AI 中文总结
本文证明了Rⁿ中满足特定条件的满维紧凸体为特定单纯形的幺模像，解决了埃哈特体积猜想的等号情形，其结果由GPT-5.6-sol等生成式AI得到。
AI 中文摘要
我们证明：Rⁿ中每个满维紧凸体，若其重心为唯一的内部格点且体积为(n+1)ⁿ/n!，则它是单纯形(n+1)Δₙ-(1,…,1)的幺模像。这解决了埃哈特体积猜想的等号情形，作为OpenAI近期证明的不等式部分的对应结果。本文主要结果由生成式AI得到，具体包括GPT-5.6-sol、Fable 5及Danus系统。
英文摘要
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.
Comments30 pages. AI generated with essential human strategical idea input. Human verified. Version 2, no math change, references updated
