Emergent Fermion Mass from Nodal-Line Gapping in the GEP Diamond Lattice

This paper derives the origin of fermion mass in Granular Entropic Physics from first principles. The fundamental structure is a bipartite tetrahedral diamond lattice with SU(2)-valued links. We show that the bipartite A/B sublattice structure naturally generates a Dirac operator, and that the structural factor of the diamond lattice vanishes on nodal lines rather than isolated points. A nonzero SU(2) saddle-point twist gaps these nodal lines through a self-consistent mechanism, generating a scalar mass term with m = t|theta|. The result is confirmed numerically with no free parameters: the gap scales as Delta = 2t|theta| exactly. Fermion mass in GEP is not a fundamental input but emerges from the geometry of the wormhole network.