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PreprintCC BY 4.0arXiv

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 ≤ KG ≤ 1.7799. Furthermore, numerical heuristics suggest the estimate KG ≈ 1.779. We start by simplifying the Gaussian duality theory of KG, 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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Cite

BibTeXRIS
BibTeX
@misc{heilman2026primaldual,
  title = {{Primal/Dual Method for the Grothendieck Constant}},
  author = {Steven Heilman and Chris Jones and Giulio Malavolta},
  howpublished = {arXiv},
  year = {2026},
  month = oct,
  doi = {10.48550/arxiv.2610.10477},
  eprint = {2610.10477},
  archivePrefix = {arXiv},
  url = {https://arxiv.org/abs/2610.10477},
  note = {CC BY 4.0},
}
RIS
TY  - UNPB
TI  - Primal/Dual Method for the Grothendieck Constant
AU  - Steven Heilman
AU  - Chris Jones
AU  - Giulio Malavolta
PY  - 2026
DA  - 2026/10/07
PB  - arXiv
DO  - 10.48550/arxiv.2610.10477
UR  - https://arxiv.org/abs/2610.10477
AB  - We determine the hundredths digit of the real Grothendieck constant by proving 1.773 ≤ K_G ≤ 1.7799. Furthermore, numerical heuristics suggest the estimate K_G ≈ 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).
ER  -