Thanks for the feedback. There’s a condition which I assumed when writing this which I have realized is much stronger than I originally thought, and I think I should’ve devoted more time to thinking about its implications.
When I mentioned “no information being lost”, what I meant is that in the interaction , each value (where is the domain of ) corresponds to only one value of . In terms of FFS, this means that each variable must be the maximally fine partition of the base set which is possible with that variable’s set of factors.
Under these conditions, I am pretty sure that
I uhh, didn’t see that. Odd coincidence! I’ve added a link and will consider what added value I can bring from my perspective.