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I have read what Fergus Duniho wrote about OR-AND Shogi, Xorix Shogi, and Assimilation Shogi. From what I can tell, not all pieces used in Xorix shogi will occur in OR-AND Shogi.
Here is a way to number these kind of variants. This is by giving a sixteen-bit number:
List of kind of promotion:
List of what happened if a piece would become no moves: