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In-context imitation learning (ICIL) adapts robot policies through test-time demonstrations, but long multimodal trajectories constrain how many examples fit in context. We ask what a compressed demonstration should preserve. We propose JEDI, which compresses demonstrations into latent slots trained to predict the query episode's next-stage keyframe in a frozen video-JEPA space. Task and process counterfactuals help the slots preserve execution details, while the predictor selects demonstrations from a bank. Post-training with keypoint tokens enables human-hand conditioning on robots. Experiments on LIBERO and real robots show that JEDI supports many-shot context; LIBERO objective controls show improved success and demonstration following over action-only compression. These findings support query-future prediction as a training objective for preserving execution-relevant information in compressed demonstrations.