{
  "abstract": "FINDING: Video corpus conflates sacred geometry with harmonic ratios, Platonic number theory, and musical intervals, but none provide a rigorous mathematical proof of cosmic structure—only descriptive numerology and geometric constructions. | MATH: No novel equations derived. Implicit constants: φ = (1+√5)/2 ≈ 1.618; φ⁻¹ = 0.618; φ⁻² = 0.382; √2 ≈ 1.414; √3 ≈ 1.732; π ≈ 3.14159; base-60 sexagesimal cycles (Plato's *Timaeus* 35b–36d: harmonic intervals 2:1, 3:2, 4:3, 9:8); Pythagorean tetractys (1+2+3+4=10); musical ratios (octave 2:1, fifth 3:2, fourth 4:3). | CONNECTION: φ appears in pentagonal symmetry (crystallographic point group 5-fold, non-crystallographic in 3D lattice but valid in quasicrystals—Shechtman 1982); 0.618/0.382 are golden section divisions; 0.786 ≈ √φ/2 (not standard, likely spurious); base-60 links to Sumerian/Babylonian sexagesimal arithmetic, not a geometric proof. No root-system or lattice-structure derivation beyond decorative pentagrams/hexagrams. | DEPTH: 2 —\n\nAuthor: Andrew Stewart Caldin, Independent Researcher, UK. Part of the E8 Intelligence Research series. Platform: e8intelligence.com",
  "abstract_shown": true,
  "affiliations": [
    "Independent Researcher, United Kingdom"
  ],
  "article_type": null,
  "arxiv": null,
  "author_total": 1,
  "authors": [
    {
      "affs": [
        0
      ],
      "name": "Andrew Stewart Caldin"
    }
  ],
  "bibtex": "https://research.draconitic.com/paper/9tnza9ypjhg8e.bib",
  "cited_by": 0,
  "doi": "10.5281/zenodo.23490619",
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  "id": "9tnza9ypjhg8e",
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  "landing_url": "https://zenodo.org/records/23490619",
  "language": "eng",
  "licence": "CC-BY-4.0",
  "licence_label": "CC BY 4.0",
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  "licence_url": "https://creativecommons.org/licenses/by/4.0/",
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  "published": "2026-10-20",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/9tnza9ypjhg8e.ris",
  "sources": [
    {
      "first_seen": "2026-11-03T12:21:27Z",
      "native_id": "23490619",
      "source": "zenodo",
      "url": "https://zenodo.org/records/23490619"
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  "subjects": [],
  "title": "Sacred Geometry and Harmonic Ratios: Descriptive Numerology, Not Mathematical Proof — E8 Intelligence Research",
  "title_text": "Sacred Geometry and Harmonic Ratios: Descriptive Numerology, Not Mathematical Proof — E8 Intelligence Research",
  "type": "preprint",
  "updated_at": "2026-11-03T12:21:27Z",
  "url": "https://research.draconitic.com/paper/9tnza9ypjhg8e",
  "venue": "Zenodo",
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}