If P=NP were proven non-constructively, we might establish equivalence without possessing the actual efficient algorithm, leaving the epistemic gap between finding and constructing intact.

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Constructively(describing how proof works in constructive logic): In a way that requires actually building or demonstrating something with concrete steps, rather than just assuming it's true based on logical rules alone.
Epistemic gap(The statement argues that the lack of a polynomial-time simulation is a gap in what we know, not proof that non-determinism is actually more powerful): A gap in our knowledge or understanding—something we don't know or can't figure out yet, rather than something that's impossible.
Equivalence(what classical and intuitionistic logic disagree about): Two statements are equivalent when they mean exactly the same thing and always have the same truth value.
P=NP(mathematics and computer science): A famous unsolved question in computer science asking whether two classes of problems (P and NP) are actually the same—if true, it would mean certain very hard problems can actually be solved quickly.

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