UntiMagnetic Kernels: A Theoretical andAlgorithmic Framework for the P vs NPProblemtled Item

We introduce the Magnetic Kernel Hypothesis, a novel structural perspective on the classical P versus NP problem. We define the Magnetic Kernel as the irreducible component of any computational problem—the minimal structural unit without which the problem ceases to exist. We present two axioms: (1) every problem, whether trivial or large, possesses a Magnetic Kernel; (2) this kernel determines the essential reduction scale of the problem. Building upon these axioms, we propose the Kernel Containment Lemma, which demonstrates that the existence of kernels in P implies their existence in NP. We further extend this by introducing the Principle of Contained Fragments, which characterizes NP-kernels as partial fragments structurally contained within P-kernels. We provide a sketch proof, a concise algorithmic description, and experimental results on SAT instances (3, 32, 100, 1000) that empirically illustrate this principle.