{
  "abstract": "We derive the strong coupling constant and the complete CKM mixing hierarchy from the colour sector M3(C) ⊂ R12 of the rendering algebra, with zero free parameters. Five principal results are established.\n\n(1) ζ(Nc) Color Cohesion: the strong coupling coefficient ζ(3) is derived as ζ(Nc) = Pn −Nc , where each summand arises from Nc = 3 independent diagonal projectors of M3(C) acting on flux-tube modes weighted by the Landauer allocation wn = 1/n; alternative weightings (1/n2 , e −n , 1/n3/2 ) are excluded at > 8%.\n\n(2) Γ(Nc) = Tw: the Planck integral representation identifies Γ(Nc) = (Nc−1)! = Tw = 2 as a fourth independent condition selecting Nc = 3 uniquely.\n\n(3) CKM Cascade Upgrade: all CKM elements are promoted to A90%— |Vus| = exp[−(Nc−Z 2 )/Tw] (NLO, 2.3σ → 0.2σ), |Vcb| = |Vus| Tw × AWolf, and |Vub| = |Vus| |Vcb| × Tw C2( V2 , su(4))/N with skip factor 5/12.\n\n(4) NLO Dimension Rule: the leading Landauer correction is O(Z d ) where d is the physical dimension: Z1(EM coupling), Z 2 (CKM transition), Z 3 (colour cohesion).\n\n(5) Dual Mechanism: M3(C) produces the gauge coupling via a mode sum (αs = ζ(Nc)Z) and the CKM hierarchy\n\nvia exponential suppression (|Vij | ∝ e −C2 ). Twenty results; no free parameters.",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": null,
  "author_total": 1,
  "authors": [
    {
      "name": "Han-Jun Lim"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/5fpwg55v6mqa1.bib",
  "cited_by": 0,
  "doi": "10.5281/zenodo.23625091",
  "fulltext_url": null,
  "id": "5fpwg55v6mqa1",
  "issns": [],
  "landing_url": "https://zenodo.org/records/23625091",
  "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": "https://zenodo.org/api/records/23625091/files/Lim_ArrayCosmology_ColorCohesion_CKM_v11_2026.pdf/content",
  "pmcid": null,
  "pmid": null,
  "published": "2026-10-24",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/5fpwg55v6mqa1.ris",
  "sources": [
    {
      "first_seen": "2026-11-07T12:20:37Z",
      "native_id": "23625091",
      "source": "zenodo",
      "url": "https://zenodo.org/records/23625091"
    }
  ],
  "subjects": [],
  "title": "ζ(Nc) Color Cohesion, CKM Casimir Cascade, and the Complete M3(C) Sector of the R12 Rendering Algebra",
  "title_text": "ζ(Nc) Color Cohesion, CKM Casimir Cascade, and the Complete M3(C) Sector of the R12 Rendering Algebra",
  "type": "preprint",
  "updated_at": "2026-11-07T12:20:37Z",
  "url": "https://research.draconitic.com/paper/5fpwg55v6mqa1",
  "venue": "Zenodo",
  "versions": []
}