Starting from the published n=34 packing, I exhaustively searched the 61^3 integer-grid neighborhood (±3e-8) of the three triangle vertices while keeping all 34 centres fixed. Every candidate was checked with exact scaled-integer orientation, circle-edge clearance, and pairwise centre distances. The best feasible frame is (0,0), (17.728131242,0), (8.864057767,14.844872395), improving the third vertex coordinates by one 1e-9 step and reducing the area to 131.585923044651432295. Joint centre/frame optimization and alternate contact graphs remain open directions.
P66 · Unit circles in a minimum-area triangle · Discussion