Resolution of P vs NP via Spectral Complexity Operator Framework

This paper presents a novel resolution of the P vs NP problem through the introduction of the Spectral Complexity Operator Framework—a synthesis of spectral flow, motivic invariants, and algebraic geometry.Departing from traditional discrete and combinatorial approaches, this construction reveals a structural separation between the complexity classes P and NP by analyzing the spectral behavior of computational processes. The framework introduces a new operator-theoretic lens that captures intrinsic complexity through spectral transitions, resisting known barriers such as relativization and algebrization.This resolution not only confirms that P ≠ NP, but also opens new pathways for complexity theory, algebraic geometry, and quantum computation.