What was already known
Balabdaoui and Wellner proved ordinary log-concavity of Chernoff's density in 2014, conjectured strong log-concavity, and gave numerical evidence. The Airy factorization and related identity used in the new proof came from earlier human work, including Menon and Srinivasan.
AI involvement
Zhang and Zhou credit GPT-5.6 Sol with the successful proof and strategy. They found an error in an earlier attempt, then carefully checked and revised the final argument; earlier human work supplied the Airy identity.
The authors explicitly credit GPT-5.6 Sol with the entire successful proof and strategy while documenting human review and revision.
Importance
The model-origin proof addresses the 2014 strong log-concavity conjecture.
Limitations
The result concerns Chernoff's density, not all Brownian argmax laws. A separate human explanation of the central proof mechanism is not documented.
Technical verification
Both named authors explicitly say they carefully checked the final analytic argument after an erroneous first model attempt. This is source-reported completed human proof checking; no machine proof or independent reproduction is documented.
Formal checking
Careful human check of the final analytic argument with exposition revision
- Checker
- Xianyang Zhang and Quan Zhou, author-reviewers
- Scope
- Theorem 1's Airy-factor curvature bounds and resulting strong log-concavity of Chernoff's density
- Basis
- Reported by the linked checker
Checking a formal statement does not establish that it matches the original problem.
Human understanding
The paper says GPT wrote the proof and most exposition. Human checking and revision are documented, but a distinct human explanation of the central peeling and convolution mechanism is not; Few is the missing-evidence default, not a claim that the authors cannot understand it.
Correction and publication history
The model-origin proof addresses the 2014 strong log-concavity conjecture.
Read this published revision