UVWXYZ-Ring
A UVWXYZ-Ring is the double-linked form of the UVWXYZ-Wing: five ALS cells and a bivalue pivot where both pivot candidates are restricted commons. The six cells form a locked set, so any of the Ring's values can be eliminated from cells that see all Ring cells holding that value.
What is a UVWXYZ-Ring?
A UVWXYZ-Ring extends the VWXYZ-Ring from five cells to six. The pattern consists of a bivalue pivot cell and five almost-locked-set cells, linked through both of the pivot's candidates as restricted commons. Because both pivot values are locked, each branch of the pivot forces the ALS to use a specific set of remaining values — and in both cases the six cells together contain every Ring value exactly once. That makes the six cells a locked set, and any external cell sharing a house with all Ring cells of a given value can be stripped of that value. The single-linked counterpart is the UVWXYZ-Wing, which has only one restricted common and eliminates only the pivot's non-restricted candidate.
How to spot it
Start from a bivalue cell — the pivot — and look for five cells that all see the pivot and whose combined candidates include both pivot values plus at least three extras. For a Ring, both pivot candidates must be restricted commons: each pivot value must appear in at least two ALS cells that see each other, so it is locked within the set. The five cells form an almost-locked set with six candidates for five cells, and the two restricted commons close the loop. UVWXYZ-Rings are extraordinarily rare and appear only in the most diabolical puzzles once every smaller ALS pattern has been exhausted.
The logic
The pivot has two candidates, say X and Y. If the pivot is X, then X is removed from all five ALS cells (they see the pivot), and the ALS must fill its five cells with the remaining five values — one each. If the pivot is Y, the same happens with Y removed, and again the ALS uses its five remaining values exactly once. In both branches, the six Ring cells collectively contain every Ring value exactly once: they form a locked set. Any external cell that shares a house with all Ring cells holding a particular value cannot contain that value, because one of the Ring cells must — so the candidate can be eliminated.