{
  "abstract": "This work presents the QDC Completion Theorem as a comprehensive substrate-level completion architecture within the Quantized Dimensional Ledger. Starting from the toroidal Quantized Dimensional Cell, the closure functional C_QDC(w)=2Σ_L−3Σ_F, and the gravitational closure cell [GM]=L^3F^2, the paper develops a finite closure framework for Standard-Model admissibility, matter-basis minimality, anomaly/Yukawa hypercharge closure, scalar Higgs compensation, three-family residual automorphism structure, charged-lepton mass-ratio access, gravitational recurrence, dark-sector residuals, and cosmological background closure. The paper distinguishes exact anchors, conditional theorems, restricted minimality results, constrained branches, candidate derivations, and open numerical/dynamical gates. Its central results are the Matter-Basis Projection Theorem, the Primitive Three-Family Automorphism Computation, and the Charged-Lepton Mass Closure Theorem. The paper does not claim to be a completed final theory. It identifies the finite mathematical and physical gates that must close for QDL to become a stronger candidate substrate-level completion theory. The graphical abstract included with this record is a schematic representation of the QDC recurrence substrate and completion architecture. The blue cycles L_1, L_2, L_3 denote the three length-type recurrence channels, and the orange cycles F_1, F_2 denote the two frequency-type recurrence channels of T^5_QDC=(S^1_L)^3×(S^1_F)^2. The toroidal rendering is a visual schematic of typed closure recurrence, not an assertion that an ordinary two-dimensional torus has five independent topological cycles.",
  "abstract_shown": true,
  "affiliations": [
    "QDL Physics Institute"
  ],
  "article_type": null,
  "arxiv": null,
  "author_total": 1,
  "authors": [
    {
      "affs": [
        0
      ],
      "name": "James D. Bourassa",
      "orcid": "0009-0008-0155-0051"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/7m3ahqn6mvrbx.bib",
  "cited_by": 6,
  "doi": "10.5281/zenodo.20692676",
  "fulltext_url": null,
  "id": "7m3ahqn6mvrbx",
  "issns": [],
  "landing_url": "https://doi.org/10.5281/zenodo.20692676",
  "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",
      "3106|Particle physics theoretical and experimental studies"
    ]
  ],
  "openalex": "W7164745078",
  "pdf_url": null,
  "pmcid": null,
  "pmid": null,
  "published": "2026-06-14",
  "publisher": "European Organization for Nuclear Research",
  "ris": "https://research.draconitic.com/paper/7m3ahqn6mvrbx.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T13:26:43Z",
      "native_id": "W7164745078",
      "source": "openalex",
      "url": "https://doi.org/10.5281/zenodo.20692676"
    }
  ],
  "subjects": [
    {
      "field": "physics",
      "origin": "openalex:3106|Particle physics theoretical and experimental studies",
      "subfield": "high-energy"
    }
  ],
  "title": "The QDC Completion Theorem: Matter-Basis Minimality, Three-Family Automorphism, Charged-Lepton Closure, and Gravitational Recurrence in the Quantized Dimensional Ledger",
  "title_text": "The QDC Completion Theorem: Matter-Basis Minimality, Three-Family Automorphism, Charged-Lepton Closure, and Gravitational Recurrence in the Quantized Dimensional Ledger",
  "type": "preprint",
  "updated_at": "2026-11-03T13:20:27Z",
  "url": "https://research.draconitic.com/paper/7m3ahqn6mvrbx",
  "venue": "Zenodo (CERN European Organization for Nuclear Research)",
  "versions": []
}