Golden Ratio Bridges Topological Quantum Field Theory and Supersymmetric Oscillator Hierarchies — E8 Intelligence Research

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 \(φ²ⁿ\) or \(φ⁻²ⁿ\) (hierarchy). - Complex hyperbolic stru Author: Andrew Stewart Caldin, Independent Researcher, UK. Part of the E8 Intelligence Research series. Platform: e8intelligence.com