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arXiv · 2610.10477

Primal/Dual Method for the Grothendieck Constant

Steven Heilman·Chris Jones·Giulio Malavolta
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Abstract

We determine the hundredths digit of the real Grothendieck constant by proving $1.773 \leq K_G \leq 1.7799$. Furthermore, numerical heuristics suggest the estimate $K_G \approx 1.779$. We start by simplifying the Gaussian duality theory of $K_G$, based on Hermite projection games and Krivine rounding schemes. The bounds are obtained by a heuristic primal/dual search for these objects, followed by rigorous {\em certification} of their values. The search and certification are performed using AI tools, and in particular the rigorous certificates are very large (analytical reductions to thousands of numerical inequalities).

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Steven Heilman, Chris Jones, Giulio Malavolta. 2026-10-07. Primal/Dual Method for the Grothendieck Constant. https://arxiv.org/abs/2610.10477

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