VWXYZ-Ring
A VWXYZ-Ring is the double-linked form of a VWXYZ ALS construction. Two almost locked sets share two different restricted common candidates, X and Y. Those two links fix the allocation between the sets and turn each ALS into a locked set within the combined construction, enabling the ring’s candidate eliminations.
What is a VWXYZ-Ring?
The two ALSs satisfy their own N-cells/N+1-digits counts and have two restricted common candidates. Every occurrence of each restricted common in one ALS must see every occurrence in the other. A restricted common may occur once in an ALS; no minimum of two occurrences is required.
How to spot it
List ALS A and ALS B and verify two separate restricted commons. For an RCC elimination, check visibility to all relevant occurrences across both sets. For another digit locked in one ALS, check visibility to every occurrence of that digit in that particular ALS. Do not replace these occurrence tests with a rule about seeing every cell in the ring.
The logic
Whichever restricted common is used by one ALS, the other allocation is forced so that both ALSs become locked. Restricted-common candidates can be removed from cells that see all of their relevant occurrences across the sets. A non-RCC digit can be removed from a cell that sees all of its occurrences in the individual ALS that must contain it.