Paper A v3.18: remove accountant-level + replication-dominated calibration + Gemini 2.5 Pro review minor fixes

Major changes (per partner red-pen + user decision):
- Delete entire accountant-level analysis (III.J, IV.E, Tables VI/VII/VIII,
  Fig 4) -- cross-year pooling assumption unjustified, removes the implicit
  "habitually stamps = always stamps" reading.
- Renumber sections III.J/K/L (was K/L/M) and IV.E/F/G/H/I (was F/G/H/I/J).
- Title: "Three-Method Convergent Thresholding" -> "Replication-Dominated
  Calibration" (the three diagnostics do NOT converge at signature level).
- Operational cosine cut anchored on whole-sample Firm A P7.5 (cos > 0.95).
- Three statistical diagnostics (Hartigan/Beta/BD-McCrary) reframed as
  descriptive characterisation, not threshold estimators.
- Firm A replication-dominated framing: 3 evidence strands -> 2.
- Discussion limitation list: drop accountant-level cross-year pooling and
  BD/McCrary diagnostic; add auditor-year longitudinal tracking as future work.
- Tone-shift: "we do not claim / do not derive" -> "we find / motivates".

Reference verification (independent web-search audit of all 41 refs):
- Fix [5] author hallucination: Hadjadj et al. -> Kao & Wen (real authors of
  Appl. Sci. 10:11:3716; report at paper/reference_verification_v3.md).
- Polish [16] [21] [22] [25] (year/volume/page-range/model-name).

Gemini 2.5 Pro peer review (Minor Revision verdict, A-F all positive):
- Neutralize script-path references in tables/appendix -> "supplementary
  materials".
- Move conflict-of-interest declaration from III-L to new Declarations
  section before References (paper_a_declarations_v3.md).

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

paper/paper_a_conclusion_v3.md

@@ -3,7 +3,7 @@
 ## Conclusion
 
 We have presented an end-to-end AI pipeline for detecting non-hand-signed auditor signatures in financial audit reports at scale.
-Applied to 90,282 audit reports from Taiwanese publicly listed companies spanning 2013--2023, our system extracted and analyzed 182,328 CPA signatures using a combination of VLM-based page identification, YOLO-based signature detection, deep feature extraction, and dual-descriptor similarity verification, with threshold selection placed on a statistically principled footing through two methodologically distinct threshold estimators and a density-smoothness diagnostic applied at two analysis levels.
+Applied to 90,282 audit reports from Taiwanese publicly listed companies spanning 2013--2023, our system extracted and analyzed 182,328 CPA signatures using a combination of VLM-based page identification, YOLO-based signature detection, deep feature extraction, and dual-descriptor similarity verification, with the operational classifier's cosine cut anchored on a whole-sample Firm A percentile heuristic and the per-signature similarity distribution characterised through two threshold estimators and a density-smoothness diagnostic.
 
 The seven numbered contributions listed in Section I can be grouped into four broader methodological themes, summarized below.
 
@@ -11,14 +11,13 @@ First, we argued that non-hand-signing detection is a distinct problem from sign
 
 Second, we showed that combining cosine similarity of deep embeddings with difference hashing is essential for meaningful classification---among 71,656 documents with high feature-level similarity, the dual-descriptor framework revealed that only 41% exhibit converging structural evidence of non-hand-signing while 7% show no structural corroboration despite near-identical feature-level appearance, demonstrating that a single-descriptor approach conflates style consistency with image reproduction.
 
-Third, we 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, 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.
+Third, we characterised the per-signature similarity distribution using three diagnostics---a Hartigan dip test, an EM-fitted Beta mixture (with logit-Gaussian robustness check), and a Burgstahler-Dichev / McCrary density-smoothness procedure---and showed that no two-mechanism mixture cleanly explains it: the dip test fails to reject unimodality for Firm A ($p = 0.17$), BIC strongly prefers a 3-component over a 2-component Beta fit ($\Delta\text{BIC} = 381$ for Firm A), and the BD/McCrary candidate transition lies inside the non-hand-signed mode rather than between modes (and is not bin-width-stable; Appendix A).
+The substantive reading is that *pixel-level output quality* is a continuous spectrum produced by firm-specific reproduction technologies (administrative stamping in early years, firm-level e-signing later) and scan conditions, rather than a discrete class cleanly separated from hand-signing.
+This reading motivates anchoring the operational classifier's cosine cut on a whole-sample Firm A P7.5 percentile heuristic (cos $> 0.95$) rather than on a mixture-fit crossing.
 
 Fourth, we introduced a *replication-dominated* calibration methodology---explicitly distinguishing replication-dominated from replication-pure calibration anchors and validating classification against a byte-level pixel-identity anchor (310 byte-identical signatures) paired with a $\sim$50,000-pair inter-CPA negative anchor.
-To document the within-firm sampling variance of using the calibration firm as its own validation reference, we split the firm's CPAs 70/30 at the CPA level and report capture rates on both folds with Wilson 95% confidence intervals; extreme rules agree across folds while rules in the operational 85-95% capture band differ by 1-5 percentage points, reflecting within-firm heterogeneity in replication intensity rather than generalization failure.
-This framing is internally consistent with all available evidence: the byte-level pair analysis finding of 145 pixel-identical calibration-firm signatures across 50 distinct partners of 180 registered (Section IV-G.1); 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.
+To document the within-firm sampling variance of using the calibration firm as its own validation reference, we split the firm's CPAs 70/30 at the CPA level and report capture rates on both folds with Wilson 95% confidence intervals; extreme rules agree across folds while rules in the operational 85--95% capture band differ by 1--5 percentage points, reflecting within-firm heterogeneity in replication intensity rather than generalization failure.
+This framing is internally consistent with the available evidence: the byte-level pair analysis finding of 145 pixel-identical calibration-firm signatures across 50 distinct partners of 180 registered (Section IV-F.1); the 92.5% / 7.5% split in signature-level cosine thresholds and the dip-test-confirmed unimodal-long-tail shape of Firm A's per-signature cosine distribution (Section IV-D.1); and the 95.9% top-decile concentration of Firm A auditor-years in the threshold-independent partner-ranking analysis (Section IV-G.2).
 
 An ablation study comparing ResNet-50, VGG-16 and EfficientNet-B0 confirmed that ResNet-50 offers the best balance of discriminative power, classification stability, and computational efficiency for this task.
 
@@ -26,7 +25,7 @@ An ablation study comparing ResNet-50, VGG-16 and EfficientNet-B0 confirmed that
 
 Several directions merit further investigation.
 Domain-adapted feature extractors, trained or fine-tuned on signature-specific datasets, may improve discriminative performance beyond the transferred ImageNet features used in this study.
-Extending the accountant-level analysis to auditor-year units---using the same convergent threshold framework at finer temporal resolution---could reveal within-accountant transitions between hand-signing and non-hand-signing over the decade.
+Extending the analysis to auditor-year units---computing per-signature statistics within each fiscal year and tracking how individual CPAs move across years---could reveal within-CPA transitions between hand-signing and non-hand-signing over the decade and is the natural next step beyond the cross-sectional analysis reported here.
 The pipeline's applicability to other jurisdictions and document types (e.g., corporate filings in other countries, legal documents, medical records) warrants exploration.
 The replication-dominated calibration strategy and the pixel-identity anchor technique are both directly generalizable to settings in which (i) a reference subpopulation has a known dominant mechanism and (ii) the target mechanism leaves a byte-level signature in the artifact itself.
 Finally, integration with regulatory monitoring systems and a larger negative-anchor study---for example drawing from inter-CPA pairs under explicit accountant-level blocking---would strengthen the practical deployment potential of this approach.