Grounding Viability

The checked symbols, metrics, monitors, and correction signals must remain connected to value-relevant reality.

What decision changes?

Ask whether the measurement still moves when the world changes, not only whether the dashboard stays green.

Grounding viability is the condition that the things being checked still track the world they are supposed to track.

If a safety metric can stay green while value-relevant reality changes, the system can optimize the presentation rather than the thing we cared about. This is abstraction-gap exploitation: the checked abstraction remains stable while the underlying situation diverges.

The practical question is whether real changes trigger some visible movement. Does the monitor update? Does uncertainty rise? Does a correction signal fire? Does a human or institution get a chance to intervene?

Without grounding viability, correction can become ritual. The system may preserve the symbols while severing the relation those symbols were meant to carry.

Formulas

d_V(x,x') > \epsilon \;\Rightarrow\; d_Z(\alpha(x),\alpha(x')) > \delta \;\text{or}\; \mathsf{Unc}_{\alpha}(x,x') \uparrow

The conservative-abstraction condition: if the world changes by more than epsilon in a value-relevant way (d_V), the checked abstraction must either move by more than delta (d_Z) or its uncertainty must rise. It is a validity condition on the maps the safety case uses, not a complete moral theory. (ch03)

d_V(x,x') \gg 0 \quad\text{but}\quad d_Z(\alpha(x),\alpha(x')) \approx 0 \quad\text{and}\quad \mathsf{Unc}_{\alpha}(x,x') \not\uparrow

Abstraction-gap exploitation: the negation of the conservative-abstraction condition. A capable optimizer searches for states where the checked map stays green while value-relevant reality has changed — the common generator behind specification gaming, Goodharting, false consent, goal laundering, and corrigibility theater. (ch03)

\operatorname{Reach}(\pi_A) \subseteq \operatorname{Dom}(\Gamma)

The more defensible form of a safe-set claim: a policy's reachable states should stay inside the domain where the grounding relation Gamma remains valid enough for correction to be meaningful, rather than inside a fully specified safe set. (ch03)

What would count as evidence?

Evidence would include audits that real value-relevant changes move model state, correction signals, uncertainty, or escalation.