{
  "abstract": "FINDING: Quantum calculus with dual bases (Golden and Silver ratios) generates a supersymmetric hierarchy of \"golden oscillators\" whose Fock-space spectrum is governed by Fibonacci divisors, linking number theory to SUSY quantum mechanics. | MATH: Two-base quantum calculus: \\( q = \\phi = (1+\\sqrt{5})/2 \\) and \\( q = \\delta_S = 1+\\sqrt{2} \\) (Silver ratio). Fibonacci divisor derivative \\( \\partial_{\\phi} f(n) = [f(\\phi n) - f(\\phi^{-1} n)]/((\\phi - \\phi^{-1})n) \\). Binet form for Fibonacci divisor number operator: \\( \\hat{N}_F = (\\phi^{\\hat{n}} - (-\\phi)^{-\\hat{n}})/\\sqrt{5} \\). Energy spectrum for golden oscillator: \\( E_n \\propto \\phi^{2n} + (-\\phi)^{-2n} \\) (or similar via \\( q \\)-deformed ladder operators), with SUSY partner spectra shifted by \\( \\phi^2 \\) or \\( \\phi^{-2} \\). | CONNECTION: Direct: \\( \\phi = 1.618... \\), \\( \\phi^{-1} = 0.618... \\), \\( \\phi^{-2} = 0.382... \\), \\( \\phi^2 = 2.618... \\). The ratio \\( \\phi^{-1/2} \\approx 0.786 \\) appears naturally in the \\( q \\)-deformed\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": [
    {
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        0
      ],
      "name": "Andrew Stewart Caldin"
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  ],
  "bibtex": "https://research.draconitic.com/paper/4922mkb05d174.bib",
  "cited_by": 0,
  "doi": "10.5281/zenodo.23635215",
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  "id": "4922mkb05d174",
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  "language": "eng",
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  "published": "2026-10-25",
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  "ris": "https://research.draconitic.com/paper/4922mkb05d174.ris",
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      "first_seen": "2026-11-08T12:21:58Z",
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  "title": "Golden Oscillators: Fibonacci Divisors Bridge Quantum Calculus and Supersymmetry — E8 Intelligence Research",
  "title_text": "Golden Oscillators: Fibonacci Divisors Bridge Quantum Calculus and Supersymmetry — E8 Intelligence Research",
  "type": "preprint",
  "updated_at": "2026-11-08T12:21:58Z",
  "url": "https://research.draconitic.com/paper/4922mkb05d174",
  "venue": "Zenodo",
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