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>
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#!/usr/bin/env python3
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"""Script 51: publication polish.
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Part A: CPA-block bootstrap (1000 reps) on per-signature HC any-pair rate, and
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document-level bootstrap on per-document HC+MC, for ABCD & BCD.
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Part B: corpus-wide KDE crossover (pair-weighted intra, reproduce 0.837) plus
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BCD-only and BCD+nonBig4 variants.
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Read-only.
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"""
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import sqlite3
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from collections import defaultdict
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import numpy as np
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from scipy.stats import gaussian_kde
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DB = '/Volumes/NV2/PDF-Processing/signature-analysis/signature_analysis.db'
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FIRM_A = '勤業眾信聯合'
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BIG4 = ('勤業眾信聯合', '安侯建業聯合', '資誠聯合', '安永聯合')
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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'}
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SEED = 42
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N_BOOT = 1000
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POP = np.array([bin(i).count('1') for i in range(256)], dtype=np.uint8)
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def load():
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conn = sqlite3.connect(f'file:{DB}?mode=ro', uri=True)
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cur = conn.cursor()
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cur.execute("""
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SELECT s.assigned_accountant, a.firm, s.source_pdf,
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s.feature_vector, s.dhash_vector
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FROM signatures s JOIN accountants a ON s.assigned_accountant=a.name
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WHERE s.assigned_accountant IS NOT NULL AND a.firm IS NOT NULL
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AND s.feature_vector IS NOT NULL AND s.dhash_vector IS NOT NULL""")
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rows = cur.fetchall()
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conn.close()
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return rows
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# ============ Part A: bootstrap on anchor rates ============
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def simulate(keep):
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n = len(keep)
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feats = np.stack([np.frombuffer(r[3], np.float32) for r in keep]).astype(np.float32)
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feats /= np.clip(np.linalg.norm(feats, axis=1, keepdims=True), 1e-9, None)
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dh = np.stack([np.frombuffer(r[4], np.uint8) for r in keep])
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cpas = np.array([r[0] for r in keep])
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docs = np.array([r[2] for r in keep])
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cpa_idx = defaultdict(list)
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for i, c in enumerate(cpas):
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cpa_idx[c].append(i)
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cpa_idx = {c: np.array(v) for c, v in cpa_idx.items()}
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pool_size = {c: len(v)-1 for c, v in cpa_idx.items()}
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rng = np.random.default_rng(SEED)
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max_cos = np.zeros(n, np.float32); min_dh = np.full(n, 64, np.int32)
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for si in range(n):
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c = cpas[si]; npool = pool_size[c]
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if npool <= 0:
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continue
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same = cpa_idx[c]
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draw = rng.integers(0, n, size=npool + same.size + 20)
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cand = draw[~np.isin(draw, same)][:npool]
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cosv = feats[cand] @ feats[si]
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dist = POP[dh[cand] ^ dh[si]].sum(axis=1)
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max_cos[si] = cosv.max(); min_dh[si] = int(dist.min())
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hc = (max_cos > 0.95) & (min_dh <= 5)
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d2 = (max_cos > 0.95) & (min_dh <= 15)
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return hc, d2, cpa_idx, docs
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def boot_part(keep, label):
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hc, d2, cpa_idx, docs = simulate(keep)
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n = len(hc)
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rng = np.random.default_rng(SEED + 1)
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cpa_list = list(cpa_idx.keys())
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# CPA-block bootstrap on per-signature HC
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bs = np.empty(N_BOOT)
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for b in range(N_BOOT):
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cs = rng.choice(len(cpa_list), len(cpa_list), replace=True)
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idx = np.concatenate([cpa_idx[cpa_list[i]] for i in cs])
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bs[b] = hc[idx].mean()
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# document-level bootstrap on per-doc D2
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doc_d2 = defaultdict(bool)
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for i in range(n):
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doc_d2[docs[i]] = doc_d2[docs[i]] or bool(d2[i])
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dl = np.array(list(doc_d2.keys())); dvals = np.array([doc_d2[d] for d in dl])
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nd = len(dl); bd = np.empty(N_BOOT)
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for b in range(N_BOOT):
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s = rng.integers(0, nd, nd)
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bd[b] = dvals[s].mean()
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print(f'\n [{label}] per-sig HC point={hc.mean():.4f} '
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f'CPA-block boot95% [{np.percentile(bs,2.5):.4f}, {np.percentile(bs,97.5):.4f}]')
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print(f' [{label}] per-doc HC+MC point={dvals.mean():.4f} '
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f'doc boot95% [{np.percentile(bd,2.5):.4f}, {np.percentile(bd,97.5):.4f}]')
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# ============ Part B: pair-weighted KDE crossover ============
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def crossover(keep, label):
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feats = np.stack([np.frombuffer(r[3], np.float32) for r in keep]).astype(np.float32)
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feats /= np.clip(np.linalg.norm(feats, axis=1, keepdims=True), 1e-9, None)
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cpas = np.array([r[0] for r in keep])
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by = defaultdict(list)
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for i, c in enumerate(cpas):
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by[c].append(i)
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by = {c: np.array(v) for c, v in by.items() if len(v) >= 3}
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accts = list(by.keys())
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pair_w = np.array([len(by[c])*(len(by[c])-1)/2 for c in accts], float)
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pair_w /= pair_w.sum()
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rng = np.random.default_rng(SEED)
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M = 100_000
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# intra: CPA sampled proportional to pair count (= uniform over all intra pairs)
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intra = np.empty(M, np.float32)
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ci = rng.choice(len(accts), M, p=pair_w)
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for t in range(M):
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a, b = rng.choice(by[accts[ci[t]]], 2, replace=False)
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intra[t] = feats[a] @ feats[b]
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inter = np.empty(M, np.float32)
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for t in range(M):
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i, j = rng.choice(len(accts), 2, replace=False)
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inter[t] = feats[rng.choice(by[accts[i]])] @ feats[rng.choice(by[accts[j]])]
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xs = np.linspace(0.3, 1.0, 10000)
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diff = gaussian_kde(intra)(xs) - gaussian_kde(inter)(xs)
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cr = [float(x) for x in xs[np.where(np.diff(np.sign(diff)))[0]] if 0.6 < x < 0.99]
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print(f' [{label}] crossover {[f"{x:.4f}" for x in cr]} '
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f'(intra {intra.mean():.4f}/{np.median(intra):.4f} inter {inter.mean():.4f}/{np.median(inter):.4f})')
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rows = load()
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abcd = [r for r in rows if r[1] in BIG4]
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bcd = [r for r in rows if r[1] in BIG4 and r[1] != FIRM_A]
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print('=== Part A: bootstrap CIs on anchor rates ===')
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boot_part(abcd, 'ABCD (verify ~0.109 / ~0.338)')
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boot_part(bcd, 'BCD-only')
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print('\n=== Part B: KDE crossover (pair-weighted intra, corpus-wide reproduces 0.837) ===')
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crossover(rows, 'corpus-wide (all firms)')
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crossover(bcd, 'BCD-only')
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crossover([r for r in rows if r[1] != FIRM_A], 'BCD + non-Big4')
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