Grokability in five inequalities
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arXiv
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| Format: | Preprint |
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2026
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| _version_ | 1866913095643824128 |
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| author | Ivanisvili, Paata Xie, Xinyuan |
| author_facet | Ivanisvili, Paata Xie, Xinyuan |
| contents | 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. |
| format | Preprint |
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arxiv_https___arxiv_org_abs_2605_05193 |
| institution | arXiv |
| publishDate | 2026 |
| record_format | arxiv |
| spellingShingle | Grokability in five inequalities Ivanisvili, Paata Xie, Xinyuan Probability Artificial Intelligence Analysis of PDEs Classical Analysis and ODEs Functional Analysis 52A40, 46E30, 42C10, 05D40, 11B13, 68T01 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. |
| title | Grokability in five inequalities |
| topic | Probability Artificial Intelligence Analysis of PDEs Classical Analysis and ODEs Functional Analysis 52A40, 46E30, 42C10, 05D40, 11B13, 68T01 |
| url | https://arxiv.org/abs/2605.05193 |