Unique Rectangle

Four cells forming a rectangle across exactly two boxes, all restricted to the same two candidates, could swap those digits freely — giving the puzzle two solutions. A proper sudoku never allows that, so the rectangle must be prevented from collapsing.

The escape routes come in five classic flavors. Type 1: three corners hold the bare pair, so the fourth drops both pair digits. Types 2 and 5: the corners with extras share one identical extra digit — it must land in one of them, clearing it from cells that see them all. Type 3: the two extra-corners act like one virtual cell that forms a naked subset with neighbors in their unit. Type 4: when one pair digit is confined to the two extra-corners of a unit, the other pair digit can't stay in either.

Different trigger, same soul: every type just refuses the two-solution rectangle. This is the one technique family that reasons about the puzzle, not just the board.