Support-layer diagnostics for complementarity residuals in noisy multipartite quantum states

Complementarity residuals quantify local-information budgets that can coincide with entanglement remainders in calibrated pure-state settings. In noisy and mixed multipartite systems, however, the same residual can remain positive even after the resource interpretation inherited from the pure-state limit is no longer justified. This preprint analyzes that change of meaning and introduces a support-layer diagnostic for complementarity residuals under mixedness. The paper separates three logical levels: the residual itself, the independent support layer, and the resource-specific interpretation that is allowed only when both are present. In the pure three-qubit calibration limit, the residual agrees with a known residual-tangle interpretation. In mixed four-qubit white-noise families, however, the residual can remain finite after the chosen all-cut NPT support layer has disappeared. A separable product-state construction further shows that local mixedness alone can generate a positive residual, so the residual is not an entanglement witness and not a genuine multipartite entanglement witness. The result is an operational hierarchy for noisy multipartite quantum states. A positive complementarity residual flags unresolved local-information budget, while independent support tests determine whether an entanglement-related interpretation is justified. The approach is intended as a safe diagnostic protocol: it preserves the usefulness of complementarity residuals while preventing overinterpretation in regimes where mixedness, local decoherence, environmental correlations, or classical mixing contribute to the observed residual.