Which data could convince experts, beyond reasonable doubts, about their origin outside our universe? From which margin should an expert consider such claim seriously?
For example, if one presented factorization of a billion-numbers run starting at 21024, with proofs of primality of all factors (that wouldn’t be a very large thing neither by amount of information nor by complexity to verify wrt 21st-century standards), it would be spectacular. But who knows which exactly complexity of integer factorization is? Who knows wasn’t factorization of this namely run facilitated by some mathematical coincidences?
But there are many problems with proven lower bounds on complexity that are really prohibitive, some of which hinder even application of powerful quantum computers (still hypothetical), and some problems are algorithmically undecidable in principle.
P.S. please, do not post answers based on trivia about transcomputational problems. Ī’m interested only in answers containing insights about how a (hypothetical) piece of information can be defended against the hypothesis that some (still unknown to experts) mathematics was employed to produce it.
Update: (related to @usul’s answer). We do not consider a totally abstract problem. Alleged “god” may use information from our civilization in input data for the problems solved, such as to use long pieces of “our” predefined data, presumedly random, to convince us that particular input data were not specially arranged.