To recover the valence contribution to the SOS moments without spoiling the convergence of X-ray response solutions, Ref. 13 introduced a hierarchy of approximations in which the fc-CVS-EOM-CCSD resolvent G k (ω) was approximated as a sum of a core fc-CVS-EOM-CCSD resolvent G core,k (ω) and a valence resolvent F val,k (ω) that approximates the valence fc-CVS-EOM-CCSD resolvent G val,k (ω), where