Paper A v3.7: demote BD/McCrary to density-smoothness diagnostic; add Appendix A

Implements codex gpt-5.4 recommendation (paper/codex_bd_mccrary_opinion.md,
"option (c) hybrid"): demote BD/McCrary in the main text from a co-equal
threshold estimator to a density-smoothness diagnostic, and add a
bin-width sensitivity appendix as an audit trail.

Why: the bin-width sweep (Script 25) confirms that at the signature
level the BD transition drifts monotonically with bin width (Firm A
cosine: 0.987 -> 0.985 -> 0.980 -> 0.975 as bin width widens 0.003 ->
0.015; full-sample dHash transitions drift from 2 to 10 to 9 across
bin widths 1 / 2 / 3) and Z statistics inflate superlinearly with bin
width, both characteristic of a histogram-resolution artifact. At the
accountant level the BD null is robust across the sweep. The paper's
earlier "three methodologically distinct estimators" framing therefore
could not be defended to an IEEE Access reviewer once the sweep was
run.

Added
- signature_analysis/25_bd_mccrary_sensitivity.py: bin-width sweep
  across 6 variants (Firm A / full-sample / accountant-level, each
  cosine + dHash_indep) and 3-4 bin widths per variant. Reports
  Z_below, Z_above, p-values, and number of significant transitions
  per cell. Writes reports/bd_sensitivity/bd_sensitivity.{json,md}.
- paper/paper_a_appendix_v3.md: new "Appendix A. BD/McCrary Bin-Width
  Sensitivity" with Table A.I (all 20 sensitivity cells) and
  interpretation linking the empirical pattern to the main-text
  framing decision.
- export_v3.py: appendix inserted into SECTIONS between conclusion
  and references.
- paper/codex_bd_mccrary_opinion.md: codex gpt-5.4 recommendation
  captured verbatim for audit trail.

Main-text reframing
- Abstract: "three methodologically distinct estimators" ->
  "two estimators plus a Burgstahler-Dichev/McCrary density-
  smoothness diagnostic". Trimmed to 243 words.
- Introduction: related-work summary, pipeline step 5, accountant-
  level convergence sentence, contribution 4, and section-outline
  line all updated. Contribution 4 renamed to "Convergent threshold
  framework with a smoothness diagnostic".
- Methodology III-I: section renamed to "Convergent Threshold
  Determination with a Density-Smoothness Diagnostic". "Method 2:
  BD/McCrary Discontinuity" converted to "Density-Smoothness
  Diagnostic" in a new subsection; Method 3 (Beta mixture) renumbered
  to Method 2. Subsections 4 and 5 updated to refer to "two threshold
  estimators" with BD as diagnostic.
- Methodology III-A pipeline overview: "three methodologically
  distinct statistical methods" -> "two methodologically distinct
  threshold estimators complemented by a density-smoothness
  diagnostic".
- Methodology III-L: "three-method analysis" -> "accountant-level
  threshold analysis (KDE antimode, Beta-2 crossing, logit-Gaussian
  robustness crossing)".
- Results IV-D.1 heading: "BD/McCrary Discontinuity" ->
  "BD/McCrary Density-Smoothness Diagnostic". Prose now notes the
  Appendix-A bin-width instability explicitly.
- Results IV-E: Table VIII restructured to label BD rows
  "(diagnostic only; bin-unstable)" and "(diagnostic; null across
  Appendix A)". Summary sentence rewritten to frame BD null as
  evidence for clustered-but-smoothly-mixed rather than as a
  convergence failure. Table cosine P5 row corrected from 0.941 to
  0.9407 to match III-K.
- Results IV-G.3 and IV-I.2: "three-method convergence/thresholds"
  -> "accountant-level convergent thresholds" (clarifies the 3
  converging estimates are KDE antimode, Beta-2, logit-Gaussian,
  not KDE/BD/Beta).
- Discussion V-B: "three-method framework" -> "convergent threshold
  framework".
- Conclusion: "three methodologically distinct methods" -> "two
  threshold estimators and a density-smoothness diagnostic";
  contribution 3 restated; future-work sentence updated.
- Impact Statement (archived): "three methodologically distinct
  threshold-selection methods" -> "two methodologically distinct
  threshold estimators plus a density-smoothness diagnostic" so the
  archived text is internally consistent if reused.

Discussion V-B / V-G already framed BD as a diagnostic in v3.5
(unchanged in this commit). The reframing therefore brings Abstract /
Introduction / Methodology / Results / Conclusion into alignment with
the Discussion framing that codex had already endorsed.

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

paper/paper_a_conclusion_v3.md

@@ -3,7 +3,7 @@
 ## Conclusion
 
 We have presented an end-to-end AI pipeline for detecting non-hand-signed auditor signatures in financial audit reports at scale.
-Applied to 90,282 audit reports from Taiwanese publicly listed companies spanning 2013--2023, our system extracted and analyzed 182,328 CPA signatures using a combination of VLM-based page identification, YOLO-based signature detection, deep feature extraction, and dual-descriptor similarity verification, with threshold selection placed on a statistically principled footing through three methodologically distinct methods applied at two analysis levels.
+Applied to 90,282 audit reports from Taiwanese publicly listed companies spanning 2013--2023, our system extracted and analyzed 182,328 CPA signatures using a combination of VLM-based page identification, YOLO-based signature detection, deep feature extraction, and dual-descriptor similarity verification, with threshold selection placed on a statistically principled footing through two methodologically distinct threshold estimators and a density-smoothness diagnostic applied at two analysis levels.
 
 Our contributions are fourfold.
 
@@ -11,7 +11,7 @@ First, we argued that non-hand-signing detection is a distinct problem from sign
 
 Second, we showed that combining cosine similarity of deep embeddings with difference hashing is essential for meaningful classification---among 71,656 documents with high feature-level similarity, the dual-descriptor framework revealed that only 41% exhibit converging structural evidence of non-hand-signing while 7% show no structural corroboration despite near-identical feature-level appearance, demonstrating that a single-descriptor approach conflates style consistency with image reproduction.
 
-Third, we introduced a three-method threshold framework combining KDE antimode (with a Hartigan unimodality test), Burgstahler-Dichev / McCrary discontinuity, and EM-fitted Beta mixture (with a logit-Gaussian robustness check).
+Third, we introduced a convergent threshold framework combining two methodologically distinct estimators---KDE antimode (with a Hartigan unimodality test) and an EM-fitted Beta mixture (with a logit-Gaussian robustness check)---together with a Burgstahler-Dichev / McCrary density-smoothness diagnostic.
 Applied at both the signature and accountant levels, this framework surfaced an informative structural asymmetry: at the per-signature level the distribution is a continuous quality spectrum for which no two-mechanism mixture provides a good fit, whereas at the per-accountant level BIC cleanly selects a three-component mixture and the KDE antimode together with the Beta-mixture and logit-Gaussian estimators agree within $\sim 0.006$ at cosine $\approx 0.975$.
 The Burgstahler-Dichev / McCrary test, by contrast, finds no significant transition at the accountant level, consistent with clustered but smoothly mixed rather than sharply discrete accountant-level heterogeneity.
 The substantive reading is therefore narrower than "discrete behavior": *pixel-level output quality* is continuous and heavy-tailed, and *accountant-level aggregate behavior* is clustered with smooth cluster boundaries.
@@ -26,7 +26,7 @@ An ablation study comparing ResNet-50, VGG-16 and EfficientNet-B0 confirmed that
 
 Several directions merit further investigation.
 Domain-adapted feature extractors, trained or fine-tuned on signature-specific datasets, may improve discriminative performance beyond the transferred ImageNet features used in this study.
-Extending the accountant-level analysis to auditor-year units---using the same three-method convergent framework but at finer temporal resolution---could reveal within-accountant transitions between hand-signing and non-hand-signing over the decade.
+Extending the accountant-level analysis to auditor-year units---using the same convergent threshold framework at finer temporal resolution---could reveal within-accountant transitions between hand-signing and non-hand-signing over the decade.
 The pipeline's applicability to other jurisdictions and document types (e.g., corporate filings in other countries, legal documents, medical records) warrants exploration.
 The replication-dominated calibration strategy and the pixel-identity anchor technique are both directly generalizable to settings in which (i) a reference subpopulation has a known dominant mechanism and (ii) the target mechanism leaves a byte-level signature in the artifact itself.
 Finally, integration with regulatory monitoring systems and a larger negative-anchor study---for example drawing from inter-CPA pairs under explicit accountant-level blocking---would strengthen the practical deployment potential of this approach.