Unary Field Theory: Tidal Locking as Time-Well Equilibrium

The Unary Field Theory (UFT) reinterprets tidal locking as an equilibrium configuration of the κt flow time-well landscape, not as a result of phenomenological dissipation. In this picture, a satellite's rotation is damped by the fundamental tendency of the κt flow to minimize time-gradient energy. The Moon's synchronous rotation, Mercury's 3:2 spin-orbit resonance, and the prevalence of tidal locking among planetary satellites all emerge naturally from multiscale time-well superposition. This paper derives the time-well torque and locking timescale from first principles: for the Earth-Moon system, the time-well asymmetry is δτ_E→M ∼ 1.0×10⁻¹³ s/s, yielding a locking timescale t_lock ∼ 4×10⁶ yr. Mercury's 3:2 resonance is explained by its orbital eccentricity (e=0.2056), which stabilizes the configuration minimizing peak time-gradient torque at perihelion. The same φ field mediating this torque also produces the φ-shroud resonance at ∼70 days (UFT Prediction Paper XI), providing a cross-link to local dark matter physics. Observational tests include Lunar Laser Ranging (LLR) for ∼70-day modulation of lunar recession and BepiColombo at Mercury for forced libration amplitudes. This is UFT Prediction Paper XII; the unified framework is in the main paper: Zou (2026), doi:10.5281/zenodo.21186809.