Hierarchical Gaussian-process test of DESI's dynamical dark-energy preference

DESI DR2 BAO combined with CMB and Type~Ia supernovae in the Chevallier--Polarski--Linder (CPL) parameterisation prefers evolving dark energy over $\Lambda$CDM at roughly $2.8$--$4.2\sigma$. 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. The baseline posterior gives $w(z\simeq 0)=-0.80^{+0.26}_{-0.23}$ (68\%~C.L.), about $0.8\sigma$ from $w=-1$, with $l=3.79^{+0.81}_{-1.12}$. A CPL fit on the identical compressed Planck pipeline improves nested $\Lambda$CDM by only $\Delta\chi^2\sim 1$ ($\sim 1\sigma$). Ablations that fix $(\sigma_f,l)$, drop SN or LRG1/2 BAO, replace the radial-basis kernel by Mat\'ern-$5/2$, or tighten the prior on $l$ leave the median $w(0)$ within $\lesssim 1\sigma$ of $-1$. The mild preference reported here is therefore specific to this compressed-CMB analysis and does not address DESI's full Planck-likelihood result.