Neutrino Mass Hierarchy

τ-Formula

r < p in exponent triplet → Normal ordering

Derivation

The $τ$-framework predicts the normal hierarchy $m_1 < m_2 < m_3$ from the ordering $r < p$ of the winding exponents:

This is a falsifiable prediction: if the inverted hierarchy is confirmed by JUNO or DUNE, the $τ$-framework’s mass structure would require revision.

All three neutrinos are predicted to be Majorana particles. The structural origin is the $σ = C_τ$ condition (Book IV, IV.T146): the zero-holonomy constraint on the $σ$-matrix requires the neutrino to be its own antiparticle. This is testable by neutrinoless double-beta decay ($0νββ$) experiments. With $Σ m_ν = 0.089$ eV in normal hierarchy, the effective Majorana mass $|m_ββ| ∼ 1$–$4$ meV is within reach of next-generation experiments (LEGEND-1000, nEXO, CUPID) by the early 2030s.

Source

This prediction is derived in the Physics Ledger (Chapter 61 — mixing-baryogenesis), Books IV–V of Panta Rhei.