Covariant informational gravity as a falsifiable effective-source model: gravitational-wave and CMB null tests

Covariant informational gravity as a falsifiable effective-source model: gravitational-wave and CMB null tests This manuscript introduces Covariant Informational Gravity (CIG) as a weak-coupling, diffeomorphism-invariant effective-source framework for testing whether coarse-grained informational structure can contribute measurably to spacetime dynamics. The model defines a normalized informational scalar field, Φ(x) = −lnρ(x)/ρ*, and derives an effective rank-two informational source from a symmetric bilocal action. The framework is constructed to recover general relativity in the limit of uniform informational structure and vanishing nonlocal coupling. The paper is presented as a falsifiable benchmark theory, not as a replacement for general relativity. Its principal observational target is a small, phase-coherent residual in high-signal-to-noise gravitational-wave events, with cosmic-microwave-background polarization rotation treated as a secondary cross-check. The manuscript develops the effective action, leading-order Gaussian kernel closure, benchmark parameter set, gravitational-wave null-test strategy, CMB consistency channel, and interpretation of decisive null results. The purpose of this upload is to provide a citable preprint version of the manuscript for open scientific discussion, priority record, and future revision. The figures and benchmark curves are intended as illustrative forecast structures rather than final posterior constraints from a full parameter-estimation pipeline.