Neutrino Mass Ordering from Spectral Geometry

Title: Neutrino Mass Ordering from Spectral Geometry: Normal Hierarchy as an RG Attractor Authors: Petar Iliev Dryanosvski Description: We show that the spectral RG flow on the eigenvalue simplex uniquely selects normal neutrino mass ordering (m₁ < m₂ < m₃) as the stable attractor of the entropy gradient. The inverted hierarchy is dynamically excluded because it requires entropy decrease along the RG flow, violating Lyapunov monotonicity. Key results: Normal ordering forced by dS/dτ ≥ 0 (Lyapunov theorem of spectral gradient flow) Absolute mass scale from boundary zero-mode structure: m₁ ≈ 0, m₂ ≈ 8. 6 × 10⁻³ eV, m₃ ≈ 5. 0 × 10⁻² eV Total sum Σ m_ν ≈ 0. 059 eV — testable with DESI, CMB-S4 at ~4σ Reactor angle θ₁₃ ∝ √ (Δm²₂₁/Δm²₃₂) · r^ (-2/3) SU (3), leading-order prediction ~7. 0° (experiment: 8. 5° ± 0. 2°) Effective Majorana mass m_ββ ~ 10⁻³ eV for normal ordering Falsifiable: if DUNE or Hyper-Kamiokande measure inverted ordering, the framework is excluded All results derived from the spectral geometry of a single positive trace-one operator K. No free parameters. Based on: Spectral Dictionary (Zenodo: 10. 5281/zenodo. 20343026).