Forcing X-Chain
A Forcing X-Chain follows one digit through strong inferences and weak inferences. An open AIC can prove that at least one of two endpoints is true, allowing a common-peer elimination. A contradiction chain instead assumes a candidate and derives its negation, allowing that assumed candidate to be removed.
What is a Forcing X-Chain?
The chain uses one candidate digit throughout. A true candidate makes every weakly linked candidate false. A false candidate makes the other side of a strong inference true. False on one side of a weak inference alone proves nothing. Keep open-chain endpoint deductions separate from contradiction deductions; reaching a false candidate does not by itself justify an elimination from every cell seeing the start and end.
How to spot it
Find strong inferences for one digit and connect them through valid weak inferences. Record each proposition and relation. For an open-chain target, establish that at least one endpoint is true and require the target to see both. For a contradiction target, trace an explicit assumption until that same proposition is forced both true and false.
The logic
For an open chain, start with the first endpoint false and propagate false through a strong inference to true, then true through a weak inference to false, until the far endpoint is true. This proves the inclusive endpoint OR. For a contradiction chain, deriving not-A from assumption A proves A false; deriving A from assumption not-A proves A true.