Control Cannot Prove Itself

Gödel demonstrated that no sufficiently expressive formal system can prove all truths about itself. If consistent, it remains incomplete: there will be truths it cannot derive from within its own rules. This paper argues that autonomous AI systems face a structurally analogous constraint: no sufficiently capable system, under realistic conditions of adaptation and self-modification, can be the final authority over its own continuation. Alignment ensures that a system pursues appropriate objectives. Control, by contrast, requires that the standing to suspend those objectives remains external to the system's own evaluative framework — a condition we term interruptive authority. When oversight is internalized as optimization, the outside collapses and authorization becomes self-referential. We call this authorization collapse. Drawing on a structural homology with Gödelian incompleteness, the paper develops operational criteria for assessing interruptibility in real systems and proposes a Networked Interruptive Architecture (NIA) in which interruptive authority is distributed across dynamically non-collapsible nodes. An Anti-Closure Mechanism (ACM) maintains the minimal divergence — the ε — that prevents the system from becoming perfectly self-consistent and therefore uninterruptible. The paper's central claim is compressed in its title: control cannot prove itself. Every autonomous system that cannot be interrupted is attempting to become Gödel-complete. It cannot succeed. But it can become dangerous while trying.