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  "problem_id": "vibemathed:bh-fdr-universal-multiplicative-bound",
  "title": "Universal Multiplicative FDR Bound for Benjamini-Hochberg",
  "canonical_statement": "The Benjamini-Hochberg procedure is known not to control the false discovery rate at its nominal level under arbitrary dependence. A folklore conjecture in the FDR literature held that it must at least control the FDR up to a universal multiplicative constant. It does not: there are finite Gaussian models whose FDR divided by $q$ diverges as $q \\downarrow 0$, with an explicit two-sided lower bound $q\\sqrt{\\log(1/q)}/(2\\sqrt{\\pi}) + 0.6493 q + o(q)$.",
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      "occurred_at": "2026-07-20T00:00:00.000Z",
      "title": "arXiv:2607.14812 - How Much Can Gaussian Dependence Inflate the Benjamini-Hochberg Procedure's FDR?",
      "summary": "VibeMathed reports this item as resolved. VibeMath preserves that report as a source assertion and has not independently authored a plain-language mathematical explanation.",
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      "provider": "OpenAI",
      "attempted_at": "2026-07-20T00:00:00.000Z",
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          "label": "arXiv:2607.14812 - How Much Can Gaussian Dependence Inflate the Benjamini-Hochberg Procedure's FDR?",
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      "label": "arXiv:2607.14812 - How Much Can Gaussian Dependence Inflate the Benjamini-Hochberg Procedure's FDR?",
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      "label": "VibeMathed: Universal Multiplicative FDR Bound for Benjamini-Hochberg",
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    "VibeMath has not independently verified the mathematical claim.",
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