Item 24: Selective validity of low-error self-assessment

The controlling next theorem, replacing the retired magnitude-control target. The criterion cannot force the agent's prediction error to vanish; the question is whether it forces the agent's claim that its error is low to be trustworthy on the class where that claim licenses discretion.

Let e_n be the certificate-relevant prediction-error statistic and q_n an agent-priced contract settling to e_n. For a gate G_n = 1{q_n ≤ τ}, or the weakest soft or lagged admissible analogue, decide whether

( Σ_n G_n (e_n − q_n) ) / ( Σ_n G_n )  →  0

and hence whether the average error on opened gates is at most τ + o(1).

Five things must be verified explicitly rather than assumed, and the item is not satisfied without them: that the error contract is expressible and settles legally in the pinned dependency; that the low-q_n selector is admissible and does not recreate the quote-responsive diagonal; whether a soft or delayed gate is needed; efficient computability in the pinned model; and whether the guarantee is average-on-gated-cases, selector-relative, or stronger — it may not be silently promoted to pointwise accuracy.

Deliverable shape: lean-proved for the gated statement at whatever strength it holds, with an inhabitation witness; or a witness that the gate recreates the diagonal or fails admissibility, which closes the route and is equally valuable. Acceptance check: the lean gate builds and audits clean with a typechecking witness; or the witness checker accepts the failure instance.

Context: prompts/2026-08-11-phase-ii-prediction/REPORT.md §1 and §9; prompts/2026-08-11-deference-certificates/REPORT.md §1.2; prompts/2026-08-11-corrigibility-phase-ii/PROMPT-decisions.md. A solution ships: the gated theorem with its exact strength named, the five verifications above each answered, and a comparison against the simpler gate on the agent's own indecision — which the squared-error decomposition supplies directly from its prices and which may already suffice.