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 ^* \GUT exclusion, vector-like exclusion, CP violation required\—establishes as formal theorems that any self-contained 4D renormalizable gauge theory must have (i) G=G_SM and (ii) $N_gen 3$ (Layer I, forced by consistency). Presentation Invariance further selects N_gen=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 (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-targeted constraints (C_2, C_3) 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,N_gen)=(4,G_SM,3) achieves the unique Layer II minimum D_ =1.0667 (Hessian _ =2.0>0). The residual D_ >0 is entirely due to C_4 (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 g_1^2/g_2^2 ratio (C_15), the bare g_3^2/g_2^2 ratio (C_16), and a multi-scale Quarter-Lock test (C_4^ ). These are machine-checked rationals in ugp-lean; the SM satisfies all three to within 2–7 Constraint independence....