{
  "schema_version": "1.0.0",
  "source": "vibemath",
  "problem_id": "vibemathed:gaussian-completely-monotone-conjecture",
  "title": "Gaussian Completely Monotone Conjecture",
  "canonical_statement": "Along the heat flow, do the successive time derivatives of the entropy of $X + \\sqrt{t}\\,Z$ alternate in sign, as conjectured by Cheng and Geng? An explicit measure on $\\mathbb{R}$ has a fifth derivative with the forbidden sign.",
  "plain_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.",
  "current_status": "resolved",
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      "id": "vibemathed:gaussian-completely-monotone-conjecture:event",
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      "type": "disproved",
      "status": "resolved",
      "occurred_at": "2026-05-12T00:00:00.000Z",
      "title": "arXiv:2605.11656 - A counterexample to the Gaussian completely monotone conjecture",
      "summary": "also refutes the McKean and Toscani conjectures",
      "ai_contribution": "ai_discovered",
      "attempt_ids": [
        "vibemathed:gaussian-completely-monotone-conjecture:attempt"
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      "model": "GPT-5.5 Pro",
      "provider": "OpenAI",
      "attempted_at": "2026-05-12T00:00:00.000Z",
      "human_collaborators": [
        "Yuzhou Gu",
        "Mark Sellke"
      ],
      "exposure": "unknown",
      "prompt_public": null,
      "outcome": "The explicit counterexample measure was found by GPT-5.5 Pro.",
      "failed_routes": [],
      "artifacts": [],
      "sources": [
        {
          "label": "arXiv:2605.11656 - A counterexample to the Gaussian completely monotone conjecture",
          "url": "https://arxiv.org/abs/2605.11656",
          "kind": "primary-mathematical-source",
          "license": null
        },
        {
          "label": "VibeMathed: Gaussian Completely Monotone Conjecture",
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      "solution_event_id": "vibemathed:gaussian-completely-monotone-conjecture:event",
      "level": "unreviewed",
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      "statement_fidelity": "unaudited",
      "peer_review": "none",
      "verifier": "VibeMathed (source-reported label)",
      "verified_at": null,
      "note": "Author-checked arXiv preprint by Gu and Sellke. Not yet peer-reviewed.",
      "sources": [
        {
          "label": "VibeMathed: Gaussian Completely Monotone Conjecture",
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          "kind": "source-assertion",
          "license": "https://vibemathed.com/data-license"
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        {
          "label": "arXiv:2605.11656 - A counterexample to the Gaussian completely monotone conjecture",
          "url": "https://arxiv.org/abs/2605.11656",
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      "label": "arXiv:2605.11656 - A counterexample to the Gaussian completely monotone conjecture",
      "url": "https://arxiv.org/abs/2605.11656",
      "kind": "primary-mathematical-source",
      "license": null
    },
    {
      "label": "VibeMathed: Gaussian Completely Monotone Conjecture",
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      "kind": "source-assertion",
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      "generated_at": "2026-09-13T16:28:40.178Z"
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  "uncertainties": [
    "VibeMath has not independently verified the mathematical claim.",
    "AI-attempt independence and training-data exposure are unknown unless explicitly documented.",
    "VibeMath has not independently audited the mathematical statement, proof, or novelty claim."
  ],
  "generated_at": "2026-09-13T16:28:40.178Z"
}