{
  "abstract": "Moser's worm problem asks for a planar region of least area containing a congruent copy of every unit arc. We show that the infimum area $α$ among convex universal covers satisfies $0.239\\leα\\le0.24633\\ldots$, reducing the gap between the previous refereed bounds by over $75\\%$. For the lower bound, we choose four unit polygonal arcs and prove by finite subdivision that, however they are placed, their convex hull has area at least $0.239$. For the upper bound, we construct a quadrilateral of area $0.24633\\ldots$ and prove cover universality by showing that its support inequalities force uncovered arcs to have length greater than one. The full proof is formalized in Lean 4 and verified by the Lean kernel. Code and certificates are available at https://github.com/ethan-keller/moser-worm-improved-bounds.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2609.21968",
  "author_total": 1,
  "authors": [
    {
      "name": "Ethan Keller"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/9tcmxype2ajvq.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2609.21968",
  "fulltext_url": null,
  "id": "9tcmxype2ajvq",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2609.21968",
  "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",
      "cs.CG"
    ],
    [
      "arxiv",
      "math.MG"
    ],
    [
      "openalex",
      "1704|Computational Geometry and Mesh Generation"
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  "openalex": "W7213902947",
  "pdf_url": "https://arxiv.org/pdf/2609.21968",
  "pmcid": null,
  "pmid": null,
  "published": "2026-09-18",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/9tcmxype2ajvq.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:23:07Z",
      "native_id": "2609.21968",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2609.21968"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "arxiv:math.MG",
      "subfield": "geometry-topology"
    }
  ],
  "title": "Improved bounds for universal convex covers of unit arcs",
  "title_text": "Improved bounds for universal convex covers of unit arcs",
  "type": "preprint",
  "updated_at": "2026-10-30T12:23:07Z",
  "url": "https://research.draconitic.com/paper/9tcmxype2ajvq",
  "venue": "arXiv",
  "versions": []
}