{
  "abstract": "We study the twelve-vertex flag triangulation $T_{12}$ of $S^3$ and the Davis $4$-manifold $M(T_{12})$ associated with it. We prove that $T_{12}$ is, up to isomorphism, the unique flag triangulation of $S^3$ with twelve vertices in which every edge is contained in a square; this proves Milizia's Conjecture~6.31. We also prove a general criterion for the tangent Euler class of a Davis $4$-manifold to be bounded, and we verify it for $T_{12}$ by means of an explicit symmetric form. Since the Euler class takes the value $256$ on the fundamental class of $M(T_{12})$, the duality between bounded cohomology and simplicial volume gives $\\|M(T_{12})\\|>0$. This answers Milizia's Question~1.7.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": "2610.34743",
  "author_total": 2,
  "authors": [
    {
      "name": "Xiaojun Lai"
    },
    {
      "name": "Xueyuan Wan"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/2ng4a4k69j8e3.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2610.34743",
  "fulltext_url": null,
  "id": "2ng4a4k69j8e3",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2610.34743",
  "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.GT"
    ],
    [
      "openalex",
      "2608|Geometric and Algebraic Topology"
    ]
  ],
  "openalex": "W7223953572",
  "pdf_url": "https://arxiv.org/pdf/2610.34743",
  "pmcid": null,
  "pmid": null,
  "published": "2026-10-26",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/2ng4a4k69j8e3.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:35:40Z",
      "native_id": "2610.34743",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2610.34743"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "arxiv:math.GT",
      "subfield": "geometry-topology"
    }
  ],
  "title": "Positivity of simplicial volume and uniqueness for the twelve-vertex flag three-spheres",
  "title_text": "Positivity of simplicial volume and uniqueness for the twelve-vertex flag three-spheres",
  "type": "preprint",
  "updated_at": "2026-10-30T12:35:40Z",
  "url": "https://research.draconitic.com/paper/2ng4a4k69j8e3",
  "venue": "arXiv",
  "versions": []
}