The new theme “Black retracts a move to regain its castling rights as its unique defense but loses them again with White’s next retraction” shown in a logical problem.
Hauptplan: -1.e4xBd5? -1...Ke8-f8 (-1...Ke8xRf8 is illegal) -2.e2-e4 (-2.e3-e4 does not prevent the check to the wK by the bR in the forward play) threatening 1.Qxd5 Kf8 2.Qd8# but Black has regained its castling rights, so 1...O-O! defends, being the unique reason why the Hauptplan fails.
Vorplan: -1.g2-g4! (threatens -2.Qh5-f3 and #2) -1…h4-h5 (unique defense) and now the Hauptplan works: -2.e4xBd5 Ke8-f8 (Black regains its castling rights) -3.e2-e4 (White loses again its castling rights: one of the wRs is promoted, as the original one on h1 was taken on h2 by the bP originally on g7. The promoted wR had to escape from the northwest corner via Rd8+, Black thus losing its castling rights. Notice that the promoted wR could have not escaped via b6 because two promotions took place on the “a” and “b” files).
On the Zweckreinheit: The Vorplan should rule out Black castling (the sole reason why the Hauptplan failed) without providing any additional advantage. Notice that in this case -1.g2-g4! also prevents the check to the wK by the bR in the forward play, but this is something that was already accounted for in the Hauptplan. And in any case, then White also needs to retract -3.e2-e4, not -3.e3-e4.
COOK reported in y.a.c.p.d.:
-1.Sb8xRc6! (legal retraction) Rd6-c6 (-1…b7-b6? is now illegal!) -2.b7-b8=S and forward 1.b8=Q/R+ Rd8 2.Q/Rxd8#
-1.Sb8xRc6! (legal retraction) Rd6-c6 (-1…b7-b6? is now illegal!) -2.b7-b8=S and forward 1.b8=Q/R+ Rd8 2.Q/Rxd8#
