{"id":"openai-math/Sharp-binary-information-contraction-on-the-discrete-cube","pdf":"https://github.com/openai/math/blob/main/preprints/Sharp-binary-information-contraction-on-the-discrete-cube-September-24-2026/main.pdf","url":"https://github.com/openai/math/tree/main/preprints/Sharp-binary-information-contraction-on-the-discrete-cube-September-24-2026","tags":["information-theory","boolean-functions","entropy"],"score":0,"title":"Sharp binary-information contraction on the discrete cube","domain":"Theoretical computer science","family":"119","origin":"ai-generated","source":"openai-math","authors":["OpenAI"],"reviews":0,"subject":"cs.CC","summary":"We prove sharp contraction of the information carried by a binary channel under independent symmetric noise on a uniform discrete cube. At fixed initial information, a noisy coordinate retains the most information. The Boolean specialization resolves the Courtade–Kumar conjecture and gives an output-entropy refinement. We also establish a stronger mean-dependent entropy-production bound. The proof combines an explicit three-point optimizer for the local joining problem, two entropy capacities, and a common-output thinning inequality, followed by dimension induction and integration along the…","category":"research","comments":0,"disputed":false,"division":"cs","mentions":0,"discussed":0,"published":"2026-09-24","reactions":{},"formalized":true,"family_title":"The Courtade–Kumar and Hellinger conjectures"}