Shared memory helps language-model agents reuse information across long workflows, yet relevant evidence may not be admissible for a particular agent or action. Because restrictions propagate through derivations, summaries can conceal private, poisoned, untrusted, or revoked sources, enabling unauthorized reads or unsafe actions. Existing approaches provide semantic retrieval, scoped access, or lineage tracking, but do not clearly separate hard authorization from graded trust or adapt evidence requirements to action risk. We introduce MAP-Graph, a provenance-aware memory layer that represents agents, sources, memories, claims, and actions in a typed execution graph. It traces ancestry, excludes permission-ineligible records, reranks eligible memories by semantic similarity and multiplicative path trust, and applies a risk-sensitive gate before action execution while retaining affected lineage for audit. On a controlled benchmark of 2,700 synthetic tasks per method across three domains, MAP-Graph achieves 94.96\% overall task success, 72.70\% exact decision accuracy, and 90.22\% in the clean setting, where success requires a correct \textsc{Allow} rather than a safe intervention. Ablations isolate the roles of permission filtering, path trust, and action gating, while transfer tests with two additional backbones preserve the exact-decision and access-control advantages. These results support provenance as an operational control signal, rather than only post-hoc audit metadata, within the evaluated setting.