Frozen vision-language-action (VLA) policies offer broad manipulation skills but execute open-loop action chunks without tracking task progress, so the agent cannot reliably decide whether to continue, retry, or terminate. External memory is a natural remedy, yet we find it can be harmful when attempted actions are recorded as completed progress: transient execution failures become persistent task-state errors, and such a memory can underperform no progress memory at all. We propose Achievement-Grounded Memory (AGM), a lightweight closed-loop framework for frozen VLA policies. AGM represents a task as a static subgoal sequence with a dynamic progress pointer and advances the pointer on physically verified achievement rather than on attempts. Proprioceptive gripper-load cues decide when to verify; coherent point tracking verifies grasps, and language-conditioned cross-view comparison, read by a single trained 2.43M-parameter verification head, verifies placements. The policy, tracker, and encoder remain frozen, the head is the only trained component, and deployment needs no auxiliary vision-language model. On the RoboMME Counting benchmark, AGM reaches 100.0% on PickXTimes and 84.0% on BinFill, surpassing the strongest memory-augmented baseline by 7.7 points on the four-task average, and the gains carry over to a physical robot, where AGM reaches 100.0% and 82.0%. These results suggest that reliable embodied memory depends more on disciplined state updates than on memory capacity.

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