Computational Universality and the Standard Model: Rule 110, Z5 Rings, and Mod-7 Structure in the Universal Generative Principle

The Universal Generative Principle (UGP) is arithmetically universal: its canonical cellular automaton, the UWCA, bisimulates Rule 110 (Wolfram/Cook, Turing-complete). This paper shows that the computational universality of UGP is not incidental but structurally load-bearing in the Standard Model's generation structure. Six results are presented: (1) CUP-4: the SM generation orbit algebraically determines all 8 bits of Rule 110 (Lean 4, zero sorry); (2) CUP-8/9: the five SM families form a closed Z5 cyclic ring under Rule 110, structural p-value ~0.003% (Lean 4); (3) CUP-11: a mod-7 CA realizing the generation orbit exists and can be made computationally universal, yielding a structural dark charge (Lean 4/computational); (4) CUP-12: the MDL-minimal universal Z7 CA has 76-bit description length; (5) the orbit constraints directly require the Rule 110 minterm set enabling glider dynamics; (6) coupling uniqueness: under CUP-4/11 winding assignment, the unique Z7 cross-dimensional coupling is Z7 addition (Lean 4). All core results machine-proved in Lean 4, zero sorry.