{
  "abstract": "We establish an exact action-multiplicity duality for finite gravity-matter systems in which spacetime, internal symmetry, and matter incidence are represented on a common carrier. The algebra generated by the complete spacetime-gauge-incidence action and the residual matter multiplicity determine one another as mutual commutants. The duality remains exact for singular and rank-deficient incidence maps and admits support-polar and multiplicity-quiver formulations, together with a positive rigidity certificate and a regulator-stable cofinal extension. On a certified structural branch, the residual multiplicity reconstructs the internal algebra of three-by-three and two-by-two complex matrices along with two copies of the complex numbers, while a canonical determinant incidence selects the special unitary gauge group S(U(3) x U(2)), which is isomorphic to the Standard Model gauge group SU(3) x SU(2) x U(1) modulo Z6. Anomaly cancellation fixes the hypercharge ratios, a distinct rank-three residual supplies the generation carrier, and a single grading-odd operator contains the finite Yukawa and Majorana sectors. Renewal Geometry provides one realization of the required joint carrier; the finite operator-algebraic results are otherwise independent of its microscopic construction.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": null,
  "author_total": 1,
  "authors": [
    {
      "name": "Aurelien Pelissier"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/dxsvrkj7pnmxy.bib",
  "cited_by": 0,
  "doi": null,
  "fulltext_url": null,
  "id": "dxsvrkj7pnmxy",
  "issns": [],
  "landing_url": "https://hal.science/hal-05755429v1",
  "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"
    ],
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      "hal",
      "0.phys"
    ],
    [
      "hal",
      "1.math.math-oa"
    ],
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      "hal",
      "1.phys.hthe"
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  "openalex": null,
  "pdf_url": "https://hal.science/hal-05755429/document",
  "pmcid": null,
  "pmid": null,
  "published": "2026-09-19",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/dxsvrkj7pnmxy.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:17:36Z",
      "native_id": "hal-05755429",
      "source": "hal",
      "url": "https://hal.science/hal-05755429v1"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "hal:1.math.math-oa",
      "subfield": "analysis-pdes"
    },
    {
      "field": "mathematics",
      "origin": "hal:1.phys.mphy",
      "subfield": "mathematical-physics"
    },
    {
      "field": "physics",
      "origin": "hal:1.phys.hthe",
      "subfield": "high-energy"
    }
  ],
  "title": "A Duality Between Spacetime-Gauge-Incidence Actions and Matter Multiplicity",
  "title_text": "A Duality Between Spacetime-Gauge-Incidence Actions and Matter Multiplicity",
  "type": "preprint",
  "updated_at": "2026-10-30T12:17:36Z",
  "url": "https://research.draconitic.com/paper/dxsvrkj7pnmxy",
  "venue": "HAL",
  "versions": []
}