Paper A v3.10: resolve Opus 4.7 round-9 paper-vs-Appendix-A contradiction
Opus round-9 review (paper/opus_final_review_v3_9.md) dissented from Gemini round-7 Accept and aligned with codex round-8 Minor, but for a DIFFERENT issue all prior reviewers missed: the paper's main text in four locations flatly claimed the BD/McCrary accountant-level null "persists across the Appendix-A bin-width sweep", yet Appendix A Table A.I itself documents a significant accountant-level cosine transition at bin 0.005 with |Z_below|=3.23, |Z_above|=5.18 (both past 1.96) located at cosine 0.980 --- on the upper edge of our two threshold estimators' convergence band [0.973, 0.979]. This is a paper-to-appendix contradiction that a careful reviewer would catch in 30 seconds. BLOCKER B1: BD/McCrary accountant-level claim softened across all four locations to match what Appendix A Table A.I actually reports: - Results IV-D.1 (lines 85-86): rewritten to say the null is not rejected at 2/3 cosine bin widths and 2/3 dHash bin widths, with the one cosine transition at bin 0.005 sitting on the upper edge of the convergence band and the one dHash transition at |Z|=1.96. - Results IV-E Table VIII row (line 145): "no transition / no transition" changed to "0.980 at bin 0.005 only; null at 0.002, 0.010" / "3.0 at bin 1.0 only ( |Z|=1.96); null at 0.2, 0.5". - Results IV-E line 130 (Third finding): "does not produce a significant transition (robust across bin-width sweep)" replaced with "largely null at the accountant level --- no significant transition at 2/3 cosine bin widths and 2/3 dHash bin widths, with the one cosine transition at bin 0.005 sitting at cosine 0.980 on the upper edge of the convergence band". - Results IV-E line 152 (Table VIII synthesis paragraph): matched reframing. - Discussion V-B (line 27): "does not produce a significant transition at the accountant level either" -> "largely null at the accountant level ... with the one cosine transition on the upper edge of the convergence band". - Conclusion (line 16): matched reframing with power caveat retained. MAJOR M1: Related Work L67 stale "well suited to detecting the boundary between two generative mechanisms" framing (residue from pre-demotion drafts) replaced with a local-density-discontinuity diagnostic framing that matches the rest of the paper and flags the signature-level bin-width sensitivity + accountant-level rarity as documented in Appendix A. MAJOR M2: Table XII orphaned in-text anchor --- Table XII is defined inside IV-G.3 but had no in-text "Table XII reports ..." pointer at its presentation location. Added a single sentence before the table comment. MINOR m1: Section IV-I.1 "4 of 30,000+ Firm A documents, 0.01%" replaced with the exact "4 of 30,226 Firm A documents, 0.013%". MINOR m2: Section IV-E "the two-dimensional two-component GMM" wording ambiguity (reader might confuse with the already-selected K*=3 GMM from BIC) replaced with explicit "a separately fit two-component 2D GMM (reported as a cross-check on the 1D accountant-level crossings)". MINOR m3: Section IV-D L59 "downstream all-pairs analyses (Tables XII, XVIII)" misnomer --- Table XII is per-signature classifier output not all-pairs; Table XVIII's all-pairs are over ~16M pairs not 168,740. Replaced with an accurate list: "same-CPA per-signature best-match analyses (Tables V and XII, and the Firm-A per-signature rows of Tables XIII and XVIII)". MINOR m4: Methodology III-H L156 "the validation role is played by ... the held-out Firm A fold" slightly overclaims what the held-out fold establishes (the fold-level rates differ by 1-5 pp with p<0.001). Parenthetical hedge added: "(which confirms the qualitative replication-dominated framing; fold-level rate differences are disclosed in Section IV-G.2)". Also add: - paper/opus_final_review_v3_9.md (Opus 4.7 max-effort review) - paper/gemini_review_v3_8.md (Gemini round-7 Accept verdict, was missing from prior commit) Abstract remains 243 words (under IEEE Access 250 limit). Co-Authored-By: Claude Opus 4.7 (1M context) <noreply@anthropic.com>
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# Independent Peer Review: Paper A (v3.8)
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**Target Venue:** IEEE Access (Regular Paper)
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**Date:** April 21, 2026
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**Reviewer:** Gemini CLI (7th Round Independent Review)
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---
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## 1. Overall Verdict
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**Verdict: Accept**
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**Rationale:**
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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.
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---
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## 2. Round-6 Follow-Up Audit
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In Round 6, three specific issues were flagged for revision. Below is the audit of their resolution in v3.8.
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### A. BD/McCrary Power-Artifact Reframe
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**Status: RESOLVED**
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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.
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* **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."
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* **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."
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* **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."
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* **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.
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* **Conclusion:** Symmetrically updated to note that the test "cannot affirmatively establish smoothness, but its non-transition is consistent with the smoothly-mixed cluster boundaries."
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* **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."
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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.
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### B. Table X EER/FRR Removal
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**Status: RESOLVED**
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The tautological presentation of FRR against the byte-identical positive anchor has been entirely resolved.
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* **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.
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* **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 $1$").
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* **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."
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This change significantly hardens the paper. By preempting the obvious critique from biometric/forensic reviewers, the authors project statistical maturity.
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### C. Section IV-I Narrative Safeguard & 15-Signature Footnote
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**Status: RESOLVED**
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Both minor narrative omissions have been addressed exactly as requested.
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* **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.
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* **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.
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---
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## 3. New Findings in v3.8
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The rewrites in v3.8 are highly successful and introduce no new regressions or inconsistencies.
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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.
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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.
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---
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## 4. Final Submission Readiness
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**v3.8 is fully submission-ready.**
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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.
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# Paper A v3.9 — Final Independent Peer Review (Opus 4.7)
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**Reviewer:** Claude Opus 4.7 (1M context), independent round 9
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**Date:** 2026-04-21
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**Commit reviewed:** 85cfefe
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**Target venue:** IEEE Access (Regular Paper)
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**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)
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---
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## 1. Overall verdict
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**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.
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---
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## 2. v3.8 → v3.9 delta verification
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I re-verified both round-8 fixes against their authoritative sources.
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**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)
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**Fix 2: Cross-reference corrections.**
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* "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.
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* 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.
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**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.
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---
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## 3. Numerical audit findings (spot-check against scripts)
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I verified 19 numerical claims against authoritative reports under `reports/`. All pass.
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| # | Paper claim | Source | Verified |
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|---|-------------|--------|----------|
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| 1 | Table IX whole-Firm-A cos>0.837 = 99.93% (60,408/60,448) | validation_recalibration.json whole_firm_a | ✓ |
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| 2 | Table IX cos>0.9407 = 95.15% (57,518/60,448) | same | ✓ (57518/60448=95.1529%) |
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| 3 | Table IX cos>0.95 = 92.51% (55,922/60,448) | same | ✓ |
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| 4 | Table IX cos>0.973 = 79.45% (48,028/60,448) | same | ✓ |
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| 5 | Table IX dual cos>0.95 AND dh≤8 = 89.95% (54,370/60,448) | same | ✓ |
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| 6 | Table XI calib cos>0.9407 = 94.99%, z=-3.19, p=0.0014 | validation_recalibration.json generalization_tests | ✓ |
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| 7 | Table XI held-out cos>0.9407 = 95.63% (14,662/15,332) | same | ✓ (rate 0.9563) |
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| 8 | Table V Firm A cos dip=0.0019, p=0.169 | dip_test_report.md | ✓ |
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| 9 | Table V Firm A dHash dip=0.1051, p<0.001 | same | ✓ |
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| 10 | Table V all-CPA 168,740 cos dip=0.0035 | same | ✓ |
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| 11 | Table VIII accountant KDE antimode cos=0.973 | accountant_three_methods_report.md | ✓ (0.9726) |
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| 12 | Table VIII accountant Beta-2 cos=0.979 | same | ✓ (0.9788) |
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| 13 | Table VIII accountant logit-GMM cos=0.976 | same | ✓ (0.9759) |
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| 14 | Table VIII accountant 2D-GMM marginal cos=0.945 | same | ✓ (0.9450) |
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| 15 | Table X FAR at 0.837=0.2062, CI [0.2027, 0.2098] | expanded_validation_report.md | ✓ |
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| 16 | Table X FAR at 0.973=0.0003 | same | ✓ |
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| 17 | Table XIV Firm A baseline 27.8% (1287/4629) | partner_ranking_report.md | ✓ |
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| 18 | 3.5× top-10% concentration ratio (95.9/27.8) | arithmetic | ✓ (3.45→3.5×) |
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| 19 | Table XVI Firm A intra-report 89.91% agreement | (26435+734+0+4)/30222 | ✓ (89.91%) |
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**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)
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**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).
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---
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## 4. Cross-reference audit findings
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I enumerated every `Section X-Y(.Z)` and `Table [roman]` reference in the submission files and checked resolution.
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* All 32 distinct section references resolve. No dangling targets.
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* 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.
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* **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.
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* **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)".
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* 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.
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---
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## 5. Arithmetic audit findings
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I recomputed every `X%`, `k of N`, `k/n` and ratio I could find. Results:
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| Claim | Computed | Paper | Status |
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|-------|----------|-------|--------|
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| 182,328 / 86,071 docs avg | 2.118 | — | — |
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| 182,328 / 85,042 with-detections | 2.144 | "2.14 sigs/doc" | ✓ (docs-with-detections denominator) |
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| 85,042 / 86,071 | 98.80% | "98.8%" | ✓ |
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| 168,755 / 182,328 | 92.55% | "92.6%" | ✓ |
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| 85,042 − 84,386 | 656 | "656 documents" | ✓ |
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| 29,529 + 36,994 + 5,133 + 12,683 + 47 | 84,386 | ✓ | ✓ |
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| 29,529 / 84,386 | 35.00% | "35.0%" | ✓ |
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| 22,970 / 30,226 | 75.99% | "76.0%" | ✓ |
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| (22,970+6,311) / 30,226 | 96.87% | "96.9%" | ✓ |
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| 26,435 / 30,222 | 87.47% | "87.5%" | ✓ |
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| (26,435+734+0+4) / 30,222 | 89.91% | "89.91%" | ✓ |
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| 4 / 30,226 | 0.0132% | "0.01%" | **△ should be 0.013%** |
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| 141 + 361 + 184 | 686 | GMM total | ✓ |
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| 0.21 + 0.51 + 0.28 | 1.00 | GMM weights | ✓ |
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| 139 / 171 | 81.3% | "81%" | ✓ |
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| 32 / 171 | 18.7% | "19%" (§V-C) | ✓ |
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| 29,529 / 71,656 | 41.21% | "41.2%" | ✓ |
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| 36,994 / 71,656 | 51.63% | "51.7%" | ✓ |
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| 5,133 / 71,656 | 7.16% | "7.2%" | ✓ |
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| 95.9 / 27.8 | 3.45 | "3.5×" | ✓ |
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| 90.1 / 27.8 | 3.24 | "3.2×" | ✓ |
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| 139+32 = 171; 141-139 | 2 | non-Firm-A in C1 | ✓ |
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| cos>0.95: 92.51%, below: 7.49% | "92.5% / 7.5%" | ✓ | ✓ |
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| Abstract word count | 244 | ≤250 | ✓ |
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**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.
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---
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## 6. Narrative / consistency findings
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### 6.1 BD/McCrary accountant-level claim — **main-text vs Appendix A contradiction (MAJOR)**
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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:
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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."
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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 |`
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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".
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But `reports/bd_sensitivity/bd_sensitivity.md` (and Appendix A Table A.I lines 23–28) actually report:
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* 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.**
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* Accountant cosine bin 0.002: no transition; bin 0.010: no transition.
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* 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.**
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* Accountant dHash bin 0.2: no transition; bin 0.5: no transition.
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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.
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**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.
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**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.*
|
||||
@@ -13,7 +13,7 @@ Second, we showed that combining cosine similarity of deep embeddings with diffe
|
||||
|
||||
Third, we introduced a convergent threshold framework combining two methodologically distinct estimators---KDE antimode (with a Hartigan unimodality test) and an EM-fitted Beta mixture (with a logit-Gaussian robustness check)---together with a Burgstahler-Dichev / McCrary density-smoothness diagnostic.
|
||||
Applied at both the signature and accountant levels, this framework surfaced an informative structural asymmetry: at the per-signature level the distribution is a continuous quality spectrum for which no two-mechanism mixture provides a good fit, whereas at the per-accountant level BIC cleanly selects a three-component mixture and the KDE antimode together with the Beta-mixture and logit-Gaussian estimators agree within $\sim 0.006$ at cosine $\approx 0.975$.
|
||||
The Burgstahler-Dichev / McCrary test, by contrast, finds no significant transition at the accountant level; at $N = 686$ accountants the test has limited power and cannot affirmatively establish smoothness, but its non-transition is consistent with the smoothly-mixed cluster boundaries implied by the accountant-level GMM.
|
||||
The Burgstahler-Dichev / McCrary test, by contrast, is largely null at the accountant level (no significant transition at two of three cosine bin widths and two of three dHash bin widths, with the one cosine transition sitting on the upper edge of the convergence band; Appendix A); at $N = 686$ accountants the test has limited power and cannot affirmatively establish smoothness, but its largely-null pattern is consistent with the smoothly-mixed cluster boundaries implied by the accountant-level GMM.
|
||||
The substantive reading is therefore narrower than "discrete behavior": *pixel-level output quality* is continuous and heavy-tailed, and *accountant-level aggregate behavior* is clustered into three recognizable groups whose inter-cluster boundaries are gradual rather than sharp.
|
||||
|
||||
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.
|
||||
|
||||
@@ -24,7 +24,7 @@ Replication quality varies continuously with scan equipment, PDF compression, st
|
||||
|
||||
At the per-accountant aggregate level the picture partly reverses.
|
||||
The distribution of per-accountant mean cosine (and mean dHash) rejects unimodality, a BIC-selected three-component Gaussian mixture cleanly separates (C1) a high-replication cluster dominated by Firm A, (C2) a middle band shared by the other Big-4 firms, and (C3) a hand-signed-tendency cluster dominated by smaller domestic firms, and the three 1D threshold methods applied at the accountant level produce mutually consistent estimates (KDE antimode $= 0.973$, Beta-2 crossing $= 0.979$, logit-GMM-2 crossing $= 0.976$).
|
||||
The BD/McCrary test, however, does not produce a significant transition at the accountant level either, in contrast to the signature level.
|
||||
The BD/McCrary test is largely null at the accountant level---no significant transition at two of three cosine bin widths and two of three dHash bin widths, and the one cosine transition (at bin 0.005, location 0.980) sits on the upper edge of the convergence band described above rather than outside it (Appendix A).
|
||||
This pattern is consistent with a clustered *but smoothly mixed* accountant-level distribution rather than with a sharp density discontinuity: accountant-level means cluster into three recognizable groups, yet the test fails to reject the smoothness null at the sample size available ($N = 686$), and the GMM cluster boundaries appear gradual rather than sheer.
|
||||
We caveat this interpretation appropriately in Section V-G: 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.
|
||||
|
||||
|
||||
@@ -153,7 +153,7 @@ Fourth, we additionally validate the Firm A benchmark through three complementar
|
||||
(b) *Partner-level similarity ranking (Section IV-H.2).* When every Big-4 auditor-year is ranked globally by its per-auditor-year mean best-match cosine, 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-H.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.
|
||||
|
||||
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.
|
||||
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 (which confirms the qualitative replication-dominated framing; fold-level rate differences are disclosed in Section IV-G.2) described in Section III-K.
|
||||
|
||||
We emphasize that Firm A's replication-dominated status was *not* derived from the thresholds we calibrate against it.
|
||||
Its identification rests on visual evidence and accountant-level clustering that is independent of the statistical pipeline.
|
||||
|
||||
@@ -64,7 +64,7 @@ The statistical validity of the unimodality-vs-multimodality dichotomy can be te
|
||||
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 is well suited to detecting the boundary between two generative mechanisms (non-hand-signed vs. hand-signed) under minimal distributional assumptions.
|
||||
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.
|
||||
|
||||
@@ -56,7 +56,7 @@ A Cohen's $d$ of 0.669 indicates a medium effect size [29], confirming that the
|
||||
## D. 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 downstream all-pairs analyses (Tables XII, 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.
|
||||
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) |
|
||||
@@ -82,8 +82,8 @@ Applying the BD/McCrary procedure (Section III-I.3) to the per-signature cosine
|
||||
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.
|
||||
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.
|
||||
We read this accountant-level pattern as *consistent with*---not affirmative proof of---clustered-but-smoothly-mixed aggregates: 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 (Section V-G).
|
||||
At the accountant level the BD/McCrary null is not rejected at two of three cosine bin widths (0.002, 0.010) and two of three dHash bin widths (0.2, 0.5); the one cosine transition that does occur (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, location dHash = 3.0) has $|Z_{\text{below}}|$ exactly at the 1.96 critical value.
|
||||
We read this pattern as *largely but not uniformly* null and *consistent with*---not affirmative proof of---clustered-but-smoothly-mixed aggregates: 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 (Section V-G), and the one bin-0.005 cosine transition, sitting at the edge rather than outside the threshold band and flanked by bin-0.002 and bin-0.010 non-rejections, is consistent with a mild histogram-resolution effect rather than a stable cross-mode density discontinuity (Appendix A).
|
||||
We therefore use BD/McCrary as a density-smoothness diagnostic rather than as an independent threshold estimator, and the substantive claim of smoothly-mixed accountant clustering rests on the joint evidence of the dip test, the BIC-selected GMM, and the BD null.
|
||||
|
||||
### 2) Beta Mixture at Signature Level: A Forced Fit
|
||||
@@ -127,8 +127,8 @@ First, of the 180 CPAs in the Firm A registry, 171 have $\geq 10$ signatures and
|
||||
Component C1 captures 139 of these 171 Firm A CPAs (81%) in a tight high-cosine / low-dHash cluster; the remaining 32 Firm A CPAs fall into C2.
|
||||
This split is consistent with the minority-hand-signers framing of Section III-H and with the unimodal-long-tail observation of Section IV-D.
|
||||
Second, the three-component partition is *not* a firm-identity partition: three of the four Big-4 firms dominate C2 together, and smaller domestic firms cluster into C3.
|
||||
Third, applying the threshold framework of Section III-I to the accountant-level cosine-mean distribution yields the estimates summarized in the accountant-level rows of Table VIII (below): KDE antimode $= 0.973$, Beta-2 crossing $= 0.979$, and the logit-GMM-2 crossing $= 0.976$ converge within $\sim 0.006$ of each other, while the BD/McCrary density-smoothness diagnostic does not produce a significant transition at the accountant level (robust across the bin-width sweep in Appendix A).
|
||||
For completeness we also report the two-dimensional two-component GMM's marginal crossings at cosine $= 0.945$ and dHash $= 8.10$; these differ from the 1D crossings because they are derived from the joint (cosine, dHash) covariance structure rather than from each 1D marginal in isolation.
|
||||
Third, applying the threshold framework of Section III-I to the accountant-level cosine-mean distribution yields the estimates summarized in the accountant-level rows of Table VIII (below): KDE antimode $= 0.973$, Beta-2 crossing $= 0.979$, and the logit-GMM-2 crossing $= 0.976$ converge within $\sim 0.006$ of each other, while the BD/McCrary density-smoothness diagnostic is largely null at the accountant level---no significant transition at two of three cosine bin widths and two of three dHash bin widths, with the one cosine transition at bin 0.005 sitting at cosine 0.980 on the upper edge of the convergence band (Appendix A).
|
||||
For completeness we also report the marginal crossings of a *separately fit* two-component 2D GMM (reported as a cross-check on the 1D accountant-level crossings) at cosine $= 0.945$ and dHash $= 8.10$; these differ from the 1D crossings because they are derived from the joint (cosine, dHash) covariance structure rather than from each 1D marginal in isolation.
|
||||
|
||||
Table VIII summarizes the threshold estimates produced by the two threshold estimators and the BD/McCrary smoothness diagnostic across the two analysis levels for a compact cross-level comparison.
|
||||
|
||||
@@ -142,14 +142,14 @@ Table VIII summarizes the threshold estimates produced by the two threshold esti
|
||||
| Accountant-level, KDE antimode (threshold estimator) | **0.973** | **4.07** |
|
||||
| Accountant-level, Beta-2 EM crossing (threshold estimator) | **0.979** | **3.41** |
|
||||
| Accountant-level, logit-GMM-2 crossing (robustness) | **0.976** | **3.93** |
|
||||
| Accountant-level, BD/McCrary transition (diagnostic; null across Appendix A) | no transition | no transition |
|
||||
| Accountant-level, BD/McCrary transition (diagnostic; largely null, Appendix A) | 0.980 at bin 0.005 only; null at 0.002, 0.010 | 3.0 at bin 1.0 only (\|Z\|=1.96); null at 0.2, 0.5 |
|
||||
| Accountant-level, 2D-GMM 2-comp marginal crossing (secondary) | 0.945 | 8.10 |
|
||||
| Firm A calibration-fold cosine P5 | 0.9407 | — |
|
||||
| Firm A calibration-fold dHash_indep P95 | — | 9 |
|
||||
| Firm A calibration-fold dHash_indep median | — | 2 |
|
||||
-->
|
||||
|
||||
At the accountant level the two threshold estimators (KDE antimode and Beta-2 crossing) together with the logit-Gaussian robustness crossing converge to a cosine threshold of $\approx 0.975 \pm 0.003$ and a dHash threshold of $\approx 3.8 \pm 0.4$; the BD/McCrary density-smoothness diagnostic produces no significant transition at the same level (a null that persists across Appendix A's bin-width sweep), which is *consistent with*---though, at $N = 686$, not sufficient to affirmatively establish---clustered-but-smoothly-mixed accountant-level aggregates.
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At the accountant level the two threshold estimators (KDE antimode and Beta-2 crossing) together with the logit-Gaussian robustness crossing converge to a cosine threshold of $\approx 0.975 \pm 0.003$ and a dHash threshold of $\approx 3.8 \pm 0.4$; the BD/McCrary density-smoothness diagnostic is largely null at the same level (two of three cosine bin widths and two of three dHash bin widths produce no significant transition; the one bin-0.005 cosine transition at 0.980 sits on the convergence-band upper edge and is flanked by non-rejections at bin 0.002 and bin 0.010, Appendix A), which is *consistent with*---though, at $N = 686$, not sufficient to affirmatively establish---clustered-but-smoothly-mixed accountant-level aggregates.
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This is the accountant-level convergence we rely on for the primary threshold interpretation; the two-dimensional GMM marginal crossings (cosine $= 0.945$, dHash $= 8.10$) differ because they reflect joint (cosine, dHash) covariance structure, and we report them as a secondary cross-check.
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The signature-level estimates are reported for completeness and as diagnostic evidence of the continuous-spectrum asymmetry (Section IV-D.2) rather than as primary classification boundaries.
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@@ -248,6 +248,7 @@ The per-signature classifier (Section III-L) uses cos $> 0.95$ as its operationa
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The accountant-level convergent threshold analysis (Section IV-E) places the primary accountant-level reference between $0.973$ and $0.979$ (KDE antimode, Beta-2 crossing, logit-Gaussian robustness crossing), and the accountant-level 2D-GMM marginal at $0.945$.
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Because the classifier operates at the signature level while these convergent accountant-level estimates are at the accountant level, they are formally non-substitutable.
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We report a sensitivity check in which the classifier's operational cut cos $> 0.95$ is replaced by the nearest accountant-level reference, cos $> 0.945$.
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Table XII reports the five-way classifier output under each cut.
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||||
<!-- TABLE XII: Classifier Sensitivity to the Operational Cosine Cut (All-Sample Five-Way Output, N = 168,740 signatures)
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| Category | cos > 0.95 count (%) | cos > 0.945 count (%) | Δ count |
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@@ -401,7 +402,7 @@ A cosine-only classifier would treat all 71,656 identically; the dual-descriptor
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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.
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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 32/171 middle-band minority identified by the accountant-level mixture (Section IV-E).
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The absence of any meaningful "likely hand-signed" rate (4 of 30,000+ Firm A documents, 0.01%) implies either that Firm A's minority hand-signers have not been captured in the lowest-cosine tail---for example, because they also exhibit high style consistency---or that their contribution is small enough to be absorbed into the uncertain category at this threshold set.
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The absence of any meaningful "likely hand-signed" rate (4 of 30,226 Firm A documents, 0.013%) implies either that Firm A's minority hand-signers have not been captured in the lowest-cosine tail---for example, because they also exhibit high style consistency---or that their contribution is small enough to be absorbed into the uncertain category at this threshold set.
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||||
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-G.2 is the corresponding external check.
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||||
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### 2) Cross-Method Agreement
|
||||
|
||||
Reference in New Issue
Block a user