Phase 1 foundation script for Paper A v4.0 Big-4 reframe.
Sections:
A. Big-4 calibration recap (replicates Script 34: K=2 marginal
crossings cos=0.9755, dh=3.7549; bootstrap 95% CI tight;
dip-test cos p<0.0001, dh p<0.0001).
B. Leave-one-firm-out (LOOO) cross-validation: refit K=2 on the
other 3 firms, predict the held-out firm's CPAs.
C. Cross-fold stability verdict.
Result: UNSTABLE.
Held-out firm Fold rule Replicated rate
Firm A cos>0.9380 AND dh<=8.7902 171/171 = 100%
KPMG cos>0.9744 AND dh<=3.9783 0/112 = 0%
PwC cos>0.9752 AND dh<=3.7470 0/102 = 0%
EY cos>0.9756 AND dh<=3.7409 0/52 = 0%
Max |dev_cos| from fold-mean = 0.028 (5.6x over 0.005 stability bar).
Methodological implication:
The Big-4 K=2 bimodality that Script 34 celebrated (dip
p<0.0001) is firm-mass driven, not mechanism driven. K=2
separates Firm A from the other three Big-4, then mis-applies
to held-out non-Firm-A firms (everyone falls below the cosine
cut). Same conceptual problem as Paper A v3.x's between-firm
threshold, just at smaller scope.
v4.0 narrative as currently planned does not survive a reviewer
who runs LOOO.
Forward options under discussion: P1 firm-templatedness reframe,
P2 K=3 primary (next: Script 37 = K=3 LOOO), P3 rollback to
v3.20.0, P4 reverse-anchor as v4.0 core.
Co-Authored-By: Claude Opus 4.7 (1M context) <noreply@anthropic.com>
