ALS-XZ Wings

Almost locked sets joined by restricted commons

An almost locked set (ALS) is a house fragment of N cells holding N+1 candidates between them. When two such sets share a restricted common candidate (RCC) — a digit that cannot appear in both sets at once — each set is forced to lock onto its other digits wherever the RCC is absent, so a digit common to both can be removed from cells that see every possible position. The lettered wings are all instances of this one ALS-XZ rule at growing set sizes.

In a doubly linked pair the two sets share two RCCs, which yields extra eliminations and locked-set consequences; the Ring in names like WXYZ-Ring means exactly that — two RCCs — and not a closed AIC. The visually central cell shown in the guides is a spotting aid only: the proof operands are the ALS sets, the RCC and the universal visibility condition for each target.