The Geometric Standard Model: Deriving Fundamental Constants from Discrete Spacetime

We present a theoretical framework deriving fundamental constants of particle physics from geometric constraints on a discrete spacetime substrate. Beginning with a cubic lattice carrying ternary states and a continuous flux field, we prove that: Gauge constraints on a minimal 2×2×2 lattice yield exactly 16 physical degrees of freedom The Gauss constraint geometry forces critical coupling λ = 1, producing the factor √2 4D spacetime symmetry uniquely selects the j = 1728 complex multiplication point (the lemniscate curve) These factors combine into the geometric coupling constant G* = √2 Γ(1/4)²/(2π) ≈ 2.9587. The master quadratic equation x² − 16(G*)²x + 16(G*)³ = 0 yields: α⁻¹ = 137.036 (fine-structure constant, 1.3 ppm accuracy) Nᶜ = 3.024 (number of color charges) The framework's integers {7, 3, 13, 4} are uniquely determined by five Fibonacci constraints. We derive the electron mass from the Planck scale, predict baryon masses via a topological composition constant Kcomp = mₑ/π (proton mass to 400 eV, neutron mass to sub-eV precision), and obtain the gravitational hierarchy to 0.06% accuracy. All derivations are explicitly labeled as Theorems, Selections, or Conjectures to clarify epistemic status.