...because paths to and from Switch spaces are no longer symmetrical with each other. This would allow one King to attack another, and the following position would count as checkmate.
I can't see anything other than a checkmate situation. The legal moves of the black king are vertically a5 and a3, horizontally b4 and diagonally b5 and b3. The move to c5 is excluded and only with that can the black king free itself.
We had such a situation in the discussion below and it involved a bishop on A4.
Also, a Bishop on A4 can move away on either light or dark spaces, but one on a4 can move away only on light spaces.
But a bishop on A4 cannot move to f8. For that he would have to be on a4.
That is correct, and I didn't say anything to the contrary. The light path from A4 goes through b3, c2, and d1.
If the bishop on A4 cannot move towards f8, then the king on A4 cannot move to c5? On the other hand, the white king can capture the black king on A4. This is undoubtedly an asymmetry that, as I understand it, cannot be avoided when handling a switch.
I guess I didn't understand your question correctly. I'll try my best to answer.
The switch is occupied, so the black pawn can move diagonally into the switch. In my opinion, the black pawn does not have a choice between A4 and a4, but moves directly to A4 and captures the white pawn there.
I can't see anything other than a checkmate situation. The legal moves of the black king are vertically a5 and a3, horizontally b4 and diagonally b5 and b3. The move to c5 is excluded and only with that can the black king free itself.
We had such a situation in the discussion below and it involved a bishop on A4.
If the bishop on A4 cannot move towards f8, then the king on A4 cannot move to c5? On the other hand, the white king can capture the black king on A4. This is undoubtedly an asymmetry that, as I understand it, cannot be avoided when handling a switch.
I guess I didn't understand your question correctly. I'll try my best to answer.
The switch is occupied, so the black pawn can move diagonally into the switch. In my opinion, the black pawn does not have a choice between A4 and a4, but moves directly to A4 and captures the white pawn there.