The 4.8.8 Archimedean Tiling as a Discrete Substrate for Effective Field Theories and Standard Model Constants

Continuous spacetime manifolds in Quantum Field Theory (QFT) and General Rela- tivity carry ultraviolet divergences as length scales approach zero. This paper proposes an ultraviolet-complete discrete substrate, Z3 ⊗Q3: a bipartite tensor network whose unit cell Q3 is the face-adjacency graph of the oblate square bipyramid, tiling Euclidean space into a 4.8.8 Archimedean structure. Continuous, Lorentz-invariant spacetime is recovered as the low-energy effective field theory of this substrate, directly analogous to the emergence of (2+1)D Dirac fermions in graphene, with the additional ingredient that the 2D vertex- figure algebra is promoted to 3D rotational invariance under C4v → Oh when the unit cells are glued on the macroscopic Z3 gauge web. Treating rest mass as localized compu- tational friction of error-correction in the bipartite code, we obtain two zero-free-parameter predictions from a single empirical input (the QCD scale ΛQCD): the bare ρ(770) mass at √2 ϕΛQCD ≈760 MeV (within 2% of experiment) and the nucleon mass at 2√2 ΛQCD ≈939 MeV (within 0.02%). We close with a structural derivation of the quadratic gauge scaling m2 W ,m2 Z from bipartite tensor orthogonality. Two steps — the orthogonal-quadrature ansatz for open-path mesons and a Dirichlet-boundary postulate for valence quarks — are explicitly flagged as substrate-level open derivations rather than first-principle results.