Paper3Unified Flavor Structure in the β Framework

This paper formulates a unified flavor manuscript for the visible fermion sector within the alpha-beta-phi framework. Its purpose is to isolate one fundamental question: whether the hierarchy of visible masses and the two observed mixing regimes (the quark CKM pattern and the leptonic PMNS pattern) can be organized by one common structural law together with explicit symmetry-broken branches. The manuscript is developed in three layers: First, the common mass law is stated for both charged fermions and the neutrino sector, treating small and large Yukawa windows within the same structural vocabulary. Second, the quark and leptonic mass matrices are written in parallel, deriving the CKM and PMNS matrices as relative left-handed diagonalizations. Third, the numerical sectors are compared branch by branch. In the leptonic regime, a mu-tau symmetric core plus controlled symmetry breaking produces observed solar, reactor, and atmospheric mixing. In the quark regime, a strongly hierarchical branch produces small CKM angles and a nonzero quark CP phase. The main result of this work is methodological and structural: it demonstrates that the quark and leptonic sectors do not require separate flavor logics. The sharp observational contrast between large PMNS mixing and small CKM mixing is attributed to two different broken branches of one common visible flavor architecture.