{"id":"openai-math/Counterexamples-to-the-duality-conjecture-for-metric-entropy","pdf":"https://github.com/openai/math/blob/main/preprints/Counterexamples-to-the-duality-conjecture-for-metric-entropy-September-24-2026/main.pdf","url":"https://github.com/openai/math/tree/main/preprints/Counterexamples-to-the-duality-conjecture-for-metric-entropy-September-24-2026","tags":["convex-geometry","metric-entropy","functional-analysis"],"score":0,"title":"Counterexamples to the duality conjecture for metric entropy","domain":"Functional analysis","family":"329","origin":"ai-generated","source":"openai-math","authors":["OpenAI"],"reviews":0,"subject":"math.FA","summary":"We disprove Pietsch's dimension-free duality conjecture for metric entropy. For every proposed pair of universal constants, we construct origin-symmetric convex bodies that violate the corresponding covering-entropy inequality, already when the covering body is a cube.","category":"research","comments":0,"disputed":false,"division":"math","mentions":0,"discussed":0,"published":"2026-09-24","reactions":{},"formalized":true,"family_title":"A counterexample to metric-entropy duality"}