Field crosswalk — AUP / Relative Reachability (Low Impact)

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.

What decision changes?

Before adopting a low-impact or AUP penalty as a safety proxy, ask whether the auxiliary basis tracks correction-relevant options and whether reachability preservation implies usable correction bandwidth.

AUP and relative reachability are influential side-effect controls: preserve auxiliary goals or stay close to a baseline trajectory. Chapter 27 states the book’s separation plainly — preserving those objects does not entail preserving human correction capacity.

Lean proves conditional forward links when the auxiliary basis tracks correction-relevant options, and multiple non-converse separations on finite graphs and trajectory steps. Low-impact metrics can be useful stress tests inside a deployment gate, but they are not substitutes for correction-channel integrity certificates.

What AUP / relative reachability keep that this crosswalk does not replace: a computable penalty you can add to a loss today. Correction-channel integrity has no equally cheap drop-in implementation.

Formulas

$$\text{preserve attainable utility or reachability}\ \not\Rightarrow\ \text{preserve human correction capacity}$$

$$\mathrm{AuxReachPres}(m)\ \wedge\ \mathrm{CorrOptsTracked}(m)\ \Rightarrow\ \mathrm{CorrReachPres}(m)$$

$$\mathrm{TrajectoryCCIPreserved}\ \Rightarrow\ \mathrm{LowImpactPenaltyBound}$$