LLM agents increasingly rely on persistent long-term memory, which creates a critical vulnerability that we study here: memory poisoning. An adversary can store untrusted content in one session that later steers a consequential action, such as a payment, a setting change, or data exfiltration, in a future session. Existing defenses base a memory item's authority to act on either its content (detection or trust-scoring) or its derivation history (lineage). We show that both signals are malleable. An attacker can launder an untrusted origin through three channels specific to LLM agents: the agent's own summarization, a trusted-tool echo, and manufactured corroboration. Each makes the content look benign and breaks or flips its derivation edge to ``trusted.'' We formalize malleability for the memory write-retrieve-act pipeline and prove a machine-checked separation theorem. No content- or lineage-based defense is sound under laundering (T1), write-time origin binding is necessary (T2), and non-malleable origin-bound authority with Sybil-resistant corroboration-gated elevation is sufficient (T3). Our construction, TMA-NM (Tamper-evident Memory Authority, Non-Malleable), instantiates non-malleable information-flow control (IFC) for LLM-agent memory. A cross-defense, cross-attack, and cross-model benchmark over eight frontier models shows that existing defenses fail exactly where the theory predicts (up to 68% laundering attack-success), while TMA-NM reaches 0% attack success on both direct and laundering attacks across all models and channels, at full legitimate utility. We release the benchmark, harness, and machine-checked TLA+ models to support reproducibility.

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