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 , and the Standard Model (SM). The full electroweak correspondence is packaged as a single 7-conjunct theorem, ugp\_r110\_sm\_joint\_unification, certified in Lean 4 with zero sorry 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 ^3/(2c_H) (-0.42 from PDG 2022 ), (GUT) = 3/8 (exact SU(5) value), and _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 theta_QCD = 0 (three independent machine-certified proofs), Casimir invariants C_F = 4/3, C_A = 3, T_F = 1/2 (), and _4D = 440.6\,MeV (). The causal-graph spectral dimension d_s = 4 is \ in the thermodynamic limit. The baryon-to-photon ratio = 6.10910^-10 (+0.15 from Planck 2018 CMB+BBN, \ via FKTT); the asymptotic kink-overlap upper bound is 6.3610^-10 (+4.3). A parameter-free neutrino mass scale follows from the same integer inputs. Zero free parameters appear in any derivation.