To check the quality of the fit given in 40, we calculate the resulting w MRF λ=1 (r s ). The relative error of w MRF λ=1 (r s ) vs. the exact w λ=1 (r s ) [Eq. 36; PW92] as a function of r s is shown in Fig. . For comparison, we also show the relative error of w MRF λ=1 (r s ) obtained with the original fluctuation function [Eq. 11]. Given the simplicity of the model and the fact that it has not been trained on the UEG, the relative error for the original MRF is reasonably small (never larger than 25%) On the other hand, the new fluctuation function [Eq. 37 with the N L part of Eq. 38 and the L part given by the fit of Eq. 40] yields w MRF λ=1 (r s ) is highly accurate for the UEG as the error in the underlying w MRF λ=1 (r s ) never exceeds 0.5% . Furthermore, the relative error in w MRF λ=1 (r s ) within the original σ λ=1 does not vanish as r s → 0 (as it misses the σx negative term of Eq. 35), whereas the new model also fixes that. 'new σ λ=1 ' denotes the MRF results obtained with the new fluctuation function [Eq. 37 with the N L part of Eq. 38 and the L part given by the fit of Eq. 40, and σ x given by Eq. 35].