P != NP via the Irreducibility Theorem

Building on the Irreducibility Theorem [ 1 ], which established that computa-
tionally irreducible structures exist in physical reality and resist shortcut from any
vantage point, we prove that P̸ = NP. The central insight is that computational
complexity and computational irreducibility are not merely correlated — they are
identical. The complexity of a problem is precisely the measure of how irreducible
its solution space is. NP-complete problems are maximally complex within NP by
definition, 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. Therefore
P̸ = NP . As a corollary, the hardness of cryptographic problems based on prime
factorization is shown to follow necessarily from the irreducibility of the prime
sequence — not as an empirical assumption but as a structural consequence.