With respect to the remark you made about my post, hmm.

I suppose, now that you mention it, that that kind of notation could also be applied to cover any arbitrary shift from being an Xian to being Yist. But I find myself averse to that usage for reasons that don't immediately come to mind. Likely it's just because I'm used to it describing a basically-one-way shift, in the context of CDT. Even though ultimately it's a symmetric notation.

I appreciate you pointing out that the thing I was posting about potentially has larger applications! :)