<b></b>Magnetic Kernels: A Theoretical and Algorithmic Framework for the P vs NP Problem

We introduce the <b>Magnetic Kernel Hypothesis</b>, 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 <b>Kernel Containment Lemma</b>, 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.