7.12 Family Symmetry: From Working Hypothesis to θ_M Freezing Theorem

Abstract

This paper closes the last core gap G2 of Conjugate Spectral Geometry. The anomalous magnetic moment article took as a working hypothesis (【Hypothesis 2.1】); this paper upgrades it to a **theorem**: (electron), (muon and τ share the same value). freezing is not an additional hypothesis — it is the natural fixed point behavior of the Birkhoff mixing matrix gradient flow on the isotropy subgroup structure of the sector parameter space. G2 is closed at the theorem level. Furthermore, G2b (the geometric root of the muon mass enhancement factor ) is closed through the complete spectral decomposition of the joint Birkhoff mixing matrix second-order structure and the sector counting theorem — (deviation ). The geometric layer of G2a (muon anomalous magnetic moment recalculation based on the theorem configuration) is closed; the Berry phase layer awaits generalization to non- paths.