Dynamic Forcing Chain
A Dynamic Forcing Chain starts from one explicit assumption and applies every forced consequence to a temporary candidate state. New singles or other deductions created in that state may extend the chain. Every intermediate result remains conditional on the starting assumption until the proof reaches and discharges a contradiction or exhaustive conclusion.
What is a Dynamic Forcing Chain?
Dynamic means later inferences may rely on candidates removed earlier under the same assumption. Removing one candidate from a bivalue cell leaves a single; removing its final candidate creates a contradiction. The temporary state must not be confused with the original grid.
How to spot it
Record the starting assumption, then annotate each consequence with the current assumed state. Use a deduction only when its premises are already forced in that state. Stop when the assumption creates a contradiction or when all exhaustive alternatives establish the same target conclusion.
The logic
A Dynamic Forcing Chain keeps one temporary state for its starting assumption. Removing one candidate from a bivalue cell leaves its other candidate as a naked single; removing the final candidate from a cell is instead a contradiction. Every new single, locked candidate, subset, fish, or wing used later must be valid in that same temporary state. If the state reaches a contradiction, the starting assumption is false. Otherwise a conclusion can be transferred to the original grid only after the assumption has been discharged or every exhaustive branch has established it.