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arXiv · 2606.03991

The Grothendieck Constant is Less Than $\frac{\pi}{2 \log (1+ \sqrt{2})} - 10^{-5}$

Alan Li·Rahul Saha·Anton Xue·Swarat Chaudhuri·Adam Klivans·Pravesh K Kothari·Raghu Meka
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Abstract

We prove that the Grothendieck constant $K_G < \frac{\pi}{2 \log (1+ \sqrt{2})} - 10^{-5}$. This improves on the work of Braverman, Makarychev, Makarychev, and Naor (2011), who proved that $K_G < \frac{\pi}{2 \log (1+ \sqrt{2})} - \epsilon$ for an unspecified $\epsilon>0$.

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Alan Li, Rahul Saha, Anton Xue, Swarat Chaudhuri, Adam Klivans, Pravesh K Kothari, Raghu Meka. 2026-06-02. The Grothendieck Constant is Less Than $\frac{\pi}{2 \log (1+ \sqrt{2})} - 10^{-5}$. https://arxiv.org/abs/2606.03991

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