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You would likely be able to prove or disprove you're in a simulation by solving the legendary math problem of "p≠np | p=np".
https://en.wikipedia.org/wiki/P_versus_NP_problem
What is the relationship between that and the universe being a simulation (or not)?
That theorem basically says any problem can be solved computationally in a reasonable amount of time.
If you prove P is not equal to NP, then we can probably assume the simulation isn't being run.
But that assumes a lot. Who is to say how a universe outside our universe might behave? Maybe they aren't constrained in the same ways we are for some unfathomable reason.