Nishio
Nishio — the Nishio Forcing Chain — starts from one candidate placement assumption and follows only forced consequences. If the assumption creates a contradiction, that assumption is false.
What is a Nishio Forcing Chain?
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. A branch choice that is not forced cannot be treated as a consequence. The final contradiction must occur in the state created by the original assumption.
How to spot it
State the source proposition or exhaustive source set, then annotate every step with its reason. Continue until the assumption forces an empty cell, a digit with no house position, or both a proposition and its negation.
The logic
If assumption A implies a contradiction, A is false; if assumption not-A implies a contradiction, A is true. Optional branches must remain alternatives rather than being reported as forced links.