Map engagement behavior between tested failure rates

Characterize how language-model explanatory engagement varies across the continuous interval between the eight tested failure rates, particularly near the observed peak around p = 0.05 and the apparent leveling region between p = 0.005 and p = 0.001, using denser or adaptive sampling.

Background

The experiment evaluates the continuous failure-rate parameter p at only eight discrete values, from 0.2 to 0.0001. The observed results therefore establish the curve only at those tested points and cannot exclude non-monotonic behavior, a collapse, or another effect occurring between them.

The paper explicitly identifies the unsampled regions as a genuine open question and proposes denser sampling around the p = 0.05 peak and the p = 0.005-to-0.001 region, or an adaptive search that concentrates measurements where the curve changes most rapidly.

References

This is not presented as a weakness that undermines the reported result — the immediate_forced finding (Section 4.2) is a real, directly measured pattern at the rates tested — but as a genuine open question and a concrete, well-defined direction for follow-up work: denser sampling specifically around the p = 0.05 peak and the p = 0.005-to-0.001 collapse region, or an adaptive search that probes new rates based on where the curve is changing fastest, rather than a fixed pre-registered schedule.

— Explanatory Engagement Under Rare Anomalous Failure: Asymptotic Rarity in Model Behavior (or: The Asymptotic AI)  (2608.13063 - Mao, 13 Aug 2026) in Section 6.1, Discrete Sampling of a Continuous Rate Parameter