{
  "abstract": "Motivated by the geometric interpretation of spatially homogeneous cosmological models, we formulate a spacetime closedness theorem directly at the Lorentzian level. A classical space-form classification theorem organizes homogeneous and isotropic spatial geometries, but by itself it does not yield a Lorentzian statement about the ambient spacetime. The main technical step is to derive finite slice-volume from genuinely Lorentzian control hypotheses on the foliation. This is achieved in a strong version, for maximally regular globally hyperbolic $(n+1)$--spacetimes with a finite-time Big Bang and homogeneous complete spacelike slices, and in a weaker version in which maximal regularity is replaced by time-integrability of the accumulated expansion rate. In both cases, the argument separates an analytic step, deriving finite slice-volume from the Big Bang and temporal control, from a geometric step, upgrading finite volume to compactness by homogeneity and completeness. The theorem is stated in arbitrary spacetime dimension and is accompanied by a Lean~4 formalization of the strong and weak abstract statements.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": "Journal reference: Journal of Geometry and Physics 230, 105983, 2026",
  "arxiv": "2609.09181",
  "author_total": 1,
  "authors": [
    {
      "name": "Robert Monjo"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/5qxb7jf64acvs.bib",
  "cited_by": 0,
  "doi": "10.48550/arxiv.2609.09181",
  "fulltext_url": null,
  "id": "5qxb7jf64acvs",
  "issns": [],
  "landing_url": "https://arxiv.org/abs/2609.09181",
  "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",
      "gr-qc"
    ],
    [
      "arxiv",
      "math-ph"
    ],
    [
      "arxiv",
      "math.DG"
    ],
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      "arxiv",
      "math.MP"
    ]
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  "openalex": null,
  "pdf_url": "https://arxiv.org/pdf/2609.09181",
  "pmcid": null,
  "pmid": null,
  "published": "2026-09-01",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/5qxb7jf64acvs.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:20:12Z",
      "native_id": "2609.09181",
      "source": "arxiv",
      "url": "https://arxiv.org/abs/2609.09181"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "arxiv:math.DG",
      "subfield": "geometry-topology"
    },
    {
      "field": "mathematics",
      "origin": "arxiv:math-ph",
      "subfield": "mathematical-physics"
    },
    {
      "field": "physics",
      "origin": "arxiv:gr-qc",
      "subfield": "gravitation"
    }
  ],
  "title": "Spacetime closedness theorem for homogeneous Lorentzian foliations",
  "title_text": "Spacetime closedness theorem for homogeneous Lorentzian foliations",
  "type": "preprint",
  "updated_at": "2026-10-30T12:20:15Z",
  "url": "https://research.draconitic.com/paper/5qxb7jf64acvs",
  "venue": "arXiv",
  "versions": [
    {
      "doi": "10.1016/j.geomphys.2026.105983",
      "pid": null,
      "relation": "published-as",
      "title": null,
      "venue": null
    }
  ]
}