24, the excessive Pauli repulsions arise from unphysically positive local contributions in the middle term of eq. 1 because the semi-local exchange-energy density is less negative locally than the EXX one. Figure shows that LH24x based on an x-LMF does not exhibit such artefacts but rather provides an only very slightly too attractive curve. Interestingly, the curve obtained with the n-LMF (i.e. for LH24n-B95) is even somewhat closer to the reference curve than the x-LMF-based one. As our initial training of the n-LMF (see discussion in Theory section) also included the EXX energy density as an input feature, we first thought that a similar mechanism may be operative as layed out in ref. 24 for the x-LMF. However, the n-LMF used finally in LH24n-B95 exhibits only meta-GGA-like input features and nevertheless suppresses the gauge problem successfully without a CF. This suggests an overall mechanism independent on whether the LMF includes the EXX energy density or not, calling for closer analysis.