Tier 4 · first asked for by Diabolical
Unique Rectangle
Four corners holding the same two candidates would give the puzzle two solutions, so the shape must be broken.
Also called Unique Rectangle, Deadly Pattern.
Consider four cells at the corners of a rectangle, spanning exactly two rows, two columns and two boxes, all holding the same two candidates. If that were the whole story, the two digits could be swapped diagonally and the puzzle would have two solutions.
A properly set puzzle has exactly one. So whatever prevents the swap must be true: the corner with extra candidates cannot be reduced to the bare pair, or the digit that would complete the rectangle must go.
This is the one family of techniques that reasons about the puzzle rather than the grid — it uses the promise that the setter made. Every puzzle here is verified unique by exhaustive search before publication, so the promise holds.
A worked example
A real position, with the pencil marks a solver would have at that point.
the pattern · what it rules out · 5 a candidate that goes
What it proves. Unique Rectangle (type 4) on (48) at R1C2, R1C4, R2C2, R2C4: 8 is locked to R1C2/R2C2 in column 2, so 4 must leave both or the rectangle becomes ambiguous.