Criterion C2: A Model–Independent Relativistic Consistency Test of Cosmic Acceleration.

This study designs a model–independent relativistic consistency test that probes directly the geometric sector of late–time cosmic acceleration, independently of any specific dark energy or modified gravity model. Using tomographic combinations of galaxy clustering, redshift–space distortions, weak lensing, and CMBlensing, this work constructs an observational reconstruction of the effective Newton coupling µ(z) and the Weyl potential normalization Σ(z), isolating the relativistic response of spacetime from background expansion and primordial normalization effects. This study demonstrates that CMB lensing–only observations are intrinsically sensitive to a single amplitude direction and cannot discriminate between primordial normalization and relativisticsector modifications. Tomographic cross–correlations break this degeneracy in principle by separating growth and lensing responses, enabling an independent reconstruction of µ(z) and Σ(z). This work further quantifies the statistical power of forthcoming Stage–IV surveys with a minimal Euclid/LSST forecast, showing that percent–level deviations in the Weyl sector are detectable with decision–level significance after marginalization over primordial amplitude and galaxy bias. Any sustained detection of µ(z) ≃ 1 with Σ(z) ̸ = 1 therefore constitutes a direct violation of the relativistic consistency relations and rules out ΛCDM, standard dark energy, and the entire class of metric theories without gravitational slip. Criterion C2 thus provides a realistic, falsifying, and model–independent relativistic test of the physical origin of cosmic acceleration.