Paper A v3.15: resolve Gemini 3.1 Pro round-15 Accept-verdict minor polish

Gemini 3.1 Pro round-15 full-paper review of v3.14 returned Accept
with four MINOR polish suggestions. All four applied in this commit.

1. Table XIII column header: "mean cosine" renamed to
   "mean best-match cosine" to match the underlying metric (per-
   signature best-match over the full same-CPA pool) and prevent
   readers from inferring a simpler per-year statistic.

2. Methodology III-L (L284): added a forward-pointer in the first
   threshold-convention note to Section IV-G.3, explicitly confirming
   that replacing the 0.95 round-number heuristic with the nearby
   accountant-level 2D-GMM marginal crossing 0.945 alters aggregate
   firm-level capture rates by at most ~1.2 percentage points. This
   pre-empts a reader who might worry about the methodological
   tension between the heuristic and the mixture-derived convergence
   band.

3. Results IV-I document-level aggregation (L383): "Document-level
   rates therefore bound the share..." rewritten as "represent the
   share..." Gemini correctly noted that worst-case aggregation
   directly assigns (subject to classifier error), so "bound"
   spuriously implies an inequality not actually present.

4. Results IV-G.4 Sanity Sample (L273): "inter-rater agreement with
   the classifier" rewritten as "full human--classifier agreement
   (30/30)". Inter-rater conventionally refers to human-vs-human
   agreement; human-vs-classifier is the correct term here.

No substantive changes; no tables recomputed.

Gemini round-15 verdict was Accept with these four items framed
as nice-to-have rather than blockers; applying them brings v3.15
to a fully polished state before manual DOCX packaging.

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

paper/paper_a_methodology_v3.md

@@ -282,6 +282,7 @@ High feature-level similarity without structural corroboration---consistent with
 
 We note three conventions about the thresholds.
 First, the cosine cutoff $0.95$ corresponds to approximately the whole-sample Firm A P7.5 of the per-signature best-match cosine distribution---that is, 92.5% of whole-sample Firm A signatures exceed this cutoff and 7.5% fall at or below it (Section III-H)---chosen as a round-number lower-tail boundary whose complement (92.5% above) has a transparent interpretation in the whole-sample reference distribution; the cosine crossover $0.837$ is the all-pairs intra/inter KDE crossover; both are derived from whole-sample distributions rather than from the 70% calibration fold, so the classifier inherits its operational cosine cuts from the whole-sample Firm A and all-pairs distributions.
+Section IV-G.3 reports a sensitivity check confirming that replacing $0.95$ with the nearby accountant-level 2D-GMM marginal crossing $0.945$ alters aggregate firm-level capture rates by at most $\approx 1.2$ percentage points, so the round-number heuristic is robust to mixture-derived alternatives within the accountant-level convergence band.
 Section IV-G.2 reports both calibration-fold and held-out-fold capture rates for this classifier so that fold-level sampling variance is visible.
 Second, the dHash cutoffs $\leq 5$ and $> 15$ are chosen from the whole-sample Firm A $\text{dHash}_\text{indep}$ distribution: $\leq 5$ captures the upper tail of the high-similarity mode (whole-sample Firm A median $\text{dHash}_\text{indep} = 2$, P75 $\approx 4$, so $\leq 5$ is the band immediately above median), while $> 15$ marks the regime in which independent-minimum structural similarity is no longer indicative of image reproduction.
 Third, the three accountant-level 1D estimators (KDE antimode $0.973$, Beta-2 crossing $0.979$, logit-GMM-2 crossing $0.976$) and the accountant-level 2D GMM marginal ($0.945$) are *not* the operational thresholds of this classifier: they are the *convergent external reference* that supports the choice of signature-level operational cut.