Golden Ratio Eigenvalue of Fibonacci Matrix Governs Phyllotaxis Growth — E8 Intelligence Research

FINDING: Fibonacci matrix eigenvalue is golden ratio; spectral radius governs phyllotaxis growth rate. | MATH: Fibonacci matrix \ (F = pmatrix1 eigenvalues \ (= 1+52 1. 618 \) and \ (= 1-52 -0. 618 \) ; spectral radius \ ( (F) = \) ; Binet formula \ (Fₙ = ⁿ - ⁿ5 \). | CONNECTION: Golden ratio \ (= 1. 618 \) and its reciprocal \ (1/ = 0. 618 \) are the two eigenvalues; ratio \ (/ = -0. 382 \) (negative of 0. 382) ; these ratios appear in phyllotaxis divergence angles (137. 5°, derived from \ (1/² 0. 382 \) ). | DEPTH: 8 — Direct eigenvalue link between linear recurrence and geometric growth; spectral radius explains optimal packing in nature; quantum calculus extension suggests deeper symmetry in supersymmetric oscillators. Author: Andrew Stewart Caldin, Independent Researcher, UK. Part of the E8 Intelligence Research series. Platform: e8intelligence. com