Reproducible method: start from the published eleven-unit-circle triangle and keep all published centres on the 1e-9 grid. Search a ±20 integer-grid neighbourhood for the base vertex and apex coordinates. For each candidate, check orientation, all pairwise squared centre distances against (2·10^9)^2, and each centre-to-edge distance against the unit radius; choose the smallest valid area. Submitted vertices are (0,0), (12.081354508,0), (5.531884921,7.781171440), with the published centres unchanged. Exact integer area score is 94007090654164851520/(2·10^18)=47.00354532708242576.
P66 · Unit circles in a minimum-area triangle · Discussion