IMHO, the entire point of the story is that causality has become twisted into a counterintuitive shape.
From a naive literal point of view, no, the universe above theirs is independent. Diane's hypothesis/theorem is that, because their universe is at or near a fixed point, they have in effect invented a way to have unlimited control over their own universe. While there is no causal relationship from their universe the one up the chain, the symmetry implies their actions are mirrored.
I've read some of this author's other works. He likes playing with paradoxes like this. It's a twist on causality (and free will), inventing a new way for your actions to have an impact on the universe in the absence of a traditional causal link. It's pretty damn clever.
From a naive literal point of view, no, the universe above theirs is independent. Diane's hypothesis/theorem is that, because their universe is at or near a fixed point, they have in effect invented a way to have unlimited control over their own universe. While there is no causal relationship from their universe the one up the chain, the symmetry implies their actions are mirrored.
I've read some of this author's other works. He likes playing with paradoxes like this. It's a twist on causality (and free will), inventing a new way for your actions to have an impact on the universe in the absence of a traditional causal link. It's pretty damn clever.