{
  "abstract": "We close nine structural logic gates in the CAT'S Theory torus knot architecture, eliminating all remaining mathematical gaps in the derivation chain from the Triadic Invariant R = P × I × Pr ≠ 0 to the physical constants of the Standard Model. The nine closures are: (1) the T(1,x) unknot sector mandates massless spin-1 mechanics with U(1) gauge symmetry and transverse polarization without importing Maxwell's equations; (2) the 1/45 topological residue forces 12-bit quantization of S³ via ord₂(45) = π(8) = 12, proven unique to d = 3; (3) the mass formula base (q²-4)/5 is derived as the conformal weight ratio h(q)/h(e) at Chern-Simons level k = 30; (4) the Triadic Invariant is formalized as a tensor product operator whose collapse axiom is a theorem of linear algebra; (5) the discrete-to-continuous category bridge is closed via π₁(T²) = Z × Z; (6) k = 30 is derived through six independent routes including the operator trace, dimensional identity k = Σ + D = 26 + 4, and the electron holonomy k + 2 = 2^(J*_e) = 32. We prove that the operators trace into each other's dimensional registers, establishing R = Φ(R) as a theorem of linear algebra. The lepton-quark duality T(2,3) ≅ T(3,2) is shown to be forced by the coprime constraint. All results carry zero free parameters. Mass predictions: muon 0.13%, tau (QED-dressed) 0.02%. Four live experimental predictions: δ_CP = 202.5° (DUNE), normal ordering (JUNO), Σm_ν = 59.5 meV, f_τ = 8.37 Hz (Einstein Telescope).",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": null,
  "author_total": 1,
  "authors": [
    {
      "name": "Coty Austin Trout",
      "orcid": "0009-0003-3401-8815"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/22kv3v7m2qj8w.bib",
  "cited_by": 6,
  "doi": "10.5281/zenodo.21956592",
  "fulltext_url": null,
  "id": "22kv3v7m2qj8w",
  "issns": [],
  "landing_url": "https://doi.org/10.5281/zenodo.21956592",
  "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",
      "3109|Advanced Mathematical Theories and Applications"
    ]
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  "openalex": "W7203528874",
  "pdf_url": null,
  "pmcid": null,
  "pmid": null,
  "published": "2026-08-15",
  "publisher": "European Organization for Nuclear Research",
  "ris": "https://research.draconitic.com/paper/22kv3v7m2qj8w.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T13:26:43Z",
      "native_id": "W7203528874",
      "source": "openalex",
      "url": "https://doi.org/10.5281/zenodo.21956592"
    }
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  "subjects": [
    {
      "field": "physics",
      "origin": "openalex:3109|Advanced Mathematical Theories and Applications",
      "subfield": "statistical-nonlinear"
    }
  ],
  "title": "The Nine Gates: Closure of the Torus Knot Architecture from the Triadic Invariant on S³",
  "title_text": "The Nine Gates: Closure of the Torus Knot Architecture from the Triadic Invariant on S³",
  "type": "preprint",
  "updated_at": "2026-11-03T13:20:27Z",
  "url": "https://research.draconitic.com/paper/22kv3v7m2qj8w",
  "venue": "Zenodo (CERN European Organization for Nuclear Research)",
  "versions": []
}