To explore the degeneracies of the parameters in the single-Schechter functions, we plot the parameter spaces of the fits to the SMFs of (Columns 1-4) the field, Hyperion as a whole, Hyperion’s outskirts, and Hyperion’s peaks. In each row, we fit over a grid of two of the three parameters in the single-Schechter function, and marginalize over the remaining parameter to minimize the χ² value. The parameter spaces explored are (row 1) log₁₀M^* − α, (row 2) log₁₀M^* − Φ^*, and (row 3) α − Φ^*. For each subplot, we plot the point with the minimum χ² value in the given parameter space (magenta X). In each row, we additionally plot a 3σ contour from the field, corresponding to Δχ² ≃ 11.8, to make comparisons between the likelihood surfaces from the field and the other populations in each column easier.