{
  "abstract": "This note proves that the truncated octahedron of Archimedes is a strict local minimizer of the isoperimetric quotient among parallelohedra in three dimensions. This extends the corresponding result from the five-dimensional lattice-Voronoi subclass to the full ten-dimensional local parameter space. A six-zone parametrization and Schur's lemma reduce the Hessian to two positive definite $2\\times 2$ matrices.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": "Journal reference: Nonlinear Anal. 276 (2027)",
  "arxiv": "2609.03093",
  "author_total": 1,
  "authors": [
    {
      "name": "Lark Song"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/7f91qatkb36t2.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2609.03093",
  "fulltext_url": null,
  "id": "7f91qatkb36t2",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2609.03093",
  "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.MG"
    ],
    [
      "openalex",
      "2604|Point processes and geometric inequalities"
    ]
  ],
  "openalex": "W7208761205",
  "pdf_url": "https://arxiv.org/pdf/2609.03093",
  "pmcid": null,
  "pmid": null,
  "published": "2026-10-14",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/7f91qatkb36t2.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:36:32Z",
      "native_id": "2609.03093",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2609.03093"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "arxiv:math.MG",
      "subfield": "geometry-topology"
    }
  ],
  "title": "Local stability for the truncated octahedral conjecture",
  "title_text": "Local stability for the truncated octahedral conjecture",
  "type": "preprint",
  "updated_at": "2026-11-01T12:20:50Z",
  "url": "https://research.draconitic.com/paper/7f91qatkb36t2",
  "venue": "arXiv",
  "versions": [
    {
      "doi": "10.1016/j.na.2026.114309",
      "pid": null,
      "relation": "published-as",
      "title": null,
      "venue": null
    }
  ]
}