The Grothendieck constant is strictly smaller than Krivine's bound

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Mark Braverman , Konstantin Makarychev , Yury Makarychev , Assaf Naor This is my paper · ORCID

classification math.FAcs.DS

keywords constantgrothendieckboundfrackrivineprovesmallersqrt

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abstract

We prove that $K_G<\frac{\pi}{2\log(1+\sqrt{2})}$, where $K_G$ is the Grothendieck constant.

Forward citations

Reviewed papers in the Pith corpus that reference this work. Sorted by Pith novelty score. Full citation record

New Lower and Upper Bounds for the Grothendieck Constant
cs.CC 2026-08 conditional novelty 8.0 of 10

New rigorous bounds pin the Grothendieck constant to [6pi/11, pi/(2 log(1+sqrt 2)) - 10^-4], improving both known lower and upper bounds.
Quasirandom quantum channels
quant-ph 2019-08 accept novelty 8.0 of 10

Irreducibly covariant quantum channels satisfy a quantum version of the expander mixing lemma: uniformity implies spectral expansion up to the optimal constant 2π².
Long-Horizon AI Research for Grothendieck Constant: A Case Study in Human-AI Mathematical Collaboration
cs.AI 2026-08 conditional novelty 6.0 of 10

A human-AI team reports new bounds on the Grothendieck constant, 6π/11 ≤ K_G ≤ π/(2 log(1+√2)) - 3.47e-4, crediting an AI model with the core idea for the lower bound.