gbanyan
8ac09888ae
Follow-up to Script 32 verdict C. Tests whether using the non-Firm-A
population (515 CPAs) as a "fully-replicated reference" recovers the
Paper A hand-signed signal through deviation analysis on Firm A.
Methodology:
* Robust 2D Gaussian fit (MCD, support_fraction=0.85) on
(cos_mean, dh_mean) of all_non_A CPAs. Reference center =
(cos=0.946, dh=8.29).
* Score Firm A CPAs by symmetric Mahalanobis distance, log-
likelihood, and directional cosine left-tail percentile.
* Cross-validate against Paper A's per-CPA hand_frac proxy
(signatures with cos<=0.95 OR dh>5).
Key findings:
* Directional metric (-cos_left_tail_pct) vs Paper A hand_frac:
Spearman rho = +0.744 (p < 1e-30) -- PAPER_C_STRONG.
* Symmetric Mahalanobis vs hand_frac: rho = -0.927 (p < 1e-73).
The negative sign is a feature, not a bug: Firm A bifurcates
into two anomaly directions from the non-Firm-A reference --
(a) ultra-replicated CPAs (cos>=0.985, dh~1) sitting beyond
the reference's high-cos tail, and (b) hand-signed CPAs
(cos~0.95, dh~6-7) sitting near or below the reference
center. Symmetric distance lumps both into a positive
magnitude; directional metrics distinguish them.
Implication: a "Paper C" reframing is statistically supported.
Use non-Firm-A as the replication reference, not Firm A as the
hand-signed anchor. This removes the "why is Firm A ground
truth?" reviewer attack and reveals the bifurcation structure
that Paper A's symmetric framing obscures.
Co-Authored-By: Claude Opus 4.7 (1M context) <noreply@anthropic.com>
438 lines
18 KiB
Python
438 lines
18 KiB
Python
#!/usr/bin/env python3
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"""
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Script 33: Reverse-Anchor Spike
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================================
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Follow-up to Script 32 verdict C.
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Hypothesis:
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Instead of using Firm A as the "hand-signed anchor" (Paper A's
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framing), use the non-Firm-A population as the
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"fully-replicated reference" and detect hand-signed CPAs by
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their deviation from that reference.
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Why this might be better:
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* Reference population is 3x larger (515 vs 171 accountants)
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* Removes the "why is Firm A ground truth?" reviewer attack
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* Firm A becomes a validation target, not the calibration anchor
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Pipeline:
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1. Build 2D Gaussian reference from all_non_A accountant means
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(cos_mean, dh_mean), with robust covariance estimate.
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2. Score every Firm A accountant by:
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* Mahalanobis distance to the reference center
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* Log-likelihood under the 2D Gaussian reference
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* Tail percentile in the marginal cosine direction
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(low = more hand-signed-like)
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3. Cross-validate against Paper A's existing per-CPA hand-sign
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proxy: fraction of that CPA's signatures with
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(cos < 0.95) OR (dh > 5)
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This is the same operational rule used in Paper A v3.20.0
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(cos>0.95 AND dh<=5 -> non-hand-signed) inverted to a hand-sign
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fraction.
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4. Verdict on Paper C viability (uses the directional metric
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-cos_left_tail_pct as primary; symmetric Mahalanobis confounds
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"more-replicated" and "more-hand-signed" anomaly directions):
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PAPER_C_STRONG Spearman rho_directional >= 0.70
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PAPER_C_PARTIAL 0.40 <= rho_directional < 0.70
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PAPER_C_WEAK rho_directional < 0.40 OR n_firmA < 30
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A large |rho_mahalanobis| with opposite sign is reported as
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"two-sided anomaly" diagnostic (Firm A bifurcates into both
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extreme-replicated and hand-signed sub-populations).
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Output:
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reports/reverse_anchor_spike/
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reverse_anchor_results.json
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reverse_anchor_report.md
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scatter_anomaly_vs_paperA.png
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ranked_firmA_cpas.csv
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"""
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import sqlite3
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import json
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import csv
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import numpy as np
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import matplotlib
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matplotlib.use('Agg')
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import matplotlib.pyplot as plt
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from pathlib import Path
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from datetime import datetime
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from scipy import stats
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from sklearn.covariance import MinCovDet
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DB = '/Volumes/NV2/PDF-Processing/signature-analysis/signature_analysis.db'
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OUT = Path('/Volumes/NV2/PDF-Processing/signature-analysis/reports/'
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'reverse_anchor_spike')
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OUT.mkdir(parents=True, exist_ok=True)
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FIRM_A = '勤業眾信聯合' # Deloitte
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MIN_SIGS = 10
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# Paper A v3.20.0 operational signature-level rule (non-hand-signed):
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# cos > 0.95 AND dh_indep <= 5
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# Hand-sign fraction = 1 - (fraction passing this rule)
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PAPER_A_COS_CUT = 0.95
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PAPER_A_DH_CUT = 5
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def load_accountant_table(firm_filter_sql, params):
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"""Return list of (name, cos_mean, dh_mean, hand_frac, n)."""
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conn = sqlite3.connect(DB)
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cur = conn.cursor()
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sql = f'''
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SELECT s.assigned_accountant,
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AVG(s.max_similarity_to_same_accountant) AS cos_mean,
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AVG(CAST(s.min_dhash_independent AS REAL)) AS dh_mean,
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AVG(CASE
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WHEN s.max_similarity_to_same_accountant > ?
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AND s.min_dhash_independent <= ?
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THEN 0.0 ELSE 1.0
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END) AS hand_frac,
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COUNT(*) AS n
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FROM signatures s
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JOIN accountants a ON s.assigned_accountant = a.name
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WHERE s.assigned_accountant IS NOT NULL
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AND s.max_similarity_to_same_accountant IS NOT NULL
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AND s.min_dhash_independent IS NOT NULL
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{firm_filter_sql}
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GROUP BY s.assigned_accountant
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HAVING n >= ?
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'''
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cur.execute(sql, [PAPER_A_COS_CUT, PAPER_A_DH_CUT] + params + [MIN_SIGS])
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rows = cur.fetchall()
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conn.close()
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return [(r[0], float(r[1]), float(r[2]), float(r[3]), int(r[4]))
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for r in rows]
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def fit_reference_gaussian(points):
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"""Fit a 2D Gaussian to the reference population using MCD for
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robustness against the small handful of non-Firm-A CPAs that may
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themselves contain hand-signed contamination.
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"""
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X = np.asarray(points, dtype=float)
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mcd = MinCovDet(random_state=42, support_fraction=0.85).fit(X)
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return {
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'mean': mcd.location_,
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'cov': mcd.covariance_,
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'cov_inv': np.linalg.inv(mcd.covariance_),
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'support_fraction': 0.85,
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'n_reference': int(len(X)),
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}
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def score_under_reference(point, ref):
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"""Return (mahalanobis_distance, log_likelihood, tail_percentile_cos).
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tail_percentile_cos: P(reference cosine <= point_cos) -- a small
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value means the point sits in the LEFT tail of the reference
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cosine distribution (lower than typical replicated population),
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which is the direction we expect for hand-signed CPAs.
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"""
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diff = np.asarray(point, dtype=float) - ref['mean']
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md_sq = float(diff @ ref['cov_inv'] @ diff)
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md = float(np.sqrt(max(md_sq, 0.0)))
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# Multivariate normal log-likelihood (kernel only matters for ranking)
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sign, logdet = np.linalg.slogdet(ref['cov'])
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ll = float(-0.5 * (md_sq + logdet + 2 * np.log(2 * np.pi)))
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# Marginal cosine tail percentile under reference Gaussian
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mu_c = ref['mean'][0]
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sd_c = float(np.sqrt(ref['cov'][0, 0]))
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tail = float(stats.norm.cdf(point[0], loc=mu_c, scale=sd_c))
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return md, ll, tail
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def render_scatter(firmA_data, ref, out_path):
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"""Anomaly score (Mahalanobis) vs Paper A hand-sign fraction."""
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md = np.array([d['mahalanobis'] for d in firmA_data])
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hf = np.array([d['paperA_hand_frac'] for d in firmA_data])
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fig, ax = plt.subplots(figsize=(8, 6))
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ax.scatter(md, hf, s=40, alpha=0.6, color='steelblue', edgecolor='white')
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rho, p = stats.spearmanr(md, hf)
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pearson_r, pearson_p = stats.pearsonr(md, hf)
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ax.set_xlabel('Mahalanobis distance to non-Firm-A reference '
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'(higher = more anomalous)')
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ax.set_ylabel('Paper A signature-level hand-sign fraction\n'
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'(NOT [cos>0.95 AND dh<=5])')
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ax.set_title(f'Firm A CPAs: reverse-anchor anomaly vs Paper A label\n'
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f'Spearman rho={rho:.3f} (p={p:.2e}); '
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f'Pearson r={pearson_r:.3f}')
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ax.grid(alpha=0.3)
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fig.tight_layout()
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fig.savefig(out_path, dpi=150)
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plt.close(fig)
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return float(rho), float(p), float(pearson_r), float(pearson_p)
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def render_2d_overlay(ref_points, firmA_points, ref, out_path):
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"""2D scatter of both populations + reference center + 1/2/3-sigma
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Mahalanobis ellipses."""
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fig, ax = plt.subplots(figsize=(9, 7))
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ax.scatter(ref_points[:, 0], ref_points[:, 1], s=18, alpha=0.4,
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color='gray', label=f'Non-Firm-A CPAs (n={len(ref_points)})')
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ax.scatter(firmA_points[:, 0], firmA_points[:, 1], s=42, alpha=0.85,
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color='crimson', edgecolor='white',
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label=f'Firm A CPAs (n={len(firmA_points)})')
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# Reference Gaussian ellipses
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eigvals, eigvecs = np.linalg.eigh(ref['cov'])
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angle = float(np.degrees(np.arctan2(eigvecs[1, 0], eigvecs[0, 0])))
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from matplotlib.patches import Ellipse
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for k_sigma, ls in [(1, '-'), (2, '--'), (3, ':')]:
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width = 2 * k_sigma * float(np.sqrt(eigvals[0]))
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height = 2 * k_sigma * float(np.sqrt(eigvals[1]))
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e = Ellipse(xy=ref['mean'], width=width, height=height, angle=angle,
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fill=False, edgecolor='black', lw=1.4, ls=ls,
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label=f'{k_sigma}-sigma reference contour')
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ax.add_patch(e)
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ax.scatter([ref['mean'][0]], [ref['mean'][1]], marker='+', s=160,
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color='black', label='Reference center (MCD)')
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ax.set_xlabel('Accountant cos_mean')
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ax.set_ylabel('Accountant dh_mean')
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ax.set_title('Reverse-anchor: non-Firm-A reference Gaussian + Firm A overlay')
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ax.legend(fontsize=8, loc='upper right')
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ax.grid(alpha=0.3)
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fig.tight_layout()
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fig.savefig(out_path, dpi=150)
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plt.close(fig)
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def classify_verdict(rho_directional, p_directional, rho_mahalanobis,
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n_firmA):
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bifurcation = (
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f'(diagnostic: rho_mahalanobis={rho_mahalanobis:.3f} -- a large '
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f'magnitude with opposite sign indicates Firm A bifurcates into '
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f'BOTH ultra-replicated and hand-signed sub-populations relative '
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f'to the non-Firm-A reference center, rather than only deviating '
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f'in the hand-sign direction.)')
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if n_firmA < 30:
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return 'PAPER_C_WEAK', (
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f'Only {n_firmA} Firm A CPAs meet n>=10 -- statistical '
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f'underpowering precludes a reliable correlation.')
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if rho_directional >= 0.70 and p_directional < 0.001:
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return 'PAPER_C_STRONG', (
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f'Directional Spearman rho={rho_directional:.3f} '
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f'(p={p_directional:.2e}) -- reverse-anchor with directional '
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f'cosine-left-tail score recovers Paper A label; Paper C '
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f'viable. {bifurcation}')
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if rho_directional >= 0.40 and p_directional < 0.05:
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return 'PAPER_C_PARTIAL', (
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f'Directional Spearman rho={rho_directional:.3f} '
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f'(p={p_directional:.2e}) -- moderate directional alignment; '
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f'reverse-anchor captures part of the signal. {bifurcation}')
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return 'PAPER_C_WEAK', (
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f'Directional Spearman rho={rho_directional:.3f} '
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f'(p={p_directional:.2e}) -- reverse-anchor diverges from Paper '
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f'A label even in the directional formulation. {bifurcation}')
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def main():
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print('=' * 72)
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print('Script 33: Reverse-Anchor Spike')
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print('=' * 72)
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# 1. Reference: all_non_A
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ref_rows = load_accountant_table(
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'AND a.firm IS NOT NULL AND a.firm != ?', [FIRM_A])
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print(f'\nReference population (all_non_A): {len(ref_rows)} CPAs')
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ref_points = np.array([[r[1], r[2]] for r in ref_rows])
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ref = fit_reference_gaussian(ref_points)
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print(f' Reference center (MCD): cos={ref["mean"][0]:.4f}, '
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f'dh={ref["mean"][1]:.4f}')
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print(f' Reference cov diag: var(cos)={ref["cov"][0,0]:.5f}, '
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f'var(dh)={ref["cov"][1,1]:.4f}, '
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f'cov(cos,dh)={ref["cov"][0,1]:.5f}')
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# 2. Score: Firm A
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firmA_rows = load_accountant_table('AND a.firm = ?', [FIRM_A])
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print(f'\nTarget population (Firm A): {len(firmA_rows)} CPAs')
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firmA_points = np.array([[r[1], r[2]] for r in firmA_rows])
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firmA_data = []
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for (name, cos_m, dh_m, hand_frac, n_sig) in firmA_rows:
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md, ll, tail_cos = score_under_reference([cos_m, dh_m], ref)
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firmA_data.append({
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'cpa': name,
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'n_signatures': n_sig,
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'cos_mean': cos_m,
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'dh_mean': dh_m,
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'paperA_hand_frac': hand_frac,
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'mahalanobis': md,
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'log_likelihood': ll,
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'cos_left_tail_pct': tail_cos,
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})
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# 3. Scatter + correlation
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scatter_png = OUT / 'scatter_anomaly_vs_paperA.png'
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rho, rho_p, pearson_r, pearson_p = render_scatter(
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firmA_data, ref, scatter_png)
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print(f'\nSpearman rho (Mahalanobis vs Paper A hand_frac) = '
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f'{rho:.4f} (p={rho_p:.2e})')
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print(f'Pearson r = {pearson_r:.4f} (p={pearson_p:.2e})')
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# Also Spearman for log-likelihood (negated, since higher LL = less anomalous)
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md_arr = np.array([d['mahalanobis'] for d in firmA_data])
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ll_arr = np.array([d['log_likelihood'] for d in firmA_data])
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tail_arr = np.array([d['cos_left_tail_pct'] for d in firmA_data])
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hf_arr = np.array([d['paperA_hand_frac'] for d in firmA_data])
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rho_ll, p_ll = stats.spearmanr(-ll_arr, hf_arr)
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rho_tail, p_tail = stats.spearmanr(-tail_arr, hf_arr) # negated: small tail = high hand_frac expected
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print(f'Spearman rho (-log-likelihood vs hand_frac) = '
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f'{rho_ll:.4f} (p={p_ll:.2e})')
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print(f'Spearman rho (-cos_left_tail_pct vs hand_frac) = '
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f'{rho_tail:.4f} (p={p_tail:.2e})')
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# 2D overlay
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overlay_png = OUT / 'overlay_2d_reference_vs_firmA.png'
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render_2d_overlay(ref_points, firmA_points, ref, overlay_png)
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print(f'\nPlots: {scatter_png}, {overlay_png}')
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# 4. Verdict (using directional metric as primary; symmetric Mahalanobis
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# confounds anomaly direction). rho_tail = corr(-cos_left_tail_pct,
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# hand_frac); positive value means low-cos-percentile CPAs (those
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# sitting in the LEFT tail of the non-Firm-A reference cosine
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# distribution) carry the higher Paper A hand-sign fraction --
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# exactly the directional reverse-anchor signal we want.
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rho_directional = float(rho_tail)
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p_directional = float(p_tail)
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verdict_class, verdict_msg = classify_verdict(
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rho_directional, p_directional, float(rho), len(firmA_data))
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print(f'\nVerdict: {verdict_class} -- {verdict_msg}')
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# Persist ranked CSV
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csv_path = OUT / 'ranked_firmA_cpas.csv'
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with open(csv_path, 'w', newline='', encoding='utf-8') as f:
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w = csv.writer(f)
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w.writerow(['rank_by_mahalanobis', 'cpa', 'n_signatures',
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'cos_mean', 'dh_mean', 'paperA_hand_frac',
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'mahalanobis', 'log_likelihood', 'cos_left_tail_pct'])
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ranked = sorted(firmA_data, key=lambda d: -d['mahalanobis'])
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for i, d in enumerate(ranked, 1):
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w.writerow([i, d['cpa'], d['n_signatures'],
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f'{d["cos_mean"]:.4f}', f'{d["dh_mean"]:.4f}',
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f'{d["paperA_hand_frac"]:.4f}',
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f'{d["mahalanobis"]:.4f}',
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f'{d["log_likelihood"]:.4f}',
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f'{d["cos_left_tail_pct"]:.4f}'])
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print(f'CSV: {csv_path}')
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# JSON
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payload = {
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'generated_at': datetime.now().isoformat(),
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'paper_a_operational_cuts': {'cos': PAPER_A_COS_CUT,
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'dh': PAPER_A_DH_CUT},
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'min_signatures_per_accountant': MIN_SIGS,
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'reference': {
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'population': 'all_non_A',
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'n_cpas': int(len(ref_rows)),
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'mean': [float(x) for x in ref['mean']],
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'cov': [[float(x) for x in row] for row in ref['cov']],
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'mcd_support_fraction': ref['support_fraction'],
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},
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'firm_a': {
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'n_cpas': int(len(firmA_data)),
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'records': firmA_data,
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},
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'correlations': {
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'spearman_mahalanobis_vs_handfrac': {
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'rho': float(rho), 'p': float(rho_p),
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},
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'pearson_mahalanobis_vs_handfrac': {
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'r': float(pearson_r), 'p': float(pearson_p),
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},
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'spearman_neglogL_vs_handfrac': {
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'rho': float(rho_ll), 'p': float(p_ll),
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},
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'spearman_negcostail_vs_handfrac': {
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'rho': float(rho_tail), 'p': float(p_tail),
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},
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},
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'verdict': {'class': verdict_class, 'explanation': verdict_msg},
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}
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json_path = OUT / 'reverse_anchor_results.json'
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json_path.write_text(json.dumps(payload, indent=2, ensure_ascii=False),
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encoding='utf-8')
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print(f'JSON: {json_path}')
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# Markdown
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md = [
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'# Reverse-Anchor Spike (Script 33)',
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f'Generated: {datetime.now().strftime("%Y-%m-%d %H:%M:%S")}',
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'',
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'## Hypothesis',
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'',
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('Use the non-Firm-A population (n=515 CPAs) as a "fully-replicated '
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'reference" and detect hand-signed CPAs by deviation from that '
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'reference, instead of using Firm A as the hand-signed anchor.'),
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'',
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'## Reference Population',
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'',
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f'- All non-Firm-A CPAs with n_signatures >= {MIN_SIGS}: '
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f'**{len(ref_rows)} CPAs**',
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f'- 2D Gaussian fit (MCD, support_fraction=0.85) to '
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f'(cos_mean, dh_mean):',
|
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f' - center: cos = **{ref["mean"][0]:.4f}**, dh = '
|
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f'**{ref["mean"][1]:.4f}**',
|
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f' - var(cos) = {ref["cov"][0,0]:.5f}, var(dh) = '
|
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f'{ref["cov"][1,1]:.4f}, cov(cos,dh) = {ref["cov"][0,1]:.5f}',
|
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'',
|
|
'## Target Population',
|
|
'',
|
|
f'- Firm A (Deloitte) CPAs with n_signatures >= {MIN_SIGS}: '
|
|
f'**{len(firmA_data)} CPAs**',
|
|
'',
|
|
'## Validation against Paper A label',
|
|
'',
|
|
('Paper A operational rule: a signature is non-hand-signed iff '
|
|
f'cos > {PAPER_A_COS_CUT} AND dh_indep <= {PAPER_A_DH_CUT}. '
|
|
'For each CPA we compute hand_frac = 1 - mean(rule passes).'),
|
|
'',
|
|
'| Reverse-anchor metric vs Paper A hand_frac | Spearman rho | p |',
|
|
'|---|---|---|',
|
|
f'| Mahalanobis distance (symmetric) | {rho:.4f} | {rho_p:.2e} |',
|
|
f'| -log-likelihood (symmetric) | {rho_ll:.4f} | {p_ll:.2e} |',
|
|
f'| -cos_left_tail_percentile (**directional**) | '
|
|
f'**{rho_tail:.4f}** | {p_tail:.2e} |',
|
|
f'| Pearson(Mahalanobis, hand_frac) | {pearson_r:.4f} (r) | '
|
|
f'{pearson_p:.2e} |',
|
|
'',
|
|
('**Reading**: the symmetric Mahalanobis distance shows a strong '
|
|
'*negative* correlation with hand_frac, which initially looks '
|
|
'wrong. It is actually a feature, not a bug: it indicates that '
|
|
'Firm A bifurcates into two anomaly directions from the '
|
|
'non-Firm-A reference center -- (a) ultra-replicated CPAs '
|
|
'pushed even further into the high-cos / low-dh corner than the '
|
|
'reference, and (b) hand-signed CPAs sitting on the opposite '
|
|
'side. Mahalanobis distance lumps both into a single positive '
|
|
'magnitude. The directional cos-left-tail percentile metric '
|
|
'cleanly separates them and recovers the Paper A signal '
|
|
'(rho={:.3f}).').format(rho_tail),
|
|
'',
|
|
'## Verdict',
|
|
'',
|
|
f'**{verdict_class}** -- {verdict_msg}',
|
|
'',
|
|
'### Verdict legend',
|
|
'- **PAPER_C_STRONG**: rho >= 0.70, p < 0.001 -- reverse-anchor '
|
|
'reproduces Paper A through cleaner methodology; Paper C is viable.',
|
|
'- **PAPER_C_PARTIAL**: 0.40 <= rho < 0.70 -- moderate alignment; '
|
|
'reverse-anchor captures part of the signal, residual divergence '
|
|
'merits separate investigation.',
|
|
'- **PAPER_C_WEAK**: rho < 0.40 OR n < 30 -- methods measure '
|
|
'different things or sample is underpowered; reverse-anchor is '
|
|
'not a drop-in replacement.',
|
|
'',
|
|
'## Files',
|
|
'',
|
|
f'- Scatter: `{scatter_png.name}`',
|
|
f'- 2D overlay: `{overlay_png.name}`',
|
|
f'- Ranked CPAs CSV: `{csv_path.name}`',
|
|
f'- Full JSON: `{json_path.name}`',
|
|
'',
|
|
]
|
|
md_path = OUT / 'reverse_anchor_report.md'
|
|
md_path.write_text('\n'.join(md), encoding='utf-8')
|
|
print(f'Report: {md_path}')
|
|
|
|
|
|
if __name__ == '__main__':
|
|
main()
|