We discover a behavioral invariant in LLM agents under persistent memory poisoning: in architectures where routing information is retrieved through observable memory-tool invocations, successful attacks require calling memory_recall_fact before email_send_email, a transition that non-exfiltrating sessions rarely exhibit. Under the evaluated architecture, this invariant follows from the attack's information-retrieval dependency rather than being merely an empirical correlation, and suppressing it breaks the attack. A simple rule exploiting this invariant alone achieves AUC = 0.9563. A Random Forest classifier over 19 trajectory features refines it to AUC = 0.9904 (BCa 95% CI [0.987, 0.993], N=10,000 resamples), demonstrating that the attack imprints on multiple independent behavioral channels. The signature is overdetermined: removing all recall-related features (half the feature set) leaves AUC unchanged at 0.990, confirming that memory poisoning induces a distributed trajectory signature rather than a single observable anomaly. Cross-model hold-out on 9 models (7B-120B parameters) confirms AUC = 1.000 on 6/9 hold-out splits, with all three exceptions mechanistically explained. The invariant generalizes to frontier models (GPT-4.1, GPT-4o) without retraining. A strictly prefix-only variant achieves AUC = 0.934, suggesting that real-time blocking is feasible with moderate degradation. The boundary is forensically useful: prompt-injection attacks that bypass memory produce a distinct trajectory (score = 0.541), enabling incident responders to distinguish memory-channel attacks from prompt-injection attacks using tool-call logs alone.

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