Universal Tension-Driven Lattice: Emergent Continuum Physics from a Minimal Pre-Stressed Diamond Cubic Substrate

We posit that the Standard Model of particle physics and the Einstein-Cartan spacetime metric are not fundamental primitives, but emerge as low-energy linear effective field theory (EFT) approximations of a singular, discrete mechanical substrate: the Diamond Cubic (DC) lattice governed by a non-linear Duffing constitutive relation. The framework is constructed from first principles around the combined rule of least structural complexity and least action.

By requiring the vacuum to span three-dimensional space with the minimal number of shear-stable bonds per node (z = 4), tetrahedral coordination and the non-centrosymmetric Diamond Cubic graph (T_d ≡ F4̄3m) follow by geometric necessity. We establish a predictive group-theoretic origin for the SU(3)_C × SU(2)_L × U(1)_Y gauge group from the 12-dimensional local Cosserat connection manifold and obtain the bare weak mixing angle sin²θ_W = 0.25 from a 1:3:8 ergodic equipartition at the kinematic yield limit. Color confinement is recovered as a physical consequence of non-linear vacuum jamming. The collective scaling exponent γ of the resulting confining flux tube is strictly bounded between the chiral macroscopic phase-space projection (S/2 = 23/14 ≈ 1.6429) and the void-channel capacity (1 + f_void ≈ 1.6599), with both exact analytical inversion and Monte Carlo sampling yielding γ ≈ 1.6539 (within 0.15% of the geometric mean γ_geom ≈ 1.6514) to reproduce the empirical Lattice QCD string tension σ ≈ 0.18 GeV².

Replacing empirical parameter fitting with strict crystallographic invariants yields parameter-free derivations of the CKM flavor-mixing hierarchy (via an exact radical cancellation A₀ = 21π/1472), the bare vacuum impedance floor (α_bare⁻¹ ≈ 136.113) and its linear EFT relaxation band ([134.66, 137.57], enclosing α⁻¹ = 137.036), the nuclear mass-excess binding ceiling (ε_y² ≈ 1.071%, bounding ⁶²Ni at 0.937%), and the late-time cosmological S₈ structural braking band ([0.821, 0.830]).