How would this work regarding monsters?
I'm assuming most sentient species would keep their species (like elves, edeinos, etc), but what about their powers? Would contradictory abilities vanish? Makes sense.
But the more interesting question for me is how they initially cause contradictions in the first place. They can disconnect when a Surge happens in a reality they aren't native to, but it seems like if they use any active abilities that require a d20 roll (like a dragon breathing fire) they should have a chance to disconnect too. But...how do you decide on the axiom for these abilities? Aysle would probably be pretty tolerant of magical-type creatures from the Nile Empire or Orrorsh, for instance, so just "if it's not from this cosm and it does anything an animal couldn't do, it's a contradiction" wouldn't seem to cut it. It could just be that active powers on monsters don't count unless they specifically list an axiom, but that seems like they are cheating a bit. I suppose the features are inherent to the creature, unlike tech, magic, spirit, or social, so it could make sense.
I'm going to assume that creatures that need a certain axiom to exist (like Technodemons and other magical creatures) don't cease to exist when they would disconnect, but rather that it refers to them existing naturally in a cosm, because it would be pretty harsh the other way.