Gauge Theory on the Metric Bundle of a Spin 4-Manifold, II: Classical Dynamics and Reduction to 4D Physics

We construct the classical dynamics of gauge theory on the 14-dimensional metric bundle Y^14 = Met (X⁴), using the mathematical foundations established in Part I. The Clifford contraction uniqueness theorem yields a two-dimensional space of G-covariant contractions: one topological (producing Pontryagin/Chern–Weil densities) and one dynamical (producing a Yang–Mills-type Lagrangian). We construct the unified action using the dynamical Clifford contraction, which incorporates the horizontal Hodge star. The action is formulated using the augmented curvature, which incorporates the soldering form bracket arising from the non-abelian translations of the inhomogeneous gauge group (the MacDowell–Mansouri mechanism). The curvature sector yields three gravitational terms upon 4-dimensional reduction: curvature-squared gravity, the Einstein–Hilbert action, and a geometric cosmological constant, together with Yang–Mills gauge theory. The torsion sector yields four-fermion contact interactions via the Einstein–Cartan mechanism. All coupling constants are determined by ratios of fiber-geometric quantities. We further analyze the 128-dimensional Cl (14) spinor decomposition under Spin (4) × Spin (10), identifying two non-chiral 32-state families, with the observed three-generation structure conjectured to arise from mixing at the SU (2) R breaking scale.