UGP Interaction Skeleton Theorem

We prove in Lean~4, with zero \ for all theorem-grade claims, that the Universal Generative Principle (UGP) winding, chirality, hypercharge, and color-fiber data determine the Standard Model's finite renormalizable interaction skeleton: gauge-fermion vertices, Yukawa mass-generating vertices, anomaly cancellation, representation-level color-singlet constraints, proton-stability forbiddance at dimension four, and a topological dark-sector isolation gap. The winding number W = N_cQ, the GTE chirality fiber T/T^ , integerized hypercharge Y_3 = 2W - T_6 = 3Y (e.g., Y_3(e_L) = -3, Y_3(Q_L) = +1, Y_3(e_R) = -6, Y_3(u_R) = +4), and the minimal gauge-boson winding spectrum \0,± 3\ suffice to reproduce all renormalizable SM vertex schemas and exclude all forbidden ones—without any additional gauge-theoretic input. The main theorem—$UGPVertex(f_1,f_2,B) ↔ SMVertex(f_1,f_2,B) for all colored fermions f_1,f_2$ and gauge bosons B—is proved by exhaustive finite case analysis. A vertex audit over 64 electroweak schemas returns MISMATCH~COUNT=0 (SHA-256: 927758a9b7801db...). Three independent proofs force N_c = 3; the SM fermion quartet is the unique anomaly-free solution at N_c = 3; proton decay at dimension four is topologically forbidden; and fermions with $W ∈ \1,-2,4\$ are isolated from all SM particles via SM bosons. Electroweak predictions from Lean-certified bare couplings give m_W = 80.364GeV (-0.42σ vs PDG 2024 world average 80.3692 ± 0.0133) and α_s(M_Z) = 0.1179 (0.0σ). These results were independently foreshadowed computationally: the PR-1/Logos cellular automaton recovered the winding-transfer structure at 87.38\% consistency with zero false negatives over 1.02 × 10^6 events, and the PR-0/MFRR field substrate exhibited force emergence from dissonance minimization, both before the Lean proofs were written.