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Fig. B.1.

Fig. B.1. Refer to the following caption and surrounding text.

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Posterior distribution of Horndeski parameters in the stable basis parametrised by D ̂ kin Mathematical equation: $ \hat{D}_{\mathrm{kin}} $ and Δ M ̂ 2 Mathematical equation: $ \Delta \hat{M}_*^2 $ (left) and D ̂ kin Mathematical equation: $ \hat{D}_{\mathrm{kin}} $ and c ̂ s 2 Mathematical equation: $ \hat{c}_{\mathrm{s}}^2 $ (right) for a fixed AL = 1. Additionally, we show the posterior distribution of the derived value of the braiding term at z = 0, αB, 0. The blue contour shows constraints from the combination of KiDS-Legacy, DESI DR2 BAO, eBOSS DR16 RSD, and Planck 2018 TTTEEE, low- TT, and low- EE datasets, while the green contour illustrates constraints from an analysis with Planck data only. For comparison, the black contour shows our fiducial constraints with free AL for the combination of all probes. The inner and outer contours of the marginalised posteriors correspond to the 68% and 95% credible intervals, respectively.

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