Structured Resonance Dynamics_ Energy–Information–Numerical Closure

CODES Framework Abstract This work establishes a deterministic equivalence between energy, information, and computation. Using the harmonic coherence invariant PAS_h, it derives explicit laws linking electromagnetic energy flow, open-system dissipation, information capacity, and fixed-point numerical continuity. Energy conservation is shown to coincide with coherence conservation, entropy is reinterpreted as coherence drainage, and probabilistic entropy is replaced by phase-resolution capacity. The closure condition PAS_h ≥ θ_L ∧ ΔPAS_ζ ≤ ε_drift defines lawful persistence across physical, symbolic, and computational domains. An empirical protocol testing ε_drift ∝ V⁻¹⁄² across optical, MEMS, Josephson, and biological oscillators provides falsifiable validation. The result unifies the laws of energy, information, and computation under one deterministic coherence substrate, completing the Structured Resonance Dynamics series.