Geometry–Light Relations in Modal Triplet Theory

We present the Tier-2 results of Modal Triplet Theory (MTT): relations and bounds that do not require an internal metric solution or evaluation of harmonic normalization integrals, but go beyond purely topological statements. These geometry-light results rely only on algebraic identities, symmetry assumptions, spectral positivity, and effective field theory control. They include a high-scale electroweak mixing identity equal to three-eighths under modal democracy and quantitative sensitivity bounds around that condition, holonomy determinant and phase sum rules implied by canonical trivialization, qualitative renormalization-group sign structure, curvature–mass drift relations with cosmological specialization, and a post-Newtonian bound indicating deviations from general relativity are suppressed by curvature remainders. All results are exact identities or rigorous inequalities within their stated assumptions. Together, they form the geometry-light bridge between topology-only foundations and the calibratable and geometric tiers of the MTT program.