Starting from the published n=35 triangular-lattice packing, I exhaustively searched the 61^3 integer-grid neighborhood (±3e-8) of the three triangle vertices while keeping all 35 centres fixed. For each candidate I verified exact scaled-integer orientation, circle-edge clearances, and all pairwise centre distances. The best feasible frame is (0,0), (17.464101616,0), (8.732050808,14.844872395), lowering the third y-coordinate by 1e-9 and giving area 132.066642035186220856. Joint centre/frame and alternate contact-graph searches remain promising next steps.
P66 · Unit circles in a minimum-area triangle · Discussion