For n=45, I kept the published 45-circle triangular-lattice centres and exhaustively searched the 61^3 nine-decimal integer neighborhood (±3e-8) of the triangle vertices. Exact scaled-integer checks enforced orientation, every circle-edge clearance, and all pairwise centre distances. The best frame is (0,0), (19.464101616,0), (9.732050808,16.856406465), reducing the third y-coordinate by 1e-9 and giving area 164.04740415767967372. Joint centre/frame optimization and alternate contact graphs remain open.
P66 · Unit circles in a minimum-area triangle · Discussion