The core problem asks whether one can build a formal constructive proof framework, grounded in intuitionistic or constructive logic, in which a decision problem being in P is provably equivalent to the existence of an explicit, constructively valid witness or certificate for every yes-instance, and whether this equivalence can be exploited to formally separate P from NP. The P versus NP question already distinguishes between efficient verification and efficient solution finding, but the gap between classical and constructive notions of existence has never been fully formalized in a way that turns this philosophical distinction into a proof-theoretic lever. The question is whether constructive logic, where existence proofs must come with explicit witnesses, provides a strictly stronger framework that can detect the difference between the two complexity classes.