When Does a Memory Descendant Need Repair? Structural Lineage vs. Stale State in Persistent Agent Memory

Persistent LLM agents store conclusions that can remain active after their sources are corrected. We show that structural provenance fidelity and repair adequacy are different quantities. We distinguish structural descendants, descendants whose task value changes under an update, and descendants whose stored value is wrong afterward. In a controlled persistent-memory testbed with two LLM readers, material-support provenance covers about two-thirds of structural descendants at shallow depth and one-half at greater depth, while reaching at least 95% of stale stored state. Repair remains near oracle with fewer re-derivations. Matched-random provenance with the same edge budget and structural precision/recall reaches only about two-thirds of stale state. A second attributor improves structural fidelity while reaching the same stale state with more work. A symbolic value-agreement graph, retaining parents aligned with the stored conclusion, reproduces the LLM graph's selectivity. For unate rules and correct stored values, we prove that current-state value-agreement support reaches every update-sensitive descendant. Public multi-hop memory experiments show that persistent intermediates sharply lower post-update accuracy when they become invalid, with little change when they remain valid. These results establish stale-state coverage, repair work, and post-repair behavior as essential measures of provenance quality alongside structural fidelity.