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Strong Log-Concavity of Chernoff's Density

Is the density of Chernoff's distribution - the law of argmaxt{W(t)t2}\operatorname{argmax}_t \{W(t) - t^2\} for two-sided Brownian motion WW - strongly log-concave, as conjectured by Balabdaoui and Wellner in 2014?

Result
Proved
Status
Resolved
AI contribution
AI-discovered
Method
Argument
Field
Probability & statistics
Posed by
Fadoua Balabdaoui & Jon A. Wellner
Year posed
2014
Years open
12y
Solved
2026-07-21
Model
GPT-5.6 Sol
Vendor
OpenAI
Collaborators
Xianyang Zhang, Quan Zhou
Verification
Unreviewed
Publication
Preprint
Significance
10 / 100
Disclosed cost
Wikipedia
No dedicated article

What the AI did

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

Verification

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 Not yet peer-reviewed.

Source

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

Discussion