{
  "abstract": "We prove that the four-pentachoron homotopy \\(4\\)-sphere \\(Q\\) singled out in the census of Burke, Burton and Spreer is PL homeomorphic to the standard \\(4\\)-sphere. The key construction identifies the compact exterior of an explicit locally flat \\(2\\)-sphere in an auxiliary 39-vertex model of \\(Q\\) with the exterior of Budney, Burton and Hillman, then certifies its fibration by a normal cut followed by a relative collapse. The exterior identification uses finite checked moves, an exact regular-neighbourhood construction and a PL lemma controlling the passage through an ideal triangulation. Cutting the compact exterior along the specified normal hypersurface gives a manifold that collapses onto one boundary copy of the punctured \\(3\\)-torus in 209,144 elementary pairs; a marked product lemma identifies the cut as a product. The resulting integral monodromy realizes \\(Q\\) as a Cappell--Shaneson filling whose two surgery framings are standard by Gompf's results. The fibration certificate is independent of Issa's earlier PL-compatible constructions. Combined with the published census, the result establishes standardness for every homotopy \\(4\\)-sphere triangulated with at most four pentachora.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2610.27283",
  "author_total": 2,
  "authors": [
    {
      "name": "Vance Faber"
    },
    {
      "name": "Michael Murphy"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/ejdzhapb7hers.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2610.27283",
  "fulltext_url": null,
  "id": "ejdzhapb7hers",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2610.27283",
  "language": null,
  "licence": "CC0-1.0",
  "licence_label": "CC0",
  "licence_source": "article",
  "licence_url": "http://creativecommons.org/publicdomain/zero/1.0/",
  "metadata_licence": "CC0-1.0",
  "native_subjects": [
    [
      "arxiv",
      "math.CO"
    ],
    [
      "openalex",
      "2608|Geometric and Algebraic Topology"
    ]
  ],
  "openalex": "W7223115914",
  "pdf_url": "https://arxiv.org/pdf/2610.27283",
  "pmcid": null,
  "pmid": null,
  "published": "2026-10-19",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/ejdzhapb7hers.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:34:08Z",
      "native_id": "2610.27283",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2610.27283"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "arxiv:math.CO",
      "subfield": "combinatorics"
    }
  ],
  "title": "PL standardness of the four-pentachoron census sphere Q",
  "title_text": "PL standardness of the four-pentachoron census sphere Q",
  "type": "preprint",
  "updated_at": "2026-10-30T12:34:08Z",
  "url": "https://research.draconitic.com/paper/ejdzhapb7hers",
  "venue": "arXiv",
  "versions": []
}