{
  "abstract": "FINDING: The only substantive mathematical result is a quantum calculus framework linking Fibonacci divisors to golden-ratio-based supersymmetric oscillators; the rest are popular expositions with no novel mathematical content. | MATH: Golden ratio φ = (1+√5)/2 ≈ 1.618; Silver ratio σ = 1+√2 ≈ 2.414. Quantum calculus with two bases (φ, σ) defines a Fibonacci divisor derivative; Binet formula F_n = (φ^n − (−φ)^−n)/√5 generalizes to a Fibonacci divisor number operator in Fock space. Energy spectrum of \"golden oscillators\" is hierarchical, built from powers of φ and σ — implying ratios φ^k and σ^k appear as level spacings. | CONNECTION: φ² = φ+1 → 1/φ = φ−1 = 0.618; φ⁻¹ = 0.618, φ⁻² = 0.382, φ⁻³ = 0.236 — these are the classical harmonic ratios. The hierarchy of golden oscillators with φ^n spacing directly encodes the 0.382/0.618/1.618/2.618 progression. Silver ratio σ relates to 1+√2, which appears in octagonal (8-fold) quasi-crystal symmetry — a crystallographic link. The Fock-space str\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/72pvx7gsa575t.bib",
  "cited_by": 0,
  "doi": "10.5281/zenodo.23635592",
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  "id": "72pvx7gsa575t",
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  "language": "eng",
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  "licence_label": "CC BY 4.0",
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  "published": "2026-10-25",
  "publisher": null,
  "ris": "https://research.draconitic.com/paper/72pvx7gsa575t.ris",
  "sources": [
    {
      "first_seen": "2026-11-08T12:21:52Z",
      "native_id": "23635592",
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  "title": "Quantum Calculus Links Fibonacci Divisors to Golden-Ratio Supersymmetric Oscillators — E8 Intelligence Research",
  "title_text": "Quantum Calculus Links Fibonacci Divisors to Golden-Ratio Supersymmetric Oscillators — E8 Intelligence Research",
  "type": "preprint",
  "updated_at": "2026-11-08T12:21:52Z",
  "url": "https://research.draconitic.com/paper/72pvx7gsa575t",
  "venue": "Zenodo",
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