  In this study, we explore model independent constraints on the universe
kinematics up to the snap and jerk hierarchical terms. To do so, we consider
the latest Baryon Acoustic Oscillation (BAO) release provided by the DESI
collaboration, tackling the $r_d$ parameter to span within the range
$[144,152]$ Mpc, with fixed step, $\delta r_d=2$ Mpc, aligning with Planck and
DESI results. Thus, employing Monte Carlo Markov chain analyses, we place
stringent constraints on the cosmographic series, incorporating three
combinations of data catalogs: the first BAO with observational Hubble data,
the second BAO with type Ia supernovae, and the last including all three data
sets. Our results conclusively constrain the cosmographic series, say the
deceleration $q_0$, the jerk $j_0$, and the snap $s_0$ parameters, at the
$2$--$\sigma$ level, showcasing a significant departure on $j_0$ even at
$1$--$\sigma$ confidence level, albeit being compatible with the $\Lambda$CDM
paradigm on $q_0$ and $s_0$, at $2$--$\sigma$ level. Analogously, the $h_0$
tension appears alleviated in the second hierarchy, say including snap.
Finally, a direct comparison with the $\Lambda$CDM, $w$CDM models and the
Chevallier-Polarski-Linder parametrization is reported, definitively favoring
the wCDM scenario.
