Cn–Phase Geometry and Discrete Monodromy: From Z3 Holonomy to Topological Torsion

Abstract We generalize the Frenkel–Kontsevich quantization scheme by embedding discrete Cn-phase carriers into the structure of quantum holonomy. The resulting model predicts measurable Z3 and Z6 Berry-like phases, introduces torsion-based topological classification, and suggests experimental protocols in photonic and atomic lattices. The Cn algebra provides a natural multi-valued extension of the phase bundle, making phase-space monodromy a physically observable phenomenon.