The UCM Lattice as a Discrete Principal Fibre Bundle (UCM Paper 52)

Paper 50 of this series established seven structural results that the UCM substrate provides as a "stage" for quantum field theory. This paper identifies the mathematical structure through which QFT docks onto that stage: the principal fibre bundle. We show that the UCM lattice carries a discrete principal SU(2)-bundle over the lattice base space: the fibre at each site is the gauge-phase freedom, and the Schwinger-constructed SU(2) link variables are the connection. All five defining axioms are verified. The curvature is the Wilson plaquette, parallel transport is the path-ordered link product, and gauge transformations are vertical automorphisms. In the continuum limit, the discrete bundle converges to the smooth principal G-bundle of Yang-Mills theory.