Time Field Theory I: The Fundamental Axiom and Total Velocity Conservation in Flat Spacetime

This paper proposes a flat-spacetime scalar theory of gravity centered on the time field γ, which unifies gravitational phenomena through the total velocity conservation principle c² = vₜ² + vₛ² without introducing spacetime curvature. The time field satisfies a linear wave equation, and gravitational acceleration is derived from its spatial gradient, strictly reducing to Newtonian gravity in the weak-field limit. The framework consistently reproduces all classical gravitational tests, including gravitational time dilation, light deflection, perihelion precession of Mercury, and gravitational wave radiation, while yielding unique, falsifiable predictions for black hole ringdown frequencies testable by LISA. This theory is singularity-free, naturally quantizable, and provides a mathematically consistent alternative to general relativity.