{
  "abstract": "FINDING: Search results are pedagogical resources on Clebsch–Gordan (CG) coefficients, with one lattice-QCD application paper; no explicit proof of golden-ratio absence is found in the returned material. | MATH: CG coefficients ⟨j₁ m₁; j₂ m₂ | J M⟩ are the overlap matrix elements between uncoupled and coupled angular-momentum bases; they satisfy orthogonality ∑_{m₁,m₂} ⟨j₁m₁;j₂m₂|JM⟩⟨j₁m₁;j₂m₂|J′M′⟩ = δ_{JJ′}δ_{MM′}, and recursion relations from ladder operators. The lattice paper uses double-valued irreps of the octahedral group (O_h^D), whose dimensions are {1,2,3,4} — no φ appears. | CONNECTION: CG coefficients for SU(2) are algebraic numbers from square roots of rationals (e.g., √(2/3), √(1/2)); the golden ratio φ = (1+√5)/2 is quadratic irrational but not of the form √(p/q) with p,q integers unless p/q = φ² — which is impossible since φ² is irrational. Thus φ cannot appear as a CG coefficient magnitude. However, φ *can* appear in SU(3) or higher-rank tensor products via ratios of\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/4d8bw0hzd5ra7.bib",
  "cited_by": 0,
  "doi": "10.5281/zenodo.23587358",
  "fulltext_url": null,
  "id": "4d8bw0hzd5ra7",
  "issns": [],
  "landing_url": "https://zenodo.org/records/23587358",
  "language": "eng",
  "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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  "pmid": null,
  "published": "2026-10-23",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/4d8bw0hzd5ra7.ris",
  "sources": [
    {
      "first_seen": "2026-11-06T12:21:46Z",
      "native_id": "23587358",
      "source": "zenodo",
      "url": "https://zenodo.org/records/23587358"
    }
  ],
  "subjects": [],
  "title": "Clebsch–Gordan Coefficients: Orthogonality, Recursion, and Lattice QCD Applications — E8 Intelligence Research",
  "title_text": "Clebsch–Gordan Coefficients: Orthogonality, Recursion, and Lattice QCD Applications — E8 Intelligence Research",
  "type": "preprint",
  "updated_at": "2026-11-06T12:21:46Z",
  "url": "https://research.draconitic.com/paper/4d8bw0hzd5ra7",
  "venue": "Zenodo",
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}