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This paper addresses that problem by using control theory to clarify, at a structural level, whether externally enforced safety-sustaining strategies can succeed and, if not, what any alternative strategy would have to satisfy in order to be viable. It establishes two main results. First, under explicit premises including a reachability condition, it proves a class-wide external impossibility result: once the system's effects exceed what bounded external control can counteract, no strategy that depends in any degree on continued external enforcement can sustain AI safety. This failure is structural across the entire externally enforced class rather than contingent on any particular strategy. 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