What question did this study set out to answer?

The study aims to define the structure of neutrino masses using forced relations while clarifying their ordering and masslessness.

July 1, 2026Open Access

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

Key Points

The study aims to define the structure of neutrino masses using forced relations while clarifying their ordering and masslessness.
Utilized a single axiom and operation to derive mass relationships among neutrinos.
Calculated mass-squared splittings leading to predictions about neutrino order and masslessness.
Provided machine-checked results with reproducible code and protocols.
Establishes a forced splitting ratio Δm²₂₁/Δm²₃₁ = 3/100 and confirms the normal ordering of neutrino masses.
Demonstrates that the lightest neutrino cannot be massless, indicating it occupies the lowest mass state.
Predicts an observable cosmological sum Σmν consistent with ongoing studies in cosmology and experiments like KATRIN.

Abstract

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

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