Holonomy Cancellation in Composite Number Geometry

This work develops a geometric–analytic framework in which the distinction between primes and composites is encoded through residue holonomy of SU(2)-valued meromorphic connections generated by Möbius iteration. The central result establishes a holonomy formula linking contour integrals to a signed residue sum, providing a precise cancellation criterion. Within this framework, composite-like structures arise from global residue cancellation and trivial holonomy, while prime-like structures correspond to persistent local defects. The model further introduces layer geometry, cyclic contraction, and Möbius node structures to describe multi-prime interactions, clearly separating proved analytic results from model-level principles and open conjectures.