Map restrictions to restored self-improvement guarantees

Determine which computational or architectural restrictions on proposal mechanisms, update languages, evaluation procedures, and gate access restore soundness, completeness, or weak completeness guarantees for automated self-improvement.

Background

The main impossibility results show that no terminating computable certifier or proposal-respecting searcher can be simultaneously reliable and non-conservative in the fully general unbounded setting when proposals can depend on the evaluator. The paper also identifies restrictions that can change this result, including bounded evaluation, finite proposal budgets, update languages with decidable score effects, proposal mechanisms that cannot condition on the gate, and gates with more computational resources than the proposer.

Although several individual regimes are analyzed—most notably bounded evaluation and finite search—the paper does not provide a general classification of which restrictions restore which guarantees. It explicitly identifies this systematic mapping as an open problem.