{
  "abstract": "Jordan, Wigner, and von Neumann classified the possible algebras of quantum mechanical observables, and found they fell into 4 “ordinary” families, plus one remarkable outlier: the exceptional Jordan algebra. We point out an intriguing relationship between the complexification of this algebra and the standard model of particle physics, its minimal left-right-symmetric SU(3) × SU(2)L × SU(2)R × U(1) extension, and Spin(10) unification. This suggests a geometric interpretation, where a single generation of standard model fermions is described by the tangent space (C⊗O)2 of the complex octonionic projective plane, and the existence of three generations is related to SO(8) triality.",
  "abstract_shown": true,
  "affiliations": [
    "Higgs Centre for Theoretical Physics, University of Edinburgh , Edinburgh EH9 3FD, and , Waterloo, Ontario N2L 2Y5,",
    "Perimeter Institute for Theoretical Physics , Edinburgh EH9 3FD, and , Waterloo, Ontario N2L 2Y5,"
  ],
  "article_type": null,
  "arxiv": null,
  "author_total": 1,
  "authors": [
    {
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        0,
        1
      ],
      "name": "Latham A. Boyle",
      "orcid": "0000-0001-5195-7599"
    }
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  "bibtex": "https://research.draconitic.com/paper/7a39x8yrhcnsa.bib",
  "cited_by": 57,
  "doi": "10.1063/5.0336175",
  "fulltext_url": null,
  "id": "7a39x8yrhcnsa",
  "issns": [
    "0022-2488",
    "1089-7658",
    "1527-2427"
  ],
  "landing_url": "https://doi.org/10.1063/5.0336175",
  "language": "en",
  "licence": "CC-BY",
  "licence_label": "CC BY",
  "licence_source": "journal",
  "licence_url": "https://creativecommons.org/licenses/by/4.0/",
  "metadata_licence": null,
  "native_subjects": [
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      "openalex",
      "2604|Algebraic and Geometric Analysis"
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  "openalex": "W3039805060",
  "pdf_url": null,
  "pmcid": null,
  "pmid": null,
  "published": "2026-07-01",
  "publisher": "American Institute of Physics",
  "ris": "https://research.draconitic.com/paper/7a39x8yrhcnsa.ris",
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      "url": "https://doi.org/10.1063/5.0336175"
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  "subjects": [
    {
      "field": "mathematics",
      "origin": "openalex:2604|Algebraic and Geometric Analysis",
      "subfield": "general"
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  "title": "The standard model, the exceptional Jordan algebra, and triality",
  "title_text": "The standard model, the exceptional Jordan algebra, and triality",
  "type": "peer-reviewed",
  "updated_at": "2026-11-09T13:20:59Z",
  "url": "https://research.draconitic.com/paper/7a39x8yrhcnsa",
  "venue": "Journal of Mathematical Physics",
  "versions": []
}