[Submitted on 2 Jun 2026 (v1), last revised 11 Aug 2026 (this version, v3)]

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: Rahul Saha [view email]
[v1] Tue, 2 Jun 2026 17:59:53 UTC (829 KB)
[v2] Sat, 6 Jun 2026 17:34:11 UTC (860 KB)
[v3] Tue, 11 Aug 2026 22:55:15 UTC (1,353 KB)

Current browse context:

cs.DS

Bookmark

Bibliographic and Citation Tools

Code, Data and Media Associated with this Article

Demos

Recommenders and Search Tools

arXivLabs: experimental projects with community collaborators

arXivLabs is a framework that allows collaborators to develop and share new arXiv features directly on our website.

Both individuals and organizations that work with arXivLabs have embraced and accepted our values of openness, community, excellence, and user data privacy. arXiv is committed to these values and only works with partners that adhere to them.

Have an idea for a project that will add value for arXiv's community? Learn more about arXivLabs.