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The Monte Carlo comparisons drew from an unseeded generator, so the suite passed or failed by luck: replaying it 60 times fails 19 times. Draw from a seeded StableRNG instead. Julia's own streams differ between releases, so a StableRNG is what makes a given commit produce the same result on every version. Two flaws surfaced while tracking this down. `GVar` propagates moments to second order, which holds only while the spread is small compared to the distance from the mean to a singularity or a sign change. The guard `μ - 3σ >= 0` admitted `log` at μ=3, σ=1, where that distance is zero: the sampled `log(x)` reaches tens of radii below `mid`, and `GVar` reports σ = 0.342 against a true 0.411. The variance test was right to reject, and did so in 13% of draws. Require μ >= 4σ, and apply it to every function rather than to `log` alone. The loop runs about 70 hypothesis tests, so a per-test threshold of 0.001 rejects a correct implementation in roughly 7% of runs. Use the corresponding Bonferroni level of 1e-5, which still detects a 25% error in σ on every draw. Assisted-by: Claude Opus 4.8 <noreply@anthropic.com>
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