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Apply codex round-24 final cleanup: §III v5 + §IV v3.1

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Codex round 24 returned Minor Revision: 3 Major CLOSED + 3 Major
PARTIAL + 4 Minor CLOSED + 2 Minor PARTIAL + 4 Editorial CLOSED
+ 1 Editorial OPEN. All 7 narrow residual fixes were §III-side
(I applied §IV fixes thoroughly in v3 but didn't mirror them to
§III v4).

§III v5 fixes:

  1. Anonymisation leak repaired:
     - "held-out-EY fold" -> "held-out-Firm-D fold" (L71)
     - "Firms B (KPMG) and D (EY)" -> "Firms B and D" (L99)
  2. K=3 LOOO weight drift 0.025 -> 0.023 at three sites
     (L71, L115, L173 provenance table). Matches Script 37 max
     C1 weight deviation and §IV v3 line 139.
  3. §III-K positive-anchor paragraph cross-ref repaired:
     "v3.x inter-CPA negative anchor (§III-J inherited; Table X)"
     -> "(§IV-I, inheriting v3.20.0 §IV-F.1 Table X)".
  4. §III-L five-way Likely-hand-signed band made inclusive:
     "Cosine below the all-pairs KDE crossover threshold." ->
     "Cosine at or below the all-pairs KDE crossover threshold
     (cos <= 0.837)." Matches Script 42 and §IV:19.
  5. Open question 1's pointer changed from current §IV-F (which
     is Convergent Internal-Consistency Checks) to v3.20.0
     Tables IX/XI/XII/XII-B + §IV-J descriptive proportions.
  6. Provenance table: new row for full-dataset n=686 citing
     Script 41 fulldataset_report.md.
  7. Draft-note header refreshed: v3 -> v5; v4 -> v5 etc.;
     "internal -- remove before submission" tag added.

§IV v3.1 fixes:

  - Close-out checklist L262 stale "codex round 23" wording
    updated to "rounds 21-24 and before partner Jimmy review".
  - Close-out item 4 "in this v2" stale wording -> "in this v3".
  - New item 5 added: internal author notes (this checklist +
    §III cross-reference index + both files' draft-note headers)
    are author working artefacts and should be moved/stripped
    before partner / submission packaging.

Round 24 finding summary post-v5/v3.1:
  Major:     3 CLOSED, 3 -> CLOSED (anonymisation + cross-ref +
             table numbering note residuals)
  Minor:     4 CLOSED, 2 -> CLOSED (weight drift 0.025 -> 0.023;
             low-cosine inclusivity cos <= 0.837)
  Editorial: 4 CLOSED, 1 PARTIAL (draft notes remain visible but
             explicitly marked as internal-only "remove before
             submission")

Phase 4 readiness: pending decision on whether to do one more
codex verification round (round 25) before drafting Abstract /
Intro / Discussion / Conclusion prose.

Co-Authored-By: Claude Opus 4.7 (1M context) <noreply@anthropic.com>
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paper/codex_review_gpt55_v4_round4.md
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# 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/v4/paper_a_methodology_v4_section_iii.md
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# Section III. Methodology — v4.0 Draft v4 (post codex rounds 21 + 22 + 23 cross-reference cleanup) # Section III. Methodology — v4.0 Draft v5 (post codex rounds 21–24)
> **Draft note (2026-05-12, v3).** This file replaces the §III-G through §III-L 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. > **Draft note (2026-05-12, v5; internal — remove before submission).** This file replaces the §III-G through §III-L 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.
> >
> **v2** incorporated codex gpt-5.5 round-21 review (`paper/codex_review_gpt55_v4_round1.md`, Major Revision); key revisions were: (i) the inherited five-way per-signature box rule restored as the **primary operational classifier** (§III-L), (ii) the K=3 Gaussian mixture positioned as **accountant-level descriptive characterisation** (§III-J), (iii) "convergent validation" softened to "convergent internal-consistency checks" since the three scores share underlying features (§III-K), (iv) the pixel-identity metric renamed from FAR to positive-anchor miss rate (§III-K), (v) five empirical/wording slips corrected. > **v2** incorporated codex gpt-5.5 round-21 review (`paper/codex_review_gpt55_v4_round1.md`, Major Revision); key revisions were: (i) the inherited five-way per-signature box rule restored as the **primary operational classifier** (§III-L), (ii) the K=3 Gaussian mixture positioned as **accountant-level descriptive characterisation** (§III-J), (iii) "convergent validation" softened to "convergent internal-consistency checks" since the three scores share underlying features (§III-K), (iv) the pixel-identity metric renamed from FAR to positive-anchor miss rate (§III-K), (v) five empirical/wording slips corrected.
> >
> **v3** incorporates codex gpt-5.5 round-22 review (`paper/codex_review_gpt55_v4_round2.md`, Minor Revision); five narrow fixes applied: (1) §III-K per-firm ranking corrected to acknowledge that Score 2 (reverse-anchor) ranks Firm D fractionally above Firm C while Scores 1 and 3 rank Firm C highest; (2) "smallest scope" / "any single firm" language narrowed to "comparison scopes tested in Script 32"; (3) §III-L corrected so the §III-K Spearman correlations are explicitly tied to the K=3 *posterior* P(C1) rather than the K=3 hard label; (4) provenance table source for $n = 150{,}442$ updated to cite Script 39 directly; (5) "max fold-to-fold deviation" wording made precise — the $0.028$ value is the maximum absolute deviation from the across-fold mean, not the pairwise across-fold range ($0.0376$). > **v3** incorporates codex gpt-5.5 round-22 review (`paper/codex_review_gpt55_v4_round2.md`, Minor Revision); five narrow fixes applied: per-firm ranking corrected (Score 2 reverse-anchor ranks Firm D fractionally above Firm C while Scores 1 and 3 rank Firm C highest), "smallest scope" language narrowed to "comparison scopes tested in Script 32", §III-L Spearman correlations explicitly tied to the K=3 *posterior* P(C1), provenance for $n = 150{,}442$ cites Script 39 directly, "max fold-to-fold deviation" wording made precise ($0.028$ = max absolute deviation from across-fold mean; pairwise range $0.0376$).
> >
> **v4** incorporates the §III ↔ §IV cross-reference cleanup that codex round-23 review flagged: §III-G unit references now point to actual §IV locations (§IV-J for five-way per-signature counts; §IV-I for inherited inter-CPA FAR), §III-G scope statement enumerates v4-new vs inherited sub-sections explicitly, §III-K cites v3.20.0 Tables IX/XI/XII/XII-B for moderate-band capture-rate (was "§IV-F" which is now Convergent Internal-Consistency), and §III-L's "without recalibration" claim is narrowed to apply only to the binary high-confidence sub-rule.
>
> **v5** incorporates codex gpt-5.5 round-24 review (`paper/codex_review_gpt55_v4_round4.md`, Minor Revision); seven narrow §III-side cleanups: (1) anonymisation leak repaired (real firm names "EY" and "KPMG" removed from §III prose; Firm A–D used throughout); (2) K=3 LOOO weight-drift value $0.025$ corrected to $0.023$ at three §III sites (matches Script 37); (3) §III-K positive-anchor paragraph cross-ref repaired (now points to §IV-I and v3.20.0 §IV-F.1 Table X, was the meaningless "§III-J inherited; Table X"); (4) §III-L five-way rule's Likely-hand-signed band made inclusive ($\text{cos} \leq 0.837$, matches Script 42); (5) open question 1's location pointer changed from current §IV-F to v3.20.0 Tables IX/XI/XII/XII-B and §IV-J descriptive proportions; (6) provenance row added for the full-dataset $n = 686$ claim citing Script 41; (7) draft-note dates and version stamps refreshed.
>
> Empirical anchors throughout reference Scripts 32–40 on branch `paper-a-v4-big4`; a provenance table appears at the end of this section listing every numerical claim with its script and report path. > Empirical anchors throughout reference Scripts 32–40 on branch `paper-a-v4-big4`; a provenance table appears at the end of this section listing every numerical claim with its script and report path.
## G. Unit of Analysis and Scope ## G. Unit of Analysis and Scope
@@ -68,7 +73,7 @@ This section develops the K=2 and K=3 Gaussian mixture fits to the Big-4 account
$\text{BIC}(K{=}3) = -1111.93$, lower than $K{=}2$ by $3.48$ (mild support for K=3 under standard BIC interpretation but not by itself decisive). $\text{BIC}(K{=}3) = -1111.93$, lower than $K{=}2$ by $3.48$ (mild support for K=3 under standard BIC interpretation but not by itself decisive).
**Why we report both K=2 and K=3.** Leave-one-firm-out cross-validation (§III-K) 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-EY fold; Script 36 stability summary). The $0.028$ value is $5.6\times$ the report's $0.005$ across-fold *stability tolerance* — not the bootstrap CI; the full-Big-4 bootstrap cosine half-width is the much smaller $0.0015$. 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 $0.025$ (Script 37). K=3 hard-posterior membership for the held-out firm is more 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`, with the explicit interpretation that "the C1 cluster exists but membership is not well-predicted by the held-out fit" and "K=3 is not predictively useful as an operational classifier" (Script 37 verdict legend). **Why we report both K=2 and K=3.** Leave-one-firm-out cross-validation (§III-K) 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* — not the bootstrap CI; the full-Big-4 bootstrap cosine half-width is the much smaller $0.0015$. 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 more 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`, with the explicit interpretation that "the C1 cluster exists but membership is not well-predicted by the held-out fit" and "K=3 is not predictively useful as an operational classifier" (Script 37 verdict legend).
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 a v4.0 operational classifier: 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 a v4.0 operational classifier:
@@ -96,7 +101,7 @@ Pairwise Spearman rank correlations among the three scores, $n = 437$ Big-4 CPAs
| Score 2 vs Score 3 | $+0.889$ | $< 10^{-149}$ | | Score 2 vs Score 3 | $+0.889$ | $< 10^{-149}$ |
| Score 1 vs Score 2 | $+0.879$ | $< 10^{-142}$ | | 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 hand-leaning ranking with $\rho > 0.87$. The three scores agree on placing Firm A as the most replication-dominated and the three non-Firm-A Big-4 firms as more hand-leaning, but they do not all rank the non-Firm-A firms identically: the K=3 posterior P(C1) and the box-rule hand-leaning rate (Scores 1 and 3) place Firm C at the most-hand-leaning end of Big-4 (mean P(C1) $= 0.311$; mean box-rule hand-leaning 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 (KPMG) and D (EY) 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 most-hand-leaning end between the three non-A Big-4 firms. 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 hand-leaning ranking with $\rho > 0.87$. The three scores agree on placing Firm A as the most replication-dominated and the three non-Firm-A Big-4 firms as more hand-leaning, but they do not all rank the non-Firm-A firms identically: the K=3 posterior P(C1) and the box-rule hand-leaning rate (Scores 1 and 3) place Firm C at the most-hand-leaning end of Big-4 (mean P(C1) $= 0.311$; mean box-rule hand-leaning 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 most-hand-leaning 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): **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):
@@ -112,11 +117,11 @@ The Script 39 report verdict is `SIG_CONVERGENCE_MODERATE`. The $\kappa = 0.870$
- *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=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 hand-leaning component shape is reproducible across folds: max deviation from the full-Big-4 baseline is $0.005$ in cosine, $0.96$ in dHash, and $0.025$ 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. - *K=3 LOOO is partially stable.* The C1 hand-leaning 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). **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 misclassified as hand-leaning. This is a one-sided check against a conservative positive subset, **not a false-alarm rate in the usual two-class sense**; we do not report a paired false-alarm rate because no signature-level hand-signed ground truth exists. The corresponding signature-level false-alarm-rate evidence comes from the v3.x inter-CPA negative anchor (§III-J inherited; Table X), which retains its v3.x interpretation: We report each candidate classifier's *positive-anchor miss rate* — the fraction of byte-identical signatures misclassified as hand-leaning. This is a one-sided check against a conservative positive subset, **not a false-alarm rate in the usual two-class sense**; we do not report a paired false-alarm rate because no signature-level hand-signed ground truth exists. The corresponding signature-level false-alarm-rate evidence comes from the v3.x inter-CPA negative anchor (§IV-I, inheriting v3.20.0 §IV-F.1 Table X), which retains its v3.x interpretation:
| Candidate classifier | Pixel-identity miss rate (Wilson 95% CI) | | Candidate classifier | Pixel-identity miss rate (Wilson 95% CI) |
|---|---| |---|---|
@@ -140,7 +145,7 @@ The v4.0 operational classifier is the inherited v3.x five-way per-signature box
4. **Uncertain:** Cosine between the all-pairs intra/inter KDE crossover (0.837) and 0.95 without sufficient convergent evidence in either direction. 4. **Uncertain:** Cosine between the all-pairs intra/inter KDE crossover (0.837) and 0.95 without sufficient convergent evidence in either direction.
5. **Likely hand-signed:** Cosine below the all-pairs KDE crossover threshold. 5. **Likely hand-signed:** Cosine at or below the all-pairs KDE crossover threshold (cos $\leq 0.837$).
The conventions about these thresholds (cosine 0.95 as an operating point chosen for capture-vs-FAR tradeoff against the inter-CPA negative anchor, with Wilson 95% inter-CPA FAR of $0.0005$ at the operating point; cosine 0.837 as the all-pairs KDE crossover; dHash 5 and 15 as the upper tail of the high-similarity mode and the structural-similarity ceiling respectively) are inherited from v3.x §III-K and retain their v3.x calibration and capture-rate evidence (v3.x Tables IX, XI, XII, XII-B). The conventions about these thresholds (cosine 0.95 as an operating point chosen for capture-vs-FAR tradeoff against the inter-CPA negative anchor, with Wilson 95% inter-CPA FAR of $0.0005$ at the operating point; cosine 0.837 as the all-pairs KDE crossover; dHash 5 and 15 as the upper tail of the high-similarity mode and the structural-similarity ceiling respectively) are inherited from v3.x §III-K and retain their v3.x calibration and capture-rate evidence (v3.x Tables IX, XI, XII, XII-B).
@@ -170,12 +175,13 @@ The conventions about these thresholds (cosine 0.95 as an operating point chosen
| $\Delta\text{BIC}(K{=}3, K{=}2) = -3.48$ | direct | Script 34 (BIC K=2 = $-1108.45$; Script 36 reports BIC K=3 = $-1111.93$) | direct (arithmetic) | | $\Delta\text{BIC}(K{=}3, K{=}2) = -3.48$ | 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 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=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 $0.025$) | direct | Script 37 stability summary | 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 | | 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 | | 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 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 | | 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 | | 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 | | Positive-anchor miss rate $0\%$ on $n = 262$ (Wilson upper $1.45\%$) | direct | Script 40 results table | direct |
| Inter-CPA FAR $0.0005$ at cos $> 0.95$ (Wilson 95% $[0.0003, 0.0007]$) | direct | v3 §IV-F.1 / Table X (inherited) | inherited from v3 | | Inter-CPA FAR $0.0005$ at cos $> 0.95$ (Wilson 95% $[0.0003, 0.0007]$) | direct | v3 §IV-F.1 / Table X (inherited) | inherited from v3 |
| Firm A byte-identical $145$ pixel-identical signatures in Big-4 subset | direct | Script 40 sample breakdown | direct | | Firm A byte-identical $145$ pixel-identical signatures in Big-4 subset | direct | Script 40 sample breakdown | direct |
@@ -195,7 +201,7 @@ The conventions about these thresholds (cosine 0.95 as an operating point chosen
## Open questions remaining for partner / reviewer ## 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 (Tables IX, XI, XII). Is this inheritance sufficient, or should v4.0 add a Big-4-specific capture-rate analysis for the moderate band in §IV-F? 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. 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.
paper/v4/paper_a_results_v4_section_iv.md
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@@ -259,9 +259,11 @@ The feature-backbone ablation (v3.20.0 Table XVIII; backbone replacement of ResN
## Phase 3 close-out checklist ## Phase 3 close-out checklist
The following items are flagged for resolution before §IV is sent for codex round 23 / partner Jimmy review: 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. 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 provisional Tables IV–XVIII numbering (with Table XV-B added in v2) should be confirmed once §IV is read end-to-end and §III–§IV cross-references are traced; some v3.x table positions (e.g., capture-rate tables Tables IX, XI, XII) are kept by reference rather than reproduced as v4.0-numbered tables. 2. **Table renumbering finalisation.** The provisional Tables IV–XVIII numbering (with Table XV-B added in v2) should be confirmed once §IV is read end-to-end and §III–§IV cross-references are traced; some v3.x table positions (e.g., capture-rate tables Tables IX, XI, XII) are kept by reference rather than reproduced as v4.0-numbered tables.
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. 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 v2: (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); (c) §IV table numbering set provisionally and to be finalised at Phase 3 close-out. 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.