A Lower Bound for Grothendieck's Constant

TL;DR

This paper establishes a new lower bound for Grothendieck's real constant, slightly exceeding the previous known bound, thus advancing the understanding of this fundamental mathematical constant.

Contribution

It provides an improved lower bound for Grothendieck's real constant, surpassing the longstanding previous estimate.

Findings

Grothendieck's real constant $K_G$ is at least c + 10^{-26}

The previous lower bound was approximately 1.676956674215576

The new bound slightly exceeds the previous estimate

Abstract

We show that Grothendieck's real constant $K_{G}$ satisfies $K_G\geq c+10^{-26}$, improving on the lower bound of $c=1.676956674215576\ldots$ of Davie and Reeds from 1984 and 1991, respectively.