Can Aggregate Invariants Accelerate Continuous Subgraph Matching? Limits, Laws, and a Dynamic Spectral Index

Spectral filtering recently delivered substantial pruning for static subgraph matching: Laplacian interlacing rejects candidates whose neighborhoods cannot host the query. We study whether such aggregate structural tests can accelerate 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 against an identical-minus-spectra control, the tests remove up to 51% of candidates or safely skip up to 47% of update enumerations, yet enumeration intermediates remain unchanged -- beyond the gates' skipped first-level bindings, typically zero -- across two engines, four real graphs, two stream types, and 77 solved queries; a constructed radius-stratified workload confirms the instrument detects the exception when one exists (-99.9% intermediates, 748× faster). Aggregate tests accelerate what scales with candidate sets -- construction, list scans -- never adjacency-guided exploration. We distill an intermediate-invariance methodology for evaluating CSM filters and release a reusable dynamic local-spectra index.