Nontrivial SU(2) Holonomy and Residual Geometric Frustration on the Diamond Lattice in Granular Entropic Physics

We compute the SU(2) Wilson loop around the minimal hexagonal cycle on the diamond lattice using holonomies prescribed by Granular Entropic Physics (GEP). For pi-rotation holonomies U = i(sigma dot e) along tetrahedral edge directions, the Wilson loop evaluates to Tr(W) = -10/27, corresponding to an effective flux angle of approximately 101 degrees. This is a gauge-invariant, non-Abelian result: the trace uniquely determines the conjugacy class in SU(2), confirming a genuine nontrivial flux sector. Unlike Z2 frustration, which is annihilated by the bipartite structure of the diamond lattice, SU(2) frustration persists due to non-commutativity. The number -10/27 is a geometric invariant determined entirely by the tetrahedral structure, not a tunable parameter. This result establishes a necessary condition for the GEP cosmological constant mechanism: microscopic frustration is not a gauge artifact but a gauge-invariant geometric property of the network.