Vacuum Response Gravity from a Conformally Coupled Reservoir Field: A Predictive Framework for Dynamics and Weak Lensing

We present a covariant “inertia-first” response theory in which local inertia is controlled by a reservoir state variable photons and matter propagate on a single physical metric g_=A² () \, g_. In the weak-field limit this yields a Helmholtz–Poisson response equation for the scalar perturbation and a modified physical potential =N+₀. A key consequence of the minimal conformal class is the absence of gravitational slip at leading order, g ₋₄₍ₒ=g ₃ₘ₍, so weak-lensing directly constrains the same response that governs matter dynamics. We derive analytic spherical solutions, with a fully worked Hernquist example including closed expressions for the response function (r) =g ₋₄₍ₒ/gN, and we provide a formally correct projection pipeline to the observable excess surface density (R). The framework replaces halo additivity by a nonlocal response structure in the effective lensing source and naturally accommodates outer relaxation to GR via coupling damping (₁₆) 0 and/or mass screening m_ (₁₆). The Zenodo archive includes the manuscript, figure files, and a self-contained notebook that reproduces Figs. 1–4.