Structural Limitations in the P vs NP Framework: A Formal Reassessment

This paper presents a formal structural audit of the classical P vs NP framework, identifying interpretive tensions across verifier logic, reduction structure, and asymptotic analysis. While the formal machinery operates consistently at the syntactic level, this paper show that common extensions, particularly in applications to security, verification, and feasibility, rely on assumptions not entailed by the original definitions. This paper doesn’t propose a new model or resolution to the P vs NP problem. Instead, I demonstrate that the framework’s compositional use as a proxy for structural hardness introduces semantic boundaries that complicate unified application. This audit highlights the need for more precise separation between decision preservation and constructive complexity.