Global Parameter Estimation and Bayesian Analysis of Grand Consistency Theory

This paper develops a unified statistical framework for Grand Consistency Theory by integrating its previously derived predictions into a single Bayesian inference problem. The microscopic parameter vector is constrained through a global likelihood incorporating particle-physics, gravitational, cosmological, and astrophysical observables. Bayesian sampling determines posterior distributions, credible regions, and parameter correlations, while Bayesian evidence and information criteria quantify the statistical performance relative to the Standard Model, General Relativity, and ΛCDM. Cross-sector consistency, posterior predictive tests, uncertainty propagation, and convergence diagnostics provide a unified assessment of statistical reliability. The resulting framework defines quantitative criteria for global consistency and falsifiability and establishes the statistical interface between the microscopic structure of Grand Consistency Theory and observational data.