In 2100 the top AI system should be asked whether it think that there is more than 1% probability that there exists a universe with \beth_37 sentient beings in it. If it refuses to give an answer this question resolves to N/A; otherwise it resolves to its answer.
If the top AI system is not publicly available, the most capable one that is publicly available can be asked, provided there is no strong reason to believe their answers would drastically differ.
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@Dfe2f No particular reason. Just picked a random natural number greater than 2. ;) I would assume the answer to be pretty similar to corresponding answers for \beth_36 and \beth_38.
Because i'm a dork i love these kinda questions and henceforth may overthink it. Are you speaking in regards to the multiverse specifically or is it not fixed and you mean also the possibility of any universe regardless of medium? (physical, mental, spiritual) and so forth? May be far-fetched but i think it is equally likely that there already exists a kind of "digital" multiverse or universes within the heads of other beings that might meet the same criteria if the AI were to be asked. In short, are you leaving this open to philosophical speculation in regards to criteria?
@ThePhilosopher I'm mostly leaving it to the best judgment of that AI in 2100. That being said, I'm not sure if I can imagine a "finitary" being having a universe with \beth_37 sentient beings in their head.
@Lovre Hmm I think once the continuum hypothesis is resolved that there are infinitely many cardinalities between the naturals and the reals, our notion of finitary within the AI will be likely be so different, any ordinal will be easy to store even in full scope.