RE: Can We Prove We Are Living In A Sim? - Yes We Can!
As a simple kitten, I would claim that P cannot be NP unless N = 1.
It's like 26 = 26
Or 26 = N*26
N must be one, if you want to use simple multiplication algebra.
If it's one, it's meaningless, so I would conclude that this reality, until scientifically proven otherwise, is a foundation reality, rather than a simulation.
I would use science here, and demand an observation that actually hints at the idea that this reality isn't a foundation reality. Without an observation, we cannot create a testable hypothesis, and without that, there is no science being done.
We must first observe the truth, because understanding it.
And as it is, there is no reason to believe on mere math alone, that this is a simulation universe, rather than a real universe. Math will be more useful once we have an observation, of course, but before the observation, I'd rather apply Occam's Razor, and simply conclude (with the idea that we do not have perfect knowledge one way or the other yet), that this is a foundational reality.