Parity Obstruction and Geometric Selection of π-Holonomy on the Diamond Lattice in Granular Entropic Physics

We show that the π-rotation holonomy U = iσ·ê on the GEP diamond lattice is not an ad hoc ansatz but the unique closest admissible SU(2) lift of the parity inversion P = −I₃ between oppositely oriented sublattices. Since SU(2) double-covers only SO(3) and cannot represent parity, we formulate an explicit optimisation problem and prove that φ = π is the unique minimising rotation angle for every conjugation-invariant, trace-monotonic distance functional. The result is axis-independent by isotropy of P. We present the operator norm as an explicit counterexample showing that not all norms select φ = π, delineating the precise scope of the geometric selection principle. The epistemic status of φ = π is upgraded from CONDITIONAL to GEOMETRICALLY SELECTED, a provisional classification introduced for results determined by structural obstruction rather than action minimisation.