Time Field Theory (TFT): Axiomatic Foundation, Dynamic Wave Equation, and Static Spherical Solution

This paper presents the complete axiomatic foundation and full derivation of Time Field Theory (TFT) in flat three‑dimensional Euclidean space. Starting from first principles, we rigorously derive the dynamic gravitational wave equation, vacuum field equation, and the static spherical solution corresponding to a central point mass. The entire derivation is self‑contained, step‑by‑step, and free of logical gaps. TFT describes gravity as the gradient of a local time flow field without invoking curved spacetime or high‑order geometry. The theory naturally recovers gravitational time dilation, the Schwarzschild radius, and consistency with classical Newtonian gravity. This work serves as the core fundamental reference for Time Field Theory.