{
  "abstract": "We derive the quasi-normal mode (QNM) spectrum of black hole ringdown from the five axioms {12, π, γ1, ln 2, φ} of Array Cosmology (AC) with zero free parameters.\n\nThe Schwarzschild (χ = 0) fundamental mode (l = 2, n = 0) frequency is ω˜R = γ1/(12π) = 0.37494 (GR exact: 0.37367, error 0.34%), and the quality factor is Q = 2 + Znoise = 2.098 (GR: 2.100, error 0.10%). For Kerr black holes,\n\nspin progressively collapses the 12-axis rendering loop to a single Volma stroke (3 axes) via the golden-ratio implosion exponent φ^−2 : the effective axis count is Neff(χ) = 3 + 9(1 − χ) φ−2 , yielding ω˜R(χ) = γ1/[π Neff(χ)] with RMS 2.3% against numerical relativity. The quality factor Q(χ) = (2+Znoise)/(1−χ) 1/2−Znoise achieves RMS 2.2%. The overtone spacing is ∆˜ωI = 2Znoise (0.8% match). Applied to GW150914 (M = 68.5 M⊙, χ = 0.69), the model predicts f = 242 Hz\n\nand τ = 4.41 ms, within 1.1σ and 0.8σ of LIGO observations respectively. All five axioms are employed: 12 (loop topology), π (angular circumference), γ1 (tension anchor), ln 2 (Landauer floor), and φ (spin collapse). This supersedes the previous\n\nAC ringdown paper, correcting the erroneous ×1.699 damping-time scaling",
  "abstract_shown": true,
  "affiliations": [],
  "article_type": null,
  "arxiv": null,
  "author_total": 1,
  "authors": [
    {
      "name": "Han-Jun Lim"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/91db3sv9vqhgc.bib",
  "cited_by": 0,
  "doi": "10.5281/zenodo.23603865",
  "fulltext_url": null,
  "id": "91db3sv9vqhgc",
  "issns": [],
  "landing_url": "https://zenodo.org/records/23603865",
  "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/23603865/files/Lim_ArrayCosmology_GW_Ringdown_2026_v5.pdf/content",
  "pmcid": null,
  "pmid": null,
  "published": "2026-10-23",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/91db3sv9vqhgc.ris",
  "sources": [
    {
      "first_seen": "2026-11-06T12:20:57Z",
      "native_id": "23603865",
      "source": "zenodo",
      "url": "https://zenodo.org/records/23603865"
    }
  ],
  "subjects": [],
  "title": "Gravitational Wave Ringdown from the Rendering Algebra R12: The Axis Count from the Modular Spectrum, the Extremal Determination of the Rendering Anchor, and the Nine-Event Confrontation",
  "title_text": "Gravitational Wave Ringdown from the Rendering Algebra R12: The Axis Count from the Modular Spectrum, the Extremal Determination of the Rendering Anchor, and the Nine-Event Confrontation",
  "type": "preprint",
  "updated_at": "2026-11-06T12:20:57Z",
  "url": "https://research.draconitic.com/paper/91db3sv9vqhgc",
  "venue": "Zenodo",
  "versions": []
}