“The game is not automatically drawn if a position occurs for the third time – one of the players, on their turn, must claim the draw with the arbiter. The claim must be made either before making the move which will produce the third repetition, or after the opponent has made a move producing a third repetition. By contrast, the fivefold repetition rule requires the arbiter to intervene and declare the game drawn if the same position occurs five times, needing no claim by the players.”
Yes, there’s state there that’s not in the board position, but technically, threefold repetition is not a draw. Play can go on. https://en.wikipedia.org/wiki/Threefold_repetition:
“The game is not automatically drawn if a position occurs for the third time – one of the players, on their turn, must claim the draw with the arbiter. The claim must be made either before making the move which will produce the third repetition, or after the opponent has made a move producing a third repetition. By contrast, the fivefold repetition rule requires the arbiter to intervene and declare the game drawn if the same position occurs five times, needing no claim by the players.”