From Compton Frequency to Deterministic Drift_ The Quantum Boundary of Structured Resonance

CODES Framework Abstract The Compton frequency f_C = m·c^2 / h defines the intrinsic oscillation rate of matter. Conventional quantum mechanics treats it as a statistical boundary separating continuous fields from probabilistic particles. Within the deterministic CODES framework, it is reinterpreted as the base clock of lawful coherence—the smallest time step a mass can advance while remaining phase-aligned with its energy content. By extending the harmonic–differential equivalence (PAS_h ⇔ dC/dt) to the quantum domain, this paper identifies ε_drift_min = h/(m·c^2) as the universal lower bound of lawful phase increment. The familiar scaling law ε_drift ∝ V^−1/2, observed from optical oscillators to biological rhythms, is shown to generalize the same constant upward across many orders of magnitude. The result is a continuous deterministic hierarchy: ε_drift_min ≤ ε_drift(V) ≤ ε_drift_macro, uniting quantum oscillation, physiological coherence, and planetary timing under a single invariant law. Planck’s constant emerges as a phase–energy coupling coefficient, not a random quantizer. The Compton relation and the CODES bounded-drift law describe the same invariant geometry viewed from different scales. Coherence, not chance, defines lawful persistence.