Scripts 34 and 35 produced the empirical foundation that triggers the
Paper A v4.0 Big-4 reframe.
Script 34 (Big-4-only pooled calibration):
Pool Firm A + KPMG + PwC + EY (437 CPAs); first time the
three-method framework yields dip-test multimodal results
(p<0.0001 on both cos and dh axes) anywhere in the analysis
family. 2D-GMM K=2 marginal crossings with bootstrap 95% CI
(n=500): cos = 0.9755 [0.974, 0.977], dh = 3.755 [3.48, 3.97].
Crossing offsets from Paper A v3.20.0 baseline (0.945, 8.10):
+0.030 (cos), -4.345 (dh) -- mid/small-firm tail had
substantially shifted the published threshold.
Script 35 (Big-4 K=3 cluster membership):
Hard-assigns each Big-4 CPA to one of the K=3 components.
Findings:
* Firm A (Deloitte): 0% in C1 (hand-sign-leaning),
17.5% in C2 (mixed), 82.5% in C3 (replicated).
* PwC has the strongest hand-sign tradition (24/102 = 23.5%
in C1), followed by EY (11.5%) and KPMG (8.9%).
* 40 CPAs total in C1 across KPMG/PwC/EY.
Implications confirmed by these scripts:
* Big-4-only scope is the methodologically defensible primary
analysis; the published 0.945/8.10 reflects between-firm
structure rather than within-pool mechanism boundary.
* Firm A's role pivots from "calibration anchor" to
"case study of templated end of Big-4."
* Paper A is being reframed as v4.0 on sub-branch
paper-a-v4-big4, per Partner Jimmy's earlier direction
suggestion.
Co-Authored-By: Claude Opus 4.7 (1M context) <noreply@anthropic.com>
gbanyan
55f9f94d9a