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 \cite{mcfarlaneblake2025zenodo}, I demonstrate a deterministic two-tiered flare predictor achieving \textbf{80\% precision} (FAR=20\%) using stiff-axis Lyapunov exponents ($\lambda$) and Hilbert-derived frequency slips ($\Delta\omega$). The 3-stage system ($\lambda>-1.99$, $|\Delta\omega|>11.99$ cycles/hour, persistence $\geq2$ consecutive 3-hour bins) identifies 5 elite alerts from 1026 PMAD collapse events, while the 2-stage system provides 64 early warnings at 53.1\% precision. This physics-constrained approach exploits quiet-Sun basin preconditioning and flare-induced phase-slips, achieving operational-grade performance without machine learning.