Exact endgame experiments that meet in the middle: enumerate a region from two ends and join on the seam, to find the true best completion with a proof rather than a heuristic's best guess. These measure a small region exactly instead of chasing the whole-board score.
Heuristic search guesses; it never knows it has the best possible finish. The experiments here take the opposite stance for a small region: enumerate it from two ends, join the halves wherever their seam colours agree and their piece sets don't overlap, and come away with the exact best completion plus a proof that nothing scores higher. It is the classic meet-in-the-middle time-for-space trade, pointed at the puzzle's endgame.
These are not attempts on the score. They answer a different question from the combination pipelines and the search studies: not how high can a heuristic climb, but what is the true best ending of this region, and where do exact methods stop being affordable. An exact answer about a small region is worth more here than another near-miss on the whole board.
The first and so far only experiment of that kind is BANDSAW. It settled a band of rows exactly on a 10×10 testbed, proved where the mismatch budget stops being affordable, and left a frame-free 437 board (counted in matched edges) as a by-product, the one proven-rigor page in this notebook. The section is named for the technique rather than the one page, because more exact endgame ideas belong alongside it as they land.