Global Irreducible Dependencies, Local Indistinguishability, and a Structural Reduction of the P vs. NP Problem

This paper reformulates a topological approach to computational complexity in semantic terms by introducing globally non-local irreducible dependencies in spaces of partial solutions. Building on earlier work that linked shallow and polynomial-time computation to hierarchical exposure of compatibility structure, it defines a formal notion of dependency that is locally invisible but globally inconsistent. Explicit SAT instances based on EXACTLY-ONE constraints on high-genus surfaces are constructed to realize this phenomenon, and are connected to Tseitin contradictions. A semantic argument against polynomial-size Frege proofs is developed. The framework reduces the P versus NP problem to the existence of such irreducible dependencies in NP-complete problems.