Time Field Theory II: Fundamental Axioms and Geometric Foundations

This paper establishes the axiomatic and geometric foundation of time field theory. Based on the invariant total speed conservation law c^2 = v_t^2 + v_s^2 and flat spacetime, the theory defines the time field γ = v_t/c as the core physical quantity. Gravity originates from the spatial gradient of the time field without spacetime curvature. The framework is mathematically simple, causal, singularity-free, and compatible with quantum unification. It provides a complete axiomatic system for a consistent alternative to general relativity.