Majorana Braiding Yields Golden Ratio Eigenvalues and Non-Abelian Statistics — E8 Intelligence Research
Year: 2026
Type: preprint
Abstract: FINDING: Braiding matrices for Majorana zero modes yield non-Abelian statistics with eigenvalues linked to the golden ratio conjugate (0.618) and its square (0.382), and the geometric constant 0.786151 (square root of golden ratio conjugate). | MATH: The braid group generator for two Majorana zero modes, when acting on a 2D Hilbert space, has eigenvalues exp(±iπ/5) = (φ⁻¹ ± i√(2+φ⁻¹))/2, where φ = (1+√5)/2 ≈ 1.618. The constant 0.786151 = √(φ⁻¹) = √(0.618) ≈ 0.786151. The braid matrix eigenvalues correspond to rotations by 36° (π/5), linking to the golden angle (137.5° = 2π(1-φ⁻¹)). | CONNECTION: Direct geometric harmony: 0.786151 is the square root of the golden ratio conjugate (0.618), and 0.382 = φ⁻². These appear in the braid matrix eigenvalues and the non-Abelian Berry phase. The 36° rotation connects to pentagonal symmetry (crystallographic point group 5m, root system H₂). Base-60 fractions: 36° = 1/10 of a full circle (360°), and 0.618 ≈ 37/60. | DEPTH: 9 — This is a profound li Author: Andrew Stewart Caldin, Independent Researcher, UK. Part of the E8 Intelligence Research series. Platform: e8intelligence.com
Author: Caldin, Andrew Stewart
Language: English
Subfield: Atomic and Molecular Physics, and Optics
Field: Physics and Astronomy
Domain: Physical Sciences
Open Access status: green
OpenAlex ID: W7171037484
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