The Neutrino Masses: A Forced Splitting Ratio, the Normal Ordering, No Massless State, and the Cosmological Sum

One axiom. One operation. Zero free parameters. Neutrinos have mass, but their masses are among the least-pinned numbers in physics: only mass-squared differences are measured, the ordering is unsettled, and whether the lightest is massless is unknown. This paper forces the structure. The single-handed neutrinos place their mass-squared splittings on the binary tower at the down covering depth five: Δm²₂₁/Δm²₃₁ = (1/32)(24/25) = 3/100, so Δm²₃₁/Δm²₂₁ = 100/3 ≈ 33 (measured ≈ 34). The normal ordering is forced. The fold forbids a massless state, so the lightest neutrino is not massless — it sits at the floor. With one measured splitting anchoring the scale, the individual masses and the cosmological sum Σmν follow as a forced lower prediction — the very quantity cosmology and KATRIN are closing in on. Machine-checked; reproduces from one command. A standalone result within the Smithian Fold Theory of Everything (SFTOE). Full corpus, code, and the run-it-yourself VERIFY.md protocol: https://github.com/MettaMazza/Smithian-Fold-Theory