Strong Log-Concavity of Chernoff's Density

Precise statement

Is the density of Chernoff's distribution - the law of $\operatorname{argmax}_t \{W(t) - t^2\}$ for two-sided Brownian motion $W$ - strongly log-concave, as conjectured by Balabdaoui and Wellner in 2014?

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-5.6 Sol

The proof was generated in its entirety by GPT-5.6 Sol; the authors checked it and prepared the manuscript.

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

Verification boundary

unreviewed

Author-checked public arXiv preprint. Not yet peer-reviewed.

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

Timeline

1. 2026-07-21

   arXiv:2607.18619 - Chernoff's density is strongly log-concave

   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

argument (source-reported)

Source-reported tools: argument.

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.