Forcing
Assume a candidate and follow the logic: a contradiction disproves it
How to use it
The method of last resort: hypothesize and follow the logic. Choose a cell with few candidate pairs, assume one of them, and solve onwards with every technique available (including further hypotheses nested inside this one, for as long as that stays worth pursuing). A hypothesis that contradicts disproves itself — block the pair and continue; one that goes too long without contradicting or solving is abandoned and set aside; the first one that solves the grid is the answer, and its chain of assumptions is the proof.
In the walkthrough each hypothesis appears as a trial beat with its verdict: the cell and pair assumed, and for a contradiction, the root cause. It is honest search — sound because every contradiction is reached through sound deductions — but it should stay rare: a trace that leans on it means the technique set is too weak for the puzzle.
Why it is sound
Each trial assumes a candidate and follows it with only sound techniques, one deduction after another, for as long as that stays worth pursuing. A line of reasoning that reaches a contradiction proves the assumption impossible: sound deductions never refute a true statement, so the assumption is absent from every solution. Blocking it preserves every solution. A line that is not abandoned either solves the grid or is followed further; how far you choose to follow it only affects how much it can prove, never whether what it does prove is sound.
A worked example
With the strongest deterministic techniques excluded, no assumption-free steps remain — the only option left is to pick a cell with few options, assume one, and follow the logic to the end. Here the very first trial — D2 at r3c1 — is the lucky one: the assumption is printed as its own trial beat with its verdict (solved), and the proof is everything that follows from it, eighteen ordinary steps each reached by sound deductions from the hypothesis. On a harder grid the beat would instead carry a contradiction and its root cause, naming the exact cell the cascade died on; that disproves the assumption and blocks the pair, and you continue from there with one dead end ruled out. Honest search, sound because every verdict is reached through sound deductions; a trace that leans on it is telling you the technique set is too weak for the puzzle.