7.8 Neutrino Mass Spectrum and Majorana Nature

Based on the established theorems of the Sole Axiom δ framework, this paper constructs a fully theorem-level theory of the neutrino mass spectrum and Majorana nature — without introducing any working hypotheses, free parameters, or experimental fits. Core results: the mass operator scaling law yields the heaviest neutrino mass eV; Birkhoff mass conservation yields the doublet masses eV, eV; mass-squared differences eV² (deviation 0.8%), eV² (deviation −8.9%); the degree-of-freedom count from the Cl(3) semisimple splitting in the ℳ sector encoding weight zero-tending limit rigorously derives that all three generations of neutrinos are Majorana fermions. **Consolidation Statement:** This paper consolidates the entire content of the originally independent articles 7.15 (Neutrino Cosmological Constraints), 9.4 (Neutrino Mass Prediction), 9.12 (Neutrino Mixing Parameters), and 9.13 (Majorana Mass Term). Theorem numbering mapping after consolidation: original 7.15 theorems → Chapter 7 of this paper; original 9.4 theorems → Chapters 3–4 of this paper; original 9.12 theorems → Chapter 5 of this paper; original 9.13 theorems → Chapter 6 of this paper. **Keywords:** neutrino mass spectrum; Birkhoff Mixing Matrix; mass operator scaling law; Majorana nature; theorem-level predictions