{
  "abstract": "In Alain Connes' noncommutative geometry, geometry is encoded by an algebra, a Hilbert space, and a Dirac operator taken as fundamental spectral data. We show that these structures can instead emerge from a more primitive predictive dynamics. A compatible first-order variation on the induced history algebra canonically generates a real even Hodge--Dirac spectral triple, while the algebra alone determines neither its metric scale nor the full Dirac operator. The resulting spectral geometry is an information-reduced description: dynamically inequivalent predictive systems can share the same effective spectral data. Nevertheless, finite geometries become reconstructible after finitely many calibrations, and on periodic three-dimensional lattice approximants the emergent spectral distance converges to a Riemannian metric reconstructed independently from the dynamics. Thus Connes-type spectral geometry may arise not as fundamental structure, but as an effective geometric description of richer underlying dynamics. This provides a concrete setting in which noncommutative geometry need not be fundamental, but may instead arise as a coarse-grained spectral description.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": null,
  "author_total": 1,
  "authors": [
    {
      "name": "Aurelien Pelissier"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/4apz3rd1z15v2.bib",
  "cited_by": 0,
  "doi": null,
  "fulltext_url": null,
  "id": "4apz3rd1z15v2",
  "issns": [],
  "landing_url": "https://hal.science/hal-05752672v1",
  "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"
    ],
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      "hal",
      "1.math.math-oa"
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  "openalex": null,
  "pdf_url": "https://hal.science/hal-05752672/document",
  "pmcid": null,
  "pmid": null,
  "published": "2026-09-17",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/4apz3rd1z15v2.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:17:35Z",
      "native_id": "hal-05752672",
      "source": "hal",
      "url": "https://hal.science/hal-05752672v1"
    }
  ],
  "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:0.phys",
      "subfield": "general"
    }
  ],
  "title": "From Predictive Dynamics to Spectral Geometry",
  "title_text": "From Predictive Dynamics to Spectral Geometry",
  "type": "preprint",
  "updated_at": "2026-10-30T12:17:35Z",
  "url": "https://research.draconitic.com/paper/4apz3rd1z15v2",
  "venue": "HAL",
  "versions": []
}