Universal Tension-Driven Lattice: A First-Principles Derivation of the Standard Model Lagrangian and Relativistic Gravity

We propose a singular mechanical substrate for the vacuum: a discrete Diamond Cubic (DC) lattice governed by a non-linear Duffing constitutive relation. The DC structure is distinguished by its tetrahedral coordination and its capacity to embed local icosahedral short-range order (ISRO), a motif observed in physical covalent solids and undercooled metallic liquids. We demonstrate that the Standard Model Lagrangian and the Einstein-Cartan metric arise as the deterministic macroscopic limits (a → 0) of this substrate. Non-Abelian gauge fields, three fermion generations, and spacetime curvature emerge from the lattice's torsional degrees of freedom and Euler buckling instability. Identifying the Higgs vacuum expectation value with the mechanical yield point of the pre-stressed lattice removes the need for independent empirical inputs. The framework yields an analytical evaluation of the inverse fine-structure constant (α_fs⁻¹ ≈ 137.0365) via Brillouin-zone projections, derives the nuclear mass scaling exponent (1.0107) from the kinematic mapping between the full icosahedral and octahedral symmetry groups, and reconstructs the ten-component metric from exactly seven macroscopic Cosserat strain modes. The constants and relations follow from the topological properties of the lattice without additional free parameters. The construction is commensurate with structures observed in nature, grounding the effective field theory in an ontologically motivated discrete substrate as least-complex emergent constants rooted in observable energy-constrained crystallography.