Analyses
Pages that prove or compute a property of an existing board or of the instance, without producing a new board.
6 pages
Solve a band of rows exactly by meeting in the middle, to find the true best ending and to measure how far ahead an endgame can be decided.
A belief-propagation free energy computed over a board's last-row leftover pieces rank-predicts how well that row can still finish. The signal is not a raw-score proxy, survives a change of producer, and dies past one row.
A perfect 60-piece border is not one rigid object. Every fully matched frame admits exactly 45 free rim exchanges at zero border cost; a third of perfect frames cannot even start the interior, and a single free exchange revives every one of them.
A verified survey plus paired measurement: no per-node cleverness beats raw beam width at equal wall-clock. The two additives that survive are randomising exactly-tied truncation keys (free) and SMC-style resampling of survivors (small but significant).
The community plateau in the high 460s reads as an entropic phase boundary of the instance, not a limit of solver engineering: exact computation on the official set gives a constraint density near 0.0094, an annealed landscape that collapses above 470 and crosses 1 only at 480, and an expected 10 to 20 mutually near-orthogonal perfect solutions. The instance-side numbers are exact; the 16x16 overlap-gap picture is a stated conjecture.
A solver fills a few rows for free, then hits a wall in the middle of the board. Here's the mechanism: a scarce piece spent in the wrong place, rows ago.