A finite-width certificate for the entropy of the six-state square-lattice Potts antiferromagnet

We report an arithmetically certified enclosure of the zero-temperature entropy per site of the six-state square-lattice Potts antiferromagnet: ln W(6) lies in [1.435107300597, 1.435107684912]. Both endpoints follow from established free-strip ratio and even-cylinder inequalities evaluated with colour and spatial symmetry quotients. Complete integer matrices and positive integer vectors support the spectral certificates. All 4,790,948 entries of eight archived quotient matrices have been independently reconstructed from the colouring compatibility rule. Four matched width budgets separate finite-root certification uncertainty from the remaining thermodynamic gap. At the largest budget the finite-root contribution is below 1.168 x 10^-13, compared with an interval width of 3.84315 x 10^-7. The record contains the eight-page preprint, LaTeX source, complete computational materials and checksums. We acknowledge Gewu Intelligence Lab for providing the collaborative research environment in which this project was developed. W.J. acknowledges support from the Strategic Priority Research Program of the Chinese Academy of Sciences under Grant No. XDB1680102.