Memory-dependent robotic manipulation often requires later actions to use information from earlier interactions. Existing vision-language-action (VLA) policies primarily rely on current observations, limiting historical information retention. Memory-augmented VLAs, such as MemoryVLA, address this limitation with external memory banks but require explicit storage and retrieval. To address these limitations, we propose StateMem, a single-state residual memory framework for VLA policies that uses prediction error to update a persistent memory token through low-rank residuals and to adaptively route cached prefixes. A training-free controller adjusts the routing threshold online, while fast correction compensates for stale prefix features during cache reuse. We evaluate StateMem on LIBERO, RoboMemArena, and real-world manipulation tasks. On LIBERO, StateMem achieves an average success rate of 97.6% and reduces the average VLM prefix refresh rate by 20.25% relative to full refresh. In the Occlusion category of RoboMemArena, StateMem achieves the best performance among single-VLA methods, reaching 21.8% Task Success Rate (TSR) and 44.3% Cumulative Success Rate (CSR). Across six real-world manipulation tasks, it achieves +21% in average success rate.

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