Validate the skew-normal fold for contact-maximum aggregation

Determine whether replacing the moment-matched Gaussian Clark fold with a skew-normal fold improves the aggregated standard-deviation estimate for uncertain terrain contact maxima, particularly in the contest-depth regime where the current method exhibits an aggregation deficit.

Background

The corrected Clark fold moment-matches each pairwise maximum to a Gaussian and then aggregates the resulting contact supports through a quadratic path-cost model. The paper finds that individual folded maxima have accurate standard deviations, but aggregation across a plan produces a systematic standard-deviation deficit that is corrected empirically using a contest-depth calibration.

A skew-normal representation is identified as a possible alternative because it could retain distributional asymmetry lost by Gaussian moment matching. However, the paper argues that its measured deficit appears primarily in cross-contact aggregation rather than in the individual fold, and the skew-normal alternative is left unevaluated.