The Core Hypothesis: Towards a Structural Understanding of P⊆NPP \subseteq NP

The relationship between the complexity classes PP and NPNP represents one of the most fundamental open problems in theoretical computer science. It is well established thatP⊆NP,P \subseteq NP,meaning that every problem that can be solved in polynomial time (PP) can also be verified in polynomial time (NPNP). However, whether this containment is strict or collapses into equality remains unresolved.In this paper, I propose a structural perspective, introducing what I call the Core Hypothesis: the idea that every computational problem in NPNP contains an essential substructure, or "core," which dictates its inherent difficulty. By isolating this core, one may reduce the exponential search space to a polynomially bounded process.