# Paper A v4.0 Phase 4 Prose Draft v2 (post codex round 26)

> **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`.

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# Abstract

> *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).

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# I. Introduction

> *Target: ~1.5 pages double-column IEEE format. Double-blind: no author/institution info.*

Financial audit reports serve as a critical mechanism for ensuring corporate accountability and investor protection. In Taiwan, the Certified Public Accountant Act (會計師法 §4) and the Financial Supervisory Commission's attestation regulations (查核簽證核准準則 §6) require certifying CPAs to affix their signature or seal (簽名或蓋章) to each audit report [1]. While the law permits either a handwritten signature or a seal, the CPA's attestation on each report is intended to represent a deliberate, individual act of professional endorsement for that specific audit engagement [2].

The digitization of financial reporting has introduced a practice that complicates this intent. As audit reports are now routinely generated, transmitted, and archived as PDF documents, it is technically and operationally straightforward to reproduce a CPA's stored signature image across many reports rather than re-executing the signing act for each one. This reproduction can occur either through an administrative stamping workflow — in which scanned signature images are affixed by staff as part of the report-assembly process — or through a firm-level electronic signing system that automates the same step. We refer to signatures produced by either workflow collectively as *non-hand-signed*. Although this practice may fall within the literal statutory requirement of "signature or seal," it raises substantive concerns about audit quality, as an identically reproduced signature applied across hundreds of reports may not represent meaningful individual attestation for each engagement. The accounting literature has examined the audit-quality consequences of partner-level engagement transparency: studies of partner-signature mandates in the United Kingdom find measurable downstream effects [31], cross-jurisdictional evidence on individual partner signature requirements highlights similar quality channels [32], and Taiwan-specific evidence on mandatory partner rotation documents how individual-partner identification interacts with audit-quality outcomes [33]. Unlike traditional signature forgery, where a third party attempts to imitate another person's handwriting, non-hand-signing involves the legitimate signer's own stored signature being reused, and is visually invisible to report users at scale.

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.

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).

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.

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.

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.

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.

The contributions of this paper are:

1. **Problem formulation.** We define non-hand-signing detection as distinct from signature forgery detection and frame it as a detection problem on intra-signer similarity distributions.

2. **End-to-end pipeline.** We present a pipeline that processes raw PDF audit reports through VLM-based page identification, YOLO-based signature detection, ResNet-50 feature extraction, and dual-descriptor similarity computation, with automated inference and no manual intervention after initial training.

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.

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.

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.

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).

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.

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.

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# II. Related Work

> *Note for the Phase 4 review pass: §II is inherited substantively unchanged from v3.20.0 §II in the master manuscript, with one new paragraph added below. The unchanged content is not reproduced in this Phase 4 file; readers reviewing this draft should consult `paper/paper_a_related_work_v3.md` for the v3.20.0 §II text covering offline signature verification, near-duplicate detection, copy-move forgery detection, perceptual hashing, deep-feature similarity, and the statistical methods adopted (Hartigan dip test, finite mixture EM, Burgstahler-Dichev / McCrary density-smoothness diagnostic). The paragraph below is the only v4.0-specific §II addition.*

**Addition for v4.0: leave-one-firm-out cross-validation in a small-cluster scope.** Cross-validation methodology in the leave-one-out tradition has been developed extensively in statistics since Stone [42] and Geisser [43], and modern surveys including Vehtari et al. [44] discuss its application to mixture models. In document-forensics calibration the technique has been used selectively, typically with the individual document or signature as the hold-out unit. Our application in §III-K differs in two respects from the standard usage: (i) the hold-out unit is the *firm* (not the individual CPA or signature), so the analysis directly probes cross-firm reproducibility of the fitted mixture rather than within-firm sampling variance; and (ii) the held-out predictions are interpreted as a *composition-sensitivity band* on the candidate mixture boundary, not as a sufficiency claim for the inherited five-way operational classifier (which is calibrated separately; §III-L). We treat LOOO drift as descriptive information about how the mixture characterisation moves when training composition changes, not as a pass/fail test for the operational classifier. Numerical references [42]–[44] are placeholders in this draft and will be replaced with the project's preferred references at copy-edit time.

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# V. Discussion

## A. Non-Hand-Signing Detection as a Distinct Problem

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

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).

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).

## 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.

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.

## D. K=2 is Firm-Mass Driven; K=3 is Reproducible in Shape

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.

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.

## 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).

## F. Pixel-Identity as a Hard Positive Anchor, Inherited Inter-CPA Negative-Anchor FAR

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 $[0.0003, 0.0007]$).

## 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.

*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 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.

*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.

*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.

*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.

*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.

*Red-stamp HSV preprocessing artifacts (inherited from v3.20.0).* The red stamp removal preprocessing uses simple HSV color-space filtering, which may introduce artifacts where handwritten strokes overlap with red seal impressions. Blended pixels are replaced with white, potentially creating small gaps in signature strokes that could reduce dHash similarity. This bias would push classifications toward false negatives rather than false positives.

*Longitudinal scan / PDF / compression confounds (inherited from v3.20.0).* Scanning equipment, PDF generation software, and compression algorithms may have changed over the 2013–2023 study period, potentially affecting similarity measurements. While cosine similarity and dHash are designed to be robust to such variations, longitudinal confounds cannot be entirely excluded.

*Source-exemplar misattribution in max/min pair logic (inherited from v3.20.0).* The max-cosine / min-dHash detection logic treats both ends of a near-identical same-CPA pair as non-hand-signed. In the rare case where one of the two documents contains a genuinely hand-signed exemplar that was subsequently reused as a stamping or e-signature template, the pair correctly identifies image reuse but misattributes non-hand-signed status to the source exemplar. This affects at most one source document per template variant per CPA and is not expected to be common.

*Legal and regulatory interpretation (inherited from v3.20.0).* Whether non-hand-signing of a CPA's own stored signature constitutes a violation of signing requirements is a jurisdiction-specific legal question. Our technical analysis can inform such determinations but cannot resolve them.

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# 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.

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.

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.

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## Notes for Phase 4 close-out

Items remaining for the Phase 4 close-out pass before §I, §II, §V, §VI prose can be moved into the manuscript master file:

1. **Abstract word count.** Current draft is 243–244 words (shell `wc -w` on the paragraph returns 243; one-token tokenization difference depending on counter); both satisfy IEEE Access's $\leq 250$ word constraint with $\sim 6$ words of margin.
2. **§I contributions list (8 items).** v3.20.0's contribution list had 7 items; v4.0's has 8 to reflect the Big-4 scope, K=3 descriptive role, and three-score convergence as separate contributions. Confirm whether the journal style supports 8 contributions or whether items can be merged.
3. **§II Related Work LOOO citation.** A standard cross-validation citation for the LOOO addition is flagged "[add citation]" in the draft and needs to be filled with a specific reference (Geisser 1975 / Stone 1974 / a modern survey).
4. **§V-G Limitations.** The seven limitations are listed flat; the journal style may prefer them grouped (scope vs ground-truth vs methodology) — consider reorganisation at copy-edit time.
5. **§VI Future Work directions.** Four directions are listed; the third (audit-quality companion analysis) ties to the Paper B placeholder in the project memory and should be cross-checked for consistency with the planned Paper B framing.
6. **Internal draft note + this close-out checklist.** Strip before submission packaging, per the across-paper "internal — remove before submission" policy applied to §III v6 and §IV v3.2 draft notes.
