{
  "abstract": "For every integer $k\\ge1$, we prove that each nonempty bounded set in real $\\ell_1^{4k+1}$ has an ambient enclosing ball of radius at most $(4k-1)/(4k)$ times its diameter. The bound is sharp in dimension five: $J(\\ell_1^5)=3/4$. If a Hadamard matrix of order $4k$ exists, then $J(\\ell_1^{4k-1})=J(\\ell_1^{4k})=J(\\ell_1^{4k+1})=(4k-1)/(4k)$. The upper bound for every $k\\ge1$ has been formalized in Lean.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2610.14055",
  "author_total": 1,
  "authors": [
    {
      "name": "Xiao Li"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/78z5md3334nwa.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2610.14055",
  "fulltext_url": null,
  "id": "78z5md3334nwa",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2610.14055",
  "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",
      "math.CO"
    ],
    [
      "arxiv",
      "math.MG"
    ],
    [
      "openalex",
      "2610|Advanced Banach Space Theory"
    ]
  ],
  "openalex": "W7221792018",
  "pdf_url": "https://arxiv.org/pdf/2610.14055",
  "pmcid": null,
  "pmid": null,
  "published": "2026-10-06",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/78z5md3334nwa.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:29:15Z",
      "native_id": "2610.14055",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2610.14055"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "arxiv:math.CO",
      "subfield": "combinatorics"
    },
    {
      "field": "mathematics",
      "origin": "arxiv:math.MG",
      "subfield": "geometry-topology"
    }
  ],
  "title": "Upper bounds for Jung constants of $\\ell_1^d$",
  "title_text": "Upper bounds for Jung constants of ℓ_1^d",
  "type": "preprint",
  "updated_at": "2026-10-30T12:29:15Z",
  "url": "https://research.draconitic.com/paper/78z5md3334nwa",
  "venue": "arXiv",
  "versions": []
}