Temporal Dynamics as Space-Growth: Kinematics and Tests with a GR Bridge

We formulate \emph{Temporal Dynamics} (TD), a clock-first description in which a universal space–growth speed $S(t)$ sets the causal baseline and a dimensionless slow–time field $\Delta T(\mathbf x,t)$ encodes local rate loss. In the quasistatic, weak field we use a single scalar to control kinematics and optics: $\mathbf g=-(S^2/2)\nabla\Delta T$ and $n(\mathbf x)=1/\sqrt{1-\Delta T(\mathbf x)}$. With the \emph{Normalization Axiom} $S\equiv c$ and the identification $N^2=1-\Delta T$, TD reproduces GR's tested content (Newtonian limit, gravitational redshift, Shapiro delay, light deflection, and standard GW degrees of freedom) without introducing a new propagating mode. Horizons occur at $\Delta T\!\to\!1$, fixing the global mass–size calibration $D_{\rm BH}=4GM/c^2$. The source law uses the GR weak-field "active density" $\rho+(p_x+p_y+p_z)/c^2$, cleanly separating EM \emph{propagation} (via $n$) from \emph{sourcing} (via stresses). Allowing a tiny homogeneous clock drift $\varepsilon(t)=\dot S/c$ yields an effective $\Lambda(t)=3\varepsilon(t)^2/c^2$, a one-parameter extension of $\Lambda$CDM with distances $E^2(z)$ modified by $(1+z)^{2p}$. We outline a falsifiable program: map $\Delta T(\mathbf x)$ with clock networks and atom interferometers, test the optical dictionary on engineered links and lensing, and fit the cosmological parameter $p$ with SN\,Ia, BAO, and $H(z)$, cross-checking growth and the turnaround scale $r_\ast=(GM/\varepsilon^2)^{1/3}$.