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The best answer seems to be to say that a piece that is about to move cannot be threatening the enemy King and therefore cannot be a Knight if a Knight's move from said King, a Bishop or Queen if in an unblocked diagonal line of it, or a Rook or Queen if in an unblocked orthogonal line of it. You might object that if six Barios are a Knight's move from the King at least one of them must be a Knight (this is not a problem with radial linepieces on a square-cell board as the King can be threatened from only four orthogonals and/or four diagonals). However at least one piece would have had to be a Knight BEFORE the new cycle begins, and therefore the King would have already had to move out of check. If it could not, checkmate would have occurred during the old cycle.