Good Sudoku puzzles have exactly one solution. A Unique Rectangle uses that promise.
Four cells in two rows, two columns, and exactly two boxes can form a deadly pattern: if they only contained the same two digits, you could swap those digits and get a second valid solution.
Why it works
A proper puzzle forbids that deadly swap. So the rectangle is not allowed to be “pure” on two digits.
If three corners are already bi-value on XY and the fourth has extras (Type 1), candidates that would complete the deadly pattern must be false. Other types force locked candidates or groups to *avoid* the deadly pattern.
You are not guessing. You are saying: “If this candidate were true, the puzzle would have two solutions — but we know it has one.”
How to spot it
Four cells must occupy exactly two boxes and align in rows and columns. If a given digit pins the order, it is not deadly.
Demonstration
A unique puzzle cannot allow a deadly pattern: four aligned cells in two boxes that could swap two digits into a second solution.
Look for four cells that would form that deadly rectangle on two digits if extras were ignored. The green cells are almost there.
If certain candidates stayed, you could swap two digits and create a second solution — illegal for a unique puzzle. Avoiding that deadly pattern involves 4 and 7.
That uniqueness argument is a Unique Rectangle. (Only use it on classic unique puzzles.)
Make the uniqueness eliminations (red) (here 4 and 7). Those marks would complete a deadly pattern.
Example 1
Find a potential UR deadly pattern with extra candidates (two boxes, aligned).
This Unique Rectangle involves 2 and 3.
Apply the uniqueness eliminations (red) (here 2 and 3). They protect the single solution — a deadly pattern is not allowed.
Example 2
Find a potential UR deadly pattern with extra candidates (two boxes, aligned).
This Unique Rectangle involves 1 and 4.
Apply the uniqueness eliminations (red) (here 1 and 4). They protect the single solution — a deadly pattern is not allowed.