Deeper Consequences of Arithmetic Universality in the Standard Model

The Standard Model (SM) generation orbit is forced to evolve under Rule~110 — a Turing-complete binary cellular automaton — by the combinatorial arithmetic of the Universal Generative Principle~. We derive the structural and dynamical consequences of this identification beyond the quantitative predictions of the companion papers~. Five results are established. (1)~The electroweak bosons W^+, Z, H^0 form a unit-step arithmetic staircase in Generative Triple Evolution branch capacity, c ∈ \11,12,13\; each step encodes one absorbed Goldstone degree of freedom via the formula c_P = - d_P, giving a cellular-automaton grounding of the Higgs mechanism. (2)~The unique Minimum Description Length (MDL)-minimal orbit-admissible function f_ MDL excludes Z_7 = 4 (the W^-/e^- sector) from its output range; this hard exclusion is arithmetically equivalent to CP violation, making matter dominance a necessary consequence of compression. (3)~The SM generation orbit is the unique maximal Garden-of-Eden-rooted chain in Z_7^5, isolated in six independent senses by the complete causal isolation master theorem; the generation count = 3 is topologically forced. (4)~The photon is the unique uniform fixed point of f_ MDL, identifying it as the cellular-automaton vacuum state, while the Rule~110 ether carries Z_7 winding number~1, placing it in the neutrino sector. (5)~The 14-neighborhood f_ MDL catalog is an emission interaction kernel complementary to the absorption kernel of the UGP dynamics framework~, establishing a temporal duality between the two derivations of the SM vertex structure. All principal results are machine-certified in Lean~4 with zero ; exceptions are the Casimir anti-enhancement (+6.3\%, computationally verified) and the SM orbit chirality (14/343 parity-violating triples, computationally verified).