Paper A v3.12: resolve Gemini 3.1 Pro round-11 full-paper review findings

Round-11 Gemini 3.1 Pro fresh full-paper review (Minor Revision)
surfaced four issues that the prior 10 rounds (codex gpt-5.4 x4, codex
gpt-5.5 x1, Gemini 3.1 Pro x2, Opus 4.7 x1, paragraph-level v3.11
review) all missed:

1. MAJOR - Percentile-terminology contradiction between Section III-L
   L290 and Section III-H L160. III-L called 0.95 the "whole-sample
   Firm A P95" of the per-signature best-match cosine distribution,
   but III-H states 92.5% of Firm A signatures exceed 0.95. Under
   standard bottom-up percentile convention this makes 0.95 the P7.5,
   not the P95; Table XI calibration-fold data (Firm A cosine
   median = 0.9862, P5 = 0.9407) confirms true P95 is near 0.998.
   Fix: rewrote III-L L290 to state 0.95 corresponds to approximately
   the whole-sample Firm A P7.5 with the 92.5%/7.5% complement stated
   explicitly. dHash P95 claims elsewhere (Table XI, L229/L233) were
   already correct under standard convention and are unchanged.

2. MINOR - Firm A CPA count inconsistency. Discussion V-C L44 said
   "Nine additional Firm A CPAs are excluded from the GMM for having
   fewer than 10 signatures" but Results IV-G.2 L216 defines 178
   valid Firm A CPAs (180 registry minus 2 disambiguation-excluded);
   178 - 171 = 7. Fix: corrected to "seven are outside the GMM" with
   explicit 178-baseline and cross-reference to IV-G.2.

3. MINOR - Table XVI mixed-firm handling broken promise. Results
   L355-356 previously said "mixed-firm reports are reported
   separately" but Table XVI only lists single-firm rows summing to
   exactly 83,970, and no subsequent prose reports the 384 mixed-firm
   agreement rate. Fix: rewrote L355-356 to state Table XVI covers
   the 83,970 single-firm reports only and that the 384 mixed-firm
   reports (0.46%) are excluded because firm-level agreement is not
   well defined when the two signers are at different firms.

4. MINOR - Contribution-count structural inconsistency. Introduction
   enumerates seven contributions, Conclusion opens with "Our
   contributions are fourfold." Fix: rewrote the Conclusion lead to
   "The seven numbered contributions listed in Section I can be
   grouped into four broader methodological themes," making the
   grouping explicit.

No re-computation. All tables (IV-XVIII) and Appendix A numbers
unchanged. Abstract unchanged (still 248/250 words).

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

paper/paper_a_discussion_v3.md

@@ -41,7 +41,7 @@ Three convergent strands of evidence support the replication-dominated framing.
 First, the visual-inspection evidence: randomly sampled Firm A reports exhibit pixel-identical signature images across different audit engagements and fiscal years for the majority of partners---a physical impossibility under independent hand-signing events.
 Second, the signature-level statistical evidence: Firm A's per-signature cosine distribution is unimodal long-tail rather than a tight single peak; 92.5% of Firm A signatures exceed cosine 0.95, with the remaining 7.5% forming the left tail.
 Third, the accountant-level evidence: of the 171 Firm A CPAs with enough signatures ($\geq 10$) to enter the accountant-level GMM, 32 (19%) fall into the middle-band C2 cluster rather than the high-replication C1 cluster---consistent with within-firm heterogeneity in signing practice (spanning a minority of hand-signers, CPAs undergoing mid-sample mechanism transitions, and CPAs whose pooled coordinates reflect mixed-quality replication) rather than a pure replication population.
-Nine additional Firm A CPAs are excluded from the GMM for having fewer than 10 signatures, so we cannot place them in a cluster from the cross-sectional analysis alone.
+Of the 178 valid Firm A CPAs (the 180 registered CPAs minus two excluded for disambiguation ties in the registry; Section IV-G.2), seven are outside the GMM for having fewer than 10 signatures, so we cannot place them in a cluster from the cross-sectional analysis alone.
 The held-out Firm A 70/30 validation (Section IV-G.2) gives capture rates on a non-calibration Firm A subset that sit in the same replication-dominated regime as the calibration fold across the full range of operating rules (extreme rules are statistically indistinguishable; operational rules in the 85–95% band differ between folds by 1–5 percentage points, reflecting within-Firm-A heterogeneity in replication intensity rather than a generalization failure).
 The accountant-level GMM (Section IV-E) and the threshold-independent partner-ranking analysis (Section IV-H.2) are the cross-checks that are robust to fold-level sampling variance.