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The Grothendieck Constant is Less Than $\frac{\pi}{2 \log (1+ \sqrt{2})} - 10^{-5}$
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Computer Science > Data Structures and Algorithms [Submitted on 2 Jun 2026 (v1), last revised 6 Jun 2026 (this version, v2)] Title:The Grothendieck Constant is Less Than $\fracπ{2 \log (1+ \sqrt{2})} - 10^{-5}$ View PDF HTML (experimental)Abstract:We prove that the Grothendieck constant $K_G 0$. Submission history From: Pravesh K Kothari [view email][v1] Tue, 2 Jun 2026 17:59:53 UTC (829 KB)
Computer Science > Data Structures and Algorithms
[Submitted on 2 Jun 2026 (v1), last revised 6 Jun 2026 (this version, v2)]
Title:The Grothendieck Constant is Less Than $\fracπ{2 \log (1+ \sqrt{2})} - 10^{-5}$
View PDF HTML (experimental)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 $\epsilon>0$.
Submission history
From: Pravesh K Kothari [view email][v1] Tue, 2 Jun 2026 17:59:53 UTC (829 KB)
[v2] Sat, 6 Jun 2026 17:34:11 UTC (860 KB)
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