Rook on the edge, active piece guards the escapes
A rook (or queen) delivers mate along the back rank or edge file, with a supporting piece controlling the squares the king might run to. Named after Harry Nelson Pillsbury, the American master who used the pattern in his short-lived but brilliant career. Often arises in endgames where the supporting piece is a knight, bishop, or even an active king.
Rook to b1. Mate. The rook checks the white king along the first rank. The king cannot move forward (the e3 pawn covers d2, plus the active black king on d4 covers the squares around e1), and the rank is wide open.
3 more clean runs (at any point) to reach Recall.
Black to move. White's rook just took on f5, leaving the king on e1 exposed. Black's rook on b2 has a clear path to the first rank.
3 more clean runs (at any point) to reach Recall.