Volume-Uniform Inverse-Quadratic Lower Bounds for Plaquette Covariances in Four-Dimensional SU(2) Wilson Gauge Theory

Let Λ = ∏_{j=1}^4 ℤ/L_jℤ, where L_j ≥ 4, and consider the finite SU(2) Wilson measure with an arbitrary signed, spatially inhomogeneous plaquette-coupling profile |λ_p| ≤ M. For the complete family of elementary plaquette observables w_p = 1 − (1/2) Re Tr U_p, we prove the volume-uniform matrix inequality Cov_{μ_λ}(w_p,w_q)_{p,q∈P} ⪰ [3 exp(−2) / (264 × 7000 × 16^4 × (1+M)^2)] I_{|P|}. The proof is nonasymptotic and applies at every finite coupling. The argument first proves a nine-dimensional covariance bound for the conditional law of two opposite links, using an integration-by-parts identity on the sphere and a reversible Metropolis kernel. A finite coloring of noninteracting link pairs then transfers this estimate to the full plaquette covariance matrix. Consequences include strong convexity of the log-partition function and quantitative bounds on relative entropy. These are finite-volume static statements, not claims about spatial decay or continuum spectral gaps.