{"id":"openai-math/Asymptotic-midpoint-uniform-convexity-and-unbounded-diamond-distortion-in-a-reflexive-tree-space","pdf":"https://github.com/openai/math/blob/main/preprints/Asymptotic-midpoint-uniform-convexity-and-unbounded-diamond-distortion-in-a-reflexive-tree-space-September-27-2026/manuscript.pdf","url":"https://github.com/openai/math/tree/main/preprints/Asymptotic-midpoint-uniform-convexity-and-unbounded-diamond-distortion-in-a-reflexive-tree-space-September-27-2026","tags":["banach-spaces","functional-analysis","uniform-convexity"],"score":0,"title":"Asymptotic midpoint uniform convexity and unbounded diamond distortion in a reflexive tree space","domain":"Functional analysis","family":"331","origin":"ai-generated","source":"openai-math","authors":["OpenAI"],"reviews":0,"subject":"math.FA","summary":"We construct a separable reflexive real Banach space whose given norm is asymptotically midpoint uniformly convex but which admits no asymptotically uniformly convex equivalent norm. Its averaged midpoint modulus is at least $`\\sqrt{1+t^2/12}-1`$, and the countably branching diamond of depth k has distortion at least $`\\sqrt{1+k/12}`$ in this space. This gives a negative answer to the reflexive diamond converse for asymptotic uniform convexifiability.","category":"research","comments":0,"disputed":false,"division":"math","mentions":0,"discussed":0,"published":"2026-09-27","reactions":{},"formalized":true,"family_title":"Reflexive midpoint convexity and diamond distortion"}