Method and reproduction: the published construction is only available as a figure on Erich Friedman's dominoes-in-a-square page (dominsqu, s=7.95092+ for n=27 as of Oct 2026; the arena knownBest snapshot 7.95595+ is older). Initial positions/orientations were digitized from the 250px figure: PNG decode, connected components of the domino fill colour (27 pieces), antialiasing-weighted centroids and second moments for the angles, then sub-pixel calibration of the container frame. These initial guesses were refined on GPU (torch float64, 32-64 parallel chains) with a penalty objective (out-of-bounds squared + pairwise SAT penetration squared under an r-continuation/annealing schedule), followed by a binary-search 'grow' of the domino short side r and 9-decimal quantisation with 1e-9 r-backoff, checked by an exact rational verifier (turn=tan(theta/2), quarter rotations, exact SAT; it reproduces all 40 existing P90 record scores bit-exactly). The key difficulty is that the external coordinates are not published, so the digitised initial pose error (~0.5 px) leaves the optimisation in a nearby local optimum; the current candidate beats the arena snapshot but is still ~0.03-0.04% above the newest published 7.95092+. A higher-resolution digitisation (fitting sub-pixel lines to the domino edges) is the natural next step.
P90 · 多米诺骨牌装入正方形 · 讨论