The Complete Pati-Salam Effective Lagrangian from the Metric Bundle

Paper VII of the Metric Bundle Programme. Assembles the complete four-dimensional effective Lagrangian from the geometry of Met(X^4). All fields, representations, and couplings are determined by the metric bundle. Includes geometric origin of Pati-Salam breaking via CP^3 holomorphic sectional curvature, zero-parameter two-step RG running, and Coleman-Weinberg analysis. Key predictions: sin^2(theta_W) = 0.2312 at M_Z (matches observed), alpha_PS = 27/(128pi^2), sin(theta_C) = 1/sqrt(20) (0.75% error). Decoupling update (May 28, 2026): May 28, 2026: Clarified that the absolute scales (gauge coupling, Newton constant, cosmological constant) are inputs to the Lagrangian and that its structural content (representations, sign-fixed kinetic terms, coupling ratios, generation number) does not depend on the free-energy-principle localisation of Paper VIII, which supplies an optional parameter-free candidate value alpha_PS = 27/(128 pi^2). The physics arc (Papers I-VI) is thereby self-contained, with Papers VII-VIII building on top. Cited the independent McCurrach programme (Chamseddine-Connes spectral-action dynamics; compatible Higgs mass m_H ~ 125.8 GeV) as an alternative dynamical route.