精选理由
Ehrhart猜想等号情形被GPT-5.6-sol等AI证明了，数学证明也能这么玩。
论文证明了 n 维空间中体积为 (n+1)^n/n! 且重心是唯一内格点的凸体必为单纯形 (n+1)Δ_n-(1,…,1) 的单模像。这一结果补上了 Ehrhart 体积猜想的等号情形，与 OpenAI 近期证明的不等式部分形成对应。论文称主要结果由生成式 AI 完成，涉及 GPT-5.6-sol、Fable 5 和 Danus 系统。
原文 · arXiv: OpenAI
The equality case of Ehrhart's volume conjecture
We prove that every full-dimensional compact convex body in $\mathbb R^n$ whose barycenter is its unique interior lattice point and whose volume is $(n+1)^n/n!$ is a unimodular image of the simplex $(n+1)Δ_n-(1,\dots,1)$. This resolves the equality case of Ehrhart's volume conjecture, as a counterpart of the inequality part recently proved by OpenAI. The main result of this paper is obtained by generative AI, particularly GPT-5.6-sol, Fable 5, and the Danus system.