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

We present the computational certificate that complements the Two-Layer PSC Theorem, together with a full constraint independence analysis and three new UGP-derived coupling-ratio predictions. Formal backbone (Papers 03 and 05). The PSC theorem chain—RC ^* exclusion, vector-like exclusion, CP violation required\—establishes as formal theorems that any self-contained 4D renormalizable gauge theory must have (i) G=GSM and (ii) Ngen 3 (Layer I, forced by consistency). Presentation Invariance further selects Ngen=3 as the unique minimal Layer I survivor (Layer II, optimality). Key steps are machine-checked in nems-lean and ugp-lean with zero sorry. Full uniqueness is now unconditional: the Residual Classification (RCC) is a Lean-certified theorem (PSC. RCCInfiniteFamilies, zero sorry). Computational certificate (TE2. 2 scan, this paper). An exhaustive enumeration of 20, 160 candidate universe descriptions minimises a PSC dissonance functional D. Only 12 pass the hard PSC Layer I filters (0. 06 The five hard filters (C₁, C₆, C₈, C₁2, C₁3) contain no reference to GSM — they encode dimensional consistency, holographic closure, unitary evolution, area law, and K\"ahler structure. The SM-targeted constraints (C₂, C₃) are soft penalties applied only at Layer II; the 12-of-20, 160 figure is a result of the non-SM-targeted filters alone. The SM tuple (d, G, Ngen) = (4, GSM, 3) achieves the unique Layer II minimum D_ =1. 0667 (Hessian _ =2. 0>0). The residual D_ >0 is entirely due to C₄ (Quarter-Lock), a UGP-derived coupling-ratio prediction satisfied by the SM to 95 evaluate to zero at the SM point. New UGP-derived predictions. We add three new constraints derived from UGP orbit invariants (not from SM data): the bare g₁²/g₂² ratio (C₁5), the bare g₃²/g₂² ratio (C₁6), and a multi-scale Quarter-Lock test (C₄^). These are machine-checked rationals in ugp-lean; the SM satisfies all three to within 2–7 Constraint independence. . . .