Temporal Dynamics as Time-First General Relativity: k = 4G/c2 Linking Local Time Offsets, Curvature, and Cosmic Acceleration

We present Temporal Dynamics (TD) as a time-first reparameterization of General Relativity (GR). In TD, mass sources a local slow-time fraction T (x) ; keeping the universal converter UC=1/c exact implies that the straight-path delay over a segment of length D corresponds to a curve-length increment L= T\, D. Fixing the single TD mass constant to k=4G/c^2 (m\, kg^-1) makes the TDGR bridge exact: L ₑ₀₃=rₛ, L ₃₈₀₌=2rₛ, and the TD horizon rule D ₁₇=kM. The TD potential =- (c^2/2) T yields the general motion law a= (c^2/2) T, reproducing the Newtonian limit aᵣ=-GM/r^2. Taking T (r) =rₛ/r reconstructs the Schwarzschild line element, so the PPN parameters match GR (==1) along with classic tests (gravitational redshift, light bending, Shapiro delay, perihelion precession). A variational formulation identifies T with the ADM lapse via N^2=1- T; varying the action yields the Einstein equations with no extra propagating degrees of freedom (GR-equivalent dynamics, including gravitational waves with speed c and GR polarizations/flux). Cosmologically, a residual micro-push per clock unit defines =/c and recovers the Hubble law v= D; constant maps to =3^2/c^2, while a slow drift (z) corresponds to w (z) -1, reframing the H₀ tension as differing ₀ estimates. TD thus organizes tested GR physics with a single constant k and provides a micromacro interpretation of dark energy via, without modifying GR’s empirical content.