Time-Scalar Field Theory (TSFT): Universality of Temporal Parameterization and Gravity as Time-Rate Gradients

Time-Scalar Field Theory (TSFT) introduces a universal scalar field Θ(x) that parameterizes physical evolution and reinterprets gravity as gradients in local time rates. We prove the necessity of temporal dependence in all predictive physical laws, derive the weak-field limit recovering Einstein’s equations, verify classical tests like light bending and Shapiro delay, and simulate anisotropic effects yielding falsifiable orbital precessions. Extending to repulsive regimes via sign inversion in ∇Θ, TSFT unifies attraction with cosmic acceleration, offering a framework for dark energy and inflation without ad-hoc parameters. Empirical signatures, including redshift asymmetries and void dynamics, provide testable levers beyond general relativity.