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 central observation is that the same arithmetic/topological invariants that identify particles in the UGP Braid Atlas also constrain their allowed interactions, without any additional gauge-theoretic input. Concretely, the winding number W = NcQ, the GTE chirality fiber T/T^, integerized hypercharge Y₃ = 2W - T₆ = 3Y (e. g. , Y₃ (eL) = -3, Y₃ (QL) = +1, Y₃ (eR) = -6, Y₃ (uR) = +4), and the minimal gauge-boson winding spectrum \0, 3 suffice to reproduce all renormalizable SM vertex schemas and exclude all forbidden ones. The main theorem — UGPVertex (f₁, f₂, B) SMVertex (f₁, f₂, B) for all colored fermions f₁, f₂ and gauge bosons B — is proved by exhaustive finite case analysis. A finite vertex audit over 64 electroweak schemas returns MISMATCH COUNT\, =\, 0 (SHA-256: c927758a9b7801db). The integer hypercharge is = 2W -, where = 6T₃ is the integerized weak isospin third component. Three independent proofs force Nc = 3; the SM fermion quartet is the unique anomaly-free solution at Nc = 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 mW = 80. 364\, GeV (-0. 42 vs PDG 2024 world average 80. 3692 0. 0133; -1. 28 vs older PDG 80. 379 0. 012) and ₛ (MZ) = 0. 1179 (0. 0). . . .