{
  "abstract": "It is known that for every partition of the sphere $S^2$ of unit diameter into four parts, the largest diameter of a part is at least $\\sqrt{(3+\\sqrt{3})/6} = 0.88807\\dots$, and this bound is attained. The conjecture of D.~Gale (1953) asserts that no set in $\\mathbb{R}^3$ has a larger ratio. In this paper, we construct a $101$-point set $V\\subset\\mathbb{R}^3$ such that every partition of $V$ into four parts contains a part of diameter greater than $0.88928 \\, \\operatorname{diam} V$.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2610.28828",
  "author_total": 1,
  "authors": [
    {
      "name": "Vsevolod Voronov"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/94g5e3e70jtps.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2610.28828",
  "fulltext_url": null,
  "id": "94g5e3e70jtps",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2610.28828",
  "language": null,
  "licence": "LicenseRef-arXiv-nonexclusive-1.0",
  "licence_label": "arXiv licence",
  "licence_source": "article",
  "licence_url": "http://arxiv.org/licenses/nonexclusive-distrib/1.0/",
  "metadata_licence": "CC0-1.0",
  "native_subjects": [
    [
      "arxiv",
      "math.CO"
    ],
    [
      "arxiv",
      "math.MG"
    ],
    [
      "openalex",
      "2604|Point processes and geometric inequalities"
    ]
  ],
  "openalex": "W7223212321",
  "pdf_url": "https://arxiv.org/pdf/2610.28828",
  "pmcid": null,
  "pmid": null,
  "published": "2026-10-20",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/94g5e3e70jtps.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:34:22Z",
      "native_id": "2610.28828",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2610.28828"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "arxiv:math.CO",
      "subfield": "combinatorics"
    },
    {
      "field": "mathematics",
      "origin": "arxiv:math.MG",
      "subfield": "geometry-topology"
    }
  ],
  "title": "A counterexample to Gale's conjecture in $\\mathbb{R}^3$",
  "title_text": "A counterexample to Gale's conjecture in ℝ^3",
  "type": "preprint",
  "updated_at": "2026-10-30T12:34:22Z",
  "url": "https://research.draconitic.com/paper/94g5e3e70jtps",
  "venue": "arXiv",
  "versions": []
}