GPT-5.5 Pro
The explicit counterexample measure was found by GPT-5.5 Pro.
Provider: OpenAI · Prompt public: unknown · Independence: unknown
Problem detail · source-aware
Gaussian Completely Monotone Conjecture
VibeMathed reports this item as resolved. VibeMath preserves that report as a source assertion and has not independently authored a plain-language mathematical explanation.
Precise 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.
The source statement is reproduced for indexing with attribution. Mathematical correctness requires domain-expert or mechanical review. VibeMath has not independently audited statement fidelity, correctness, priority, or novelty.
What AI did
Verification boundary
Author-checked arXiv preprint by Gu and Sellke. Not yet peer-reviewed.
Correctness: unknown · statement fidelity: unaudited · peer review: none
Timeline
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arXiv:2605.11656 - A counterexample to the Gaussian completely monotone conjecture
also refutes the McKean and Toscani conjectures
Known method families
construction (source-reported)
Source-reported tools: construction.
Independent: unknown · difference confidence: 0
What remains uncertain
VibeMath has not independently audited the mathematical statement, proof, or novelty claim.
- 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.