OpenAI · 087-01 · 2026-09-22 · Convex and metric geometry
The symmetric Mahler conjecture and its equality cases
preprints/The-symmetric-Mahler-conjecture-and-its-equality-cases-September-22-2026
Family 087. The Mahler conjectures and symplectic width.
The authors are OpenAI. This companion does not verify the proof and does not adopt it as a theorem of Ngo Cheung’s series. It is not a premise. O.1 stays NOT_CLOSED. Anti-de Sitter results are not a de Sitter state, not Em02-E’s relational lapse, not XVI-P’s QdS scheme, and not XVI-Q’s sigma-image record. No quantum coefficient is admitted. No compilation is asserted.
Read against the standing problems
Standing problems. No standing problem is named in this text. It was still read against the nine problems and does not close any of them. The authors are OpenAI. The companion does not verify the proof. This is not a premise of a manuscript by Ngo Cheung. O.1 stays NOT_CLOSED. No quantum coefficient is admitted. No compilation is asserted. XVI-P · XVI-N
Resolves the symmetric and nonsymmetric geometric Mahler conjectures in every dimension, with Hanner polytopes and simplices as the respective volume-product minimizers and all equality cases classified. The corresponding sharp functional Mahler inequalities also hold. For , every symmetric polar product in dimension has Gromov width .
We resolve the symmetric Mahler conjecture positively, including its equality classification. Every origin-symmetric convex body in ℝn has volume product at least , with equality exactly for invertible linear images of Hanner polytopes.
Preprint source and Lean scope
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This preprint is named in the Lean scope note for 087: The Mahler conjectures, functional inequalities and polar-product symplectic width. The authors are OpenAI. This companion does not verify the formalization. It is not a premise. The OAI library is not imported. No compilation is asserted. O.1 stays NOT_CLOSED.