Manuscript OpenAI@2026-10-07 · OpenAI.tex · remark · 6a931f8f
Remark: 101-01. A sharp entropy bound and the simplex inequality for isotropic constants
Manuscript map · lines 4435–4444
OpenAI@2026-10-07#rem:oai-p-101-01
Authors: OpenAI. Family 101.
Title: A sharp entropy bound and the simplex inequality for isotropic constants.
Abstract: We prove the strong isotropic constant conjecture: in each dimension, simplices are the unique maximizers of the isotropic constant among convex bodies. We also prove the sharp entropy bound $h(f){}ge m+{}tfrac12{}log{}det{}mathop{{}mathrm{Cov}}{}nolimits (f)$ for every log-concave probability density on ℝm, with equality precisely for invertible affine images of products of one-sided exponential laws.
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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