{
  "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).",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2610.10477",
  "author_total": 3,
  "authors": [
    {
      "name": "Steven Heilman"
    },
    {
      "name": "Chris Jones"
    },
    {
      "name": "Giulio Malavolta"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/fv46h1tb9bpa8.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2610.10477",
  "fulltext_url": null,
  "id": "fv46h1tb9bpa8",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2610.10477",
  "language": null,
  "licence": "CC-BY-4.0",
  "licence_label": "CC BY 4.0",
  "licence_source": "article",
  "licence_url": "http://creativecommons.org/licenses/by/4.0/",
  "metadata_licence": "CC0-1.0",
  "native_subjects": [
    [
      "arxiv",
      "cs.CC"
    ],
    [
      "arxiv",
      "math.FA"
    ],
    [
      "openalex",
      "1703|Complexity and Algorithms in Graphs"
    ]
  ],
  "openalex": "W7220983275",
  "pdf_url": "https://arxiv.org/pdf/2610.10477",
  "pmcid": null,
  "pmid": null,
  "published": "2026-10-07",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/fv46h1tb9bpa8.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:27:42Z",
      "native_id": "2610.10477",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2610.10477"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "arxiv:math.FA",
      "subfield": "analysis-pdes"
    }
  ],
  "title": "Primal/Dual Method for the Grothendieck Constant",
  "title_text": "Primal/Dual Method for the Grothendieck Constant",
  "type": "preprint",
  "updated_at": "2026-10-30T12:27:42Z",
  "url": "https://research.draconitic.com/paper/fv46h1tb9bpa8",
  "venue": "arXiv",
  "versions": []
}