Magnetic Kernels: A Theoretical and Algorithmic Framework for the P vs NP Problem

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 PP implies their existence in NPNP, thus establishing a universal foundation for Magnetic Kernels. We further provide a sketch proof, describe an algorithmic approach for kernel discovery based on intelligent random sampling, and report preliminary experimental evidence showing unprecedented reduction ratios in SAT and Vertex Cover instances.