Log-Convexity of Fisher Information Along Heat Flow

Precise 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?

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

GPT-5.5 Pro

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.

Provider: OpenAI · Prompt public: unknown · Independence: unknown

Verification boundary

unreviewed

Public arXiv preprint with an explicit construction and numerics. Not yet peer-reviewed.

Correctness: unknown · statement fidelity: unaudited · peer review: none

Timeline

1. 2026-05-18

   arXiv:2605.18081 - A hexagonal counterexample to log-convexity of Fisher information

   VibeMathed reports this item as resolved. VibeMath preserves that report as a source assertion and has not independently authored a plain-language mathematical explanation.

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.