Contact-rich teleoperation logs expose a policy I/O design choice: demonstrations may contain the robot execution (E), leader command (C), or both. These signals are not interchangeable: E2E may discard contact-generating command offsets, whereas E2C preserves these offsets but omits the robot's execution response. We propose Dual-State Conditioning (EC2C), which conditions on both E and C while predicting future C, exposing command-execution mismatch as a cue for contact, latency, payload, and operator compensation; in quasi-static contact, this cue is often force-correlated. On a low-cost setup without force, tactile, or motor-current policy input, EC2C outperforms E2E and a strong E2C baseline across several real-world contact-rich, force-sensitive, and dynamic tasks. These results support EC2C as a practical default I/O setting for contact-rich imitation learning. We further formulate latency-adaptive inpainting as a temporal extension of this I/O choice for action-chunking policies, and discuss when long histories help dynamic inference or introduce causal confounding.

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