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

We propose a unification between optical refractive structure and gravitational mass density via\[\nabla^2 \ln n(x) = -\frac{8\pi G}{c^2}\,\rho(x),\]whose Gauss (flux) form yields falsifiable closures and enables bidirectional inference between $G$ and $c$.Our main construction is a Phase–Poisson mass mapping that injects Riemann zeta phase into density:with the phase-to-index map $\ln n(x)=g(\theta(U(x))-\langle\theta\rangle)$, $U(x)=k\!\cdot\!x+b$, and thestructure–phase reciprocity $g=1/K$, the high-height limit $g\to \tfrac{1}{2}$ gives\[\rho(x)\;\approx\;-\frac{c^2}{16\pi G}\,\nabla^2 \theta(U(x)).\]Beyond the weak-field baseline, we \emph{predict} a strong-field refractive correction governed by\[\nabla^2\phi + \beta(x)\,\mathcal N(|\nabla\phi|^2) = -\kappa\,\rho, \qquad \phi=\ln n,\ \ \kappa=\frac{8\pi G}{c^2},\]which implies a nonzero deflection shift $\Delta\boldsymbol\alpha=\nabla\phi_{\rm NL}-\nabla\phi_{\rm Lin}\neq\mathbf 0$and a \emph{three-term} flux certificate (flux $+$ mass $+$ nonlinear)---a structure absent from the GR weak-field thin-lens limit. \textbf{Validation.} (i) Without any phase prior, spectral Poisson solves with DC correction achieve machine-precision differential closure and sub-percent multi-shell Gauss closures, with bidirectional recovery of $G$ and $c$. (ii) On real data (Abell 2744 CATS v4 $\kappa$ map), we observe localized,high-gradient deflection corrections ($\Delta\boldsymbol\alpha\neq\mathbf 0$) and multi-shell closure of the three-term certificate at the $10^{-3}$--$10^{-2}$ level; a $\beta_0{=}0$ control removes both effects.(iii) SCI fingerprints further separate zeta-driven structure from GUE/Poisson controls with high significance.Together these results provide falsifiable, real-data evidence for strong-field nonlinear deflection in the unified refractive framework, distinguishing it from the GR weak-field baseline while retaining a Phase–Poisson bridge to arithmetic structure.