{"id":"openai-math/A-product-counterexample-to-the-simplex-maximum-for-projection-body-volume","pdf":"https://github.com/openai/math/blob/main/preprints/A-product-counterexample-to-the-simplex-maximum-for-projection-body-volume-September-24-2026/paper.pdf","url":"https://github.com/openai/math/tree/main/preprints/A-product-counterexample-to-the-simplex-maximum-for-projection-body-volume-September-24-2026","tags":["convex-geometry","projection-bodies","geometric-inequalities"],"score":0,"title":"A product counterexample to the simplex maximum for projection-body volume","domain":"Convex and metric geometry","family":"088","origin":"ai-generated","source":"openai-math","authors":["OpenAI"],"reviews":0,"subject":"math.MG","summary":"The product of two ten-dimensional simplices has larger normalized projection-body volume than a twenty-dimensional simplex. This gives a counterexample to Brannen's proposed simplex maximum.","category":"research","comments":0,"disputed":false,"division":"math","mentions":0,"discussed":0,"published":"2026-09-24","reactions":{},"formalized":true,"family_title":"Sharp projection-body inequalities and a counterexample to simplex maximization"}