Grand Consistency Theory: Spectral Flavor, Neutrino, and Mixing Predictions

This paper develops the flavor-sector prediction framework of Grand Consistency Theory, with emphasis on charged-fermion mass hierarchies, neutrino structure, and quark and lepton mixing. The framework separates two complementary forms of microscopic information: spectral eigenvalues, which determine fermion and neutrino hierarchies, and relative left-handed eigenspaces, which determine CKM and PMNS mixing and CP structure. The analysis introduces normalization-independent charged-fermion mass-ratio tests, a derived hierarchy-shape diagnostic, neutrino mass-ordering and spectral-shape observables, and a unified treatment of quark and lepton mixing. These quantities are combined into a frozen flavor prediction framework designed to test whether a single microscopic GCT realization can simultaneously account for charged-fermion hierarchies, neutrino properties, and flavor mixing without sector-specific phenomenological adjustment. A central requirement is refinement stability. The predicted observables must converge as the microscopic construction is refined before they qualify as robust predictions. The paper therefore provides a numerical extraction protocol based on diagonalization of the microscopic flavor operators, determination of their eigenvalues and left-handed eigenspaces, refinement-convergence testing, and subsequent comparison with independent experimental measurements. The resulting framework establishes a joint flavor-neutrino-mixing closure test for Grand Consistency Theory. Its decisive future test is whether one common microscopic flavor realization can reproduce charged-fermion hierarchies, the physical light-neutrino spectrum, and CKM and PMNS mixing while remaining stable under refinement.