After sampling 125,000 GBOMs, evaluating µ (3) and µ (4) and computing the ideal prefactor Φ for each GBOM using the metric κ(Φ), resulting data of Φ(µ (3) , µ (4) ) was then averaged across cells of ∆µ (3) × ∆µ (4) , with ∆µ (3) = 0.026 and ∆µ (4) = 0.030. A cubic bivariate spline was fit through the resulting data to create a continuous function for Φ (see SI Sec. VI B), that can then be used to predict the appropriate correction factor for arbitrary systems. Only cells of ∆µ (3) × ∆µ (4) sampled with at least three distinct GBOMs were considered in the spline fit. We emphasize that predicted prefactor values outside of the contour of Fig. are extrapolated from the collected model system data using the spline fitting. While prefactors obtained in this fashion are likely reliable in regions close to the sampled bounds, the third order cumulant correction should be discarded entirely for systems exhibiting extreme values of |µ (3) | or |µ (4) |, as even the corrected third order cumulant approach likely becomes unreliable due to the missing higher order cumulant contributions. We will explore how well the parameter space explicitly sampled by the 125,000 GBOMs corresponds to skewness and kurtosis values in realistic condensed phase systems in Sec. IV C.