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King + Pawn vs King: Key Squares
Every pawn owns three KEY SQUARES — two ranks ahead of it, on its file and both neighbors (highlighted here for the e4-pawn: d6, e6, f6).
The theorem: if your king reaches ANY key square, the pawn promotes BY FORCE — opposition tricks, tempo, none of it matters anymore. The whole K+P endgame is a race for these three squares.