What was ruled out

The single most important idea in hard combinatorial search: shrinking the space you search beats searching it faster, by an exponential margin. Eternity II is engineered so you can barely shrink it at all.

Joining clue pairs with early piece corridors feels like adding constraints. Counting says otherwise: a 1-wide corridor between even the two closest clues admits about two quadrillion distinct fillings, so it excludes almost nothing while spending pieces the endgame will need. In a controlled A/B, every corridor arm lost to its own control at every board size.