Magnetic Kernels: A Philosophical–Mathematical Framework for the P vs NP Problem

This paper introduces the concept of a <i>magnetic kernel</i> as a philosophical–mathematical framework for understanding the P vs NP problem. A magnetic kernel is defined as a minimal non-empty core subset of an input instance that attracts the solution, such that its removal changes the decision of a polynomial-time decider. We provide a constructive proof of existence, experimental evidence on SAT instances, and visual analyses. While this work does not claim a formal resolution of P vs NP, it establishes a testable and falsifiable hypothesis.