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Does the Benjamini-Hochberg procedure always control the false-discovery rate at its nominal level for correlated two-sided Gaussian p-values? A factor model gives $\mathrm{FDR} > 0.0104$ at nominal level $\alpha = 0.01$.
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The counterexample was obtained by GPT-5.6 Pro and carefully checked by the author, with a rigorous interval-arithmetic certificate valid for all sufficiently large numbers of hypotheses.
Provider: OpenAI · Prompt public: unknown · Independence: unknown
Author-checked arXiv preprint with an interval-arithmetic certificate. Not yet peer-reviewed.
Correctness: unknown · statement fidelity: unaudited · peer review: none
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Independent: unknown · difference confidence: 0
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