{
  "abstract": "FINDING: The search results converge on a deep structural link between 5-fold symmetry, hyperbolic geometry, and quantum invariants — specifically, that pentagonal tiling (impossible in Euclidean plane) becomes natural in hyperbolic space, and this connects to Fibonacci anyons and quantum group invariants. | MATH: (1) Fibonacci anyons obey fusion rule τ × τ = 1 + τ, with quantum dimension φ = (1+√5)/2 ≈ 1.618. (2) Hyperbolic tiling {5,4} (pentagons, 4 meeting at vertex) has curvature -1, area per pentagon = π/5. (3) Binet formula: F_n = (φ^n − (−φ)^−n)/√5. (4) Quantum invariant Z(M) for hyperbolic 3-manifolds relates to volume via Witten–Reshetikhin–Turaev invariants at root of unity q = e^{2πi/(k+2)}. | CONNECTION: **CRITICAL** — 5-fold symmetry (forbidden in Euclidean crystals, Penrose tilings) is *allowed* in hyperbolic plane. The golden ratio φ appears as: (a) quantum dimension of Fibonacci anyon, (b) scaling factor in hyperbolic pentagon tilings, (c) the ratio of diagonal to side\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/6ba0ywgja7wf7.bib",
  "cited_by": 0,
  "doi": "10.5281/zenodo.23587117",
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  "id": "6ba0ywgja7wf7",
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  "landing_url": "https://zenodo.org/records/23587117",
  "language": "eng",
  "licence": "CC-BY-4.0",
  "licence_label": "CC BY 4.0",
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  "published": "2026-10-23",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/6ba0ywgja7wf7.ris",
  "sources": [
    {
      "first_seen": "2026-11-06T12:21:52Z",
      "native_id": "23587117",
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      "url": "https://zenodo.org/records/23587117"
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  "subjects": [],
  "title": "Hyperbolic Pentagons, Fibonacci Anyons, and Quantum Group Invariants — E8 Intelligence Research",
  "title_text": "Hyperbolic Pentagons, Fibonacci Anyons, and Quantum Group Invariants — E8 Intelligence Research",
  "type": "preprint",
  "updated_at": "2026-11-06T12:21:52Z",
  "url": "https://research.draconitic.com/paper/6ba0ywgja7wf7",
  "venue": "Zenodo",
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}