Certification-Under-Manipulation Problem

For each load-bearing certification measurand, does there exist a capability threshold κ* below which honest measurement is adversarially verifiable and above which it provably is not?

What decision changes?

For every metric in a deployment gate, ask for the constructive cost-of-faking relation and the capability level at which theater becomes affordable.

Every load-bearing measurand in the book — boundary residual, value-bundle activation, correction-channel integrity, conserved-property score, laundering index — shares one antecedent: can the certification channel stay honest against a capable adversary?

The Certification-Under-Manipulation Problem names it explicitly (Chapter 43):

Given measurand (M) used to gate deployment or successor creation, and system capability (\kappa) that can act on the world before, during, and after (M) is evaluated: does there exist (\kappa^{}) such that for all (\kappa < \kappa^{}), (M) is adversarially verifiable (cost of faking grows faster than affordable surplus), and for (\kappa \geq \kappa^{*}) it provably is not?

This is ELK-shaped, not merely “metrics can be gamed.” Generic Goodhart warns that optimizing a proxy degrades it. This problem asks for the actual threshold at which a specific measurand flips from honest to fakeable, with a constructive cost relation — and it is parasitic on capability: the target already “knows” whether (M) is honest.

Current status: the cost-relation definition is formalized generically; (c_{\mathrm{fake}}) is not established for any concrete measurand against a real adversary. Treating correlated steerability as one chokepoint rather than independent failures is part of the same problem.

What would count as evidence?

Positive resolution requires a calibrated c_fake dominating affordable surplus up to stated κ*; negative resolution requires showing every candidate measurand fails below needed capability.