We propose a geometric framework in which continuous perturbations are discretised into integer holonomy winding through defect formation. Exponential neck expansion decomposes a single loop into two independent U(1) cycles on a torus, achieving full independence only at integer matching. The residual phase is governed by a sine-Gordon-type equation, driving the system toward Laplacian decoupling. Composite structures emerge as multi-defect networks, while irreducible obstruction modes correspond to primes. The construction admits a natural lift to SU(2)/SU(3) gauge fields via progressive Cartan reduction.
Jeong Min Yeon (Sat,) studied this question.