Bounding the Scalar Coupling Constant γ from Precision Atomic Clock Comparisons: Implications for Temporal Resonance Models

In the scalar resonance framework of Dynamic Location Theory, a non-zero coupling constant γ between matter and a background scalar field predicts anomalous phase shifts in precision timing experiments: Δϕ ≈ γ ∫ (ω₁(t) − ω₂(t)) dt. Using 2024–2025 optical atomic clock comparison data (fractional uncertainties ≤ 3.2 × 10^{-18}), we derive upper bounds |γ| ≲ 10^{-16}–10^{-17} over integration times T ∼ 10^4–10^6 s from null detections of such anomalies. A simple coupled-oscillator simulation illustrates expected signatures, falsifiable at |γ| > 10^{-17} with near-future entanglement-enhanced clocks. These constraints reinforce the prohibitive energy regime for macroscopic temporal re-localization (Type II) while preserving low-energy informational access (Type III). This work extends prior frameworks on emergent location and temporal mechanics.