A Channel-by-Channel Response Criterion for the Recovery of General Relativity and Controlled Gravitational Transitions

We present an effective framework for determining, channel by channel, when gravitational dynamics reproduces the linear response of general relativity (GR) and when it departs from it within a regime that remains controlled. We start from Γgrav = ΓEH + ΔΓ, without claiming novelty for this decomposition or for the local operator basis used as an example. The procedure requires physical matching of backgrounds, reduction of gauge freedom and constraints, separation of shared and extra modes, and comparison of the response through pole positions, residues, damping, observable weight, and the regular part. For locally meromorphic responses with isolated simple poles, we derive an explicit bound on the difference between retarded responses saturated by physical sources away from pole neighborhoods. GR recovery is defined through channel-specific tolerances, and a controlled transition occurs when one of them is saturated before effective field theory control is lost. Two analytical tests—khronometric gravity and weak-field Brans–Dicke theory—illustrate, respectively, partial recovery with an uncontrolled extra mode and decoupling through response weight. The framework is completed by a proposed statistical validation protocol using independent data without refitting; no complete empirical validation is performed here. The scope is linear response around specified backgrounds; neither global nonlinear equivalence nor a new fundamental theory of gravity is claimed.