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

We propose a unified field relation connecting the optical refractive index field n(x) to the gravitational mass density ρ(x):

∇² ln n(x) = − (8πG / c²) ρ(x).

The flux (Gauss) form provides a stable, falsifiable certificate and enables bidirectional inference between Newton’s constant G and the speed of light c.

We further integrate a zeta-phase prior—mapping the spectral phase of the Riemann zeta function into n(x)—and validate the theory via ray-based vector certificates, group-delay predictions, and structural complexity indices (SCI).

Numerically, a spectral Laplacian with DC correction and multi-shell Gauss closures achieves percent-level consistency. SCI windows further distinguish Riemann statistics from GUE and Poisson controls with high significance.