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 sorry; exceptions are the Casimir anti-enhancement (+6.3 verified) and the SM orbit chirality (14/343 parity-violating triples, computationally verified).