Gravitational Response Kernel: Empirical Identification from Cosmological Lensing

We empirically identify the source variable that most strongly governs a scale-selective gravitational response observed in cosmological lensing–large-scale structure cross-correlations. Using a controlled competition among candidate predictors derived from galaxy overdensity maps—density, curvature, and anisotropy proxies—we show that a curvature-based description provides the strongest and most robust predictive coupling to the observed lensing convergence field under rotation nulls and region splits. The response exhibits smooth gating behavior rather than a sharp threshold. These results constrain the effective source characterization of the response and define an empirical gravitational response kernel suitable for subsequent microphysical investigation.