Normal neutrino mass ordering from topological constraints on S²

We show that a type-I seesaw mechanism anchored to the CP¹ sigma model on S² with K₄ internal structure requires normal neutrino mass ordering as the unique consistent solution. The framework derives all three neutrino masses, two mass-squared splittings, and three PMNS mixing angles from a single scale (Mₚₗ) and a single dimensionless ratio (ε = 1/π²), with no free parameters. All five oscillation observables agree with current data within 1.1σ (χ²/dof = 2.63/5, p = 0.76). Six explicit falsification criteria are stated, testable by JUNO, KATRIN, LEGEND-1000, and precision cosmology. Companion paper to "From a Field to the Standard Model: 227 Constants from ε = 1/π²" (doi:10.5281/zenodo.18776344).