Yeah thanks, that version is indeed false, but I’ve been looking at a weakened version which might be true which I still like better than the sum version because it seems cleaner. I’ll write the conjecture up formally when I get the chance.
It’s funny how I’ve spent so many tokens (not much of my own time) on this problem even though I really don’t think it’s particularly important for the broader natural abstractions agenda relative to lots of other stuff, but it’s been a fun challenge, definitely one of the trickier formal math problems that’s been come across in this area.
Yeah thanks, that version is indeed false, but I’ve been looking at a weakened version which might be true which I still like better than the sum version because it seems cleaner. I’ll write the conjecture up formally when I get the chance.
It’s funny how I’ve spent so many tokens (not much of my own time) on this problem even though I really don’t think it’s particularly important for the broader natural abstractions agenda relative to lots of other stuff, but it’s been a fun challenge, definitely one of the trickier formal math problems that’s been come across in this area.