Correct Firm A framing: replication-dominated, not pure

Interview evidence from multiple Firm A accountants confirms that MOST
use replication (stamping / firm-level e-signing) but a MINORITY may
still hand-sign. Firm A is therefore a "replication-dominated" population,
not a "pure" one. This framing is consistent with:

- 92.5% of Firm A signatures exceed cosine 0.95 (majority replication)
- The long left tail (~7%) captures the minority hand-signers, not scan
  noise or preprocessing artifacts
- Hartigan dip test: Firm A cosine unimodal long-tail (p=0.17)
- Accountant-level GMM: of 180 Firm A accountants, 139 cluster in C1
  (high-replication) and 32 in C2 (middle band = minority hand-signers)

Updates docstrings and report text in Scripts 15, 16, 18, 19 to match.
Partner v3's "near-universal non-hand-signing" language corrected.

Script 19 regenerated with the updated text.

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

signature_analysis/15_hartigan_dip_test.py

@@ -10,6 +10,17 @@ Purpose:
   Prior finding (2026-04-16): signature-level distribution is unimodal long-tail;
   the story is that bimodality only emerges at the accountant level.
 
+Firm A framing (2026-04-20, corrected):
+  Interviews with multiple Firm A accountants confirm that MOST use
+  replication (stamping / firm-level e-signing) but do NOT exclude a
+  minority of hand-signers. Firm A is therefore a "replication-dominated"
+  population, NOT a "pure" one. This framing is consistent with:
+    - 92.5% of Firm A signatures exceed cosine 0.95
+    - The long left tail (7.5% below 0.95) captures the minority
+      hand-signers, not scan noise
+    - Script 18: of 180 Firm A accountants, 139 cluster in C1
+      (high-replication) and 32 in C2 (middle band = minority hand-signers)
+
 Tests:
   1. Firm A (Deloitte) cosine max-similarity       -> expected UNIMODAL
   2. Firm A (Deloitte) independent min dHash       -> expected UNIMODAL

signature_analysis/16_bd_mccrary_discontinuity.py

@@ -306,8 +306,10 @@ def main():
         '* Multiple candidate transitions are ranked by total |Z| magnitude',
         '  on both sides of the boundary; the strongest is reported.',
         '* Absence of a significant transition is itself informative: it',
-        '  is consistent with a single generative mechanism (e.g. Firm A',
+        '  is consistent with a single dominant generative mechanism (e.g.',
-        '  which is near-universally non-hand-signed).',
+        '  Firm A, a replication-dominated population per interviews with',
+        '  multiple Firm A accountants -- most use replication, a minority',
+        '  may hand-sign).',
     ]
     md_path = OUT / 'bd_mccrary_report.md'
     md_path.write_text('\n'.join(md), encoding='utf-8')

signature_analysis/18_accountant_mixture.py

@@ -19,6 +19,14 @@ The script:
   4. For the 2-component fit derives the natural threshold (crossing of
      marginal densities in cosine-mean and dhash-mean).
 
+Firm A framing note (2026-04-20, corrected):
+  Interviews with Firm A accountants confirm MOST use replication but a
+  MINORITY may hand-sign. Firm A is thus a "replication-dominated"
+  population, NOT pure. Empirically: of ~180 Firm A accountants, ~139
+  land in C1 (high-replication) and ~32 land in C2 (middle band) under
+  the 3-component fit. The C2 Firm A members are the interview-suggested
+  minority hand-signers.
+
 Output:
   reports/accountant_mixture/accountant_mixture_report.md
   reports/accountant_mixture/accountant_mixture_results.json

signature_analysis/19_pixel_identity_validation.py

@@ -11,9 +11,15 @@ occurring reference populations instead of manual labels:
       => absolute ground truth for replication.
 
   Positive anchor 2:  Firm A (Deloitte) signatures
-      Interview + visual evidence establishes near-universal non-hand-
+      Interview evidence from multiple Firm A accountants confirms that
-      signing across 2013-2023 (see memories 2026-04-08, 2026-04-14).
+      MOST use replication (stamping / firm-level e-signing) but a
-      We treat Firm A as a strong prior positive.
+      MINORITY may still hand-sign. Firm A is therefore a
+      "replication-dominated" population (not a pure one). We use it as
+      a strong prior positive for the majority regime, while noting that
+      ~7% of Firm A signatures fall below cosine 0.95 consistent with
+      the minority hand-signers. This matches the long left tail
+      observed in the dip test (Script 15) and the Firm A members who
+      land in C2 (middle band) of the accountant-level GMM (Script 18).
 
   Negative anchor:    signatures with cosine <= low threshold
       Pairs with very low cosine similarity cannot plausibly be pixel
@@ -354,7 +360,11 @@ def main():
         f'({int(neg_mask.sum()):,} signatures). Treated as',
         '  confirmed not-replicated.',
         f'* **Firm A anchor:** Deloitte ({int(firm_a_mask.sum()):,} signatures),',
-        '  near-universally non-hand-signed per partner interviews.',
+        '  a replication-dominated population per interviews with multiple',
+        '  Firm A accountants: most use replication (stamping / firm-level',
+        '  e-signing), but a minority may still hand-sign. Used as a strong',
+        '  prior positive for the majority regime, with the ~7% below',
+        '  cosine 0.95 reflecting the minority hand-signers.',
         '',
         '## Equal Error Rate (EER)',
         '',