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Research / Jul 2026

Sharp thin-shell variance bound for log-concave distributions

What is the optimal universal bound on Var(|X|²) for a mean-zero log-concave random vector with identity covariance?

Model / AI: GPT-5.6 Pro

self-reported
Jul 2026

Optimal constant in the thin-shell inequality

Model / AI: GPT-5.6 Pro

self-reported

Chen and Klartag present the sharp constant 8, attained by independent centered exponential coordinates. They credit GPT-5.6 Pro with finding the proof after Chen supplied prompts informed by the authors’ discussions. The arXiv submission includes the chat log.

Source read 2026-09-08. Located through seewoo5/awesome-ai-for-math. Read the preprint abstract, AI-use disclosure and ancillary-file listing. The argument was not independently verified.