Chapter S The Lepton Sector: Neutron Curvature, Koide Formula, and PMNS Mixing

The lepton sector is derived from four physical principles, each tracing to Bharathi's insights (2026): (1) Every electron starts life in a neutron a topological theorem of the G2 Fano lattice. The G2 generator Le7 maps every T3 = + 1 2 Fano node to a T3 = −1 2 partner, giving P T3 = 0 over all quark nodes making electric charge neutrality a theorem, not an assumption. After QCD connement, the T3 = −1 2 states are locked inside neutrons; β-decay liberates them as free leptons. The electron is the T3 = −1 2 brane mode knocked o the neutron's T ∗ 2 boundary (rT ∗ 2 = 32.75 fm) by weak decay. (2) Lepton origin from pair production and Raman/Compton coupling: leptons are not primary Fano nodes they are secondary modes, born from photon condensation in the H+ sector, calibrated by the meson mass scale (mµ ∼mπ ∼ΛQCD). (3) The Koide formula K = 2/3 from the Gen 1 H+ fraction: the empirical Koide constant equals the H+ fraction of the Gen 1 generation line (2/3 nodes are H+), a structural theorem of the G2 composition. The Koide formula is observed to hold to 0.001%. (4) Near-maximal PMNS mixing from absence of the H−penalty: all leptons are purely H+ (no colour charge), so the PMNS hop rule has no Gen 3 H−penalty, giving mixing angles of order arcsin( p 3/8) ≈38 naturally near-maximal vs the CKM Cabibbo angle of 13. Part of the One-Octonion Brane-Bulk Framework series. Anchor DOI: 10.5281/zenodo.19120873. Community: one-octonion-brane-bulk. Author: Bharathi Dasan Jagadeesan, M.D., University of Minnesota. ORCID: 0000-0002-1143-941X.