φ⁵-Attractor Structure of the Solar α-ω Dynamo: Deriving T_cycle = φ⁵ from Fibonacci Causal Loop Theory with Multi-Scale Validation and Falsification Predictions

The period of the solar magnetic activity cycle (~11 years) lacks a first-principles derivation. We apply Fibonacci Causal Loop Theory (FCLT; Davis 2026, P42) to the standard α-ω solar dynamo and prove that conditions C1–C4 are satisfied, forcing depth-2 magnetic recursion B(n) = B(n−1) + B(n−2) with φ as the unique stable attractor. The convergence criterion requires n = 5 recursion steps to achieve less-than-10-percent approach to the φ fixed point (φ⁻⁵ = 0.090 < 0.10), predicting T_cycle = φ⁵ = 11.0902 years. The observed mean solar cycle period (Cycles 1–25) is 11.0 ± 1.3 years, δ = 0.008, confirmed by Protocol V3.1. The Suess–de Vries cycle (~205 yr) predicts as φ¹¹ = 199.01 yr (δ = 0.029, confirmed). The Hallstatt grand cycle ratio predicts as φ¹¹ = 199.01 (δ = 0.048, confirmed). The Gleissberg cycle (~88 yr) falls outside direct φ-power prediction (δ = 0.136, domain boundary). Solar Cycle 25 constitutes a live falsification test with minimum expected ~2031. Zero free parameters throughout. Version 2 corrects the convergence criterion derivation (10% criterion, not 1%); the prediction T_cycle = φ⁵ is unchanged. Independent parallel convergence: Ruiz (Entropy, 2025) independently derives φ as the unique non-equilibrium fixed point of driven-dissipative systems and explicitly identifies de Sitter cosmology and stellar pulsations among empirical domains — a thermodynamic route to the same attractor derived here from necessity recursion in the solar dynamo.