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In retrograde analysis problems, castling is assumed to be allowed unless it could be proven that either the king or the rook has previously moved.

It is well known, of course, that one could never be sure whether castling is allowed if the king and the rook cannot be shown to have previously moved, since one could simply start the game with silly moves of the knights and rooks for the sake of disabling castling.

Namely, one could just do the following silly moves of the knights and rooks for the sake of disabling castling on both sides (do only the first four moves to only disable kingside castling, or only the last four to only disable queenside castling):

  1. Nf3 (or Nh3) Nf6 (or Nh6)
  2. Rg1 Rg8
  3. Rh1 Rh8
  4. Ng1 Ng8
  5. Na3 (or Nc3) Na6 (or Nc6)
  6. Rb1 Rb8
  7. Ra1 Ra8
  8. Nb1 Nb8

Now, suppose that one requires the first move by each player to be a pawn move, implying that the initial configuration of the pieces could never be repeated regardless of castling rights.

Then, with that opening requirement, could castling ever be proven to be legally allowed for sure?

I think that the answer is still no even if the first move by each player is required to be a pawn move rather than a knight move.

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    "I think that the answer is still no even if the first move by each player is required to be a pawn move rather than a knight move." Indeed. You can use exactly the same device Nf3, Rg1, Rh1, Ng1, etc, but starting on move 2 rather than on move 1. If the first move was known to be 1.f3, then replace Nf3 by Nh3. Sep 6, 2023 at 16:53
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    You may in fact be able to prove that castling is possible, for example if you are given information about the number of moves made in the game. Sep 6, 2023 at 16:56

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As the commentators already mentioned, a pawn move doesn't suffice. Not even f3, h3, a3, c3 since the castling destruction manouvre can be prepended. Only information about the number of played moves helps.

Not all hope is lost, though. In fairy chess of all kind it might be possible. Actually, semi-orthodox already suffices: Take a Chess960 position where the rooks are locked, e.g. NBRQKRBN.

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