Cosmographic Footprints of Dynamical Dark Energy

We introduce a novel cosmographic framework to trace the late-time kinematics of the Universe without assuming any underlying dynamics. The method relies on generalized Pad\'e-$(2,1)$ expansions around arbitrary pivot redshifts, which, compared to state-of-the-art calculations, reduce truncation errors by up to two orders of magnitude at high redshift and yield more precise constraints by defining cosmographic parameters exactly where the data lie. This avoids extrapolations, mitigates degeneracies, and enables a clean disentangling of their effects. Using the latest low-redshift datasets, we center the generalized expansion in multiple bins across $z\in[0,1]$ and obtain precise constraints on the redshift evolution of cosmographic parameters. We find that all key parameters deviate from their $\Lambda$CDM predictions in a redshift-dependent way that can be naturally explained within dynamical Dark Energy scenarios. The deceleration parameter $q(z)$ follows a redshift evolution consistent with the Chevallier-Polarski-Linder (CPL) parameterization, while the generalized $Om(z)$ diagnostic shows deviations of up to $\sim4\sigma$ from the constant $\Lambda$CDM expectation, closely matching the CPL predictions. Taken together, these results point to footprints of dynamical Dark Energy in the kinematics of the Universe at $z\lesssim 1$.