Local Mismatch as a Source of Closed-Loop Holonomy in a Self-Consistent Discrete Geometry

We introduce and study a discrete transport model on a two-dimensional periodic Voronoi lattice in which local field mismatch sources nontrivial closed-loop holonomy through a self-consistent feedback mechanism. Each site hosts an internal field that relaxes locally, leaving a heterogeneous residual mismatch measured along radial spokes connecting the site to its neighbors. An internal SU(2) transport is then defined along the angularly ordered neighbor ring, producing a loop holonomy that depends on path-ordered rotations whose axis precesses according to an integer-valued spectral winding parameter $N_\star$. Crucially, the transport is closed self-consistently: local mismatch modifies the transport itself via an under-relaxed fixed-point iteration, allowing mismatch and holonomy to co-evolve. This construction enables stringent cross-channel tests, in which mismatch measured on radial spokes predicts holonomy accumulated on closed neighbor loops, ensuring the effect is not a trivial reuse of the same data. We find a robust, non-monotone dependence of mismatch--holonomy correlation on the torsion coupling strength, with a clear optimal regime beyond which over-rotation degrades coherence. Moreover, sweeping the spectral winding integer reveals sharp, reproducible selectivity: specific values of $N_\star$ produce significantly stronger and more stable correlations across random seeds and fully relaxed hexagonal geometries. In particular, $N_\star=777$ consistently maximizes both correlation strength and a geometric coherence diagnostic measuring constructive accumulation of path-ordered rotations. These results demonstrate an emergent, geometry-sensitive mechanism by which local incoherence can source coherent loop transport in a discrete setting, exhibiting integer-selective resonance without fine tuning. The model is fully controlled, falsifiable, and independent of continuum assumptions, providing a minimal testbed for studying self-consistent transport, holonomy, and resonance phenomena in discrete geometric systems.