{
  "abstract": "We present the complete mathematical formulation of the Universal Trajectory Architecture (UTA), an operator-algebraic, spectral-geometric, and topological framework that embeds continuous geometric flows, non-Archimedean arithmetic branching, and non-equilibrium state transitions into a single \\theta-twisted algebra \\mathcal{A}(\\theta) over the global Adèle Class Space: \\mathbb{X}_{\\mathbb{Q}} \\equiv \\mathbb{A}_{\\mathbb{Q}}/\\mathbb{Q}^\\times\n\nPhysical trajectories are demonstrated to be neither purely smooth classical continuum curves nor disconnected stochastic jumps, but complementary spectral projections of the global infinitesimal scaling generator: \\mathbf{H} \\equiv x \\frac{d}{dx} + \\frac{1}{2} = -i \\frac{d}{du}, \\qquad u \\equiv \\ln|x|",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": null,
  "author_total": 1,
  "authors": [
    {
      "name": "August Tudor"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/bh02wmma3523k.bib",
  "cited_by": 0,
  "doi": "10.5281/zenodo.23547273",
  "fulltext_url": null,
  "id": "bh02wmma3523k",
  "issns": [],
  "landing_url": "https://zenodo.org/records/23547273",
  "language": null,
  "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": [],
  "openalex": null,
  "pdf_url": null,
  "pmcid": null,
  "pmid": null,
  "published": "2026-10-21",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/bh02wmma3523k.ris",
  "sources": [
    {
      "first_seen": "2026-11-04T12:20:54Z",
      "native_id": "23547273",
      "source": "zenodo",
      "url": "https://zenodo.org/records/23547273"
    }
  ],
  "subjects": [],
  "title": "The Universal Trajectory Architecture: Continuous Flows, Non-Archimedean Branching, Cauchy–Poisson Spectral Windows, and the Tripartite Index on the Adèle Class Space",
  "title_text": "The Universal Trajectory Architecture: Continuous Flows, Non-Archimedean Branching, Cauchy–Poisson Spectral Windows, and the Tripartite Index on the Adèle Class Space",
  "type": "preprint",
  "updated_at": "2026-11-04T12:20:54Z",
  "url": "https://research.draconitic.com/paper/bh02wmma3523k",
  "venue": "Zenodo",
  "versions": []
}