Explicit Strong Uniqueness and Local Stability for Weakly Coupled SU(3) Cube Lattices

We consider the three-dimensional SU(3) lattice gauge Hamiltonian of the G4A/G4B series: every site is a complete cube of twelve links at internal coupling β = 1/2 or a single bridge link, and neighbouring blocks interact only through external plaquettes with face couplings 0 ≤ sp ≤ s. Inheriting the certified one-cube inputs and the generator (fixed-point) formalism of G4A, we prove an explicit strong uniqueness theorem. For two normal states on a finite region that satisfy the same interior ground-state condition, the expectation values of an observable supported in the interior differ by at most Cint(βe2ρ)|I|μD(I)/2∥A∥, where D(I) is the graph distance of the support to the exterior. Boundary terms of arbitrary strength acting only outside the interior do not enter the constants. For the main certificate, 0 ≤ sp ≤ 64/191447953125 ≈ 3.34 × 10−10 gives |ω′(A) − ω′′(A)| ≤ min{2, 3 · 10−6 3|I|2−D(I)/2}∥A∥. Consequently there is at most one locally normal infinite-volume ground state for the full kinematic test algebra; for uniform couplings it exists by G4B and coincides with the G4B vacuum. As auxiliary results we prove that the uniform gap 2/9 of G4A is stable under arbitrary bounded local perturbations within explicit tolerances, that the unperturbed threshold improves to s ≤ 1/5577, and an explicit weighted bound for the G4A generator. All numerical conditions are decided by exact rational arithmetic with outward rounding, and the verification code and expected outputs are provided. Strong uniqueness itself is known in general from work of Yarotsky and of Henheik–Teufel–Wessel; the contribution here is an explicit, reproducible version for this specific model, with stated inherited inputs, weights, prefactors and coupling thresholds. The results hold at fixed lattice spacing and fixed bare coupling, for weak inter-block coupling; they do not address the isotropic point s = 1, renormalisation, or the continuum limit.