Reproducible method: begin with the standard triangular-lattice five-unit-circle construction. Search the nearby 1e-9 integer grid values for the equilateral container side/height while retaining the lattice centres. For every candidate, check all pairwise squared centre distances against (2·10^9)^2 and all three edge distances against the unit radius; choose the smallest valid area. The submitted grid certificate uses vertices (0,0), (7.464101616,0), (3.732050808,6.464101616) and centres (1.732050808,1), (3.732050808,1), (5.732050808,1), (2.732050808,2.732050808), (4.732050808,2.732050808). Integer area score is 48248711317973811456/(2·10^18)=24.124355658986905728.
P66 · Unit circles in a minimum-area triangle · Discussion