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Fig. 2.

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Impact of the Tikhonov regularisation used to suppress oscillating solutions fδ(k, z). Shown are, for a noise-free mock data vector and the KiDS-1000 error covariance, the posterior constraints (68% credible regions) on fδ averaged over the redshift bin Z1 = [0, 0.3] (left), Z2 = [0.3, 0.6] (middle), and Z3 = [0.6, 2] (right) with and without regularisation (dark orange τ = 5.0 with median as dashed line or light orange τ = 0). To boost scale-dependence and evolution, fδ(k, z) is here defined relative to the power spectrum at fixed redshift, probing the relative structure growth since z = 1. The solid line is the median posterior fδ for 100× reduced measurement errors, providing a nearly noise-free reference (noise/100) that averages the growth over the redshift bin while still exhibiting artefacts near the edges. The dotted lines are the theoretical P δ fid ( k , z ¯ ) / P δ fid ( k , z = 1 ) $ P_\delta^{\mathrm{fid}}(k,\bar{z})/P_\delta^{\mathrm{fid}}(k,z = 1) $ for one specific z ¯ $ \bar{z} $ chosen to most closely match the solid lines, indicating the redshift with highest weight in the average.

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