Numerical Gravity and Cosmology from Grand Consistency Theory

This paper develops the numerical cosmological realization of Grand Consistency Theory (GCT) by mapping its established gravitational sector into a correlated set of observable predictions. The framework calculates the background expansion, baryon acoustic oscillation distances, growth of cosmic structure, matter power spectrum, weak-lensing observables, and gravitational-wave luminosity distance within a common numerical realization. Scale-dependent scalar responses and tensor-sector modifications are retained where required, while theoretical, calibration, numerical, and modelling uncertainties are propagated through the corresponding covariance structure. Distinctive GCT signatures are defined relative to CDM across redshift, wavenumber, angular multipole, and tomographic domains. The resulting predictions are confronted with cosmological data through joint likelihoods that preserve observational and theoretical correlations. Model comparison incorporates goodness of fit, independently adjustable parameter freedom, information criteria, and Bayesian evidence where applicable. Numerical robustness is assessed under resolution refinement and integration variations, while the independent predictive dimensionality is quantified through the rank of the reduced parameter-to-observable map. The framework therefore provides a unified numerical procedure for determining whether a fixed GCT cosmological realization can simultaneously account for geometrical expansion, structure formation, gravitational lensing, and gravitational-wave propagation with predictive content distinguishable from CDM.