{
  "abstract": "We derive the complete quasi-normal mode (QNM) spectrum of Schwarzschild black holes from the rendering algebra R12 = M3(C)⊗M4(C) with zero free parameters. The spacetime angular multipole l is identified with the spin-l representation of SO(3) ⊂ SU(3), the rotation subgroup of the colour algebra. Three formulae follow from a single mechanism—the Casimir ratio Csu(3)/l(l+1): ~~ where Csu(3)=4/9 is the Haar rendering cost (Paper XLIX). Verification: ω˜R RMS 0.11%, ω˜I RMS 0.10%, Q RMS 0.04%. The l=3 prediction (ω˜R: 0.12%, ω˜I : 0.04%) is a genuine forecast for the Einstein Telescope. The SU(4) ⊃ SU(3) × U(1) Pati-Salam decomposition yields C 4=3+1 (space + time). Three structural results connect the colour algebra\n\nto black hole physics: dim(su(3))=23 is uniquely binary (Mihailescu), colour confinement implies the no-hair theorem, and colour–holography forces S∝area. Twenty-eight results; zero 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/0c74c9trn7bpg.bib",
  "cited_by": 0,
  "doi": "10.5281/zenodo.23603618",
  "fulltext_url": null,
  "id": "0c74c9trn7bpg",
  "issns": [],
  "landing_url": "https://zenodo.org/records/23603618",
  "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,
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  "pdf_url": "https://zenodo.org/api/records/23603618/files/Lim_ArrayCosmology_BlackHole_QNM_Complete_2026_v4.pdf/content",
  "pmcid": null,
  "pmid": null,
  "published": "2026-10-23",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/0c74c9trn7bpg.ris",
  "sources": [
    {
      "first_seen": "2026-11-06T12:20:58Z",
      "native_id": "23603618",
      "source": "zenodo",
      "url": "https://zenodo.org/records/23603618"
    }
  ],
  "subjects": [],
  "title": "Black Holes in the R12 Rendering Algebra: QNM l-Spectrum from SO(3) ⊂ SU(3), Colour–Holography, and Spacetime Emergence",
  "title_text": "Black Holes in the R12 Rendering Algebra: QNM l-Spectrum from SO(3) ⊂ SU(3), Colour–Holography, and Spacetime Emergence",
  "type": "preprint",
  "updated_at": "2026-11-06T12:20:58Z",
  "url": "https://research.draconitic.com/paper/0c74c9trn7bpg",
  "venue": "Zenodo",
  "versions": []
}