A Geometric Origin for the Neutrino Mass Hierarchy

Standard particle physics treats the neutrino mass spectrum as an input rather than a geometric consequence. In the Elastic Spacetime Theory (EST) framework, particles are modeled as topological defects of a hyperelastic vacuum medium. Within this picture, the neutrino acts as a screw dislocation—a structural "aglet" coupling the twisted closed standing-wave geometry of a charged lepton to the relaxed background vacuum.

The Moiré beat interference of two near-commensurate defect scales yields a closed-form relation between the atmospheric-to-solar mass-squared splitting ratio R and a small closure strain ε. If the inherited closure strain is identified with the fine-structure constant α, the model predicts the closure strain required to match the observed splitting ratio is numerically 1/137.02, indistinguishable from the fine-structure constant. Identifying the two yields a parameter-free prediction for the splitting ratio and forces an inverted ordering:

R = (2/r² - 1) / (1 - 1/r⁴), where r = 1 + α

This evaluates to R_EST = 33.879. The same relation can be inverted algebraically: inserting a representative observed ratio in the low-30s returns ε ≈ 1/137, numerically coincident with α. The construction strictly produces an inverted mass ordering (m₃ ≪ m₁ < m₂), providing a sharp experimental discriminator for future oscillation and direct-mass measurements.