Barrier Analysis for Structural Complexity Approaches

This preprint analyzes structural complexity research programs under the known meta-theoretical barriers of relativization, natural proofs, and algebrization. The paper evaluates ordinal stratification, stabilization operators, and layered search models within a formal barrier-sensitivity framework. It introduces criteria for assessing whether structural invariants relativize, define natural properties, or algebrize. No claim is made regarding resolution of P versus NP or other open problems. The work contributes a methodological classification scheme for frontier complexity research.