Phase 6 round-7 codex 3-axis review fixes: 11 MAJOR + 5 MINOR

Codex GPT-5.5 3-axis peer review (paper/codex_review_gpt55_v4_round_3axis.md)
identified 11 MAJOR + 5 MINOR + 0 BLOCKER on three axes: (1) abstract/body
tone consistency, (2) methodology clarity / v3 residue, (3) no implicit
within-CPA or cross-year signature-consistency assumptions. 13 patches
applied across 4 source files; mirrored in paper_a_v4_combined.md.

Axis 1 (tone consistency between abstract and body):
- S I L33: "resolves the ambiguity" -> "provides complementary evidence
  for screening cases where ... hypotheses diverge"
- S I L35: "disproves the distributional-threshold path" -> "does not
  support the distributional-threshold path"
- S I L37 / S V-F L29: "characterise the deployed five-way classifier
  at three units" -> "characterise the deployed HC sub-rule and
  document-level HC+MC alarm derived from the five-way classifier at
  three units" (consistent with S V-H which says only HC sub-rule and
  HC+MC alarm are re-characterised by the present ICCR battery)
- S I L39 / S V-C / S III-L.4: "consistent with firm-specific template,
  stamp, or document-production reuse mechanisms" -> "consistent with --
  but does not independently establish -- firm-level template-like
  reuse, digitisation-pipeline homogeneity, or signing-style
  homogeneity, which descriptor-only data cannot separate (S V-H)"
  (mirrors abstract)

Axis 2 (methodology clarity / v3 residue):
- S III-G: added unit-bridge sentence distinguishing "descriptor-summary
  units" (signature/accountant) from "operational reporting units"
  (per-comparison/per-signature/per-document, S III-L)
- S III-H.2: "The calibration distinguishes two reference populations"
  -> "The supporting diagnostics use two reference populations" with
  explicit "neither is the calibration anchor"
- S III-L.1: "specificity" -> "ICCR refinement"
- S III-L.2: added "descriptive intuition, not an independence
  assumption used for estimation" caveat after the 1-(1-p)^n form

Axis 3 (no implicit signature-consistency assumptions):
- S III-F: hand-signing motivation rewritten as working hypothesis that
  "the classifier does not require ... to hold for all CPAs"
- S III-G A1: added "A1 does not assume temporal stability of
  handwriting or scanning workflow within or across years"
- S III-H.1: added label-caveat paragraph (operational rule outputs,
  not validated ground-truth classes); HC "strong replication evidence"
  -> "image-similarity evidence consistent with replication"; HSC
  "consistent with a CPA who signs very consistently" -> "mechanism not
  resolved by descriptor data alone"; LH explicitly owns that
  cross-year handwriting drift, scanner workflow change, or template
  variant rotation can also yield low max-cosine within a same-CPA pool
- S III-L.6 / S IV-M.6: "same-CPA repeatability signal" -> "observed
  same-CPA-pool excess ... not attributed to within-CPA handwriting
  repeatability"

Deferred (structural, not single-sentence patch): codex S III-I.2 /
S III-J K=2/K=3 deduplication; codex S III-K LOOO / S III-J duplication.
Both are MINOR stylistic redundancies, not reviewer-rejection risks.

DOCX rebuilt via export_v3.py; v4.0_20260515 file refreshed.

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

paper/paper_a_discussion_v3.md

@@ -12,7 +12,7 @@ The Big-4 accountant-level descriptor distribution rejects unimodality on both m
 
 Firm A is empirically the firm whose CPAs are most concentrated in the high-cosine, low-dHash corner of the Big-4 descriptor plane. In the Big-4 K=3 hard-posterior assignment (now interpreted as a firm-compositional position assignment; §III-J), Firm A accounts for $0\%$ of C1 (low-cos / high-dHash position) and $82.5\%$ of C3 (high-cos / low-dHash position); the opposite pattern holds at Firm C, which has the highest C1 concentration at $23.5\%$. Firm A also accounts for 145 of the 262 byte-identical signatures in the Big-4 byte-identical anchor of §IV-H (with Firm B 8, Firm C 107, Firm D 2). Byte-level decomposition of the 145 Firm A pixel-identical signatures (see supplementary materials) shows they span 50 distinct Firm A partners (of 180 registered), with 35 byte-identical matches occurring across different fiscal years.
 
-We treat Firm A as a *templated-end case study within the Big-4 sub-corpus* rather than as the calibration anchor for the operational threshold. Firm A enters the Big-4 anchor-based ICCR calibration on equal footing with the other three Big-4 firms (§III-L). The cross-firm hit matrix of §III-L.4 strengthens this framing: under the deployed any-pair rule, within-firm collision concentration is $98.8\%$ at Firm A and $76.7$–$83.7\%$ at Firms B/C/D (the stricter same-pair joint event saturates at $97.0$–$99.96\%$ within-firm across all four firms). Firm A's per-document D2 inter-CPA proxy ICCR of $0.6201$ (versus Firms B/C/D's $0.09$–$0.16$) — the counterfactual rate at which Firm A documents would fire HC$+$MC if same-CPA pools were replaced by random inter-CPA candidates — reflects high inter-CPA collision concentration under the deployed rule, consistent with firm-specific template, stamp, or document-production reuse. (The corresponding observed rate on real same-CPA pools, from Table XVI, is substantially higher: $97.5\%$ HC$+$MC for Firm A; the proxy and observed rates measure different quantities and are not directly comparable.) The inter-CPA-anchor analysis alone is not diagnostic of deliberate template sharing. The byte-level evidence above (Firm A's 145 pixel-identical signatures across $\sim 50$ distinct partners) provides direct evidence of image-level reuse among Firm A signatures; the distribution across many partners is consistent with a firm-level template or production workflow, and the within-firm collision pattern at all four Big-4 firms is consistent with similar, milder production-related reuse patterns at Firms B/C/D.
+We treat Firm A as a *templated-end case study within the Big-4 sub-corpus* rather than as the calibration anchor for the operational threshold. Firm A enters the Big-4 anchor-based ICCR calibration on equal footing with the other three Big-4 firms (§III-L). The cross-firm hit matrix of §III-L.4 strengthens this framing: under the deployed any-pair rule, within-firm collision concentration is $98.8\%$ at Firm A and $76.7$–$83.7\%$ at Firms B/C/D (the stricter same-pair joint event saturates at $97.0$–$99.96\%$ within-firm across all four firms). Firm A's per-document D2 inter-CPA proxy ICCR of $0.6201$ (versus Firms B/C/D's $0.09$–$0.16$) — the counterfactual rate at which Firm A documents would fire HC$+$MC if same-CPA pools were replaced by random inter-CPA candidates — reflects high inter-CPA collision concentration under the deployed rule, consistent with firm-specific template, stamp, or document-production reuse. (The corresponding observed rate on real same-CPA pools, from Table XVI, is substantially higher: $97.5\%$ HC$+$MC for Firm A; the proxy and observed rates measure different quantities and are not directly comparable.) The inter-CPA-anchor analysis alone is not diagnostic of deliberate template sharing. The byte-level evidence above (Firm A's 145 pixel-identical signatures across $\sim 50$ distinct partners) provides direct evidence of image-level reuse among Firm A signatures; the distribution across many partners is consistent with a firm-level template or production workflow, and the within-firm collision pattern at all four Big-4 firms is consistent with similar, milder within-firm collision patterns at Firms B/C/D, whose mechanisms may include template-like reuse, digitisation-pipeline homogeneity, or signing-style homogeneity (§V-H).
 
 ## D. K=2 / K=3 as Descriptive Firm-Compositional Partitions
 
@@ -26,7 +26,7 @@ Three feature-derived scores agree on the per-CPA descriptor-position ranking at
 
 ## F. Anchor-Based Multi-Level Calibration
 
-The operational specificity-proxy behaviour of the deployed five-way classifier is characterised at three units of analysis (§III-L), all against the same inter-CPA negative-anchor coincidence-rate proxy. The per-comparison ICCR is consistent with the corpus-wide rate reported in §IV-I (cos$>0.95 \to 0.00060$) and extends it to the structural dimension (dHash$\leq 5 \to 0.00129$; joint $\to 0.00014$). The pool-normalised per-signature ICCR captures the deployed rule's effective per-signature rate under inter-CPA candidate-pool replacement ($0.1102$ pooled Big-4 any-pair HC), exposing that the per-comparison rate is not the deployed-rule rate at the per-signature classifier level: the deployed classifier takes max-cosine and min-dHash over a same-CPA pool of size $n_{\text{pool}}$, so the inter-CPA-equivalent rate scales approximately as $1 - (1 - p_{\text{pair}})^{n_{\text{pool}}}$ in the independence limit. The per-document ICCR aggregates to operational alarm-rate units: HC alone $0.18$, the operational HC$+$MC alarm $0.34$.
+The operational specificity-proxy behaviour of the deployed HC sub-rule and document-level HC$+$MC alarm derived from the five-way classifier is characterised at three units of analysis (§III-L), all against the same inter-CPA negative-anchor coincidence-rate proxy. The per-comparison ICCR is consistent with the corpus-wide rate reported in §IV-I (cos$>0.95 \to 0.00060$) and extends it to the structural dimension (dHash$\leq 5 \to 0.00129$; joint $\to 0.00014$). The pool-normalised per-signature ICCR captures the deployed rule's effective per-signature rate under inter-CPA candidate-pool replacement ($0.1102$ pooled Big-4 any-pair HC), exposing that the per-comparison rate is not the deployed-rule rate at the per-signature classifier level: the deployed classifier takes max-cosine and min-dHash over a same-CPA pool of size $n_{\text{pool}}$, so the inter-CPA-equivalent rate scales approximately as $1 - (1 - p_{\text{pair}})^{n_{\text{pool}}}$ in the independence limit. The per-document ICCR aggregates to operational alarm-rate units: HC alone $0.18$, the operational HC$+$MC alarm $0.34$.
 
 Two additional findings refine the calibration story. First, the per-pair conditional ICCR for dHash$\leq 5$ given cos$>0.95$ is $0.234$ (Wilson 95% $[0.190, 0.285]$): given the cosine gate, the structural dimension provides further per-comparison specificity at $\sim 4.3\times$ refinement. Second, the alert-rate sensitivity analysis (§III-L.5) shows the deployed HC threshold is locally sensitive rather than plateau-stable (local gradient $\approx 25\times$ the median for cosine, $\approx 3.8\times$ for dHash); alternative operating points can be characterised by inverting the ICCR curves (e.g., a tighter rule cos$>0.95$ AND dHash$\leq 3$ on the same-pair joint corresponds to per-signature ICCR $\approx 0.045$). The MC/HSC sub-band boundary at dHash$=15$, by contrast, *is* plateau-like (local-to-median ratio $\approx 0.08$), consistent with high-dHash-tail saturation.