{
  "abstract": "The rendering algebra R12 = M3(C) ⊗ M4(C) of Array Cosmology carries the isotypic energy series Z(τ) = 1+8q3 +15q4 +120q7, with 144 = 122 states organized as End(C12) = (1⊕8)⊗(1⊕15). Thispapersettlesthemodularidentityof Z. First, the height-12 forcing theorem: writing E = C2/2 for the AC energy and h = C2/2(k+h∨) for the affine conformal weight, the finite-index identity E = 12h holds on every sector if and only if k + h∨ = 12 for each factor, which selects the unique level pair (k3,k4) = (9,8) — the co-Coxeter complements of 12 — with central charge c = 16 and exact T-order 12 on the four AC sectors(288 on the fulltheory).",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": null,
  "author_total": 1,
  "authors": [
    {
      "name": "Han-Jun Lim"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/d8n4s5amqata0.bib",
  "cited_by": 0,
  "doi": "10.5281/zenodo.23603953",
  "fulltext_url": null,
  "id": "d8n4s5amqata0",
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  "landing_url": "https://zenodo.org/records/23603953",
  "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/",
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  "pdf_url": "https://zenodo.org/api/records/23603953/files/Lim_ArrayCosmology_ModularAlgebraicBridge_2026_v2.pdf/content",
  "pmcid": null,
  "pmid": null,
  "published": "2026-10-23",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/d8n4s5amqata0.ris",
  "sources": [
    {
      "first_seen": "2026-11-06T12:20:56Z",
      "native_id": "23603953",
      "source": "zenodo",
      "url": "https://zenodo.org/records/23603953"
    }
  ],
  "subjects": [],
  "title": "The Modular–Algebraic Bridge Height-12 Forcing, Level–Rank Completion, and the Branching Theorem for the Rendering Character",
  "title_text": "The Modular–Algebraic Bridge Height-12 Forcing, Level–Rank Completion, and the Branching Theorem for the Rendering Character",
  "type": "preprint",
  "updated_at": "2026-11-06T12:20:56Z",
  "url": "https://research.draconitic.com/paper/d8n4s5amqata0",
  "venue": "Zenodo",
  "versions": []
}