Left panel : completeness of the SPT-3G EDF-S cluster catalog as a function of mass at four different slices in redshift, z = 0.25,0.75,1.25, and 1.75. The sample is expected to be more than 90% complete above 2.5 × 10¹⁴ M_⊙/h₇₀ at z > 0.25. Right panel : number of false detections and purity of the cluster catalog as a function of minimum detection significance. We find a purity of 99% at ξ> 5, which was also found in previous SPT publications, and a purity of 87% above the minimum significance threshold of ξ = 4, corresponding to about 30 predicted false detections in the catalog.