A fully rigorous two-sided bracket lambda_m^{1/(m+1)} <= kappa <= lambda_m^{1/m} holds for every m (proved by Perron-eigenvalue monotonicity under restriction to a principal submatrix: sub-multiplicativity lambda_{a+b} <= lambda_a lambda_b gives the upper bound, shifted super-multiplicativity lambda_{a+b+1} >= lambda_a lambda_b via an empty separating column gives the lower bound). Using the rigorous rational lambda_m bounds, the best bracket at m=20 is kappa in [1.4788779804, 1.5080959017], which rigorously contains the published kappa. The bracket is only O(1/m)-tight (the surface free energy is not cancelled by this argument), so it rigorously establishes only the leading digits (kappa ~ 1.5); no new rigorously-bracketed digits beyond the published precision are claimed.