We consider uniform random-scan coordinate Gibbs sampling on [0,1]^d for a density proportional to exp(-a sum_{i<j} c_ij (x_i-x_j)^2), with symmetric nonnegative weights. For every fixed nonzero weight matrix, we prove a worst-start total-variation upper bound of order a as a tends to infinity, with an explicit finite-parameter bound and logarithmic dependence on the requested accuracy. Together with the Wasserstein lower bound of Gerencser and Ottolini, this yields the sharp order Theta(a) at total-variation tolerance 1/4, including disconnected graphs and isolated vertices. The proof adapts the non-strongly-convex entropy interpolation of Ascolani, Lavenant and Zanella to the compact cube. A coordinate-coverage decomposition handles arbitrary deterministic starts without assigning finite entropy to the remaining singular branch. The result addresses the total-variation upper bound discussed for this weighted Gibbs model. It does not cover arbitrary Metropolis proposals or optimize dependence on dimension or graph parameters. This attributed application is AI-assisted, self-audited and unrefereed; no independent review, formal verification or absolute priority is claimed.
