{
  "abstract": "FINDING: Golden ratio emerges from the simplest continued fraction [1;1,1,1,...], with Fibonacci convergents; recent work extends this to quantum calculus via Fibonacci divisors and supersymmetric oscillators. | MATH: φ = (1+√5)/2 = [1;1,1,1,...]; convergents p_n/q_n = F_{n+1}/F_n → φ; φ² = φ+1; 1/φ = φ−1 = 0.618…; φ−1/φ = 1/φ² = 0.382…; √φ ≈ 1.272; φ/√5 ≈ 0.724; Binet: F_n = (φⁿ − (−φ)⁻ⁿ)/√5; quantum calculus with bases φ and 1+√2 (silver ratio) defines Fibonacci divisor derivative and Fock-space operators with golden oscillator spectrum E_n ∝ φ^n. | CONNECTION: Direct — φ is the geometric mean of 1 and 2 (φ = √(1·2) − 1? No, φ = (1+√5)/2, but φ−1 = 1/φ = 0.618; φ−1/φ = 0.382; φ² = 2.618; 1/φ² = 0.382. Parastichy divergence angle in phyllotaxis = 2π/φ² ≈ 137.5° (or 2π − 2π/φ² ≈ 222.5°), the most irrational number (continued fraction all 1s) maximizing spacing. Fibonacci spirals in sunflowers, pinecones, nautilus — crystallographic-like 5-fold symmetry (quasicrystal Penrose tilings use\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"
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  "bibtex": "https://research.draconitic.com/paper/22db94fscet4n.bib",
  "cited_by": 0,
  "doi": "10.5281/zenodo.23587197",
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  "id": "22db94fscet4n",
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  "published": "2026-10-23",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/22db94fscet4n.ris",
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    {
      "first_seen": "2026-11-06T12:21:51Z",
      "native_id": "23587197",
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  "title": "Golden Ratio's Quantum Leap: Fibonacci Divisors and Supersymmetric Oscillators — E8 Intelligence Research",
  "title_text": "Golden Ratio's Quantum Leap: Fibonacci Divisors and Supersymmetric Oscillators — E8 Intelligence Research",
  "type": "preprint",
  "updated_at": "2026-11-06T12:21:51Z",
  "url": "https://research.draconitic.com/paper/22db94fscet4n",
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