GTE Unification: A Bidirectional Correspondence between Rule 110 Orbit Arithmetic and the Standard Model Electroweak Sector

We establish a bidirectional correspondence between Generative Triple Evolution (GTE) arithmetic over Z_7, the MDL-minimal cellular automaton , its continuum field limit φmdl, and the Standard Model (SM). The full electroweak correspondence is packaged as a single 7-conjunct theorem, \_r110\_sm\_joint\_unification, certified in Lean~4 with zero and zero new axioms. From the single integer = 3 (machine-certified Garden-of-Eden orbit depth), the arithmetic cascade yields (EW) = 3/13, corrected to 384729/1664000 ≈ 0.23121 by the Wolfenstein radiative term λ^3/(2c_H) (-0.42σ from PDG~2022~ ), (GUT) = 3/8 (exact SU(5) value), and λ_ CKM = 9/40 = 0.225 (0.000\% from PDG~ ). Exactly three generations are uniquely predicted ( ). Charge neutrality and anomaly cancellation follow as machine-certified bundle theorems. QCD predictions from = include the asymptotic-freedom coefficient b_0 = 7 ( ), strong CP angle θ_ QCD = 0 (three independent machine-certified proofs), Casimir invariants C_F = 4/3, C_A = 3, T_F = 1/2 ( ), and √(σ_4D) = 440.6MeV ( ). The causal-graph spectral dimension d_s = 4 is \ in the thermodynamic limit. The baryon-to-photon ratio ηB = 6.109×10^-10 (+0.15σ from Planck~2018 CMB+BBN,~ \ via FKTT); the asymptotic kink-overlap upper bound is ηB ≈ 6.36×10^-10 (+4.3σ). A parameter-free neutrino mass scale follows from the same integer inputs. Zero free parameters appear in any derivation.