Three Generations from the BCC Lattice of Truncated Octahedra

The number of fermion generations N_gen = F_sq/2 = 3 is derived as a theorem of the BCC truncated octahedral honeycomb. Within a single cell, Schur's lemma restricts T₁u to a scalar coupling (2 mass levels). On the BCC lattice, 6 square faces define 3 cubic axes, splitting T₁u into 3 generations. Complementary mixing angles θ₁ + θ₂ = 90° exactly. Part XLIX of the Unified Foam Field Theory.