Extend the attainable frontier beyond identifiable magnitude channels and known geometry

Extend the attainable leading-log learning–assessment frontier for realized trained-gain assessment beyond the scalar Gaussian experiment's identifiable magnitude channels and known intervention geometry, while determining whether the same guarantees continue to hold under alternative magnitude channels, unequal experimental variances, or unknown intervention directions.

Background

The paper's matching upper bound relies on a magnitude statistic that estimates h^2 at auxiliary precision, a common Gaussian variance structure, known intervention geometry, and a scalar diagnostic direction. The sign-based lower bound is shown to be more robust, but the attainable upper frontier is not established under broader experimental designs.

Consequently, extending the attainable frontier would require new methods for magnitude calibration, variance handling, or directional uncertainty. The paper explicitly limits its claims outside the stated Gaussian experiment.