Hidden Single
A Hidden Single resolves the exact-one constraint for one digit in a house. Eight positions are already excluded, leaving one candidate true. Resolving it excludes every other digit from that cell and excludes the digit from the 12 peers outside the source house; a large solved digit is only the compact record of those exclusions.
What is Hidden Single?
Every house contains each digit exactly once. For a Hidden Single, one digit is already false in eight positions of a row, column, or box, so its ninth position is true. The cell may still show other candidates because the digit is single in the house, not necessarily in the cell.
Crosshatch down to one
Choose one digit in one house and crosshatch the positions blocked by intersecting rows, columns, boxes, or earlier sound deductions. When eight positions are excluded, the remaining position is the Hidden Single. Written candidates record the same position-by-position scan but are not required for the proof.
Apply both sets of exclusions
Resolving the surviving position makes every other digit false in that cell. It also makes the resolved digit false in all of the cell's peers. The eight peers in the source house were already excluded by the Hidden Single premise, leaving 12 new peer exclusions outside that house. If the cell had no other candidates, the same candidate was both hidden and naked.