Computational Invariance, Effective Witnesses, and a Structural Reduction of the P vs. NP Problem

This paper establishes a structural principle governing deterministic polynomial-time computation based on invariance of computational states. Building on earlier work introducing bounded exposure and effective witnesses, it proves the Computational Invariance Theorem, which asserts that no computation can eliminate global compatibility without producing a finite, explicit, and extractable certificate. The theorem is shown to be equivalent to bounded exposure normal forms and strong semantic determinism, and implies the Strong Bounded Exposure with Effective Witnesses principle. The paper identifies Globally Non–Local Irreducible Dependencies as the unique obstruction to invariance and provides a topological characterization of this phenomenon. As a consequence, the P versus NP problem is reduced to the existence of such dependencies in NP-complete problems.