Formal and Computational Concordance on PSC-Selected Standard Model Structure: Axiomatic Closure Theorems and Finite Universe Enumeration

We present the computational certificate complementing the Two-Layer PSC Theorem~, with a full constraint independence analysis and three new UGP-derived coupling-ratio predictions. The PSC theorem chain establishes that any self-contained 4D renormalizable gauge theory must have G = G_ SM and N_ gen ≥ 3 (Layer I, forced by consistency); Presentation Invariance uniquely selects N_ gen = 3 (Layer II, optimality). Key steps are machine-certified in Lean~4 with zero , including the Residual Classification theorem .RCCInfiniteFamilies~. An exhaustive enumeration of 20,160 candidate universe descriptions minimizes a PSC dissonance functional D[Ψ]. Only 12 pass the hard Layer~I filters (0.06\%); all 12 are SM-like. The five hard filters (C_1, C_6, C_8, C_12, C_13) contain no reference to G_ SM; they encode dimensional consistency, holographic closure, unitary evolution, area law, and K"ahler structure. The SM tuple (d,G,N_ gen) = (4,G_ SM,3) achieves the unique Layer~II minimum D_ = 1.0667 (Hessian λ_ = 2.0 > 0). The residual D_ > 0 is entirely due to C_4 (Quarter-Lock), a UGP-derived prediction satisfied by the SM to 95\% at M_Z. Three new UGP-orbit-invariant constraints (C_15: bare g_1^2/g_2^2; C_16: bare g_3^2/g_2^2; C_4': multi-scale Quarter-Lock) are machine-checked rationals; the SM satisfies all three to within 2–7\% after RG running. A pre-committed ablation study confirms the SM as the unique D-minimizer. Extended scans covering Pati-Salam, E_6, G_2, and SU(6) all fail the PSC sieve.