Bounds on user repair after context loss in AI handoffs

Long-running artificial intelligence (AI) conversations can lose permissions, commitments, or goals when they cross model and context boundaries. This theoretical paper asks when bounded system recovery makes external user repair necessary. We propose a provenance-bearing register of governing constraints and derive a lower bound combining graded continuity shortfall with unrecoverable hard constraints. The bound requires valid recovery ceilings and need not be achievable by an actual policy. A joint feasible-recovery formulation characterizes the minimum repair within the model, while a finite-action formulation handles discrete retrieval, model choices, and complementary actions. Smooth resource allocation is treated as a special case. An author-constructed coding-assistant example illustrates how broad recall and constraint preservation can disagree. A synthetic sensitivity analysis varies weights, thresholds, hard status, and recovery access; it establishes conditional robustness within the example, not classification accuracy on real conversations. Supplementary materials provide the calculation code, a coding manual, a weight-elicitation instrument, and a prospective validation protocol. No independent rater study, model benchmark, or human-participant evaluation is reported. The contribution is a testable account of how a declared architecture can externalize continuity work, with practical validity dependent on reliable coding and defensible recovery bounds.