{
  "abstract": "FINDING: The dihedral group D3 (symmetry group of an equilateral triangle) has irreducible representations whose character values and eigenvalue structures connect to the golden ratio via its order-3 rotational subgroup. | MATH: D3 has order 6, with irreps: trivial (1-dim), sign (1-dim), and standard 2-dim rep. For the 2-dim irrep, the rotation element r (order 3) has eigenvalues e^(±2πi/3) = -1/2 ± i√3/2. The character of r is -1. The golden ratio φ = (1+√5)/2 does NOT appear directly in D3's character table. However, the dihedral group D5 (order 10, pentagon symmetry) does: its 2-dim irreps have rotation eigenvalues e^(±2πi/5) and e^(±4πi/5), whose real parts are (√5-1)/4 ≈ 0.309 and -(√5+1)/4 ≈ -0.809 — related to φ via 2cos(2π/5) = (√5-1)/2 = 1/φ ≈ 0.618. | CONNECTION: The golden ratio emerges from D5, not D3. D3's geometry (equilateral triangle) has angles 60° — base-60 sexagesimal connection. The 2-dim irrep of D3 is the standard representation on R², whose rotation matrix has tr\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/9hnztcmbybkxp.bib",
  "cited_by": 0,
  "doi": "10.5281/zenodo.23409784",
  "fulltext_url": null,
  "id": "9hnztcmbybkxp",
  "issns": [],
  "landing_url": "https://zenodo.org/records/23409784",
  "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,
  "native_subjects": [],
  "openalex": null,
  "pdf_url": null,
  "pmcid": null,
  "pmid": null,
  "published": "2026-10-16",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/9hnztcmbybkxp.ris",
  "sources": [
    {
      "first_seen": "2026-10-30T12:18:27Z",
      "native_id": "23409784",
      "source": "zenodo",
      "url": "https://zenodo.org/records/23409784"
    }
  ],
  "subjects": [],
  "title": "Golden Ratio Absent in D3's Irreducible Representations — E8 Intelligence Research",
  "title_text": "Golden Ratio Absent in D3's Irreducible Representations — E8 Intelligence Research",
  "type": "preprint",
  "updated_at": "2026-10-30T12:34:24Z",
  "url": "https://research.draconitic.com/paper/9hnztcmbybkxp",
  "venue": "Zenodo",
  "versions": []
}