When Graph Ablations Change Nothing: Locating Where Time-Series Anomaly Detectors Absorb a Graph Replacement

Graph-based time-series anomaly detectors are often ablated by replacing their graph with a reversed or random one; when detection is unchanged, the graph is declared irrelevant. Similar ablation outcomes, however, can arise from different internal responses: the replacement can be absorbed at execution, predictive information, utilization by the fitted model, or anomaly scoring. We introduce layered graph-ablation diagnosis, an executable protocol with one measurement and one decision rule per layer that distinguishes these responses and names the component to examine next. At the information layer, we identify a history information retention mechanism: older states of a replacement neighbor can still predict the current target, and in Gaussian directed $m$-cycles under the specified forecasting interface a reversed neighbor first becomes predictive at lag $m-1$, as window and lag interventions on trained forecasters confirm. On a pre-registered benchmark of twelve planted absorbers, four cases have ablation contrasts within $\pm 0.005$ yet absorbers at three different layers; blind rules recover 101 of 120 labels, with all misses in two partial-utilization cases, whereas importance readouts such as GraphMask confound the layers. Applied to public detectors, the execution check finds that four of seven implementations ignore a supplied graph when they learn the graph. On a directed cycle, the diagnosis locates GDN's near-chance detection in its source selection and static attention, and replacing both lifts AP to 0.967. On SMD, it uncovers and repairs a prediction deficit hidden behind a null learned-versus-random contrast, a contrast that stays unresolved after the repair, consistent with redundant sources.