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Fig. 8.

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Kinematics correction term σaxiP/σsphP − 1 versus the projected axis ratio q′ as a result of combining the two curves in Figure 7 (lower panel). We use the misalignment angle between the kinematics major axis and the photometric major axis of the SLACS lenses measured in Knabel et al. (2025b), and a simple model for the fraction of oblates in a population (see Appendix B), to determine the weight used to combine the two curves. The solid dots in the lower panel are the median of the conditional probability P(σaxiP/σsphP − 1|q′), while the shaded area is the 1σ interval. The upper panel is to illustrate the distribution of the projected axis ratios of the early-type SLACS lenses from Bolton et al. (2008). Averaging over all these SLACS lenses, and under the choice of β = 0, we obtain the median correction to be ( σ axi P / σ sph P 1 ) SLACS = 0.016 0.007 + 0.009 $ (\sigma_{\mathrm{axi}}^P/\sigma_{\mathrm{sph}}^P - 1)_{\mathrm{SLACS}} = {-0.016}^{+0.009}_{-0.007} $.

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