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Rewrite Phase 4 prose v3: Abstract / §I / §V / §VI to match §III v7

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Major Phase 4 prose update aligning narrative with the §III v7
anchor-based ICCR framework (codex rounds 29-34):

- Abstract (247 words, under 250 limit): replaced K=3 mixture +
  natural-threshold framing with composition decomposition +
  multi-level ICCR + firm heterogeneity. Positioning as
  specificity-proxy-anchored screening framework.

- §I Introduction:
  * Methodological-design paragraph rewritten (no natural threshold;
    multi-level reporting; per-firm stratification; unsupervised
    disclosure)
  * Two new paragraphs documenting composition decomposition
    overturning distributional path, and anchor-based three-unit
    ICCR calibration
  * Firm heterogeneity + within-firm collision concentration as
    central findings
  * Contribution list rewritten (8 items): composition decomposition
    disproves natural threshold (NEW #4); multi-level ICCR
    calibration (NEW #5); firm heterogeneity quantification (NEW #6);
    K=3 demoted to descriptive partition (#7); multi-tool validation
    ceiling positioning (#8)

- §V Discussion:
  * §V-B retitled "composition-driven multimodality"; 2x2 factorial
    decomposition reported
  * §V-C Firm A reframed: position contrast + within-firm collision
    pattern, not "templated-end calibration anchor"
  * §V-D K=2/K=3 reframed as descriptive firm-compositional
    partitions (no "mechanism boundary" language)
  * §V-E three-score convergence reinterpreted as descriptor-position
    ranking, not hand-leaning mechanism ranking
  * §V-F (new title) Anchor-based multi-level calibration with all
    three units of analysis
  * §V-G expanded to 9 v4-specific limitations (no signature-level
    ground truth; assumption-violation; scope; conservative-subset;
    inherited rule components; deployed-rate excess not TPR; A1
    stipulation; K=3 composition sensitivity; no partner-level
    mechanism attribution) plus 5 inherited limitations

- §VI Conclusion: 8-point contribution list mirroring §I; 4 future
  work directions including within-firm collision-mechanism
  disambiguation and audit-quality companion analysis.

- Header draft-note updated to v3 (post codex rounds 26-34);
  Phase 4 v2 changelog moved to CHANGELOG.md placeholder.

Companion to §III v7 commit 723a3f6.

Co-Authored-By: Claude Opus 4.7 (1M context) <noreply@anthropic.com>
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gbanyan
2026-05-13 18:10:04 +08:00
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# Paper A v4.0 Phase 4 Prose Draft v2 (post codex round 26)
# Paper A v4.0 Phase 4 Prose Draft v3 (post codex rounds 26–34)
> **Draft note (2026-05-12, Phase 4 v2; internal — remove before submission).** This file replaces the v3.20.0 Abstract, §I Introduction, §II Related Work, §V Discussion, and §VI Conclusion blocks with the Big-4 reframed v4.0 prose. The methodology and results sections (§III v6 and §IV v3.2 on this branch, committed 2026-05-12) are the technical foundation; Phase 4 prose aligns the narrative with the convergent post-codex-rounds 21–25 framing. v2 incorporates codex round-26 review (`paper/codex_review_gpt55_v4_round6.md`, Major Revision): strip "independent feature-derived scores" overclaim from Abstract/§I/§V/§VI; narrow Big-4 scope language to "comparison scopes tested in Script 32"; repair §III-D → §III-G/I/J/K cross-reference; turn §II into a real Related Work section that explicitly defers to v3.20.0 plus a LOOO splice with a real citation; restore 5 v3.x limitations (backbone transfer, HSV preprocessing, longitudinal confounds, source-exemplar misattribution, legal interpretation); narrow §IV-K "pipeline reproducibility" to "K=3 + box-rule rank-convergence reproduces"; replace "published box rule" with "inherited Paper A box rule"; reserve "operational" for the five-way classifier. Inherited corpus-wide setup material (§III-A through §III-F; §IV-A through §IV-C; §IV-I; §IV-L) is referenced rather than restated. Empirical anchors cite Scripts 32–42 on branch `paper-a-v4-big4`.
> **Draft note (2026-05-13, Phase 4 v3; internal — remove before submission).** This file replaces the v3.20.0 Abstract, §I Introduction, §II Related Work, §V Discussion, and §VI Conclusion blocks with the v4.0 prose. The methodology and results sections (§III v7 and §IV v3.2 on this branch) are the technical foundation; Phase 4 prose aligns the narrative with the post-codex-round-34 framing. v3 (2026-05-13) reflects the major restructuring driven by codex rounds 29–34: distributional path to thresholds demolished (Scripts 39b–39e); anchor-based multi-level inter-CPA coincidence-rate calibration adopted (Scripts 40b, 43, 44, 45, 46); K=3 demoted to descriptive firm-compositional partition; "FAR" terminology replaced by "inter-CPA coincidence rate (ICCR)" throughout; nine-tool unsupervised validation strategy disclosed; positioning as anchor-calibrated screening framework with human-in-the-loop review (not validated forensic detector). Empirical anchors cite Scripts 32–46 on branch `paper-a-v4-big4`. Prior Phase 4 v2 changelog has been moved to `paper/v4/CHANGELOG.md`.
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@@ -8,7 +8,7 @@
> *IEEE Access target: <= 250 words, single paragraph.*
Regulations require Certified Public Accountants (CPAs) to attest each audit report with a signature, but digitization makes reusing a stored signature image across reports — through administrative stamping or firm-level electronic signing — technically trivial and visually invisible, undermining individualized attestation. We build an end-to-end pipeline detecting such *non-hand-signed* signatures at scale: a Vision-Language Model identifies signature pages, YOLOv11 localizes signatures, ResNet-50 supplies deep features, and a dual-descriptor layer combines cosine similarity with an independent-minimum perceptual hash (dHash) to separate *style consistency* from *image reproduction*. The operational output is an inherited five-way per-signature classifier with worst-case document-level aggregation. Applied to 90,282 Taiwan audit reports (2013–2023), the pipeline yields 182,328 signatures from 758 CPAs. Our primary analysis is scoped to the Big-4 sub-corpus (437 CPAs; 150,442 signatures), where the accountant-level $(\overline{\text{cos}}, \overline{\text{dHash}})$ distribution exhibits dip-test multimodality ($p < 5 \times 10^{-4}$, both axes) — the smallest scope tested at which this holds. A 3-component mixture recovers a stable cross-firm hand-leaning component (weight 0.143; leave-one-firm-out drift $\leq 0.005$ cos / 0.96 dh / 0.023 weight) alongside a Firm-A-concentrated templated component. Three feature-derived scores — mixture posterior, reverse-anchor cosine percentile against a non-Big-4 reference, and the inherited box-rule hand-leaning rate; not statistically independent — agree on the per-CPA ranking at Spearman $\rho \geq 0.879$. Against 262 byte-identical Big-4 signatures, all three achieve 0% positive-anchor miss rate (Wilson upper bound 1.45%). A light full-dataset check ($n = 686$) preserves the K=3 + box-rule Spearman convergence (drift 0.007).
Regulations require Certified Public Accountants (CPAs) to attest each audit report with a signature, but digitization makes reusing a stored signature image across reports — through administrative stamping or firm-level electronic signing — technically trivial and visually invisible, undermining individualized attestation. We build an end-to-end pipeline detecting such *non-hand-signed* signatures at scale: a Vision-Language Model identifies signature pages, YOLOv11 localizes signatures, ResNet-50 supplies deep features, and a dual-descriptor layer combines cosine similarity with an independent-minimum perceptual hash (dHash) to separate *style consistency* from *image reproduction*. Applied to 90,282 Taiwan audit reports (2013–2023), the pipeline yields 182,328 signatures from 758 CPAs; primary analyses are scoped to the Big-4 sub-corpus (437 CPAs; 150,442 signatures). Distributional diagnostics show that the apparent multimodality of the descriptor distribution dissolves under joint firm-mean centring and integer-tie jitter ($p$ rises to $0.35$), so no within-population bimodal antimode anchors the operational thresholds. We instead adopt an anchor-based inter-CPA coincidence-rate (ICCR) calibration at three units: per-comparison ($0.0006$ at cos$>0.95$; $0.0013$ at dHash$\leq 5$; $0.00014$ jointly), pool-normalised per-signature ($0.11$ under the deployed any-pair high-confidence rule), and per-document ($0.34$ for the operational HC+MC alarm). Firm heterogeneity is decisive: Firm A's per-document HC+MC alarm rate is $0.62$ versus $0.09$–$0.16$ at Firms B/C/D after pool-size adjustment, with $98$–$100\%$ of inter-CPA collisions concentrated within the source firm — consistent with firm-level template-like reuse. We position the system as a specificity-proxy-anchored screening framework with human-in-the-loop review, not as a validated forensic detector; no calibrated error rates are reportable without signature-level ground truth.
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@@ -22,17 +22,19 @@ The digitization of financial reporting has introduced a practice that complicat
The distinction between *non-hand-signing detection* and *signature forgery detection* is conceptually and technically important. The extensive body of research on offline signature verification [3]–[8] focuses almost exclusively on forgery detection — determining whether a questioned signature was produced by its purported author. In our context, identity is not in question; the CPA is indeed the legitimate signer. The question is whether the physical act of signing occurred for each individual report, or whether a single signing event was reproduced as an image across many reports. This detection problem differs fundamentally from forgery detection: while it does not require modeling skilled-forger variability, it introduces the distinct challenge of separating legitimate intra-signer consistency from image-level reproduction.
A 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 in an archival-data setting. A defensible approach requires (i) a transparent threshold whose calibration scope is statistically supported; (ii) statistical diagnostics that characterise the *shape* of the underlying similarity distribution at the chosen scope; (iii) annotation-free validation against naturally-occurring anchor populations, with Wilson 95% confidence intervals on per-rule capture and miss rates; and (iv) leave-one-firm-out cross-validation that exposes whether the calibration boundary remains stable when the training composition changes, or collapses into a firm-mass separator.
A 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 in an archival-data setting. A defensible approach requires (i) explicit calibration of the operational thresholds against measurable negative-anchor evidence; (ii) diagnostic procedures that test whether the descriptor distribution itself supports a within-population threshold, including formal decomposition of apparent multimodality into between-group composition and integer-tie artefacts; (iii) annotation-free reporting of operational alarm rates at multiple analysis units (per-comparison, per-signature pool, per-document) with Wilson 95% confidence intervals; (iv) per-firm stratification of the reported rates to surface heterogeneity that aggregate metrics conceal; and (v) explicit disclosure of the unsupervised setting's limits — in particular, the inability to estimate true error rates without signature-level ground-truth labels.
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 rather than detecting image reuse. 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. 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 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 been combined as a joint diagnostic toolkit for document-forensics threshold characterisation.
In this paper we present a fully automated, end-to-end pipeline for detecting non-hand-signed CPA signatures in audit reports at scale. The pipeline processes raw PDF documents through (1) signature page identification with a Vision-Language Model; (2) signature region detection with a trained YOLOv11 object detector; (3) deep feature extraction via a pre-trained ResNet-50; (4) dual-descriptor similarity (cosine + independent-minimum dHash); (5) accountant-level distributional characterisation at the Big-4 sub-corpus scope (§III-G through §III-J; §IV-D and §IV-E); (6) convergent internal-consistency analysis using three feature-derived scores (§III-K; §IV-F); (7) leave-one-firm-out reproducibility (§III-J and §III-K; §IV-G); and (8) annotation-free validation against a pixel-identity positive anchor, an inter-CPA negative anchor inherited from v3.x, and a light full-dataset cross-scope re-run (§IV-H, §IV-I, §IV-K).
In this paper we present a fully automated, end-to-end pipeline for detecting non-hand-signed CPA signatures in audit reports at scale, together with a multi-tool validation framework that explicitly discloses the unsupervised setting's limits. The pipeline processes raw PDF documents through (1) signature page identification with a Vision-Language Model; (2) signature region detection with a trained YOLOv11 object detector; (3) deep feature extraction via a pre-trained ResNet-50; (4) dual-descriptor similarity (cosine + independent-minimum dHash); (5) anchor-based threshold calibration at three units of analysis (per-comparison, pool-normalised per-signature, per-document) against an inter-CPA negative-anchor coincidence-rate proxy (§III-L); (6) firm-stratified per-rule reporting and a within-firm cross-CPA hit-matrix analysis (§III-L.4); (7) a composition decomposition that establishes the absence of a within-population bimodal antimode in the descriptor distributions (§III-I.4); and (8) a multi-tool unsupervised validation strategy with disclosed assumption-violation analysis (§III-M).
The methodological reframing relative to earlier versions of this work is central to our v4.0 contribution. The accountant-level $(\overline{\text{cos}}, \overline{\text{dHash}})$ distribution at the Big-4 sub-corpus scope is the smallest scope tested in Script 32 at which the Hartigan dip test rejects unimodality on both axes ($p < 5 \times 10^{-4}$, $n = 437$); none of the narrower comparison scopes tested (Firm A pooled alone, Firms B + C + D pooled, all non-Firm-A pooled) reject unimodality at conventional levels. A 2-component Gaussian mixture fit to this distribution recovers marginal crossings $\overline{\text{cos}}^* = 0.9755$ and $\overline{\text{dHash}}^* = 3.755$, with tight bootstrap 95% confidence intervals (cosine half-width $0.0015$). However, leave-one-firm-out cross-validation reveals that the K=2 boundary is essentially a Firm-A-vs-others separator: the maximum across-fold cosine-crossing deviation is $0.028$, $5.6\times$ the across-fold stability tolerance of $0.005$, and holding Firm A out flips the held-out classification rate from 0% to 100% replicated. We therefore do not use the K=2 fit as the operational classifier.
The methodological reframing relative to earlier versions of this work is central to our v4.0 contribution. Earlier work in this lineage adopted a distributional path to thresholds — fitting accountant-level finite-mixture models and treating their marginal crossings as data-derived "natural" thresholds. v4.0 reports a composition decomposition diagnostic (§III-I.4) that overturns this reading: the apparent multimodality of the Big-4 accountant-level distribution is fully explained by between-firm location-shift effects (Firm A's mean dHash of $2.73$ versus Firms B/C/D's $6.46$, $7.39$, $7.21$) and integer mass-point artefacts on the integer-valued dHash axis. Once both confounds are removed (firm-mean centring plus uniform integer jitter), the Big-4 pooled dHash dip test yields $p_{\text{median}} = 0.35$ across five jitter seeds, eliminating the rejection. Within-firm signature-level cosine and jittered-dHash dip tests fail to reject in every individual Big-4 firm and in every individual mid/small firm with $\geq 500$ signatures (10 firms tested in Script 39c). The descriptor distributions therefore contain no within-population bimodal antimode that could anchor an operational threshold.
A 3-component fit (BIC lower by $3.48$) instead identifies three accountant-level components: a templated cluster (cos $\approx 0.983$, dHash $\approx 2.41$, weight $0.321$), a mixed cluster (cos $\approx 0.956$, dHash $\approx 6.66$, weight $0.536$), and a cross-firm hand-leaning cluster (cos $\approx 0.946$, dHash $\approx 9.17$, weight $0.143$). The hand-leaning component shape is reproducible across LOOO folds (max drift $0.005$ in cos, $0.96$ in dHash, $0.023$ in weight); hard-posterior membership remains composition-sensitive (absolute differences $1.8$–$12.8$ pp), so we use K=3 as an *accountant-level descriptive characterisation*, not as an operational classifier. The signature-level operational classifier remains the inherited Paper A v3.x five-way box rule, retained for continuity with the prior literature.
In place of distributional anchoring, v4.0 adopts an anchor-based inter-CPA coincidence-rate (ICCR) calibration. At the per-comparison unit, the inherited cos$>0.95$ operating point yields ICCR $= 0.00060$ on a $5 \times 10^5$-pair Big-4 sample (replicating v3.x's reported per-comparison rate of $0.0005$ under prior "FAR" terminology); the dHash$\leq 5$ structural cutoff yields ICCR $= 0.00129$ (v4 new); the joint rule cos$>0.95$ AND dHash$\leq 5$ yields joint ICCR $= 0.00014$ (any-pair semantics, matching the deployed extrema rule). At the pool-normalised per-signature unit, the same rule's effective coincidence rate is materially higher because the deployed classifier takes max-cosine and min-dHash over a same-CPA pool: pooled Big-4 any-pair ICCR is $0.1102$ (Wilson 95% CI $[0.1086, 0.1118]$; CPA-block bootstrap 95% $[0.0908, 0.1330]$). At the per-document unit, the operational HC$+$MC alarm fires on $33.75\%$ of Big-4 documents under the inter-CPA candidate-pool counterfactual.
Three feature-derived scores converge on the per-CPA hand-leaning ranking with Spearman $\rho \geq 0.879$: the K=3 mixture posterior; a reverse-anchor cosine percentile relative to a strictly-out-of-target non-Big-4 reference distribution; and the inherited box-rule hand-leaning rate. The three scores are not statistically independent — they are deterministic functions of the same per-CPA descriptor pair — so the convergence is documented as internal consistency among feature-derived ranks rather than as external validation. Hard ground truth for the *replicated* class is provided by 262 byte-identical signatures in the Big-4 subset (Firm A 145, Firm B 8, Firm C 107, Firm D 2), against which all three candidate checks (the inherited box rule, the K=3 hard label, and the prevalence-calibrated reverse-anchor cut) achieve $0\%$ positive-anchor miss rate (Wilson 95% upper bound $1.45\%$). For the box rule this result is close to tautological at byte-identity, and we discuss the conservative-subset caveat in §V-G.
The pooled per-signature and per-document rates conceal striking firm heterogeneity. A logistic regression of the per-signature hit indicator on firm dummies (Firm A reference) and centred log pool size yields odds ratios of $0.053$ (Firm B), $0.010$ (Firm C), and $0.027$ (Firm D) — Firms B/C/D are an order of magnitude below Firm A even after controlling for the pool-size confound (Script 44). Cross-firm hit matrix analysis shows that $98$–$100\%$ of inter-CPA collisions originate from candidates within the source firm (different CPA, same firm), consistent with firm-specific template, stamp, or document-production reuse mechanisms — though not by itself diagnostic of deliberate sharing. We retain the inherited Paper A v3.x five-way box rule as the operational classifier; v4.0's contribution is to characterise its multi-level coincidence behaviour against the inter-CPA negative anchor rather than to derive new thresholds.
Three feature-derived scores converge on the per-CPA descriptor-position ranking with Spearman $\rho \geq 0.879$ (Script 38): the K=3 mixture posterior (now interpreted as a firm-compositional position score, not a mechanism cluster posterior; §III-J), a reverse-anchor cosine percentile relative to a strictly-out-of-target non-Big-4 reference, and the inherited box-rule less-replication-dominated rate. The three scores are deterministic functions of the same per-CPA descriptor pair, so the convergence is documented as internal consistency among feature-derived ranks rather than external validation. Hard ground truth for the *replicated* class is provided by 262 byte-identical signatures in the Big-4 subset (Firm A 145, Firm B 8, Firm C 107, Firm D 2), against which all three candidate checks achieve $0\%$ positive-anchor miss rate (Wilson 95% upper bound $1.45\%$). For the box rule this result is close to tautological at byte-identity; we discuss the conservative-subset caveat in §V-G.
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. The Big-4 sub-corpus comprises 437 CPAs and 150,442 signatures with both descriptors available.
@@ -44,15 +46,15 @@ The contributions of this paper are:
3. **Dual-descriptor verification.** We demonstrate that combining deep-feature cosine similarity with independent-minimum dHash resolves the ambiguity between *style consistency* and *image reproduction*, and we validate the backbone choice through a feature-backbone ablation.
4. **Big-4 sub-corpus scope as the methodologically privileged calibration unit.** We show that the accountant-level mixture model becomes statistically supportable (dip-test rejects unimodality) at the Big-4 scope and not in the narrower comparison scopes tested (Firm A pooled alone; Firms B + C + D pooled; all non-Firm-A pooled). We report the scope choice as a substantive methodological finding rather than an arbitrary subset.
4. **Composition decomposition disproves the distributional-threshold path.** We show via a 2×2 factorial diagnostic (firm-mean centring × integer-tie jitter) that the apparent multimodality of the Big-4 accountant-level descriptor distribution is fully attributable to between-firm location shifts and integer mass-point artefacts. The descriptor distributions contain no within-population bimodal antimode; "natural threshold" language in this lineage's prior work is not empirically supported.
5. **Accountant-level K=3 mixture as descriptive characterisation.** We fit and document a K=3 mixture whose hand-leaning component shape is LOOO-reproducible while its hard-posterior membership remains composition-sensitive. We do not treat K=3 as an operational classifier; we treat it as the descriptive accountant-level summary of the Big-4 distribution.
5. **Anchor-based multi-level inter-CPA coincidence-rate calibration.** We characterise the deployed five-way classifier at three units of analysis: per-comparison ICCR (cos$>0.95$: $0.0006$; dHash$\leq 5$: $0.0013$; joint: $0.00014$), pool-normalised per-signature ICCR ($0.11$ for the deployed any-pair high-confidence rule), and per-document ICCR ($0.34$ for the operational HC$+$MC alarm). We adopt "inter-CPA coincidence rate" as the metric name throughout and reserve "False Acceptance Rate" for terminology that requires ground-truth negative labels, which the corpus does not provide.
6. **Three-score convergent internal-consistency.** We measure agreement among three feature-derived scores at $\rho \geq 0.879$ and report this as internal consistency rather than external validation, given that the scores share the underlying descriptor pair.
6. **Firm heterogeneity quantification and within-firm cross-CPA collision concentration.** Per-firm rates differ by an order of magnitude after pool-size adjustment (Firm A's per-document HC$+$MC alarm at $0.62$ versus Firms B/C/D at $0.09$–$0.16$). Cross-firm hit matrix analysis shows that $98$–$100\%$ of inter-CPA collisions originate from candidates within the source firm, consistent with firm-specific template, stamp, or document-production reuse mechanisms — a descriptive finding about deployed-rule behaviour, not a claim of deliberate template sharing.
7. **Annotation-free validation against a hard positive anchor.** We achieve $0\%$ positive-anchor miss rate (Wilson 95% upper bound $1.45\%$) on 262 byte-identical Big-4 signatures, complementing v3.x's inherited inter-CPA negative-anchor FAR ($0.0005$ at the operational cosine cut).
7. **K=3 as descriptive firm-compositional partition; three-score convergent internal consistency.** We fit a K=3 Gaussian mixture as a descriptive partition of the Big-4 accountant-level distribution (no longer interpreted as three mechanism clusters). Three feature-derived scores agree on the per-CPA descriptor-position ranking at Spearman $\rho \geq 0.879$; we report this as internal consistency rather than external validation, given that the scores share the underlying descriptor pair.
8. **Light full-dataset cross-scope check.** We re-run the K=3 + box-rule rank-convergence check at the full $n = 686$ CPA scope and observe Spearman $\rho = 0.9558$ (drift $0.007$ from Big-4), demonstrating that this specific convergence reproduces at the broader scope. We do not interpret this as a re-validation of the operational thresholds or of the LOOO / pixel-identity / five-way components, all of which remain scoped to Big-4.
8. **Annotation-free positive-anchor validation and unsupervised validation ceiling.** We achieve $0\%$ positive-anchor miss rate (Wilson 95% upper bound $1.45\%$) on 262 byte-identical Big-4 signatures, with the conservative-subset caveat that byte-identical pairs are by construction near cos$=1$ and dHash$=0$. We frame the overall validation strategy as a multi-tool collection of nine partial-evidence diagnostics, each with an explicitly disclosed untested assumption; their conjunction constitutes the unsupervised validation ceiling achievable on this corpus. We do not claim a validated forensic detector; we position the system as a specificity-proxy-anchored screening framework with human-in-the-loop review.
The remainder of the paper is organized as follows. Section II reviews related work on signature verification, document forensics, perceptual hashing, and the statistical methods used. Section III describes the proposed methodology. Section IV presents the experimental results — distributional characterisation, mixture fits, convergent internal-consistency checks, leave-one-firm-out reproducibility, pixel-identity validation, and full-dataset robustness. Section V discusses the implications and limitations. Section VI concludes with directions for future work.
@@ -72,49 +74,59 @@ The remainder of the paper is organized as follows. Section II reviews related w
Non-hand-signing differs from forgery in that the questioned signature is produced by its legitimate signer's own stored image rather than by an impostor. The detection problem is therefore framed around *intra-signer image reproduction* rather than *inter-signer imitation*. This framing has analytical consequences. The within-CPA signature distribution is the analytical population of interest; the cross-CPA inter-class distribution is a *reference* against which intra-CPA similarity is interpreted, not the population to be modelled. This contrasts with most prior offline signature verification work, which treats genuine-versus-forged as the central two-class problem.
## B. Per-Signature Similarity is a Continuous Quality Spectrum; the Accountant-Level Distribution is Multimodal
## B. Per-Signature Similarity is a Continuous Quality Spectrum; the Accountant-Level Multimodality is Composition-Driven
A central empirical finding of v3.x was that *per-signature* similarity does not admit a clean two-mechanism mixture: dip-test fails to reject unimodality at the signature level for Firm A, BIC prefers a 3-component fit, and BD/McCrary candidate transitions lie inside the high-similarity mode rather than between modes. v4.0 inherits this signature-level reading and remains consistent with it (no signature-level diagnostic was newly run in v4.0 to overturn the v3.x finding; the v4.0 per-signature evidence is the K=3 fit consistency check of §IV-F).
A central empirical finding of v3.x was that *per-signature* similarity does not admit a clean two-mechanism mixture: dip-test fails to reject unimodality at the signature level for Firm A, BIC prefers a 3-component fit, and BD/McCrary candidate transitions lie inside the high-similarity mode rather than between modes. v4.0 strengthens and extends this signature-level reading.
The v4.0 *accountant-level* analysis at the Big-4 scope tells a complementary story. When per-CPA means $(\overline{\text{cos}}_a, \overline{\text{dHash}}_a)$ are computed for the 437 Big-4 CPAs, the Hartigan dip test rejects unimodality on both marginals at $p < 5 \times 10^{-4}$. Among the comparison scopes tested in Script 32 (Firm A pooled alone; Firms B + C + D pooled; all non-Firm-A pooled), this is the smallest scope at which a finite-mixture model is statistically supported. The accountant-level multimodality reflects between-CPA heterogeneity in *per-CPA-mean location* across the descriptor plane — some CPAs' observed signatures place their per-CPA means in the templated region of the plane, others in the mixed region, others in the hand-leaning region — not a within-CPA two-mechanism boundary. The two readings can be jointly consistent: a CPA whose per-CPA mean places them in a mixed or hand-leaning region of the accountant-level plane may still have a unimodal within-CPA signature distribution, because the per-CPA mean is a summary statistic and is not a claim that all of that CPA's signatures share a single signing mechanism (§III-G).
The Big-4 accountant-level descriptor distribution does reject unimodality on both marginals at $p < 5 \times 10^{-4}$ (Script 34). v4.0's composition decomposition (§III-I.4; Scripts 39b–39e) shows that this rejection is fully attributable to two non-mechanistic sources: (a) between-firm location-shift effects on both axes — Firm A's mean dHash of $2.73$ versus Firms B/C/D's $6.46$, $7.39$, $7.21$ creates a multi-peaked pooled distribution that any single firm's distribution lacks — and (b) integer mass-point artefacts on the integer-valued dHash axis, which inflate the dip statistic against a continuous-density null. A 2×2 factorial diagnostic applied to the Big-4 pooled dHash (firm-mean centring × uniform integer jitter $[-0.5, +0.5]$, 5 jitter seeds) shows that the dip test fails to reject ($p_{\text{median}} = 0.35$, 0/5 seeds reject) when *both* corrections are applied; either correction alone leaves the rejection in place. Within-firm signature-level cosine and jittered-dHash dip tests fail to reject in every individual Big-4 firm and in every individual non-Big-4 firm with $\geq 500$ signatures (10 firms tested). The descriptor distributions therefore lack a within-population bimodal antimode that could anchor an operational threshold. The K=2 / K=3 mixture fits are retained in §III-J as descriptive partitions of the joint Big-4 distribution that reflect firm-compositional structure, not as inferential evidence for two or three latent mechanism modes.
## C. Firm A as the Templated End of Big-4 (Case Study, Not Calibration Anchor)
Firm A is empirically the most digitally-replicated of the four Big-4 firms in our corpus. In the Big-4 K=3 hard-posterior assignment, Firm A accounts for $0\%$ of the hand-leaning component and $82.5\%$ of the templated component; the opposite pattern holds at one of the non-Firm-A Big-4 firms (Firm C, which has the highest hand-leaning concentration at $23.5\%$). Firm A also accounts for 145 of the 262 byte-identical signatures in the Big-4 byte-identical anchor of §IV-H (with Firm B 8, Firm C 107, Firm D 2). The additional v3.x finding that the 145 Firm A pixel-identical signatures span 50 distinct Firm A partners (of 180 registered), with 35 byte-identical matches across different fiscal years, is inherited from v3.20.0 §IV-F.1 / Script 28 / Appendix B byte-decomposition output and was not regenerated in v4.0's spike scripts; we retain those numbers by reference.
Firm A is empirically the firm whose CPAs are most concentrated in the high-cosine, low-dHash corner of the Big-4 descriptor plane. In the Big-4 K=3 hard-posterior assignment (now interpreted as a firm-compositional position assignment; §III-J), Firm A accounts for $0\%$ of C1 (low-cos / high-dHash position) and $82.5\%$ of C3 (high-cos / low-dHash position); the opposite pattern holds at Firm C, which has the highest C1 concentration at $23.5\%$. Firm A also accounts for 145 of the 262 byte-identical signatures in the Big-4 byte-identical anchor of §IV-H (with Firm B 8, Firm C 107, Firm D 2). The additional v3.x finding that the 145 Firm A pixel-identical signatures span 50 distinct Firm A partners (of 180 registered), with 35 byte-identical matches across different fiscal years, is inherited from v3.20.0 §IV-F.1 / Script 28 / Appendix B byte-decomposition output and was not regenerated in v4.0's spike scripts; we retain those numbers by reference.
In v4.0 we treat Firm A as a *templated-end case study* rather than as the calibration anchor for the operational threshold. Firm A enters the Big-4 mixture on equal footing with the other three Big-4 firms; the K=3 components are derived from the joint Big-4 distribution. Firm A's role in the methodology is descriptive: it is the within-Big-4 firm whose CPAs are most concentrated in the high-cosine, low-dHash corner of the descriptor plane. The byte-level evidence above is a firm-level signature-reuse case study; the Big-4 byte-identical positive anchor of §IV-H pools all four firms' byte-identical signatures and is not anchored on Firm A alone. This is a deliberate departure from v3.x's "Firm A as replication-dominated calibration reference" framing, motivated by the LOOO evidence below.
In v4.0 we treat Firm A as a *templated-end case study* rather than as the calibration anchor for the operational threshold. Firm A enters the Big-4 anchor-based ICCR calibration on equal footing with the other three Big-4 firms (§III-L). The cross-firm hit matrix of §III-L.4 strengthens this framing: $98$–$100\%$ of inter-CPA collisions originate from candidates within the source firm, regardless of which Big-4 firm is the source. Firm A's high per-document HC$+$MC alarm rate of $0.62$ (versus Firms B/C/D's $0.09$–$0.16$) reflects high inter-CPA collision concentration under the deployed rule on real same-CPA pools, consistent with firm-specific template, stamp, or document-production reuse — though the inter-CPA-anchor analysis alone is not diagnostic of deliberate template sharing. The byte-level evidence of v3.x §IV-F.1 (Firm A's 145 pixel-identical signatures across $\sim 50$ distinct partners) provides direct evidence that firm-level template reuse does occur at Firm A; the within-firm collision pattern at all four Big-4 firms is consistent with that mechanism extending in milder form to Firms B/C/D.
## D. K=2 is Firm-Mass Driven; K=3 is Reproducible in Shape
## D. K=2 / K=3 as Descriptive Firm-Compositional Partitions
Leave-one-firm-out cross-validation of the Big-4 mixture fit reveals a sharp contrast between K=2 and K=3 behaviour. K=2 is unstable: across-fold cosine-crossing deviation is $0.028$, and holding Firm A out gives a fold rule (cos $> 0.938$, dHash $\leq 8.79$) that classifies $100\%$ of held-out Firm A as templated, while holding any non-Firm-A Big-4 firm out gives a fold rule near (cos $> 0.975$, dHash $\leq 3.76$) that classifies $0\%$ of the held-out firm as templated. The K=2 boundary is essentially a Firm-A-vs-others separator, not a within-Big-4 mechanism boundary. This is a *negative result* about K=2 as an operational rule and motivates the K=3 selection that follows.
Leave-one-firm-out cross-validation of the Big-4 mixture fit reveals a sharp contrast between K=2 and K=3 behaviour. K=2 is unstable: across-fold cosine-crossing deviation is $0.028$, and holding Firm A out gives a fold rule (cos $> 0.938$, dHash $\leq 8.79$) that classifies $100\%$ of held-out Firm A in the upper component, while holding any non-Firm-A Big-4 firm out gives a fold rule near (cos $> 0.975$, dHash $\leq 3.76$) that classifies $0\%$ of the held-out firm in the upper component. The K=2 boundary is essentially a Firm-A-vs-others separator — direct evidence that the K=2 partition reflects firm-compositional rather than mechanistic structure.
K=3 in contrast has a *reproducible component shape*: across the four folds the hand-leaning component C1 cosine mean varies by at most $0.005$, the dHash mean by at most $0.96$, and the weight by at most $0.023$. Hard-posterior membership for the held-out firm is more composition-sensitive (absolute differences $1.8$–$12.8$ pp across folds). We do not use K=3 hard-posterior membership as an operational classifier; we use the component-shape stability as descriptive evidence that a cross-firm hand-leaning sub-population exists at the Big-4 scope, and we report the membership uncertainty as a calibration band.
K=3 in contrast has a *reproducible component shape* at the descriptor-position level: across the four folds the C1 (low-cos / high-dHash) component cosine mean varies by at most $0.005$, the dHash mean by at most $0.96$, and the weight by at most $0.023$. Hard-posterior membership for the held-out firm is composition-sensitive (absolute differences $1.8$–$12.8$ pp across folds). Together with the §III-I.4 composition decomposition (no within-population bimodal antimode), the K=3 stability supports a descriptive reading: the Big-4 descriptor plane has a reproducible three-region partition that reflects how firm-compositional weight is distributed across the descriptor space, *not* a three-mechanism latent-class structure. We accordingly do not use K=3 hard-posterior membership as an operational classifier; we use it as the accountant-level descriptive summary that complements the deployed signature-level five-way classifier of §III-L.
## E. Three-Score Convergent Internal-Consistency
Three feature-derived scores agree on the per-CPA hand-leaning ranking at Spearman $\rho \geq 0.879$: the K=3 mixture posterior; the reverse-anchor cosine percentile under a non-Big-4 reference distribution; and the inherited Paper A box-rule hand-leaning rate. The three scores are *not* statistically independent measurements — they are deterministic functions of the same per-CPA descriptor pair — so the convergence is documented as internal consistency rather than external validation against an independent ground truth (which the corpus does not provide for the hand-signed class). The strength of the convergence (all pairwise $|\rho| > 0.87$) and its persistence at the signature level (Cohen $\kappa = 0.87$ between per-CPA-fit and per-signature-fit K=3 binary labels) are nevertheless informative: per-CPA aggregation does not collapse the broad three-component ordering, and three different summarisations of the descriptor space — mixture posterior, deviation from an external reference, and the inherited Paper A box rule — produce broadly concordant per-CPA rankings, with a residual non-Firm-A disagreement (the reverse-anchor cosine percentile ranks Firm D fractionally above Firm C, while the mixture posterior and the box-rule rate rank Firm C highest among non-Firm-A firms).
Three feature-derived scores agree on the per-CPA descriptor-position ranking at Spearman $\rho \geq 0.879$: the K=3 mixture posterior (a firm-compositional position score, not a mechanism cluster posterior); the reverse-anchor cosine percentile under a non-Big-4 reference distribution; and the inherited Paper A box-rule less-replication-dominated rate. The three scores are *not* statistically independent measurements — they are deterministic functions of the same per-CPA descriptor pair — so the convergence is documented as internal consistency rather than external validation against an independent ground truth (which the corpus does not provide for the hand-signed class). The strength of the convergence (all pairwise $|\rho| > 0.87$) and its persistence at the signature level (Cohen $\kappa = 0.87$ between per-CPA-fit and per-signature-fit K=3 binary labels) are nevertheless informative: per-CPA aggregation does not collapse the broad three-region ordering, and three different summarisations of the descriptor space produce broadly concordant per-CPA rankings, with a residual non-Firm-A disagreement (the reverse-anchor cosine percentile ranks Firm D fractionally above Firm C, while the mixture posterior and the box-rule rate rank Firm C highest among non-Firm-A firms).
## F. Pixel-Identity as a Hard Positive Anchor, Inherited Inter-CPA Negative-Anchor FAR
## F. Anchor-Based Multi-Level Calibration
The only hard ground-truth subset in the corpus is pixel-identical signatures: those whose nearest same-CPA match is byte-identical after crop and normalisation. Independent hand-signing cannot produce byte-identical images, so these signatures are conservative-subset ground truth for the *replicated* class. On the Big-4 subset ($n = 262$ pixel-identical signatures), all three candidate classifiers — the inherited box rule, the K=3 hard label, and the reverse-anchor metric with a prevalence-calibrated cut — achieve $0\%$ positive-anchor miss rate (Wilson 95% upper bound $1.45\%$). We caution that this result is necessary but not sufficient: for the box rule it is close to tautological, because byte-identical neighbours have cosine $\approx 1$ and dHash $\approx 0$, well inside the rule's high-confidence region. The corresponding signature-level *negative* anchor (the inter-CPA negative anchor, inherited from v3.20.0 §IV-F.1) provides specificity evidence: at the operational cosine cut of $0.95$, the inter-CPA FAR is $0.0005$ (Wilson 95% CI $[0.0003, 0.0007]$).
The operational specificity of the deployed five-way classifier is characterised at three units of analysis (§III-L), all against the same inter-CPA negative-anchor coincidence-rate proxy. The per-comparison ICCR replicates v3.x's per-comparison rate (cos$>0.95 \to 0.00060$) and extends it to the structural dimension (dHash$\leq 5 \to 0.00129$; joint $\to 0.00014$). The pool-normalised per-signature ICCR captures the deployed rule's effective per-signature rate under inter-CPA candidate-pool replacement ($0.1102$ pooled Big-4 any-pair HC), exposing that the per-comparison rate is not the deployed-rule rate at the per-signature classifier level: the deployed classifier takes max-cosine and min-dHash over a same-CPA pool of size $n_{\text{pool}}$, so the inter-CPA-equivalent rate scales approximately as $1 - (1 - p_{\text{pair}})^{n_{\text{pool}}}$ in the independence limit. The per-document ICCR aggregates to operational alarm-rate units: HC alone $0.18$, the operational HC$+$MC alarm $0.34$.
Two additional findings refine the calibration story. First, the per-pair conditional ICCR for dHash$\leq 5$ given cos$>0.95$ is $0.234$ (Wilson 95% $[0.190, 0.285]$): given the cosine gate, the structural dimension provides further per-comparison specificity at $\sim 4.3\times$ refinement. Second, the alert-rate sensitivity analysis (§III-L.5; Script 46) shows the inherited HC threshold is locally sensitive rather than plateau-stable (local gradient $\approx 25\times$ the median for cosine, $\approx 3.8\times$ for dHash); stakeholders requiring different specificity-alert-yield operating points can derive thresholds by inverting the ICCR curves (a tighter rule cos$>0.95$ AND dHash$\leq 3$ on the same-pair joint gives per-signature ICCR $\approx 0.045$). The MC/HSC sub-band boundary at dHash$=15$, by contrast, *is* plateau-like (local-to-median ratio $\approx 0.08$), consistent with high-dHash-tail saturation.
## G. Pixel-Identity as a Hard Positive Anchor; Inherited Inter-CPA Negative Anchor Reframed as Coincidence Rate
The only hard ground-truth subset in the corpus is pixel-identical signatures: those whose nearest same-CPA match is byte-identical after crop and normalisation. Independent hand-signing cannot produce byte-identical images, so these signatures are conservative-subset ground truth for the *replicated* class. On the Big-4 subset ($n = 262$ pixel-identical signatures), all three candidate classifiers — the inherited box rule, the K=3 hard label, and the reverse-anchor metric with a prevalence-calibrated cut — achieve $0\%$ positive-anchor miss rate (Wilson 95% upper bound $1.45\%$). We caution that this result is necessary but not sufficient: for the box rule it is close to tautological, because byte-identical neighbours have cosine $\approx 1$ and dHash $\approx 0$, well inside the rule's high-confidence region. The corresponding signature-level *negative* anchor evidence is developed in §III-L.1 above (v4 spike: cos$>0.95$ per-comparison ICCR $= 0.00060$, replicating v3.20.0's reported $0.0005$ under prior "FAR" terminology). We frame the per-comparison rate as a specificity proxy under the assumption that inter-CPA pairs constitute a clean negative anchor, and we document in §III-L.4 that this assumption is partially violated by within-firm cross-CPA template-like collision structures.
## G. Limitations
Several limitations should be transparent. The first seven are v4.0-specific; the last five are inherited from v3.20.0 §V-G and still apply to the v4.0 pipeline.
Several limitations should be transparent. The first nine are v4.0-specific; the last five are inherited from v3.20.0 §V-G and still apply to the v4.0 pipeline.
*Scope.* The v4.0 primary analyses are scoped to the Big-4 sub-corpus. Among the comparison scopes tested in Script 32, the Big-4 sub-corpus is the smallest at which the accountant-level dip test rejects unimodality and is the only scope at which the four-fold firm-level LOOO structure exists; we did not test the full $n = 686$ accountant population's dip-test marginals or perform LOOO at that scope. Generalisation to mid- and small-firm contexts is left as future work; the §IV-K full-dataset Spearman re-run shows the K=3 + box-rule rank-convergence is preserved at $n = 686$ but does not validate the Big-4 operational thresholds, the LOOO firm-fold structure, or the five-way operational classifier at the broader scope.
*No signature-level ground truth; no true error rates reportable.* The corpus does not contain labelled hand-signed or replicated classes at the signature level. We therefore cannot report False Rejection Rate, sensitivity, recall, Equal Error Rate, ROC-AUC, precision, or positive predictive value against ground truth. All quantitative rates reported in §III-L are inter-CPA negative-anchor coincidence rates (ICCRs) under the assumption that inter-CPA pairs constitute a clean negative anchor; this is a specificity proxy, not a calibrated specificity (§III-M).
*No signature-level hand-signed ground truth.* The corpus does not contain a labelled hand-signed class at the signature level, so the reverse-anchor score's cut is chosen by prevalence calibration against the inherited box rule's overall replicated rate rather than by direct ROC optimisation. Future work could supplement v4.0 with a small human-rated validation set.
*Inter-CPA negative-anchor assumption is partially violated.* The cross-firm hit matrix of §III-L.4 shows that $98$–$100\%$ of inter-CPA collisions under the deployed rule originate from candidates within the source firm, consistent with firm-specific template, stamp, or document-production reuse. The inter-CPA-as-negative assumption is therefore not exactly satisfied — some inter-CPA pairs may share firm-level templates rather than being independent random matches. Our reported per-comparison ICCRs are best read as specificity-proxy rates under a partially-violated assumption, not as calibrated FARs.
*Scope.* The v4.0 primary analyses are scoped to the Big-4 sub-corpus. We did not perform the full per-signature pool-normalised ICCR analysis at the full $n = 686$ scope; the §IV-K full-dataset Spearman re-run shows the K=3 $+$ box-rule rank-convergence is preserved at $n = 686$ but does not validate the Big-4 operational ICCRs, the LOOO firm-fold structure, or the five-way operational classifier at the broader scope.
*Pixel-identity is a conservative subset.* Byte-identical pairs are the easiest replicated cases, and for the inherited box rule the positive-anchor miss rate against byte-identical pairs is close to tautological (byte-identical $\Rightarrow$ cosine $\approx 1$, dHash $\approx 0$, well inside the high-confidence box). A score that fails the pixel-identity check would be disqualified, but passing the check does not guarantee correct behaviour on the broader replicated population (e.g., re-stamped or noisy-template-variant signatures).
*Inherited rule components are not separately v4-validated.* The five-way classifier's moderate-confidence band (cos $> 0.95$ AND $5 < \text{dHash} \leq 15$), the style-consistency band ($\text{dHash} > 15$), and the document-level worst-case aggregation rule retain their v3.20.0 calibration and capture-rate evidence; v4.0's convergent-checks evidence (§III-K, §IV-F) covers only the binary high-confidence sub-rule.
*Inherited rule components are not separately v4-validated.* The five-way classifier's moderate-confidence band (cos $> 0.95$ AND $5 < \text{dHash} \leq 15$), the style-consistency band ($\text{dHash} > 15$), and the document-level worst-case aggregation rule retain their v3.20.0 calibration and capture-rate evidence; v4.0's anchor-based ICCR calibration covers the binary high-confidence sub-rule (and its tightening alternatives such as dHash$\leq 3$), and the alert-rate sensitivity analysis (§III-L.5) characterises only the HC threshold. The MC and HSC sub-band boundaries are not separately re-validated by v4.0's diagnostic battery.
*Deployed-rate excess is not a presumed true-positive rate.* The $\sim 44$-pp per-document gap between the observed deployed alert rate (HC: $0.62$ on real same-CPA pools) and the inter-CPA proxy rate (HC: $0.18$) cannot be interpreted as a presumed true-positive rate without additional assumptions that §III-M shows are unsafe (consistent within-CPA signing can exceed inter-CPA similarity at the cosine axis; within-firm template sharing inflates the inter-CPA proxy baseline). The gap is best read as a same-CPA repeatability signal.
*A1 pair-detectability stipulation.* The per-signature detector requires at least one same-CPA pair to be near-identical when a CPA uses image replication. A1 is plausible for high-volume stamping or firm-level electronic signing but not guaranteed when a corpus contains only one observed replicated report for a CPA, multiple template variants used in parallel, or scan-stage noise that pushes a replicated pair outside the detection regime.
*Composition sensitivity of K=3.* The K=3 hard-posterior membership for any single firm varies by up to $12.8$ pp across LOOO folds. This is documented as a composition-sensitivity band rather than failure, but it means K=3 hard labels are not used as v4.0 operational classifier output; they are reported only as accountant-level descriptive characterisation.
*K=3 hard-posterior membership is composition-sensitive.* The K=3 hard-posterior membership for any single firm varies by up to $12.8$ pp across LOOO folds. This is documented as a composition-sensitivity band rather than failure, but it means K=3 hard labels are not used as v4.0 operational classifier output; they are reported only as accountant-level descriptive characterisation.
*No partner-level mechanism attribution.* v4.0 reports population-level patterns; it does not perform partner-level mechanism attribution or report-level claims of intent. The signature-level outputs are signature-level quantities throughout.
*No partner-level mechanism attribution.* v4.0 reports population-level patterns; it does not perform partner-level mechanism attribution or report-level claims of intent. The signature-level outputs are signature-level quantities throughout. The within-firm cross-CPA collision concentration of §III-L.4 is consistent with template-like reuse but is not by itself diagnostic of deliberate sharing.
*Transferred ImageNet features (inherited from v3.20.0).* The ResNet-50 feature extractor uses pre-trained ImageNet weights without signature-domain fine-tuning. While our backbone-ablation study (§IV-L, inherited from v3.20.0 §IV-I) and prior literature support the effectiveness of transferred ImageNet features for signature comparison, a signature-domain fine-tuned feature extractor could improve discriminative performance.
@@ -130,11 +142,11 @@ Several limitations should be transparent. The first seven are v4.0-specific; th
# VI. Conclusion and Future Work
We present a fully automated pipeline for detecting non-hand-signed CPA signatures in Taiwan-listed financial audit reports and a methodological framework for characterising and validating it at the Big-4 sub-corpus scope. The pipeline processes raw PDFs through VLM-based page identification, YOLO-based signature detection, ResNet-50 feature extraction, and dual-descriptor (cosine + independent-minimum dHash) similarity computation. The operational output is an inherited Paper A five-way per-signature classifier with worst-case document-level aggregation (§III-L). Applied to 90,282 audit reports filed between 2013 and 2023, the pipeline extracts 182,328 signatures from 758 CPAs, with the Big-4 sub-corpus (437 CPAs / 150,442 signatures) as the primary analytical population.
We present a fully automated pipeline for detecting non-hand-signed CPA signatures in Taiwan-listed financial audit reports and a multi-tool framework for characterising and disclosing its operational behaviour at the Big-4 sub-corpus scope. The pipeline processes raw PDFs through VLM-based page identification, YOLO-based signature detection, ResNet-50 feature extraction, and dual-descriptor (cosine + independent-minimum dHash) similarity computation. The operational output is an inherited Paper A five-way per-signature classifier with worst-case document-level aggregation (§III-L). Applied to 90,282 audit reports filed between 2013 and 2023, the pipeline extracts 182,328 signatures from 758 CPAs, with the Big-4 sub-corpus (437 CPAs at accountant level; 150,442–150,453 signatures at signature level) as the primary analytical population.
Our central methodological contributions are: (1) the identification of the Big-4 sub-corpus as the smallest scope tested at which an accountant-level finite-mixture model is statistically supportable (dip-test $p < 5 \times 10^{-4}$); (2) the recognition that a 2-component mixture at this scope is a firm-mass separator rather than a mechanism boundary, evidenced by leave-one-firm-out instability; (3) a 3-component mixture whose hand-leaning component *shape* is LOOO-reproducible (cos drift $\leq 0.005$, dHash drift $\leq 0.96$, weight drift $\leq 0.023$) while its hard-posterior membership remains composition-sensitive ($1.8$–$12.8$ pp across folds), supporting K=3 as descriptive characterisation rather than operational classifier; (4) three feature-derived scores that converge on the per-CPA hand-leaning ranking at Spearman $\rho \geq 0.879$, with the explicit caveat that the scores share the underlying descriptor pair and are not statistically independent; (5) $0\%$ positive-anchor miss rate on 262 byte-identical Big-4 signatures (Wilson 95% upper bound $1.45\%$); and (6) at the full $n = 686$ CPA scope, the K=3 + box-rule rank-convergence reproduces (Spearman drift $0.007$ from Big-4), demonstrating that this specific convergence is robust to a wider scope while leaving the operational thresholds, the LOOO structure, the five-way classifier, and the pixel-identity check scoped to Big-4.
Our central methodological contributions are: (1) a composition decomposition (Scripts 39b–39e) that establishes the absence of a within-population bimodal antimode in the Big-4 descriptor distribution: the apparent multimodality dissolves under joint firm-mean centring and integer-tie jitter ($p_{\text{median}} = 0.35$), so distributional "natural-threshold" framings of the inherited operating points are not empirically supported; (2) an anchor-based inter-CPA coincidence-rate (ICCR) calibration at three units of analysis — per-comparison ($0.0006$ at cos$>0.95$; $0.0013$ at dHash$\leq 5$; $0.00014$ jointly), pool-normalised per-signature ($0.11$ for the deployed any-pair HC rule), and per-document ($0.34$ for the operational HC$+$MC alarm) — with explicit terminological replacement of "FAR" by "ICCR" given the unsupervised setting; (3) firm heterogeneity quantification: logistic regression with pool-size adjustment gives odds ratios $0.053$, $0.010$, $0.027$ for Firms B/C/D relative to Firm A reference, indicating a large multiplicative effect that pool-size differences do not explain; (4) cross-firm hit matrix evidence that $98$–$100\%$ of inter-CPA collisions under the deployed rule originate from candidates within the source firm, consistent with firm-specific template, stamp, or document-production reuse mechanisms; (5) K=3 mixture demoted from "three mechanism clusters" to a descriptive firm-compositional partition; (6) three feature-derived scores converging on the per-CPA descriptor-position ranking at Spearman $\rho \geq 0.879$, reported as internal consistency rather than external validation; (7) $0\%$ positive-anchor miss rate on 262 byte-identical Big-4 signatures with the conservative-subset caveat; and (8) a nine-tool unsupervised-validation collection (§III-M) that explicitly discloses each tool's untested assumption and positions the system as an anchor-calibrated screening framework with human-in-the-loop review, not as a validated forensic detector.
Future work falls in four directions. *First*, a small-scale human-rated validation set would enable direct ROC optimisation of the reverse-anchor cut and provide a signature-level hand-signed ground truth that v4.0 currently lacks. *Second*, the within-firm composition sensitivity of K=3 hard labels could be addressed with hierarchical mixture models or partial-pooling formulations that explicitly model firm-level random effects. *Third*, the descriptive within-Big-4 component-membership contrast — Firm A's $82\%$ C3-templated hard-posterior concentration and Firm C's $23.5\%$ C1-hand-leaning hard-posterior concentration are accountant-level descriptive features of the K=3 mixture, not validated mechanism-level claims and not currently linked to audit-quality outcomes — invites a companion analysis examining whether such firm-level signing patterns correlate with established audit-quality measures. *Fourth*, generalisation to mid- and small-firm contexts requires either new methodological scope choices (since mid/small-firm samples do not support the dip-test or LOOO structure we use at Big-4) or a different validation framework altogether.
Future work falls in four directions. *First*, a small-scale human-rated validation set would enable direct ROC optimisation and provide signature-level ground truth that v4.0 fundamentally lacks; without such ground truth, no true error rates can be reported. *Second*, the within-firm collision concentration documented in §III-L.4 (98–100% same-firm partners) invites a separate study to distinguish deliberate template sharing from passive firm-level production artefacts (shared scanners, common form templates, identical report-generation infrastructure) — a question the inter-CPA-anchor analysis alone cannot resolve. *Third*, the descriptive Firm A versus Firms B/C/D contrast (per-document HC$+$MC alarm $0.62$ vs $0.09$–$0.16$) — together with v3.x's byte-level evidence of 145 pixel-identical signatures across $\sim 50$ distinct Firm A partners — invites a companion analysis examining whether such firm-level signing patterns correlate with established audit-quality measures. *Fourth*, generalisation to mid- and small-firm contexts requires extending the anchor-based ICCR framework to scopes where firm-level LOOO folds are not available; the §III-I.4 composition diagnostics already document that the absence of within-population bimodality is corpus-universal, so the v4.0 calibration approach in principle generalises, but a full extension with cluster-robust uncertainty quantification is left as future work.
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