New Lower and Upper Bounds for the Grothendieck Constant

[Submitted connected 11 Aug 2026 (v1), past revised 12 Aug 2026 (this version, v2)]

View PDF HTML (experimental)

Abstract:We found caller bounds connected the Grothendieck changeless $K_G$: \[
\frac{6\pi}{11}
\le
K_G
\le
\frac{\pi}{2\log(1+\sqrt2)} - 10^{-4}. \] Methodologically, our little bound attack differs from erstwhile useful by establishing limitations connected the asymptotically optimal Krivine schemes, alternatively than giving definitive constructions of spread instances. Our precocious bound is obtained by proposing and analyzing the first asymptotic building of rounding schemes, whereas erstwhile useful only see low-dimensional schemes. Together, these bounds find the antecedently chartless tenths digit of $K_G$ to beryllium $7$. The bounds were discovered by a long-running collaborative effort of humans and a long-horizon AI investigation strategy that we engineered.