Phase 6 round-6: soften firm-heterogeneity framing, fix DOCX table render

Framing softening (per partner tone decision: own the limitation rather
than defend the strong claim).

Abstract: "Firm heterogeneity is decisive ... consistent with firm-level
template-like reuse" -> "The framework surfaces pronounced firm-level
heterogeneity ... consistent with firm-level template-like reuse but not
independently diagnostic, since descriptor-only data cannot separate
reuse from digitisation-pipeline or signing-style homogeneity within a
firm; we report it as a scope limitation rather than a mechanism finding."

S V-H Limitations: new bullet "Mechanism attribution for the firm-level
heterogeneity is not identifiable from descriptor-only data." enumerates
three non-mutually-exclusive firm-level mechanisms (template-like reuse /
digitisation-pipeline homogeneity / signing-style homogeneity), notes the
(cosine, dHash) descriptor pair is by construction indifferent to which
mechanism generated a near-identical pair, and lists what additional data
would be needed for attribution.

S VI Conclusion items (3) and (4): "firm heterogeneity quantification" ->
"firm-level heterogeneity surfaced by the framework ... reported as a
framework-discriminative observation rather than a mechanism finding";
item (4) expanded from template/stamp/document-production reuse alone to
the three-mechanism scope, with explicit "not independently establishing"
and S V-H cross-reference.

DOCX export fix (export_v3.py): add missing LaTeX-to-Unicode tokens
(\checkmark, \lvert/\rvert, \lVert/\rVert, \in, \notin, \max, \min,
\log, \ln, \exp, \bullet) that were silently dropping content from
Table III rows 2-4 (integer-jitter robustness check marks empty) and
Table XVIII drift column (|Delta| empty).

Rebuild Paper_A_IEEE_Access_Draft_v3.docx via export_v3.py and install
copy as Paper_A_IEEE_Access_Draft_v4.0_20260515.docx (replaces prior
pandoc-built v4 DOCX which had empty cells in every table header with
LaTeX math and inconsistent column widths). All 43 tables now have
non-empty cells with sub/superscript runs.

Mirrored in paper_a_v4_combined.md for consistency with the single-file
combined source.

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

paper/paper_a_conclusion_v3.md

@@ -2,6 +2,6 @@
 
 We present a fully automated pipeline for screening non-hand-signed CPA signatures in Taiwan-listed financial audit reports, together with an anchor-calibrated screening framework that characterises the pipeline's operational behaviour at the Big-4 sub-corpus scope under explicit unsupervised assumptions. 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 the deployed five-way per-signature classifier with worst-case document-level aggregation (§III-H.1; calibrated in §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) a composition decomposition 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 deployed 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 under the deployed any-pair rule, within-firm collision concentration is $98.8\%$ at Firm A and $76.7$–$83.7\%$ at Firms B/C/D (the stricter same-pair joint event saturates at $97.0$–$99.96\%$ within-firm across all four firms), 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) explicit disclosure of each diagnostic's untested assumption (Appendix A Table A.II), positioning the system as an anchor-calibrated screening framework with human-in-the-loop review rather than as a validated forensic detector.
+Our central methodological contributions are: (1) a composition decomposition 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 deployed 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-level heterogeneity surfaced by the framework: 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, a contrast that pool-size differences do not explain and that we report as a framework-discriminative observation rather than a mechanism finding (§V-H); (4) cross-firm hit matrix evidence that under the deployed any-pair rule, within-firm collision concentration is $98.8\%$ at Firm A and $76.7$–$83.7\%$ at Firms B/C/D (the stricter same-pair joint event saturates at $97.0$–$99.96\%$ within-firm across all four firms), consistent with — but not independently establishing — firm-level template-like reuse, digitisation-pipeline homogeneity, or signing-style similarity, which descriptor-only data cannot separate (§V-H); (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) explicit disclosure of each diagnostic's untested assumption (Appendix A Table A.II), positioning the system as an anchor-calibrated screening framework with human-in-the-loop review rather than as a validated forensic detector.
 
 Future work falls in four directions. *First*, a small-scale human-rated labelled set would enable direct ROC optimisation and provide the signature-level ground truth that the present analysis fundamentally lacks; without such ground truth, no true error rates can be reported. *Second*, the within-firm collision concentration documented in §III-L.4 (any-pair $76.7$–$98.8\%$ across Big-4; same-pair joint $97.0$–$99.96\%$) 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 the 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 holds across the tested eligible scopes, so the calibration approach in principle generalises, but a full extension with cluster-robust uncertainty quantification is left as future work.