Emergent Fermions and Gauge Structure from a Bipartite Tetrahedral Spacetime Network (v2.0)

We investigate a discrete spacetime model in which fermions and gauge interactions emerge from a bipartite tetrahedral network at the Planck scale. The network is represented by a diamond-type lattice whose dynamics is described by a nearest-neighbour lattice Hamiltonian. The bipartite structure implies an exact chiral symmetry, placing the Hamiltonian in symmetry class AIII. We show that the condition D (k) = 0 defines nodal lines in the Brillouin zone carrying non-trivial winding number W = ±1, corresponding to a Berry phase of π. Linearization near these nodal lines yields Weyl fermions which combine into Dirac spinors at low energies. We derive analytically that the Fermi velocity satisfies vF = t·a exactly, independent of position along the nodal line and identical for all three generation pairs — a consequence of the Pythagorean identity cos² (α) + sin² (α) = 1. Consequently, all generation-dependent structure arises from the Higgs sector, with masses mₙ = |φₙ| determined by the condensate profile. Local phase fluctuations of hopping amplitudes generate an emergent U (1) gauge field. The internal symmetry structure leads to sectors related to SU (3) ×SU (2) ×U (1). The theory predicts a modification of the dispersion relation testable with gamma-ray burst observations.