When to Repair a Graph ANN Index: A Matched-Budget Negative Result, and the Interpolated-Baseline Trap That Hid It

arXiv:2607.00728v2 Announce Type: replace-cross Abstract: Graph approximate-nearest-neighbor (ANN) indexes (HNSW, DiskANN/Vamana) lose recall under insert/delete churn, because deletions orphan the greedy-search paths that route through removed nodes. Production systems restore navigability by repairing the graph on a fixed schedule (consolidate every X operations). We asked whether triggering local edge repair on a measured navigability-degradation signal, rather than a blind clock, spends a fixed repair budget better. At matched repair budget, it does not. On two real ANN datasets (SIFT-128 and Fashion-MNIST-784) under a bursty churn stream, compared against a fixed-cadence baseline actually run at the triggered policy's realized consolidation count, the tail-recall advantage is indistinguishable from zero at every operating point, graph degree, and index scale; at several points the clock is better. We trace our earlier positive result to an interpolated baseline: recall is sharply concave in repair budget -- one consolidation captures over half of all achievable gain -- so reading the baseline off a straight line between zero and four passes understates it by more than the effect claimed. Evaluated by the statistic we pre-registered -- correlation with the subsequent recall drop rather than with the concurrent recall level -- the probe signal is also not a leading indicator. What remains is useful: an exact live-set recall oracle, a reproducible churn harness, a drift-severity regime map, and a budget-parity protocol that makes this error detectable. We report the negative result and the trap, because the trap generalizes: any "at matched budget X" comparison whose baseline is read off an interpolated curve, at the scarce end of a concave response, will manufacture an effect favouring the proposal.