Holonomy Quantisation from Complex Differential Identity

We present a holonomy-based framework in which continuous perturbations are reduced to integer winding numbers through a fundamental complex differential identity dW/W=dx+idχdW/W = dx + i d/W=dx+idχ. Using contour integration and topological invariance, we show that the phase integral is quantised as ∮dχ=2πn d = 2 n∮dχ=2πn, independent of local perturbations. A layered cancellation mechanism ensures that global holonomy is determined solely by defect cores, while a torus decomposition yields a path-dependent locking condition. The resulting structure separates radial and angular dynamics and provides a unified description of defect formation, winding conservation, and holonomy locking.