{"id":"openai-math/The-Gaussian-Propeller-Bound-in-Every-Dimension","pdf":"https://github.com/openai/math/blob/main/preprints/The-Gaussian-Propeller-Bound-in-Every-Dimension-September-24-2026/main.pdf","url":"https://github.com/openai/math/tree/main/preprints/The-Gaussian-Propeller-Bound-in-Every-Dimension-September-24-2026","tags":["geometry","gaussian-measure","partitions","extremal-problems"],"score":0,"title":"The Gaussian propeller bound in every dimension","domain":"Convex and metric geometry","family":"096","origin":"ai-generated","source":"openai-math","authors":["OpenAI"],"reviews":0,"subject":"math.MG","summary":"We prove the Gaussian propeller conjecture: for every finite measurable partition of a Euclidean space, the sum of the squared lengths of its Gaussian first moments is at most $`9/(8\\pi)`$. For dimension at least two and at least three cells, three planar sectors of angle $`2\\pi/3`$, extended by an orthogonal Euclidean factor, attain the bound.","category":"research","comments":0,"disputed":false,"division":"math","mentions":0,"discussed":0,"published":"2026-09-24","reactions":{},"formalized":true,"family_title":"The Gaussian propeller conjecture in every dimension"}