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 Z₇, 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/ (2cH) (-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 b₀ = 7 (), strong CP angle thetaQCD = 0 (three independent machine-certified proofs), Casimir invariants CF = 4/3, CA = 3, TF = 1/2 (), and ₄D = 440. 6\, MeV (). The causal-graph spectral dimension dₛ = 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.