Phase-Mediated Collapse: Deterministic Solar Flare Forecasting from Lyapunov Proxies and Arnold Tongue Phase-Slips in 3-Hour AIA 171 Å Dynamics

Building on the phase-mediated metastable basin structure identified in doi:10.5281/zenodo.18478416, I demonstrate a deterministic two-tiered flare predictor exploiting stiff-axis Lyapunov exponents (λ) and Hilbert-derived frequency slips (Δω). The 3-stage system (λ>-1.99, |Δω|>11.99 cycles/hour, persistence ≥2 consecutive 3-hour bins) identifies 5 elite alerts from 1088 PMAD collapse events with 80% precision. The 2-stage system produces broader early-warning coverage, yielding 259 alerts at 40.2% precision for a 40% Lyapunov threshold and 105 alerts at 57.1% precision for a 60% threshold, demonstrating tunable tradeoffs between recall and precision. Permutation testing against random alert placement yields Z=2.22,5.18 ( p≈ 0.0163, p≪0.001), confirming that the phase-slip signatures contain statistically significant predictive information. Unlike supervised ML approaches, this dynamical systems method derives thresholds directly from empirical PMAD statistics, offering transparent and reproducible operational forecasting that could serve as high-fidelity inputs for ML pipelines.