A Classical Response Action for RT Nonlocal Gravity with Exact Recovery of the Solution Set

We give a real nonlocal classical response action for the full nonlinear RT gravitational equation, retaining the original prescribed retarded inverses. Independent response variations recover every original metric equation, and every original solution has a stationary lift with zero response. No spurious metrics occur in the projection of the stationary set. The construction applies the established adjoint-variable principle. It does not establish equality of physical degrees of freedom or a quantum effective action. The deposit includes the PDF, LaTeX sources, Lean proofs and audit logs, and exact multiplier-search and causal-kernel calculations. A fresh Lean build passed five targets and audited 25 public theorems without sorry or additional axioms. The proof uses actual four-dimensional integrals and the nonlinear coordinate equation, conditional on explicit regularity and a fixed pair of prescribed inverse maps. The analytic construction and causal uniqueness of those maps are not formalized.