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We reconstruct the same late-time expansion history with a hierarchical Gaussian process (GP) that co-samples the kernel hyperparameters $(\\sigma_f,l)$ together with $(H_0, \\Omega_m, \\Omega_k, \\omega_b h^2)$, coupling BAO, compressed Planck distance priors, and Pantheon+ through a Monte-Carlo effective likelihood conditioned on 37 cosmic-chronometer $H(z)$ points. 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