Production vector search must continuously ingest, delete, and re-tenant vectors while serving low-latency, high-recall, metadata-filtered approximate nearest-neighbor (ANN) queries for many tenants with per-tenant service-level objectives. Existing graph-based ANN systems address these requirements largely in isolation, leaving recall during concurrent re-optimization without an analytical bound. We develop a graph-based index that combines streaming updates, filtered search, and multi-tenancy, with one theoretical result and two system mechanisms. Our theory decomposes per-tenant recall loss into staleness from updates not yet integrated into the graph and filtered navigability determined by the local density of points satisfying a tenant's predicate. The staleness component exhibits anti-amortization on a merge-based graph, integrating a larger batch of inserts increases recall degradation super-linearly, so larger merges do not reduce total staleness loss. Holding the insert horizon fixed while increasing merge size 20x, we observe a monotonic decrease in terminal recall@10 from 99.44% to 99.01%. For filtered search, the theory gives a parameter-free frontier-mass relationship in local predicate density and a query-averaged per-tenant recall bound. We instantiate the bound with a filter and tenant-aware staging cache and a select-not-resize scheduler with per-tenant staleness ceilings. On a FreshDiskANN substrate, the ceiling eliminates tight-tier SLA violations under the evaluated churn workload, while merge reordering changes terminal recall by only 0.02 percentage points. The results show how recall bounds can guide background maintenance without relying on merge resizing as a recall control mechanism.

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