Numerical Realization of Grand Consistency Theory: From the Microscopic Constraint Operator to Computable Predictions

This paper develops the numerical realization of Grand Consistency Theory (GCT), establishing a computational pathway from the microscopic constraint structure to quantitative physical predictions. The framework constructs a finite Constraint Laplacian as a sparse operator and develops procedures for spectral diagonalization, zero-mode separation, refinement analysis, continuum extrapolation, and extraction of converged spectral invariants. Numerical susceptibilities, response Jacobians, singular-value analysis, and numerical-rank diagnostics provide the interface between microscopic spectral data and effective physical parameters. The resulting computational architecture propagates spectral uncertainties into a joint prediction vector while incorporating convergence, stability, cross-sector consistency, and reproducibility criteria. The framework establishes the computational foundation required for direct quantitative testing of GCT predictions against experimental and observational data.