{
  "abstract": "This paper establishes the complete axiomatic foundation and intrinsic differential geometry of the priority-axis Z-algebra, a real 16-dimensional semisimple associative algebra defined by seven axioms Z1–Z7, generated by quaternionic units i, j, k and a hyperbolic time axis τ. The Wedderburn theorem yields Z ≅ M₂(C) ⊕ M₂(C); a bootstrap theorem shows that the priority axis is necessarily forced by algebraic self-consistency. Although Z ≅ Cl(3) as a bare algebra, the novelty lies in the priority-axis presentation and its structure theory. The axioms are mutually independent, with {Z1, Z2, Z4, Z5} a minimal core; the centre, the chiral Peirce sectors and the frozen–active dichotomy are completely determined; the derivation algebra Der(Z) ≅ sl(2,C)ᵣ ⊕ sl(2,C)ᵣ, closing open problem O.23; fibre-bundle impossibility and non-embeddability into Cl(1,3) delimit the external boundary. The intrinsic derivation Dτ = ad_τ obeys the spectral rigidity Dτ²|_Im = 4·id and admits closed-form integration and a propagator; torsion-freeness uniquely fixes the connection ∇_WY = ½[W, Y], and the curvature is purely algebraic, R(X, Y)Z = −¼[[X, Y], Z]; the physical tangent space is a three-dimensional Einstein space of constant curvature K ≡ −1 (Ric = −2η). All 112 propositions (77 algebraic, 35 differential-geometric) pass exact symbolic verification with strictly zero residuals.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": null,
  "author_total": 1,
  "authors": [
    {
      "name": "Yunfei Wang",
      "orcid": "0009-0007-3261-8170"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/59qd9xqyw6g9h.bib",
  "cited_by": 5,
  "doi": "10.5281/zenodo.21917284",
  "fulltext_url": null,
  "id": "59qd9xqyw6g9h",
  "issns": [],
  "landing_url": "https://doi.org/10.5281/zenodo.21917284",
  "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": [
    [
      "openalex",
      "2604|Algebraic and Geometric Analysis"
    ]
  ],
  "openalex": "W7202373700",
  "pdf_url": null,
  "pmcid": null,
  "pmid": null,
  "published": "2026-08-13",
  "publisher": "European Organization for Nuclear Research",
  "ris": "https://research.draconitic.com/paper/59qd9xqyw6g9h.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:17:17Z",
      "native_id": "W7202373700",
      "source": "openalex",
      "url": "https://doi.org/10.5281/zenodo.21917284"
    }
  ],
  "subjects": [
    {
      "field": "mathematics",
      "origin": "openalex:2604|Algebraic and Geometric Analysis",
      "subfield": "general"
    }
  ],
  "title": "The Priority-Axis Z-Algebra: A Unified Framework of Axioms, Structure Theory, and Intrinsic Differential Geometry",
  "title_text": "The Priority-Axis Z-Algebra: A Unified Framework of Axioms, Structure Theory, and Intrinsic Differential Geometry",
  "type": "preprint",
  "updated_at": "2026-11-04T13:21:00Z",
  "url": "https://research.draconitic.com/paper/59qd9xqyw6g9h",
  "venue": "Zenodo (CERN European Organization for Nuclear Research)",
  "versions": []
}