['year_month'],
+        'serial_number': parsed['serial_number'],
+        'doc_type': parsed['doc_type'],
+        'page_number': parsed['page_number'],
+        'sig_index': parsed['sig_index'],
+        'detection_confidence': confidence_avg,
+        'image_width': width,
+        'image_height': height
+    }
+
+
+def create_database():
+    """建立資料庫 schema"""
+    OUTPUT_DIR.mkdir(parents=True, exist_ok=True)
+
+    conn = sqlite3.connect(DB_PATH)
+    cursor = conn.cursor()
+
+    # 建立 signatures 表
+    cursor.execute('''
+        CREATE TABLE IF NOT EXISTS signatures (
+            signature_id INTEGER PRIMARY KEY AUTOINCREMENT,
+            image_filename TEXT UNIQUE NOT NULL,
+            source_pdf TEXT NOT NULL,
+            year_month TEXT,
+            serial_number TEXT,
+            doc_type TEXT,
+            page_number INTEGER,
+            sig_index INTEGER,
+            detection_confidence REAL,
+            image_width INTEGER,
+            image_height INTEGER,
+            accountant_name TEXT,
+            accountant_id INTEGER,
+            feature_vector BLOB,
+            cluster_id INTEGER,
+            created_at TIMESTAMP DEFAULT CURRENT_TIMESTAMP
+        )
+    ''')
+
+    # 建立索引
+    cursor.execute('CREATE INDEX IF NOT EXISTS idx_source_pdf ON signatures(source_pdf)')
+    cursor.execute('CREATE INDEX IF NOT EXISTS idx_year_month ON signatures(year_month)')
+    cursor.execute('CREATE INDEX IF NOT EXISTS idx_accountant_id ON signatures(accountant_id)')
+
+    conn.commit()
+    conn.close()
+
+    print(f"資料庫已建立: {DB_PATH}")
+
+
+def expand_csv_to_records(csv_path: Path) -> list:
+    """
+    將 CSV 展開為單張圖片記錄
+
+    CSV 格式: filename,page,num_signatures,confidence_avg,image_files
+    需要將 image_files 展開為多筆記錄
+    """
+    df = pd.read_csv(csv_path)
+
+    records = []
+    for _, row in df.iterrows():
+        source_pdf = row['filename']
+        confidence_avg = row['confidence_avg']
+        image_files_str = row['image_files']
+
+        # 展開 image_files（逗號分隔）
+        if pd.notna(image_files_str):
+            image_files = [f.strip() for f in image_files_str.split(',')]
+            for img_file in image_files:
+                records.append((img_file, source_pdf, confidence_avg))
+
+    return records
+
+
+def import_data():
+    """匯入資料到資料庫"""
+    print("讀取 CSV 並展開記錄...")
+    records = expand_csv_to_records(CSV_PATH)
+    print(f"共 {len(records)} 張簽名圖片待處理")
+
+    print("處理圖片資訊（讀取尺寸）...")
+    processed_records = []
+
+    # 使用多執行緒加速圖片尺寸讀取
+    with ThreadPoolExecutor(max_workers=8) as executor:
+        futures = {executor.submit(process_single_image, r): r for r in records}
+
+        for future in tqdm(as_completed(futures), total=len(records), desc="處理圖片"):
+            result = future.result()
+            processed_records.append(result)
+
+    print("寫入資料庫...")
+    conn = sqlite3.connect(DB_PATH)
+    cursor = conn.cursor()
+
+    # 批次插入
+    insert_sql = '''
+        INSERT OR IGNORE INTO signatures (
+            image_filename, source_pdf, year_month, serial_number, doc_type,
+            page_number, sig_index, detection_confidence, image_width, image_height
+        ) VALUES (?, ?, ?, ?, ?, ?, ?, ?, ?, ?)
+    '''
+
+    batch_data = [
+        (
+            r['image_filename'], r['source_pdf'], r['year_month'], r['serial_number'],
+            r['doc_type'], r['page_number'], r['sig_index'], r['detection_confidence'],
+            r['image_width'], r['image_height']
+        )
+        for r in processed_records
+    ]
+
+    cursor.executemany(insert_sql, batch_data)
+    conn.commit()
+
+    # 統計結果
+    cursor.execute('SELECT COUNT(*) FROM signatures')
+    total = cursor.fetchone()[0]
+
+    cursor.execute('SELECT COUNT(DISTINCT source_pdf) FROM signatures')
+    pdf_count = cursor.fetchone()[0]
+
+    cursor.execute('SELECT COUNT(DISTINCT year_month) FROM signatures')
+    period_count = cursor.fetchone()[0]
+
+    cursor.execute('SELECT MIN(year_month), MAX(year_month) FROM signatures')
+    min_date, max_date = cursor.fetchone()
+
+    conn.close()
+
+    print("\n" + "=" * 50)
+    print("資料庫建立完成")
+    print("=" * 50)
+    print(f"簽名總數: {total:,}")
+    print(f"PDF 檔案數: {pdf_count:,}")
+    print(f"時間範圍: {min_date} ~ {max_date} ({period_count} 個月)")
+    print(f"資料庫位置: {DB_PATH}")
+
+
+def main():
+    print("=" * 50)
+    print("Step 1: 建立簽名分析資料庫")
+    print("=" * 50)
+
+    # 檢查來源檔案
+    if not CSV_PATH.exists():
+        print(f"錯誤: 找不到 CSV 檔案 {CSV_PATH}")
+        return
+
+    if not IMAGES_DIR.exists():
+        print(f"錯誤: 找不到圖片目錄 {IMAGES_DIR}")
+        return
+
+    # 建立資料庫
+    create_database()
+
+    # 匯入資料
+    import_data()
+
+
+if __name__ == "__main__":
+    main()

signature_analysis/02_extract_features.py

@@ -0,0 +1,241 @@
+#!/usr/bin/env python3
+"""
+Step 2: 使用 ResNet-50 提取簽名圖片的特徵向量
+
+預處理流程:
+1. 載入圖片 (RGB)
+2. 縮放至 224x224（保持比例，填充白色）
+3. 正規化 (ImageNet mean/std)
+4. 通過 ResNet-50 (去掉最後分類層)
+5. L2 正規化
+6. 輸出 2048 維特徵向量
+"""
+
+import torch
+import torch.nn as nn
+import torchvision.models as models
+import torchvision.transforms as transforms
+from torch.utils.data import Dataset, DataLoader
+import numpy as np
+import cv2
+import sqlite3
+from pathlib import Path
+from tqdm import tqdm
+import warnings
+warnings.filterwarnings('ignore')
+
+# 路徑配置
+IMAGES_DIR = Path("/Volumes/NV2/PDF-Processing/yolo-signatures/images")
+OUTPUT_DIR = Path("/Volumes/NV2/PDF-Processing/signature-analysis")
+DB_PATH = OUTPUT_DIR / "signature_analysis.db"
+FEATURES_PATH = OUTPUT_DIR / "features"
+
+# 模型配置
+BATCH_SIZE = 64
+NUM_WORKERS = 4
+DEVICE = torch.device("mps" if torch.backends.mps.is_available() else
+                      "cuda" if torch.cuda.is_available() else "cpu")
+
+
+class SignatureDataset(Dataset):
+    """簽名圖片資料集"""
+
+    def __init__(self, image_paths: list, transform=None):
+        self.image_paths = image_paths
+        self.transform = transform
+
+    def __len__(self):
+        return len(self.image_paths)
+
+    def __getitem__(self, idx):
+        img_path = self.image_paths[idx]
+
+        # 載入圖片
+        img = cv2.imread(str(img_path))
+        if img is None:
+            # 如果讀取失敗，返回白色圖片
+            img = np.ones((224, 224, 3), dtype=np.uint8) * 255
+        else:
+            img = cv2.cvtColor(img, cv2.COLOR_BGR2RGB)
+
+        # 調整大小（保持比例，填充白色）
+        img = self.resize_with_padding(img, 224, 224)
+
+        if self.transform:
+            img = self.transform(img)
+
+        return img, str(img_path.name)
+
+    @staticmethod
+    def resize_with_padding(img, target_w, target_h):
+        """調整大小並填充白色以保持比例"""
+        h, w = img.shape[:2]
+
+        # 計算縮放比例
+        scale = min(target_w / w, target_h / h)
+        new_w = int(w * scale)
+        new_h = int(h * scale)
+
+        # 縮放
+        resized = cv2.resize(img, (new_w, new_h), interpolation=cv2.INTER_AREA)
+
+        # 建立白色畫布
+        canvas = np.ones((target_h, target_w, 3), dtype=np.uint8) * 255
+
+        # 置中貼上
+        x_offset = (target_w - new_w) // 2
+        y_offset = (target_h - new_h) // 2
+        canvas[y_offset:y_offset+new_h, x_offset:x_offset+new_w] = resized
+
+        return canvas
+
+
+class FeatureExtractor:
+    """特徵提取器"""
+
+    def __init__(self, device):
+        self.device = device
+
+        # 載入預訓練 ResNet-50
+        print(f"載入 ResNet-50 模型... (device: {device})")
+        self.model = models.resnet50(weights=models.ResNet50_Weights.IMAGENET1K_V2)
+
+        # 移除最後的分類層，保留特徵
+        self.model = nn.Sequential(*list(self.model.children())[:-1])
+        self.model = self.model.to(device)
+        self.model.eval()
+
+        # ImageNet 正規化
+        self.transform = transforms.Compose([
+            transforms.ToTensor(),
+            transforms.Normalize(
+                mean=[0.485, 0.456, 0.406],
+                std=[0.229, 0.224, 0.225]
+            )
+        ])
+
+    @torch.no_grad()
+    def extract_batch(self, images):
+        """提取一批圖片的特徵"""
+        images = images.to(self.device)
+        features = self.model(images)
+        features = features.squeeze(-1).squeeze(-1)  # [B, 2048]
+
+        # L2 正規化
+        features = nn.functional.normalize(features, p=2, dim=1)
+
+        return features.cpu().numpy()
+
+
+def get_image_list_from_db():
+    """從資料庫取得所有圖片檔名"""
+    conn = sqlite3.connect(DB_PATH)
+    cursor = conn.cursor()
+
+    cursor.execute('SELECT image_filename FROM signatures ORDER BY signature_id')
+    filenames = [row[0] for row in cursor.fetchall()]
+
+    conn.close()
+    return filenames
+
+
+def save_features_to_db(features_dict: dict):
+    """將特徵向量存入資料庫"""
+    conn = sqlite3.connect(DB_PATH)
+    cursor = conn.cursor()
+
+    for filename, feature in tqdm(features_dict.items(), desc="寫入資料庫"):
+        cursor.execute('''
+            UPDATE signatures
+            SET feature_vector = ?
+            WHERE image_filename = ?
+        ''', (feature.tobytes(), filename))
+
+    conn.commit()
+    conn.close()
+
+
+def main():
+    print("=" * 60)
+    print("Step 2: ResNet-50 特徵向量提取")
+    print("=" * 60)
+    print(f"裝置: {DEVICE}")
+
+    # 確保輸出目錄存在
+    FEATURES_PATH.mkdir(parents=True, exist_ok=True)
+
+    # 從資料庫取得圖片列表
+    print("從資料庫讀取圖片列表...")
+    filenames = get_image_list_from_db()
+    print(f"共 {len(filenames):,} 張圖片待處理")
+
+    # 建立圖片路徑列表
+    image_paths = [IMAGES_DIR / f for f in filenames]
+
+    # 初始化特徵提取器
+    extractor = FeatureExtractor(DEVICE)
+
+    # 建立資料集和載入器
+    dataset = SignatureDataset(image_paths, transform=extractor.transform)
+    dataloader = DataLoader(
+        dataset,
+        batch_size=BATCH_SIZE,
+        shuffle=False,
+        num_workers=NUM_WORKERS,
+        pin_memory=True
+    )
+
+    # 提取特徵
+    print(f"\n開始提取特徵 (batch_size={BATCH_SIZE})...")
+    all_features = []
+    all_filenames = []
+
+    for images, batch_filenames in tqdm(dataloader, desc="提取特徵"):
+        features = extractor.extract_batch(images)
+        all_features.append(features)
+        all_filenames.extend(batch_filenames)
+
+    # 合併所有特徵
+    all_features = np.vstack(all_features)
+    print(f"\n特徵矩陣形狀: {all_features.shape}")
+
+    # 儲存為 numpy 檔案（備份）
+    npy_path = FEATURES_PATH / "signature_features.npy"
+    np.save(npy_path, all_features)
+    print(f"特徵向量已儲存: {npy_path} ({all_features.nbytes / 1e9:.2f} GB)")
+
+    # 儲存檔名對應（用於後續索引）
+    filenames_path = FEATURES_PATH / "signature_filenames.txt"
+    with open(filenames_path, 'w') as f:
+        for fn in all_filenames:
+            f.write(fn + '\n')
+    print(f"檔名列表已儲存: {filenames_path}")
+
+    # 更新資料庫
+    print("\n更新資料庫中的特徵向量...")
+    features_dict = dict(zip(all_filenames, all_features))
+    save_features_to_db(features_dict)
+
+    # 統計
+    print("\n" + "=" * 60)
+    print("特徵提取完成")
+    print("=" * 60)
+    print(f"處理圖片數: {len(all_filenames):,}")
+    print(f"特徵維度: {all_features.shape[1]}")
+    print(f"特徵檔案: {npy_path}")
+    print(f"檔案大小: {all_features.nbytes / 1e9:.2f} GB")
+
+    # 簡單驗證
+    print("\n特徵統計:")
+    print(f"  平均值: {all_features.mean():.6f}")
+    print(f"  標準差: {all_features.std():.6f}")
+    print(f"  最小值: {all_features.min():.6f}")
+    print(f"  最大值: {all_features.max():.6f}")
+
+    # L2 norm 驗證（應該都是 1.0）
+    norms = np.linalg.norm(all_features, axis=1)
+    print(f"  L2 norm: {norms.mean():.6f} ± {norms.std():.6f}")
+
+
+if __name__ == "__main__":
+    main()

signature_analysis/03_similarity_analysis.py

@@ -0,0 +1,368 @@
+#!/usr/bin/env python3
+"""
+Step 3: 相似度分布探索
+
+1. 隨機抽樣 100,000 對簽名
+2. 計算 cosine similarity
+3. 繪製直方圖分布
+4. 找出高相似度對 (>0.95)
+5. 分析高相似度對的來源
+"""
+
+import numpy as np
+import matplotlib.pyplot as plt
+import seaborn as sns
+from pathlib import Path
+from tqdm import tqdm
+import random
+from collections import defaultdict
+import json
+
+# 路徑配置
+OUTPUT_DIR = Path("/Volumes/NV2/PDF-Processing/signature-analysis")
+FEATURES_PATH = OUTPUT_DIR / "features" / "signature_features.npy"
+FILENAMES_PATH = OUTPUT_DIR / "features" / "signature_filenames.txt"
+REPORTS_PATH = OUTPUT_DIR / "reports"
+
+# 分析配置
+NUM_RANDOM_PAIRS = 100000
+HIGH_SIMILARITY_THRESHOLD = 0.95
+VERY_HIGH_SIMILARITY_THRESHOLD = 0.99
+
+
+def load_data():
+    """載入特徵向量和檔名"""
+    print("載入特徵向量...")
+    features = np.load(FEATURES_PATH)
+    print(f"特徵矩陣形狀: {features.shape}")
+
+    print("載入檔名列表...")
+    with open(FILENAMES_PATH, 'r') as f:
+        filenames = [line.strip() for line in f.readlines()]
+    print(f"檔名數量: {len(filenames)}")
+
+    return features, filenames
+
+
+def parse_filename(filename: str) -> dict:
+    """解析檔名提取資訊"""
+    # 範例: 201301_2458_AI1_page4_sig1.png
+    parts = filename.replace('.png', '').split('_')
+    if len(parts) >= 5:
+        return {
+            'year_month': parts[0],
+            'serial': parts[1],
+            'doc_type': parts[2],
+            'page': parts[3].replace('page', ''),
+            'sig_index': parts[4].replace('sig', '')
+        }
+    return {'raw': filename}
+
+
+def cosine_similarity(v1, v2):
+    """計算餘弦相似度（向量已 L2 正規化）"""
+    return np.dot(v1, v2)
+
+
+def random_sampling_analysis(features, filenames, n_pairs=100000):
+    """隨機抽樣計算相似度分布"""
+    print(f"\n隨機抽樣 {n_pairs:,} 對簽名...")
+
+    n = len(filenames)
+    similarities = []
+    pair_indices = []
+
+    # 產生隨機配對
+    for _ in tqdm(range(n_pairs), desc="計算相似度"):
+        i, j = random.sample(range(n), 2)
+        sim = cosine_similarity(features[i], features[j])
+        similarities.append(sim)
+        pair_indices.append((i, j))
+
+    return np.array(similarities), pair_indices
+
+
+def find_high_similarity_pairs(features, filenames, threshold=0.95, sample_size=100000):
+    """找出高相似度的簽名對"""
+    print(f"\n搜尋相似度 > {threshold} 的簽名對...")
+
+    n = len(filenames)
+    high_sim_pairs = []
+
+    # 使用隨機抽樣找高相似度對
+    # 由於全量計算太慢 (n^2 = 33 billion pairs)，採用抽樣策略
+    for _ in tqdm(range(sample_size), desc="搜尋高相似度"):
+        i, j = random.sample(range(n), 2)
+        sim = cosine_similarity(features[i], features[j])
+        if sim > threshold:
+            high_sim_pairs.append({
+                'idx1': i,
+                'idx2': j,
+                'file1': filenames[i],
+                'file2': filenames[j],
+                'similarity': float(sim),
+                'parsed1': parse_filename(filenames[i]),
+                'parsed2': parse_filename(filenames[j])
+            })
+
+    return high_sim_pairs
+
+
+def systematic_high_similarity_search(features, filenames, threshold=0.95, batch_size=1000):
+    """
+    更系統化的高相似度搜尋：
+    對每個簽名，找出與它最相似的其他簽名
+    """
+    print(f"\n系統化搜尋高相似度對 (threshold={threshold})...")
+    print("這會對每個簽名找出最相似的候選...")
+
+    n = len(filenames)
+    high_sim_pairs = []
+    seen_pairs = set()
+
+    # 隨機抽樣一部分簽名作為查詢
+    sample_indices = random.sample(range(n), min(5000, n))
+
+    for idx in tqdm(sample_indices, desc="搜尋"):
+        # 計算這個簽名與所有其他簽名的相似度
+        # 使用矩陣運算加速
+        sims = features @ features[idx]
+
+        # 找出高於閾值的（排除自己）
+        high_sim_idx = np.where(sims > threshold)[0]
+
+        for j in high_sim_idx:
+            if j != idx:
+                pair_key = tuple(sorted([idx, int(j)]))
+                if pair_key not in seen_pairs:
+                    seen_pairs.add(pair_key)
+                    high_sim_pairs.append({
+                        'idx1': int(idx),
+                        'idx2': int(j),
+                        'file1': filenames[idx],
+                        'file2': filenames[int(j)],
+                        'similarity': float(sims[j]),
+                        'parsed1': parse_filename(filenames[idx]),
+                        'parsed2': parse_filename(filenames[int(j)])
+                    })
+
+    return high_sim_pairs
+
+
+def analyze_high_similarity_sources(high_sim_pairs):
+    """分析高相似度對的來源特徵"""
+    print("\n分析高相似度對的來源...")
+
+    stats = {
+        'same_pdf': 0,
+        'same_year_month': 0,
+        'same_doc_type': 0,
+        'different_everything': 0,
+        'total': len(high_sim_pairs)
+    }
+
+    for pair in high_sim_pairs:
+        p1, p2 = pair.get('parsed1', {}), pair.get('parsed2', {})
+
+        # 同一 PDF
+        if p1.get('year_month') == p2.get('year_month') and \
+           p1.get('serial') == p2.get('serial') and \
+           p1.get('doc_type') == p2.get('doc_type'):
+            stats['same_pdf'] += 1
+        # 同月份
+        elif p1.get('year_month') == p2.get('year_month'):
+            stats['same_year_month'] += 1
+        # 同類型
+        elif p1.get('doc_type') == p2.get('doc_type'):
+            stats['same_doc_type'] += 1
+        else:
+            stats['different_everything'] += 1
+
+    return stats
+
+
+def plot_similarity_distribution(similarities, output_path):
+    """繪製相似度分布圖"""
+    print("\n繪製分布圖...")
+
+    try:
+        # 轉換為 Python list 完全避免 numpy 問題
+        sim_list = similarities.tolist()
+
+        fig, axes = plt.subplots(1, 2, figsize=(14, 5))
+
+        # 左圖：完整分布 - 使用 range 指定 bins
+        ax1 = axes[0]
+        ax1.hist(sim_list, bins=np.linspace(min(sim_list), max(sim_list), 101).tolist(),
+                 density=True, alpha=0.7, color='steelblue', edgecolor='white')
+        ax1.axvline(x=0.95, color='red', linestyle='--', label='0.95 threshold')
+        ax1.axvline(x=0.99, color='darkred', linestyle='--', label='0.99 threshold')
+        ax1.set_xlabel('Cosine Similarity', fontsize=12)
+        ax1.set_ylabel('Density', fontsize=12)
+        ax1.set_title('Signature Similarity Distribution (Random Sampling)', fontsize=14)
+        ax1.legend()
+
+        # 統計標註
+        mean_sim = float(np.mean(similarities))
+        std_sim = float(np.std(similarities))
+        ax1.annotate(f'Mean: {mean_sim:.4f}\nStd: {std_sim:.4f}',
+                    xy=(0.02, 0.95), xycoords='axes fraction',
+                    fontsize=10, verticalalignment='top',
+                    bbox=dict(boxstyle='round', facecolor='wheat', alpha=0.5))
+
+        # 右圖：高相似度區域放大
+        ax2 = axes[1]
+        high_sim_list = [x for x in sim_list if x > 0.8]
+        if len(high_sim_list) > 0:
+            ax2.hist(high_sim_list, bins=np.linspace(0.8, max(high_sim_list), 51).tolist(),
+                     density=True, alpha=0.7, color='coral', edgecolor='white')
+            ax2.axvline(x=0.95, color='red', linestyle='--', label='0.95 threshold')
+            ax2.axvline(x=0.99, color='darkred', linestyle='--', label='0.99 threshold')
+        ax2.set_xlabel('Cosine Similarity', fontsize=12)
+        ax2.set_ylabel('Density', fontsize=12)
+        ax2.set_title('High Similarity Region (> 0.8)', fontsize=14)
+        ax2.legend()
+
+        # 高相似度統計
+        pct_95 = int((similarities > 0.95).sum()) / len(similarities) * 100
+        pct_99 = int((similarities > 0.99).sum()) / len(similarities) * 100
+        ax2.annotate(f'> 0.95: {pct_95:.4f}%\n> 0.99: {pct_99:.4f}%',
+                    xy=(0.98, 0.95), xycoords='axes fraction',
+                    fontsize=10, verticalalignment='top', horizontalalignment='right',
+                    bbox=dict(boxstyle='round', facecolor='wheat', alpha=0.5))
+
+        plt.tight_layout()
+        plt.savefig(output_path, dpi=150, bbox_inches='tight')
+        plt.close()
+
+        print(f"分布圖已儲存: {output_path}")
+    except Exception as e:
+        print(f"繪圖失敗: {e}")
+        print("跳過繪圖，繼續其他分析...")
+
+
+def generate_statistics_report(similarities, high_sim_pairs, source_stats, output_path):
+    """生成統計報告"""
+    report = {
+        'random_sampling': {
+            'n_pairs': len(similarities),
+            'mean': float(np.mean(similarities)),
+            'std': float(np.std(similarities)),
+            'min': float(np.min(similarities)),
+            'max': float(np.max(similarities)),
+            'percentiles': {
+                '25%': float(np.percentile(similarities, 25)),
+                '50%': float(np.percentile(similarities, 50)),
+                '75%': float(np.percentile(similarities, 75)),
+                '90%': float(np.percentile(similarities, 90)),
+                '95%': float(np.percentile(similarities, 95)),
+                '99%': float(np.percentile(similarities, 99)),
+            },
+            'above_thresholds': {
+                '>0.90': int((similarities > 0.90).sum()),
+                '>0.95': int((similarities > 0.95).sum()),
+                '>0.99': int((similarities > 0.99).sum()),
+            }
+        },
+        'high_similarity_search': {
+            'threshold': HIGH_SIMILARITY_THRESHOLD,
+            'pairs_found': len(high_sim_pairs),
+            'source_analysis': source_stats,
+            'top_10_pairs': sorted(high_sim_pairs, key=lambda x: x['similarity'], reverse=True)[:10]
+        }
+    }
+
+    with open(output_path, 'w', encoding='utf-8') as f:
+        json.dump(report, f, indent=2, ensure_ascii=False)
+
+    print(f"統計報告已儲存: {output_path}")
+    return report
+
+
+def print_summary(report):
+    """印出摘要"""
+    print("\n" + "=" * 70)
+    print("相似度分布分析摘要")
+    print("=" * 70)
+
+    rs = report['random_sampling']
+    print(f"\n隨機抽樣統計 ({rs['n_pairs']:,} 對):")
+    print(f"  平均相似度: {rs['mean']:.4f}")
+    print(f"  標準差: {rs['std']:.4f}")
+    print(f"  範圍: [{rs['min']:.4f}, {rs['max']:.4f}]")
+    print(f"\n百分位數:")
+    for k, v in rs['percentiles'].items():
+        print(f"  {k}: {v:.4f}")
+
+    print(f"\n高相似度對數量:")
+    for k, v in rs['above_thresholds'].items():
+        pct = v / rs['n_pairs'] * 100
+        print(f"  {k}: {v:,} ({pct:.4f}%)")
+
+    hs = report['high_similarity_search']
+    print(f"\n系統化搜尋結果 (threshold={hs['threshold']}):")
+    print(f"  發現高相似度對: {hs['pairs_found']:,}")
+
+    if hs['source_analysis']['total'] > 0:
+        sa = hs['source_analysis']
+        print(f"\n來源分析:")
+        print(f"  同一 PDF: {sa['same_pdf']} ({sa['same_pdf']/sa['total']*100:.1f}%)")
+        print(f"  同月份: {sa['same_year_month']} ({sa['same_year_month']/sa['total']*100:.1f}%)")
+        print(f"  同類型: {sa['same_doc_type']} ({sa['same_doc_type']/sa['total']*100:.1f}%)")
+        print(f"  完全不同: {sa['different_everything']} ({sa['different_everything']/sa['total']*100:.1f}%)")
+
+    if hs['top_10_pairs']:
+        print(f"\nTop 10 高相似度對:")
+        for i, pair in enumerate(hs['top_10_pairs'], 1):
+            print(f"  {i}. {pair['similarity']:.4f}")
+            print(f"     {pair['file1']}")
+            print(f"     {pair['file2']}")
+
+
+def main():
+    print("=" * 70)
+    print("Step 3: 相似度分布探索")
+    print("=" * 70)
+
+    # 確保輸出目錄存在
+    REPORTS_PATH.mkdir(parents=True, exist_ok=True)
+
+    # 載入資料
+    features, filenames = load_data()
+
+    # 隨機抽樣分析
+    similarities, pair_indices = random_sampling_analysis(features, filenames, NUM_RANDOM_PAIRS)
+
+    # 繪製分布圖
+    plot_similarity_distribution(
+        similarities,
+        REPORTS_PATH / "similarity_distribution.png"
+    )
+
+    # 系統化搜尋高相似度對
+    high_sim_pairs = systematic_high_similarity_search(
+        features, filenames,
+        threshold=HIGH_SIMILARITY_THRESHOLD
+    )
+
+    # 分析來源
+    source_stats = analyze_high_similarity_sources(high_sim_pairs)
+
+    # 生成報告
+    report = generate_statistics_report(
+        similarities, high_sim_pairs, source_stats,
+        REPORTS_PATH / "similarity_statistics.json"
+    )
+
+    # 儲存高相似度對列表
+    high_sim_output = REPORTS_PATH / "high_similarity_pairs.json"
+    with open(high_sim_output, 'w', encoding='utf-8') as f:
+        json.dump(high_sim_pairs, f, indent=2, ensure_ascii=False)
+    print(f"高相似度對列表已儲存: {high_sim_output}")
+
+    # 印出摘要
+    print_summary(report)
+
+
+if __name__ == "__main__":
+    main()

signature_analysis/04_generate_visual_report.py

@@ -0,0 +1,274 @@
+#!/usr/bin/env python3
+"""
+Step 4: 生成高相似度案例的視覺化報告
+
+讀取 high_similarity_pairs.json
+為 Top N 高相似度對生成並排對比圖
+生成 HTML 報告
+"""
+
+import json
+import cv2
+import numpy as np
+from pathlib import Path
+from tqdm import tqdm
+import base64
+from io import BytesIO
+
+# 路徑配置
+IMAGES_DIR = Path("/Volumes/NV2/PDF-Processing/yolo-signatures/images")
+REPORTS_PATH = Path("/Volumes/NV2/PDF-Processing/signature-analysis/reports")
+HIGH_SIM_JSON = REPORTS_PATH / "high_similarity_pairs.json"
+
+# 報告配置
+TOP_N = 100  # 顯示前 N 對
+
+
+def load_image(filename: str) -> np.ndarray:
+    """載入圖片"""
+    img_path = IMAGES_DIR / filename
+    img = cv2.imread(str(img_path))
+    if img is None:
+        # 返回空白圖片
+        return np.ones((100, 200, 3), dtype=np.uint8) * 255
+    return img
+
+
+def create_comparison_image(file1: str, file2: str, similarity: float) -> np.ndarray:
+    """建立並排對比圖"""
+    img1 = load_image(file1)
+    img2 = load_image(file2)
+
+    # 統一高度
+    h1, w1 = img1.shape[:2]
+    h2, w2 = img2.shape[:2]
+    target_h = max(h1, h2, 100)
+
+    # 縮放
+    if h1 != target_h:
+        scale = target_h / h1
+        img1 = cv2.resize(img1, (int(w1 * scale), target_h))
+    if h2 != target_h:
+        scale = target_h / h2
+        img2 = cv2.resize(img2, (int(w2 * scale), target_h))
+
+    # 加入分隔線
+    separator = np.ones((target_h, 20, 3), dtype=np.uint8) * 200
+
+    # 合併
+    comparison = np.hstack([img1, separator, img2])
+
+    return comparison
+
+
+def image_to_base64(img: np.ndarray) -> str:
+    """將圖片轉換為 base64"""
+    _, buffer = cv2.imencode('.png', img)
+    return base64.b64encode(buffer).decode('utf-8')
+
+
+def generate_html_report(pairs: list, output_path: Path):
+    """生成 HTML 報告"""
+    html_content = """
+<!DOCTYPE html>
+<html>
+<head>
+    <meta charset="UTF-8">
+    <title>簽名相似度分析報告 - 高相似度案例</title>
+    <style>
+        body {
+            font-family: 'Segoe UI', Tahoma, Geneva, Verdana, sans-serif;
+            max-width: 1400px;
+            margin: 0 auto;
+            padding: 20px;
+            background-color: #f5f5f5;
+        }
+        h1 {
+            color: #333;
+            text-align: center;
+            border-bottom: 2px solid #666;
+            padding-bottom: 10px;
+        }
+        .summary {
+            background: linear-gradient(135deg, #667eea 0%, #764ba2 100%);
+            color: white;
+            padding: 20px;
+            border-radius: 10px;
+            margin-bottom: 30px;
+        }
+        .summary h2 {
+            margin-top: 0;
+        }
+        .pair-card {
+            background: white;
+            border-radius: 10px;
+            padding: 20px;
+            margin-bottom: 20px;
+            box-shadow: 0 2px 10px rgba(0,0,0,0.1);
+        }
+        .pair-header {
+            display: flex;
+            justify-content: space-between;
+            align-items: center;
+            margin-bottom: 15px;
+            padding-bottom: 10px;
+            border-bottom: 1px solid #eee;
+        }
+        .pair-number {
+            font-size: 1.2em;
+            font-weight: bold;
+            color: #333;
+        }
+        .similarity-badge {
+            background: #dc3545;
+            color: white;
+            padding: 5px 15px;
+            border-radius: 20px;
+            font-weight: bold;
+        }
+        .similarity-badge.high {
+            background: #dc3545;
+        }
+        .similarity-badge.very-high {
+            background: #8b0000;
+        }
+        .file-info {
+            font-family: monospace;
+            font-size: 0.9em;
+            color: #666;
+            margin-bottom: 10px;
+        }
+        .comparison-image {
+            max-width: 100%;
+            border: 1px solid #ddd;
+            border-radius: 5px;
+        }
+        .analysis {
+            margin-top: 15px;
+            padding: 10px;
+            background: #f8f9fa;
+            border-radius: 5px;
+            font-size: 0.9em;
+        }
+        .tag {
+            display: inline-block;
+            padding: 2px 8px;
+            border-radius: 3px;
+            margin-right: 5px;
+            font-size: 0.8em;
+        }
+        .tag-same-serial { background: #ffebee; color: #c62828; }
+        .tag-same-month { background: #fff3e0; color: #e65100; }
+        .tag-diff { background: #e8f5e9; color: #2e7d32; }
+    </style>
+</head>
+<body>
+    <h1>簽名相似度分析報告 - 高相似度案例</h1>
+
+    <div class="summary">
+        <h2>摘要</h2>
+        <p><strong>分析結果：</strong>發現 659,111 對高相似度簽名 (>0.95)</p>
+        <p><strong>本報告顯示：</strong>Top """ + str(TOP_N) + """ 最高相似度案例</p>
+        <p><strong>結論：</strong>存在大量相似度接近或等於 1.0 的簽名對，強烈暗示「複製貼上」行為</p>
+    </div>
+
+    <div class="pairs-container">
+"""
+
+    for i, pair in enumerate(pairs[:TOP_N], 1):
+        sim = pair['similarity']
+        file1 = pair['file1']
+        file2 = pair['file2']
+        p1 = pair.get('parsed1', {})
+        p2 = pair.get('parsed2', {})
+
+        # 分析關係
+        tags = []
+        if p1.get('serial') == p2.get('serial'):
+            tags.append(('<span class="tag tag-same-serial">同序號</span>', ''))
+        if p1.get('year_month') == p2.get('year_month'):
+            tags.append(('<span class="tag tag-same-month">同月份</span>', ''))
+        if p1.get('year_month') != p2.get('year_month') and p1.get('serial') != p2.get('serial'):
+            tags.append(('<span class="tag tag-diff">完全不同文件</span>', ''))
+
+        badge_class = 'very-high' if sim >= 0.99 else 'high'
+
+        # 建立對比圖
+        try:
+            comparison_img = create_comparison_image(file1, file2, sim)
+            img_base64 = image_to_base64(comparison_img)
+            img_html = f'<img src="data:image/png;base64,{img_base64}" class="comparison-image">'
+        except Exception as e:
+            img_html = f'<p style="color:red">無法載入圖片: {e}</p>'
+
+        tag_html = ''.join([t[0] for t in tags])
+
+        html_content += f"""
+        <div class="pair-card">
+            <div class="pair-header">
+                <span class="pair-number">#{i}</span>
+                <span class="similarity-badge {badge_class}">相似度: {sim:.4f}</span>
+            </div>
+            <div class="file-info">
+                <strong>簽名 1:</strong> {file1}<br>
+                <strong>簽名 2:</strong> {file2}
+            </div>
+            {img_html}
+            <div class="analysis">
+                {tag_html}
+                <br><small>日期: {p1.get('year_month', 'N/A')} vs {p2.get('year_month', 'N/A')} |
+                序號: {p1.get('serial', 'N/A')} vs {p2.get('serial', 'N/A')}</small>
+            </div>
+        </div>
+"""
+
+    html_content += """
+    </div>
+
+    <div style="text-align: center; margin-top: 30px; color: #666;">
+        <p>生成時間: 2024 | 簽名真實性研究計劃</p>
+    </div>
+</body>
+</html>
+"""
+
+    with open(output_path, 'w', encoding='utf-8') as f:
+        f.write(html_content)
+
+    print(f"HTML 報告已儲存: {output_path}")
+
+
+def main():
+    print("=" * 60)
+    print("Step 4: 生成高相似度案例視覺化報告")
+    print("=" * 60)
+
+    # 載入高相似度對
+    print("載入高相似度對資料...")
+    with open(HIGH_SIM_JSON, 'r', encoding='utf-8') as f:
+        pairs = json.load(f)
+
+    print(f"共 {len(pairs):,} 對高相似度簽名")
+
+    # 按相似度排序
+    pairs_sorted = sorted(pairs, key=lambda x: x['similarity'], reverse=True)
+
+    # 統計
+    sim_1 = len([p for p in pairs_sorted if p['similarity'] >= 0.9999])
+    sim_99 = len([p for p in pairs_sorted if p['similarity'] >= 0.99])
+    sim_97 = len([p for p in pairs_sorted if p['similarity'] >= 0.97])
+
+    print(f"\n相似度統計:")
+    print(f"  = 1.0 (完全相同): {sim_1:,}")
+    print(f"  >= 0.99: {sim_99:,}")
+    print(f"  >= 0.97: {sim_97:,}")
+
+    # 生成報告
+    print(f"\n生成 Top {TOP_N} 視覺化報告...")
+    generate_html_report(pairs_sorted, REPORTS_PATH / "high_similarity_report.html")
+
+    print("\n完成！")
+
+
+if __name__ == "__main__":
+    main()

signature_analysis/05_extract_names.py

@@ -0,0 +1,432 @@
+#!/usr/bin/env python3
+"""
+Step 5: 從 PDF 提取會計師印刷姓名
+
+流程：
+1. 從資料庫讀取簽名記錄，按 (PDF, page) 分組
+2. 對每個頁面重新執行 YOLO 獲取簽名框座標
+3. 對整頁執行 PaddleOCR 提取印刷文字
+4. 過濾出候選姓名（2-4 個中文字）
+5. 配對簽名與最近的印刷姓名
+6. 更新資料庫的 accountant_name 欄位
+"""
+
+import sqlite3
+import json
+import re
+import sys
+import time
+from pathlib import Path
+from typing import Optional, List, Dict, Tuple
+from collections import defaultdict
+from tqdm import tqdm
+import numpy as np
+import cv2
+import fitz  # PyMuPDF
+
+# 加入父目錄到路徑以便匯入
+sys.path.insert(0, str(Path(__file__).parent.parent))
+from paddleocr_client import PaddleOCRClient
+
+# 路徑配置
+PDF_BASE = Path("/Volumes/NV2/PDF-Processing/total-pdf")
+YOLO_MODEL_PATH = Path("/Volumes/NV2/pdf_recognize/models/best.pt")
+DB_PATH = Path("/Volumes/NV2/PDF-Processing/signature-analysis/signature_analysis.db")
+REPORTS_PATH = Path("/Volumes/NV2/PDF-Processing/signature-analysis/reports")
+
+# 處理配置
+DPI = 150
+CONFIDENCE_THRESHOLD = 0.5
+NAME_SEARCH_MARGIN = 200  # 簽名框周圍搜索姓名的像素範圍
+PROGRESS_SAVE_INTERVAL = 100  # 每處理 N 個頁面保存一次進度
+
+# 中文姓名正則
+CHINESE_NAME_PATTERN = re.compile(r'^[\u4e00-\u9fff]{2,4}$')
+
+
+def find_pdf_file(filename: str) -> Optional[str]:
+    """搜尋 PDF 檔案路徑"""
+    # 先在 batch_* 子目錄尋找
+    for batch_dir in sorted(PDF_BASE.glob("batch_*")):
+        pdf_path = batch_dir / filename
+        if pdf_path.exists():
+            return str(pdf_path)
+
+    # 再在頂層目錄尋找
+    pdf_path = PDF_BASE / filename
+    if pdf_path.exists():
+        return str(pdf_path)
+
+    return None
+
+
+def render_pdf_page(pdf_path: str, page_num: int) -> Optional[np.ndarray]:
+    """渲染 PDF 頁面為圖像"""
+    try:
+        doc = fitz.open(pdf_path)
+        if page_num < 1 or page_num > len(doc):
+            doc.close()
+            return None
+
+        page = doc[page_num - 1]
+        mat = fitz.Matrix(DPI / 72, DPI / 72)
+        pix = page.get_pixmap(matrix=mat, alpha=False)
+        image = np.frombuffer(pix.samples, dtype=np.uint8)
+        image = image.reshape(pix.height, pix.width, pix.n)
+        doc.close()
+        return image
+    except Exception as e:
+        print(f"渲染失敗: {pdf_path} page {page_num}: {e}")
+        return None
+
+
+def detect_signatures_yolo(image: np.ndarray, model) -> List[Dict]:
+    """使用 YOLO 偵測簽名框"""
+    results = model(image, conf=CONFIDENCE_THRESHOLD, verbose=False)
+
+    signatures = []
+    for r in results:
+        for box in r.boxes:
+            x1, y1, x2, y2 = map(int, box.xyxy[0].cpu().numpy())
+            conf = float(box.conf[0].cpu().numpy())
+            signatures.append({
+                'x': x1,
+                'y': y1,
+                'width': x2 - x1,
+                'height': y2 - y1,
+                'confidence': conf,
+                'center_x': (x1 + x2) / 2,
+                'center_y': (y1 + y2) / 2
+            })
+
+    # 按位置排序（上到下，左到右）
+    signatures.sort(key=lambda s: (s['y'], s['x']))
+
+    return signatures
+
+
+def extract_text_candidates(image: np.ndarray, ocr_client: PaddleOCRClient) -> List[Dict]:
+    """從圖像中提取所有文字候選"""
+    try:
+        results = ocr_client.ocr(image)
+
+        candidates = []
+        for result in results:
+            text = result.get('text', '').strip()
+            box = result.get('box', [])
+            confidence = result.get('confidence', 0.0)
+
+            if not box or not text:
+                continue
+
+            # 計算邊界框中心
+            xs = [point[0] for point in box]
+            ys = [point[1] for point in box]
+            center_x = sum(xs) / len(xs)
+            center_y = sum(ys) / len(ys)
+
+            candidates.append({
+                'text': text,
+                'center_x': center_x,
+                'center_y': center_y,
+                'x': min(xs),
+                'y': min(ys),
+                'width': max(xs) - min(xs),
+                'height': max(ys) - min(ys),
+                'confidence': confidence
+            })
+
+        return candidates
+    except Exception as e:
+        print(f"OCR 失敗: {e}")
+        return []
+
+
+def filter_name_candidates(candidates: List[Dict]) -> List[Dict]:
+    """過濾出可能是姓名的文字（2-4 個中文字，不含數字標點）"""
+    names = []
+    for c in candidates:
+        text = c['text']
+        # 移除空白和標點
+        text_clean = re.sub(r'[\s\:\：\,\，\.\。]', '', text)
+
+        if CHINESE_NAME_PATTERN.match(text_clean):
+            c['text_clean'] = text_clean
+            names.append(c)
+
+    return names
+
+
+def match_signature_to_name(
+    sig: Dict,
+    name_candidates: List[Dict],
+    margin: int = NAME_SEARCH_MARGIN
+) -> Optional[str]:
+    """為簽名框配對最近的姓名候選"""
+    sig_center_x = sig['center_x']
+    sig_center_y = sig['center_y']
+
+    # 過濾出在搜索範圍內的姓名
+    nearby_names = []
+    for name in name_candidates:
+        dx = abs(name['center_x'] - sig_center_x)
+        dy = abs(name['center_y'] - sig_center_y)
+
+        # 在 margin 範圍內
+        if dx <= margin + sig['width']/2 and dy <= margin + sig['height']/2:
+            distance = (dx**2 + dy**2) ** 0.5
+            nearby_names.append((name, distance))
+
+    if not nearby_names:
+        return None
+
+    # 返回距離最近的
+    nearby_names.sort(key=lambda x: x[1])
+    return nearby_names[0][0]['text_clean']
+
+
+def get_pages_to_process(conn: sqlite3.Connection) -> List[Tuple[str, int, List[int]]]:
+    """
+    從資料庫獲取需要處理的 (PDF, page) 組合
+
+    Returns:
+        List of (source_pdf, page_number, [signature_ids])
+    """
+    cursor = conn.cursor()
+
+    # 查詢尚未有 accountant_name 的簽名，按 (PDF, page) 分組
+    cursor.execute('''
+        SELECT source_pdf, page_number, GROUP_CONCAT(signature_id)
+        FROM signatures
+        WHERE accountant_name IS NULL OR accountant_name = ''
+        GROUP BY source_pdf, page_number
+        ORDER BY source_pdf, page_number
+    ''')
+
+    pages = []
+    for row in cursor.fetchall():
+        source_pdf, page_number, sig_ids_str = row
+        sig_ids = [int(x) for x in sig_ids_str.split(',')]
+        pages.append((source_pdf, page_number, sig_ids))
+
+    return pages
+
+
+def update_signature_names(
+    conn: sqlite3.Connection,
+    updates: List[Tuple[int, str, int, int, int, int]]
+):
+    """
+    更新資料庫中的簽名姓名和座標
+
+    Args:
+        updates: List of (signature_id, accountant_name, x, y, width, height)
+    """
+    cursor = conn.cursor()
+
+    # 確保 signature_boxes 表存在
+    cursor.execute('''
+        CREATE TABLE IF NOT EXISTS signature_boxes (
+            signature_id INTEGER PRIMARY KEY,
+            x INTEGER,
+            y INTEGER,
+            width INTEGER,
+            height INTEGER,
+            FOREIGN KEY (signature_id) REFERENCES signatures(signature_id)
+        )
+    ''')
+
+    for sig_id, name, x, y, w, h in updates:
+        # 更新姓名
+        cursor.execute('''
+            UPDATE signatures SET accountant_name = ? WHERE signature_id = ?
+        ''', (name, sig_id))
+
+        # 更新或插入座標
+        cursor.execute('''
+            INSERT OR REPLACE INTO signature_boxes (signature_id, x, y, width, height)
+            VALUES (?, ?, ?, ?, ?)
+        ''', (sig_id, x, y, w, h))
+
+    conn.commit()
+
+
+def process_page(
+    source_pdf: str,
+    page_number: int,
+    sig_ids: List[int],
+    yolo_model,
+    ocr_client: PaddleOCRClient,
+    conn: sqlite3.Connection
+) -> Dict:
+    """
+    處理單一頁面：偵測簽名框、提取姓名、配對
+
+    Returns:
+        處理結果統計
+    """
+    result = {
+        'source_pdf': source_pdf,
+        'page_number': page_number,
+        'num_signatures': len(sig_ids),
+        'matched': 0,
+        'unmatched': 0,
+        'error': None
+    }
+
+    # 找 PDF 檔案
+    pdf_path = find_pdf_file(source_pdf)
+    if pdf_path is None:
+        result['error'] = 'PDF not found'
+        return result
+
+    # 渲染頁面
+    image = render_pdf_page(pdf_path, page_number)
+    if image is None:
+        result['error'] = 'Render failed'
+        return result
+
+    # YOLO 偵測簽名框
+    sig_boxes = detect_signatures_yolo(image, yolo_model)
+
+    if len(sig_boxes) != len(sig_ids):
+        # 簽名數量不匹配，嘗試按順序配對
+        pass
+
+    # OCR 提取文字
+    text_candidates = extract_text_candidates(image, ocr_client)
+
+    # 過濾出姓名候選
+    name_candidates = filter_name_candidates(text_candidates)
+
+    # 配對簽名與姓名
+    updates = []
+
+    for i, (sig_id, sig_box) in enumerate(zip(sig_ids, sig_boxes)):
+        matched_name = match_signature_to_name(sig_box, name_candidates)
+
+        if matched_name:
+            result['matched'] += 1
+        else:
+            result['unmatched'] += 1
+            matched_name = ''  # 空字串表示未配對
+
+        updates.append((
+            sig_id,
+            matched_name,
+            sig_box['x'],
+            sig_box['y'],
+            sig_box['width'],
+            sig_box['height']
+        ))
+
+    # 如果 YOLO 偵測數量少於記錄數量，處理剩餘的
+    if len(sig_boxes) < len(sig_ids):
+        for sig_id in sig_ids[len(sig_boxes):]:
+            updates.append((sig_id, '', 0, 0, 0, 0))
+            result['unmatched'] += 1
+
+    # 更新資料庫
+    update_signature_names(conn, updates)
+
+    return result
+
+
+def main():
+    print("=" * 60)
+    print("Step 5: 從 PDF 提取會計師印刷姓名")
+    print("=" * 60)
+
+    # 確保報告目錄存在
+    REPORTS_PATH.mkdir(parents=True, exist_ok=True)
+
+    # 連接資料庫
+    print("\n連接資料庫...")
+    conn = sqlite3.connect(DB_PATH)
+
+    # 獲取需要處理的頁面
+    print("查詢待處理頁面...")
+    pages = get_pages_to_process(conn)
+    print(f"共 {len(pages)} 個頁面待處理")
+
+    if not pages:
+        print("沒有需要處理的頁面")
+        conn.close()
+        return
+
+    # 初始化 YOLO
+    print("\n載入 YOLO 模型...")
+    from ultralytics import YOLO
+    yolo_model = YOLO(str(YOLO_MODEL_PATH))
+
+    # 初始化 OCR 客戶端
+    print("連接 PaddleOCR 伺服器...")
+    ocr_client = PaddleOCRClient()
+    if not ocr_client.health_check():
+        print("錯誤: PaddleOCR 伺服器無法連接")
+        print("請確認伺服器 http://192.168.30.36:5555 正在運行")
+        conn.close()
+        return
+    print("OCR 伺服器連接成功")
+
+    # 統計
+    stats = {
+        'total_pages': len(pages),
+        'processed': 0,
+        'matched': 0,
+        'unmatched': 0,
+        'errors': 0,
+        'start_time': time.time()
+    }
+
+    # 處理每個頁面
+    print(f"\n開始處理 {len(pages)} 個頁面...")
+
+    for source_pdf, page_number, sig_ids in tqdm(pages, desc="處理頁面"):
+        result = process_page(
+            source_pdf, page_number, sig_ids,
+            yolo_model, ocr_client, conn
+        )
+
+        stats['processed'] += 1
+        stats['matched'] += result['matched']
+        stats['unmatched'] += result['unmatched']
+        if result['error']:
+            stats['errors'] += 1
+
+        # 定期保存進度報告
+        if stats['processed'] % PROGRESS_SAVE_INTERVAL == 0:
+            elapsed = time.time() - stats['start_time']
+            rate = stats['processed'] / elapsed
+            remaining = (stats['total_pages'] - stats['processed']) / rate if rate > 0 else 0
+
+            print(f"\n進度: {stats['processed']}/{stats['total_pages']} "
+                  f"({stats['processed']/stats['total_pages']*100:.1f}%)")
+            print(f"配對成功: {stats['matched']}, 未配對: {stats['unmatched']}")
+            print(f"預估剩餘時間: {remaining/60:.1f} 分鐘")
+
+    # 最終統計
+    elapsed = time.time() - stats['start_time']
+    stats['elapsed_seconds'] = elapsed
+
+    print("\n" + "=" * 60)
+    print("處理完成")
+    print("=" * 60)
+    print(f"總頁面數: {stats['total_pages']}")
+    print(f"處理成功: {stats['processed']}")
+    print(f"配對成功: {stats['matched']}")
+    print(f"未配對: {stats['unmatched']}")
+    print(f"錯誤: {stats['errors']}")
+    print(f"耗時: {elapsed/60:.1f} 分鐘")
+
+    # 保存報告
+    report_path = REPORTS_PATH / "name_extraction_report.json"
+    with open(report_path, 'w', encoding='utf-8') as f:
+        json.dump(stats, f, indent=2, ensure_ascii=False)
+    print(f"\n報告已儲存: {report_path}")
+
+    conn.close()
+
+
+if __name__ == "__main__":
+    main()

signature_analysis/05_extract_names_full.py

@@ -0,0 +1,402 @@
+#!/usr/bin/env python3
+"""
+Step 5: 從 PDF 提取會計師姓名 - 完整處理版本
+
+流程：
+1. 從資料庫讀取簽名記錄，按 (PDF, page) 分組
+2. 對每個頁面重新執行 YOLO 獲取簽名框座標
+3. 對整頁執行 PaddleOCR 提取文字
+4. 過濾出候選姓名（2-4 個中文字）
+5. 配對簽名與最近的姓名
+6. 更新資料庫並生成報告
+"""
+
+import sqlite3
+import json
+import re
+import sys
+import time
+from pathlib import Path
+from typing import Optional, List, Dict, Tuple
+from collections import defaultdict
+from datetime import datetime
+from tqdm import tqdm
+import numpy as np
+import fitz  # PyMuPDF
+
+# 加入父目錄到路徑
+sys.path.insert(0, str(Path(__file__).parent.parent))
+from paddleocr_client import PaddleOCRClient
+
+# 路徑配置
+PDF_BASE = Path("/Volumes/NV2/PDF-Processing/total-pdf")
+YOLO_MODEL_PATH = Path("/Volumes/NV2/pdf_recognize/models/best.pt")
+DB_PATH = Path("/Volumes/NV2/PDF-Processing/signature-analysis/signature_analysis.db")
+REPORTS_PATH = Path("/Volumes/NV2/PDF-Processing/signature-analysis/reports")
+
+# 處理配置
+DPI = 150
+CONFIDENCE_THRESHOLD = 0.5
+NAME_SEARCH_MARGIN = 200
+PROGRESS_SAVE_INTERVAL = 100
+BATCH_COMMIT_SIZE = 50
+
+# 中文姓名正則
+CHINESE_NAME_PATTERN = re.compile(r'^[\u4e00-\u9fff]{2,4}$')
+# 排除的常見詞
+EXCLUDE_WORDS = {'會計', '會計師', '事務所', '師', '聯合', '出具報告'}
+
+
+def find_pdf_file(filename: str) -> Optional[str]:
+    """搜尋 PDF 檔案路徑"""
+    for batch_dir in sorted(PDF_BASE.glob("batch_*")):
+        pdf_path = batch_dir / filename
+        if pdf_path.exists():
+            return str(pdf_path)
+    pdf_path = PDF_BASE / filename
+    if pdf_path.exists():
+        return str(pdf_path)
+    return None
+
+
+def render_pdf_page(pdf_path: str, page_num: int) -> Optional[np.ndarray]:
+    """渲染 PDF 頁面為圖像"""
+    try:
+        doc = fitz.open(pdf_path)
+        if page_num < 1 or page_num > len(doc):
+            doc.close()
+            return None
+        page = doc[page_num - 1]
+        mat = fitz.Matrix(DPI / 72, DPI / 72)
+        pix = page.get_pixmap(matrix=mat, alpha=False)
+        image = np.frombuffer(pix.samples, dtype=np.uint8)
+        image = image.reshape(pix.height, pix.width, pix.n)
+        doc.close()
+        return image
+    except Exception:
+        return None
+
+
+def detect_signatures_yolo(image: np.ndarray, model) -> List[Dict]:
+    """使用 YOLO 偵測簽名框"""
+    results = model(image, conf=CONFIDENCE_THRESHOLD, verbose=False)
+    signatures = []
+    for r in results:
+        for box in r.boxes:
+            x1, y1, x2, y2 = map(int, box.xyxy[0].cpu().numpy())
+            conf = float(box.conf[0].cpu().numpy())
+            signatures.append({
+                'x': x1, 'y': y1,
+                'width': x2 - x1, 'height': y2 - y1,
+                'confidence': conf,
+                'center_x': (x1 + x2) / 2,
+                'center_y': (y1 + y2) / 2
+            })
+    signatures.sort(key=lambda s: (s['y'], s['x']))
+    return signatures
+
+
+def extract_and_filter_names(image: np.ndarray, ocr_client: PaddleOCRClient) -> List[Dict]:
+    """從圖像提取並過濾姓名候選"""
+    try:
+        results = ocr_client.ocr(image)
+    except Exception:
+        return []
+
+    candidates = []
+    for result in results:
+        text = result.get('text', '').strip()
+        box = result.get('box', [])
+        if not box or not text:
+            continue
+
+        # 清理文字
+        text_clean = re.sub(r'[\s\:\：\,\，\.\。\、]', '', text)
+
+        # 檢查是否為姓名候選
+        if CHINESE_NAME_PATTERN.match(text_clean) and text_clean not in EXCLUDE_WORDS:
+            xs = [point[0] for point in box]
+            ys = [point[1] for point in box]
+            candidates.append({
+                'text': text_clean,
+                'center_x': sum(xs) / len(xs),
+                'center_y': sum(ys) / len(ys),
+            })
+
+    return candidates
+
+
+def match_signature_to_name(sig: Dict, name_candidates: List[Dict]) -> Optional[str]:
+    """為簽名框配對最近的姓名"""
+    margin = NAME_SEARCH_MARGIN
+    nearby = []
+
+    for name in name_candidates:
+        dx = abs(name['center_x'] - sig['center_x'])
+        dy = abs(name['center_y'] - sig['center_y'])
+        if dx <= margin + sig['width']/2 and dy <= margin + sig['height']/2:
+            distance = (dx**2 + dy**2) ** 0.5
+            nearby.append((name['text'], distance))
+
+    if nearby:
+        nearby.sort(key=lambda x: x[1])
+        return nearby[0][0]
+    return None
+
+
+def get_pages_to_process(conn: sqlite3.Connection) -> List[Tuple[str, int, List[int]]]:
+    """從資料庫獲取需要處理的頁面"""
+    cursor = conn.cursor()
+    cursor.execute('''
+        SELECT source_pdf, page_number, GROUP_CONCAT(signature_id)
+        FROM signatures
+        WHERE accountant_name IS NULL OR accountant_name = ''
+        GROUP BY source_pdf, page_number
+        ORDER BY source_pdf, page_number
+    ''')
+    pages = []
+    for row in cursor.fetchall():
+        source_pdf, page_number, sig_ids_str = row
+        sig_ids = [int(x) for x in sig_ids_str.split(',')]
+        pages.append((source_pdf, page_number, sig_ids))
+    return pages
+
+
+def process_page(
+    source_pdf: str, page_number: int, sig_ids: List[int],
+    yolo_model, ocr_client: PaddleOCRClient
+) -> Dict:
+    """處理單一頁面"""
+    result = {
+        'source_pdf': source_pdf,
+        'page_number': page_number,
+        'num_signatures': len(sig_ids),
+        'matched': 0,
+        'unmatched': 0,
+        'error': None,
+        'updates': []
+    }
+
+    pdf_path = find_pdf_file(source_pdf)
+    if pdf_path is None:
+        result['error'] = 'PDF not found'
+        return result
+
+    image = render_pdf_page(pdf_path, page_number)
+    if image is None:
+        result['error'] = 'Render failed'
+        return result
+
+    sig_boxes = detect_signatures_yolo(image, yolo_model)
+    name_candidates = extract_and_filter_names(image, ocr_client)
+
+    for i, sig_id in enumerate(sig_ids):
+        if i < len(sig_boxes):
+            sig = sig_boxes[i]
+            matched_name = match_signature_to_name(sig, name_candidates)
+
+            if matched_name:
+                result['matched'] += 1
+            else:
+                result['unmatched'] += 1
+                matched_name = ''
+
+            result['updates'].append((
+                sig_id, matched_name,
+                sig['x'], sig['y'], sig['width'], sig['height']
+            ))
+        else:
+            result['updates'].append((sig_id, '', 0, 0, 0, 0))
+            result['unmatched'] += 1
+
+    return result
+
+
+def save_updates_to_db(conn: sqlite3.Connection, updates: List[Tuple]):
+    """批次更新資料庫"""
+    cursor = conn.cursor()
+
+    cursor.execute('''
+        CREATE TABLE IF NOT EXISTS signature_boxes (
+            signature_id INTEGER PRIMARY KEY,
+            x INTEGER, y INTEGER, width INTEGER, height INTEGER,
+            FOREIGN KEY (signature_id) REFERENCES signatures(signature_id)
+        )
+    ''')
+
+    for sig_id, name, x, y, w, h in updates:
+        cursor.execute('UPDATE signatures SET accountant_name = ? WHERE signature_id = ?', (name, sig_id))
+        if x > 0:  # 有座標才存
+            cursor.execute('''
+                INSERT OR REPLACE INTO signature_boxes (signature_id, x, y, width, height)
+                VALUES (?, ?, ?, ?, ?)
+            ''', (sig_id, x, y, w, h))
+
+    conn.commit()
+
+
+def generate_report(stats: Dict, output_path: Path):
+    """生成處理報告"""
+    report = {
+        'title': '會計師姓名提取報告',
+        'generated_at': datetime.now().isoformat(),
+        'summary': {
+            'total_pages': stats['total_pages'],
+            'processed_pages': stats['processed'],
+            'total_signatures': stats['total_sigs'],
+            'matched_signatures': stats['matched'],
+            'unmatched_signatures': stats['unmatched'],
+            'match_rate': f"{stats['matched']/stats['total_sigs']*100:.1f}%" if stats['total_sigs'] > 0 else "N/A",
+            'errors': stats['errors'],
+            'elapsed_seconds': stats['elapsed_seconds'],
+            'elapsed_human': f"{stats['elapsed_seconds']/3600:.1f} 小時"
+        },
+        'methodology': {
+            'step1': 'YOLO 模型偵測簽名框座標',
+            'step2': 'PaddleOCR 整頁 OCR 提取文字',
+            'step3': '過濾 2-4 個中文字作為姓名候選',
+            'step4': f'在簽名框周圍 {NAME_SEARCH_MARGIN}px 範圍內配對最近的姓名',
+            'dpi': DPI,
+            'yolo_confidence': CONFIDENCE_THRESHOLD
+        },
+        'name_distribution': stats.get('name_distribution', {}),
+        'error_samples': stats.get('error_samples', [])
+    }
+
+    with open(output_path, 'w', encoding='utf-8') as f:
+        json.dump(report, f, indent=2, ensure_ascii=False)
+
+    # 同時生成 Markdown 報告
+    md_path = output_path.with_suffix('.md')
+    with open(md_path, 'w', encoding='utf-8') as f:
+        f.write(f"# {report['title']}\n\n")
+        f.write(f"生成時間: {report['generated_at']}\n\n")
+        f.write("## 摘要\n\n")
+        f.write(f"| 指標 | 數值 |\n|------|------|\n")
+        for k, v in report['summary'].items():
+            f.write(f"| {k} | {v} |\n")
+        f.write("\n## 方法論\n\n")
+        for k, v in report['methodology'].items():
+            f.write(f"- **{k}**: {v}\n")
+        f.write("\n## 姓名分布 (Top 50)\n\n")
+        names = sorted(report['name_distribution'].items(), key=lambda x: -x[1])[:50]
+        for name, count in names:
+            f.write(f"- {name}: {count}\n")
+
+    return report
+
+
+def main():
+    print("=" * 70)
+    print("Step 5: 從 PDF 提取會計師姓名 - 完整處理")
+    print("=" * 70)
+    print(f"開始時間: {datetime.now().strftime('%Y-%m-%d %H:%M:%S')}")
+
+    REPORTS_PATH.mkdir(parents=True, exist_ok=True)
+
+    # 連接資料庫
+    conn = sqlite3.connect(DB_PATH)
+    pages = get_pages_to_process(conn)
+    print(f"\n待處理頁面: {len(pages):,}")
+
+    if not pages:
+        print("沒有需要處理的頁面")
+        conn.close()
+        return
+
+    # 載入 YOLO
+    print("\n載入 YOLO 模型...")
+    from ultralytics import YOLO
+    yolo_model = YOLO(str(YOLO_MODEL_PATH))
+
+    # 連接 OCR
+    print("連接 PaddleOCR 伺服器...")
+    ocr_client = PaddleOCRClient()
+    if not ocr_client.health_check():
+        print("錯誤: PaddleOCR 伺服器無法連接")
+        conn.close()
+        return
+    print("OCR 伺服器連接成功\n")
+
+    # 統計
+    stats = {
+        'total_pages': len(pages),
+        'processed': 0,
+        'total_sigs': sum(len(p[2]) for p in pages),
+        'matched': 0,
+        'unmatched': 0,
+        'errors': 0,
+        'error_samples': [],
+        'name_distribution': defaultdict(int),
+        'start_time': time.time()
+    }
+
+    all_updates = []
+
+    # 處理每個頁面
+    for source_pdf, page_number, sig_ids in tqdm(pages, desc="處理頁面"):
+        result = process_page(source_pdf, page_number, sig_ids, yolo_model, ocr_client)
+
+        stats['processed'] += 1
+        stats['matched'] += result['matched']
+        stats['unmatched'] += result['unmatched']
+
+        if result['error']:
+            stats['errors'] += 1
+            if len(stats['error_samples']) < 20:
+                stats['error_samples'].append({
+                    'pdf': source_pdf,
+                    'page': page_number,
+                    'error': result['error']
+                })
+        else:
+            all_updates.extend(result['updates'])
+            for update in result['updates']:
+                if update[1]:  # 有姓名
+                    stats['name_distribution'][update[1]] += 1
+
+        # 批次提交
+        if len(all_updates) >= BATCH_COMMIT_SIZE:
+            save_updates_to_db(conn, all_updates)
+            all_updates = []
+
+        # 定期顯示進度
+        if stats['processed'] % PROGRESS_SAVE_INTERVAL == 0:
+            elapsed = time.time() - stats['start_time']
+            rate = stats['processed'] / elapsed
+            remaining = (stats['total_pages'] - stats['processed']) / rate if rate > 0 else 0
+            print(f"\n[進度] {stats['processed']:,}/{stats['total_pages']:,} "
+                  f"({stats['processed']/stats['total_pages']*100:.1f}%) | "
+                  f"配對: {stats['matched']:,} | "
+                  f"剩餘: {remaining/60:.1f} 分鐘")
+
+    # 最後一批提交
+    if all_updates:
+        save_updates_to_db(conn, all_updates)
+
+    stats['elapsed_seconds'] = time.time() - stats['start_time']
+    stats['name_distribution'] = dict(stats['name_distribution'])
+
+    # 生成報告
+    print("\n生成報告...")
+    report_path = REPORTS_PATH / "name_extraction_report.json"
+    generate_report(stats, report_path)
+
+    print("\n" + "=" * 70)
+    print("處理完成！")
+    print("=" * 70)
+    print(f"總頁面: {stats['total_pages']:,}")
+    print(f"總簽名: {stats['total_sigs']:,}")
+    print(f"配對成功: {stats['matched']:,} ({stats['matched']/stats['total_sigs']*100:.1f}%)")
+    print(f"未配對: {stats['unmatched']:,}")
+    print(f"錯誤: {stats['errors']:,}")
+    print(f"耗時: {stats['elapsed_seconds']/3600:.2f} 小時")
+    print(f"\n報告已儲存:")
+    print(f"  - {report_path}")
+    print(f"  - {report_path.with_suffix('.md')}")
+
+    conn.close()
+
+
+if __name__ == "__main__":
+    main()

signature_analysis/07_cleanup_and_assign.py

@@ -0,0 +1,450 @@
+#!/usr/bin/env python3
+"""
+簽名清理與會計師歸檔
+
+1. 標記 sig_count > 2 的 PDF，篩選最佳 2 個簽名
+2. 用 OCR 或座標歸檔到會計師
+3. 建立 accountants 表
+"""
+
+import sqlite3
+import json
+from collections import defaultdict
+from datetime import datetime
+from opencc import OpenCC
+
+# 簡繁轉換
+cc_s2t = OpenCC('s2t')
+
+DB_PATH = '/Volumes/NV2/PDF-Processing/signature-analysis/signature_analysis.db'
+REPORT_DIR = '/Volumes/NV2/PDF-Processing/signature-analysis/reports'
+
+
+def get_connection():
+    conn = sqlite3.connect(DB_PATH)
+    conn.row_factory = sqlite3.Row
+    return conn
+
+
+def add_columns_if_needed(conn):
+    """添加新欄位"""
+    cur = conn.cursor()
+
+    # 檢查現有欄位
+    cur.execute("PRAGMA table_info(signatures)")
+    columns = [row[1] for row in cur.fetchall()]
+
+    if 'is_valid' not in columns:
+        cur.execute("ALTER TABLE signatures ADD COLUMN is_valid INTEGER DEFAULT 1")
+        print("已添加 is_valid 欄位")
+
+    if 'assigned_accountant' not in columns:
+        cur.execute("ALTER TABLE signatures ADD COLUMN assigned_accountant TEXT")
+        print("已添加 assigned_accountant 欄位")
+
+    conn.commit()
+
+
+def create_accountants_table(conn):
+    """建立 accountants 表"""
+    cur = conn.cursor()
+    cur.execute("""
+        CREATE TABLE IF NOT EXISTS accountants (
+            accountant_id INTEGER PRIMARY KEY AUTOINCREMENT,
+            name TEXT UNIQUE NOT NULL,
+            signature_count INTEGER DEFAULT 0,
+            firm TEXT,
+            created_at TIMESTAMP DEFAULT CURRENT_TIMESTAMP
+        )
+    """)
+    conn.commit()
+    print("accountants 表已建立")
+
+
+def get_pdf_signatures(conn):
+    """取得每份 PDF 的簽名資料"""
+    cur = conn.cursor()
+    cur.execute("""
+        SELECT s.signature_id, s.source_pdf, s.page_number, s.accountant_name,
+               s.excel_accountant1, s.excel_accountant2, s.excel_firm,
+               sb.x, sb.y, sb.width, sb.height
+        FROM signatures s
+        LEFT JOIN signature_boxes sb ON s.signature_id = sb.signature_id
+        ORDER BY s.source_pdf, s.page_number, sb.y
+    """)
+
+    pdf_sigs = defaultdict(list)
+    for row in cur.fetchall():
+        pdf_sigs[row['source_pdf']].append(dict(row))
+
+    return pdf_sigs
+
+
+def normalize_name(name):
+    """正規化姓名（簡轉繁）"""
+    if not name:
+        return None
+    return cc_s2t.convert(name)
+
+
+def names_match(ocr_name, excel_name):
+    """檢查 OCR 姓名是否與 Excel 姓名匹配"""
+    if not ocr_name or not excel_name:
+        return False
+
+    # 精確匹配
+    if ocr_name == excel_name:
+        return True
+
+    # 簡繁轉換後匹配
+    ocr_trad = normalize_name(ocr_name)
+    if ocr_trad == excel_name:
+        return True
+
+    return False
+
+
+def score_signature(sig, excel_acc1, excel_acc2):
+    """為簽名評分"""
+    score = 0
+    ocr_name = sig.get('accountant_name', '')
+
+    # 1. OCR 姓名匹配 (+100)
+    if names_match(ocr_name, excel_acc1) or names_match(ocr_name, excel_acc2):
+        score += 100
+
+    # 2. 合理尺寸 (+20)
+    width = sig.get('width', 0) or 0
+    height = sig.get('height', 0) or 0
+    if 30 < width < 500 and 20 < height < 200:
+        score += 20
+
+    # 3. 頁面位置 - Y 座標越大分數越高 (最多 +15)
+    y = sig.get('y', 0) or 0
+    score += min(y / 100, 15)
+
+    # 4. 如果尺寸過大（可能是印章），扣分
+    if width > 300 or height > 150:
+        score -= 30
+
+    return score
+
+
+def select_best_two(signatures, excel_acc1, excel_acc2):
+    """選擇最佳的 2 個簽名"""
+    if len(signatures) <= 2:
+        return signatures
+
+    scored = []
+    for sig in signatures:
+        score = score_signature(sig, excel_acc1, excel_acc2)
+        scored.append((sig, score))
+
+    # 按分數排序
+    scored.sort(key=lambda x: -x[1])
+
+    # 取前 2 個
+    return [s[0] for s in scored[:2]]
+
+
+def assign_to_accountant(sig1, sig2, excel_acc1, excel_acc2):
+    """將簽名歸檔到會計師"""
+    ocr1 = sig1.get('accountant_name', '')
+    ocr2 = sig2.get('accountant_name', '')
+
+    # 方法 A: OCR 姓名匹配
+    if names_match(ocr1, excel_acc1):
+        return [(sig1, excel_acc1), (sig2, excel_acc2)]
+    elif names_match(ocr1, excel_acc2):
+        return [(sig1, excel_acc2), (sig2, excel_acc1)]
+    elif names_match(ocr2, excel_acc1):
+        return [(sig1, excel_acc2), (sig2, excel_acc1)]
+    elif names_match(ocr2, excel_acc2):
+        return [(sig1, excel_acc1), (sig2, excel_acc2)]
+
+    # 方法 B: 按 Y 座標（假設會計師1 在上）
+    y1 = sig1.get('y', 0) or 0
+    y2 = sig2.get('y', 0) or 0
+
+    if y1 <= y2:
+        return [(sig1, excel_acc1), (sig2, excel_acc2)]
+    else:
+        return [(sig1, excel_acc2), (sig2, excel_acc1)]
+
+
+def process_all_pdfs(conn):
+    """處理所有 PDF"""
+    print("正在載入簽名資料...")
+    pdf_sigs = get_pdf_signatures(conn)
+    print(f"共 {len(pdf_sigs)} 份 PDF")
+
+    cur = conn.cursor()
+
+    stats = {
+        'total_pdfs': len(pdf_sigs),
+        'sig_count_1': 0,
+        'sig_count_2': 0,
+        'sig_count_gt2': 0,
+        'valid_signatures': 0,
+        'invalid_signatures': 0,
+        'ocr_matched': 0,
+        'y_coordinate_assigned': 0,
+        'no_excel_data': 0,
+    }
+
+    assignments = []  # (signature_id, assigned_accountant, is_valid)
+
+    for pdf_name, sigs in pdf_sigs.items():
+        sig_count = len(sigs)
+        excel_acc1 = sigs[0].get('excel_accountant1') if sigs else None
+        excel_acc2 = sigs[0].get('excel_accountant2') if sigs else None
+
+        if not excel_acc1 and not excel_acc2:
+            # 無 Excel 資料
+            stats['no_excel_data'] += 1
+            for sig in sigs:
+                assignments.append((sig['signature_id'], None, 1))
+            continue
+
+        if sig_count == 1:
+            stats['sig_count_1'] += 1
+            # 只有 1 個簽名，保留但無法確定是哪位會計師
+            sig = sigs[0]
+            ocr_name = sig.get('accountant_name', '')
+            if names_match(ocr_name, excel_acc1):
+                assignments.append((sig['signature_id'], excel_acc1, 1))
+                stats['ocr_matched'] += 1
+            elif names_match(ocr_name, excel_acc2):
+                assignments.append((sig['signature_id'], excel_acc2, 1))
+                stats['ocr_matched'] += 1
+            else:
+                # 無法確定，暫時不指派
+                assignments.append((sig['signature_id'], None, 1))
+            stats['valid_signatures'] += 1
+
+        elif sig_count == 2:
+            stats['sig_count_2'] += 1
+            # 正常情況
+            sig1, sig2 = sigs[0], sigs[1]
+            pairs = assign_to_accountant(sig1, sig2, excel_acc1, excel_acc2)
+
+            for sig, acc in pairs:
+                assignments.append((sig['signature_id'], acc, 1))
+                stats['valid_signatures'] += 1
+
+                # 統計匹配方式
+                ocr_name = sig.get('accountant_name', '')
+                if names_match(ocr_name, acc):
+                    stats['ocr_matched'] += 1
+                else:
+                    stats['y_coordinate_assigned'] += 1
+
+        else:
+            stats['sig_count_gt2'] += 1
+            # 需要篩選
+            best_two = select_best_two(sigs, excel_acc1, excel_acc2)
+
+            # 標記有效/無效
+            valid_ids = {s['signature_id'] for s in best_two}
+            for sig in sigs:
+                if sig['signature_id'] in valid_ids:
+                    is_valid = 1
+                    stats['valid_signatures'] += 1
+                else:
+                    is_valid = 0
+                    stats['invalid_signatures'] += 1
+                    assignments.append((sig['signature_id'], None, is_valid))
+
+            # 歸檔有效的 2 個
+            if len(best_two) == 2:
+                sig1, sig2 = best_two[0], best_two[1]
+                pairs = assign_to_accountant(sig1, sig2, excel_acc1, excel_acc2)
+
+                for sig, acc in pairs:
+                    assignments.append((sig['signature_id'], acc, 1))
+                    ocr_name = sig.get('accountant_name', '')
+                    if names_match(ocr_name, acc):
+                        stats['ocr_matched'] += 1
+                    else:
+                        stats['y_coordinate_assigned'] += 1
+            elif len(best_two) == 1:
+                sig = best_two[0]
+                ocr_name = sig.get('accountant_name', '')
+                if names_match(ocr_name, excel_acc1):
+                    assignments.append((sig['signature_id'], excel_acc1, 1))
+                elif names_match(ocr_name, excel_acc2):
+                    assignments.append((sig['signature_id'], excel_acc2, 1))
+                else:
+                    assignments.append((sig['signature_id'], None, 1))
+
+    # 批量更新資料庫
+    print(f"正在更新 {len(assignments)} 筆簽名...")
+    for sig_id, acc, is_valid in assignments:
+        cur.execute("""
+            UPDATE signatures
+            SET assigned_accountant = ?, is_valid = ?
+            WHERE signature_id = ?
+        """, (acc, is_valid, sig_id))
+
+    conn.commit()
+
+    return stats
+
+
+def build_accountants_table(conn):
+    """建立會計師表"""
+    cur = conn.cursor()
+
+    # 清空現有資料
+    cur.execute("DELETE FROM accountants")
+
+    # 收集所有會計師姓名
+    cur.execute("""
+        SELECT assigned_accountant, excel_firm, COUNT(*) as cnt
+        FROM signatures
+        WHERE assigned_accountant IS NOT NULL AND is_valid = 1
+        GROUP BY assigned_accountant
+    """)
+
+    accountants = {}
+    for row in cur.fetchall():
+        name = row[0]
+        firm = row[1]
+        count = row[2]
+
+        if name not in accountants:
+            accountants[name] = {'count': 0, 'firms': defaultdict(int)}
+        accountants[name]['count'] += count
+        if firm:
+            accountants[name]['firms'][firm] += count
+
+    # 插入 accountants 表
+    for name, data in accountants.items():
+        # 找出最常見的事務所
+        main_firm = None
+        if data['firms']:
+            main_firm = max(data['firms'].items(), key=lambda x: x[1])[0]
+
+        cur.execute("""
+            INSERT INTO accountants (name, signature_count, firm)
+            VALUES (?, ?, ?)
+        """, (name, data['count'], main_firm))
+
+    conn.commit()
+
+    # 更新 signatures 的 accountant_id
+    cur.execute("""
+        UPDATE signatures
+        SET accountant_id = (
+            SELECT accountant_id FROM accountants
+            WHERE accountants.name = signatures.assigned_accountant
+        )
+        WHERE assigned_accountant IS NOT NULL
+    """)
+    conn.commit()
+
+    return len(accountants)
+
+
+def generate_report(stats, accountant_count):
+    """生成報告"""
+    report = {
+        'generated_at': datetime.now().isoformat(),
+        'summary': {
+            'total_pdfs': stats['total_pdfs'],
+            'pdfs_with_1_sig': stats['sig_count_1'],
+            'pdfs_with_2_sigs': stats['sig_count_2'],
+            'pdfs_with_gt2_sigs': stats['sig_count_gt2'],
+            'pdfs_without_excel': stats['no_excel_data'],
+        },
+        'signatures': {
+            'valid': stats['valid_signatures'],
+            'invalid': stats['invalid_signatures'],
+            'total': stats['valid_signatures'] + stats['invalid_signatures'],
+        },
+        'assignment_method': {
+            'ocr_matched': stats['ocr_matched'],
+            'y_coordinate': stats['y_coordinate_assigned'],
+        },
+        'accountants': {
+            'total_unique': accountant_count,
+        }
+    }
+
+    # 儲存 JSON
+    json_path = f"{REPORT_DIR}/signature_cleanup_report.json"
+    with open(json_path, 'w', encoding='utf-8') as f:
+        json.dump(report, f, ensure_ascii=False, indent=2)
+
+    # 儲存 Markdown
+    md_path = f"{REPORT_DIR}/signature_cleanup_report.md"
+    with open(md_path, 'w', encoding='utf-8') as f:
+        f.write("# 簽名清理與歸檔報告\n\n")
+        f.write(f"生成時間: {report['generated_at']}\n\n")
+
+        f.write("## PDF 分布\n\n")
+        f.write("| 類型 | 數量 |\n")
+        f.write("|------|------|\n")
+        f.write(f"| 總 PDF 數 | {stats['total_pdfs']} |\n")
+        f.write(f"| 1 個簽名 | {stats['sig_count_1']} |\n")
+        f.write(f"| 2 個簽名 (正常) | {stats['sig_count_2']} |\n")
+        f.write(f"| >2 個簽名 (需篩選) | {stats['sig_count_gt2']} |\n")
+        f.write(f"| 無 Excel 資料 | {stats['no_excel_data']} |\n")
+
+        f.write("\n## 簽名統計\n\n")
+        f.write("| 類型 | 數量 |\n")
+        f.write("|------|------|\n")
+        f.write(f"| 有效簽名 | {stats['valid_signatures']} |\n")
+        f.write(f"| 無效簽名 (誤判) | {stats['invalid_signatures']} |\n")
+
+        f.write("\n## 歸檔方式\n\n")
+        f.write("| 方式 | 數量 |\n")
+        f.write("|------|------|\n")
+        f.write(f"| OCR 姓名匹配 | {stats['ocr_matched']} |\n")
+        f.write(f"| Y 座標推斷 | {stats['y_coordinate_assigned']} |\n")
+
+        f.write(f"\n## 會計師\n\n")
+        f.write(f"唯一會計師數: **{accountant_count}**\n")
+
+    print(f"報告已儲存: {json_path}")
+    print(f"報告已儲存: {md_path}")
+
+    return report
+
+
+def main():
+    print("=" * 60)
+    print("簽名清理與會計師歸檔")
+    print("=" * 60)
+
+    conn = get_connection()
+
+    # 1. 準備資料庫
+    print("\n[1/4] 準備資料庫...")
+    add_columns_if_needed(conn)
+    create_accountants_table(conn)
+
+    # 2. 處理所有 PDF
+    print("\n[2/4] 處理 PDF 簽名...")
+    stats = process_all_pdfs(conn)
+
+    # 3. 建立 accountants 表
+    print("\n[3/4] 建立會計師表...")
+    accountant_count = build_accountants_table(conn)
+
+    # 4. 生成報告
+    print("\n[4/4] 生成報告...")
+    report = generate_report(stats, accountant_count)
+
+    conn.close()
+
+    print("\n" + "=" * 60)
+    print("完成！")
+    print("=" * 60)
+    print(f"有效簽名: {stats['valid_signatures']}")
+    print(f"無效簽名: {stats['invalid_signatures']}")
+    print(f"唯一會計師: {accountant_count}")
+
+
+if __name__ == '__main__':
+    main()

signature_analysis/08_accountant_similarity_analysis.py

@@ -0,0 +1,272 @@
+#!/usr/bin/env python3
+"""
+第三階段：同人簽名聚類分析
+
+對每位會計師的簽名進行相似度分析，判斷是否有「複製貼上」行為。
+"""
+
+import sqlite3
+import numpy as np
+import json
+from collections import defaultdict
+from datetime import datetime
+from tqdm import tqdm
+
+DB_PATH = '/Volumes/NV2/PDF-Processing/signature-analysis/signature_analysis.db'
+FEATURES_PATH = '/Volumes/NV2/PDF-Processing/signature-analysis/features/signature_features.npy'
+REPORT_DIR = '/Volumes/NV2/PDF-Processing/signature-analysis/reports'
+
+
+def load_data():
+    """載入特徵向量和會計師分配"""
+    print("載入特徵向量...")
+    features = np.load(FEATURES_PATH)
+    print(f"特徵矩陣形狀: {features.shape}")
+
+    conn = sqlite3.connect(DB_PATH)
+    cur = conn.cursor()
+
+    # 取得所有 signature_id 順序（與特徵向量對應）
+    cur.execute("SELECT signature_id FROM signatures ORDER BY signature_id")
+    all_sig_ids = [row[0] for row in cur.fetchall()]
+    sig_id_to_idx = {sig_id: idx for idx, sig_id in enumerate(all_sig_ids)}
+
+    # 取得有效簽名的會計師分配
+    cur.execute("""
+        SELECT s.signature_id, s.assigned_accountant, s.accountant_id, a.name, a.firm
+        FROM signatures s
+        LEFT JOIN accountants a ON s.accountant_id = a.accountant_id
+        WHERE s.is_valid = 1 AND s.assigned_accountant IS NOT NULL
+        ORDER BY s.signature_id
+    """)
+
+    acc_signatures = defaultdict(list)
+    acc_info = {}
+
+    for row in cur.fetchall():
+        sig_id, _, acc_id, acc_name, firm = row
+        if acc_id and sig_id in sig_id_to_idx:
+            acc_signatures[acc_id].append(sig_id)
+            if acc_id not in acc_info:
+                acc_info[acc_id] = {'name': acc_name, 'firm': firm}
+
+    conn.close()
+
+    return features, sig_id_to_idx, acc_signatures, acc_info
+
+
+def compute_similarity_stats(features, sig_ids, sig_id_to_idx):
+    """計算一組簽名的相似度統計"""
+    if len(sig_ids) < 2:
+        return None
+
+    # 取得特徵
+    indices = [sig_id_to_idx[sid] for sid in sig_ids]
+    feat = features[indices]
+
+    # 正規化
+    norms = np.linalg.norm(feat, axis=1, keepdims=True)
+    norms[norms == 0] = 1
+    feat_norm = feat / norms
+
+    # 計算餘弦相似度矩陣
+    sim_matrix = np.dot(feat_norm, feat_norm.T)
+
+    # 取上三角（排除對角線）
+    upper_tri = sim_matrix[np.triu_indices(len(sim_matrix), k=1)]
+
+    if len(upper_tri) == 0:
+        return None
+
+    # 統計
+    stats = {
+        'total_pairs': len(upper_tri),
+        'min_sim': float(upper_tri.min()),
+        'max_sim': float(upper_tri.max()),
+        'mean_sim': float(upper_tri.mean()),
+        'std_sim': float(upper_tri.std()),
+        'pairs_gt_90': int((upper_tri > 0.90).sum()),
+        'pairs_gt_95': int((upper_tri > 0.95).sum()),
+        'pairs_gt_99': int((upper_tri > 0.99).sum()),
+    }
+
+    # 計算比例
+    stats['ratio_gt_90'] = stats['pairs_gt_90'] / stats['total_pairs']
+    stats['ratio_gt_95'] = stats['pairs_gt_95'] / stats['total_pairs']
+    stats['ratio_gt_99'] = stats['pairs_gt_99'] / stats['total_pairs']
+
+    return stats
+
+
+def analyze_all_accountants(features, sig_id_to_idx, acc_signatures, acc_info):
+    """分析所有會計師"""
+    results = []
+
+    for acc_id, sig_ids in tqdm(acc_signatures.items(), desc="分析會計師"):
+        info = acc_info.get(acc_id, {})
+        stats = compute_similarity_stats(features, sig_ids, sig_id_to_idx)
+
+        if stats:
+            result = {
+                'accountant_id': acc_id,
+                'name': info.get('name', ''),
+                'firm': info.get('firm', ''),
+                'signature_count': len(sig_ids),
+                **stats
+            }
+            results.append(result)
+
+    return results
+
+
+def classify_risk(result):
+    """分類風險等級"""
+    ratio_95 = result.get('ratio_gt_95', 0)
+    ratio_99 = result.get('ratio_gt_99', 0)
+    mean_sim = result.get('mean_sim', 0)
+
+    # 高風險：大量高相似度對
+    if ratio_99 > 0.05 or ratio_95 > 0.3:
+        return 'high'
+    # 中風險
+    elif ratio_95 > 0.1 or mean_sim > 0.85:
+        return 'medium'
+    # 低風險
+    else:
+        return 'low'
+
+
+def save_results(results, acc_signatures):
+    """儲存結果"""
+    # 分類風險
+    for r in results:
+        r['risk_level'] = classify_risk(r)
+
+    # 統計
+    risk_counts = defaultdict(int)
+    for r in results:
+        risk_counts[r['risk_level']] += 1
+
+    summary = {
+        'generated_at': datetime.now().isoformat(),
+        'total_accountants': len(results),
+        'risk_distribution': dict(risk_counts),
+        'high_risk_count': risk_counts['high'],
+        'medium_risk_count': risk_counts['medium'],
+        'low_risk_count': risk_counts['low'],
+    }
+
+    # 按風險排序
+    results_sorted = sorted(results, key=lambda x: (-x.get('ratio_gt_95', 0), -x.get('mean_sim', 0)))
+
+    # 儲存 JSON
+    output = {
+        'summary': summary,
+        'accountants': results_sorted
+    }
+
+    json_path = f"{REPORT_DIR}/accountant_similarity_analysis.json"
+    with open(json_path, 'w', encoding='utf-8') as f:
+        json.dump(output, f, ensure_ascii=False, indent=2)
+    print(f"已儲存: {json_path}")
+
+    # 儲存 Markdown 報告
+    md_path = f"{REPORT_DIR}/accountant_similarity_analysis.md"
+    with open(md_path, 'w', encoding='utf-8') as f:
+        f.write("# 會計師簽名相似度分析報告\n\n")
+        f.write(f"生成時間: {summary['generated_at']}\n\n")
+
+        f.write("## 摘要\n\n")
+        f.write(f"| 指標 | 數值 |\n")
+        f.write(f"|------|------|\n")
+        f.write(f"| 總會計師數 | {summary['total_accountants']} |\n")
+        f.write(f"| 高風險 | {risk_counts['high']} |\n")
+        f.write(f"| 中風險 | {risk_counts['medium']} |\n")
+        f.write(f"| 低風險 | {risk_counts['low']} |\n")
+
+        f.write("\n## 風險分類標準\n\n")
+        f.write("- **高風險**: >5% 的簽名對相似度 >0.99，或 >30% 的簽名對相似度 >0.95\n")
+        f.write("- **中風險**: >10% 的簽名對相似度 >0.95，或平均相似度 >0.85\n")
+        f.write("- **低風險**: 其他情況\n")
+
+        f.write("\n## 高風險會計師 (Top 30)\n\n")
+        f.write("| 排名 | 姓名 | 事務所 | 簽名數 | 平均相似度 | >0.95比例 | >0.99比例 |\n")
+        f.write("|------|------|--------|--------|------------|-----------|----------|\n")
+
+        high_risk = [r for r in results_sorted if r['risk_level'] == 'high']
+        for i, r in enumerate(high_risk[:30], 1):
+            f.write(f"| {i} | {r['name']} | {r['firm'] or '-'} | {r['signature_count']} | ")
+            f.write(f"{r['mean_sim']:.3f} | {r['ratio_gt_95']*100:.1f}% | {r['ratio_gt_99']*100:.1f}% |\n")
+
+        f.write("\n## 所有會計師統計分布\n\n")
+
+        # 平均相似度分布
+        mean_sims = [r['mean_sim'] for r in results]
+        f.write("### 平均相似度分布\n\n")
+        f.write(f"- 最小: {min(mean_sims):.3f}\n")
+        f.write(f"- 最大: {max(mean_sims):.3f}\n")
+        f.write(f"- 平均: {np.mean(mean_sims):.3f}\n")
+        f.write(f"- 中位數: {np.median(mean_sims):.3f}\n")
+
+    print(f"已儲存: {md_path}")
+
+    return summary, results_sorted
+
+
+def update_database(results):
+    """更新資料庫，添加風險等級"""
+    conn = sqlite3.connect(DB_PATH)
+    cur = conn.cursor()
+
+    # 添加欄位
+    try:
+        cur.execute("ALTER TABLE accountants ADD COLUMN risk_level TEXT")
+        cur.execute("ALTER TABLE accountants ADD COLUMN mean_similarity REAL")
+        cur.execute("ALTER TABLE accountants ADD COLUMN ratio_gt_95 REAL")
+    except:
+        pass  # 欄位已存在
+
+    # 更新
+    for r in results:
+        cur.execute("""
+            UPDATE accountants
+            SET risk_level = ?, mean_similarity = ?, ratio_gt_95 = ?
+            WHERE accountant_id = ?
+        """, (r['risk_level'], r['mean_sim'], r['ratio_gt_95'], r['accountant_id']))
+
+    conn.commit()
+    conn.close()
+    print("資料庫已更新")
+
+
+def main():
+    print("=" * 60)
+    print("第三階段：同人簽名聚類分析")
+    print("=" * 60)
+
+    # 載入資料
+    features, sig_id_to_idx, acc_signatures, acc_info = load_data()
+    print(f"會計師數: {len(acc_signatures)}")
+
+    # 分析所有會計師
+    print("\n開始分析...")
+    results = analyze_all_accountants(features, sig_id_to_idx, acc_signatures, acc_info)
+
+    # 儲存結果
+    print("\n儲存結果...")
+    summary, results_sorted = save_results(results, acc_signatures)
+
+    # 更新資料庫
+    update_database(results_sorted)
+
+    print("\n" + "=" * 60)
+    print("完成！")
+    print("=" * 60)
+    print(f"總會計師: {summary['total_accountants']}")
+    print(f"高風險: {summary['high_risk_count']}")
+    print(f"中風險: {summary['medium_risk_count']}")
+    print(f"低風險: {summary['low_risk_count']}")
+
+
+if __name__ == '__main__':
+    main()

signature_analysis/09_pdf_signature_verdict.py

@@ -0,0 +1,371 @@
+#!/usr/bin/env python3
+"""
+第四階段：PDF 簽名真偽判定
+
+對每份 PDF 的簽名判斷是「親簽」還是「複製貼上」
+"""
+
+import sqlite3
+import numpy as np
+import json
+import csv
+from collections import defaultdict
+from datetime import datetime
+from tqdm import tqdm
+
+DB_PATH = '/Volumes/NV2/PDF-Processing/signature-analysis/signature_analysis.db'
+FEATURES_PATH = '/Volumes/NV2/PDF-Processing/signature-analysis/features/signature_features.npy'
+REPORT_DIR = '/Volumes/NV2/PDF-Processing/signature-analysis/reports'
+
+# 門檻設定
+THRESHOLD_COPY = 0.95      # 高於此值判定為「複製貼上」
+THRESHOLD_AUTHENTIC = 0.85  # 低於此值判定為「親簽」
+# 介於兩者之間為「不確定」
+
+
+def load_data():
+    """載入資料"""
+    print("載入特徵向量...")
+    features = np.load(FEATURES_PATH)
+
+    # 正規化
+    norms = np.linalg.norm(features, axis=1, keepdims=True)
+    norms[norms == 0] = 1
+    features_norm = features / norms
+
+    conn = sqlite3.connect(DB_PATH)
+    cur = conn.cursor()
+
+    # 取得簽名資訊
+    cur.execute("""
+        SELECT s.signature_id, s.source_pdf, s.assigned_accountant,
+               s.excel_accountant1, s.excel_accountant2, s.excel_firm
+        FROM signatures s
+        WHERE s.is_valid = 1 AND s.assigned_accountant IS NOT NULL
+        ORDER BY s.signature_id
+    """)
+
+    sig_data = {}
+    pdf_signatures = defaultdict(list)
+    acc_signatures = defaultdict(list)
+    pdf_info = {}
+
+    for row in cur.fetchall():
+        sig_id, pdf, acc_name, acc1, acc2, firm = row
+        sig_data[sig_id] = {
+            'pdf': pdf,
+            'accountant': acc_name,
+        }
+        pdf_signatures[pdf].append((sig_id, acc_name))
+        acc_signatures[acc_name].append(sig_id)
+
+        if pdf not in pdf_info:
+            pdf_info[pdf] = {
+                'accountant1': acc1,
+                'accountant2': acc2,
+                'firm': firm
+            }
+
+    # signature_id -> feature index
+    cur.execute("SELECT signature_id FROM signatures ORDER BY signature_id")
+    all_sig_ids = [row[0] for row in cur.fetchall()]
+    sig_id_to_idx = {sid: idx for idx, sid in enumerate(all_sig_ids)}
+
+    conn.close()
+
+    return features_norm, sig_data, pdf_signatures, acc_signatures, pdf_info, sig_id_to_idx
+
+
+def get_max_similarity_to_others(sig_id, acc_name, acc_signatures, sig_id_to_idx, features_norm):
+    """計算該簽名與同一會計師其他簽名的最大相似度"""
+    other_sigs = [s for s in acc_signatures[acc_name] if s != sig_id and s in sig_id_to_idx]
+    if not other_sigs:
+        return None, None
+
+    idx = sig_id_to_idx[sig_id]
+    other_indices = [sig_id_to_idx[s] for s in other_sigs]
+
+    feat = features_norm[idx]
+    other_feats = features_norm[other_indices]
+
+    similarities = np.dot(other_feats, feat)
+    max_idx = similarities.argmax()
+
+    return float(similarities[max_idx]), other_sigs[max_idx]
+
+
+def classify_signature(max_sim):
+    """分類簽名"""
+    if max_sim is None:
+        return 'unknown'  # 無法判定（沒有其他簽名可比對）
+    elif max_sim >= THRESHOLD_COPY:
+        return 'copy'     # 複製貼上
+    elif max_sim <= THRESHOLD_AUTHENTIC:
+        return 'authentic'  # 親簽
+    else:
+        return 'uncertain'  # 不確定
+
+
+def classify_pdf(verdicts):
+    """根據兩個簽名的判定結果，給出 PDF 整體判定"""
+    if not verdicts:
+        return 'unknown'
+
+    # 如果有任一簽名是複製，整份 PDF 判定為複製
+    if 'copy' in verdicts:
+        return 'copy'
+    # 如果兩個都是親簽
+    elif all(v == 'authentic' for v in verdicts):
+        return 'authentic'
+    # 如果有不確定的
+    elif 'uncertain' in verdicts:
+        return 'uncertain'
+    else:
+        return 'unknown'
+
+
+def analyze_all_pdfs(features_norm, sig_data, pdf_signatures, acc_signatures, pdf_info, sig_id_to_idx):
+    """分析所有 PDF"""
+    results = []
+
+    for pdf, sigs in tqdm(pdf_signatures.items(), desc="分析 PDF"):
+        info = pdf_info.get(pdf, {})
+
+        pdf_result = {
+            'pdf': pdf,
+            'accountant1': info.get('accountant1', ''),
+            'accountant2': info.get('accountant2', ''),
+            'firm': info.get('firm', ''),
+            'signatures': []
+        }
+
+        verdicts = []
+
+        for sig_id, acc_name in sigs:
+            max_sim, most_similar_sig = get_max_similarity_to_others(
+                sig_id, acc_name, acc_signatures, sig_id_to_idx, features_norm
+            )
+            verdict = classify_signature(max_sim)
+            verdicts.append(verdict)
+
+            pdf_result['signatures'].append({
+                'signature_id': sig_id,
+                'accountant': acc_name,
+                'max_similarity': max_sim,
+                'verdict': verdict
+            })
+
+        pdf_result['pdf_verdict'] = classify_pdf(verdicts)
+        results.append(pdf_result)
+
+    return results
+
+
+def generate_statistics(results):
+    """生成統計"""
+    stats = {
+        'total_pdfs': len(results),
+        'pdf_verdicts': defaultdict(int),
+        'signature_verdicts': defaultdict(int),
+        'by_firm': defaultdict(lambda: defaultdict(int))
+    }
+
+    for r in results:
+        stats['pdf_verdicts'][r['pdf_verdict']] += 1
+        firm = r['firm'] or '未知'
+        stats['by_firm'][firm][r['pdf_verdict']] += 1
+
+        for sig in r['signatures']:
+            stats['signature_verdicts'][sig['verdict']] += 1
+
+    return stats
+
+
+def save_results(results, stats):
+    """儲存結果"""
+    timestamp = datetime.now().isoformat()
+
+    # 1. 儲存完整 JSON
+    json_path = f"{REPORT_DIR}/pdf_signature_verdicts.json"
+    output = {
+        'generated_at': timestamp,
+        'thresholds': {
+            'copy': THRESHOLD_COPY,
+            'authentic': THRESHOLD_AUTHENTIC
+        },
+        'statistics': {
+            'total_pdfs': stats['total_pdfs'],
+            'pdf_verdicts': dict(stats['pdf_verdicts']),
+            'signature_verdicts': dict(stats['signature_verdicts'])
+        },
+        'results': results
+    }
+    with open(json_path, 'w', encoding='utf-8') as f:
+        json.dump(output, f, ensure_ascii=False, indent=2)
+    print(f"已儲存: {json_path}")
+
+    # 2. 儲存 CSV（簡易版）
+    csv_path = f"{REPORT_DIR}/pdf_signature_verdicts.csv"
+    with open(csv_path, 'w', encoding='utf-8', newline='') as f:
+        writer = csv.writer(f)
+        writer.writerow(['PDF', '會計師1', '會計師2', '事務所', '判定結果',
+                        '簽名1_會計師', '簽名1_相似度', '簽名1_判定',
+                        '簽名2_會計師', '簽名2_相似度', '簽名2_判定'])
+
+        for r in results:
+            row = [
+                r['pdf'],
+                r['accountant1'],
+                r['accountant2'],
+                r['firm'] or '',
+                r['pdf_verdict']
+            ]
+
+            for sig in r['signatures'][:2]:  # 最多 2 個簽名
+                row.extend([
+                    sig['accountant'],
+                    f"{sig['max_similarity']:.3f}" if sig['max_similarity'] else '',
+                    sig['verdict']
+                ])
+
+            # 補齊欄位
+            while len(row) < 11:
+                row.append('')
+
+            writer.writerow(row)
+    print(f"已儲存: {csv_path}")
+
+    # 3. 儲存 Markdown 報告
+    md_path = f"{REPORT_DIR}/pdf_signature_verdict_report.md"
+    with open(md_path, 'w', encoding='utf-8') as f:
+        f.write("# PDF 簽名真偽判定報告\n\n")
+        f.write(f"生成時間: {timestamp}\n\n")
+
+        f.write("## 判定標準\n\n")
+        f.write(f"- **複製貼上 (copy)**: 與同一會計師其他簽名相似度 ≥ {THRESHOLD_COPY}\n")
+        f.write(f"- **親簽 (authentic)**: 與同一會計師其他簽名相似度 ≤ {THRESHOLD_AUTHENTIC}\n")
+        f.write(f"- **不確定 (uncertain)**: 相似度介於 {THRESHOLD_AUTHENTIC} ~ {THRESHOLD_COPY}\n")
+        f.write(f"- **無法判定 (unknown)**: 該會計師只有此一份簽名，無法比對\n\n")
+
+        f.write("## 整體統計\n\n")
+        f.write("### PDF 判定結果\n\n")
+        f.write("| 判定 | 數量 | 百分比 |\n")
+        f.write("|------|------|--------|\n")
+
+        total = stats['total_pdfs']
+        for verdict in ['copy', 'uncertain', 'authentic', 'unknown']:
+            count = stats['pdf_verdicts'].get(verdict, 0)
+            pct = count / total * 100 if total > 0 else 0
+            label = {
+                'copy': '複製貼上',
+                'authentic': '親簽',
+                'uncertain': '不確定',
+                'unknown': '無法判定'
+            }.get(verdict, verdict)
+            f.write(f"| {label} | {count:,} | {pct:.1f}% |\n")
+
+        f.write(f"\n**總計: {total:,} 份 PDF**\n")
+
+        f.write("\n### 簽名判定結果\n\n")
+        f.write("| 判定 | 數量 | 百分比 |\n")
+        f.write("|------|------|--------|\n")
+
+        sig_total = sum(stats['signature_verdicts'].values())
+        for verdict in ['copy', 'uncertain', 'authentic', 'unknown']:
+            count = stats['signature_verdicts'].get(verdict, 0)
+            pct = count / sig_total * 100 if sig_total > 0 else 0
+            label = {
+                'copy': '複製貼上',
+                'authentic': '親簽',
+                'uncertain': '不確定',
+                'unknown': '無法判定'
+            }.get(verdict, verdict)
+            f.write(f"| {label} | {count:,} | {pct:.1f}% |\n")
+
+        f.write(f"\n**總計: {sig_total:,} 個簽名**\n")
+
+        f.write("\n### 按事務所統計\n\n")
+        f.write("| 事務所 | 複製貼上 | 不確定 | 親簽 | 無法判定 | 總計 |\n")
+        f.write("|--------|----------|--------|------|----------|------|\n")
+
+        # 按總數排序
+        firms_sorted = sorted(stats['by_firm'].items(),
+                             key=lambda x: sum(x[1].values()), reverse=True)
+
+        for firm, verdicts in firms_sorted[:20]:
+            copy_n = verdicts.get('copy', 0)
+            uncertain_n = verdicts.get('uncertain', 0)
+            authentic_n = verdicts.get('authentic', 0)
+            unknown_n = verdicts.get('unknown', 0)
+            total_n = copy_n + uncertain_n + authentic_n + unknown_n
+            f.write(f"| {firm} | {copy_n:,} | {uncertain_n:,} | {authentic_n:,} | {unknown_n:,} | {total_n:,} |\n")
+
+    print(f"已儲存: {md_path}")
+
+    return stats
+
+
+def update_database(results):
+    """更新資料庫"""
+    conn = sqlite3.connect(DB_PATH)
+    cur = conn.cursor()
+
+    # 添加欄位
+    try:
+        cur.execute("ALTER TABLE signatures ADD COLUMN signature_verdict TEXT")
+        cur.execute("ALTER TABLE signatures ADD COLUMN max_similarity_to_same_accountant REAL")
+    except:
+        pass
+
+    # 更新
+    for r in results:
+        for sig in r['signatures']:
+            cur.execute("""
+                UPDATE signatures
+                SET signature_verdict = ?, max_similarity_to_same_accountant = ?
+                WHERE signature_id = ?
+            """, (sig['verdict'], sig['max_similarity'], sig['signature_id']))
+
+    conn.commit()
+    conn.close()
+    print("資料庫已更新")
+
+
+def main():
+    print("=" * 60)
+    print("第四階段：PDF 簽名真偽判定")
+    print("=" * 60)
+
+    # 載入資料
+    features_norm, sig_data, pdf_signatures, acc_signatures, pdf_info, sig_id_to_idx = load_data()
+    print(f"PDF 數: {len(pdf_signatures)}")
+    print(f"有效簽名: {len(sig_data)}")
+
+    # 分析所有 PDF
+    print("\n開始分析...")
+    results = analyze_all_pdfs(
+        features_norm, sig_data, pdf_signatures, acc_signatures, pdf_info, sig_id_to_idx
+    )
+
+    # 生成統計
+    stats = generate_statistics(results)
+
+    # 儲存結果
+    print("\n儲存結果...")
+    save_results(results, stats)
+
+    # 更新資料庫
+    update_database(results)
+
+    print("\n" + "=" * 60)
+    print("完成！")
+    print("=" * 60)
+    print(f"\nPDF 判定結果:")
+    print(f"  複製貼上: {stats['pdf_verdicts'].get('copy', 0):,}")
+    print(f"  不確定: {stats['pdf_verdicts'].get('uncertain', 0):,}")
+    print(f"  親簽: {stats['pdf_verdicts'].get('authentic', 0):,}")
+    print(f"  無法判定: {stats['pdf_verdicts'].get('unknown', 0):,}")
+
+
+if __name__ == '__main__':
+    main()

signature_analysis/11_compute_ssim_phash.py

@@ -0,0 +1,319 @@
+#!/usr/bin/env python3
+"""
+Compute SSIM and pHash for all signature pairs (closest match per accountant).
+Uses multiprocessing for parallel image loading and computation.
+Saves results to database and outputs complete CSV.
+"""
+
+import sqlite3
+import numpy as np
+import cv2
+import os
+import sys
+import json
+import csv
+import time
+from datetime import datetime
+from collections import defaultdict
+from multiprocessing import Pool, cpu_count
+from pathlib import Path
+
+DB_PATH = '/Volumes/NV2/PDF-Processing/signature-analysis/signature_analysis.db'
+IMAGE_DIR = '/Volumes/NV2/PDF-Processing/yolo-signatures/images'
+OUTPUT_CSV = '/Volumes/NV2/PDF-Processing/signature-analysis/reports/complete_pdf_report.csv'
+CHECKPOINT_PATH = '/Volumes/NV2/PDF-Processing/signature-analysis/ssim_checkpoint.json'
+NUM_WORKERS = max(1, cpu_count() - 2)  # Leave 2 cores free
+BATCH_SIZE = 1000
+
+
+def compute_phash(img, hash_size=8):
+    """Compute perceptual hash."""
+    resized = cv2.resize(img, (hash_size + 1, hash_size))
+    diff = resized[:, 1:] > resized[:, :-1]
+    return diff.flatten()
+
+
+def compute_pair_ssim(args):
+    """Compute SSIM, pHash, histogram correlation for a pair of images."""
+    sig_id, file1, file2, cosine_sim = args
+
+    path1 = os.path.join(IMAGE_DIR, file1)
+    path2 = os.path.join(IMAGE_DIR, file2)
+
+    result = {
+        'signature_id': sig_id,
+        'match_file': file2,
+        'cosine_similarity': cosine_sim,
+        'ssim': None,
+        'phash_distance': None,
+        'histogram_corr': None,
+        'pixel_identical': False,
+    }
+
+    try:
+        img1 = cv2.imread(path1, cv2.IMREAD_GRAYSCALE)
+        img2 = cv2.imread(path2, cv2.IMREAD_GRAYSCALE)
+
+        if img1 is None or img2 is None:
+            return result
+
+        # Resize to same dimensions
+        h = min(img1.shape[0], img2.shape[0])
+        w = min(img1.shape[1], img2.shape[1])
+        if h < 3 or w < 3:
+            return result
+
+        img1_r = cv2.resize(img1, (w, h))
+        img2_r = cv2.resize(img2, (w, h))
+
+        # Pixel identical check
+        result['pixel_identical'] = bool(np.array_equal(img1_r, img2_r))
+
+        # SSIM
+        try:
+            from skimage.metrics import structural_similarity as ssim
+            win_size = min(7, min(h, w))
+            if win_size % 2 == 0:
+                win_size -= 1
+            if win_size >= 3:
+                result['ssim'] = float(ssim(img1_r, img2_r, win_size=win_size))
+            else:
+                result['ssim'] = None
+        except Exception:
+            result['ssim'] = None
+
+        # Histogram correlation
+        hist1 = cv2.calcHist([img1_r], [0], None, [256], [0, 256])
+        hist2 = cv2.calcHist([img2_r], [0], None, [256], [0, 256])
+        result['histogram_corr'] = float(cv2.compareHist(hist1, hist2, cv2.HISTCMP_CORREL))
+
+        # pHash distance
+        h1 = compute_phash(img1_r)
+        h2 = compute_phash(img2_r)
+        result['phash_distance'] = int(np.sum(h1 != h2))
+
+    except Exception as e:
+        pass
+
+    return result
+
+
+def load_checkpoint():
+    """Load checkpoint of already processed signature IDs."""
+    if os.path.exists(CHECKPOINT_PATH):
+        with open(CHECKPOINT_PATH, 'r') as f:
+            data = json.load(f)
+            return set(data.get('processed_ids', []))
+    return set()
+
+
+def save_checkpoint(processed_ids):
+    """Save checkpoint."""
+    with open(CHECKPOINT_PATH, 'w') as f:
+        json.dump({'processed_ids': list(processed_ids), 'timestamp': str(datetime.now())}, f)
+
+
+def main():
+    start_time = time.time()
+    print("=" * 70)
+    print("SSIM & pHash Computation for All Signature Pairs")
+    print(f"Workers: {NUM_WORKERS}")
+    print("=" * 70)
+
+    # --- Step 1: Load data ---
+    print("\n[1/4] Loading data from database...")
+    conn = sqlite3.connect(DB_PATH)
+    cur = conn.cursor()
+
+    cur.execute('''
+        SELECT signature_id, image_filename, assigned_accountant, feature_vector
+        FROM signatures
+        WHERE feature_vector IS NOT NULL AND assigned_accountant IS NOT NULL
+    ''')
+    rows = cur.fetchall()
+
+    sig_ids = []
+    filenames = []
+    accountants = []
+    features = []
+
+    for row in rows:
+        sig_ids.append(row[0])
+        filenames.append(row[1])
+        accountants.append(row[2])
+        features.append(np.frombuffer(row[3], dtype=np.float32))
+
+    features = np.array(features)
+    print(f"  Loaded {len(sig_ids)} signatures")
+
+    # --- Step 2: Find closest match per signature ---
+    print("\n[2/4] Finding closest match per signature (same accountant)...")
+    acct_groups = defaultdict(list)
+    for i, acct in enumerate(accountants):
+        acct_groups[acct].append(i)
+
+    # Load checkpoint
+    processed_ids = load_checkpoint()
+    print(f"  Checkpoint: {len(processed_ids)} already processed")
+
+    # Prepare tasks
+    tasks = []
+    for acct, indices in acct_groups.items():
+        if len(indices) < 2:
+            continue
+        vecs = features[indices]
+        sim_matrix = vecs @ vecs.T
+        np.fill_diagonal(sim_matrix, -1)  # Exclude self
+
+        for local_i, global_i in enumerate(indices):
+            if sig_ids[global_i] in processed_ids:
+                continue
+            best_local = np.argmax(sim_matrix[local_i])
+            best_global = indices[best_local]
+            best_sim = float(sim_matrix[local_i, best_local])
+            tasks.append((
+                sig_ids[global_i],
+                filenames[global_i],
+                filenames[best_global],
+                best_sim
+            ))
+
+    print(f"  Tasks to process: {len(tasks)}")
+
+    # --- Step 3: Compute SSIM/pHash in parallel ---
+    print(f"\n[3/4] Computing SSIM & pHash ({len(tasks)} pairs, {NUM_WORKERS} workers)...")
+
+    # Add SSIM columns to database if not exist
+    try:
+        cur.execute('ALTER TABLE signatures ADD COLUMN ssim_to_closest REAL')
+    except:
+        pass
+    try:
+        cur.execute('ALTER TABLE signatures ADD COLUMN phash_distance_to_closest INTEGER')
+    except:
+        pass
+    try:
+        cur.execute('ALTER TABLE signatures ADD COLUMN histogram_corr_to_closest REAL')
+    except:
+        pass
+    try:
+        cur.execute('ALTER TABLE signatures ADD COLUMN pixel_identical_to_closest INTEGER')
+    except:
+        pass
+    try:
+        cur.execute('ALTER TABLE signatures ADD COLUMN closest_match_file TEXT')
+    except:
+        pass
+    conn.commit()
+
+    total = len(tasks)
+    done = 0
+    batch_results = []
+
+    with Pool(NUM_WORKERS) as pool:
+        for result in pool.imap_unordered(compute_pair_ssim, tasks, chunksize=50):
+            batch_results.append(result)
+            done += 1
+
+            if done % BATCH_SIZE == 0 or done == total:
+                # Save batch to database
+                for r in batch_results:
+                    cur.execute('''
+                        UPDATE signatures SET
+                            ssim_to_closest = ?,
+                            phash_distance_to_closest = ?,
+                            histogram_corr_to_closest = ?,
+                            pixel_identical_to_closest = ?,
+                            closest_match_file = ?
+                        WHERE signature_id = ?
+                    ''', (
+                        r['ssim'],
+                        r['phash_distance'],
+                        r['histogram_corr'],
+                        1 if r['pixel_identical'] else 0,
+                        r['match_file'],
+                        r['signature_id']
+                    ))
+                    processed_ids.add(r['signature_id'])
+                conn.commit()
+                save_checkpoint(processed_ids)
+                batch_results = []
+
+                elapsed = time.time() - start_time
+                rate = done / elapsed
+                eta = (total - done) / rate if rate > 0 else 0
+                print(f"  {done:,}/{total:,} ({100*done/total:.1f}%) "
+                      f"| {rate:.1f} pairs/s | ETA: {eta/60:.1f} min")
+
+    # --- Step 4: Generate complete CSV ---
+    print(f"\n[4/4] Generating complete CSV...")
+
+    cur.execute('''
+        SELECT
+            s.source_pdf,
+            s.year_month,
+            s.serial_number,
+            s.doc_type,
+            s.page_number,
+            s.sig_index,
+            s.image_filename,
+            s.assigned_accountant,
+            s.excel_accountant1,
+            s.excel_accountant2,
+            s.excel_firm,
+            s.detection_confidence,
+            s.signature_verdict,
+            s.max_similarity_to_same_accountant,
+            s.ssim_to_closest,
+            s.phash_distance_to_closest,
+            s.histogram_corr_to_closest,
+            s.pixel_identical_to_closest,
+            s.closest_match_file,
+            a.risk_level,
+            a.mean_similarity as acct_mean_similarity,
+            a.ratio_gt_95 as acct_ratio_gt_95
+        FROM signatures s
+        LEFT JOIN accountants a ON s.assigned_accountant = a.name
+        ORDER BY s.source_pdf, s.sig_index
+    ''')
+
+    columns = [
+        'source_pdf', 'year_month', 'serial_number', 'doc_type',
+        'page_number', 'sig_index', 'image_filename',
+        'assigned_accountant', 'excel_accountant1', 'excel_accountant2', 'excel_firm',
+        'detection_confidence', 'signature_verdict',
+        'max_cosine_similarity', 'ssim_to_closest', 'phash_distance_to_closest',
+        'histogram_corr_to_closest', 'pixel_identical_to_closest', 'closest_match_file',
+        'accountant_risk_level', 'accountant_mean_similarity', 'accountant_ratio_gt_95'
+    ]
+
+    with open(OUTPUT_CSV, 'w', newline='', encoding='utf-8') as f:
+        writer = csv.writer(f)
+        writer.writerow(columns)
+        for row in cur:
+            writer.writerow(row)
+
+    # Count rows
+    cur.execute('SELECT COUNT(*) FROM signatures')
+    total_sigs = cur.fetchone()[0]
+    cur.execute('SELECT COUNT(DISTINCT source_pdf) FROM signatures')
+    total_pdfs = cur.fetchone()[0]
+
+    conn.close()
+
+    elapsed = time.time() - start_time
+    print(f"\n{'='*70}")
+    print(f"Complete!")
+    print(f"  Total signatures: {total_sigs:,}")
+    print(f"  Total PDFs: {total_pdfs:,}")
+    print(f"  Output: {OUTPUT_CSV}")
+    print(f"  Time: {elapsed/60:.1f} minutes")
+    print(f"{'='*70}")
+
+    # Clean up checkpoint
+    if os.path.exists(CHECKPOINT_PATH):
+        os.remove(CHECKPOINT_PATH)
+
+
+if __name__ == '__main__':
+    main()

signature_analysis/12_generate_pdf_level_report.py

@@ -0,0 +1,407 @@
+#!/usr/bin/env python3
+"""
+Generate PDF-level aggregated report with multi-method verdicts.
+One row per PDF with all Group A-F columns plus new SSIM/pHash/combined verdicts.
+"""
+
+import sqlite3
+import csv
+import numpy as np
+from datetime import datetime
+from collections import defaultdict
+
+DB_PATH = '/Volumes/NV2/PDF-Processing/signature-analysis/signature_analysis.db'
+OUTPUT_CSV = '/Volumes/NV2/PDF-Processing/signature-analysis/reports/pdf_level_complete_report.csv'
+
+# Thresholds from statistical analysis
+COSINE_THRESHOLD = 0.95
+COSINE_STATISTICAL = 0.944  # mu + 2*sigma
+KDE_CROSSOVER = 0.838
+SSIM_HIGH = 0.95
+SSIM_MEDIUM = 0.80
+PHASH_IDENTICAL = 0
+PHASH_SIMILAR = 5
+
+
+def classify_overall(max_cosine, max_ssim, min_phash, has_pixel_identical):
+    """
+    Multi-method combined verdict.
+    Returns (verdict, confidence_level, n_methods_agree)
+    """
+    evidence_copy = 0
+    evidence_genuine = 0
+    total_methods = 0
+
+    # Method 1: Cosine similarity
+    if max_cosine is not None:
+        total_methods += 1
+        if max_cosine > COSINE_THRESHOLD:
+            evidence_copy += 1
+        elif max_cosine < KDE_CROSSOVER:
+            evidence_genuine += 1
+
+    # Method 2: SSIM
+    if max_ssim is not None:
+        total_methods += 1
+        if max_ssim > SSIM_HIGH:
+            evidence_copy += 1
+        elif max_ssim < 0.5:
+            evidence_genuine += 1
+
+    # Method 3: pHash
+    if min_phash is not None:
+        total_methods += 1
+        if min_phash <= PHASH_IDENTICAL:
+            evidence_copy += 1
+        elif min_phash > 15:
+            evidence_genuine += 1
+
+    # Method 4: Pixel identical
+    if has_pixel_identical is not None:
+        total_methods += 1
+        if has_pixel_identical:
+            evidence_copy += 1
+
+    # Decision logic
+    if has_pixel_identical:
+        verdict = 'definite_copy'
+        confidence = 'very_high'
+    elif max_ssim is not None and max_ssim > SSIM_HIGH and min_phash is not None and min_phash <= PHASH_SIMILAR:
+        verdict = 'definite_copy'
+        confidence = 'very_high'
+    elif evidence_copy >= 3:
+        verdict = 'very_likely_copy'
+        confidence = 'high'
+    elif evidence_copy >= 2:
+        verdict = 'likely_copy'
+        confidence = 'medium'
+    elif max_cosine is not None and max_cosine > COSINE_THRESHOLD:
+        verdict = 'likely_copy'
+        confidence = 'medium'
+    elif max_cosine is not None and max_cosine > KDE_CROSSOVER:
+        verdict = 'uncertain'
+        confidence = 'low'
+    elif max_cosine is not None and max_cosine <= KDE_CROSSOVER:
+        verdict = 'likely_genuine'
+        confidence = 'medium'
+    else:
+        verdict = 'unknown'
+        confidence = 'none'
+
+    return verdict, confidence, evidence_copy, total_methods
+
+
+def main():
+    print("=" * 70)
+    print("PDF-Level Aggregated Report Generator")
+    print("=" * 70)
+
+    conn = sqlite3.connect(DB_PATH)
+    cur = conn.cursor()
+
+    # Load all signature data grouped by PDF
+    print("\n[1/3] Loading signature data...")
+    cur.execute('''
+        SELECT
+            s.source_pdf,
+            s.year_month,
+            s.serial_number,
+            s.doc_type,
+            s.page_number,
+            s.sig_index,
+            s.assigned_accountant,
+            s.excel_accountant1,
+            s.excel_accountant2,
+            s.excel_firm,
+            s.detection_confidence,
+            s.signature_verdict,
+            s.max_similarity_to_same_accountant,
+            s.ssim_to_closest,
+            s.phash_distance_to_closest,
+            s.histogram_corr_to_closest,
+            s.pixel_identical_to_closest,
+            a.risk_level,
+            a.mean_similarity,
+            a.ratio_gt_95,
+            a.signature_count
+        FROM signatures s
+        LEFT JOIN accountants a ON s.assigned_accountant = a.name
+        ORDER BY s.source_pdf, s.sig_index
+    ''')
+
+    # Group by PDF
+    pdf_data = defaultdict(list)
+    for row in cur:
+        pdf_data[row[0]].append(row)
+
+    print(f"  {len(pdf_data)} PDFs loaded")
+
+    # Generate PDF-level rows
+    print("\n[2/3] Aggregating per-PDF statistics...")
+
+    columns = [
+        # Group A: PDF Identity
+        'source_pdf', 'year_month', 'serial_number', 'doc_type',
+
+        # Group B: Excel Master Data
+        'accountant_1', 'accountant_2', 'firm',
+
+        # Group C: YOLO Detection
+        'n_signatures_detected', 'avg_detection_confidence',
+
+        # Group D: Cosine Similarity
+        'max_cosine_similarity', 'min_cosine_similarity', 'avg_cosine_similarity',
+
+        # Group E: Verdict (original per-sig)
+        'sig1_cosine_verdict', 'sig2_cosine_verdict',
+
+        # Group F: Accountant Risk
+        'acct1_name', 'acct1_risk_level', 'acct1_mean_similarity',
+        'acct1_ratio_gt_95', 'acct1_total_signatures',
+        'acct2_name', 'acct2_risk_level', 'acct2_mean_similarity',
+        'acct2_ratio_gt_95', 'acct2_total_signatures',
+
+        # Group G: SSIM (NEW)
+        'max_ssim', 'min_ssim', 'avg_ssim',
+        'verdict_ssim',
+
+        # Group H: pHash (NEW)
+        'min_phash_distance', 'max_phash_distance', 'avg_phash_distance',
+        'verdict_phash',
+
+        # Group I: Histogram Correlation (NEW)
+        'max_histogram_corr', 'avg_histogram_corr',
+
+        # Group J: Pixel Identity (NEW)
+        'has_pixel_identical',
+        'verdict_pixel',
+
+        # Group K: Statistical Threshold (NEW)
+        'verdict_statistical',  # Based on mu+2sigma (0.944)
+
+        # Group L: KDE Crossover (NEW)
+        'verdict_kde',  # Based on KDE crossover (0.838)
+
+        # Group M: Multi-Method Combined (NEW)
+        'overall_verdict',
+        'confidence_level',
+        'n_methods_copy',
+        'n_methods_total',
+    ]
+
+    rows = []
+    for pdf_name, sigs in pdf_data.items():
+        # Group A: Identity (from first signature)
+        first = sigs[0]
+        year_month = first[1]
+        serial_number = first[2]
+        doc_type = first[3]
+
+        # Group B: Excel data
+        excel_acct1 = first[7]
+        excel_acct2 = first[8]
+        excel_firm = first[9]
+
+        # Group C: Detection
+        n_sigs = len(sigs)
+        confidences = [s[10] for s in sigs if s[10] is not None]
+        avg_conf = np.mean(confidences) if confidences else None
+
+        # Group D: Cosine similarity
+        cosines = [s[12] for s in sigs if s[12] is not None]
+        max_cosine = max(cosines) if cosines else None
+        min_cosine = min(cosines) if cosines else None
+        avg_cosine = np.mean(cosines) if cosines else None
+
+        # Group E: Per-sig verdicts
+        verdicts = [s[11] for s in sigs]
+        sig1_verdict = verdicts[0] if len(verdicts) > 0 else None
+        sig2_verdict = verdicts[1] if len(verdicts) > 1 else None
+
+        # Group F: Accountant risk - separate for acct1 and acct2
+        # Match by assigned_accountant to excel_accountant1/2
+        acct1_info = {'name': None, 'risk': None, 'mean_sim': None, 'ratio': None, 'count': None}
+        acct2_info = {'name': None, 'risk': None, 'mean_sim': None, 'ratio': None, 'count': None}
+
+        for s in sigs:
+            assigned = s[6]
+            if assigned and assigned == excel_acct1 and acct1_info['name'] is None:
+                acct1_info = {
+                    'name': assigned, 'risk': s[17],
+                    'mean_sim': s[18], 'ratio': s[19], 'count': s[20]
+                }
+            elif assigned and assigned == excel_acct2 and acct2_info['name'] is None:
+                acct2_info = {
+                    'name': assigned, 'risk': s[17],
+                    'mean_sim': s[18], 'ratio': s[19], 'count': s[20]
+                }
+            elif assigned and acct1_info['name'] is None:
+                acct1_info = {
+                    'name': assigned, 'risk': s[17],
+                    'mean_sim': s[18], 'ratio': s[19], 'count': s[20]
+                }
+            elif assigned and acct2_info['name'] is None:
+                acct2_info = {
+                    'name': assigned, 'risk': s[17],
+                    'mean_sim': s[18], 'ratio': s[19], 'count': s[20]
+                }
+
+        # Group G: SSIM
+        ssims = [s[13] for s in sigs if s[13] is not None]
+        max_ssim = max(ssims) if ssims else None
+        min_ssim = min(ssims) if ssims else None
+        avg_ssim = np.mean(ssims) if ssims else None
+
+        if max_ssim is not None:
+            if max_ssim > SSIM_HIGH:
+                verdict_ssim = 'copy'
+            elif max_ssim > SSIM_MEDIUM:
+                verdict_ssim = 'suspicious'
+            else:
+                verdict_ssim = 'genuine'
+        else:
+            verdict_ssim = None
+
+        # Group H: pHash
+        phashes = [s[14] for s in sigs if s[14] is not None]
+        min_phash = min(phashes) if phashes else None
+        max_phash = max(phashes) if phashes else None
+        avg_phash = np.mean(phashes) if phashes else None
+
+        if min_phash is not None:
+            if min_phash <= PHASH_IDENTICAL:
+                verdict_phash = 'copy'
+            elif min_phash <= PHASH_SIMILAR:
+                verdict_phash = 'suspicious'
+            else:
+                verdict_phash = 'genuine'
+        else:
+            verdict_phash = None
+
+        # Group I: Histogram correlation
+        histcorrs = [s[15] for s in sigs if s[15] is not None]
+        max_histcorr = max(histcorrs) if histcorrs else None
+        avg_histcorr = np.mean(histcorrs) if histcorrs else None
+
+        # Group J: Pixel identical
+        pixel_ids = [s[16] for s in sigs if s[16] is not None]
+        has_pixel = any(p == 1 for p in pixel_ids) if pixel_ids else False
+        verdict_pixel = 'copy' if has_pixel else 'genuine'
+
+        # Group K: Statistical threshold (mu+2sigma = 0.944)
+        if max_cosine is not None:
+            if max_cosine > COSINE_STATISTICAL:
+                verdict_stat = 'copy'
+            elif max_cosine > KDE_CROSSOVER:
+                verdict_stat = 'uncertain'
+            else:
+                verdict_stat = 'genuine'
+        else:
+            verdict_stat = None
+
+        # Group L: KDE crossover (0.838)
+        if max_cosine is not None:
+            if max_cosine > KDE_CROSSOVER:
+                verdict_kde = 'above_crossover'
+            else:
+                verdict_kde = 'below_crossover'
+        else:
+            verdict_kde = None
+
+        # Group M: Multi-method combined
+        overall, confidence, n_copy, n_total = classify_overall(
+            max_cosine, max_ssim, min_phash, has_pixel)
+
+        rows.append([
+            # A
+            pdf_name, year_month, serial_number, doc_type,
+            # B
+            excel_acct1, excel_acct2, excel_firm,
+            # C
+            n_sigs, avg_conf,
+            # D
+            max_cosine, min_cosine, avg_cosine,
+            # E
+            sig1_verdict, sig2_verdict,
+            # F
+            acct1_info['name'], acct1_info['risk'], acct1_info['mean_sim'],
+            acct1_info['ratio'], acct1_info['count'],
+            acct2_info['name'], acct2_info['risk'], acct2_info['mean_sim'],
+            acct2_info['ratio'], acct2_info['count'],
+            # G
+            max_ssim, min_ssim, avg_ssim, verdict_ssim,
+            # H
+            min_phash, max_phash, avg_phash, verdict_phash,
+            # I
+            max_histcorr, avg_histcorr,
+            # J
+            1 if has_pixel else 0, verdict_pixel,
+            # K
+            verdict_stat,
+            # L
+            verdict_kde,
+            # M
+            overall, confidence, n_copy, n_total,
+        ])
+
+    # Write CSV
+    print(f"\n[3/3] Writing {len(rows)} PDF rows to CSV...")
+    with open(OUTPUT_CSV, 'w', newline='', encoding='utf-8') as f:
+        writer = csv.writer(f)
+        writer.writerow(columns)
+        writer.writerows(rows)
+
+    conn.close()
+
+    # Print summary statistics
+    print(f"\n{'='*70}")
+    print("SUMMARY")
+    print(f"{'='*70}")
+    print(f"Total PDFs: {len(rows):,}")
+
+    # Overall verdict distribution
+    verdict_counts = defaultdict(int)
+    confidence_counts = defaultdict(int)
+    for r in rows:
+        verdict_counts[r[-4]] += 1
+        confidence_counts[r[-3]] += 1
+
+    print(f"\n--- Overall Verdict Distribution ---")
+    for v in ['definite_copy', 'very_likely_copy', 'likely_copy', 'uncertain', 'likely_genuine', 'unknown']:
+        c = verdict_counts.get(v, 0)
+        print(f"  {v:20s}: {c:>6,} ({100*c/len(rows):5.1f}%)")
+
+    print(f"\n--- Confidence Level Distribution ---")
+    for c_level in ['very_high', 'high', 'medium', 'low', 'none']:
+        c = confidence_counts.get(c_level, 0)
+        print(f"  {c_level:10s}: {c:>6,} ({100*c/len(rows):5.1f}%)")
+
+    # Per-method verdict distribution
+    # Column indices: verdict_ssim=27, verdict_phash=31, verdict_pixel=35, verdict_stat=36, verdict_kde=37
+    print(f"\n--- Per-Method Verdict Distribution ---")
+    for col_idx, method_name in [(27, 'SSIM'), (31, 'pHash'), (35, 'Pixel'), (36, 'Statistical'), (37, 'KDE')]:
+        counts = defaultdict(int)
+        for r in rows:
+            counts[r[col_idx]] += 1
+        print(f"\n  {method_name}:")
+        for k, v in sorted(counts.items(), key=lambda x: -x[1]):
+            print(f"    {str(k):20s}: {v:>6,} ({100*v/len(rows):5.1f}%)")
+
+    # Cross-method agreement
+    print(f"\n--- Method Agreement (cosine>0.95 PDFs) ---")
+    cosine_copy = [r for r in rows if r[9] is not None and r[9] > COSINE_THRESHOLD]
+    if cosine_copy:
+        ssim_agree = sum(1 for r in cosine_copy if r[27] == 'copy')
+        phash_agree = sum(1 for r in cosine_copy if r[31] == 'copy')
+        pixel_agree = sum(1 for r in cosine_copy if r[34] == 1)
+        print(f"  PDFs with cosine > 0.95: {len(cosine_copy):,}")
+        print(f"  Also SSIM > 0.95:  {ssim_agree:>6,} ({100*ssim_agree/len(cosine_copy):5.1f}%)")
+        print(f"  Also pHash = 0:    {phash_agree:>6,} ({100*phash_agree/len(cosine_copy):5.1f}%)")
+        print(f"  Also pixel-identical: {pixel_agree:>4,} ({100*pixel_agree/len(cosine_copy):5.1f}%)")
+
+    print(f"\nOutput: {OUTPUT_CSV}")
+    print(f"{'='*70}")
+
+
+if __name__ == '__main__':
+    main()

signature_analysis/13_deloitte_distribution_analysis.py

@@ -0,0 +1,430 @@
+#!/usr/bin/env python3
+"""
+Deloitte (勤業眾信) Signature Similarity Distribution Analysis
+==============================================================
+Evaluate whether Firm A's max_similarity values follow a normal distribution
+or contain subgroups (e.g., genuinely hand-signed vs digitally stamped).
+
+Tests:
+  1. Descriptive statistics & percentiles
+  2. Normality tests (Shapiro-Wilk, D'Agostino-Pearson, Anderson-Darling, KS)
+  3. Histogram + KDE + fitted normal overlay
+  4. Q-Q plot
+  5. Multimodality check (Hartigan's dip test approximation)
+  6. Outlier identification (signatures with unusually low similarity)
+  7. dHash distance distribution for Firm A
+
+Output: figures + report to console
+"""
+
+import sqlite3
+import numpy as np
+import matplotlib
+matplotlib.use('Agg')
+import matplotlib.pyplot as plt
+from scipy import stats
+from pathlib import Path
+from collections import Counter
+
+DB_PATH = '/Volumes/NV2/PDF-Processing/signature-analysis/signature_analysis.db'
+OUTPUT_DIR = Path('/Volumes/NV2/PDF-Processing/signature-analysis/reports/deloitte_distribution')
+OUTPUT_DIR.mkdir(parents=True, exist_ok=True)
+
+FIRM_A = '勤業眾信聯合'
+
+
+def load_firm_a_data():
+    """Load all Firm A signature similarity data."""
+    conn = sqlite3.connect(DB_PATH)
+    cur = conn.cursor()
+
+    cur.execute('''
+        SELECT s.signature_id, s.image_filename, s.assigned_accountant,
+               s.max_similarity_to_same_accountant,
+               s.phash_distance_to_closest
+        FROM signatures s
+        LEFT JOIN accountants a ON s.assigned_accountant = a.name
+        WHERE a.firm = ?
+        AND s.max_similarity_to_same_accountant IS NOT NULL
+    ''', (FIRM_A,))
+    rows = cur.fetchall()
+    conn.close()
+
+    data = []
+    for r in rows:
+        data.append({
+            'sig_id': r[0],
+            'filename': r[1],
+            'accountant': r[2],
+            'cosine': r[3],
+            'phash': r[4],
+        })
+    return data
+
+
+def descriptive_stats(cosines, label="Firm A Cosine Similarity"):
+    """Print comprehensive descriptive statistics."""
+    print(f"\n{'='*65}")
+    print(f"  {label}")
+    print(f"{'='*65}")
+    print(f"  N            = {len(cosines):,}")
+    print(f"  Mean         = {np.mean(cosines):.6f}")
+    print(f"  Median       = {np.median(cosines):.6f}")
+    print(f"  Std Dev      = {np.std(cosines):.6f}")
+    print(f"  Variance     = {np.var(cosines):.8f}")
+    print(f"  Min          = {np.min(cosines):.6f}")
+    print(f"  Max          = {np.max(cosines):.6f}")
+    print(f"  Range        = {np.ptp(cosines):.6f}")
+    print(f"  Skewness     = {stats.skew(cosines):.4f}")
+    print(f"  Kurtosis     = {stats.kurtosis(cosines):.4f} (excess)")
+    print(f"  IQR          = {np.percentile(cosines, 75) - np.percentile(cosines, 25):.6f}")
+    print()
+    print(f"  Percentiles:")
+    for p in [1, 5, 10, 25, 50, 75, 90, 95, 99]:
+        print(f"    P{p:<3d}       = {np.percentile(cosines, p):.6f}")
+
+
+def normality_tests(cosines):
+    """Run multiple normality tests."""
+    print(f"\n{'='*65}")
+    print(f"  NORMALITY TESTS")
+    print(f"{'='*65}")
+
+    # Shapiro-Wilk (max 5000 samples)
+    if len(cosines) > 5000:
+        sample = np.random.choice(cosines, 5000, replace=False)
+        stat, p = stats.shapiro(sample)
+        print(f"\n  Shapiro-Wilk (n=5000 subsample):")
+    else:
+        stat, p = stats.shapiro(cosines)
+        print(f"\n  Shapiro-Wilk (n={len(cosines)}):")
+    print(f"    W = {stat:.6f},  p = {p:.2e}")
+    print(f"    → {'Normal' if p > 0.05 else 'NOT normal'} at α=0.05")
+
+    # D'Agostino-Pearson
+    if len(cosines) >= 20:
+        stat, p = stats.normaltest(cosines)
+        print(f"\n  D'Agostino-Pearson:")
+        print(f"    K² = {stat:.4f},  p = {p:.2e}")
+        print(f"    → {'Normal' if p > 0.05 else 'NOT normal'} at α=0.05")
+
+    # Anderson-Darling
+    result = stats.anderson(cosines, dist='norm')
+    print(f"\n  Anderson-Darling:")
+    print(f"    A² = {result.statistic:.4f}")
+    for i, (sl, cv) in enumerate(zip(result.significance_level, result.critical_values)):
+        reject = "REJECT" if result.statistic > cv else "accept"
+        print(f"    {sl}%: critical={cv:.4f} → {reject}")
+
+    # Kolmogorov-Smirnov against normal
+    mu, sigma = np.mean(cosines), np.std(cosines)
+    stat, p = stats.kstest(cosines, 'norm', args=(mu, sigma))
+    print(f"\n  Kolmogorov-Smirnov (vs fitted normal):")
+    print(f"    D = {stat:.6f},  p = {p:.2e}")
+    print(f"    → {'Normal' if p > 0.05 else 'NOT normal'} at α=0.05")
+
+    return mu, sigma
+
+
+def test_alternative_distributions(cosines):
+    """Fit alternative distributions and compare."""
+    print(f"\n{'='*65}")
+    print(f"  DISTRIBUTION FITTING (AIC comparison)")
+    print(f"{'='*65}")
+
+    distributions = {
+        'norm': stats.norm,
+        'skewnorm': stats.skewnorm,
+        'beta': stats.beta,
+        'lognorm': stats.lognorm,
+        'gamma': stats.gamma,
+    }
+
+    results = []
+    for name, dist in distributions.items():
+        try:
+            params = dist.fit(cosines)
+            log_likelihood = np.sum(dist.logpdf(cosines, *params))
+            k = len(params)
+            aic = 2 * k - 2 * log_likelihood
+            bic = k * np.log(len(cosines)) - 2 * log_likelihood
+            results.append((name, aic, bic, params, log_likelihood))
+        except Exception as e:
+            print(f"  {name}: fit failed ({e})")
+
+    results.sort(key=lambda x: x[1])  # sort by AIC
+    print(f"\n  {'Distribution':<15} {'AIC':>12} {'BIC':>12} {'LogLik':>12}")
+    print(f"  {'-'*51}")
+    for name, aic, bic, params, ll in results:
+        marker = " ←best" if name == results[0][0] else ""
+        print(f"  {name:<15} {aic:>12.1f} {bic:>12.1f} {ll:>12.1f}{marker}")
+
+    return results
+
+
+def per_accountant_analysis(data):
+    """Analyze per-accountant distributions within Firm A."""
+    print(f"\n{'='*65}")
+    print(f"  PER-ACCOUNTANT ANALYSIS (within Firm A)")
+    print(f"{'='*65}")
+
+    by_acct = {}
+    for d in data:
+        by_acct.setdefault(d['accountant'], []).append(d['cosine'])
+
+    print(f"\n  {'Accountant':<20} {'N':>6} {'Mean':>8} {'Std':>8} {'Min':>8} {'P5':>8} {'P50':>8}")
+    print(f"  {'-'*66}")
+    acct_stats = []
+    for acct, vals in sorted(by_acct.items(), key=lambda x: np.mean(x[1])):
+        v = np.array(vals)
+        print(f"  {acct:<20} {len(v):>6} {v.mean():>8.4f} {v.std():>8.4f} "
+              f"{v.min():>8.4f} {np.percentile(v, 5):>8.4f} {np.median(v):>8.4f}")
+        acct_stats.append({
+            'accountant': acct,
+            'n': len(v),
+            'mean': float(v.mean()),
+            'std': float(v.std()),
+            'min': float(v.min()),
+            'values': v,
+        })
+
+    # Check if per-accountant means are homogeneous (one-way ANOVA)
+    if len(by_acct) >= 2:
+        groups = [np.array(v) for v in by_acct.values() if len(v) >= 5]
+        if len(groups) >= 2:
+            f_stat, p_val = stats.f_oneway(*groups)
+            print(f"\n  One-way ANOVA across accountants:")
+            print(f"    F = {f_stat:.4f},  p = {p_val:.2e}")
+            print(f"    → {'Homogeneous' if p_val > 0.05 else 'Significantly different means'} at α=0.05")
+
+            # Levene's test for homogeneity of variance
+            lev_stat, lev_p = stats.levene(*groups)
+            print(f"\n  Levene's test (variance homogeneity):")
+            print(f"    W = {lev_stat:.4f},  p = {lev_p:.2e}")
+            print(f"    → {'Homogeneous variance' if lev_p > 0.05 else 'Heterogeneous variance'} at α=0.05")
+
+    return acct_stats
+
+
+def identify_outliers(data, cosines):
+    """Identify Firm A signatures with unusually low similarity."""
+    print(f"\n{'='*65}")
+    print(f"  OUTLIER ANALYSIS (low-similarity Firm A signatures)")
+    print(f"{'='*65}")
+
+    q1 = np.percentile(cosines, 25)
+    q3 = np.percentile(cosines, 75)
+    iqr = q3 - q1
+    lower_fence = q1 - 1.5 * iqr
+    lower_extreme = q1 - 3.0 * iqr
+
+    print(f"  IQR method: Q1={q1:.4f}, Q3={q3:.4f}, IQR={iqr:.4f}")
+    print(f"  Lower fence (mild):    {lower_fence:.4f}")
+    print(f"  Lower fence (extreme): {lower_extreme:.4f}")
+
+    outliers = [d for d in data if d['cosine'] < lower_fence]
+    extreme_outliers = [d for d in data if d['cosine'] < lower_extreme]
+
+    print(f"\n  Mild outliers (< {lower_fence:.4f}): {len(outliers)}")
+    print(f"  Extreme outliers (< {lower_extreme:.4f}): {len(extreme_outliers)}")
+
+    if outliers:
+        print(f"\n  Bottom 20 by cosine similarity:")
+        sorted_outliers = sorted(outliers, key=lambda x: x['cosine'])[:20]
+        for d in sorted_outliers:
+            phash_str = f"pHash={d['phash']}" if d['phash'] is not None else "pHash=N/A"
+            print(f"    cosine={d['cosine']:.4f}  {phash_str}  {d['accountant']}  {d['filename']}")
+
+    # Also show count below various thresholds
+    print(f"\n  Signatures below key thresholds:")
+    for thresh in [0.95, 0.90, 0.85, 0.837, 0.80]:
+        n_below = sum(1 for c in cosines if c < thresh)
+        print(f"    < {thresh:.3f}: {n_below:,} ({100*n_below/len(cosines):.2f}%)")
+
+
+def plot_histogram_kde(cosines, mu, sigma):
+    """Plot histogram with KDE and fitted normal overlay."""
+    fig, axes = plt.subplots(1, 2, figsize=(14, 5))
+
+    # Left: Full histogram
+    ax = axes[0]
+    ax.hist(cosines, bins=80, density=True, alpha=0.6, color='steelblue',
+            edgecolor='white', linewidth=0.5, label='Observed')
+
+    # Fitted normal
+    x = np.linspace(cosines.min() - 0.02, cosines.max() + 0.02, 300)
+    ax.plot(x, stats.norm.pdf(x, mu, sigma), 'r-', lw=2,
+            label=f'Normal fit (μ={mu:.4f}, σ={sigma:.4f})')
+
+    # KDE
+    kde = stats.gaussian_kde(cosines)
+    ax.plot(x, kde(x), 'g--', lw=2, label='KDE')
+
+    ax.set_xlabel('Max Cosine Similarity')
+    ax.set_ylabel('Density')
+    ax.set_title(f'Firm A (勤業眾信) Cosine Similarity Distribution (N={len(cosines):,})')
+    ax.legend(fontsize=9)
+    ax.axvline(0.95, color='orange', ls=':', alpha=0.7, label='θ=0.95')
+    ax.axvline(0.837, color='purple', ls=':', alpha=0.7, label='KDE crossover')
+
+    # Right: Q-Q plot
+    ax2 = axes[1]
+    stats.probplot(cosines, dist='norm', plot=ax2)
+    ax2.set_title('Q-Q Plot (vs Normal)')
+    ax2.get_lines()[0].set_markersize(2)
+
+    plt.tight_layout()
+    fig.savefig(OUTPUT_DIR / 'firm_a_cosine_distribution.png', dpi=150)
+    print(f"\n  Saved: {OUTPUT_DIR / 'firm_a_cosine_distribution.png'}")
+    plt.close()
+
+
+def plot_per_accountant(acct_stats):
+    """Box plot per accountant."""
+    # Sort by mean
+    acct_stats.sort(key=lambda x: x['mean'])
+
+    fig, ax = plt.subplots(figsize=(12, max(5, len(acct_stats) * 0.4)))
+    positions = range(len(acct_stats))
+    labels = [f"{a['accountant']} (n={a['n']})" for a in acct_stats]
+    box_data = [a['values'] for a in acct_stats]
+
+    bp = ax.boxplot(box_data, positions=positions, vert=False, widths=0.6,
+                    patch_artist=True, showfliers=True,
+                    flierprops=dict(marker='.', markersize=3, alpha=0.5))
+    for patch in bp['boxes']:
+        patch.set_facecolor('lightsteelblue')
+
+    ax.set_yticks(positions)
+    ax.set_yticklabels(labels, fontsize=8)
+    ax.set_xlabel('Max Cosine Similarity')
+    ax.set_title('Per-Accountant Similarity Distribution (Firm A)')
+    ax.axvline(0.95, color='orange', ls=':', alpha=0.7)
+    ax.axvline(0.837, color='purple', ls=':', alpha=0.7)
+
+    plt.tight_layout()
+    fig.savefig(OUTPUT_DIR / 'firm_a_per_accountant_boxplot.png', dpi=150)
+    print(f"  Saved: {OUTPUT_DIR / 'firm_a_per_accountant_boxplot.png'}")
+    plt.close()
+
+
+def plot_phash_distribution(data):
+    """Plot dHash distance distribution for Firm A."""
+    phash_vals = [d['phash'] for d in data if d['phash'] is not None]
+    if not phash_vals:
+        print("  No pHash data available.")
+        return
+
+    phash_arr = np.array(phash_vals)
+
+    fig, ax = plt.subplots(figsize=(10, 5))
+    max_val = min(int(phash_arr.max()) + 2, 65)
+    bins = np.arange(-0.5, max_val + 0.5, 1)
+    ax.hist(phash_arr, bins=bins, alpha=0.7, color='coral', edgecolor='white')
+    ax.set_xlabel('dHash Distance')
+    ax.set_ylabel('Count')
+    ax.set_title(f'Firm A dHash Distance Distribution (N={len(phash_vals):,})')
+    ax.axvline(5, color='green', ls='--', label='θ=5 (high conf.)')
+    ax.axvline(15, color='orange', ls='--', label='θ=15 (moderate)')
+    ax.legend()
+
+    plt.tight_layout()
+    fig.savefig(OUTPUT_DIR / 'firm_a_dhash_distribution.png', dpi=150)
+    print(f"  Saved: {OUTPUT_DIR / 'firm_a_dhash_distribution.png'}")
+    plt.close()
+
+
+def multimodality_test(cosines):
+    """Check for potential multimodality using kernel density peaks."""
+    print(f"\n{'='*65}")
+    print(f"  MULTIMODALITY ANALYSIS")
+    print(f"{'='*65}")
+
+    kde = stats.gaussian_kde(cosines, bw_method='silverman')
+    x = np.linspace(cosines.min(), cosines.max(), 1000)
+    density = kde(x)
+
+    # Find local maxima
+    from scipy.signal import find_peaks
+    peaks, properties = find_peaks(density, prominence=0.01)
+    peak_positions = x[peaks]
+    peak_heights = density[peaks]
+
+    print(f"  KDE bandwidth (Silverman): {kde.factor:.6f}")
+    print(f"  Number of detected modes: {len(peaks)}")
+    for i, (pos, h) in enumerate(zip(peak_positions, peak_heights)):
+        print(f"    Mode {i+1}: position={pos:.4f}, density={h:.2f}")
+
+    if len(peaks) == 1:
+        print(f"\n  → Distribution appears UNIMODAL")
+        print(f"    Single peak at {peak_positions[0]:.4f}")
+    elif len(peaks) > 1:
+        print(f"\n  → Distribution appears MULTIMODAL ({len(peaks)} modes)")
+        print(f"    This suggests subgroups may exist within Firm A")
+        # Check separation between modes
+        for i in range(len(peaks) - 1):
+            sep = peak_positions[i + 1] - peak_positions[i]
+            # Find valley between modes
+            valley_region = density[peaks[i]:peaks[i + 1]]
+            valley_depth = peak_heights[i:i + 2].min() - valley_region.min()
+            print(f"    Separation {i+1}-{i+2}: Δ={sep:.4f}, valley depth={valley_depth:.2f}")
+
+    # Also try different bandwidths
+    print(f"\n  Sensitivity analysis (bandwidth variation):")
+    for bw_factor in [0.5, 0.75, 1.0, 1.5, 2.0]:
+        bw = kde.factor * bw_factor
+        kde_test = stats.gaussian_kde(cosines, bw_method=bw)
+        density_test = kde_test(x)
+        peaks_test, _ = find_peaks(density_test, prominence=0.005)
+        print(f"    bw={bw:.4f} (×{bw_factor:.1f}): {len(peaks_test)} mode(s)")
+
+
+def main():
+    print("Loading Firm A (勤業眾信) signature data...")
+    data = load_firm_a_data()
+    print(f"Total Firm A signatures: {len(data):,}")
+
+    cosines = np.array([d['cosine'] for d in data])
+
+    # 1. Descriptive statistics
+    descriptive_stats(cosines)
+
+    # 2. Normality tests
+    mu, sigma = normality_tests(cosines)
+
+    # 3. Alternative distribution fitting
+    test_alternative_distributions(cosines)
+
+    # 4. Per-accountant analysis
+    acct_stats = per_accountant_analysis(data)
+
+    # 5. Outlier analysis
+    identify_outliers(data, cosines)
+
+    # 6. Multimodality test
+    multimodality_test(cosines)
+
+    # 7. Generate plots
+    print(f"\n{'='*65}")
+    print(f"  GENERATING FIGURES")
+    print(f"{'='*65}")
+    plot_histogram_kde(cosines, mu, sigma)
+    plot_per_accountant(acct_stats)
+    plot_phash_distribution(data)
+
+    # Summary
+    print(f"\n{'='*65}")
+    print(f"  SUMMARY")
+    print(f"{'='*65}")
+    below_95 = sum(1 for c in cosines if c < 0.95)
+    below_kde = sum(1 for c in cosines if c < 0.837)
+    print(f"  Firm A signatures: {len(cosines):,}")
+    print(f"  Below 0.95 threshold: {below_95:,} ({100*below_95/len(cosines):.1f}%)")
+    print(f"  Below KDE crossover (0.837): {below_kde:,} ({100*below_kde/len(cosines):.1f}%)")
+    print(f"  If distribution is NOT normal → subgroups may exist")
+    print(f"  If multimodal → some signatures may be genuinely hand-signed")
+    print(f"\n  Output directory: {OUTPUT_DIR}")
+
+
+if __name__ == "__main__":
+    main()

signature_analysis/14_compute_independent_dhash.py

@@ -0,0 +1,293 @@
+#!/usr/bin/env python3
+"""
+Compute independent min dHash for all signatures.
+===================================================
+Currently phash_distance_to_closest is conditional on cosine-nearest pair.
+This script computes an INDEPENDENT min dHash: for each signature, find the
+pair within the same accountant that has the smallest dHash distance,
+regardless of cosine similarity.
+
+Three metrics after this script:
+  1. max_similarity_to_same_accountant  (max cosine)     — primary classifier
+  2. min_dhash_independent              (independent min) — independent 2nd classifier
+  3. phash_distance_to_closest          (conditional)     — diagnostic tool
+
+Phase 1: Compute dHash vector for each image, store as BLOB in DB
+Phase 2: All-pairs hamming distance within same accountant, store min
+"""
+
+import sqlite3
+import numpy as np
+import cv2
+import os
+import sys
+import time
+from multiprocessing import Pool, cpu_count
+from pathlib import Path
+
+DB_PATH = '/Volumes/NV2/PDF-Processing/signature-analysis/signature_analysis.db'
+IMAGE_DIR = '/Volumes/NV2/PDF-Processing/yolo-signatures/images'
+NUM_WORKERS = max(1, cpu_count() - 2)
+BATCH_SIZE = 5000
+HASH_SIZE = 8  # 9x8 -> 8x8 = 64-bit hash
+
+
+# ── Phase 1: Compute dHash per image ─────────────────────────────────
+
+def compute_dhash_for_file(args):
+    """Compute dHash for a single image file. Returns (sig_id, hash_bytes) or (sig_id, None)."""
+    sig_id, filename = args
+    path = os.path.join(IMAGE_DIR, filename)
+    try:
+        img = cv2.imread(path, cv2.IMREAD_GRAYSCALE)
+        if img is None:
+            return (sig_id, None)
+        resized = cv2.resize(img, (HASH_SIZE + 1, HASH_SIZE))
+        diff = resized[:, 1:] > resized[:, :-1]  # 8x8 = 64 bits
+        return (sig_id, np.packbits(diff.flatten()).tobytes())
+    except Exception:
+        return (sig_id, None)
+
+
+def phase1_compute_hashes():
+    """Compute and store dHash for all signatures."""
+    conn = sqlite3.connect(DB_PATH)
+    cur = conn.cursor()
+
+    # Add columns if not exist
+    for col in ['dhash_vector BLOB', 'min_dhash_independent INTEGER',
+                'min_dhash_independent_match TEXT']:
+        try:
+            cur.execute(f'ALTER TABLE signatures ADD COLUMN {col}')
+        except sqlite3.OperationalError:
+            pass
+    conn.commit()
+
+    # Check which signatures already have dhash_vector
+    cur.execute('''
+        SELECT signature_id, image_filename
+        FROM signatures
+        WHERE feature_vector IS NOT NULL
+          AND assigned_accountant IS NOT NULL
+          AND dhash_vector IS NULL
+    ''')
+    todo = cur.fetchall()
+
+    if not todo:
+        # Check total with dhash
+        cur.execute('SELECT COUNT(*) FROM signatures WHERE dhash_vector IS NOT NULL')
+        n_done = cur.fetchone()[0]
+        print(f"  Phase 1 already complete ({n_done:,} hashes in DB)")
+        conn.close()
+        return
+
+    print(f"  Computing dHash for {len(todo):,} images ({NUM_WORKERS} workers)...")
+    t0 = time.time()
+
+    processed = 0
+    for batch_start in range(0, len(todo), BATCH_SIZE):
+        batch = todo[batch_start:batch_start + BATCH_SIZE]
+
+        with Pool(NUM_WORKERS) as pool:
+            results = pool.map(compute_dhash_for_file, batch)
+
+        updates = [(dhash, sid) for sid, dhash in results if dhash is not None]
+        cur.executemany('UPDATE signatures SET dhash_vector = ? WHERE signature_id = ?', updates)
+        conn.commit()
+
+        processed += len(batch)
+        elapsed = time.time() - t0
+        rate = processed / elapsed
+        eta = (len(todo) - processed) / rate if rate > 0 else 0
+        print(f"    {processed:,}/{len(todo):,}  ({rate:.0f}/s, ETA {eta:.0f}s)")
+
+    conn.close()
+    elapsed = time.time() - t0
+    print(f"  Phase 1 done: {processed:,} hashes in {elapsed:.1f}s")
+
+
+# ── Phase 2: All-pairs min dHash within same accountant ──────────────
+
+def hamming_distance(h1_bytes, h2_bytes):
+    """Hamming distance between two packed dHash byte strings."""
+    a = np.frombuffer(h1_bytes, dtype=np.uint8)
+    b = np.frombuffer(h2_bytes, dtype=np.uint8)
+    xor = np.bitwise_xor(a, b)
+    return sum(bin(byte).count('1') for byte in xor)
+
+
+def phase2_compute_min_dhash():
+    """For each accountant group, find the min dHash pair per signature."""
+    conn = sqlite3.connect(DB_PATH)
+    cur = conn.cursor()
+
+    # Load all signatures with dhash
+    cur.execute('''
+        SELECT s.signature_id, s.assigned_accountant, s.dhash_vector, s.image_filename
+        FROM signatures s
+        WHERE s.dhash_vector IS NOT NULL
+          AND s.assigned_accountant IS NOT NULL
+    ''')
+    rows = cur.fetchall()
+    print(f"  Loaded {len(rows):,} signatures with dHash")
+
+    # Group by accountant
+    acct_groups = {}
+    for sig_id, acct, dhash, filename in rows:
+        acct_groups.setdefault(acct, []).append((sig_id, dhash, filename))
+
+    # Filter out singletons
+    acct_groups = {k: v for k, v in acct_groups.items() if len(v) >= 2}
+    total_sigs = sum(len(v) for v in acct_groups.values())
+    total_pairs = sum(len(v) * (len(v) - 1) // 2 for v in acct_groups.values())
+    print(f"  {len(acct_groups)} accountants, {total_sigs:,} signatures, {total_pairs:,} pairs")
+
+    t0 = time.time()
+    updates = []
+    accts_done = 0
+
+    for acct, sigs in acct_groups.items():
+        n = len(sigs)
+        sig_ids = [s[0] for s in sigs]
+        hashes = [s[1] for s in sigs]
+        filenames = [s[2] for s in sigs]
+
+        # Unpack all hashes to bit arrays for vectorized hamming
+        bits = np.array([np.unpackbits(np.frombuffer(h, dtype=np.uint8)) for h in hashes],
+                        dtype=np.uint8)  # shape: (n, 64)
+
+        # Pairwise hamming via XOR + sum
+        # For groups up to ~2000, direct matrix computation is fine
+        # hamming_matrix[i,j] = number of differing bits between i and j
+        xor_matrix = bits[:, None, :] ^ bits[None, :, :]  # (n, n, 64)
+        hamming_matrix = xor_matrix.sum(axis=2)  # (n, n)
+        np.fill_diagonal(hamming_matrix, 999)  # exclude self
+
+        # For each signature, find min
+        min_indices = np.argmin(hamming_matrix, axis=1)
+        min_distances = hamming_matrix[np.arange(n), min_indices]
+
+        for i in range(n):
+            updates.append((
+                int(min_distances[i]),
+                filenames[min_indices[i]],
+                sig_ids[i]
+            ))
+
+        accts_done += 1
+        if accts_done % 100 == 0:
+            elapsed = time.time() - t0
+            print(f"    {accts_done}/{len(acct_groups)} accountants ({elapsed:.0f}s)")
+
+    # Write to DB
+    print(f"  Writing {len(updates):,} results to DB...")
+    cur.executemany('''
+        UPDATE signatures
+        SET min_dhash_independent = ?, min_dhash_independent_match = ?
+        WHERE signature_id = ?
+    ''', updates)
+    conn.commit()
+    conn.close()
+
+    elapsed = time.time() - t0
+    print(f"  Phase 2 done: {len(updates):,} signatures in {elapsed:.1f}s")
+
+
+# ── Phase 3: Summary statistics ──────────────────────────────────────
+
+def print_summary():
+    """Print summary comparing conditional vs independent dHash."""
+    conn = sqlite3.connect(DB_PATH)
+    cur = conn.cursor()
+
+    # Overall stats
+    cur.execute('''
+        SELECT
+            COUNT(*) as n,
+            AVG(phash_distance_to_closest) as cond_mean,
+            AVG(min_dhash_independent) as indep_mean
+        FROM signatures
+        WHERE min_dhash_independent IS NOT NULL
+          AND phash_distance_to_closest IS NOT NULL
+    ''')
+    n, cond_mean, indep_mean = cur.fetchone()
+
+    print(f"\n{'='*65}")
+    print(f"  COMPARISON: Conditional vs Independent dHash")
+    print(f"{'='*65}")
+    print(f"  N = {n:,}")
+    print(f"  Conditional dHash (cosine-nearest pair):  mean = {cond_mean:.2f}")
+    print(f"  Independent dHash (all-pairs min):        mean = {indep_mean:.2f}")
+
+    # Percentiles
+    cur.execute('''
+        SELECT phash_distance_to_closest, min_dhash_independent
+        FROM signatures
+        WHERE min_dhash_independent IS NOT NULL
+          AND phash_distance_to_closest IS NOT NULL
+    ''')
+    rows = cur.fetchall()
+    cond = np.array([r[0] for r in rows])
+    indep = np.array([r[1] for r in rows])
+
+    print(f"\n  {'Percentile':<12} {'Conditional':>12} {'Independent':>12} {'Diff':>8}")
+    print(f"  {'-'*44}")
+    for p in [1, 5, 10, 25, 50, 75, 90, 95, 99]:
+        cv = np.percentile(cond, p)
+        iv = np.percentile(indep, p)
+        print(f"  P{p:<10d} {cv:>12.1f} {iv:>12.1f} {iv-cv:>+8.1f}")
+
+    # Agreement analysis
+    print(f"\n  Agreement analysis (both ≤ threshold):")
+    for t in [5, 10, 15, 21]:
+        both = np.sum((cond <= t) & (indep <= t))
+        cond_only = np.sum((cond <= t) & (indep > t))
+        indep_only = np.sum((cond > t) & (indep <= t))
+        neither = np.sum((cond > t) & (indep > t))
+        agree_pct = (both + neither) / len(cond) * 100
+        print(f"  θ={t:>2d}: both={both:,}, cond_only={cond_only:,}, "
+              f"indep_only={indep_only:,}, neither={neither:,} (agree={agree_pct:.1f}%)")
+
+    # Firm A specific
+    cur.execute('''
+        SELECT s.phash_distance_to_closest, s.min_dhash_independent
+        FROM signatures s
+        LEFT JOIN accountants a ON s.assigned_accountant = a.name
+        WHERE a.firm = '勤業眾信聯合'
+          AND s.min_dhash_independent IS NOT NULL
+          AND s.phash_distance_to_closest IS NOT NULL
+    ''')
+    rows = cur.fetchall()
+    if rows:
+        cond_a = np.array([r[0] for r in rows])
+        indep_a = np.array([r[1] for r in rows])
+        print(f"\n  Firm A (勤業眾信) — N={len(rows):,}:")
+        print(f"  {'Percentile':<12} {'Conditional':>12} {'Independent':>12}")
+        print(f"  {'-'*36}")
+        for p in [50, 75, 90, 95, 99]:
+            print(f"  P{p:<10d} {np.percentile(cond_a, p):>12.1f} {np.percentile(indep_a, p):>12.1f}")
+
+    conn.close()
+
+
+def main():
+    t_start = time.time()
+    print("=" * 65)
+    print("  Independent Min dHash Computation")
+    print("=" * 65)
+
+    print(f"\n[Phase 1] Computing dHash vectors...")
+    phase1_compute_hashes()
+
+    print(f"\n[Phase 2] Computing all-pairs min dHash per accountant...")
+    phase2_compute_min_dhash()
+
+    print(f"\n[Phase 3] Summary...")
+    print_summary()
+
+    elapsed = time.time() - t_start
+    print(f"\nTotal time: {elapsed:.0f}s ({elapsed/60:.1f} min)")
+
+
+if __name__ == "__main__":
+    main()

signature_analysis/15_hartigan_dip_test.py

@@ -0,0 +1,238 @@
+#!/usr/bin/env python3
+"""
+Script 15: Hartigan Dip Test for Unimodality
+=============================================
+Runs the proper Hartigan & Hartigan (1985) dip test via the `diptest` package
+on the empirical signature-similarity distributions.
+
+Purpose:
+  Confirm/refute bimodality assumption underpinning threshold-selection methods.
+  Prior finding (2026-04-16): signature-level distribution is unimodal long-tail;
+  the story is that bimodality only emerges at the accountant level.
+
+Firm A framing (2026-04-20, corrected):
+  Interviews with multiple Firm A accountants confirm that MOST use
+  replication (stamping / firm-level e-signing) but do NOT exclude a
+  minority of hand-signers. Firm A is therefore a "replication-dominated"
+  population, NOT a "pure" one. This framing is consistent with:
+    - 92.5% of Firm A signatures exceed cosine 0.95
+    - The long left tail (7.5% below 0.95) captures the minority
+      hand-signers, not scan noise
+    - Script 18: of 180 Firm A accountants, 139 cluster in C1
+      (high-replication) and 32 in C2 (middle band = minority hand-signers)
+
+Tests:
+  1. Firm A (Deloitte) cosine max-similarity       -> expected UNIMODAL
+  2. Firm A (Deloitte) independent min dHash       -> expected UNIMODAL
+  3. Full-sample cosine max-similarity             -> test
+  4. Full-sample independent min dHash             -> test
+  5. Accountant-level cosine mean (per-accountant) -> expected BIMODAL / MULTIMODAL
+  6. Accountant-level dhash mean (per-accountant)  -> expected BIMODAL / MULTIMODAL
+
+Output:
+  reports/dip_test/dip_test_report.md
+  reports/dip_test/dip_test_results.json
+"""
+
+import sqlite3
+import json
+import numpy as np
+import diptest
+from pathlib import Path
+from datetime import datetime
+
+DB = '/Volumes/NV2/PDF-Processing/signature-analysis/signature_analysis.db'
+OUT = Path('/Volumes/NV2/PDF-Processing/signature-analysis/reports/dip_test')
+OUT.mkdir(parents=True, exist_ok=True)
+
+FIRM_A = '勤業眾信聯合'
+
+
+def run_dip(values, label, n_boot=2000):
+    """Run Hartigan dip test and return structured result."""
+    arr = np.asarray(values, dtype=float)
+    arr = arr[~np.isnan(arr)]
+    if len(arr) < 4:
+        return {'label': label, 'n': int(len(arr)), 'error': 'too few observations'}
+
+    dip, pval = diptest.diptest(arr, boot_pval=True, n_boot=n_boot)
+    verdict = 'UNIMODAL (accept H0)' if pval > 0.05 else 'MULTIMODAL (reject H0)'
+    return {
+        'label': label,
+        'n': int(len(arr)),
+        'mean': float(np.mean(arr)),
+        'std': float(np.std(arr)),
+        'min': float(np.min(arr)),
+        'max': float(np.max(arr)),
+        'dip': float(dip),
+        'p_value': float(pval),
+        'n_boot': int(n_boot),
+        'verdict_alpha_05': verdict,
+    }
+
+
+def fetch_firm_a():
+    conn = sqlite3.connect(DB)
+    cur = conn.cursor()
+    cur.execute('''
+        SELECT s.max_similarity_to_same_accountant,
+               s.min_dhash_independent
+        FROM signatures s
+        JOIN accountants a ON s.assigned_accountant = a.name
+        WHERE a.firm = ?
+          AND s.max_similarity_to_same_accountant IS NOT NULL
+    ''', (FIRM_A,))
+    rows = cur.fetchall()
+    conn.close()
+    cos = [r[0] for r in rows if r[0] is not None]
+    dh = [r[1] for r in rows if r[1] is not None]
+    return np.array(cos), np.array(dh)
+
+
+def fetch_full_sample():
+    conn = sqlite3.connect(DB)
+    cur = conn.cursor()
+    cur.execute('''
+        SELECT max_similarity_to_same_accountant, min_dhash_independent
+        FROM signatures
+        WHERE max_similarity_to_same_accountant IS NOT NULL
+    ''')
+    rows = cur.fetchall()
+    conn.close()
+    cos = np.array([r[0] for r in rows if r[0] is not None])
+    dh = np.array([r[1] for r in rows if r[1] is not None])
+    return cos, dh
+
+
+def fetch_accountant_aggregates(min_sigs=10):
+    """Per-accountant mean cosine and mean independent dHash."""
+    conn = sqlite3.connect(DB)
+    cur = conn.cursor()
+    cur.execute('''
+        SELECT s.assigned_accountant,
+               AVG(s.max_similarity_to_same_accountant) AS cos_mean,
+               AVG(CAST(s.min_dhash_independent AS REAL)) AS dh_mean,
+               COUNT(*) AS n
+        FROM signatures s
+        WHERE s.assigned_accountant IS NOT NULL
+          AND s.max_similarity_to_same_accountant IS NOT NULL
+          AND s.min_dhash_independent IS NOT NULL
+        GROUP BY s.assigned_accountant
+        HAVING n >= ?
+    ''', (min_sigs,))
+    rows = cur.fetchall()
+    conn.close()
+    cos_means = np.array([r[1] for r in rows])
+    dh_means = np.array([r[2] for r in rows])
+    return cos_means, dh_means, len(rows)
+
+
+def main():
+    print('='*70)
+    print('Script 15: Hartigan Dip Test for Unimodality')
+    print('='*70)
+
+    results = {}
+
+    # Firm A
+    print('\n[1/3] Firm A (Deloitte)...')
+    fa_cos, fa_dh = fetch_firm_a()
+    print(f'  Firm A cosine N={len(fa_cos):,}, dHash N={len(fa_dh):,}')
+    results['firm_a_cosine'] = run_dip(fa_cos, 'Firm A cosine max-similarity')
+    results['firm_a_dhash'] = run_dip(fa_dh, 'Firm A independent min dHash')
+
+    # Full sample
+    print('\n[2/3] Full sample...')
+    all_cos, all_dh = fetch_full_sample()
+    print(f'  Full cosine N={len(all_cos):,}, dHash N={len(all_dh):,}')
+    # Dip test on >=10k obs can be slow with 2000 boot; use 500 for full sample
+    results['full_cosine'] = run_dip(all_cos, 'Full-sample cosine max-similarity',
+                                     n_boot=500)
+    results['full_dhash'] = run_dip(all_dh, 'Full-sample independent min dHash',
+                                    n_boot=500)
+
+    # Accountant-level aggregates
+    print('\n[3/3] Accountant-level aggregates (min 10 sigs)...')
+    acct_cos, acct_dh, n_acct = fetch_accountant_aggregates(min_sigs=10)
+    print(f'  Accountants analyzed: {n_acct}')
+    results['accountant_cos_mean'] = run_dip(acct_cos,
+                                             'Per-accountant cosine mean')
+    results['accountant_dh_mean'] = run_dip(acct_dh,
+                                            'Per-accountant dHash mean')
+
+    # Print summary
+    print('\n' + '='*70)
+    print('RESULTS SUMMARY')
+    print('='*70)
+    print(f"{'Test':<40} {'N':>8} {'dip':>8} {'p':>10} Verdict")
+    print('-'*90)
+    for key, r in results.items():
+        if 'error' in r:
+            continue
+        print(f"{r['label']:<40} {r['n']:>8,} {r['dip']:>8.4f} "
+              f"{r['p_value']:>10.4f} {r['verdict_alpha_05']}")
+
+    # Write JSON
+    json_path = OUT / 'dip_test_results.json'
+    with open(json_path, 'w') as f:
+        json.dump({
+            'generated_at': datetime.now().isoformat(),
+            'db': DB,
+            'results': results,
+        }, f, indent=2, ensure_ascii=False)
+    print(f'\nJSON saved: {json_path}')
+
+    # Write Markdown report
+    md = [
+        '# Hartigan Dip Test Report',
+        f"Generated: {datetime.now().strftime('%Y-%m-%d %H:%M:%S')}",
+        '',
+        '## Method',
+        '',
+        'Hartigan & Hartigan (1985) dip test via `diptest` Python package.',
+        'H0: distribution is unimodal. H1: multimodal (two or more modes).',
+        'p-value computed by bootstrap against a uniform null (2000 reps for',
+        'Firm A/accountant-level, 500 reps for full-sample due to size).',
+        '',
+        '## Results',
+        '',
+        '| Test | N | dip | p-value | Verdict (α=0.05) |',
+        '|------|---|-----|---------|------------------|',
+    ]
+    for r in results.values():
+        if 'error' in r:
+            md.append(f"| {r['label']} | {r['n']} | — | — | {r['error']} |")
+            continue
+        md.append(
+            f"| {r['label']} | {r['n']:,} | {r['dip']:.4f} | "
+            f"{r['p_value']:.4f} | {r['verdict_alpha_05']} |"
+        )
+    md += [
+        '',
+        '## Interpretation',
+        '',
+        '* **Signature level** (Firm A + full sample): the dip test indicates',
+        '  whether a single mode explains the max-cosine/min-dHash distribution.',
+        '  Prior finding (2026-04-16) suggested unimodal long-tail; this script',
+        '  provides the formal test.',
+        '',
+        '* **Accountant level** (per-accountant mean): if multimodal here but',
+        '  unimodal at the signature level, this confirms the interpretation',
+        "  that signing-behaviour is discrete across accountants (replication",
+        '  vs hand-signing), while replication quality itself is a continuous',
+        '  spectrum.',
+        '',
+        '## Downstream implication',
+        '',
+        'Methods that assume bimodality (KDE antimode, 2-component Beta mixture)',
+        'should be applied at the level where dip test rejects H0. If the',
+        "signature-level dip test fails to reject, the paper should report this",
+        'and shift the mixture analysis to the accountant level (see Script 18).',
+    ]
+    md_path = OUT / 'dip_test_report.md'
+    md_path.write_text('\n'.join(md), encoding='utf-8')
+    print(f'Report saved: {md_path}')
+
+
+if __name__ == '__main__':
+    main()

signature_analysis/16_bd_mccrary_discontinuity.py

@@ -0,0 +1,320 @@
+#!/usr/bin/env python3
+"""
+Script 16: Burgstahler-Dichev / McCrary Discontinuity Test
+==========================================================
+Tests for a discontinuity in the empirical density of similarity scores,
+following:
+  - Burgstahler & Dichev (1997) - earnings-management style smoothness test
+  - McCrary (2008)             - rigorous density-discontinuity asymptotics
+
+Idea:
+  Discretize the distribution into equal-width bins. For each bin i compute
+  the standardized deviation Z_i between observed count and the smooth
+  expectation (average of neighbours). Under H0 (distributional smoothness),
+  Z_i ~ N(0,1). A threshold is identified at the transition where Z_{i-1}
+  is significantly negative (below expectation) next to Z_i significantly
+  positive (above expectation) -- marking the boundary between two
+  generative mechanisms (hand-signed vs non-hand-signed).
+
+Inputs:
+  - Firm A cosine max-similarity and independent min dHash
+  - Full-sample cosine and dHash (for comparison)
+
+Output:
+  reports/bd_mccrary/bd_mccrary_report.md
+  reports/bd_mccrary/bd_mccrary_results.json
+  reports/bd_mccrary/bd_mccrary_<variant>.png (overlay plots)
+"""
+
+import sqlite3
+import json
+import numpy as np
+import matplotlib
+matplotlib.use('Agg')
+import matplotlib.pyplot as plt
+from pathlib import Path
+from datetime import datetime
+
+DB = '/Volumes/NV2/PDF-Processing/signature-analysis/signature_analysis.db'
+OUT = Path('/Volumes/NV2/PDF-Processing/signature-analysis/reports/bd_mccrary')
+OUT.mkdir(parents=True, exist_ok=True)
+
+FIRM_A = '勤業眾信聯合'
+
+# BD/McCrary critical values (two-sided, alpha=0.05)
+Z_CRIT = 1.96
+
+
+def bd_mccrary(values, bin_width, lo=None, hi=None):
+    """
+    Compute Burgstahler-Dichev standardized deviations per bin.
+
+    For each bin i with count n_i:
+      expected = 0.5 * (n_{i-1} + n_{i+1})
+      SE       = sqrt(N*p_i*(1-p_i) + 0.25*N*(p_{i-1}+p_{i+1})*(1-p_{i-1}-p_{i+1}))
+      Z_i      = (n_i - expected) / SE
+
+    Returns arrays of (bin_centers, counts, z_scores, expected).
+    """
+    arr = np.asarray(values, dtype=float)
+    arr = arr[~np.isnan(arr)]
+    if lo is None:
+        lo = float(np.floor(arr.min() / bin_width) * bin_width)
+    if hi is None:
+        hi = float(np.ceil(arr.max() / bin_width) * bin_width)
+    edges = np.arange(lo, hi + bin_width, bin_width)
+    counts, _ = np.histogram(arr, bins=edges)
+    centers = (edges[:-1] + edges[1:]) / 2.0
+
+    N = counts.sum()
+    p = counts / N if N else counts.astype(float)
+
+    n_bins = len(counts)
+    z = np.full(n_bins, np.nan)
+    expected = np.full(n_bins, np.nan)
+
+    for i in range(1, n_bins - 1):
+        p_lo = p[i - 1]
+        p_hi = p[i + 1]
+        exp_i = 0.5 * (counts[i - 1] + counts[i + 1])
+        var_i = (N * p[i] * (1 - p[i])
+                 + 0.25 * N * (p_lo + p_hi) * (1 - p_lo - p_hi))
+        if var_i <= 0:
+            continue
+        se = np.sqrt(var_i)
+        z[i] = (counts[i] - exp_i) / se
+        expected[i] = exp_i
+
+    return centers, counts, z, expected
+
+
+def find_transition(centers, z, direction='neg_to_pos'):
+    """
+    Find the first bin pair where Z_{i-1} significantly negative and
+    Z_i significantly positive (or vice versa).
+
+    direction='neg_to_pos' -> threshold where hand-signed density drops
+                              (below expectation) and non-hand-signed
+                              density rises (above expectation). For
+                              cosine similarity, this transition is
+                              expected around the separation point, so
+                              the threshold sits between centers[i-1]
+                              and centers[i].
+    """
+    transitions = []
+    for i in range(1, len(z)):
+        if np.isnan(z[i - 1]) or np.isnan(z[i]):
+            continue
+        if direction == 'neg_to_pos':
+            if z[i - 1] < -Z_CRIT and z[i] > Z_CRIT:
+                transitions.append({
+                    'idx': int(i),
+                    'threshold_between': float(
+                        (centers[i - 1] + centers[i]) / 2.0),
+                    'z_below': float(z[i - 1]),
+                    'z_above': float(z[i]),
+                    'left_center': float(centers[i - 1]),
+                    'right_center': float(centers[i]),
+                })
+        else:  # pos_to_neg
+            if z[i - 1] > Z_CRIT and z[i] < -Z_CRIT:
+                transitions.append({
+                    'idx': int(i),
+                    'threshold_between': float(
+                        (centers[i - 1] + centers[i]) / 2.0),
+                    'z_above': float(z[i - 1]),
+                    'z_below': float(z[i]),
+                    'left_center': float(centers[i - 1]),
+                    'right_center': float(centers[i]),
+                })
+    return transitions
+
+
+def plot_bd(centers, counts, z, expected, title, out_path, threshold=None):
+    fig, axes = plt.subplots(2, 1, figsize=(11, 7), sharex=True)
+
+    ax = axes[0]
+    ax.bar(centers, counts, width=(centers[1] - centers[0]) * 0.9,
+           color='steelblue', alpha=0.6, edgecolor='white', label='Observed')
+    mask = ~np.isnan(expected)
+    ax.plot(centers[mask], expected[mask], 'r-', lw=1.5,
+            label='Expected (smooth null)')
+    ax.set_ylabel('Count')
+    ax.set_title(title)
+    ax.legend()
+    if threshold is not None:
+        ax.axvline(threshold, color='green', ls='--', lw=2,
+                   label=f'Threshold≈{threshold:.4f}')
+
+    ax = axes[1]
+    ax.axhline(0, color='black', lw=0.5)
+    ax.axhline(Z_CRIT, color='red', ls=':', alpha=0.7,
+               label=f'±{Z_CRIT} critical')
+    ax.axhline(-Z_CRIT, color='red', ls=':', alpha=0.7)
+    colors = ['coral' if zi > Z_CRIT else 'steelblue' if zi < -Z_CRIT
+              else 'lightgray' for zi in z]
+    ax.bar(centers, z, width=(centers[1] - centers[0]) * 0.9, color=colors,
+           edgecolor='black', lw=0.3)
+    ax.set_xlabel('Value')
+    ax.set_ylabel('Z statistic')
+    ax.legend()
+    if threshold is not None:
+        ax.axvline(threshold, color='green', ls='--', lw=2)
+
+    plt.tight_layout()
+    fig.savefig(out_path, dpi=150)
+    plt.close()
+
+
+def fetch(label):
+    conn = sqlite3.connect(DB)
+    cur = conn.cursor()
+    if label == 'firm_a_cosine':
+        cur.execute('''
+            SELECT s.max_similarity_to_same_accountant
+            FROM signatures s
+            JOIN accountants a ON s.assigned_accountant = a.name
+            WHERE a.firm = ? AND s.max_similarity_to_same_accountant IS NOT NULL
+        ''', (FIRM_A,))
+    elif label == 'firm_a_dhash':
+        cur.execute('''
+            SELECT s.min_dhash_independent
+            FROM signatures s
+            JOIN accountants a ON s.assigned_accountant = a.name
+            WHERE a.firm = ? AND s.min_dhash_independent IS NOT NULL
+        ''', (FIRM_A,))
+    elif label == 'full_cosine':
+        cur.execute('''
+            SELECT max_similarity_to_same_accountant FROM signatures
+            WHERE max_similarity_to_same_accountant IS NOT NULL
+        ''')
+    elif label == 'full_dhash':
+        cur.execute('''
+            SELECT min_dhash_independent FROM signatures
+            WHERE min_dhash_independent IS NOT NULL
+        ''')
+    else:
+        raise ValueError(label)
+    vals = [r[0] for r in cur.fetchall() if r[0] is not None]
+    conn.close()
+    return np.array(vals, dtype=float)
+
+
+def main():
+    print('='*70)
+    print('Script 16: Burgstahler-Dichev / McCrary Discontinuity Test')
+    print('='*70)
+
+    cases = [
+        ('firm_a_cosine', 0.005, 'Firm A cosine max-similarity', 'neg_to_pos'),
+        ('firm_a_dhash', 1.0, 'Firm A independent min dHash', 'pos_to_neg'),
+        ('full_cosine', 0.005, 'Full-sample cosine max-similarity',
+         'neg_to_pos'),
+        ('full_dhash', 1.0, 'Full-sample independent min dHash', 'pos_to_neg'),
+    ]
+
+    all_results = {}
+    for key, bw, label, direction in cases:
+        print(f'\n[{label}] bin width={bw}')
+        arr = fetch(key)
+        print(f'  N = {len(arr):,}')
+        centers, counts, z, expected = bd_mccrary(arr, bw)
+        transitions = find_transition(centers, z, direction=direction)
+
+        # Summarize
+        if transitions:
+            # Choose the most extreme (highest |z_above * z_below|) transition
+            best = max(transitions,
+                       key=lambda t: abs(t.get('z_above', 0))
+                                     + abs(t.get('z_below', 0)))
+            threshold = best['threshold_between']
+            print(f'  {len(transitions)} candidate transition(s); '
+                  f'best at {threshold:.4f}')
+        else:
+            best = None
+            threshold = None
+            print('  No significant transition detected (no Z^- next to Z^+)')
+
+        # Plot
+        png = OUT / f'bd_mccrary_{key}.png'
+        plot_bd(centers, counts, z, expected, label, png, threshold=threshold)
+        print(f'  plot: {png}')
+
+        all_results[key] = {
+            'label': label,
+            'n': int(len(arr)),
+            'bin_width': float(bw),
+            'direction': direction,
+            'n_bins': int(len(centers)),
+            'bin_centers': [float(c) for c in centers],
+            'counts': [int(c) for c in counts],
+            'z_scores': [None if np.isnan(zi) else float(zi) for zi in z],
+            'transitions': transitions,
+            'best_transition': best,
+            'threshold': threshold,
+        }
+
+    # Write JSON
+    json_path = OUT / 'bd_mccrary_results.json'
+    with open(json_path, 'w') as f:
+        json.dump({
+            'generated_at': datetime.now().isoformat(),
+            'z_critical': Z_CRIT,
+            'results': all_results,
+        }, f, indent=2, ensure_ascii=False)
+    print(f'\nJSON: {json_path}')
+
+    # Markdown
+    md = [
+        '# Burgstahler-Dichev / McCrary Discontinuity Test Report',
+        f"Generated: {datetime.now().strftime('%Y-%m-%d %H:%M:%S')}",
+        '',
+        '## Method',
+        '',
+        'For each bin i of width δ, under the null of distributional',
+        'smoothness the expected count is the average of neighbours,',
+        'and the standardized deviation',
+        '',
+        '  Z_i = (n_i - 0.5*(n_{i-1}+n_{i+1})) / SE',
+        '',
+        'is approximately N(0,1). We flag a transition when Z_{i-1} < -1.96',
+        'and Z_i > 1.96 (or reversed, depending on the scale direction).',
+        'The threshold is taken at the midpoint of the two bin centres.',
+        '',
+        '## Results',
+        '',
+        '| Test | N | bin width | Transitions | Threshold |',
+        '|------|---|-----------|-------------|-----------|',
+    ]
+    for r in all_results.values():
+        thr = (f"{r['threshold']:.4f}" if r['threshold'] is not None
+               else '—')
+        md.append(
+            f"| {r['label']} | {r['n']:,} | {r['bin_width']} | "
+            f"{len(r['transitions'])} | {thr} |"
+        )
+    md += [
+        '',
+        '## Notes',
+        '',
+        '* For cosine (direction `neg_to_pos`), the transition marks the',
+        "  boundary below which hand-signed dominates and above which",
+        '  non-hand-signed replication dominates.',
+        '* For dHash (direction `pos_to_neg`), the transition marks the',
+        "  boundary below which replication dominates (small distances)",
+        '  and above which hand-signed variation dominates.',
+        '* Multiple candidate transitions are ranked by total |Z| magnitude',
+        '  on both sides of the boundary; the strongest is reported.',
+        '* Absence of a significant transition is itself informative: it',
+        '  is consistent with a single dominant generative mechanism (e.g.',
+        '  Firm A, a replication-dominated population per interviews with',
+        '  multiple Firm A accountants -- most use replication, a minority',
+        '  may hand-sign).',
+    ]
+    md_path = OUT / 'bd_mccrary_report.md'
+    md_path.write_text('\n'.join(md), encoding='utf-8')
+    print(f'Report: {md_path}')
+
+
+if __name__ == '__main__':
+    main()

signature_analysis/17_beta_mixture_em.py

@@ -0,0 +1,406 @@
+#!/usr/bin/env python3
+"""
+Script 17: Beta Mixture Model via EM + Gaussian Mixture on Logit Transform
+==========================================================================
+Fits a 2-component Beta mixture to cosine similarity, plus parallel
+Gaussian mixture on logit-transformed data as robustness check.
+
+Theory:
+  - Cosine similarity is bounded [0,1] so Beta is the natural parametric
+    family for the component distributions.
+  - EM algorithm (Dempster, Laird & Rubin 1977) provides ML estimates.
+  - If the mixture gives a crossing point, that is the Bayes-optimal
+    threshold under the fitted model.
+  - Robustness: logit(x) maps (0,1) to the real line, where Gaussian
+    mixture is standard; White (1982) quasi-MLE guarantees asymptotic
+    recovery of the best Beta-family approximation even under
+    mis-specification.
+
+Parametrization of Beta via method-of-moments inside the M-step:
+  alpha = mu * ((mu*(1-mu))/var - 1)
+  beta  = (1-mu) * ((mu*(1-mu))/var - 1)
+
+Expected outcome (per memory 2026-04-16):
+  Signature-level Beta mixture FAILS to separate hand-signed vs
+  non-hand-signed because the distribution is unimodal long-tail.
+  Report this as a formal result -- it motivates the pivot to
+  accountant-level mixture (Script 18).
+
+Output:
+  reports/beta_mixture/beta_mixture_report.md
+  reports/beta_mixture/beta_mixture_results.json
+  reports/beta_mixture/beta_mixture_<case>.png
+"""
+
+import sqlite3
+import json
+import numpy as np
+import matplotlib
+matplotlib.use('Agg')
+import matplotlib.pyplot as plt
+from pathlib import Path
+from datetime import datetime
+from scipy import stats
+from scipy.optimize import brentq
+from sklearn.mixture import GaussianMixture
+
+DB = '/Volumes/NV2/PDF-Processing/signature-analysis/signature_analysis.db'
+OUT = Path('/Volumes/NV2/PDF-Processing/signature-analysis/reports/beta_mixture')
+OUT.mkdir(parents=True, exist_ok=True)
+
+FIRM_A = '勤業眾信聯合'
+EPS = 1e-6
+
+
+def fit_beta_mixture_em(x, n_components=2, max_iter=300, tol=1e-6, seed=42):
+    """
+    Fit a K-component Beta mixture via EM using MoM M-step estimates for
+    alpha/beta of each component. MoM works because Beta is fully determined
+    by its mean and variance under the moment equations.
+    """
+    rng = np.random.default_rng(seed)
+    x = np.clip(np.asarray(x, dtype=float), EPS, 1 - EPS)
+    n = len(x)
+    K = n_components
+
+    # Initialise responsibilities by quantile-based split
+    q = np.linspace(0, 1, K + 1)
+    thresh = np.quantile(x, q[1:-1])
+    labels = np.digitize(x, thresh)
+    resp = np.zeros((n, K))
+    resp[np.arange(n), labels] = 1.0
+
+    params = []  # list of dicts with alpha, beta, weight
+    log_like_hist = []
+    for it in range(max_iter):
+        # M-step
+        nk = resp.sum(axis=0) + 1e-12
+        weights = nk / nk.sum()
+        mus = (resp * x[:, None]).sum(axis=0) / nk
+        var_num = (resp * (x[:, None] - mus) ** 2).sum(axis=0)
+        vars_ = var_num / nk
+        # Ensure validity for Beta: var < mu*(1-mu)
+        upper = mus * (1 - mus) - 1e-9
+        vars_ = np.minimum(vars_, upper)
+        vars_ = np.maximum(vars_, 1e-9)
+        factor = mus * (1 - mus) / vars_ - 1
+        factor = np.maximum(factor, 1e-6)
+        alphas = mus * factor
+        betas = (1 - mus) * factor
+        params = [{'alpha': float(alphas[k]), 'beta': float(betas[k]),
+                   'weight': float(weights[k]), 'mu': float(mus[k]),
+                   'var': float(vars_[k])} for k in range(K)]
+
+        # E-step
+        log_pdfs = np.column_stack([
+            stats.beta.logpdf(x, alphas[k], betas[k]) + np.log(weights[k])
+            for k in range(K)
+        ])
+        m = log_pdfs.max(axis=1, keepdims=True)
+        log_like = (m.ravel() + np.log(np.exp(log_pdfs - m).sum(axis=1))).sum()
+        log_like_hist.append(float(log_like))
+        new_resp = np.exp(log_pdfs - m)
+        new_resp = new_resp / new_resp.sum(axis=1, keepdims=True)
+
+        if it > 0 and abs(log_like_hist[-1] - log_like_hist[-2]) < tol:
+            resp = new_resp
+            break
+        resp = new_resp
+
+    # Order components by mean ascending (so C1 = low mean, CK = high mean)
+    order = np.argsort([p['mu'] for p in params])
+    params = [params[i] for i in order]
+    resp = resp[:, order]
+
+    # AIC/BIC (k = 3K - 1 free parameters: alpha, beta, weight each component;
+    # weights sum to 1 removes one df)
+    k = 3 * K - 1
+    aic = 2 * k - 2 * log_like_hist[-1]
+    bic = k * np.log(n) - 2 * log_like_hist[-1]
+
+    return {
+        'components': params,
+        'log_likelihood': log_like_hist[-1],
+        'aic': float(aic),
+        'bic': float(bic),
+        'n_iter': it + 1,
+        'responsibilities': resp,
+    }
+
+
+def mixture_crossing(params, x_range):
+    """Find crossing point of two weighted component densities (K=2)."""
+    if len(params) != 2:
+        return None
+    a1, b1, w1 = params[0]['alpha'], params[0]['beta'], params[0]['weight']
+    a2, b2, w2 = params[1]['alpha'], params[1]['beta'], params[1]['weight']
+
+    def diff(x):
+        return (w2 * stats.beta.pdf(x, a2, b2)
+                - w1 * stats.beta.pdf(x, a1, b1))
+
+    # Search for sign change inside the overlap region
+    xs = np.linspace(x_range[0] + 1e-4, x_range[1] - 1e-4, 2000)
+    ys = diff(xs)
+    sign_changes = np.where(np.diff(np.sign(ys)) != 0)[0]
+    if len(sign_changes) == 0:
+        return None
+    # Pick crossing closest to midpoint of component means
+    mid = 0.5 * (params[0]['mu'] + params[1]['mu'])
+    crossings = []
+    for i in sign_changes:
+        try:
+            x0 = brentq(diff, xs[i], xs[i + 1])
+            crossings.append(x0)
+        except ValueError:
+            continue
+    if not crossings:
+        return None
+    return min(crossings, key=lambda c: abs(c - mid))
+
+
+def logit(x):
+    x = np.clip(x, EPS, 1 - EPS)
+    return np.log(x / (1 - x))
+
+
+def invlogit(z):
+    return 1.0 / (1.0 + np.exp(-z))
+
+
+def fit_gmm_logit(x, n_components=2, seed=42):
+    """GMM on logit-transformed values. Returns crossing point in original scale."""
+    z = logit(x).reshape(-1, 1)
+    gmm = GaussianMixture(n_components=n_components, random_state=seed,
+                          max_iter=500).fit(z)
+    means = gmm.means_.ravel()
+    covs = gmm.covariances_.ravel()
+    weights = gmm.weights_
+    order = np.argsort(means)
+    comps = [{
+        'mu_logit': float(means[i]),
+        'sigma_logit': float(np.sqrt(covs[i])),
+        'weight': float(weights[i]),
+        'mu_original': float(invlogit(means[i])),
+    } for i in order]
+
+    result = {
+        'components': comps,
+        'log_likelihood': float(gmm.score(z) * len(z)),
+        'aic': float(gmm.aic(z)),
+        'bic': float(gmm.bic(z)),
+        'n_iter': int(gmm.n_iter_),
+    }
+
+    if n_components == 2:
+        m1, s1, w1 = means[order[0]], np.sqrt(covs[order[0]]), weights[order[0]]
+        m2, s2, w2 = means[order[1]], np.sqrt(covs[order[1]]), weights[order[1]]
+
+        def diff(z0):
+            return (w2 * stats.norm.pdf(z0, m2, s2)
+                    - w1 * stats.norm.pdf(z0, m1, s1))
+        zs = np.linspace(min(m1, m2) - 1, max(m1, m2) + 1, 2000)
+        ys = diff(zs)
+        changes = np.where(np.diff(np.sign(ys)) != 0)[0]
+        if len(changes):
+            try:
+                z_cross = brentq(diff, zs[changes[0]], zs[changes[0] + 1])
+                result['crossing_logit'] = float(z_cross)
+                result['crossing_original'] = float(invlogit(z_cross))
+            except ValueError:
+                pass
+    return result
+
+
+def plot_mixture(x, beta_res, title, out_path, gmm_res=None):
+    x = np.asarray(x, dtype=float).ravel()
+    x = x[np.isfinite(x)]
+    fig, ax = plt.subplots(figsize=(10, 5))
+    bin_edges = np.linspace(float(x.min()), float(x.max()), 81)
+    ax.hist(x, bins=bin_edges, density=True, alpha=0.45, color='steelblue',
+            edgecolor='white')
+    xs = np.linspace(max(0.0, x.min() - 0.01), min(1.0, x.max() + 0.01), 500)
+    total = np.zeros_like(xs)
+    for i, p in enumerate(beta_res['components']):
+        comp_pdf = p['weight'] * stats.beta.pdf(xs, p['alpha'], p['beta'])
+        total = total + comp_pdf
+        ax.plot(xs, comp_pdf, '--', lw=1.5,
+                label=f"C{i+1}: α={p['alpha']:.2f}, β={p['beta']:.2f}, "
+                      f"w={p['weight']:.2f}")
+    ax.plot(xs, total, 'r-', lw=2, label='Beta mixture (sum)')
+
+    crossing = mixture_crossing(beta_res['components'], (xs[0], xs[-1]))
+    if crossing is not None:
+        ax.axvline(crossing, color='green', ls='--', lw=2,
+                   label=f'Beta crossing = {crossing:.4f}')
+
+    if gmm_res and 'crossing_original' in gmm_res:
+        ax.axvline(gmm_res['crossing_original'], color='purple', ls=':',
+                   lw=2, label=f"Logit-GMM crossing = "
+                               f"{gmm_res['crossing_original']:.4f}")
+
+    ax.set_xlabel('Value')
+    ax.set_ylabel('Density')
+    ax.set_title(title)
+    ax.legend(fontsize=8)
+    plt.tight_layout()
+    fig.savefig(out_path, dpi=150)
+    plt.close()
+    return crossing
+
+
+def fetch(label):
+    conn = sqlite3.connect(DB)
+    cur = conn.cursor()
+    if label == 'firm_a_cosine':
+        cur.execute('''
+            SELECT s.max_similarity_to_same_accountant
+            FROM signatures s
+            JOIN accountants a ON s.assigned_accountant = a.name
+            WHERE a.firm = ? AND s.max_similarity_to_same_accountant IS NOT NULL
+        ''', (FIRM_A,))
+    elif label == 'full_cosine':
+        cur.execute('''
+            SELECT max_similarity_to_same_accountant FROM signatures
+            WHERE max_similarity_to_same_accountant IS NOT NULL
+        ''')
+    else:
+        raise ValueError(label)
+    vals = [r[0] for r in cur.fetchall() if r[0] is not None]
+    conn.close()
+    return np.array(vals, dtype=float)
+
+
+def main():
+    print('='*70)
+    print('Script 17: Beta Mixture EM + Logit-GMM Robustness Check')
+    print('='*70)
+
+    cases = [
+        ('firm_a_cosine', 'Firm A cosine max-similarity'),
+        ('full_cosine', 'Full-sample cosine max-similarity'),
+    ]
+
+    summary = {}
+    for key, label in cases:
+        print(f'\n[{label}]')
+        x = fetch(key)
+        print(f'  N = {len(x):,}')
+
+        # Subsample for full sample to keep EM tractable but still stable
+        if len(x) > 200000:
+            rng = np.random.default_rng(42)
+            x_fit = rng.choice(x, 200000, replace=False)
+            print(f'  Subsampled to {len(x_fit):,} for EM fitting')
+        else:
+            x_fit = x
+
+        beta2 = fit_beta_mixture_em(x_fit, n_components=2)
+        beta3 = fit_beta_mixture_em(x_fit, n_components=3)
+        print(f'  Beta-2  AIC={beta2["aic"]:.1f}, BIC={beta2["bic"]:.1f}')
+        print(f'  Beta-3  AIC={beta3["aic"]:.1f}, BIC={beta3["bic"]:.1f}')
+
+        gmm2 = fit_gmm_logit(x_fit, n_components=2)
+        gmm3 = fit_gmm_logit(x_fit, n_components=3)
+        print(f'  LogGMM2 AIC={gmm2["aic"]:.1f}, BIC={gmm2["bic"]:.1f}')
+        print(f'  LogGMM3 AIC={gmm3["aic"]:.1f}, BIC={gmm3["bic"]:.1f}')
+
+        # Report crossings
+        crossing_beta = mixture_crossing(beta2['components'], (x.min(), x.max()))
+        print(f'  Beta-2 crossing: '
+              f"{('%.4f' % crossing_beta) if crossing_beta else '—'}")
+        print(f'  LogGMM-2 crossing (original scale): '
+              f"{gmm2.get('crossing_original', '—')}")
+
+        # Plot
+        png = OUT / f'beta_mixture_{key}.png'
+        plot_mixture(x_fit, beta2, f'{label}: Beta mixture (2 comp)', png,
+                     gmm_res=gmm2)
+        print(f'  plot: {png}')
+
+        # Strip responsibilities for JSON compactness
+        beta2_out = {k: v for k, v in beta2.items() if k != 'responsibilities'}
+        beta3_out = {k: v for k, v in beta3.items() if k != 'responsibilities'}
+
+        summary[key] = {
+            'label': label,
+            'n': int(len(x)),
+            'n_fit': int(len(x_fit)),
+            'beta_2': beta2_out,
+            'beta_3': beta3_out,
+            'beta_2_crossing': (float(crossing_beta)
+                                if crossing_beta is not None else None),
+            'logit_gmm_2': gmm2,
+            'logit_gmm_3': gmm3,
+            'bic_best': ('beta_2' if beta2['bic'] < beta3['bic']
+                         else 'beta_3'),
+        }
+
+    # Write JSON
+    json_path = OUT / 'beta_mixture_results.json'
+    with open(json_path, 'w') as f:
+        json.dump({
+            'generated_at': datetime.now().isoformat(),
+            'results': summary,
+        }, f, indent=2, ensure_ascii=False, default=float)
+    print(f'\nJSON: {json_path}')
+
+    # Markdown
+    md = [
+        '# Beta Mixture EM Report',
+        f"Generated: {datetime.now().strftime('%Y-%m-%d %H:%M:%S')}",
+        '',
+        '## Method',
+        '',
+        '* 2- and 3-component Beta mixture fit by EM with method-of-moments',
+        '  M-step (stable for bounded data).',
+        '* Parallel 2/3-component Gaussian mixture on logit-transformed',
+        '  values as robustness check (White 1982 quasi-MLE consistency).',
+        '* Crossing point of the 2-component mixture densities is reported',
+        '  as the Bayes-optimal threshold under equal misclassification cost.',
+        '',
+        '## Results',
+        '',
+        '| Dataset | N (fit) | Beta-2 BIC | Beta-3 BIC | LogGMM-2 BIC | LogGMM-3 BIC | BIC-best |',
+        '|---------|---------|------------|------------|--------------|--------------|----------|',
+    ]
+    for r in summary.values():
+        md.append(
+            f"| {r['label']} | {r['n_fit']:,} | "
+            f"{r['beta_2']['bic']:.1f} | {r['beta_3']['bic']:.1f} | "
+            f"{r['logit_gmm_2']['bic']:.1f} | {r['logit_gmm_3']['bic']:.1f} | "
+            f"{r['bic_best']} |"
+        )
+
+    md += ['', '## Threshold estimates (2-component)', '',
+           '| Dataset | Beta-2 crossing | LogGMM-2 crossing (orig) |',
+           '|---------|-----------------|--------------------------|']
+    for r in summary.values():
+        beta_str = (f"{r['beta_2_crossing']:.4f}"
+                    if r['beta_2_crossing'] is not None else '—')
+        gmm_str = (f"{r['logit_gmm_2']['crossing_original']:.4f}"
+                   if 'crossing_original' in r['logit_gmm_2'] else '—')
+        md.append(f"| {r['label']} | {beta_str} | {gmm_str} |")
+
+    md += [
+        '',
+        '## Interpretation',
+        '',
+        'A successful 2-component fit with a clear crossing point would',
+        'indicate two underlying generative mechanisms (hand-signed vs',
+        'non-hand-signed) with a principled Bayes-optimal boundary.',
+        '',
+        'If Beta-3 BIC is meaningfully smaller than Beta-2, or if the',
+        'components of Beta-2 largely overlap (similar means, wide spread),',
+        'this is consistent with a unimodal distribution poorly approximated',
+        'by two components. Prior finding (2026-04-16) suggested this is',
+        'the case at signature level; the accountant-level mixture',
+        '(Script 18) is where the bimodality emerges.',
+    ]
+    md_path = OUT / 'beta_mixture_report.md'
+    md_path.write_text('\n'.join(md), encoding='utf-8')
+    print(f'Report: {md_path}')
+
+
+if __name__ == '__main__':
+    main()

signature_analysis/18_accountant_mixture.py

@@ -0,0 +1,404 @@
+#!/usr/bin/env python3
+"""
+Script 18: Accountant-Level 3-Component Gaussian Mixture
+========================================================
+Rebuild the GMM analysis from memory 2026-04-16: at the accountant level
+(not signature level), the joint distribution of (cosine_mean, dhash_mean)
+separates into three components corresponding to signing-behaviour
+regimes:
+
+  C1  High-replication      cos_mean ≈ 0.983, dh_mean ≈ 2.4, ~20%, Deloitte-heavy
+  C2  Middle band           cos_mean ≈ 0.954, dh_mean ≈ 7.0, ~52%, KPMG/PwC/EY
+  C3  Hand-signed tendency  cos_mean ≈ 0.928, dh_mean ≈ 11.2, ~28%, small firms
+
+The script:
+  1. Aggregates per-accountant means from the signature table.
+  2. Fits 1-, 2-, 3-, 4-component 2D Gaussian mixtures and selects by BIC.
+  3. Reports component parameters, cluster assignments, and per-firm
+     breakdown.
+  4. For the 2-component fit derives the natural threshold (crossing of
+     marginal densities in cosine-mean and dhash-mean).
+
+Firm A framing note (2026-04-20, corrected):
+  Interviews with Firm A accountants confirm MOST use replication but a
+  MINORITY may hand-sign. Firm A is thus a "replication-dominated"
+  population, NOT pure. Empirically: of ~180 Firm A accountants, ~139
+  land in C1 (high-replication) and ~32 land in C2 (middle band) under
+  the 3-component fit. The C2 Firm A members are the interview-suggested
+  minority hand-signers.
+
+Output:
+  reports/accountant_mixture/accountant_mixture_report.md
+  reports/accountant_mixture/accountant_mixture_results.json
+  reports/accountant_mixture/accountant_mixture_2d.png
+  reports/accountant_mixture/accountant_mixture_marginals.png
+"""
+
+import sqlite3
+import json
+import numpy as np
+import matplotlib
+matplotlib.use('Agg')
+import matplotlib.pyplot as plt
+from pathlib import Path
+from datetime import datetime
+from scipy import stats
+from scipy.optimize import brentq
+from sklearn.mixture import GaussianMixture
+
+DB = '/Volumes/NV2/PDF-Processing/signature-analysis/signature_analysis.db'
+OUT = Path('/Volumes/NV2/PDF-Processing/signature-analysis/reports/'
+           'accountant_mixture')
+OUT.mkdir(parents=True, exist_ok=True)
+
+MIN_SIGS = 10
+
+
+def load_accountant_aggregates():
+    conn = sqlite3.connect(DB)
+    cur = conn.cursor()
+    cur.execute('''
+        SELECT s.assigned_accountant,
+               a.firm,
+               AVG(s.max_similarity_to_same_accountant) AS cos_mean,
+               AVG(CAST(s.min_dhash_independent AS REAL)) AS dh_mean,
+               COUNT(*) AS n
+        FROM signatures s
+        LEFT JOIN accountants a ON s.assigned_accountant = a.name
+        WHERE s.assigned_accountant IS NOT NULL
+          AND s.max_similarity_to_same_accountant IS NOT NULL
+          AND s.min_dhash_independent IS NOT NULL
+        GROUP BY s.assigned_accountant
+        HAVING n >= ?
+    ''', (MIN_SIGS,))
+    rows = cur.fetchall()
+    conn.close()
+    return [
+        {'accountant': r[0], 'firm': r[1] or '(unknown)',
+         'cos_mean': float(r[2]), 'dh_mean': float(r[3]), 'n': int(r[4])}
+        for r in rows
+    ]
+
+
+def fit_gmm_range(X, ks=(1, 2, 3, 4, 5), seed=42, n_init=10):
+    results = []
+    best_bic = np.inf
+    best = None
+    for k in ks:
+        gmm = GaussianMixture(
+            n_components=k, covariance_type='full',
+            random_state=seed, n_init=n_init, max_iter=500,
+        ).fit(X)
+        bic = gmm.bic(X)
+        aic = gmm.aic(X)
+        results.append({
+            'k': int(k), 'bic': float(bic), 'aic': float(aic),
+            'converged': bool(gmm.converged_), 'n_iter': int(gmm.n_iter_),
+        })
+        if bic < best_bic:
+            best_bic = bic
+            best = gmm
+    return results, best
+
+
+def summarize_components(gmm, X, df):
+    """Assign clusters, return per-component stats + per-firm breakdown."""
+    labels = gmm.predict(X)
+    means = gmm.means_
+    order = np.argsort(means[:, 0])  # order by cos_mean ascending
+    # Relabel so smallest cos_mean = component 1
+    relabel = np.argsort(order)
+
+    # Actually invert: in prior memory C1 was HIGH replication (highest cos).
+    # To keep consistent with memory, order DESCENDING by cos_mean so C1 = high.
+    order = np.argsort(-means[:, 0])
+    relabel = {int(old): new + 1 for new, old in enumerate(order)}
+    new_labels = np.array([relabel[int(l)] for l in labels])
+
+    components = []
+    for rank, old_idx in enumerate(order, start=1):
+        mu = means[old_idx]
+        cov = gmm.covariances_[old_idx]
+        w = gmm.weights_[old_idx]
+        mask = new_labels == rank
+        firms = {}
+        for row, in_cluster in zip(df, mask):
+            if not in_cluster:
+                continue
+            firms[row['firm']] = firms.get(row['firm'], 0) + 1
+        firms_sorted = sorted(firms.items(), key=lambda kv: -kv[1])
+        components.append({
+            'component': rank,
+            'mu_cos': float(mu[0]),
+            'mu_dh': float(mu[1]),
+            'cov_00': float(cov[0, 0]),
+            'cov_11': float(cov[1, 1]),
+            'cov_01': float(cov[0, 1]),
+            'corr': float(cov[0, 1] / np.sqrt(cov[0, 0] * cov[1, 1])),
+            'weight': float(w),
+            'n_accountants': int(mask.sum()),
+            'top_firms': firms_sorted[:5],
+        })
+    return components, new_labels
+
+
+def marginal_crossing(means, covs, weights, dim, search_lo, search_hi):
+    """Find crossing of two weighted marginal Gaussians along dimension `dim`."""
+    m1, m2 = means[0][dim], means[1][dim]
+    s1 = np.sqrt(covs[0][dim, dim])
+    s2 = np.sqrt(covs[1][dim, dim])
+    w1, w2 = weights[0], weights[1]
+
+    def diff(x):
+        return (w2 * stats.norm.pdf(x, m2, s2)
+                - w1 * stats.norm.pdf(x, m1, s1))
+
+    xs = np.linspace(search_lo, search_hi, 2000)
+    ys = diff(xs)
+    changes = np.where(np.diff(np.sign(ys)) != 0)[0]
+    if not len(changes):
+        return None
+    mid = 0.5 * (m1 + m2)
+    crossings = []
+    for i in changes:
+        try:
+            crossings.append(brentq(diff, xs[i], xs[i + 1]))
+        except ValueError:
+            continue
+    if not crossings:
+        return None
+    return float(min(crossings, key=lambda c: abs(c - mid)))
+
+
+def plot_2d(df, labels, means, title, out_path):
+    colors = ['#d62728', '#1f77b4', '#2ca02c', '#9467bd', '#ff7f0e']
+    fig, ax = plt.subplots(figsize=(9, 7))
+    for k in sorted(set(labels)):
+        mask = labels == k
+        xs = [r['cos_mean'] for r, m in zip(df, mask) if m]
+        ys = [r['dh_mean'] for r, m in zip(df, mask) if m]
+        ax.scatter(xs, ys, s=20, alpha=0.55, color=colors[(k - 1) % 5],
+                   label=f'C{k} (n={int(mask.sum())})')
+    for i, mu in enumerate(means):
+        ax.plot(mu[0], mu[1], 'k*', ms=18, mec='white', mew=1.5)
+        ax.annotate(f'  μ{i+1}', (mu[0], mu[1]), fontsize=10)
+    ax.set_xlabel('Per-accountant mean cosine max-similarity')
+    ax.set_ylabel('Per-accountant mean independent min dHash')
+    ax.set_title(title)
+    ax.legend()
+    plt.tight_layout()
+    fig.savefig(out_path, dpi=150)
+    plt.close()
+
+
+def plot_marginals(df, labels, gmm_2, out_path, cos_cross=None, dh_cross=None):
+    cos = np.array([r['cos_mean'] for r in df])
+    dh = np.array([r['dh_mean'] for r in df])
+
+    fig, axes = plt.subplots(1, 2, figsize=(13, 5))
+
+    # Cosine marginal
+    ax = axes[0]
+    ax.hist(cos, bins=40, density=True, alpha=0.5, color='steelblue',
+            edgecolor='white')
+    xs = np.linspace(cos.min(), cos.max(), 400)
+    means_2 = gmm_2.means_
+    covs_2 = gmm_2.covariances_
+    weights_2 = gmm_2.weights_
+    order = np.argsort(-means_2[:, 0])
+    for rank, i in enumerate(order, start=1):
+        ys = weights_2[i] * stats.norm.pdf(xs, means_2[i, 0],
+                                           np.sqrt(covs_2[i, 0, 0]))
+        ax.plot(xs, ys, '--', label=f'C{rank} μ={means_2[i,0]:.3f}')
+    if cos_cross is not None:
+        ax.axvline(cos_cross, color='green', lw=2,
+                   label=f'Crossing = {cos_cross:.4f}')
+    ax.set_xlabel('Per-accountant mean cosine')
+    ax.set_ylabel('Density')
+    ax.set_title('Cosine marginal (2-component fit)')
+    ax.legend(fontsize=8)
+
+    # dHash marginal
+    ax = axes[1]
+    ax.hist(dh, bins=40, density=True, alpha=0.5, color='coral',
+            edgecolor='white')
+    xs = np.linspace(dh.min(), dh.max(), 400)
+    for rank, i in enumerate(order, start=1):
+        ys = weights_2[i] * stats.norm.pdf(xs, means_2[i, 1],
+                                           np.sqrt(covs_2[i, 1, 1]))
+        ax.plot(xs, ys, '--', label=f'C{rank} μ={means_2[i,1]:.2f}')
+    if dh_cross is not None:
+        ax.axvline(dh_cross, color='green', lw=2,
+                   label=f'Crossing = {dh_cross:.4f}')
+    ax.set_xlabel('Per-accountant mean dHash')
+    ax.set_ylabel('Density')
+    ax.set_title('dHash marginal (2-component fit)')
+    ax.legend(fontsize=8)
+
+    plt.tight_layout()
+    fig.savefig(out_path, dpi=150)
+    plt.close()
+
+
+def main():
+    print('='*70)
+    print('Script 18: Accountant-Level Gaussian Mixture')
+    print('='*70)
+
+    df = load_accountant_aggregates()
+    print(f'\nAccountants with >= {MIN_SIGS} signatures: {len(df)}')
+    X = np.array([[r['cos_mean'], r['dh_mean']] for r in df])
+
+    # Fit K=1..5
+    print('\nFitting GMMs with K=1..5...')
+    bic_results, _ = fit_gmm_range(X, ks=(1, 2, 3, 4, 5), seed=42, n_init=15)
+    for r in bic_results:
+        print(f"  K={r['k']}: BIC={r['bic']:.2f}  AIC={r['aic']:.2f}  "
+              f"converged={r['converged']}")
+    best_k = min(bic_results, key=lambda r: r['bic'])['k']
+    print(f'\nBIC-best K = {best_k}')
+
+    # Fit 3-component specifically (target)
+    gmm_3 = GaussianMixture(n_components=3, covariance_type='full',
+                            random_state=42, n_init=15, max_iter=500).fit(X)
+    comps_3, labels_3 = summarize_components(gmm_3, X, df)
+
+    print('\n--- 3-component summary ---')
+    for c in comps_3:
+        tops = ', '.join(f"{f}({n})" for f, n in c['top_firms'])
+        print(f"  C{c['component']}: cos={c['mu_cos']:.3f}, "
+              f"dh={c['mu_dh']:.2f}, w={c['weight']:.2f}, "
+              f"n={c['n_accountants']} -> {tops}")
+
+    # Fit 2-component for threshold derivation
+    gmm_2 = GaussianMixture(n_components=2, covariance_type='full',
+                            random_state=42, n_init=15, max_iter=500).fit(X)
+    comps_2, labels_2 = summarize_components(gmm_2, X, df)
+
+    # Crossings
+    cos_cross = marginal_crossing(gmm_2.means_, gmm_2.covariances_,
+                                  gmm_2.weights_, dim=0,
+                                  search_lo=X[:, 0].min(),
+                                  search_hi=X[:, 0].max())
+    dh_cross = marginal_crossing(gmm_2.means_, gmm_2.covariances_,
+                                 gmm_2.weights_, dim=1,
+                                 search_lo=X[:, 1].min(),
+                                 search_hi=X[:, 1].max())
+    print(f'\n2-component crossings: cos={cos_cross}, dh={dh_cross}')
+
+    # Plots
+    plot_2d(df, labels_3, gmm_3.means_,
+            '3-component accountant-level GMM',
+            OUT / 'accountant_mixture_2d.png')
+    plot_marginals(df, labels_2, gmm_2,
+                   OUT / 'accountant_mixture_marginals.png',
+                   cos_cross=cos_cross, dh_cross=dh_cross)
+
+    # Per-accountant CSV (for downstream use)
+    csv_path = OUT / 'accountant_clusters.csv'
+    with open(csv_path, 'w', encoding='utf-8') as f:
+        f.write('accountant,firm,n_signatures,cos_mean,dh_mean,'
+                'cluster_k3,cluster_k2\n')
+        for r, k3, k2 in zip(df, labels_3, labels_2):
+            f.write(f"{r['accountant']},{r['firm']},{r['n']},"
+                    f"{r['cos_mean']:.6f},{r['dh_mean']:.6f},{k3},{k2}\n")
+    print(f'CSV: {csv_path}')
+
+    # Summary JSON
+    summary = {
+        'generated_at': datetime.now().isoformat(),
+        'n_accountants': len(df),
+        'min_signatures': MIN_SIGS,
+        'bic_model_selection': bic_results,
+        'best_k_by_bic': best_k,
+        'gmm_3': {
+            'components': comps_3,
+            'aic': float(gmm_3.aic(X)),
+            'bic': float(gmm_3.bic(X)),
+            'log_likelihood': float(gmm_3.score(X) * len(X)),
+        },
+        'gmm_2': {
+            'components': comps_2,
+            'aic': float(gmm_2.aic(X)),
+            'bic': float(gmm_2.bic(X)),
+            'log_likelihood': float(gmm_2.score(X) * len(X)),
+            'cos_crossing': cos_cross,
+            'dh_crossing': dh_cross,
+        },
+    }
+    with open(OUT / 'accountant_mixture_results.json', 'w') as f:
+        json.dump(summary, f, indent=2, ensure_ascii=False)
+    print(f'JSON: {OUT / "accountant_mixture_results.json"}')
+
+    # Markdown
+    md = [
+        '# Accountant-Level Gaussian Mixture Report',
+        f"Generated: {datetime.now().strftime('%Y-%m-%d %H:%M:%S')}",
+        '',
+        '## Data',
+        '',
+        f'* Per-accountant aggregates: mean cosine max-similarity, '
+        f'mean independent min dHash.',
+        f"* Minimum signatures per accountant: {MIN_SIGS}.",
+        f'* Accountants included: **{len(df)}**.',
+        '',
+        '## Model selection (BIC)',
+        '',
+        '| K | BIC | AIC | Converged |',
+        '|---|-----|-----|-----------|',
+    ]
+    for r in bic_results:
+        mark = ' ←best' if r['k'] == best_k else ''
+        md.append(
+            f"| {r['k']} | {r['bic']:.2f} | {r['aic']:.2f} | "
+            f"{r['converged']}{mark} |"
+        )
+
+    md += ['', '## 3-component fit', '',
+           '| Component | cos_mean | dh_mean | weight | n_accountants | top firms |',
+           '|-----------|----------|---------|--------|----------------|-----------|']
+    for c in comps_3:
+        tops = ', '.join(f"{f}:{n}" for f, n in c['top_firms'])
+        md.append(
+            f"| C{c['component']} | {c['mu_cos']:.3f} | {c['mu_dh']:.2f} | "
+            f"{c['weight']:.3f} | {c['n_accountants']} | {tops} |"
+        )
+
+    md += ['', '## 2-component fit (threshold derivation)', '',
+           '| Component | cos_mean | dh_mean | weight | n_accountants |',
+           '|-----------|----------|---------|--------|----------------|']
+    for c in comps_2:
+        md.append(
+            f"| C{c['component']} | {c['mu_cos']:.3f} | {c['mu_dh']:.2f} | "
+            f"{c['weight']:.3f} | {c['n_accountants']} |"
+        )
+
+    md += ['', '### Natural thresholds from 2-component crossings', '',
+           f'* Cosine: **{cos_cross:.4f}**' if cos_cross
+           else '* Cosine: no crossing found',
+           f'* dHash:  **{dh_cross:.4f}**' if dh_cross
+           else '* dHash: no crossing found',
+           '',
+           '## Interpretation',
+           '',
+           'The accountant-level mixture separates signing-behaviour regimes,',
+           'while the signature-level distribution is a continuous spectrum',
+           '(see Scripts 15 and 17). The BIC-best model chooses how many',
+           'discrete regimes the data supports. The 2-component crossings',
+           'are the natural per-accountant thresholds for classifying a',
+           "CPA's signing behaviour.",
+           '',
+           '## Artifacts',
+           '',
+           '* `accountant_mixture_2d.png` - 2D scatter with 3-component fit',
+           '* `accountant_mixture_marginals.png` - 1D marginals with 2-component fit',
+           '* `accountant_clusters.csv` - per-accountant cluster assignments',
+           '* `accountant_mixture_results.json` - full numerical results',
+           ]
+    (OUT / 'accountant_mixture_report.md').write_text('\n'.join(md),
+                                                      encoding='utf-8')
+    print(f'Report: {OUT / "accountant_mixture_report.md"}')
+
+
+if __name__ == '__main__':
+    main()

signature_analysis/19_pixel_identity_validation.py

@@ -0,0 +1,424 @@
+#!/usr/bin/env python3
+"""
+Script 19: Pixel-Identity Validation (No Human Annotation Required)
+===================================================================
+Validates the cosine + dHash dual classifier using three naturally
+occurring reference populations instead of manual labels:
+
+  Positive anchor 1:  pixel_identical_to_closest = 1
+      Two signature images byte-identical after crop/resize.
+      Mathematically impossible to arise from independent hand-signing
+      => pair-level proof of image reuse and a CONSERVATIVE-SUBSET
+      ground truth for non-hand-signing (only those whose nearest
+      same-CPA match happens to be byte-identical).
+
+  Positive anchor 2:  Firm A signatures
+      Treated in the manuscript as a REPLICATION-DOMINATED population
+      based on the paper's own image evidence: the byte-level pair
+      analysis, the Firm A per-signature similarity distribution, the
+      partner-ranking concentration, and the intra-report consistency
+      gap. Approximately 7% of Firm A signatures fall below cosine
+      0.95, forming the long left tail observed in the dip test
+      (Script 15).
+
+  Negative anchor:    signatures with cosine <= low threshold
+      Pairs with very low cosine similarity cannot plausibly be pixel
+      duplicates, so they serve as a conservative supplementary
+      negative reference.
+
+Metrics computed (legacy; NOT all reported in the manuscript):
+  - FAR against the inter-CPA negative anchor is the primary metric
+    reported (Table X). The byte-identical positive anchor has cosine
+    ~= 1 by construction, so FRR / EER / Precision / F1 against that
+    subset are arithmetic tautologies (FRR is trivially 0 below
+    threshold 1) and are intentionally OMITTED from Table X. Legacy
+    EER/FRR/precision/F1 helper functions remain in this script for
+    diagnostic use only and their outputs are NOT cited as biometric
+    performance in the paper.
+  - Convergence with Firm A anchor (what fraction of Firm A signatures
+    are correctly classified at each threshold).
+
+Output:
+  reports/pixel_validation/pixel_validation_report.md
+  reports/pixel_validation/pixel_validation_results.json
+  reports/pixel_validation/roc_cosine.png, roc_dhash.png
+"""
+
+import sqlite3
+import json
+import numpy as np
+import matplotlib
+matplotlib.use('Agg')
+import matplotlib.pyplot as plt
+from pathlib import Path
+from datetime import datetime
+
+DB = '/Volumes/NV2/PDF-Processing/signature-analysis/signature_analysis.db'
+OUT = Path('/Volumes/NV2/PDF-Processing/signature-analysis/reports/'
+           'pixel_validation')
+OUT.mkdir(parents=True, exist_ok=True)
+
+FIRM_A = '勤業眾信聯合'
+NEGATIVE_COSINE_UPPER = 0.70   # pairs with max-cosine < 0.70 assumed not replicated
+SANITY_SAMPLE_SIZE = 30
+
+
+def load_signatures():
+    conn = sqlite3.connect(DB)
+    cur = conn.cursor()
+    cur.execute('''
+        SELECT s.signature_id, s.image_filename, s.assigned_accountant,
+               a.firm, s.max_similarity_to_same_accountant,
+               s.phash_distance_to_closest, s.min_dhash_independent,
+               s.pixel_identical_to_closest, s.closest_match_file
+        FROM signatures s
+        LEFT JOIN accountants a ON s.assigned_accountant = a.name
+        WHERE s.max_similarity_to_same_accountant IS NOT NULL
+    ''')
+    rows = cur.fetchall()
+    conn.close()
+    data = []
+    for r in rows:
+        data.append({
+            'sig_id': r[0], 'filename': r[1], 'accountant': r[2],
+            'firm': r[3] or '(unknown)',
+            'cosine': float(r[4]),
+            'dhash_cond': None if r[5] is None else int(r[5]),
+            'dhash_indep': None if r[6] is None else int(r[6]),
+            'pixel_identical': int(r[7] or 0),
+            'closest_match': r[8],
+        })
+    return data
+
+
+def confusion(y_true, y_pred):
+    tp = int(np.sum((y_true == 1) & (y_pred == 1)))
+    fp = int(np.sum((y_true == 0) & (y_pred == 1)))
+    fn = int(np.sum((y_true == 1) & (y_pred == 0)))
+    tn = int(np.sum((y_true == 0) & (y_pred == 0)))
+    return tp, fp, fn, tn
+
+
+def classification_metrics(y_true, y_pred):
+    tp, fp, fn, tn = confusion(y_true, y_pred)
+    denom_p = max(tp + fp, 1)
+    denom_r = max(tp + fn, 1)
+    precision = tp / denom_p
+    recall = tp / denom_r
+    f1 = (2 * precision * recall / (precision + recall)
+          if precision + recall > 0 else 0.0)
+    far = fp / max(fp + tn, 1)  # false acceptance rate (over negatives)
+    frr = fn / max(fn + tp, 1)  # false rejection rate (over positives)
+    return {
+        'tp': tp, 'fp': fp, 'fn': fn, 'tn': tn,
+        'precision': float(precision),
+        'recall': float(recall),
+        'f1': float(f1),
+        'far': float(far),
+        'frr': float(frr),
+    }
+
+
+def sweep_threshold(scores, y, directions, thresholds):
+    """For direction 'above' a prediction is positive if score > threshold;
+    for 'below' it is positive if score < threshold."""
+    out = []
+    for t in thresholds:
+        if directions == 'above':
+            y_pred = (scores > t).astype(int)
+        else:
+            y_pred = (scores < t).astype(int)
+        m = classification_metrics(y, y_pred)
+        m['threshold'] = float(t)
+        out.append(m)
+    return out
+
+
+def find_eer(sweep):
+    """EER = point where FAR ≈ FRR; interpolated from nearest pair."""
+    thr = np.array([s['threshold'] for s in sweep])
+    far = np.array([s['far'] for s in sweep])
+    frr = np.array([s['frr'] for s in sweep])
+    diff = far - frr
+    signs = np.sign(diff)
+    changes = np.where(np.diff(signs) != 0)[0]
+    if len(changes) == 0:
+        idx = int(np.argmin(np.abs(diff)))
+        return {'threshold': float(thr[idx]), 'far': float(far[idx]),
+                'frr': float(frr[idx]), 'eer': float(0.5 * (far[idx] + frr[idx]))}
+    i = int(changes[0])
+    w = abs(diff[i]) / (abs(diff[i]) + abs(diff[i + 1]) + 1e-12)
+    thr_i = (1 - w) * thr[i] + w * thr[i + 1]
+    far_i = (1 - w) * far[i] + w * far[i + 1]
+    frr_i = (1 - w) * frr[i] + w * frr[i + 1]
+    return {'threshold': float(thr_i), 'far': float(far_i),
+            'frr': float(frr_i), 'eer': float(0.5 * (far_i + frr_i))}
+
+
+def plot_roc(sweep, title, out_path):
+    far = np.array([s['far'] for s in sweep])
+    frr = np.array([s['frr'] for s in sweep])
+    thr = np.array([s['threshold'] for s in sweep])
+    fig, axes = plt.subplots(1, 2, figsize=(13, 5))
+
+    ax = axes[0]
+    ax.plot(far, 1 - frr, 'b-', lw=2)
+    ax.plot([0, 1], [0, 1], 'k--', alpha=0.4)
+    ax.set_xlabel('FAR')
+    ax.set_ylabel('1 - FRR (True Positive Rate)')
+    ax.set_title(f'{title} - ROC')
+    ax.set_xlim(0, 1)
+    ax.set_ylim(0, 1)
+    ax.grid(alpha=0.3)
+
+    ax = axes[1]
+    ax.plot(thr, far, 'r-', lw=2, label='FAR')
+    ax.plot(thr, frr, 'b-', lw=2, label='FRR')
+    ax.set_xlabel('Threshold')
+    ax.set_ylabel('Error rate')
+    ax.set_title(f'{title} - FAR / FRR vs threshold')
+    ax.legend()
+    ax.grid(alpha=0.3)
+
+    plt.tight_layout()
+    fig.savefig(out_path, dpi=150)
+    plt.close()
+
+
+def main():
+    print('='*70)
+    print('Script 19: Pixel-Identity Validation (No Annotation)')
+    print('='*70)
+
+    data = load_signatures()
+    print(f'\nTotal signatures loaded: {len(data):,}')
+    cos = np.array([d['cosine'] for d in data])
+    dh_indep = np.array([d['dhash_indep'] if d['dhash_indep'] is not None
+                         else -1 for d in data])
+    pix = np.array([d['pixel_identical'] for d in data])
+    firm = np.array([d['firm'] for d in data])
+
+    print(f'Pixel-identical: {int(pix.sum()):,} signatures')
+    print(f'Firm A signatures: {int((firm == FIRM_A).sum()):,}')
+    print(f'Negative anchor (cosine < {NEGATIVE_COSINE_UPPER}): '
+          f'{int((cos < NEGATIVE_COSINE_UPPER).sum()):,}')
+
+    # Build labelled set:
+    #   positive = pixel_identical == 1
+    #   negative = cosine < NEGATIVE_COSINE_UPPER (and not pixel_identical)
+    pos_mask = pix == 1
+    neg_mask = (cos < NEGATIVE_COSINE_UPPER) & (~pos_mask)
+    labelled_mask = pos_mask | neg_mask
+    y = pos_mask[labelled_mask].astype(int)
+    cos_l = cos[labelled_mask]
+    dh_l = dh_indep[labelled_mask]
+
+    # --- Sweep cosine threshold
+    cos_thresh = np.linspace(0.50, 1.00, 101)
+    cos_sweep = sweep_threshold(cos_l, y, 'above', cos_thresh)
+    cos_eer = find_eer(cos_sweep)
+    print(f'\nCosine EER: threshold={cos_eer["threshold"]:.4f}, '
+          f'EER={cos_eer["eer"]:.4f}')
+
+    # --- Sweep dHash threshold (independent)
+    dh_l_valid = dh_l >= 0
+    y_dh = y[dh_l_valid]
+    dh_valid = dh_l[dh_l_valid]
+    dh_thresh = np.arange(0, 40)
+    dh_sweep = sweep_threshold(dh_valid, y_dh, 'below', dh_thresh)
+    dh_eer = find_eer(dh_sweep)
+    print(f'dHash  EER: threshold={dh_eer["threshold"]:.4f}, '
+          f'EER={dh_eer["eer"]:.4f}')
+
+    # Plots
+    plot_roc(cos_sweep, 'Cosine (pixel-identity anchor)',
+             OUT / 'roc_cosine.png')
+    plot_roc(dh_sweep, 'Independent dHash (pixel-identity anchor)',
+             OUT / 'roc_dhash.png')
+
+    # --- Evaluate canonical thresholds
+    canonical = [
+        ('cosine', 0.837, 'above', cos, pos_mask, neg_mask),
+        ('cosine', 0.941, 'above', cos, pos_mask, neg_mask),
+        ('cosine', 0.95, 'above', cos, pos_mask, neg_mask),
+        ('dhash_indep', 5, 'below', dh_indep, pos_mask,
+         neg_mask & (dh_indep >= 0)),
+        ('dhash_indep', 8, 'below', dh_indep, pos_mask,
+         neg_mask & (dh_indep >= 0)),
+        ('dhash_indep', 15, 'below', dh_indep, pos_mask,
+         neg_mask & (dh_indep >= 0)),
+    ]
+    canonical_results = []
+    for name, thr, direction, scores, p_mask, n_mask in canonical:
+        labelled = p_mask | n_mask
+        valid = labelled & (scores >= 0 if 'dhash' in name else np.ones_like(
+            labelled, dtype=bool))
+        y_local = p_mask[valid].astype(int)
+        s = scores[valid]
+        if direction == 'above':
+            y_pred = (s > thr).astype(int)
+        else:
+            y_pred = (s < thr).astype(int)
+        m = classification_metrics(y_local, y_pred)
+        m.update({'indicator': name, 'threshold': float(thr),
+                  'direction': direction})
+        canonical_results.append(m)
+        print(f"  {name} @ {thr:>5} ({direction}): "
+              f"P={m['precision']:.3f}, R={m['recall']:.3f}, "
+              f"F1={m['f1']:.3f}, FAR={m['far']:.4f}, FRR={m['frr']:.4f}")
+
+    # --- Firm A anchor validation
+    firm_a_mask = firm == FIRM_A
+    firm_a_cos = cos[firm_a_mask]
+    firm_a_dh = dh_indep[firm_a_mask]
+
+    firm_a_rates = {}
+    for thr in [0.837, 0.941, 0.95]:
+        firm_a_rates[f'cosine>{thr}'] = float(np.mean(firm_a_cos > thr))
+    for thr in [5, 8, 15]:
+        valid = firm_a_dh >= 0
+        firm_a_rates[f'dhash_indep<={thr}'] = float(
+            np.mean(firm_a_dh[valid] <= thr))
+    # Dual thresholds
+    firm_a_rates['cosine>0.95 AND dhash_indep<=8'] = float(
+        np.mean((firm_a_cos > 0.95) &
+                (firm_a_dh >= 0) & (firm_a_dh <= 8)))
+
+    print('\nFirm A anchor validation:')
+    for k, v in firm_a_rates.items():
+        print(f'  {k}: {v*100:.2f}%')
+
+    # --- Stratified sanity sample (30 signatures across 5 strata)
+    rng = np.random.default_rng(42)
+    strata = [
+        ('pixel_identical', pix == 1),
+        ('high_cos_low_dh',
+         (cos > 0.95) & (dh_indep >= 0) & (dh_indep <= 5) & (pix == 0)),
+        ('borderline',
+         (cos > 0.837) & (cos < 0.95) & (dh_indep >= 0) & (dh_indep <= 15)),
+        ('style_consistency_only',
+         (cos > 0.95) & (dh_indep >= 0) & (dh_indep > 15)),
+        ('likely_genuine', cos < NEGATIVE_COSINE_UPPER),
+    ]
+    sanity_sample = []
+    per_stratum = SANITY_SAMPLE_SIZE // len(strata)
+    for stratum_name, m in strata:
+        idx = np.where(m)[0]
+        pick = rng.choice(idx, size=min(per_stratum, len(idx)), replace=False)
+        for i in pick:
+            d = data[i]
+            sanity_sample.append({
+                'stratum': stratum_name, 'sig_id': d['sig_id'],
+                'filename': d['filename'], 'accountant': d['accountant'],
+                'firm': d['firm'], 'cosine': d['cosine'],
+                'dhash_indep': d['dhash_indep'],
+                'pixel_identical': d['pixel_identical'],
+                'closest_match': d['closest_match'],
+            })
+
+    csv_path = OUT / 'sanity_sample.csv'
+    with open(csv_path, 'w', encoding='utf-8') as f:
+        keys = ['stratum', 'sig_id', 'filename', 'accountant', 'firm',
+                'cosine', 'dhash_indep', 'pixel_identical', 'closest_match']
+        f.write(','.join(keys) + '\n')
+        for row in sanity_sample:
+            f.write(','.join(str(row[k]) if row[k] is not None else ''
+                             for k in keys) + '\n')
+    print(f'\nSanity sample CSV: {csv_path}')
+
+    # --- Save results
+    summary = {
+        'generated_at': datetime.now().isoformat(),
+        'n_signatures': len(data),
+        'n_pixel_identical': int(pos_mask.sum()),
+        'n_firm_a': int(firm_a_mask.sum()),
+        'n_negative_anchor': int(neg_mask.sum()),
+        'negative_cosine_upper': NEGATIVE_COSINE_UPPER,
+        'eer_cosine': cos_eer,
+        'eer_dhash_indep': dh_eer,
+        'canonical_thresholds': canonical_results,
+        'firm_a_anchor_rates': firm_a_rates,
+        'cosine_sweep': cos_sweep,
+        'dhash_sweep': dh_sweep,
+    }
+    with open(OUT / 'pixel_validation_results.json', 'w') as f:
+        json.dump(summary, f, indent=2, ensure_ascii=False)
+    print(f'JSON: {OUT / "pixel_validation_results.json"}')
+
+    # --- Markdown
+    md = [
+        '# Pixel-Identity Validation Report',
+        f"Generated: {datetime.now().strftime('%Y-%m-%d %H:%M:%S')}",
+        '',
+        '## Anchors (no human annotation required)',
+        '',
+        f'* **Pixel-identical anchor (gold positive):** '
+        f'{int(pos_mask.sum()):,} signatures whose closest same-accountant',
+        '  match is byte-identical after crop/normalise. Under handwriting',
+        '  physics this can only arise from image duplication.',
+        f'* **Negative anchor:** signatures whose maximum same-accountant',
+        f'  cosine is below {NEGATIVE_COSINE_UPPER} '
+        f'({int(neg_mask.sum()):,} signatures). Treated as',
+        '  confirmed not-replicated.',
+        f'* **Firm A anchor:** Deloitte ({int(firm_a_mask.sum()):,} signatures),',
+        '  a replication-dominated population per interviews with multiple',
+        '  Firm A accountants: most use replication (stamping / firm-level',
+        '  e-signing), but a minority may still hand-sign. Used as a strong',
+        '  prior positive for the majority regime, with the ~7% below',
+        '  cosine 0.95 reflecting the minority hand-signers.',
+        '',
+        '## Equal Error Rate (EER)',
+        '',
+        '| Indicator | Direction | EER threshold | EER |',
+        '|-----------|-----------|---------------|-----|',
+        f"| Cosine max-similarity | > t | {cos_eer['threshold']:.4f} | "
+        f"{cos_eer['eer']:.4f} |",
+        f"| Independent min dHash | < t | {dh_eer['threshold']:.4f} | "
+        f"{dh_eer['eer']:.4f} |",
+        '',
+        '## Canonical thresholds',
+        '',
+        '| Indicator | Threshold | Precision | Recall | F1 | FAR | FRR |',
+        '|-----------|-----------|-----------|--------|----|-----|-----|',
+    ]
+    for c in canonical_results:
+        md.append(
+            f"| {c['indicator']} | {c['threshold']} "
+            f"({c['direction']}) | {c['precision']:.3f} | "
+            f"{c['recall']:.3f} | {c['f1']:.3f} | "
+            f"{c['far']:.4f} | {c['frr']:.4f} |"
+        )
+
+    md += ['', '## Firm A anchor validation', '',
+           '| Rule | Firm A rate |',
+           '|------|-------------|']
+    for k, v in firm_a_rates.items():
+        md.append(f'| {k} | {v*100:.2f}% |')
+
+    md += ['', '## Sanity sample', '',
+           f'A stratified sample of {len(sanity_sample)} signatures '
+           '(pixel-identical, high-cos/low-dh, borderline, style-only, '
+           'likely-genuine) is exported to `sanity_sample.csv` for visual',
+           'spot-check. These are **not** used to compute metrics.',
+           '',
+           '## Interpretation',
+           '',
+           'Because the gold positive is a *subset* of the true replication',
+           'positives (only those that happen to be pixel-identical to their',
+           'nearest match), recall is conservative: the classifier should',
+           'catch pixel-identical pairs reliably and will additionally flag',
+           'many non-pixel-identical replications (low dHash but not zero).',
+           'FAR against the low-cosine negative anchor is the meaningful',
+           'upper bound on spurious replication flags.',
+           '',
+           'Convergence of thresholds across Scripts 15 (dip test), 16 (BD),',
+           '17 (Beta mixture), 18 (accountant mixture) and the EER here',
+           'should be reported in the paper as multi-method validation.',
+           ]
+    (OUT / 'pixel_validation_report.md').write_text('\n'.join(md),
+                                                    encoding='utf-8')
+    print(f'Report: {OUT / "pixel_validation_report.md"}')
+
+
+if __name__ == '__main__':
+    main()

signature_analysis/20_accountant_level_three_methods.py

@@ -0,0 +1,526 @@
+#!/usr/bin/env python3
+"""
+Script 20: Three-Method Threshold Determination at the Accountant Level
+=======================================================================
+Completes the three-method convergent framework at the analysis level
+where the mixture structure is statistically supported (per Script 15
+dip test: accountant cos_mean p<0.001).
+
+Runs on the per-accountant aggregates (mean best-match cosine, mean
+independent minimum dHash) for 686 CPAs with >=10 signatures:
+
+  Method 1: KDE antimode with Hartigan dip test (formal unimodality test)
+  Method 2: Burgstahler-Dichev / McCrary discontinuity
+  Method 3: 2-component Beta mixture via EM + parallel logit-GMM
+
+Also re-runs the accountant-level 2-component GMM crossings from
+Script 18 for completeness and side-by-side comparison.
+
+Output:
+  reports/accountant_three_methods/accountant_three_methods_report.md
+  reports/accountant_three_methods/accountant_three_methods_results.json
+  reports/accountant_three_methods/accountant_cos_panel.png
+  reports/accountant_three_methods/accountant_dhash_panel.png
+"""
+
+import sqlite3
+import json
+import numpy as np
+import matplotlib
+matplotlib.use('Agg')
+import matplotlib.pyplot as plt
+from pathlib import Path
+from datetime import datetime
+from scipy import stats
+from scipy.signal import find_peaks
+from scipy.optimize import brentq
+from sklearn.mixture import GaussianMixture
+import diptest
+
+DB = '/Volumes/NV2/PDF-Processing/signature-analysis/signature_analysis.db'
+OUT = Path('/Volumes/NV2/PDF-Processing/signature-analysis/reports/'
+           'accountant_three_methods')
+OUT.mkdir(parents=True, exist_ok=True)
+
+EPS = 1e-6
+Z_CRIT = 1.96
+MIN_SIGS = 10
+
+
+def load_accountant_means(min_sigs=MIN_SIGS):
+    conn = sqlite3.connect(DB)
+    cur = conn.cursor()
+    cur.execute('''
+        SELECT s.assigned_accountant,
+               AVG(s.max_similarity_to_same_accountant) AS cos_mean,
+               AVG(CAST(s.min_dhash_independent AS REAL)) AS dh_mean,
+               COUNT(*) AS n
+        FROM signatures s
+        WHERE s.assigned_accountant IS NOT NULL
+          AND s.max_similarity_to_same_accountant IS NOT NULL
+          AND s.min_dhash_independent IS NOT NULL
+        GROUP BY s.assigned_accountant
+        HAVING n >= ?
+    ''', (min_sigs,))
+    rows = cur.fetchall()
+    conn.close()
+    cos = np.array([r[1] for r in rows])
+    dh = np.array([r[2] for r in rows])
+    return cos, dh
+
+
+# ---------- Method 1: KDE antimode with dip test ----------
+def method_kde_antimode(values, name):
+    arr = np.asarray(values, dtype=float)
+    arr = arr[np.isfinite(arr)]
+    dip, pval = diptest.diptest(arr, boot_pval=True, n_boot=2000)
+    kde = stats.gaussian_kde(arr, bw_method='silverman')
+    xs = np.linspace(arr.min(), arr.max(), 2000)
+    density = kde(xs)
+    # Find modes (local maxima) and antimodes (local minima)
+    peaks, _ = find_peaks(density, prominence=density.max() * 0.02)
+    # Antimodes = local minima between peaks
+    antimodes = []
+    for i in range(len(peaks) - 1):
+        seg = density[peaks[i]:peaks[i + 1]]
+        if len(seg) == 0:
+            continue
+        local = peaks[i] + int(np.argmin(seg))
+        antimodes.append(float(xs[local]))
+    # Sensitivity analysis across bandwidth factors
+    sens = {}
+    for bwf in [0.5, 0.75, 1.0, 1.5, 2.0]:
+        kde_s = stats.gaussian_kde(arr, bw_method=kde.factor * bwf)
+        d_s = kde_s(xs)
+        p_s, _ = find_peaks(d_s, prominence=d_s.max() * 0.02)
+        sens[f'bw_x{bwf}'] = int(len(p_s))
+    return {
+        'name': name,
+        'n': int(len(arr)),
+        'dip': float(dip),
+        'dip_pvalue': float(pval),
+        'unimodal_alpha05': bool(pval > 0.05),
+        'kde_bandwidth_silverman': float(kde.factor),
+        'n_modes': int(len(peaks)),
+        'mode_locations': [float(xs[p]) for p in peaks],
+        'antimodes': antimodes,
+        'primary_antimode': (antimodes[0] if antimodes else None),
+        'bandwidth_sensitivity_n_modes': sens,
+    }
+
+
+# ---------- Method 2: Burgstahler-Dichev / McCrary ----------
+def method_bd_mccrary(values, bin_width, direction, name):
+    arr = np.asarray(values, dtype=float)
+    arr = arr[np.isfinite(arr)]
+    lo = float(np.floor(arr.min() / bin_width) * bin_width)
+    hi = float(np.ceil(arr.max() / bin_width) * bin_width)
+    edges = np.arange(lo, hi + bin_width, bin_width)
+    counts, _ = np.histogram(arr, bins=edges)
+    centers = (edges[:-1] + edges[1:]) / 2.0
+
+    N = counts.sum()
+    p = counts / N if N else counts.astype(float)
+    n_bins = len(counts)
+    z = np.full(n_bins, np.nan)
+    expected = np.full(n_bins, np.nan)
+
+    for i in range(1, n_bins - 1):
+        p_lo = p[i - 1]
+        p_hi = p[i + 1]
+        exp_i = 0.5 * (counts[i - 1] + counts[i + 1])
+        var_i = (N * p[i] * (1 - p[i])
+                 + 0.25 * N * (p_lo + p_hi) * (1 - p_lo - p_hi))
+        if var_i <= 0:
+            continue
+        z[i] = (counts[i] - exp_i) / np.sqrt(var_i)
+        expected[i] = exp_i
+
+    # Identify transitions
+    transitions = []
+    for i in range(1, len(z)):
+        if np.isnan(z[i - 1]) or np.isnan(z[i]):
+            continue
+        ok = False
+        if direction == 'neg_to_pos' and z[i - 1] < -Z_CRIT and z[i] > Z_CRIT:
+            ok = True
+        elif direction == 'pos_to_neg' and z[i - 1] > Z_CRIT and z[i] < -Z_CRIT:
+            ok = True
+        if ok:
+            transitions.append({
+                'threshold_between': float((centers[i - 1] + centers[i]) / 2.0),
+                'z_before': float(z[i - 1]),
+                'z_after': float(z[i]),
+            })
+
+    best = None
+    if transitions:
+        best = max(transitions,
+                   key=lambda t: abs(t['z_before']) + abs(t['z_after']))
+    return {
+        'name': name,
+        'n': int(len(arr)),
+        'bin_width': float(bin_width),
+        'direction': direction,
+        'n_transitions': len(transitions),
+        'transitions': transitions,
+        'best_transition': best,
+        'threshold': (best['threshold_between'] if best else None),
+        'bin_centers': [float(c) for c in centers],
+        'counts': [int(c) for c in counts],
+        'z_scores': [None if np.isnan(zi) else float(zi) for zi in z],
+    }
+
+
+# ---------- Method 3: Beta mixture + logit-GMM ----------
+def fit_beta_mixture_em(x, K=2, max_iter=300, tol=1e-6, seed=42):
+    rng = np.random.default_rng(seed)
+    x = np.clip(np.asarray(x, dtype=float), EPS, 1 - EPS)
+    n = len(x)
+    q = np.linspace(0, 1, K + 1)
+    thresh = np.quantile(x, q[1:-1])
+    labels = np.digitize(x, thresh)
+    resp = np.zeros((n, K))
+    resp[np.arange(n), labels] = 1.0
+    ll_hist = []
+    for it in range(max_iter):
+        nk = resp.sum(axis=0) + 1e-12
+        weights = nk / nk.sum()
+        mus = (resp * x[:, None]).sum(axis=0) / nk
+        var_num = (resp * (x[:, None] - mus) ** 2).sum(axis=0)
+        vars_ = var_num / nk
+        upper = mus * (1 - mus) - 1e-9
+        vars_ = np.minimum(vars_, upper)
+        vars_ = np.maximum(vars_, 1e-9)
+        factor = np.maximum(mus * (1 - mus) / vars_ - 1, 1e-6)
+        alphas = mus * factor
+        betas = (1 - mus) * factor
+        log_pdfs = np.column_stack([
+            stats.beta.logpdf(x, alphas[k], betas[k]) + np.log(weights[k])
+            for k in range(K)
+        ])
+        m = log_pdfs.max(axis=1, keepdims=True)
+        ll = (m.ravel() + np.log(np.exp(log_pdfs - m).sum(axis=1))).sum()
+        ll_hist.append(float(ll))
+        new_resp = np.exp(log_pdfs - m)
+        new_resp = new_resp / new_resp.sum(axis=1, keepdims=True)
+        if it > 0 and abs(ll_hist[-1] - ll_hist[-2]) < tol:
+            resp = new_resp
+            break
+        resp = new_resp
+    order = np.argsort(mus)
+    alphas, betas, weights, mus = alphas[order], betas[order], weights[order], mus[order]
+    k_params = 3 * K - 1
+    ll_final = ll_hist[-1]
+    return {
+        'K': K,
+        'alphas': [float(a) for a in alphas],
+        'betas': [float(b) for b in betas],
+        'weights': [float(w) for w in weights],
+        'mus': [float(m) for m in mus],
+        'log_likelihood': float(ll_final),
+        'aic': float(2 * k_params - 2 * ll_final),
+        'bic': float(k_params * np.log(n) - 2 * ll_final),
+        'n_iter': it + 1,
+    }
+
+
+def beta_crossing(fit):
+    if fit['K'] != 2:
+        return None
+    a1, b1, w1 = fit['alphas'][0], fit['betas'][0], fit['weights'][0]
+    a2, b2, w2 = fit['alphas'][1], fit['betas'][1], fit['weights'][1]
+
+    def diff(x):
+        return (w2 * stats.beta.pdf(x, a2, b2)
+                - w1 * stats.beta.pdf(x, a1, b1))
+    xs = np.linspace(EPS, 1 - EPS, 2000)
+    ys = diff(xs)
+    changes = np.where(np.diff(np.sign(ys)) != 0)[0]
+    if not len(changes):
+        return None
+    mid = 0.5 * (fit['mus'][0] + fit['mus'][1])
+    crossings = []
+    for i in changes:
+        try:
+            crossings.append(brentq(diff, xs[i], xs[i + 1]))
+        except ValueError:
+            continue
+    if not crossings:
+        return None
+    return float(min(crossings, key=lambda c: abs(c - mid)))
+
+
+def fit_logit_gmm(x, K=2, seed=42):
+    x = np.clip(np.asarray(x, dtype=float), EPS, 1 - EPS)
+    z = np.log(x / (1 - x)).reshape(-1, 1)
+    gmm = GaussianMixture(n_components=K, random_state=seed,
+                          max_iter=500).fit(z)
+    order = np.argsort(gmm.means_.ravel())
+    means = gmm.means_.ravel()[order]
+    stds = np.sqrt(gmm.covariances_.ravel())[order]
+    weights = gmm.weights_[order]
+    crossing = None
+    if K == 2:
+        m1, s1, w1 = means[0], stds[0], weights[0]
+        m2, s2, w2 = means[1], stds[1], weights[1]
+
+        def diff(z0):
+            return (w2 * stats.norm.pdf(z0, m2, s2)
+                    - w1 * stats.norm.pdf(z0, m1, s1))
+        zs = np.linspace(min(m1, m2) - 2, max(m1, m2) + 2, 2000)
+        ys = diff(zs)
+        ch = np.where(np.diff(np.sign(ys)) != 0)[0]
+        if len(ch):
+            try:
+                z_cross = brentq(diff, zs[ch[0]], zs[ch[0] + 1])
+                crossing = float(1 / (1 + np.exp(-z_cross)))
+            except ValueError:
+                pass
+    return {
+        'K': K,
+        'means_logit': [float(m) for m in means],
+        'stds_logit': [float(s) for s in stds],
+        'weights': [float(w) for w in weights],
+        'means_original_scale': [float(1 / (1 + np.exp(-m))) for m in means],
+        'aic': float(gmm.aic(z)),
+        'bic': float(gmm.bic(z)),
+        'crossing_original': crossing,
+    }
+
+
+def method_beta_mixture(values, name, is_cosine=True):
+    arr = np.asarray(values, dtype=float)
+    arr = arr[np.isfinite(arr)]
+    if not is_cosine:
+        # normalize dHash into [0,1] by dividing by 64 (max Hamming)
+        x = arr / 64.0
+    else:
+        x = arr
+    beta2 = fit_beta_mixture_em(x, K=2)
+    beta3 = fit_beta_mixture_em(x, K=3)
+    cross_beta2 = beta_crossing(beta2)
+    # Transform back to original scale for dHash
+    if not is_cosine and cross_beta2 is not None:
+        cross_beta2 = cross_beta2 * 64.0
+    gmm2 = fit_logit_gmm(x, K=2)
+    gmm3 = fit_logit_gmm(x, K=3)
+    if not is_cosine and gmm2.get('crossing_original') is not None:
+        gmm2['crossing_original'] = gmm2['crossing_original'] * 64.0
+    return {
+        'name': name,
+        'n': int(len(x)),
+        'scale_transform': ('identity' if is_cosine else 'dhash/64'),
+        'beta_2': beta2,
+        'beta_3': beta3,
+        'bic_preferred_K': (2 if beta2['bic'] < beta3['bic'] else 3),
+        'beta_2_crossing_original': cross_beta2,
+        'logit_gmm_2': gmm2,
+        'logit_gmm_3': gmm3,
+    }
+
+
+# ---------- Plot helpers ----------
+def plot_panel(values, methods, title, out_path, bin_width=None,
+               is_cosine=True):
+    arr = np.asarray(values, dtype=float)
+    fig, axes = plt.subplots(2, 1, figsize=(11, 7),
+                             gridspec_kw={'height_ratios': [3, 1]})
+
+    ax = axes[0]
+    if bin_width is None:
+        bins = 40
+    else:
+        lo = float(np.floor(arr.min() / bin_width) * bin_width)
+        hi = float(np.ceil(arr.max() / bin_width) * bin_width)
+        bins = np.arange(lo, hi + bin_width, bin_width)
+    ax.hist(arr, bins=bins, density=True, alpha=0.55, color='steelblue',
+            edgecolor='white')
+    # KDE overlay
+    kde = stats.gaussian_kde(arr, bw_method='silverman')
+    xs = np.linspace(arr.min(), arr.max(), 500)
+    ax.plot(xs, kde(xs), 'g-', lw=1.5, label='KDE (Silverman)')
+
+    # Annotate thresholds from each method
+    colors = {'kde': 'green', 'bd': 'red', 'beta': 'purple', 'gmm2': 'orange'}
+    for key, (val, lbl) in methods.items():
+        if val is None:
+            continue
+        ax.axvline(val, color=colors.get(key, 'gray'), lw=2, ls='--',
+                   label=f'{lbl} = {val:.4f}')
+    ax.set_xlabel(title + ' value')
+    ax.set_ylabel('Density')
+    ax.set_title(title)
+    ax.legend(fontsize=8)
+
+    ax2 = axes[1]
+    ax2.set_title('Thresholds across methods')
+    ax2.set_xlim(ax.get_xlim())
+    for i, (key, (val, lbl)) in enumerate(methods.items()):
+        if val is None:
+            continue
+        ax2.scatter([val], [i], color=colors.get(key, 'gray'), s=100, zorder=3)
+        ax2.annotate(f'  {lbl}: {val:.4f}', (val, i), fontsize=8,
+                     va='center')
+    ax2.set_yticks(range(len(methods)))
+    ax2.set_yticklabels([m for m in methods.keys()])
+    ax2.set_xlabel(title + ' value')
+    ax2.grid(alpha=0.3)
+
+    plt.tight_layout()
+    fig.savefig(out_path, dpi=150)
+    plt.close()
+
+
+# ---------- GMM 2-comp crossing from Script 18 ----------
+def marginal_2comp_crossing(X, dim):
+    gmm = GaussianMixture(n_components=2, covariance_type='full',
+                          random_state=42, n_init=15, max_iter=500).fit(X)
+    means = gmm.means_
+    covs = gmm.covariances_
+    weights = gmm.weights_
+    m1, m2 = means[0][dim], means[1][dim]
+    s1 = np.sqrt(covs[0][dim, dim])
+    s2 = np.sqrt(covs[1][dim, dim])
+    w1, w2 = weights[0], weights[1]
+
+    def diff(x):
+        return (w2 * stats.norm.pdf(x, m2, s2)
+                - w1 * stats.norm.pdf(x, m1, s1))
+    xs = np.linspace(float(X[:, dim].min()), float(X[:, dim].max()), 2000)
+    ys = diff(xs)
+    ch = np.where(np.diff(np.sign(ys)) != 0)[0]
+    if not len(ch):
+        return None
+    mid = 0.5 * (m1 + m2)
+    crossings = []
+    for i in ch:
+        try:
+            crossings.append(brentq(diff, xs[i], xs[i + 1]))
+        except ValueError:
+            continue
+    if not crossings:
+        return None
+    return float(min(crossings, key=lambda c: abs(c - mid)))
+
+
+def main():
+    print('=' * 70)
+    print('Script 20: Three-Method Threshold at Accountant Level')
+    print('=' * 70)
+    cos, dh = load_accountant_means()
+    print(f'\nN accountants (>={MIN_SIGS} sigs) = {len(cos)}')
+
+    results = {}
+
+    for desc, arr, bin_width, direction, is_cosine in [
+        ('cos_mean', cos, 0.002, 'neg_to_pos', True),
+        ('dh_mean', dh, 0.2, 'pos_to_neg', False),
+    ]:
+        print(f'\n[{desc}]')
+        m1 = method_kde_antimode(arr, f'{desc} KDE')
+        print(f'  Method 1 (KDE + dip): dip={m1["dip"]:.4f} '
+              f'p={m1["dip_pvalue"]:.4f} '
+              f'n_modes={m1["n_modes"]} '
+              f'antimode={m1["primary_antimode"]}')
+        m2 = method_bd_mccrary(arr, bin_width, direction, f'{desc} BD')
+        print(f'  Method 2 (BD/McCrary): {m2["n_transitions"]} transitions, '
+              f'threshold={m2["threshold"]}')
+        m3 = method_beta_mixture(arr, f'{desc} Beta', is_cosine=is_cosine)
+        print(f'  Method 3 (Beta mixture): BIC-preferred K={m3["bic_preferred_K"]}, '
+              f'Beta-2 crossing={m3["beta_2_crossing_original"]}, '
+              f'LogGMM-2 crossing={m3["logit_gmm_2"].get("crossing_original")}')
+
+        # GMM 2-comp crossing (for completeness / reproduce Script 18)
+        X = np.column_stack([cos, dh])
+        dim = 0 if desc == 'cos_mean' else 1
+        gmm2_crossing = marginal_2comp_crossing(X, dim)
+        print(f'  (Script 18 2-comp GMM marginal crossing = {gmm2_crossing})')
+
+        results[desc] = {
+            'method_1_kde_antimode': m1,
+            'method_2_bd_mccrary': m2,
+            'method_3_beta_mixture': m3,
+            'script_18_gmm_2comp_crossing': gmm2_crossing,
+        }
+
+        methods_for_plot = {
+            'kde': (m1.get('primary_antimode'), 'KDE antimode'),
+            'bd': (m2.get('threshold'), 'BD/McCrary'),
+            'beta': (m3.get('beta_2_crossing_original'), 'Beta-2 crossing'),
+            'gmm2': (gmm2_crossing, 'GMM 2-comp crossing'),
+        }
+        png = OUT / f'accountant_{desc}_panel.png'
+        plot_panel(arr, methods_for_plot,
+                   f'Accountant-level {desc}: three-method thresholds',
+                   png, bin_width=bin_width, is_cosine=is_cosine)
+        print(f'  plot: {png}')
+
+    # Write JSON
+    with open(OUT / 'accountant_three_methods_results.json', 'w') as f:
+        json.dump({'generated_at': datetime.now().isoformat(),
+                   'n_accountants': int(len(cos)),
+                   'min_signatures': MIN_SIGS,
+                   'results': results}, f, indent=2, ensure_ascii=False)
+    print(f'\nJSON: {OUT / "accountant_three_methods_results.json"}')
+
+    # Markdown
+    md = [
+        '# Accountant-Level Three-Method Threshold Report',
+        f"Generated: {datetime.now().strftime('%Y-%m-%d %H:%M:%S')}",
+        '',
+        f'N accountants (>={MIN_SIGS} signatures): {len(cos)}',
+        '',
+        '## Accountant-level cosine mean',
+        '',
+        '| Method | Threshold | Supporting statistic |',
+        '|--------|-----------|----------------------|',
+    ]
+    r = results['cos_mean']
+    md.append(f"| Method 1: KDE antimode (with dip test) | "
+              f"{r['method_1_kde_antimode']['primary_antimode']} | "
+              f"dip={r['method_1_kde_antimode']['dip']:.4f}, "
+              f"p={r['method_1_kde_antimode']['dip_pvalue']:.4f} "
+              f"({'unimodal' if r['method_1_kde_antimode']['unimodal_alpha05'] else 'multimodal'}) |")
+    md.append(f"| Method 2: Burgstahler-Dichev / McCrary | "
+              f"{r['method_2_bd_mccrary']['threshold']} | "
+              f"{r['method_2_bd_mccrary']['n_transitions']} transition(s) "
+              f"at α=0.05 |")
+    md.append(f"| Method 3: 2-component Beta mixture | "
+              f"{r['method_3_beta_mixture']['beta_2_crossing_original']} | "
+              f"Beta-2 BIC={r['method_3_beta_mixture']['beta_2']['bic']:.2f}, "
+              f"Beta-3 BIC={r['method_3_beta_mixture']['beta_3']['bic']:.2f} "
+              f"(BIC-preferred K={r['method_3_beta_mixture']['bic_preferred_K']}) |")
+    md.append(f"| Method 3': LogGMM-2 on logit-transformed | "
+              f"{r['method_3_beta_mixture']['logit_gmm_2'].get('crossing_original')} | "
+              f"White 1982 quasi-MLE robustness check |")
+    md.append(f"| Script 18 GMM 2-comp marginal crossing | "
+              f"{r['script_18_gmm_2comp_crossing']} | full 2D mixture |")
+
+    md += ['', '## Accountant-level dHash mean', '',
+           '| Method | Threshold | Supporting statistic |',
+           '|--------|-----------|----------------------|']
+    r = results['dh_mean']
+    md.append(f"| Method 1: KDE antimode | "
+              f"{r['method_1_kde_antimode']['primary_antimode']} | "
+              f"dip={r['method_1_kde_antimode']['dip']:.4f}, "
+              f"p={r['method_1_kde_antimode']['dip_pvalue']:.4f} |")
+    md.append(f"| Method 2: BD/McCrary | "
+              f"{r['method_2_bd_mccrary']['threshold']} | "
+              f"{r['method_2_bd_mccrary']['n_transitions']} transition(s) |")
+    md.append(f"| Method 3: 2-component Beta mixture | "
+              f"{r['method_3_beta_mixture']['beta_2_crossing_original']} | "
+              f"Beta-2 BIC={r['method_3_beta_mixture']['beta_2']['bic']:.2f}, "
+              f"Beta-3 BIC={r['method_3_beta_mixture']['beta_3']['bic']:.2f} |")
+    md.append(f"| Method 3': LogGMM-2 | "
+              f"{r['method_3_beta_mixture']['logit_gmm_2'].get('crossing_original')} | |")
+    md.append(f"| Script 18 GMM 2-comp crossing | "
+              f"{r['script_18_gmm_2comp_crossing']} | |")
+
+    (OUT / 'accountant_three_methods_report.md').write_text('\n'.join(md),
+                                                            encoding='utf-8')
+    print(f'Report: {OUT / "accountant_three_methods_report.md"}')
+
+
+if __name__ == '__main__':
+    main()

signature_analysis/21_expanded_validation.py

@@ -0,0 +1,472 @@
+#!/usr/bin/env python3
+"""
+Script 21: Expanded Validation with Larger Negative Anchor + Held-out Firm A
+============================================================================
+Addresses three weaknesses of Script 19's pixel-identity validation:
+
+  (a) Negative anchor of n=35 (cosine<0.70) is too small to give
+      meaningful FAR confidence intervals.
+  (b) Pixel-identical positive anchor is a CONSERVATIVE SUBSET of the
+      true non-hand-signed class, not representative of the broader
+      positive class. Recall against this subset is therefore a
+      lower-bound calibration check, not a generalizable recall
+      estimate.
+  (c) Firm A is both the calibration anchor and a validation anchor
+      (circular). The 70/30 fold split makes within-Firm-A sampling
+      variance visible without claiming external validation.
+
+This script:
+  1. Constructs a large inter-CPA negative anchor (~50,000 pairs) by
+     randomly sampling pairs from different CPAs. Inter-CPA high
+     similarity is highly unlikely to arise from legitimate signing.
+  2. Splits Firm A CPAs 70/30 into CALIBRATION and HELDOUT folds.
+     Re-derives signature-level thresholds from the calibration fold
+     only, then reports capture rates on the heldout fold.
+  3. Computes 95% Wilson confidence intervals for FAR at canonical
+     thresholds (Table X in the manuscript).
+
+Legacy / diagnostic-only metrics:
+  Helper functions for EER, Precision, Recall, F1, and FRR remain in
+  this script for backward compatibility. The manuscript intentionally
+  OMITS these metrics from Table X because the byte-identical positive
+  anchor has cosine ~= 1 by construction (so FRR / EER are arithmetic
+  tautologies) and because positive and negative anchors are
+  constructed from different sampling units, making prevalence
+  arbitrary (so Precision and F1 have no meaningful population
+  interpretation). Only FAR against the large inter-CPA negative
+  anchor is reported as a biometric metric in the paper.
+
+Output:
+  reports/expanded_validation/expanded_validation_report.md
+  reports/expanded_validation/expanded_validation_results.json
+"""
+
+import sqlite3
+import json
+import numpy as np
+from pathlib import Path
+from datetime import datetime
+from scipy.stats import norm
+
+DB = '/Volumes/NV2/PDF-Processing/signature-analysis/signature_analysis.db'
+OUT = Path('/Volumes/NV2/PDF-Processing/signature-analysis/reports/'
+           'expanded_validation')
+OUT.mkdir(parents=True, exist_ok=True)
+
+FIRM_A = '勤業眾信聯合'
+N_INTER_PAIRS = 50_000
+SEED = 42
+
+
+def wilson_ci(k, n, alpha=0.05):
+    if n == 0:
+        return (0.0, 1.0)
+    z = norm.ppf(1 - alpha / 2)
+    phat = k / n
+    denom = 1 + z * z / n
+    center = (phat + z * z / (2 * n)) / denom
+    pm = z * np.sqrt(phat * (1 - phat) / n + z * z / (4 * n * n)) / denom
+    return (max(0.0, center - pm), min(1.0, center + pm))
+
+
+def load_signatures():
+    conn = sqlite3.connect(DB)
+    cur = conn.cursor()
+    cur.execute('''
+        SELECT s.signature_id, s.assigned_accountant, a.firm,
+               s.max_similarity_to_same_accountant,
+               s.min_dhash_independent, s.pixel_identical_to_closest
+        FROM signatures s
+        LEFT JOIN accountants a ON s.assigned_accountant = a.name
+        WHERE s.max_similarity_to_same_accountant IS NOT NULL
+    ''')
+    rows = cur.fetchall()
+    conn.close()
+    return rows
+
+
+def load_signature_ids_for_negative_pool(seed=SEED):
+    """Load lightweight (sig_id, accountant) pool from the entire matched
+    corpus. Per Gemini round-19 review, the prior implementation drew
+    50,000 inter-CPA pairs from a tiny LIMIT-3000 random subset, reusing
+    each signature ~33 times and artificially tightening Wilson FAR CIs.
+    The corrected implementation samples pairs i.i.d. across the FULL
+    matched corpus (~168k signatures); only the unique signatures that
+    actually appear in the sampled pairs need feature vectors loaded.
+    """
+    conn = sqlite3.connect(DB)
+    cur = conn.cursor()
+    cur.execute('''
+        SELECT signature_id, assigned_accountant
+        FROM signatures
+        WHERE feature_vector IS NOT NULL
+          AND assigned_accountant IS NOT NULL
+    ''')
+    rows = cur.fetchall()
+    conn.close()
+    sig_ids = np.array([r[0] for r in rows], dtype=np.int64)
+    accts = np.array([r[1] for r in rows])
+    return sig_ids, accts
+
+
+def load_features_for_ids(sig_ids):
+    conn = sqlite3.connect(DB)
+    cur = conn.cursor()
+    placeholders = ','.join('?' * len(sig_ids))
+    cur.execute(
+        f'SELECT signature_id, feature_vector FROM signatures '
+        f'WHERE signature_id IN ({placeholders})',
+        [int(s) for s in sig_ids],
+    )
+    rows = cur.fetchall()
+    conn.close()
+    feat_by_id = {}
+    for sid, blob in rows:
+        feat_by_id[int(sid)] = np.frombuffer(blob, dtype=np.float32)
+    return feat_by_id
+
+
+def build_inter_cpa_negative(sig_ids, accts, n_pairs=N_INTER_PAIRS, seed=SEED):
+    """Sample i.i.d. random cross-CPA pairs from the full matched corpus
+    and return their cosine similarities.
+    """
+    rng = np.random.default_rng(seed)
+    n = len(sig_ids)
+    pairs = []
+    tries = 0
+    seen_pairs = set()
+    while len(pairs) < n_pairs and tries < n_pairs * 10:
+        i = rng.integers(n)
+        j = rng.integers(n)
+        if i == j or accts[i] == accts[j]:
+            tries += 1
+            continue
+        a, b = (i, j) if i < j else (j, i)
+        if (a, b) in seen_pairs:
+            tries += 1
+            continue
+        seen_pairs.add((a, b))
+        pairs.append((a, b))
+        tries += 1
+
+    needed_ids = sorted({int(sig_ids[i]) for pair in pairs for i in pair})
+    feat_by_id = load_features_for_ids(needed_ids)
+
+    sims = []
+    for i, j in pairs:
+        fi = feat_by_id[int(sig_ids[i])]
+        fj = feat_by_id[int(sig_ids[j])]
+        sims.append(float(fi @ fj))
+    return np.array(sims)
+
+
+def classification_metrics(y_true, y_pred):
+    y_true = np.asarray(y_true).astype(int)
+    y_pred = np.asarray(y_pred).astype(int)
+    tp = int(np.sum((y_true == 1) & (y_pred == 1)))
+    fp = int(np.sum((y_true == 0) & (y_pred == 1)))
+    fn = int(np.sum((y_true == 1) & (y_pred == 0)))
+    tn = int(np.sum((y_true == 0) & (y_pred == 0)))
+    p_den = max(tp + fp, 1)
+    r_den = max(tp + fn, 1)
+    far_den = max(fp + tn, 1)
+    frr_den = max(fn + tp, 1)
+    precision = tp / p_den
+    recall = tp / r_den
+    f1 = (2 * precision * recall / (precision + recall)
+          if (precision + recall) > 0 else 0.0)
+    far = fp / far_den
+    frr = fn / frr_den
+    far_ci = wilson_ci(fp, far_den)
+    frr_ci = wilson_ci(fn, frr_den)
+    return {
+        'tp': tp, 'fp': fp, 'fn': fn, 'tn': tn,
+        'precision': float(precision),
+        'recall': float(recall),
+        'f1': float(f1),
+        'far': float(far),
+        'frr': float(frr),
+        'far_ci95': [float(x) for x in far_ci],
+        'frr_ci95': [float(x) for x in frr_ci],
+        'n_pos': int(tp + fn),
+        'n_neg': int(tn + fp),
+    }
+
+
+def sweep_threshold(scores, y, direction, thresholds):
+    out = []
+    for t in thresholds:
+        if direction == 'above':
+            y_pred = (scores > t).astype(int)
+        else:
+            y_pred = (scores < t).astype(int)
+        m = classification_metrics(y, y_pred)
+        m['threshold'] = float(t)
+        out.append(m)
+    return out
+
+
+def find_eer(sweep):
+    thr = np.array([s['threshold'] for s in sweep])
+    far = np.array([s['far'] for s in sweep])
+    frr = np.array([s['frr'] for s in sweep])
+    diff = far - frr
+    signs = np.sign(diff)
+    changes = np.where(np.diff(signs) != 0)[0]
+    if len(changes) == 0:
+        idx = int(np.argmin(np.abs(diff)))
+        return {'threshold': float(thr[idx]), 'far': float(far[idx]),
+                'frr': float(frr[idx]),
+                'eer': float(0.5 * (far[idx] + frr[idx]))}
+    i = int(changes[0])
+    w = abs(diff[i]) / (abs(diff[i]) + abs(diff[i + 1]) + 1e-12)
+    thr_i = (1 - w) * thr[i] + w * thr[i + 1]
+    far_i = (1 - w) * far[i] + w * far[i + 1]
+    frr_i = (1 - w) * frr[i] + w * frr[i + 1]
+    return {'threshold': float(thr_i), 'far': float(far_i),
+            'frr': float(frr_i),
+            'eer': float(0.5 * (far_i + frr_i))}
+
+
+def main():
+    print('=' * 70)
+    print('Script 21: Expanded Validation')
+    print('=' * 70)
+
+    rows = load_signatures()
+    print(f'\nLoaded {len(rows):,} signatures')
+    sig_ids = [r[0] for r in rows]
+    accts = [r[1] for r in rows]
+    firms = [r[2] or '(unknown)' for r in rows]
+    cos = np.array([r[3] for r in rows], dtype=float)
+    dh = np.array([-1 if r[4] is None else r[4] for r in rows], dtype=float)
+    pix = np.array([r[5] or 0 for r in rows], dtype=int)
+
+    firm_a_mask = np.array([f == FIRM_A for f in firms])
+    print(f'Firm A signatures: {int(firm_a_mask.sum()):,}')
+
+    # --- (1) INTER-CPA NEGATIVE ANCHOR ---
+    print(f'\n[1] Building inter-CPA negative anchor ({N_INTER_PAIRS} '
+          f'i.i.d. pairs from full matched corpus)...')
+    pool_sig_ids, pool_accts = load_signature_ids_for_negative_pool()
+    print(f'  pool size: {len(pool_sig_ids):,} matched signatures')
+    inter_cos = build_inter_cpa_negative(pool_sig_ids, pool_accts,
+                                         n_pairs=N_INTER_PAIRS)
+    print(f'  inter-CPA cos: mean={inter_cos.mean():.4f}, '
+          f'p95={np.percentile(inter_cos, 95):.4f}, '
+          f'p99={np.percentile(inter_cos, 99):.4f}, '
+          f'max={inter_cos.max():.4f}')
+
+    # --- (2) POSITIVES ---
+    # Pixel-identical (gold) + optional Firm A extension
+    pos_pix_mask = pix == 1
+    n_pix = int(pos_pix_mask.sum())
+    print(f'\n[2] Positive anchors:')
+    print(f'  pixel-identical signatures: {n_pix}')
+
+    # Build negative anchor scores = inter-CPA cosine distribution
+    # Positive anchor scores = pixel-identical signatures' max same-CPA cosine
+    # NB: the two distributions are not drawn from the same random variable
+    # (one is intra-CPA max, the other is inter-CPA random), so we treat the
+    # inter-CPA distribution as a negative reference for threshold sweep.
+
+    # Combined labeled set: positives=pixel-identical sigs' max cosine,
+    #                       negatives=inter-CPA random pair cosines.
+    pos_scores = cos[pos_pix_mask]
+    neg_scores = inter_cos
+    y = np.concatenate([np.ones(len(pos_scores)),
+                        np.zeros(len(neg_scores))])
+    scores = np.concatenate([pos_scores, neg_scores])
+
+    # Sweep thresholds
+    thr = np.linspace(0.30, 1.00, 141)
+    sweep = sweep_threshold(scores, y, 'above', thr)
+    eer = find_eer(sweep)
+    print(f'\n[3] Cosine EER (pos=pixel-identical, neg=inter-CPA n={len(inter_cos)}):')
+    print(f"    threshold={eer['threshold']:.4f}, EER={eer['eer']:.4f}")
+    # Canonical threshold evaluations with Wilson CIs
+    canonical = {}
+    for tt in [0.70, 0.80, 0.837, 0.90, 0.9407, 0.945, 0.95, 0.973, 0.977,
+               0.979, 0.985]:
+        y_pred = (scores > tt).astype(int)
+        m = classification_metrics(y, y_pred)
+        m['threshold'] = float(tt)
+        canonical[f'cos>{tt:.3f}'] = m
+        print(f"    @ {tt:.3f}: P={m['precision']:.3f}, R={m['recall']:.3f}, "
+              f"FAR={m['far']:.4f} (CI95={m['far_ci95'][0]:.4f}-"
+              f"{m['far_ci95'][1]:.4f}), FRR={m['frr']:.4f}")
+
+    # --- (3) HELD-OUT FIRM A ---
+    print('\n[4] Held-out Firm A 70/30 split:')
+    rng = np.random.default_rng(SEED)
+    firm_a_accts = sorted(set(a for a, f in zip(accts, firms) if f == FIRM_A))
+    rng.shuffle(firm_a_accts)
+    n_calib = int(0.7 * len(firm_a_accts))
+    calib_accts = set(firm_a_accts[:n_calib])
+    heldout_accts = set(firm_a_accts[n_calib:])
+    print(f'  Calibration fold CPAs: {len(calib_accts)}, '
+          f'heldout fold CPAs: {len(heldout_accts)}')
+
+    calib_mask = np.array([a in calib_accts for a in accts])
+    heldout_mask = np.array([a in heldout_accts for a in accts])
+    print(f'  Calibration sigs: {int(calib_mask.sum())}, '
+          f'heldout sigs: {int(heldout_mask.sum())}')
+
+    # Derive per-signature thresholds from calibration fold:
+    # - Firm A cos median, 1st-pct, 5th-pct
+    # - Firm A dHash median, 95th-pct
+    calib_cos = cos[calib_mask]
+    calib_dh = dh[calib_mask]
+    calib_dh = calib_dh[calib_dh >= 0]
+    cal_cos_med = float(np.median(calib_cos))
+    cal_cos_p1 = float(np.percentile(calib_cos, 1))
+    cal_cos_p5 = float(np.percentile(calib_cos, 5))
+    cal_dh_med = float(np.median(calib_dh))
+    cal_dh_p95 = float(np.percentile(calib_dh, 95))
+    print(f'  Calib Firm A  cos: median={cal_cos_med:.4f}, P1={cal_cos_p1:.4f}, P5={cal_cos_p5:.4f}')
+    print(f'  Calib Firm A dHash: median={cal_dh_med:.2f}, P95={cal_dh_p95:.2f}')
+
+    # Apply canonical rules to heldout fold
+    held_cos = cos[heldout_mask]
+    held_dh = dh[heldout_mask]
+    held_dh_valid = held_dh >= 0
+    held_rates = {}
+    for tt in [0.837, 0.945, 0.95, cal_cos_p5]:
+        rate = float(np.mean(held_cos > tt))
+        k = int(np.sum(held_cos > tt))
+        lo, hi = wilson_ci(k, len(held_cos))
+        held_rates[f'cos>{tt:.4f}'] = {
+            'rate': rate, 'k': k, 'n': int(len(held_cos)),
+            'wilson95': [float(lo), float(hi)],
+        }
+    for tt in [5, 8, 15, cal_dh_p95]:
+        rate = float(np.mean(held_dh[held_dh_valid] <= tt))
+        k = int(np.sum(held_dh[held_dh_valid] <= tt))
+        lo, hi = wilson_ci(k, int(held_dh_valid.sum()))
+        held_rates[f'dh_indep<={tt:.2f}'] = {
+            'rate': rate, 'k': k, 'n': int(held_dh_valid.sum()),
+            'wilson95': [float(lo), float(hi)],
+        }
+    # Dual rule
+    dual_mask = (held_cos > 0.95) & (held_dh >= 0) & (held_dh <= 8)
+    rate = float(np.mean(dual_mask))
+    k = int(dual_mask.sum())
+    lo, hi = wilson_ci(k, len(dual_mask))
+    held_rates['cos>0.95 AND dh<=8'] = {
+        'rate': rate, 'k': k, 'n': int(len(dual_mask)),
+        'wilson95': [float(lo), float(hi)],
+    }
+    print('  Heldout Firm A rates:')
+    for k, v in held_rates.items():
+        print(f'    {k}: {v["rate"]*100:.2f}% '
+              f'[{v["wilson95"][0]*100:.2f}, {v["wilson95"][1]*100:.2f}]')
+
+    # --- Save ---
+    summary = {
+        'generated_at': datetime.now().isoformat(),
+        'n_signatures': len(rows),
+        'n_firm_a': int(firm_a_mask.sum()),
+        'n_pixel_identical': n_pix,
+        'n_inter_cpa_negatives': len(inter_cos),
+        'inter_cpa_cos_stats': {
+            'mean': float(inter_cos.mean()),
+            'p95': float(np.percentile(inter_cos, 95)),
+            'p99': float(np.percentile(inter_cos, 99)),
+            'max': float(inter_cos.max()),
+        },
+        'cosine_eer': eer,
+        'canonical_thresholds': canonical,
+        'held_out_firm_a': {
+            'calibration_cpas': len(calib_accts),
+            'heldout_cpas': len(heldout_accts),
+            'calibration_sig_count': int(calib_mask.sum()),
+            'heldout_sig_count': int(heldout_mask.sum()),
+            'calib_cos_median': cal_cos_med,
+            'calib_cos_p1': cal_cos_p1,
+            'calib_cos_p5': cal_cos_p5,
+            'calib_dh_median': cal_dh_med,
+            'calib_dh_p95': cal_dh_p95,
+            'heldout_rates': held_rates,
+        },
+    }
+    with open(OUT / 'expanded_validation_results.json', 'w') as f:
+        json.dump(summary, f, indent=2, ensure_ascii=False)
+    print(f'\nJSON: {OUT / "expanded_validation_results.json"}')
+
+    # Markdown
+    md = [
+        '# Expanded Validation Report',
+        f"Generated: {datetime.now().strftime('%Y-%m-%d %H:%M:%S')}",
+        '',
+        '## 1. Inter-CPA Negative Anchor',
+        '',
+        f'* N random cross-CPA pairs sampled: {len(inter_cos):,}',
+        f'* Inter-CPA cosine: mean={inter_cos.mean():.4f}, '
+        f'P95={np.percentile(inter_cos, 95):.4f}, '
+        f'P99={np.percentile(inter_cos, 99):.4f}, max={inter_cos.max():.4f}',
+        '',
+        'This anchor is a meaningful negative set because inter-CPA pairs',
+        'cannot arise from legitimate reuse of a single signer\'s image.',
+        '',
+        '## 2. Cosine Threshold Sweep (pos=pixel-identical, neg=inter-CPA)',
+        '',
+        f"EER threshold: {eer['threshold']:.4f}, EER: {eer['eer']:.4f}",
+        '',
+        '| Threshold | Precision | Recall | F1 | FAR | FAR 95% CI | FRR |',
+        '|-----------|-----------|--------|----|-----|------------|-----|',
+    ]
+    for k, m in canonical.items():
+        md.append(
+            f"| {m['threshold']:.3f} | {m['precision']:.3f} | "
+            f"{m['recall']:.3f} | {m['f1']:.3f} | {m['far']:.4f} | "
+            f"[{m['far_ci95'][0]:.4f}, {m['far_ci95'][1]:.4f}] | "
+            f"{m['frr']:.4f} |"
+        )
+    md += [
+        '',
+        '## 3. Held-out Firm A 70/30 Validation',
+        '',
+        f'* Firm A CPAs randomly split by CPA (not by signature) into',
+        f'  calibration (n={len(calib_accts)}) and heldout (n={len(heldout_accts)}).',
+        f'* Calibration Firm A signatures: {int(calib_mask.sum()):,}. '
+        f'Heldout signatures: {int(heldout_mask.sum()):,}.',
+        '',
+        '### Calibration-fold anchor statistics (for thresholds)',
+        '',
+        f'* Firm A cosine: median = {cal_cos_med:.4f}, '
+        f'P1 = {cal_cos_p1:.4f}, P5 = {cal_cos_p5:.4f}',
+        f'* Firm A dHash (independent min): median = {cal_dh_med:.2f}, '
+        f'P95 = {cal_dh_p95:.2f}',
+        '',
+        '### Heldout-fold capture rates (with Wilson 95% CIs)',
+        '',
+        '| Rule | Heldout rate | Wilson 95% CI | k / n |',
+        '|------|--------------|---------------|-------|',
+    ]
+    for k, v in held_rates.items():
+        md.append(
+            f"| {k} | {v['rate']*100:.2f}% | "
+            f"[{v['wilson95'][0]*100:.2f}%, {v['wilson95'][1]*100:.2f}%] | "
+            f"{v['k']}/{v['n']} |"
+        )
+    md += [
+        '',
+        '## Interpretation',
+        '',
+        'The inter-CPA negative anchor (N ~50,000) gives tight confidence',
+        'intervals on FAR at each threshold, addressing the small-negative',
+        'anchor limitation of Script 19 (n=35).',
+        '',
+        'The 70/30 Firm A split breaks the circular-validation concern of',
+        'using the same calibration anchor for threshold derivation and',
+        'validation. Calibration-fold percentiles derive the thresholds;',
+        'heldout-fold rates with Wilson 95% CIs show how those thresholds',
+        'generalize to Firm A CPAs that did not contribute to calibration.',
+    ]
+    (OUT / 'expanded_validation_report.md').write_text('\n'.join(md),
+                                                       encoding='utf-8')
+    print(f'Report: {OUT / "expanded_validation_report.md"}')
+
+
+if __name__ == '__main__':
+    main()