We perform the continuum expansion of SU (2) Wilson loops on the diamond lattice as prescribed by Granular Entropic Physics (GEP). For a slowly varying gauge field, the holonomy around the minimal hexagonal cycle expands as W = I + ia² Sigma^mu nu F₌ₔ ₍ₔ + O (a³), where Sigma is the oriented area tensor and F is the Yang-Mills field strength. We prove an isotropy theorem: the four tetrahedrally related hexagon classes satisfy SumI nIʳho nIˢigma = (4/3) delta^rho sigma, producing an exactly isotropic leading-order effective action despite the discrete tetrahedral geometry. The resulting theory is 3D SU (2) Yang-Mills with coupling g² = 3/ (2|Sigma|² a). The area tensor Sigma is dimensionless (constructed from unit vectors), and g² diverges as a goes to 0, consistent with the super-renormalisable nature of 3D Yang-Mills. We note that the GEP vacuum has Tr (W₀) = -10/27, so a physically motivated expansion should be performed around the frustrated background rather than trivial holonomy. This is the first explicit leading-order lattice-to-continuum bridge in GEP, connecting the discrete diamond lattice structure to standard gauge theory.
Štěpán Sekanina (Tue,) studied this question.