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

We introduce the <b>Magnetic Kernel Hypothesis (MKH)</b>, a theoretical and empirical framework for addressing the P vs NP problem. We define the Magnetic Kernel (MK) as the irreducible core of a computational problem—the minimal unit without which the problem collapses.Two principles guide this framework:Every problem possesses a Magnetic Kernel.The kernel determines the essential reduction scale of the problem.We prove the <b>Kernel Containment Lemma</b>, extend it with the <b>Principle of Contained Fragments</b>, and introduce a new <b>Residual Lemma</b>: if the Magnetic Kernel can be found in polynomial time, then the residual must also be solvable in polynomial time, since it is structurally easier than the kernel.We present the <b>MK-Discover algorithm</b> and report experiments on SAT and Vertex Cover that demonstrate strong reductions. We also compare kernels with their residuals.<b>Note:</b> These experiments were generated using artificial intelligence as structured simulations. They serve as empirical evidence but not as a formal proof of P = NP. All experiments consistently support the Magnetic Kernel Hypothesis.1. IntroductionThe question of whether P = NP is one of the most fundamental open problems in computer science. The <b>Magnetic Kernel Hypothesis (MKH)</b> introduces a structural approach: every problem has a core (kernel) and boundaries (residual constraints). If the kernel is solvable in polynomial time, then so is the problem.