Follow-up to Script 36's K=2 UNSTABLE finding. Tests whether K=3's
C1 hand-leaning component (~14% weight, cos~0.946, dh~9.17 from
Script 35) is firm-mass driven or a real cross-firm sub-population.
Result: C1 component shape IS stable across LOOO folds.
Fold C1 cos C1 dh C1 weight
baseline 0.9457 9.1715 0.143
-FirmA 0.9425 10.1263 0.145
-KPMG 0.9441 9.1591 0.127
-PwC 0.9504 8.4068 0.126
-EY 0.9439 9.2897 0.120
Max drift vs baseline: cos 0.0047, dh 0.955, weight 0.023
-- all within heuristic stability bars (0.01, 1.0, 0.10).
Held-out prediction divergence vs Script 35 baseline:
Firm A predicted 4.68% vs baseline 0.0% (+4.68 pp)
KPMG predicted 7.14% vs baseline 8.9% (-1.76 pp)
PwC predicted 36.27% vs baseline 23.5% (+12.77 pp)
EY predicted 17.31% vs baseline 11.5% (+5.81 pp)
Verdict: P2_PARTIAL.
Methodological insight: K=3 disentangles the firm-mass/mechanism
confound that broke K=2. C3 (cos~0.983, dh~2.4) absorbs Firm A's
templated mass; C1 (cos~0.946, dh~9.17) captures cross-firm
hand-leaning. Membership boundary shifts slightly (±5-13 pp)
across folds, reflecting honest calibration uncertainty rather
than collapse.
Implication: v4.0 can pivot to a "characterized cluster structure
with bounded reproducibility" framing instead of the original
"clean natural threshold" pitch. Honest, defensible, but a
different paper than v3.20.0 was building.
Co-Authored-By: Claude Opus 4.7 (1M context) <noreply@anthropic.com>
