Spike for the from-outside-of-firmA branch. Runs the three-method
threshold framework (KDE+dip, BD/McCrary, Beta mixture / logit-GMM,
2D-GMM) on three subsets:
Subset I big4_non_A KPMG+PwC+EY pooled (266 CPAs, 89.9k sigs)
Subset II all_non_A every firm except Firm A (515 CPAs, 108k sigs)
Subset III firm_A reference baseline (171 CPAs, 60.4k sigs)
Plus pre_2018 / post_2020 time-stratified secondary on subsets I and II.
Result: verdict C -- every subset is unimodal at the dip-test level
(dip p > 0.76 across the board), including Firm A itself. Time
stratification does not recover bimodality.
Cross-subset Beta-2 cosine crossings: Firm A 0.977, big4_non_A 0.930,
all_non_A 0.938; Paper A's published 0.945 sits between the two mass
centers, indicating the published "natural threshold" is effectively
a between-firm separator rather than a within-pool mechanism boundary.
This finding motivates a follow-up reverse-anchor spike (script 33).
Co-Authored-By: Claude Opus 4.7 (1M context) <noreply@anthropic.com>
gbanyan
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