The width-m hard-square strip transfer-matrix Perron eigenvalues lambda_m (computed rigorously to ~52 digits for m=1..20 by exact integer power iteration + Collatz-Wielandt bounds), fed through the ratio estimator r_m = lambda_{m+1}/lambda_m and Wynn's epsilon-algorithm, reproduce the hard-square entropy constant to 23 significant digits: kappa_est = 1.503048082475332264322064..., agreeing with the published kappa = 1.5030480824753322643220663329... The extrapolation is a numerical estimate (non-rigorous), internally self-consistent to ~6e-22; the raw ratio r_19 alone already agrees to 17 digits.