Posterior distribution function of key parameters describing the time-delay lens RX J1131−1231, based on velocity dispersion profiles presented in this paper from the Keck-KCWI and JWST-NIRSpec data, and in combination with the lens model inferred power-law density slope by Suyu et al. (2013). The individual analysis of this system is shown to demonstrate that the three datasets are mutually consistent and can therefore be combined, and to illustrate the key degeneracies between the parameters. The inferred H₀ from this system is consistent with that obtained by Shajib et al. (2023) based on the analysis of 2D kinematic maps from the KCWI. In the hierarchical analysis presented in the main body of the paper, H₀ and λ_int are population-level parameters, jointly constrained by all the lenses in the sample.