If you can't improve a great board by polishing it, maybe you can jump to a different great board. On every record pair tested, you can't, and the structural reason why is worth seeing.
Reproduce this result: heavy compute — script and results are committed
Two top boards look totally different, but they're related: you can turn one into the other by picking up a set of pieces and shifting each one into the spot the next was using, all the way around a loop. Mathematicians call that loop a cycle. Do the whole loop and you arrive at the other board.
Here's the catch. Between the best boards, that loop is enormous and there's only one of it. Going from a 459 board to McGavin's 469 means one single interlocking cycle of 154 cells, spanning the entire interior of the board.
This is no diagram: the live engine finds two real solutions, computes the actual cycles between them, and scores every step you take.
We computed the exact cycles between three different record boards and then tried every partial move: apply just some of the loop and see what the score does. The result is blunt. Every partial application makes the score worse, with drops ranging from a few points to over a hundred. There is no subset of the loop that helps, not one.
That's what makes it a wall. To move from one good board toward a better one you'd have to commit to shifting up to 154 cells at once, with no improving step along the way to guide you there. Every search that works in steps is blind to a move like that.
Together with the rigidity wall, this closes off the two obvious escape routes at once. You can't climb out of a good board locally, and (on every record pair measured here) you can't hop to a neighbour either, because the nearest better board is one indivisible move of 80 to 154 cells away. This is a plausible part of why the 470 record has stood since 2021: the moves that would beat it appear too large for any step-by-step search to find.
Cycles are computed exactly from pairs of record boards by composing their piece permutations; the subset tests enumerate sub-cycles and rescore. The animation above is a schematic of the mechanism, not the 154-cell cycle itself.