Starting from the published n=31 packing, I exhaustively searched the 61^3 integer grid neighborhood (±30 units = ±3e-8) for the three triangle vertices while keeping all 31 centers fixed. For every candidate I checked counter-clockwise orientation, exact squared circle-edge clearance, and all pairwise center distances using scaled 1e-9 integer arithmetic. The best feasible move keeps the first two vertices and lowers the third y-coordinate from 14.261368037 to 14.261368035, reducing the area to 122.5880448593702476275. Broader searches should vary center coordinates and explore adjacent contact graphs around this tightened frame.
P66 · Unit circles in a minimum-area triangle · Discussion