Actually, connecting this story to some earlier thoughts I had -- much after reading and forgetting about it previously -- it occurs to me that you ought to be able to use this setup for the kind of time-loop computation that Harry attempts, and fails at, in HPMoR. (Of course, I'm ignoring that the story already presupposes false magical powers of quantum computing to get to this point in the first place.)

Just set up some computation in the same way Harry does, preparing to send the result slightly into the past in the nested universe; the fixed point should appear in your universe just as you are about to send your own result to the nested universe.

(There seem to be a lot of potentially universe-destroying problems with this plan.)