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We study whether such aggregate structural tests can accelerate \\emph{continuous} subgraph matching (CSM) over dynamic graphs, and answer in three parts. First, lazily maintained spectral bounds are infeasible exactly where spectral pruning has value: we characterize the tightest safe rule over a formalized perturbation relaxation and show that even it loses essentially all pruning power within four touching updates. Second, exact maintenance is affordable when selective: pruning utility and recomputation cost are anti-correlated across vertices -- hubs provably never prune -- so recomputing small-neighborhood spectra on touch sustains exact local spectra at microseconds per update, complete by construction. Third, integrated into a decoupled CSM benchmark again","title":"Can Aggregate Invariants Accelerate Continuous Subgraph Matching? 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