Simplicial Lattice Field Theory (Vol V): Deterministic Mass Ratios, Symplectic Phase Space, and the Lepton-Quark Hierarchy

The Wilson-Dirac operator on the D4 lattice evades the Nielsen-Ninomiya doubler theorem. The adjacency spectrum {8,4,0,−2,−4} assigns physical representations: scalar, vector, tensor, spinor, and longitudinal. The λ=−2 eigenspace (dimension 8) hosts the three fermion sectors via SO(8) triality.