{
  "abstract": "FINDING: Quantum calculus with dual bases (Golden/Silver ratios) unifies Fibonacci divisor derivatives with Binet-form number operators, generating an infinite hierarchy of N=2 supersymmetric oscillators. | MATH: Silver ratio σ = 1 + √2 ≈ 2.4142; its inverse σ⁻¹ = √2 − 1 ≈ 0.4142. Golden ratio φ = (1+√5)/2 ≈ 1.618; φ⁻¹ = φ − 1 ≈ 0.618. Quantum calculus bases: q₁ = φ, q₂ = σ (or their powers). Fibonacci divisor derivative: ∂_q f(n) = [f(qn) − f(n)] / [(q−1)n] in q-calculus. Binet formula: F_n = (φⁿ − (−φ)⁻ⁿ)/√5. Number operator: N̂ = a†a with spectrum {n} — here generalized to Fibonacci divisor number operator with eigenvalues F_n or Lucas-type combinations. Supersymmetric hierarchy: H_k = {Q_k, Q_k†} with Witten index Δ_k = F_{k+1} − F_k alternating, yielding N=2 SUSY for each k. | CONNECTION: Silver ratio σ = 1 + √2 is the **Pell number** limit (P_n/P_{n−1} → σ), and √2 is the diagonal of the unit square — directly tied to **crystallographic root system B₂** (square lattice) and the *\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/4jbxtrnvcmp6x.bib",
  "cited_by": 0,
  "doi": "10.5281/zenodo.23610264",
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  "id": "4jbxtrnvcmp6x",
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  "landing_url": "https://zenodo.org/records/23610264",
  "language": "eng",
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  "published": "2026-10-24",
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  "ris": "https://research.draconitic.com/paper/4jbxtrnvcmp6x.ris",
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    {
      "first_seen": "2026-11-07T12:21:35Z",
      "native_id": "23610264",
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  "title": "Quantum Calculus Unifies Fibonacci Divisors with Supersymmetric Oscillators via Golden and Silver Ratios — E8 Intelligence Research",
  "title_text": "Quantum Calculus Unifies Fibonacci Divisors with Supersymmetric Oscillators via Golden and Silver Ratios — E8 Intelligence Research",
  "type": "preprint",
  "updated_at": "2026-11-07T12:21:35Z",
  "url": "https://research.draconitic.com/paper/4jbxtrnvcmp6x",
  "venue": "Zenodo",
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