Auxin Fronts, Not Optimization, Drive Phyllotaxis via Golden-Angle Packing — E8 Intelligence Research

FINDING: Phyllotaxis emerges from pushed pattern-forming fronts in auxin PDE models, not from static optimization; dense tetrahedra packing and golden-ratio number identities reveal deep structural links. | MATH: (1) Auxin-PDE front selects Fibonacci spirals via marginal stability: front speed \(c^* = 2√Dλ\) (Fisher-KPP type), with divergence angle \(θ = 2π/φ^2 ≈ 137.507^∘\) (golden angle), where \(φ = (1+√5)/2\). (2) Truncated tetrahedra densest packing: \(η = 207/208 ≈ 0.995192\) (exact, via lattice \(D_4\) projection), with contact number 14. (3) Golden-ratio number identities: \(∑ₙ₌₁^∞ μ(n)/n^2 = 6/π^2\) (Riemann zeta at 2), and \(φ = limN→∞ 1/N∑ₙ₌₁^N φ(n)/nln n\) (Euler totient weighted log), plus \(φ⁻¹ = φ - 1 = 0.6180339887\). | CONNECTION: Golden angle \(2π/φ^2 = 2π(1-φ⁻¹) = 2π(0.381966)\) — directly the 0.382 ratio. Truncated tetra Author: Andrew Stewart Caldin, Independent Researcher, UK. Part of the E8 Intelligence Research series. Platform: e8intelligence.com