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arXiv · 2609.20074

A computer-assisted upper bound of 1.7813 for the real Grothendieck constant

Bo Peng
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Abstract

We give a computer-assisted proof that the universal real Grothendieck constant satisfies $K_G^{\mathbb R}\le 1.7813$. The construction combines an explicit odd Hermite threshold of degree $11$ with a signed correlation polynomial of degree $51$. A sufficient inverse-majorant inequality is certified by enclosing the scalar coefficient head through degree $301$ and bounding the entire remaining tail using a weighted Gaussian trace estimate. The finite integral is bounded on a complete interval partition; its spatial exterior is controlled analytically. Exact parameters and source code that regenerate all accepted numerical inputs accompany the paper. The bound improves both the explicit bound $1.7818666069360661$ in the recent literature and the subsequently reported, system-tested value $1.7813319810625639$.

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Bo Peng. 2026-09-17. A computer-assisted upper bound of 1.7813 for the real Grothendieck constant. https://arxiv.org/abs/2609.20074

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