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​ ≈ 0.0086 , well under one percentage point. The paper’s own forty-percent threshold sits 0.40 - 0.3333 $\approx$ 0.0667 above that null mean, which is z $\approx$ 7.75 standard deviations out — a one-sided tail probability, by the normal approximation to the binomial (valid here since n$p_0(1-p_0)$ $\approx$ 667 , far above the usual rule-of-thumb minimum), of roughly 4.7 $\times$ 10^{-15} . At three thousand trials per dataset, in other words, a classifier with no position sensitivity of any kind would essentially never cross this threshold by chance, in either direction. Whatever explains the measured pattern, it is not noise inflated by a lenient bar. This computation does not touch the paper’s…

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