PAS_ From Phase Alignment to Deterministic Collapse Laws

Full CODES Framework Abstract The Phase Alignment Score (PAS) is introduced as a deterministic alternative to probabilistic stability analysis. Defined as: PAS_s = Σ cos(θ_k − θ̄) / N with extensions ΔPAS (drift slope) and PAS_zeta (drift curvature), the PAS stack replaces likelihood and entropy with reduction invariants of coherence. Collapse is no longer stochastic but lawfully measurable when thresholds are crossed. A decision grid of twelve scenarios demonstrates how PAS_s, ΔPAS, and PAS_zeta classify persistence, recovery, and collapse across emissions. Applications are outlined in physics (oscillator stability, interference), biology (neural synchrony, cardiac coherence), and cognition (proof-checking, compiler stability, translation persistence). The PAS stack provides a bounded, recurrence-tested framework that displaces entropy and Lyapunov averages, anchoring collapse and persistence in deterministic law.