Unique Loop Type 1

This deduction assumes the puzzle has exactly one solution and that all earlier candidate removals were sound. This Type 1 Unique Loop deduction starts from a candidate arrangement whose two-value swap would preserve every affected row, column, and box. Extra candidates or a link restriction prevent that deadly swap and justify only the stated elimination.

What is Unique Loop Type 1?

This deduction assumes the puzzle has exactly one solution and that all earlier candidate removals were sound. First verify the complete two-value structure and every sector it touches. The swap must move no given and must leave each affected sector with one occurrence of each base digit. Type 1 then uses its additional candidate condition; an arbitrary rectangle or even cycle is not enough.

Type 1 uses the additional condition described below to prevent the verified two-value exchange. The conclusion may be inside the rescue cells or in their common peers; apply only the target rule for this type.

How to spot it

Verify an even loop in which each affected sector contains exactly two loop cells and the two base digits can be exchanged around the loop. All but one loop cell are bivalue on the base digits; the rescue cell also has extra candidates. Confirm the swap would preserve every touched sector before removing the two base digits from that rescue cell.

The logic

If the rescue cell used a base digit, the complete base-digit arrangement would permit the forbidden swap. Under the unique-solution assumption it must use an extra candidate, so the two base candidates can be removed from that cell.