Manuscript OpenAI@2026-10-07 · OpenAI.tex · remark · 6a931f8f
Remark: 087-03. Symplectic Balls in Symmetric Polar Products
Manuscript map · lines 4165–4174
OpenAI@2026-10-07#rem:oai-p-087-03
Authors: OpenAI. Family 087.
Title: Symplectic Balls in Symmetric Polar Products.
Abstract: For every integer n ≥ 2 and every origin-symmetric convex body $K{}subset{}mathbb R{}n$, we prove that the Gromov width of ${}mathop{{}mathrm{int}}{}nolimits K{}times{}mathop{{}mathrm{int}}{}nolimits K{}{}circ$ is 4. We construct smooth symplectic embeddings of standard balls of every capacity $0{}lt c{}lt 4$ into this polar product. Volume preservation then resolves the symmetric Mahler conjecture positively in every dimension.
This abstract is a catalogue record. It is not a verification and not a premise. It does not close O.1. O.1 stays NOT_CLOSED. No quantum coefficient is admitted. No compilation is asserted.
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