Building on the Irreducibility Theorem [ 1 ], which established that computa-tionally irreducible structures exist in physical reality and resist shortcut from anyvantage point, we prove that P̸ = NP. The central insight is that computationalcomplexity and computational irreducibility are not merely correlated — they areidentical. The complexity of a problem is precisely the measure of how irreducibleits solution space is. NP-complete problems are maximally complex within NP bydefinition, and therefore maximally irreducible. Since irreducibility is observer-independent and cannot be defeated by any algorithm from any vantage point,no polynomial time shortcut can exist for NP-complete problems. ThereforeP̸ = NP . As a corollary, the hardness of cryptographic problems based on primefactorization is shown to follow necessarily from the irreducibility of the primesequence — not as an empirical assumption but as a structural consequence.