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  "problem_id": "vibemathed:fisher-information-log-convexity",
  "title": "Log-Convexity of Fisher Information Along Heat Flow",
  "canonical_statement": "For every smooth positive density $f$ on $\\mathbb{R}^d$, must the Fisher information $t \\mapsto I(f * \\gamma_t)$ be log-convex along the heat flow?",
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      "type": "disproved",
      "status": "resolved",
      "occurred_at": "2026-05-18T00:00:00.000Z",
      "title": "arXiv:2605.18081 - A hexagonal counterexample to log-convexity of Fisher information",
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      "attempted_at": "2026-05-18T00:00:00.000Z",
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      "outcome": "The hexagonal counterexample - a smooth positive Gaussian-decaying density on the plane - was found with GPT-5.5 Pro; tensorization extends the disproof to every dimension at least two.",
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