Time, Light, and Gravity from a Single Leak: How a Non-Split Parity Fiber Generates the Three Pillars of Spacetime

We collect and extend two internal notes (``Note V'' and ``Note VI'') that propose a single algebraic mechanism---projection leakage from a non-split parity fiber---as a common origin for (i) physical time, (ii) a finite causal speed $c$, and (iii) a curvature signal that reproduces the Einstein tensor for a conformal metric.The framework identifies ``fine time'' with the generator $K\mapsto K+1$ of the non-split exact sequence $0\to \mathbb{Z}_{24}\to \mathbb{Z}_{48}\to \mathbb{Z}_2\to 0$, where each fine step toggles a hidden parity fiber $p\in \mathbb{Z}_2$.A parity-blind projection $\Pi_p$ leaves a residual leakage $\varepsilon>0$ that (a) converts the projected equation from elliptic to hyperbolic (creating time), (b) sets $c^2=Z_x/(2\varepsilon Z_t)$ (a finite causal cone), and (c) when promoted to a field $s(x)=\log \varepsilon(x)$ yields the Einstein tensor through the identity\[G_{\mu\nu}=\nabla_\mu\nabla_\nu s-g_{\mu\nu}\Box s-\tfrac12\,\partial_\mu s\,\partial_\nu s-\tfrac14\,g_{\mu\nu}(\partial s)^2\quad\text{for}\quadg_{\mu\nu}=e^{-s}\eta_{\mu\nu}.\]The identity is verified numerically in homogeneous FRW backgrounds (two independent computation paths agree at near machine precision; worst-case $\sim 10^{-12}$ conditioning in one de Sitter component), and extended to fully inhomogeneous static 3+1D fields $\varepsilon(x,y,z)$ on periodic lattices with matched discretization, achieving $20/20$ PASS and $O(dx^2)$ convergence (measured order $\approx 2.3$) across five synthetic configurations.We emphasize that the \emph{mathematical} structure is a known conformal-geometry formula; the proposed novelty is \emph{physical interpretation}: $s$ is not an ad hoc scalar but the logarithm of a projection leakage cost inherited from a non-split parity fiber.Finally, we propose (P0) an operational ``two-path'' geometry pipeline that treats the identity as a fast Einstein builder with built-in oracle checks, and (P1) a sector-dependent leakage generalization suggested by the $\mathbb{Z}_{48}\to\mathbb{Z}_{24}\to\mathbb{Z}_4$ IRIS chain, in which four scalar leakage fields provide the correct counting for the two tensor polarizations of gravitational waves.