Left: Hypothesis (i). Posterior distribution of β and 𝒟_resid from the combined estimate using NVSS, RACS-low, and CatWISE. The 1-,2-, and 3-σ uncertainties are indicated by the black contours. The dotted lines indicate the maximum posterior values for these parameters. The canonical CMB velocity of β = 1.23 × 10⁻³ is indicated by the dotted red line, with the red dot indicating the kinematic dipole expected in the standard cosmology; this is assuming a negligible structure dipole (𝒟_resid ≈ 0). Right: Hypothesis (iii). Posterior distribution of 𝒟_resid, where the kinematic dipole is fixed to the CMB dipole. We note the respective evidence for and against these posteriors’ hypotheses in Table 2.