Relational Geometric Mechanics XI: Electroweak Unification — The Weinberg Angle and Neutrino Mass Structure from Descriptor Geometry

This is the eleventh paper in the Relational Geometric Mechanics (RGM) series. We derive the Weinberg angle sin²θ_W = 3/13 from first principles using only the descriptor geometry of Paper I and the force derivations of Papers II and V. No measurement input is required. The result — 0.2308 against the measured Z-pole value of 0.2312 — follows from making the descriptor space metric h_AB explicit: the spinor structure S contributes exactly one topological generator to the 13-dimensional descriptor space, and the Weinberg angle is the ratio of the SU(2) footprint to the full descriptor geometry. The same framework yields the neutrino mass matrix structure: with q_e = 0, the generation ring Hamiltonian produces an exact two-fold degeneracy, which is the geometric origin of large PMNS mixing angles.