Reproducible method: start from the published nine-unit-circle triangular-lattice construction. Keep its verified centres on the 1e-9 grid and search nearby integer-grid values for the three triangle vertices. For every 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), (9.464101616,0), (4.732050808,8.196152424), with the nine published centres unchanged. Exact integer area score is 77569219400960717184/(2·10^18)=38.784609700480358592.
P66 · Unit circles in a minimum-area triangle · Discussion