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_introduction_v3.md

@@ -26,13 +26,13 @@ This detection problem differs fundamentally from forgery detection: while it do
 A secondary methodological concern shapes the research design.
 Many prior similarity-based classification studies rely on ad-hoc thresholds---declaring two images equivalent above a hand-picked cosine cutoff, for example---without principled statistical justification.
 Such thresholds are fragile and invite reviewer skepticism, particularly in an archival-data setting where the cost of misclassification propagates into downstream inference.
-A defensible approach requires (i) a statistically principled threshold-determination procedure, ideally anchored to an empirical reference population drawn from the target corpus; (ii) convergent validation across multiple threshold-determination methods that rest on different distributional assumptions; and (iii) external validation against naturally-occurring anchor populations---byte-level identical pairs as a conservative gold positive subset and large random inter-CPA pairs as a gold negative population---reported with Wilson 95% confidence intervals on per-rule capture / FAR rates, since precision and $F_1$ are not meaningful when the positive and negative anchor populations are sampled from different units.
+A defensible approach requires (i) a transparent threshold anchored to an empirical reference population drawn from the target corpus; (ii) statistical diagnostics that characterise the *shape* of the underlying similarity distribution and so motivate the choice of anchor; and (iii) external validation against naturally-occurring anchor populations---byte-level identical pairs as a conservative gold positive subset and large random inter-CPA pairs as a gold negative population---reported with Wilson 95% confidence intervals on per-rule capture / FAR rates, since precision and $F_1$ are not meaningful when the positive and negative anchor populations are sampled from different units.
 
 Despite the significance of the problem for audit quality and regulatory oversight, no prior work has specifically addressed non-hand-signing detection in financial audit documents at scale with these methodological safeguards.
 Woodruff et al. [9] developed an automated pipeline for signature analysis in corporate filings for anti-money-laundering investigations, but their work focused on author clustering (grouping signatures by signer identity) rather than detecting reuse of a stored image.
 Copy-move forgery detection methods [10], [11] address duplicated regions within or across images but are designed for natural images and do not account for the specific characteristics of scanned document signatures, where legitimate visual similarity between a signer's authentic signatures is expected and must be distinguished from image reproduction.
 Research on near-duplicate image detection using perceptual hashing combined with deep learning [12], [13] provides relevant methodological foundations but has not been applied to document forensics or signature analysis.
-From the statistical side, the methods we adopt for threshold determination---the Hartigan dip test [37] and finite mixture modelling via the EM algorithm [40], [41], complemented by a Burgstahler-Dichev / McCrary density-smoothness diagnostic [38], [39]---have been developed in statistics and accounting-econometrics but have not, to our knowledge, been combined as a convergent threshold framework for document-forensics threshold selection.
+From the statistical side, the methods we adopt for distributional characterisation---the Hartigan dip test [37] and finite mixture modelling via the EM algorithm [40], [41], complemented by a Burgstahler-Dichev / McCrary density-smoothness diagnostic [38], [39]---have been developed in statistics and accounting-econometrics but have not, to our knowledge, been combined as a joint diagnostic toolkit for document-forensics threshold selection.
 
 In this paper, we present a fully automated, end-to-end pipeline for detecting non-hand-signed CPA signatures in audit reports at scale.
 Our approach processes raw PDF documents through the following stages:
@@ -40,7 +40,7 @@ Our approach processes raw PDF documents through the following stages:
 (2) signature region detection using a trained YOLOv11 object detector;
 (3) deep feature extraction via a pre-trained ResNet-50 convolutional neural network;
 (4) dual-descriptor similarity computation combining cosine similarity on deep embeddings with difference hash (dHash) distance;
-(5) threshold determination using two methodologically distinct estimators---KDE antimode with a Hartigan unimodality test and finite Beta mixture via EM with a logit-Gaussian robustness check---complemented by a Burgstahler-Dichev / McCrary density-smoothness diagnostic, all applied at both the signature level and the accountant level; and
+(5) signature-level distributional characterisation using two threshold estimators---KDE antimode with a Hartigan unimodality test and finite Beta mixture via EM with a logit-Gaussian robustness check---complemented by a Burgstahler-Dichev / McCrary density-smoothness diagnostic, used to read the structure of the per-signature similarity distribution and to motivate a percentile-based operational anchor rather than a mixture-fit crossing; and
 (6) validation against a pixel-identical anchor, a low-similarity anchor, and a replication-dominated Big-4 calibration firm.
 
 The dual-descriptor verification is central to our contribution.
@@ -51,14 +51,13 @@ By requiring convergent evidence from both descriptors, we can differentiate *st
 A second distinctive feature is our framing of the calibration reference.
 One major Big-4 accounting firm in Taiwan (hereafter "Firm A") is widely recognized within the audit profession as making substantial use of non-hand-signing for the majority of its certifying partners, while not ruling out that a minority may continue to hand-sign some reports.
 We therefore treat Firm A as a *replication-dominated* calibration reference rather than a pure positive class.
-This framing is important because the statistical signature of a replication-dominated population is visible in our data: Firm A's per-signature cosine distribution is unimodal with a long left tail, 92.5% of Firm A signatures exceed cosine 0.95 but 7.5% fall below, and 32 of the 171 Firm A CPAs with enough signatures to enter our accountant-level analysis (of 180 Firm A CPAs in the registry; 178 after excluding two with disambiguation ties, see Section IV-G.2) cluster into an accountant-level "middle band" rather than the high-replication mode.
-Adopting the replication-dominated framing---rather than a near-universal framing that would have to absorb these residuals as noise---ensures internal coherence among the byte-level pixel-identity evidence, the signature-level statistics, and the accountant-level mixture.
+This framing is important because the statistical signature of a replication-dominated population is visible in our data: Firm A's per-signature cosine distribution is unimodal with a long left tail (Hartigan dip $p = 0.17$), 92.5% of Firm A signatures exceed cosine 0.95 with the remaining 7.5% forming the left tail, and 145 Firm A signatures across 50 distinct partners are byte-identical to a same-CPA match in a different audit report (35 spanning different fiscal years).
+Adopting the replication-dominated framing---rather than a near-universal framing that would have to absorb the 7.5% residual as noise---ensures internal coherence between the byte-level pixel-identity evidence and the signature-level distributional shape.
 
-A third distinctive feature is our unit-of-analysis treatment.
-Our threshold-framework analysis reveals an informative asymmetry between the signature level and the accountant level: per-signature similarity forms a continuous quality spectrum for which no two-mechanism mixture provides a good fit, whereas per-accountant aggregates are clustered into three recognizable groups (BIC-best $K = 3$).
-The substantive reading is that *pixel-level output quality* is a continuous spectrum shaped by firm-specific reproduction technologies and scan conditions, while *accountant-level aggregate behaviour* is clustered but not sharply discrete: each CPA's cross-year-pooled coordinates sit closest to one of three recognizable groups (high-replication, middle-band, or hand-signed-tendency), reflecting a pooled observed tendency rather than a time-invariant regime, with smooth rather than discontinuous boundaries between groups.
-At the accountant level, the KDE antimode and the two mixture-based estimators (Beta-2 crossing and its logit-Gaussian robustness counterpart) converge within $\sim 0.006$ on a cosine threshold of approximately $0.975$, while the Burgstahler-Dichev / McCrary density-smoothness diagnostic finds no significant transition---an outcome (robust across a bin-width sweep, Appendix A) consistent with smoothly mixed clusters.
-The two-dimensional GMM marginal crossings (cosine $= 0.945$, dHash $= 8.10$) are reported as a complementary cross-check rather than as the primary accountant-level threshold.
+A third distinctive feature is the empirical reading we take from the per-signature distributional analysis.
+Three diagnostics applied to the per-signature similarity distribution---the Hartigan dip test, an EM-fitted Beta mixture (with logit-Gaussian robustness check), and the Burgstahler-Dichev / McCrary density-smoothness procedure---jointly indicate that no two-mechanism mixture cleanly explains per-signature similarity: the dip test fails to reject unimodality for Firm A, BIC strongly prefers a 3-component over a 2-component Beta fit, and the BD/McCrary candidate transition lies *inside* the non-hand-signed mode rather than between modes (and is not bin-width-stable; Appendix A).
+The substantive reading is that *pixel-level output quality* is a continuous spectrum shaped by firm-specific reproduction technologies (administrative stamping in early years, firm-level e-signing later) and scan conditions, rather than a discrete class cleanly separated from hand-signing.
+This reading motivates anchoring the operational classifier on a percentile heuristic over the Firm A reference distribution rather than on a mixture-fit crossing, and it motivates the byte-level pixel-identity anchor (Section IV-F.1) as a threshold-free positive reference that does not depend on resolving signature-level mixture structure.
 
 We apply this pipeline to 90,282 audit reports filed by publicly listed companies in Taiwan between 2013 and 2023, extracting and analyzing 182,328 individual CPA signatures from 758 unique accountants.
 To our knowledge, this represents the largest-scale forensic analysis of signature authenticity in financial documents reported in the literature.
@@ -71,17 +70,17 @@ The contributions of this paper are summarized as follows:
 
 3. **Dual-descriptor verification.** We demonstrate that combining deep-feature cosine similarity with perceptual hashing resolves the fundamental ambiguity between style consistency and image reproduction, and we validate the backbone choice through an ablation study comparing three feature-extraction architectures.
 
-4. **Convergent threshold framework with a smoothness diagnostic.** We introduce a threshold-selection framework that applies two methodologically distinct estimators---KDE antimode with Hartigan unimodality test and EM-fitted Beta mixture with a logit-Gaussian robustness check---at both the signature and accountant levels, and uses a Burgstahler-Dichev / McCrary density-smoothness diagnostic to characterize the local density structure. The convergence of the two estimators, combined with the presence or absence of a BD/McCrary transition, is used as evidence about the mixture structure of the data.
+4. **Percentile-anchored operational threshold.** We anchor the operational classifier's cosine cut on the whole-sample Firm A P7.5 percentile (cos $> 0.95$), a transparent and reproducible reference drawn from a known-majority-positive population, and complement it with dHash structural cuts derived from the same reference distribution. Operational thresholds are therefore explained by an empirical reference rather than asserted.
 
-5. **Continuous-quality / clustered-accountant finding.** We empirically establish that per-signature similarity is a continuous quality spectrum poorly approximated by any two-mechanism mixture, whereas per-accountant aggregates cluster into three recognizable groups with smoothly mixed rather than sharply discrete boundaries---an asymmetry with direct implications for how threshold selection and mixture modelling should be applied in document forensics.
+5. **Distributional characterisation of per-signature similarity.** We apply three statistical diagnostics---a Hartigan dip test, an EM-fitted Beta mixture with logit-Gaussian robustness check, and a Burgstahler-Dichev / McCrary density-smoothness procedure---to characterise the shape of the per-signature similarity distribution. The three diagnostics jointly find that per-signature similarity forms a continuous quality spectrum, which both motivates the percentile-based operational anchor over a mixture-fit crossing and is itself a substantive finding for the document-forensics literature on similarity-threshold selection.
 
 6. **Replication-dominated calibration methodology.** We introduce a calibration strategy using a known-majority-positive reference group, distinguishing *replication-dominated* from *replication-pure* anchors; and we validate classification using byte-level pixel identity as an annotation-free gold positive, requiring no manual labeling.
 
 7. **Large-scale empirical analysis.** We report findings from the analysis of over 90,000 audit reports spanning a decade, providing the first large-scale empirical evidence on non-hand-signing practices in financial reporting under a methodology designed for peer-review defensibility.
 
 The remainder of this paper is organized as follows.
-Section II reviews related work on signature verification, document forensics, perceptual hashing, and the statistical methods we adopt for threshold determination.
+Section II reviews related work on signature verification, document forensics, perceptual hashing, and the statistical methods we adopt for distributional characterisation.
 Section III describes the proposed methodology.
-Section IV presents experimental results including the convergent threshold analysis, accountant-level mixture, pixel-identity validation, and backbone ablation study.
+Section IV presents experimental results including the signature-level distributional characterisation, pixel-identity validation, and backbone ablation study.
 Section V discusses the implications and limitations of our findings.
 Section VI concludes with directions for future work.