Author here.
Two things that are worth repeating up front: corpus A is 84% of the pooled bill, so the pooled −0.01% is pretty much "corpus A plus noise" so read it per-rows instead.
And p_fire is a lower bound because of the detector's sensitivity taken as 1 (which it obviously isn't). Caveman's real fire rate is somewhat higher than 50.6%.
Code and commands: github.com/jaynapp/jayn-caveman