Time Field Theory (TFT): Axiomatic Foundation, Dynamics and Classical Gravitational Tests

Based on the framework of flat three-dimensional Euclidean space, this paper constructs a self-consistent scalar time field gravitational theory (TFT) taking the local intrinsic total speed conservation as the first principle axiom. Without additional ad hoc assumptions or artificial patches, this paper strictly derives from the axiom system the definition of time field, covariant field equation, exact analytical solution of static spherically symmetric field, particle dynamic equation and variational principle. Complete derivations are successively presented for gravitational time dilation, gravitational light deflection, Mercury perihelion precession and GPS atomic clock spacetime correction. The weak field limit strictly recovers the Newtonian gravitational limit. The theory maintains full mathematical self-consistency and logical closure throughout, without spacetime curvature or geometric singularity. All classical gravitational tests and satellite clock correction effects are in high agreement with astronomical observations and engineering measurements, possessing inherent potential for quantization expansion. --- **Archive Note**This work serves as the **core foundational main paper** of the Time Field Theory (TFT) theoretical system. Together with its companion paper *The Divergence Between Mathematics and Physics: A Demonstration of the Inevitability of Flux Conservation Based on Time Field Theory*, the two works form the two fundamental pillars of the complete TFT framework:1. **Formal & Empirical Pillar (this paper)**: Establishes the full axiomatic system, covariant field equation, exact analytical solutions, particle dynamics, and quantitative verification against all classical gravitational observations, providing the complete mathematical formalism and empirical basis of the theory.2. **Meta-logical & Philosophical Pillar (companion paper)**: Proves the ontological inevitability of spacetime flux conservation from the fundamental distinction between mathematical formalism and physical reality, laying the first-principle meta-theoretical foundation for the entire axiomatic system.