五项数学新发现，由人与Grok协作验证，涵盖凸集、概率不等式等多个领域。
Grokability in five inequalities
- 通过人机协作发现五类数学不等式的新边界
- 改进了高维凸集的高斯周长下界和$g$-Sidon集大小渐近界
- 适用于分析数学、概率论及组合优化研究者
本文报告与Grok协作发现的五项数学成果，均已由作者验证。包括：$ \mathbb{R}^n$中凸集最大高斯周长的更优下界；哈密顿立方体$\{-1,1\}^n$上更紧的$L_2$-$L_1$矩比较不等式；自卷积不等式的强化形式；$\{1,\dots,n\}$中$g$-Sidon集最大尺寸的改进渐近界；以及最优平衡的Szarek不等式。
原文摘要 · Abstract (English)
In this note, we report five mathematical discoveries made in collaboration with Grok, all of which have been subsequently verified by the authors. These include an improved lower bound on the maximal Gaussian perimeter of convex sets in $\mathbb{R}^n$, sharper $L_2$-$L_1$ moment comparison inequalities on the Hamming cube $\{-1,1\}^n$, a strengthened autoconvolution inequality, improved asymptotic bounds on the size of the largest $g$-Sidon sets in $\{1,\dots,n\}$, and an optimal balanced Szarek's inequality.
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