Confluent Semantics, Local Certification, and a Structural Reformulation of the P versus NP Problem

This paper develops a semantic and structural characterization of deterministic polynomial-time computation based on confluence and local certifiability. Building on earlier work that ruled out local constructions as sources of irreducible dependencies, it introduces monotone extensibility and proves the Confluent Compactness Theorem, showing that any global incompatibility must be witnessed by a constant-size set of accessible semantic predicates. As a consequence, the class P is characterized as the class of languages with confluent computational semantics. The framework establishes an equivalence between the absence of global irreducible dependencies and polynomial-time decidability, and reduces the P versus NP problem to the existence of such dependencies in NP-complete languages.