Paper A v3.13: resolve Opus 4.7 round-12 + codex gpt-5.5 round-13 findings

Opus 4.7 max-effort round-12 on v3.12 found 1 MAJOR + 7 MINOR residues;
codex gpt-5.5 xhigh round-13 cross-verified 11/11 RESOLVED and caught
one additional cosine-P95 ambiguity Opus missed (methodology L255).
Total 12 text-only edits across 5 files.

MAJOR M1 - Cosine P95→P7.5 terminology residue at two sites that cite
the v3.12-corrected Section III-L but still wrote "P95" (self-
contradiction). Fix: methodology L165 and results L247 both restated
as "whole-sample Firm A P7.5 heuristic" with the 92.5%/7.5%
complement spelled out.

MINOR findings and fixes:
- m1 Big-4 scope slip: methodology III-H(b) L166 and results IV-H.2
  L311 said "every Big-4 auditor-year" but IV-H.2 ranking actually
  pools all 4,629 auditor-years across Big-4 and Non-Big-4. Both
  sites now say "every auditor-year ... across all firms."
- m2 178 vs 180 Firm A CPA breakdown: intro L54 and conclusion L21
  now add "of 180 registered CPAs; 178 after excluding two with
  disambiguation ties, Section IV-G.2" parenthetical to avoid the
  misleading 180−171=9 reading.
- m3 IV-H.1 A2 citation: results L286 now explicitly invokes the
  A2 within-year label-uniformity convention (Section III-G) when
  reading the left-tail share as a partner-level "minority of hand-
  signers."
- m4 IV-F L177 cross-ref / fold distinction: corrected Section III-H
  → Section III-L anchor, and added explicit note that the 0.95
  heuristic is a whole-sample anchor while Table XI thresholds are
  calibration-fold-derived (cosine P5 = 0.9407).
- m5 Table XVI (30,222) vs Table XVII (30,226) Firm A count gap:
  results L406 now explains the 4-report difference (XVI restricts
  to both-signers-Firm-A single-firm two-signer reports; XVII counts
  at-least-one-Firm-A signer under the 84,386-document cohort).
- m6 Methodology L156 "four independent quantitative analyses"
  actually enumerated 6 items: rephrased as "three primary
  independent quantitative analyses plus a fourth strand comprising
  three complementary checks."
- m7 Abstract "cluster into three groups" restored the "smoothly-
  mixed" qualifier to match Discussion V-B and Conclusion L17.
- Codex-caught residue at methodology L255 ("Median, 1st percentile,
  and 95th percentile of signature-level cosine/dHash distributions")
  grammatically applied P95 to cosine too. Rewrote as
  "cosine median, P1, and P5 (lower-tail) and dHash_indep median
  and P95 (upper-tail)" matching Table XI L233 exactly.

No re-computation. All tables (IV-XVIII) and Appendix A numbers
unchanged. Abstract at 249/250 words after smoothly-mixed qualifier.

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

paper/paper_a_introduction_v3.md

@@ -51,7 +51,7 @@ By requiring convergent evidence from both descriptors, we can differentiate *st
 A second distinctive feature is our framing of the calibration reference.
 One major Big-4 accounting firm in Taiwan (hereafter "Firm A") is widely recognized within the audit profession as making substantial use of non-hand-signing for the majority of its certifying partners, while not ruling out that a minority may continue to hand-sign some reports.
 We therefore treat Firm A as a *replication-dominated* calibration reference rather than a pure positive class.
-This framing is important because the statistical signature of a replication-dominated population is visible in our data: Firm A's per-signature cosine distribution is unimodal with a long left tail, 92.5% of Firm A signatures exceed cosine 0.95 but 7.5% fall below, and 32 of the 171 Firm A CPAs with enough signatures to enter our accountant-level analysis (of 180 Firm A CPAs in total) cluster into an accountant-level "middle band" rather than the high-replication mode.
+This framing is important because the statistical signature of a replication-dominated population is visible in our data: Firm A's per-signature cosine distribution is unimodal with a long left tail, 92.5% of Firm A signatures exceed cosine 0.95 but 7.5% fall below, and 32 of the 171 Firm A CPAs with enough signatures to enter our accountant-level analysis (of 180 Firm A CPAs in the registry; 178 after excluding two with disambiguation ties, see Section IV-G.2) cluster into an accountant-level "middle band" rather than the high-replication mode.
 Adopting the replication-dominated framing---rather than a near-universal framing that would have to absorb these residuals as noise---ensures internal coherence among the visual-inspection evidence, the signature-level statistics, and the accountant-level mixture.
 
 A third distinctive feature is our unit-of-analysis treatment.