Golden Ratio Bridges Topological Quantum Field Theory and Supersymmetric Oscillator Hierarchies — E8 Intelligence Research
- 1Independent Researcher, United Kingdom
Abstract
FINDING: Fibonacci TQFT yields mapping class group representations into pseudo-unitary groups, linking the golden ratio to complex hyperbolic geometry on moduli spaces; a separate quantum-calculus framework uses golden/silver ratios for supersymmetric oscillator hierarchies.
MATH: - Fibonacci TQFT: Representations of mapping class groups → PU(p,q) (pseudo-unitary), with exceptional cases tied to the golden ratio φ = (1+√5)/2. - Golden ratio identities: φ2 = φ + 1, φ−1 = φ − 1 = 0.618..., φ−2 = 2 − φ = 0.382.... - Quantum calculus (arXiv:2410.04169): Two-base derivative with bases φ (golden) and 1+√2 (silver). Fibonacci divisor operator N̂F acting on Fock space; Binet formula: Fn = (φn − (−φ)−n)/√5. Energy spectrum of "golden oscillators" scales as φ2n or φ−2n (hierarchy). - Complex hyperbolic stru
Author: Andrew Stewart Caldin, Independent Researcher, UK. Part of the E8 Intelligence Research series. Platform: e8intelligence.com
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BibTeX
@misc{caldin2026golden,
title = {{Golden Ratio Bridges Topological Quantum Field Theory and Supersymmetric Oscillator Hierarchies — E8 Intelligence Research}},
author = {Andrew Stewart Caldin},
howpublished = {Zenodo},
year = {2026},
month = oct,
doi = {10.5281/zenodo.23587212},
url = {https://zenodo.org/records/23587212},
note = {CC BY 4.0},
}
RIS
TY - UNPB
TI - Golden Ratio Bridges Topological Quantum Field Theory and Supersymmetric Oscillator Hierarchies — E8 Intelligence Research
AU - Andrew Stewart Caldin
PY - 2026
DA - 2026/10/23
PB - Zenodo
DO - 10.5281/zenodo.23587212
UR - https://zenodo.org/records/23587212
AB - FINDING: Fibonacci TQFT yields mapping class group representations into pseudo-unitary groups, linking the golden ratio to complex hyperbolic geometry on moduli spaces; a separate quantum-calculus framework uses golden/silver ratios for supersymmetric oscillator hierarchies. MATH: - Fibonacci TQFT: Representations of mapping class groups → PU(p,q) (pseudo-unitary), with exceptional cases tied to the golden ratio φ = (1+√5)/2. - Golden ratio identities: φ^2 = φ + 1, φ^−1 = φ − 1 = 0.618..., φ^−2 = 2 − φ = 0.382.... - Quantum calculus (arXiv:2410.04169): Two-base derivative with bases φ (golden) and 1+√2 (silver). Fibonacci divisor operator N̂_F acting on Fock space; Binet formula: F_n = (φ^n − (−φ)^−n)/√5. Energy spectrum of "golden oscillators" scales as φ^2n or φ^−2n (hierarchy). - Complex hyperbolic stru Author: Andrew Stewart Caldin, Independent Researcher, UK. Part of the E8 Intelligence Research series. Platform: e8intelligence.com
ER -