11.4 Active counter-witness interventions

An active follow-up tests whether abstention can itself guide experiment selection. DIAL-SKFM–1C leaves every confident first-stage decision unchanged. After first-stage abstention, it selects one operator from a registered library of off-diagonal matrix units. The chosen operator maximizes the minimum separation between the leading supported residual template and the two unsupported diagnostic alternatives. A fresh trajectory block estimates the resulting nested-bracket response, which is scored jointly with the original commutator. A random-probe control receives exactly the same additional sample budget.

This active counter-witness produces a substantive but incomplete repair. Across the \(1{,}620\) admission worlds, overall action accuracy rises from 72.2% without a counter-witness to 80.3%, and supported coverage rises from 68.2% to 83.9%, while selective accuracy remains 95.3% and the H0 false extension rate remains zero. Active choice also dominates random choice at the same 49.7% probe rate: random probes reach 75.9% accuracy, 80.0% supported coverage, and 76.3% unsupported abstention, compared with 80.3%, 83.9%, and 81.1% for active probes. The price is a rise in mean trajectory observations from 149.3 to 185.1 per world.

The study nevertheless receives a registered abstain. Overall accuracy remains below the 85% admission gate, and unsupported abstention remains below 90%. The reason reveals a design requirement. A probe is currently requested only after abstention, so it can rescue genuinely supported cases but cannot inspect a confident, incorrect supported decision made on an unsupported world. Moreover, 24 initially correct abstentions become false supported admissions after the extra noisy measurement. At sample size 128, the active rule reaches 89.8% accuracy and 90.0% unsupported abstention; at sample size 32 these fall to 71.3% and 72.8%. Active acquisition is therefore useful, but its trigger must depend on the risk of an unsupported alternative, not merely on whether the supported-family posterior has already abstained.

Experiment: DIAL-SKFM–1C. Action: after first-stage abstention, select one registered operator that maximally separates the leading supported repair from unsupported residual structures.
Controls: no counter-witness, random counter-witness at the same sample budget, and oracle.
Result: active acquisition improves accuracy from 72.2% to 80.3% and beats random acquisition by 4.4 points, but attains only 81.1% unsupported abstention. The preregistered decision is abstain.
Open boundary: request evidence when an unsupported alternative is plausible even if the supported-family classifier is confident, and require the counter-witness to confirm rather than merely replace an abstention.