XY-chain
A chain of bivalue cells whose ends share a candidate clears it from common peers
How to use it
Follow bivalue cells like a fuse. A chain of bivalue cells, each sharing one candidate with the next, starts and ends on the same candidate z. If the first cell is not z, it takes its other value, which forces the next cell off its shared candidate and onto its own other value, and so on down the chain: one end or the other is z. Every cell that sees both chain ends loses z.
Grow the chain from a bivalue cell outward through shared candidates and check whether the far end shares a value with the start. Even short chains (three or four cells) clear useful candidates.
Why it is sound
A chain of bivalue cells where consecutive cells share a candidate: if the first cell is not z, it takes its other value, which forces the next cell to its own other value; the exclusion propagates cell by cell to the far end, so either the first cell or the last is z in every solution. Common peers of the two ends can therefore never be z. Each link is a sound peer exclusion; the composition is a finite case split over the first cell's two values.
A worked example
A chain of bivalue letter cells runs from r1c2 to r4c2. If r1c2 is not A, it takes its other letter; that exclusion forces the next cell in the chain, which forces the next, and so on to the far end — which must then be A. Either way, one of the two chain ends is A, so every cell seeing both ends loses A: the letter is struck from r2c2, which shares column 2 with both ends. The chain here visits r1c2, r1c3, r2c3, r2c4, r5c4, r5c5, r4c5 and r4c2, in that order — eight cells, each sharing one candidate with the next. Grow the chain from any bivalue cell through shared values and check whether the far end matches the start.