Effective Gravitational Response and the Einstein Limit

We present an effective formulation of gravitational response and a quantitative criterion for comparing it with that of General Relativity on physically matched backgrounds and sources. The construction uses tools from linear response and effective field theory to connect retarded correlators, causal kernels, and the gravitational action. The Einstein–Hilbert sector defines the dominant geometric limit, while additional operators, extra modes, and memory are retained as components of the dynamics. The contribution consists in organizing pole shifts, residue changes, and additional, regular, or continuum contributions within a response budget with stated tolerances and conditions for theoretical control. For meromorphic responses with isolated simple poles, an explicit bound provides a sufficient condition for closeness; its application distinguishes a controlled deviation from Einstein gravity from a loss of validity of the effective approximation. We present a local two-derivative realization with a clock field, two analytical checks—khronometric and weak-field Brans–Dicke—and a memory example with a controlled expansion. These checks distinguish partial agreement in one channel from the observable decoupling of an additional mode. Finally, we formulate a protocol for predictive testing with independent data.