Paper A v3.14: remove A2 assumption + soften all partner-level claims

The within-auditor-year uniformity assumption (A2) introduced in v3.11
Section III-G was empirically tested via a new within-year uniformity
check (signature_analysis/27_within_year_uniformity.py; output in
reports/within_year_uniformity/). The check found that within-year
pairwise cosine distributions even at the calibration firm show
substantial heterogeneity inconsistent with strict single-mechanism
uniformity (Firm A 2023 CPAs typically have median pairwise cosine
around 0.85 with 20-70% of pairs below the all-pairs KDE crossover
0.837). A2 as stated ("a CPA who replicates any signature image in
that year is treated as doing so for every report") is therefore
falsified empirically.

Three explanations are compatible with the data and cannot be
disambiguated without manual inspection: (i) true within-year
mechanism mixing, (ii) multi-template replication workflows at the
same firm within a year, (iii) feature-extraction noise on repeatedly
scanned stamped images. Since A2 is falsified and its implications
cannot be restored under any of the three explanations, we remove
A2 entirely rather than downgrading it to an "approximation" or
"interpretive convention."

Changes applied:

1. Methodology Section III-G: A2 block deleted. Section now has only
   A1 (pair-detectability, cross-year pair-existence). Replaced A2
   with an explicit statement that we make no within-year or
   across-year uniformity assumption, that per-signature labels are
   signature-level quantities throughout, and that we abstain from
   partner-level frequency inferences. Three candidate explanations
   for within-year signature heterogeneity are listed (single-template
   replication, multi-template replication in parallel, within-year
   mixing, or combinations) without attempting disaggregation.

2. Methodology III-H strand 2 (L154) softened: "7.5% form a long left
   tail consistent with a minority of hand-signers" rewritten as
   reflecting "within-firm heterogeneity in signing output (we do not
   disaggregate partner-level mechanism here; see Section III-G)."

3. Methodology III-H visual-inspection strand (L152) and the
   corresponding Discussion V-C first strand (L41) and Conclusion L21
   softened: "for the majority of partners" changed to "for many of
   the sampled partners" (Codex round-14 MAJOR: "majority of partners"
   is itself a partner-level frequency claim under the new scope-of-
   claims regime).

4. Methodology III-K.3 Firm A anchor (L247): dropped "(consistent
   with a minority of hand-signers)" parenthetical.

5. Results IV-D cosine distribution narrative (L72): softened to
   "within-firm heterogeneity in signing outputs (see Section IV-E
   and Section III-G for the scope of partner-level claims)."

6. Results IV-E cluster split framing (L128): "minority-hand-signers
   framing of Section III-H" renamed to "within-firm heterogeneity
   framing of Section III-H" (matches the new III-H text).

7. Results IV-H.1 partner-level reading (L286): removed entirely.
   The v3.13 text "Under the within-year label-uniformity convention
   A2, this left-tail share is read as a partner-level minority of
   hand-signing CPAs" is replaced by a signature-level statement
   that explicitly lists hand-signing partners, multi-template
   replication, or a combination as possibilities without attempting
   attribution.

8. Results IV-H.1 stability argument (L308): softened from "persistent
   minority of hand-signing Firm A partners" to "persistent within-
   firm heterogeneity component," preserving the substantive argument
   that stability across production technologies is inconsistent with
   a noise-only explanation.

9. Results IV-I Firm A Capture Profile (L407): rewrote the "Firm A's
   minority hand-signers have not been captured" phrasing as a
   signature-level framing about the 7.5% left tail not projecting
   into the lowest-cosine document-level category under the dual-
   descriptor rules.

10. Abstract (L5): softened "alongside within-firm heterogeneity
    consistent with a minority of hand-signers" to "alongside residual
    within-firm heterogeneity." Abstract at 244/250 words.

11. Discussion V-C third strand (L43): added "multi-template
    replication workflows" to the list of possibilities and added
    a local "we do not disaggregate these mechanisms; see Section
    III-G for the scope of claims" disclaimer (Codex round-14 MINOR 5).

12. Discussion Limitations: added an Eighth limitation explicitly
    stating that partner-level frequency inferences are not made and
    why (no within-year uniformity assumption is adopted).

13. Methodology L124 opening: "We make one stipulation about within-
    auditor-year structure" fixed to "same-CPA pair detectability,"
    since A1 is a cross-year pair-existence property, not a within-
    year claim (Codex round-14 MINOR 3).

14. Two broken cross-references fixed (Codex round-14 MINOR 6):
    methodology L86 Section V-D -> V-G (Limitations is G, not D which
    is Style-Replication Gap); methodology L167 Section III-I ->
    Section IV-D (the empirical cosine distribution is in IV-D, not
    III-I).

Script 27 and its output (reports/within_year_uniformity/*) remain
in the repository as internal due-diligence evidence but are not
cited from the paper. The paper's substantive claims at signature-
level and accountant (cross-year pooled) level are unchanged; only
the partner-level interpretive overlay is removed. All tables
(IV-XVIII), Appendix A (BD/McCrary sensitivity), and all reported
numbers are unchanged.

Codex round-14 (gpt-5.5 xhigh) verification: Major Revision caused
by one BLOCKER (stale DOCX artifact, not part of this commit) plus
one MAJOR ("majority of partners" partner-frequency claim) plus
four MINOR findings. All five markdown findings addressed in this
commit. DOCX regeneration deferred to pre-submission packaging.

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

paper/paper_a_discussion_v3.md

@@ -38,9 +38,9 @@ A recurring theme in prior work that treats Firm A or an analogous reference gro
 Our evidence across multiple analyses rules out that assumption for Firm A while affirming its utility as a calibration reference.
 
 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.
+First, the visual-inspection evidence: randomly sampled Firm A reports exhibit pixel-identical signature images across different audit engagements and fiscal years for many of the sampled 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.
+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 output (potentially spanning hand-signing partners, multi-template replication workflows, CPAs undergoing mid-sample mechanism transitions, and CPAs whose pooled coordinates reflect mixed-quality replication; we do not disaggregate these mechanisms---see Section III-G for the scope of claims) rather than a pure replication population.
 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.
@@ -111,5 +111,9 @@ Seventh, the max/min detection logic treats both ends of a near-identical same-C
 In the rare case that one of the two documents contains a genuinely hand-signed exemplar that was subsequently reused as the stamping or e-signature template, the pair correctly identifies image reuse but misattributes the non-hand-signed status to the source exemplar.
 This misattribution affects at most one source document per template variant per CPA (the exemplar from which the template was produced), is not expected to be common given that stored signature templates are typically generated in a separate acquisition step rather than extracted from submitted audit reports, and does not materially affect aggregate capture rates at the firm level.
 
+Eighth, our analyses remain at the signature level and the accountant (cross-year pooled) level; we abstain from partner-level frequency inferences such as "X% of CPAs hand-sign in a given year."
+Per-signature labels in this paper are not translated to per-report or per-partner mechanism assignments, because making such a translation would require an assumption of within-year uniformity of signing mechanisms that we do not adopt: a CPA's signatures within a single fiscal year may reflect a single replication template, multiple templates used in parallel (e.g., for different engagement positions or reporting pipelines), within-year mechanism mixing, or a combination, and the data at hand do not disambiguate these possibilities (Section III-G).
+The signature-level rates we report, including the 92.5% / 7.5% Firm A split and the year-by-year left-tail share of Section IV-H.1, should accordingly be read as signature-level quantities rather than partner-level frequencies.
+
 Finally, the legal and regulatory implications of our findings depend on jurisdictional definitions of "signature" and "signing."
 Whether non-hand-signing of a CPA's own stored signature constitutes a violation of signing requirements is a legal question that our technical analysis can inform but cannot resolve.