This paper resolves the final E2 bottleneck in Universal Grid Mechanics (UGM) by proving that admissibility and grid ontology jointly force branch-independence of the sharp Level-2 write scalar CW (b) = Hb χb + Δb F′ (Sb). The central result is a derived state-completeness theorem: using Axiom 0 (local information consistency under repeated updates) as an exclusion principle, together with Axioms 1 and 2 (grid ontology and ontological precedence), it is shown that every admissible persistent coarse distinction must be carried within the minimal local state X = (S, M). This removes the need for any closure commitment and establishes state completeness as a theorem within the frozen five-axiom canon. As a consequence, the response coefficient χ becomes uniquely determined by canonical continuation data, yielding branch-independent CW and a universal primitive write coefficient ωW = κ CW / (Δτ Δupdₘax). The MOND-like transition scale g† = (ωW τM⁻¹ / τM) S̄₀ is therefore structurally determined and branch-independent, with only two remaining empirical inputs: τM and S̄₀. The framework yields a direct falsifiability condition: any additional admissible carrier beyond X = (S, M) would generate irreducible scatter in the radial acceleration relation (RAR). The observed low scatter across 153 galaxies (~2700 measurements, McGaugh, Lelli & Schombert 2016) is consistent with the absence of such carriers at detectable amplitude, providing empirical support for the derived closure. Finally, universality of ωW eliminates normalization ambiguity and reduces the dimensional sector to a single scalar ℓ, completing the structural bridge to dimensional closure.
J. G. Villarroel H. (Tue,) studied this question.