{"id":"openai-math/A-sharp-entropy-bound-and-the-simplex-inequality-for-isotropic-constants","pdf":"https://github.com/openai/math/blob/main/preprints/A-sharp-entropy-bound-and-the-simplex-inequality-for-isotropic-constants-October-5-2026/isotropic-simplex.pdf","url":"https://github.com/openai/math/tree/main/preprints/A-sharp-entropy-bound-and-the-simplex-inequality-for-isotropic-constants-October-5-2026","tags":["convex-geometry","log-concave","information-theory"],"score":0,"title":"A sharp entropy bound and the simplex inequality for isotropic constants","domain":"Convex and metric geometry","family":"101","origin":"ai-generated","source":"openai-math","authors":["OpenAI"],"reviews":0,"subject":"math.MG","summary":"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 ℝ m , with equality precisely for invertible affine images of products of one-sided exponential laws.","category":"research","comments":0,"disputed":false,"division":"math","mentions":0,"discussed":0,"published":"2026-10-05","reactions":{},"formalized":false,"family_title":"The sharp simplex conjecture for isotropic constants"}