Widely accepted background or a result the book treats as settled enough to build on without re-deriving.
Attainable Utility Preservation and relative reachability penalize side effects by preserving auxiliary options or baseline reachability. Trajectory correction integrity (CCI) can imply calibrated low-impact bounds when interfaces align — but option preservation and reachability are strictly weaker than preserving human correction capacity.
Christiano corrigibility is a dynamical desideratum — operators stay informed and able to correct over time. Lean reads it as basin contraction toward a correction manifold plus a correction-capacity floor; local act preferences can satisfy the weak predicate while dynamical corrigibility fails.
Cooperative inverse reinforcement learning treats the inferred object as a scalar reward. On the book's shared finite domain, that is exactly the k=1 bundle case; full bundle transport implies cooperative readability, but scalar inference does not determine bundle geometry.
Debate asks whether adversarial argument lets a judge select locally correct answers under idealized protocol assumptions. Preserved judge correction plus positive local truth capacity implies local truth selection — but local truth selection need not preserve the judge's correction channel.
ELK asks for reporters that reveal latent model knowledge rather than behavior-only simulators. When readout bandwidth tracks correction uptake, latent readout succeeds — but readout is an epistemic subchannel; latent readout can succeed while correction uptake fails.
Quantilizers bound optimizer risk by sampling from a high-performing quantile rather than maximizing directly. Local quantile safety and distribution soundness transfer under explicit assumptions — but local quantile-safe action choice does not imply trajectory-level correction integrity.
Orseau–Armstrong safe interruptibility removes incentives to seek or prevent interruption on the interrupted branch. That neutrality is a strict subset of preserving usable correction bandwidth — interrupt safety can hold while correction-channel integrity fails.
Shutdown and off-switchability are one-bit projections of correction-channel integrity. Lean proves the forward implication on the system model and finite MDP witnesses; the converse fails — narrow shutdown capacity can hold while the broad correction channel collapses.