Phase 1.6 (G2 path) script. Tests whether three INDEPENDENT
statistical approaches converge on the same Big-4 CPA ranking:
1. K=3 GMM cluster posterior P_C1 (hand-leaning)
-- from full Big-4 K=3 fit (Script 37 baseline).
2. Reverse-anchor directional score
-- non-Big-4 (n=249, mid/small firms only) as the
reference Gaussian; -cos_left_tail_pct as score.
-- Strict separation: no Big-4 CPA in the reference.
3. Paper A v3.x operational rule per-CPA hand_frac
-- (cos > 0.95 AND dh <= 5) failure rate per CPA.
Pairwise Spearman correlations:
p_c1 vs paperA_hand_frac rho = +0.9627 (p < 1e-248)
reverse_anchor vs paperA_hand_frac rho = +0.8890 (p < 1e-149)
p_c1 vs reverse_anchor rho = +0.8794 (p < 1e-142)
Verdict: CONVERGENCE_STRONG (all 3 |rho| >= 0.7).
Per-firm consistency across lenses:
Firm n C1% C3% E[P_C1] E[rev] E[hand]
FirmA 171 0.00% 82.46% 0.007 -0.973 0.193
KPMG 112 8.93% 0.00% 0.141 -0.820 0.696
PwC 102 23.53% 0.98% 0.311 -0.767 0.790
EY 52 11.54% 1.92% 0.241 -0.713 0.761
Same monotone ordering by all three metrics:
Firm A < KPMG < EY ~= PwC on hand-leaning.
Implication for v4.0: methodology paper now has THREE
independent lines of evidence converging on the same population
structure -- a much harder thing for a reviewer to dismiss
than any single lens.
Co-Authored-By: Claude Opus 4.7 (1M context) <noreply@anthropic.com>
gbanyan
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