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_impact_statement_v3.md

@@ -17,5 +17,5 @@ external use.
 Auditor signatures on financial reports are a key safeguard of corporate accountability.
 When the signature on an audit report is produced by reproducing a stored image instead of by the partner's own hand---whether through an administrative stamping workflow or a firm-level electronic signing system---this safeguard is weakened, yet detecting the practice through manual inspection is infeasible at the scale of modern financial markets.
 We developed a pipeline that automatically extracts and analyzes signatures from over 90,000 audit reports spanning a decade of filings by publicly listed companies in Taiwan.
-Combining deep-learning visual features with perceptual hashing and three methodologically distinct threshold-selection methods, the system stratifies signatures into a five-way confidence-graded classification and quantifies how the practice varies across firms and over time.
+Combining deep-learning visual features with perceptual hashing and two methodologically distinct threshold estimators (plus a density-smoothness diagnostic), the system stratifies signatures into a five-way confidence-graded classification and quantifies how the practice varies across firms and over time.
 After further validation, the technology could support financial regulators in screening signature authenticity at national scale.