"A switch is an overlapping pair of spaces that in some ways operate together as a single space."

From my point of view it looks different. The square a4 of a switch is an independent square and is completely identical to the square a4 in normal chess. 4 (A4) is a composite square consisting of a half and triangle part of a4 and the new triangle due to board geometry. The new square 4 (A4) gets the same play options as all squares of the game board - 4 (A4) is considered equal.

This means that the squares a4/4 (A4) must first be seen independently. These independent fields get an additional function when they work together and act as a switch, as described.

I didn't say anything different. We're in agreement that the spaces composing a switch are separate from each other. But since they cannot be simultaneously occupied, and occupation of one space blocks movement through the other, and they share a common edge and a common corner, they also function in some ways like the same space.

It is possible to agree on the sides from which the switch should be accessible. We have clarified access from below and from the side, access from above is also not a problem and is already part of my proposal. The only question is whether it is access to the switch as a unit or to the individual square of a switch. According to my intention, the second applies.

Agreed. Use of the switch as a switch is possible only from below. That is due to the nature of how it works. If a piece moves to a switch through a diagonal move or a Knight move, it will have to stop on the switch, which will prevent it from using the switch to alter the direction of its movement. The same is true if a Rook or Queen moves to a switch from the side. It will have to stop there, which will prevent its use as a switch. And if a Rook or Queen moves to a switch from above, it will have only one path through the switch. So, it won't be utilizing the switch as a switch. This shows that access to the spaces composing a switch is a completely different matter than using it as a switch.

"Allow pieces access to the spaces of a switch from any direction, and when a piece moves to a switch, allow capture of any piece on the switch even if the capturing piece moves to the other space. For example, if a bishop is on A4, and a Rook moves to a4, consider the Bishop on A4 to be captured."

As described, access to the switch from all sides is not a problem. It is possible to agree on the proposal, but it does not fit my intention. However, if the game becomes more playable and programmable - so what.

What I'm proposing fits with the rule that both spaces of a switch cannot be occupied at the same time and the rule that occupancy of either space blocks vertical movement through the switch even when that movement would technically be going through the other space in the switch.

To the Knight: I can't allow anything here, but I can say what my point of view is. If we stick to the fact that the squares of a switch should be seen separately, then knight moves ending on the same line are not possible. However, as the game becomes more playable and programmable, compromises should be possible.

We could just say that because of the way that switches affect the geometry of the board, some spaces may be reached by either a vertical move or a Knight move. This would also correct the injustice done to the Knight of making the weakest piece even weaker around a switch while it gives all other pieces greater mobility.

"One last rule change I would suggest is to let Rooks, Queens, and Kings use their ability to move horizontally to switch between the spaces constituting the switch. This would basically involve lifting one more restriction on movement to the spaces making up a switch. "

I have problems with that. I have emphasized that the squares of a switch represent independent squares. This would rather mean that moves between the squares of a switch are possible.

Precisely.

The independence of the squares on the one hand and the functionality of a switch on the other compete with each other. Regarding the direct change between the squares of a switch, I tend towards the superordinate function, so a direct change should not be possible.

Allowing a piece that can move horizontally to move from one space to the other in a switch as a normal move does not affect the functioning of the switch. While the piece is on either space, other pieces can't pass through the switch, and once the piece leaves the switch, pieces will be able to pass through it again.