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

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

arxiv: 2606.03991 · v2 · pith:CU4PLLDRnew · submitted 2026-06-02 · 💻 cs.DS

The Grothendieck Constant is Less Than frac{π}{2 log (1+ sqrt{2})} - 10⁻⁵

Alan Li , Rahul Saha , Anton Xue , Swarat Chaudhuri , Adam Klivans , Pravesh K Kothari , Raghu Meka This is my paper

classification 💻 cs.DS

keywords fracsqrtconstantepsilongrothendieckmakarychevbravermanimproves

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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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The Grothendieck Constant is Less Than frac{π}{2 log (1+ sqrt{2})} - 10⁻⁵

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