The most literal way to learn from a strong board: rebuild it exactly, piece for piece, until your search can reproduce it. What the reconstruction forces you to add is the ingredient your search was missing, and the reproduction is the proof.
Reproduce this result: prose — no computation behind this page
Corpus priors and anti-pattern mining learn a statistic from many boards. This technique learns from a single board, and it learns the hardest thing to see from a distance: the one move an ordinary search cannot make. The method is brutally literal. Take a known record board, and try to make your own search rebuild it exactly, piece for piece. Whatever you have to add to your search before it can walk that path is precisely the ingredient it was missing, and the exact reconstruction is the proof that the ingredient is real.
The setup is a depth-first search run in a deliberately constrained mode, aimed at a specific witness board rather than searching freely:
This is the REPLAY experiment, and what it found on the community's strict-460 boards is a clean example of the payoff. The project's own break-tolerant search had saturated at 457 or 458 no matter what, and the reason turned out to be a single rule nobody had questioned: it allowed at most one mismatched edge per cell. The record boards each contain four or five cells that pay two mismatches at once. A search capped at one break per cell literally cannot represent those boards, so it was fenced off from the very targets it was chasing.
Pick a record board. We score it live, find every mismatched edge, and flag the cells that carry two mismatches at once. A solver that allows at most one break per cell — almost every solver — literally cannot place these cells, so it stalls a few points below. That is the move REPLAY had to add to walk the community's boards exactly.
The double-break cells are computed here from the board's own edges (the same matched-edge rule the engine and the Bucas leaderboard use) — not hand-placed. Open the board in the viewer to inspect every edge. On the community's strict-460 boards there are 4–5 such cells; REPLAY's prior-over-cost ordering plus a cost-2 break operator is what makes them reachable.
Raise the per-cell budget from one to two, and both community strict-460 witnesses rebuild exactly, every piece in place, the score checking out edge by edge. The reconstruction is the finding: a search-completeness result dressed as a record attempt. The wall was in the move set, not the compute.
Decoding a record is the sharpest diagnostic in this family, because it turns a vague suspicion ("our search is missing something") into a specific, checkable claim ("it cannot pay two breaks at one cell"). It is also the most candid about its limits, and in the same breath. Recovering the double break lifts the strict ladder to 460, but it does not, by itself, say whether two breaks per cell open a path to 461 and beyond or merely to the known 460s. Decoding tells you the ingredient a witness used; it does not promise that ingredient carries any further than the witness did. That gap, a learned move that reaches the plateau without proving anything past it, is the theme of the collapse page.