Observational mis-centering between the input X-ray surface brightness peaks and the output positions of clusters in the eROSITA digital twin, θ_sep, scaled by the best-fit average offset, ⟨θ_sep⟩, shown in blue as a histogram. Overlaid in orange are realizations of mock offsets drawn from the posterior of our model. The data is indistinguishable from the mock draws. Our model is also validated by comparing, in the insert, the likelihood of the data in blue with the likelihood of the mocks in orange.