The Unified Field of Time-Driven Dynamics: A Dynamic Extension of General Relativity with an Endogenous Time Scalar Field

We present a \emph{complete} (no-omission) theoretical unification that: (i) couples optical refractive structure to gravitational mass density via a flux-certified field equation; (ii) endogenizes time through a scalar clock $U$ with coupling $W(U)$ yielding a dynamic time--energy exchange and exact total conservation; and (iii) stitches an arithmetic microstructure to geometry using a \emph{zeta--$U$ bridge} with structure--phase reciprocity $g=\!1/K$. The \textbf{pure-theory core} works without Einstein--Hilbert (EH) terms and without any zeta prior; a \textbf{covariant extension} with EH can be toggled on to align with GR. When the zeta prior is enabled, the Phase--Poisson mapping produces falsifiable morphology-level predictions; SCI/KS statistics (windowed) empirically support the reciprocity with median $1/K\!\approx\!0.53$ ($p<10^{-5}$ vs.\ controls). This manuscript consolidates all key formulae (including (4$'$) and (6)), the flux certificates, and the UTH variational sector in one document.