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  3. Identical positions in the sense of castling.

#7 I agree this is the most logical. I can't figure it out of the FIDE rules though.

The FIDE rules don't explicitly talk about castling rights when considering positions to be the same. Quoting from the FIDE handbook:

"Positions as in (a) and (b) are considered the same, if the same player has the move, pieces of the same kind and colour occupy the same squares, and the possible moves of all the pieces of both players are the same."

That would suggest that positions are the same if you cannot castle -- regardless on whether you permanently have lost the right to castle, or the position prevents you from castling right now.

The FIDE rules 2014 till today, see last sentence:


9.2
The game is drawn upon a correct claim by the player having the move, when the same position, for at least the third time (not necessarily by a repetition of moves):

a.
is about to appear, if he first writes his move on his scoresheet and declares to the arbiter his intention to make this move, or

b.
has just appeared, and the player claiming the draw has the move.

Positions as in (a) and (b) areconsidered the same, if the same player has the move, pieces of the same kind and colour occupy the same squares, and the possible moves of all the pieces of both players are the same.
Positions are not the same if a pawn that could have been captured en passant can no longer be captured in this manner. When a king or a rook is forced to move, it will lose its castling rights, if any, only after it is moved.

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