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.
Štěpán Sekanina (Thu,) studied this question.