Abstract

This work establishes the universal deterministic law of coherence underlying all stable systems—physical, biological, and cognitive. The core relation PAS_h ≥ θ_L ∧ ΔPAS_zeta ≤ ε_drift defines persistence as sustained phase alignment within bounded drift. Probability and entropy emerge as coarse-grained representations of lost phase information. Structured Resonance Dynamics (SRD) formalizes coherence as the primary invariant of reality, replacing statistical inference with lawful phase alignment. The framework integrates: • Prime-indexed harmonic structure (Chiral Prime Lattice) • Measurement bridge linking PAS variables to energy, mass, and information • Scaling laws ensuring invariance from quantum to cosmological domains • The Chiral Vessel Theorem explaining why life and matter maintain asymmetry • Deterministic computational verification via RIC (Q32 fixed-point substrate) All constants and apparatus are empirically calibrated (ε_drift ≈ 10⁻⁶ PAS units). This paper completes the mathematical and empirical closure of the CODES framework, uniting physics, biology, and cognition under a single coherence law.