{
  "abstract": "We derive the inverse fine-structure constant α −1 = 137.035 999 083 from the rendering algebra R12 ∼= M12(C) through NNLO with zero free parameters.\n\nPart I (LO + NLO). The regular 12-gon inscribed in the unit circle has area exactly Nc = 3 (since sin(π/6) = 1 2 ), making the geometric defect δ = π − Nc; Niven’s theorem proves N=12 unique. The Generalised Landauer Allocation gives the defect\n\nleakage 1/δ with normalisation c=1. The Dimensional Allocation Theorem classifies the self-referential series Z/Nk by sector (k=1 excluded at 30σ as M3; k≥4 truncated by D=3), yielding Kknot = Z(N+1)/N3 with KMS normalisation 1/Tw. Result: α−1 NLO = 137.036 000 (43σ residual).\n\nPart II (NNLO). The defect operator V on M12 has M4-sector matrix D =v1v † 1 − v2v†2 (rank-1 difference). Five structural identities: rank(D) = 2 = Tw; eigenvalues of D2 are {N+1, N+1, 0, 0}; |⟨v1|v2⟩|2 = Nc; ⟨v1|D|v2⟩ = 0; dim(stabsu(4)(D)) =\n\n5 = Tw C2(∧2). This stabiliser–Casimir identity holds only for N/Nc = 4 (cubic k3−6k 2+7k+4=0, unique integer root k=4), providing a new N=12 uniqueness proof. Three exact cancellations–(N+1), b0, (N/Nc)/8=1/Tw–reduce the perturbation to NNLO =−Z 2/(TwN2· 5 2).",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": null,
  "author_total": 1,
  "authors": [
    {
      "name": "Han-Jun Lim"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/6exy52gr15f0k.bib",
  "cited_by": 0,
  "doi": "10.5281/zenodo.23603817",
  "fulltext_url": null,
  "id": "6exy52gr15f0k",
  "issns": [],
  "landing_url": "https://zenodo.org/records/23603817",
  "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/23603817/files/Lim_ArrayCosmology_FineStructureDerivation_2026_v6.pdf/content",
  "pmcid": null,
  "pmid": null,
  "published": "2026-10-23",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/6exy52gr15f0k.ris",
  "sources": [
    {
      "first_seen": "2026-11-06T12:20:57Z",
      "native_id": "23603817",
      "source": "zenodo",
      "url": "https://zenodo.org/records/23603817"
    }
  ],
  "subjects": [],
  "title": "The 12-gon Area Identity, Defect Operator, Stabiliser–Casimir Duality, and the Derivation of α−1 from the R12 Rendering Algebra",
  "title_text": "The 12-gon Area Identity, Defect Operator, Stabiliser–Casimir Duality, and the Derivation of α−1 from the R12 Rendering Algebra",
  "type": "preprint",
  "updated_at": "2026-11-06T12:20:57Z",
  "url": "https://research.draconitic.com/paper/6exy52gr15f0k",
  "venue": "Zenodo",
  "versions": []
}