What question did this study set out to answer?

The study aims to derive predictions for absolute neutrino masses based on the ratio of mass eigenvalues and the golden ratio.

March 13, 2026Open Access

Neutrino KATRIN Prediction

Key Points

The study aims to derive predictions for absolute neutrino masses based on the ratio of mass eigenvalues and the golden ratio.
Analyzed the ratio of the third to second neutrino mass eigenvalues from oscillation data
Applied the fundamental golden ratio identity to mass predictions
Utilized the Generative Quasiperiodic Framework to derive values without free parameters
Established a falsification criterion for testing the predictions against future measurements
Predicted absolute neutrino masses: m1 = 3.98 meV, m2 = 8.68 meV, m3 = 49.49 meV
Total mass Σmi = 62.2 meV, consistent with cosmological bounds
Calculated effective mass mβ = 9.33 meV
Verified the ratio m3/m2 = φ(φ+2) to within 0.08%

Abstract

We report that the ratio of the third to second neutrino mass eigenvalues, derived from oscillation data, satisfies m3/m2 = φ(φ+2) to within 0.08%, where φ = (1+√5)/2 is the golden ratio. The exponent φ+2 = φ2+1 is precisely the fundamental golden ratio identity. This relation, combined with m2/m1 = φφ, predicts absolute neutrino masses: m1 = 3.98 meV, m2 = 8.68 meV, m3 = 49.49 meV, giving Σmi = 62.2 meV (consistent with cosmological bounds) and mβ = 9.33 meV. These predictions are derived from zero free parameters within the Generative Quasiperiodic Framework (GQG) and are published prior to the final KATRIN measurement. Falsification criterion: m3/m2 ≠ φ(φ+2) beyond 10%.

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