Numerical Standard Model from Grand Consistency Theory

This paper develops the numerical Standard Model stage of Grand Consistency Theory (GCT) by mapping the converged microscopic spectral dataset into a correlated set of particle-physics observables. The calculation extracts gauge couplings, fermion masses, Higgs-sector quantities, quark flavor mixing, and lepton flavor and neutrino observables from a common particle-sector realization. Gauge couplings are evolved from the microscopic matching scale to specified experimental scales using consistent renormalization-group conventions, while fermion masses and flavor structures are obtained from the corresponding projected mass operators and their left-handed eigenspaces. The scalar sector determines the electroweak vacuum and Higgs mass through the canonically normalized effective potential. The resulting CKM and PMNS matrices provide additional tests through mixing angles, CP-violating invariants, neutrino mass splittings, and mass ordering. Correlations generated by the common microscopic input are retained in the full theoretical covariance matrix and incorporated into comparison with particle-physics data. Numerical robustness is assessed under refinement, spectral truncation, matching-scale variation, and algorithmic uncertainty. Calibration quantities and redundant observables are explicitly separated from the reduced independent prediction space, allowing the predictive dimensionality to be quantified through the rank of the corresponding parameter-to-observable map. The framework therefore defines a unified numerical procedure for testing whether a single microscopic spectral realization can account simultaneously for the measured structure of Standard Model parameters with fewer independent inputs than experimentally constrained observables.