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OpenAI reports: Mahler’s conjecture for general convex bodies

For every convex body K in R^n, n≥1, the manuscript reports volume product at its Santaló point at least (n+1)^(n+1)/(n!)², with equality exactly for simplices.

Sources for this record

What was already known

Known planar and asymptotic bounds do not give the exact simplex minimum in all dimensions. The centrally symmetric conjecture has a different sharper target.

What changed and why it matters

Determines the exact minimum and equality cases for unrestricted convex bodies in every dimension.

The AI contribution

OpenAI attributes the manuscript to an internal frontier model. Release-wide attribution does not establish the precise human role in this individual argument.

Limitations

The general and symmetric Mahler statements are distinct even though the manuscripts share a source family. AIProofWatch has not audited this proof or run a formal checker.

Verification evidence

Evidence labels show what supports the claim. Importance rates its impact if correct.

Author claim

The source reports this precise contribution; statement review does not establish a proof audit.

Accessible artifact / proof

Accessible supporting proof or code; not compiled or reproduced by AIProofWatch.

Correction and publication history

2026-10-11 · publication

Public-discussion audit found this substantive scoped contribution missing. Source statement, baseline, attribution and importance reviewed; no full proof audit. Historical addition without subscriber alerts.

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