Paper A v3.14: remove A2 assumption + soften all partner-level claims

The within-auditor-year uniformity assumption (A2) introduced in v3.11 Section III-G was empirically tested via a new within-year uniformity check (signature_analysis/27_within_year_uniformity.py; output in reports/within_year_uniformity/). The check found that within-year pairwise cosine distributions even at the calibration firm show substantial heterogeneity inconsistent with strict single-mechanism uniformity (Firm A 2023 CPAs typically have median pairwise cosine around 0.85 with 20-70% of pairs below the all-pairs KDE crossover 0.837). A2 as stated ("a CPA who replicates any signature image in that year is treated as doing so for every report") is therefore falsified empirically. Three explanations are compatible with the data and cannot be disambiguated without manual inspection: (i) true within-year mechanism mixing, (ii) multi-template replication workflows at the same firm within a year, (iii) feature-extraction noise on repeatedly scanned stamped images. Since A2 is falsified and its implications cannot be restored under any of the three explanations, we remove A2 entirely rather than downgrading it to an "approximation" or "interpretive convention." Changes applied: 1. Methodology Section III-G: A2 block deleted. Section now has only A1 (pair-detectability, cross-year pair-existence). Replaced A2 with an explicit statement that we make no within-year or across-year uniformity assumption, that per-signature labels are signature-level quantities throughout, and that we abstain from partner-level frequency inferences. Three candidate explanations for within-year signature heterogeneity are listed (single-template replication, multi-template replication in parallel, within-year mixing, or combinations) without attempting disaggregation. 2. Methodology III-H strand 2 (L154) softened: "7.5% form a long left tail consistent with a minority of hand-signers" rewritten as reflecting "within-firm heterogeneity in signing output (we do not disaggregate partner-level mechanism here; see Section III-G)." 3. Methodology III-H visual-inspection strand (L152) and the corresponding Discussion V-C first strand (L41) and Conclusion L21 softened: "for the majority of partners" changed to "for many of the sampled partners" (Codex round-14 MAJOR: "majority of partners" is itself a partner-level frequency claim under the new scope-of- claims regime). 4. Methodology III-K.3 Firm A anchor (L247): dropped "(consistent with a minority of hand-signers)" parenthetical. 5. Results IV-D cosine distribution narrative (L72): softened to "within-firm heterogeneity in signing outputs (see Section IV-E and Section III-G for the scope of partner-level claims)." 6. Results IV-E cluster split framing (L128): "minority-hand-signers framing of Section III-H" renamed to "within-firm heterogeneity framing of Section III-H" (matches the new III-H text). 7. Results IV-H.1 partner-level reading (L286): removed entirely. The v3.13 text "Under the within-year label-uniformity convention A2, this left-tail share is read as a partner-level minority of hand-signing CPAs" is replaced by a signature-level statement that explicitly lists hand-signing partners, multi-template replication, or a combination as possibilities without attempting attribution. 8. Results IV-H.1 stability argument (L308): softened from "persistent minority of hand-signing Firm A partners" to "persistent within- firm heterogeneity component," preserving the substantive argument that stability across production technologies is inconsistent with a noise-only explanation. 9. Results IV-I Firm A Capture Profile (L407): rewrote the "Firm A's minority hand-signers have not been captured" phrasing as a signature-level framing about the 7.5% left tail not projecting into the lowest-cosine document-level category under the dual- descriptor rules. 10. Abstract (L5): softened "alongside within-firm heterogeneity consistent with a minority of hand-signers" to "alongside residual within-firm heterogeneity." Abstract at 244/250 words. 11. Discussion V-C third strand (L43): added "multi-template replication workflows" to the list of possibilities and added a local "we do not disaggregate these mechanisms; see Section III-G for the scope of claims" disclaimer (Codex round-14 MINOR 5). 12. Discussion Limitations: added an Eighth limitation explicitly stating that partner-level frequency inferences are not made and why (no within-year uniformity assumption is adopted). 13. Methodology L124 opening: "We make one stipulation about within- auditor-year structure" fixed to "same-CPA pair detectability," since A1 is a cross-year pair-existence property, not a within- year claim (Codex round-14 MINOR 3). 14. Two broken cross-references fixed (Codex round-14 MINOR 6): methodology L86 Section V-D -> V-G (Limitations is G, not D which is Style-Replication Gap); methodology L167 Section III-I -> Section IV-D (the empirical cosine distribution is in IV-D, not III-I). Script 27 and its output (reports/within_year_uniformity/*) remain in the repository as internal due-diligence evidence but are not cited from the paper. The paper's substantive claims at signature- level and accountant (cross-year pooled) level are unchanged; only the partner-level interpretive overlay is removed. All tables (IV-XVIII), Appendix A (BD/McCrary sensitivity), and all reported numbers are unchanged. Codex round-14 (gpt-5.5 xhigh) verification: Major Revision caused by one BLOCKER (stale DOCX artifact, not part of this commit) plus one MAJOR ("majority of partners" partner-frequency claim) plus four MINOR findings. All five markdown findings addressed in this commit. DOCX regeneration deferred to pre-submission packaging. Co-Authored-By: Claude Opus 4.7 (1M context) <noreply@anthropic.com>
2026-04-24 22:06:22 +08:00
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@@ -18,7 +18,7 @@ The substantive reading is therefore narrower than "discrete behavior": *pixel-l

 Fourth, we introduced a *replication-dominated* calibration methodology---explicitly distinguishing replication-dominated from replication-pure calibration anchors and validating classification against a byte-level pixel-identity anchor (310 byte-identical signatures) paired with a $\sim$50,000-pair inter-CPA negative anchor.
 To document the within-firm sampling variance of using the calibration firm as its own validation reference, we split the firm's CPAs 70/30 at the CPA level and report capture rates on both folds with Wilson 95% confidence intervals; extreme rules agree across folds while rules in the operational 85-95% capture band differ by 1-5 percentage points, reflecting within-firm heterogeneity in replication intensity rather than generalization failure.
-This framing is internally consistent with all available evidence: the visual-inspection observation of pixel-identical signatures across unrelated audit engagements for the majority of calibration-firm partners; the 92.5% / 7.5% split in signature-level cosine thresholds; and, among the 171 calibration-firm CPAs with enough signatures to enter the accountant-level GMM (of 180 registered CPAs; 178 after excluding two with disambiguation ties, Section IV-G.2), the 139 / 32 split between the high-replication and middle-band clusters.
+This framing is internally consistent with all available evidence: the visual-inspection observation of pixel-identical signatures across unrelated audit engagements for many of the sampled calibration-firm partners; the 92.5% / 7.5% split in signature-level cosine thresholds; and, among the 171 calibration-firm CPAs with enough signatures to enter the accountant-level GMM (of 180 registered CPAs; 178 after excluding two with disambiguation ties, Section IV-G.2), the 139 / 32 split between the high-replication and middle-band clusters.

 An ablation study comparing ResNet-50, VGG-16 and EfficientNet-B0 confirmed that ResNet-50 offers the best balance of discriminative power, classification stability, and computational efficiency for this task.