Paper A v4.1: BCD-baseline reframe + screening positioning + trim

- Re-anchor inter-CPA coincidence-rate (ICCR) calibration on a normative
  non-Firm-A baseline (Firms B/C/D); Firm A held out as an out-of-sample
  target. Locked canonical numbers (codex-audited; Scripts 46/52/53):
  per-comparison HC 0.00014->0.000018, per-signature HC 0.0116, per-document
  HC+MC 0.34->0.1905; KDE crossover 0.837 retained corpus-wide.
- Reposition as an operator-tunable, semi-automated screening/triage framework
  (title -> "Automated Screening..."): HC = high-specificity operating point;
  MC band demoted to low-specificity advisory; Firm A = demonstration that the
  screening surfaces a templated end, audit-quality implications deferred.
- Apply codex prose-review fixes: triage-neutral five-way labels, soften
  mechanism/specificity wording, supersede MC claim-strength, update stale
  Appendix script references (40b/43/45 -> 46/52/53).
- Trim pass: compress Sec. V discussion + Sec. III echoes (27.7k -> 26.8k
  words); no substantive content removed.
- Add analysis scripts 45-53 (firm-year trends; BCD-only ICCR recompute;
  canonical-sampler locked numbers; Firm-A out-of-sample; BCD regression +
  cross-firm hit matrix).

Co-Authored-By: Claude Opus 4.8 (1M context) <noreply@anthropic.com>

signature_analysis/49_firmA_outofsample.py

@@ -0,0 +1,104 @@
+#!/usr/bin/env python3
+"""Script 49: Firm A as out-of-sample target against a clean BCD baseline.
+(1) A signatures scored against a BCD-only candidate pool (true out-of-sample
+    inter-firm coincidence).
+(2) Observed deployed rate on ACTUAL same-CPA pools, per firm (the real fired
+    rate, from precomputed deployed descriptors), to juxtapose against the
+    clean BCD inter-CPA coincidence floor. Read-only.
+"""
+import sqlite3
+from collections import defaultdict
+import numpy as np
+
+DB = '/Volumes/NV2/PDF-Processing/signature-analysis/signature_analysis.db'
+FIRM_A = '勤業眾信聯合'
+BIG4 = ('勤業眾信聯合', '安侯建業聯合', '資誠聯合', '安永聯合')
+ALIAS = {'勤業眾信聯合': 'A', '安侯建業聯合': 'B', '資誠聯合': 'C', '安永聯合': 'D'}
+SEED = 42
+POP = np.array([bin(i).count('1') for i in range(256)], dtype=np.uint8)
+
+
+def wilson(k, n, z=1.96):
+    if n == 0:
+        return (None, None)
+    p = k/n; d = 1+z*z/n
+    c = (p+z*z/(2*n))/d
+    h = z*np.sqrt(p*(1-p)/n+z*z/(4*n*n))/d
+    return (max(0.0, c-h), min(1.0, c+h))
+
+
+conn = sqlite3.connect(f'file:{DB}?mode=ro', uri=True)
+cur = conn.cursor()
+cur.execute("""
+    SELECT s.assigned_accountant, a.firm, s.source_pdf, s.feature_vector,
+           s.dhash_vector, s.max_similarity_to_same_accountant, s.min_dhash_independent
+    FROM signatures s JOIN accountants a ON s.assigned_accountant=a.name
+    WHERE s.assigned_accountant IS NOT NULL AND a.firm IN (?,?,?,?)
+      AND s.feature_vector IS NOT NULL AND s.dhash_vector IS NOT NULL""", BIG4)
+rows = cur.fetchall()
+conn.close()
+
+# ---- (1) Firm A source vs BCD-only candidate pool ----
+print('=== (1) Firm A out-of-sample vs clean BCD candidate pool ===')
+A = [r for r in rows if r[1] == FIRM_A]
+BCD = [r for r in rows if r[1] in BIG4 and r[1] != FIRM_A]
+bcd_feat = np.stack([np.frombuffer(r[3], np.float32) for r in BCD]).astype(np.float32)
+bcd_feat /= np.clip(np.linalg.norm(bcd_feat, axis=1, keepdims=True), 1e-9, None)
+bcd_dh = np.stack([np.frombuffer(r[4], np.uint8) for r in BCD])
+nb = len(BCD)
+# A CPA pool sizes (their own same-CPA count - 1), to match negative-anchor construction
+a_cpa_idx = defaultdict(list)
+for i, r in enumerate(A):
+    a_cpa_idx[r[0]].append(i)
+pool_size = {c: len(v)-1 for c, v in a_cpa_idx.items()}
+rng = np.random.default_rng(SEED)
+sig_hc = np.zeros(len(A), bool)
+doc_hcmc = defaultdict(bool)
+for i, r in enumerate(A):
+    npool = max(pool_size[r[0]], 1)
+    cand = rng.integers(0, nb, size=npool)
+    sf = np.frombuffer(r[3], np.float32).astype(np.float32)
+    sf /= max(np.linalg.norm(sf), 1e-9)
+    cosv = bcd_feat[cand] @ sf
+    cg = cosv > 0.95
+    doc_hcmc.setdefault(r[2], False)
+    if cg.any():
+        dist = POP[bcd_dh[cand] ^ np.frombuffer(r[4], np.uint8)].sum(axis=1)
+        sig_hc[i] = bool((cg & (dist <= 5)).any())
+        if (cg & (dist <= 15)).any():
+            doc_hcmc[r[2]] = True
+k = int(sig_hc.sum()); n = len(A); lo, hi = wilson(k, n)
+print(f'  A-source vs BCD-pool  per-SIGNATURE HC (cos>0.95 & dh<=5): '
+      f'{k/n:.4f} ({k}/{n}) Wilson95% [{lo:.4f},{hi:.4f}]')
+dv = np.array(list(doc_hcmc.values())); dk = int(dv.sum()); dm = len(dv)
+dlo, dhi = wilson(dk, dm)
+print(f'  A-source vs BCD-pool  per-DOCUMENT HC+MC (cos>0.95 & dh<=15): '
+      f'{dk/dm:.4f} ({dk}/{dm}) Wilson95% [{dlo:.4f},{dhi:.4f}]')
+
+# ---- (2) Observed deployed rate on ACTUAL same-CPA pools, per firm ----
+print('\n=== (2) Observed deployed rate on actual same-CPA pools (real fired rate) ===')
+print('   per-signature HC = max_sim>0.95 & min_dh<=5 ; per-doc HC+MC worst-case dh<=15')
+by_firm_sig = defaultdict(lambda: [0, 0])
+doc_obs = {}
+doc_firm = {}
+for r in rows:
+    fm = ALIAS[r[1]]
+    ms, md = r[5], r[6]
+    if ms is None or md is None:
+        continue
+    hc = (ms > 0.95) and (md <= 5)
+    hcmc = (ms > 0.95) and (md <= 15)
+    by_firm_sig[fm][0] += int(hc); by_firm_sig[fm][1] += 1
+    doc_firm.setdefault(r[2], fm)
+    doc_obs[r[2]] = doc_obs.get(r[2], False) or hcmc
+for fm in sorted(by_firm_sig):
+    k, n = by_firm_sig[fm]
+    lo, hi = wilson(k, n)
+    print(f'  Firm {fm} per-SIGNATURE HC: {k/n:.4f} ({k}/{n}) [{lo:.4f},{hi:.4f}]')
+dd = defaultdict(lambda: [0, 0])
+for d, hit in doc_obs.items():
+    fm = doc_firm[d]; dd[fm][0] += int(hit); dd[fm][1] += 1
+for fm in sorted(dd):
+    k, n = dd[fm]
+    print(f'  Firm {fm} per-DOCUMENT HC+MC: {k/n:.4f} ({k}/{n})')
+print(f'\n  Clean BCD inter-CPA coincidence FLOOR: per-sig HC=0.0048, per-doc HC+MC=0.1281')