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OpenAI reports: The symmetric Mahler conjecture

OpenAI reports that every origin-symmetric convex body in n-dimensional real space has volume product at least 4^n/n!, with equality precisely for invertible linear images of Hanner polytopes.

Sources for this record

What was already known

Special dimensions and classes of convex bodies do not establish the all-dimensional symmetric volume-product minimum. The target also includes a complete equality classification.

What changed and why it matters

Determines the stated all-dimensional symmetric minimum and its equality cases.

The AI contribution

OpenAI attributes these manuscripts to its internal model. The entry does not infer individual human contributions beyond that publisher attribution.

Limitations

Origin symmetry is essential to this statement. The general nonsymmetric Mahler manuscript and the symplectic companion are distinct claims, not counted again in this entry. Preprint. This is a source-statement and significance assessment, not a proof audit. No independent checking or successful formal compilation is asserted by this entry.

Verification evidence

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

Author claim

The publisher reports the scoped result. AIProofWatch has not independently validated its correctness.

Accessible artifact / proof

The original written argument is accessible. Availability does not establish a successful proof check or Lean verification.

Correction and publication history

2026-10-11 · publication

Historical report added after statement, scope, and importance review. No proof audit or formal checking asserted; subscriber alerts disabled.

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