Prime-Induced Holonomy Collapse and Defect Dissipation

We develop a unified framework linking cohomological defects, holonomy, and prime-induced phase structure in a three-layer Möbius phase system. A perturbation generates a nontrivial cohomological obstruction, which cannot be resolved continuously and instead induces integer winding defects. We show that prime factorisation naturally lifts to a discrete phase structure, where each prime contributes a quarter-turn generator. The resulting branch mismatch collapses to a residual phase determined solely by the prime-weight sum modulo four, yielding a complete reduction of factorisation complexity to a finite holonomy class. Extending this structure to matrix holonomy, we prove that the observable holonomy depends only on this residual class, while the remaining bulk winding is absorbed into a dissipative defect channel. This leads to a generalised holonomy matrix whose determinant encodes irreversible defect dissipation. At the topological level, defect activity preserves the phase-torus structure, while defect depletion induces an orbifold degeneration that eliminates non-Abelian generators and leaves a terminal U(1) symmetry. This establishes a structural mechanism in which complexity is dynamically reduced through defect-mediated holonomy collapse. The framework provides a unified description of topological obstruction, arithmetic phase structure, and dissipative dynamics, suggesting a new perspective on the interplay between number theory, geometry, and gauge systems.