Geometric phases in quantum systems give rise to holonomies associated with cyclic evolution. In mixed-state settings, these holonomies arise from Uhlmann parallel transport on the purification bundle of density operators and depend on the global geometry of density-operator trajectories. In this work we introduce discretized mixed-state holonomy as a geometric encoding primitive. The public object is a density-operator trajectory, while the encoded information resides in a finite family of purification gauges associated with the same holonomy conjugacy class. By discretizing the gauge freedom of the purification bundle, continuous mixed-state holonomy is converted into finite alphabets suit... More >