{
  "abstract": "Moser's worm problem asks for a planar region of minimum area containing a congruent copy of every rectifiable planar arc of length one. We study the Bellman's lost-in-a-forest problem escape path for the isosceles triangle \\[ T=\\text{conv}\\{(-c,0),(c,0),(0,s)\\},\\qquad s=\\frac{766}{\\sqrt{625565}},\\qquad c=\\frac{197}{\\sqrt{625565}}. \\] The paper gives an exact positive four-source support calibration, a continuum to standard-polygonal reduction, a selected $Λ$-gap estimate, a corrected high-angle side-meeting argument, and exact finite ledgers. The original inner-anchor ledger covers 25 temporal orders: its 275 nonzero suffix states reduce to 13 exact squared norms and satisfy $\\|R\\|<27131/25000$. If either near anchor fails, a new delimiter-gap lemma produces one or two omitted hull edges whose normals range over an exact compact fan interval. A dependency-free rational replay checks 512 one-delimiter orders over 1540 signed half-angle intervals and 4096 two-delimiter orders over a finite signed rectangle cover. These three exhaustive branches give unconditionally \\[ E(T)\\ge D:=\\frac{82074390584}{84861020075} =0.9671624323094728\\ldots \\] Hence, the convex universal cover of Moser's worm \\[ \\frac{\\text{area}(T)}{D^2} =\\frac{11511821678274125}{44639604443512928} =0.257883595112076188\\ldots. \\]",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2609.04591",
  "author_total": 1,
  "authors": [
    {
      "name": "Zhipeng Deng"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/b4z5ark1b6x4v.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2609.04591",
  "fulltext_url": null,
  "id": "b4z5ark1b6x4v",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2609.04591",
  "language": null,
  "licence": "CC-BY-NC-ND-4.0",
  "licence_label": "CC BY-NC-ND 4.0",
  "licence_source": "article",
  "licence_url": "http://creativecommons.org/licenses/by-nc-nd/4.0/",
  "metadata_licence": "CC0-1.0",
  "native_subjects": [
    [
      "arxiv",
      "math.MG"
    ],
    [
      "openalex",
      "1704|Computational Geometry and Mesh Generation"
    ]
  ],
  "openalex": "W7211901191",
  "pdf_url": "https://arxiv.org/pdf/2609.04591",
  "pmcid": null,
  "pmid": null,
  "published": "2026-09-04",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/b4z5ark1b6x4v.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:19:18Z",
      "native_id": "2609.04591",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2609.04591"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "arxiv:math.MG",
      "subfield": "geometry-topology"
    }
  ],
  "title": "Balanced Support Calibrations for Moser's Worm Problem: Exact Certificate and Bound of Triangular Cover",
  "title_text": "Balanced Support Calibrations for Moser's Worm Problem: Exact Certificate and Bound of Triangular Cover",
  "type": "preprint",
  "updated_at": "2026-10-30T12:19:18Z",
  "url": "https://research.draconitic.com/paper/b4z5ark1b6x4v",
  "venue": "arXiv",
  "versions": []
}