Abstract
Orbital timing, black hole imaging, and ringdown probe strong gravity through timelike, null, and perturbative dynamics, but they are commonly analyzed separately. We formulate and implement a shared coupling closure test that requires one dimensionful gravity coupling to reproduce all three sectors while mass, distance, emission radius, environment, and channel specific astrophysics are treated as nuisance structure. Ringdown is supplied by the theory specific perturbation spectrum rather than inferred from photon geometry. For the primary Einstein–dilaton–Gauss–Bonnet branch, the static forward model combines a relativistic precession QPO pair, the critical impact scale, and the axial fundamental quasinormal mode on one coupling grid. Because the leading EdGB responses are even in the coupling, inference is performed in the nonnegative squared coupling coordinate, with explicit treatment of the GR boundary and prior Jacobian. A controlled mock likelihood with correlated errors, nuisance parameters, theory covariance, null calibration, coverage checks, and a shared versus saturated comparison verifies that closure is statistically identifiable at the adopted stress test precision. The rotating results are retained as external robustness diagnostics rather than promoted to a common grid likelihood. No observational EdGB bound is inferred.