We establish six theorems (T1–T6) and two closed results (P1, P2) deriving the three Standard Model gauge couplings from the minimal discrete épure G■ = (ℤ², d■), where d■ (P, Q) = |Δx| + 2|Δy| is the unique Minkowski metric on ℤ² minimising the discrete π-invariant π■ = 1. The algebraic invariants c₂ (G■) = √5/π and ξ₂ (G■) = 37/1296 (T1–T3) encode all coupling information. The causal vertex Θ■ = arctan (2) is the angular horizon of G■, whose derivative jump Δ = √5/2 = 2c₃ (G■) encodes the 3D unfolding coefficient (T4). Four simultaneous unfoldings of G■ into four-dimensional spacetime produce total anisotropy αG■ = 4Θ■ − π (T6). Cartan diagonality implies √rank displacement scaling (T5). The Flux Theorem (P1) is proved exactly via the Fundamental Theorem of Calculus. The stable mode v₂ is characterised by a self-consistent fixed-point equation (P2) with unique solution c* = 1/αw (G■) = 29. 600. Predictions with zero free parameters: 1/αEM = 137. 036043 (error 3×10⁻⁵%), 1/αw = 29. 600 (error <10⁻⁴%), 1/αₛ = 8. 477 (error 0. 077%). SU (5) is geometrically excluded.
Florian Gisbert (Tue,) studied this question.