Grokability in five inequalities

TL;DR

This paper reports five new mathematical inequalities and bounds related to convex geometry, probability, and additive combinatorics, verified through collaboration and analysis.

Contribution

It introduces five novel inequalities and bounds, improving previous results in Gaussian perimeter, moment comparisons, autoconvolution, Sidon sets, and Szarek's inequality.

Findings

Enhanced lower bound on Gaussian perimeter of convex sets

Sharper $L_2$-$L_1$ moment comparison inequalities on the Hamming cube

Improved asymptotic bounds on the size of $g$-Sidon sets

Abstract

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.