PAS Evolution and Clarification_ From PAS_s to PAS_h to ΔPAS_zeta

CODES Framework Abstract (v38 PAS Clarification Paper) CODES (Chirality of Dynamic Emergent Systems) introduced the Phase Alignment Score (PAS) as a universal scalar measure of coherence. PAS_s (first-harmonic order parameter) provided the first deterministic closure law but suffered blind spots (antiphase, quadrature, higher-harmonic locks). ΔPAS captured drift dynamics but inherited PAS_s limitations. PAS_h generalizes coherence to the multiharmonic invariant, uniquely scalar across N, ω, and harmonic bases. ΔPAS_zeta extends drift detection to a vector law, sealing legality in dynamic systems. This paper clarifies the PAS lineage (PAS_s → ΔPAS → PAS_h → ΔPAS_zeta), defines all notation, and situates the invariants against competing measures (entropy, Lyapunov exponents, order parameters). It connects theory to RIC engineering (deterministic inference substrate, v38+) and demonstrates applied use cases across physics (AMOC bifurcation, BEC oscillations), biology (protein folding, fMRI coherence), cognition (working memory collapse), institutions (contradiction detection), and engineering (contract checkers, legality stack). Thesis: probability is not ontology but incomplete phase detection. PAS_h and ΔPAS_zeta constitute the canonical closure law of coherence across domains.