Why uniqueness lets you eliminate
Every DIGIGMA puzzle has one solution. That is a fact about the board you opened, not a hope.
Because only one finish is legal, you can erase. If a candidate would leave two ways to complete a group, it is wrong. If a fill would force a clash in a row, column, or box, drop it.
You do not need a second solution to appear. You need to notice that a candidate would create a fork, or would break a rule. Then that candidate goes.
That is why notes get smaller. You are not choosing between two real worlds. Only one world is on the board. Play Sudoku, Play Star Battle, or Play Binary Puzzle — the same fact holds.