{
  "abstract": "We construct a finite predictive framework in which Lorentzian spacetime and vacuum Einstein dynamics are reconstructed from operational renewal data. Quotienting histories by equality of their conditional futures yields a canonical predictive carrier, a positive history algebra, and an intrinsic word-Gram hierarchy; together these define the Renewal Grand Tensor, from which relational geometry is reconstructed. Two independent finite criteria select three spatial dimensions, while one additional protected signed direction fixes a (1,3) Lorentzian signature. Calibrated renewal statistics then reconstruct the spatial metric, lapse, and shift. A variational structure is reconstructed directly from the finite dynamics. On certified noncollapsed continuum branches, it converges to Palatini--Holst gravity and yields the vacuum Einstein equation, while failure of the certification conditions produces explicit obstructions. The same framework also supports a cutoff-uniform nonsymmetric 3+1 class with arbitrary three-dimensional dependence, stable across an open family of renewal laws sharing the same continuum limit.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": null,
  "author_total": 1,
  "authors": [
    {
      "name": "Aurelien Pelissier"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/e4yrws2k0dghc.bib",
  "cited_by": 0,
  "doi": null,
  "fulltext_url": null,
  "id": "e4yrws2k0dghc",
  "issns": [],
  "landing_url": "https://hal.science/hal-05744772v2",
  "language": "en",
  "licence": "CC-BY-4.0",
  "licence_label": "CC BY 4.0",
  "licence_source": "article",
  "licence_url": "https://creativecommons.org/licenses/by/4.0/",
  "metadata_licence": null,
  "native_subjects": [
    [
      "hal",
      "0.math"
    ],
    [
      "hal",
      "0.phys"
    ],
    [
      "hal",
      "1.math.math-dg"
    ],
    [
      "hal",
      "1.math.math-oa"
    ],
    [
      "hal",
      "1.phys.grqc"
    ],
    [
      "hal",
      "1.phys.mphy"
    ]
  ],
  "openalex": null,
  "pdf_url": "https://hal.science/hal-05744772/document",
  "pmcid": null,
  "pmid": null,
  "published": "2026-09-21",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/e4yrws2k0dghc.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:17:36Z",
      "native_id": "hal-05744772",
      "source": "hal",
      "url": "https://hal.science/hal-05744772v2"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "hal:1.math.math-oa",
      "subfield": "analysis-pdes"
    },
    {
      "field": "mathematics",
      "origin": "hal:1.math.math-dg",
      "subfield": "geometry-topology"
    },
    {
      "field": "mathematics",
      "origin": "hal:1.phys.mphy",
      "subfield": "mathematical-physics"
    },
    {
      "field": "physics",
      "origin": "hal:1.phys.grqc",
      "subfield": "gravitation"
    }
  ],
  "title": "Renewal Geometry and the Emergence of Lorentzian Spacetime",
  "title_text": "Renewal Geometry and the Emergence of Lorentzian Spacetime",
  "type": "preprint",
  "updated_at": "2026-10-30T12:17:36Z",
  "url": "https://research.draconitic.com/paper/e4yrws2k0dghc",
  "venue": "HAL",
  "versions": []
}