Optical–Gravitational Unification: A Field Equation for Refractive Structure and Mass Density

We propose a unified field relation linking the optical refractive index \(n(\mathbf x)\) to the gravitational mass density \(\rho(\mathbf x)\):
\[
\nabla^2 \ln n \;=\; -\Bigl(\tfrac{8\pi G}{c^2}\Bigr)\rho.
\]
Its Gauss (flux) form yields falsifiable closures and enables bidirectional inference between \(G\) and \(c\).
Our main contribution is a \emph{Phase--Poisson mass mapping} that injects the Riemann zeta phase into density:
starting from the phase-to-index map \(\ln n(\mathbf x)=g\big(\theta(U(\mathbf x))-\langle\theta\rangle\big)\) with \(U(\mathbf x)=\mathbf k\!\cdot\!\mathbf x+b\) and the SCI reciprocity \(g=1/K\), the high-height limit gives \(g\to \tfrac12\), leading to
\[
\rho(\mathbf x)\;\approx\;-\frac{c^2}{16\pi G}\,\nabla^2 \theta\!\big(U(\mathbf x)\big).
\]
We validate the unified law independently of any phase prior via spectral Poisson solves, DC correction, and multi-shell Gauss closures (sub-percent); we then instantiate the phase-driven mapping and test it against lensing-style flux certificates and structural fingerprints (SCI) separating Riemann from GUE/Poisson with high significance.