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. Version 1.1 — core verification supplement, 28 October 2026. A fresh verification passed 33/33 build targets and audited 91 public theorems. It verifies the actual nonlinear integral first variation and exact projection of the classical response-action stationary set onto the complete original RT equation, with zero-response lifts for all original solutions. The original prescribed inverse maps and their explicit regularity and analytic laws remain inputs; this is not an existence or causal-uniqueness theorem for retarded inverses on arbitrary spacetimes. The source paper discusses the missing action in a quantum-effective-action context. The present construction is a classical extended response action and does not construct that quantum effective action, establish quantum equivalence, or close that stronger question. It does not certify every supplementary discussion or multiplier-search classification in the manuscript, physical degrees-of-freedom equivalence, or bibliographic priority. Use RT_Response_Core_Verification_Scope_20261028.pdf and RT_Response_Core_Lean_Verification_20261028.zip for the current formal scope. The five-target/25-theorem counts above describe the historical package, which is retained with the original manuscript. AI tools were used to assist Lean code development and verification, translation, and to accelerate multiplier searches and tests.