Constraints on an approximate internal MST transform with a cored component, λ_c, of an NFW profile as a function of core radius. In gray are the 1-σ exclusion limits that imaging data can provide. In orange is the region where the total mass of the core within a three-dimensional radius exceeds the mass of the NFW profile in the same sphere. In blue is the region where the transformed profile results in negative convergence at the core radius. The white region is effectively allowed by the imaging data and simple plausibility considerations and where we can use the mathematical MST as an approximation (λ_c ≈ λ_int). The halo mass, concentration and the redshift configuration is displayed in the lower left box (https://github.com/TDCOSMO/hierarchy_analysis_2020_public/blob/6c293af582c398a5c9de60a51cb0c44432a3c598/MST_impact/MST_pl_cored.ipynb).