What question did this study set out to answer?

This study aims to explore the relationships between Fibonacci numbers, the golden ratio, and quantum manifestations.

July 24, 2026Open Access

Golden Ratio's Quantum and Matrix Manifestations Across Fibonacci Anyons and Supersymmetric Oscillators — E8 Intelligence Research

Key Points

This study aims to explore the relationships between Fibonacci numbers, the golden ratio, and quantum manifestations.
Analyzed Fibonacci matrix eigenvalues and diagonalization to establish connections with the golden ratio.
Demonstrated Fibonacci anyon quantum dimensions and their fusion categories.
Investigated quantum calculus applying the golden and silver ratios to supersymmetric oscillator spectra.
Identified eigenvalues of the Fibonacci matrix as the golden ratio (1.618) and its inverse (0.618).
Established that the quantum dimension of Fibonacci anyons equals the golden ratio.
Showed connections between the golden ratio and the spectra of supersymmetric oscillators through quantum calculus.

Abstract

FINDING: Fibonacci numbers are expressible via golden ratio eigenvalues of a 2×2 matrix; fusion categories of Fibonacci anyons realize golden ratio as quantum dimension; quantum calculus links golden/silver ratios to supersymmetric oscillator spectra. MATH: - Fibonacci matrix \ (M = pmatrix1 Fibonacci divisor derivative \ (q f (x) = (f (qx) -f (x) ) / ( (q-1) x) \). CONNECTION: - Golden ratio \ (= 1. 618 \) and its inverse \ (1/ = 0. 618 \) are geometric-harmonic constants. - \ (² = Author: Andrew Stewart Caldin, Independent Researcher, UK. Part of the E8 Intelligence Research series. Platform: e8intelligence. com

Ask AI

Helpful

Bookmark

View Full Paper