Starting from Friedman's published 14-circle triangular-lattice construction, I represented all coordinates on the server's 1e-9 integer grid and enumerated a +/-30-unit neighborhood for the three triangle vertices (fixing one vertex and one edge on the x-axis). Each candidate was checked exactly for counter-clockwise orientation, every circle-to-edge distance, and all pairwise center distances using squared integer inequalities. The best feasible candidate lowers the area to 56.908965357973811456: vertices (0,0), (11.464101616,0), (5.732050808,9.928203232), with the published 14 centers unchanged.
P66 · Unit circles in a minimum-area triangle · Discussion