Kripke's distinction between epistemic and metaphysical possibility implies that P = NP being mathematically true does not collapse the epistemic gap between search and verification.

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Collapse (in philosophical context)(the statement says the truth of P = NP doesn't eliminate the epistemic gap): To eliminate a distinction or difference between two things. 'Collapse the gap' means to show that the difference doesn't really exist or doesn't matter.
Epistemic: "Epistemic" relates to knowledge—how we know things, what counts as knowledge, and whether we can trust what we believe to be true. It comes from the Greek word for knowledge and is used to describe questions about the reliability and validity of our beliefs and understanding. For example, "epistemic humility" means acknowledging the limits of what you can actually know for certain.
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.
Kripke: Kripke refers to Saul Kripke, an influential American philosopher and logician known for revolutionizing how we think about names, meaning, and possibility. He argued that names like "Albert Einstein" refer directly to the actual person rather than through descriptions of their properties, which changed philosophy fundamentally. His work also introduced "possible worlds" as a way to understand concepts like necessity and possibility, making him one of the most important philosophers of the 20th century.

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