No finite rulebook can certify every safe program: an impossibility theorem for gatekeeping AI agents

arXiv:2611.13367v1 Announce Type: new Abstract: An AI assistant writes small programs, and a gatekeeper must decide, from the code alone, whether each one may run. Suppose the rules are fixed: never perform a forbidden action, never let the output depend on a secret, always answer eventually. Can two rulebooks, one listing what is allowed and one listing what is not, both be complete, if every rule must be backed by evidence that a machine can check in finite time? We prove that they cannot. Checkable evidence can only establish what a finite record settles, and ``never'' and ``eventually'' ar

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