Reconstructing the slope of a nearly flat quintessence potential from cosmography

We revisit thawing quintessence models with nearly flat scalar-field potentials using a cosmographic framework. Earlier work indicates that the cosmographic reconstruction of the slope $\lambda=-(dV/d\phi)/V$ of the quintessence potential in the general case requires the knowledge of the cosmographic paremeters up to the jerk parameter $j$. In this work we show that the slow-roll conditions $[(dV/d\phi)/V]^2 \ll 1$ and $|(d^2V/d\phi^2)/V| \ll 1$ allow the reconstruction of the slope of a nearly flat potential with knowledge of only the deceleration parameter $q$ (and the density parameter $\Omega_\phi$). Confronting the assumption of near-flatness with the cosmographic data after DESI DR2, however, reveals possible tension between the two. We further show that these models exhibit attractor behaviour in the $w$--$\Omega_\phi$ and $w$--$w'$ phase planes, corresponding to a universal thawing evolution with $w \approx -1$ at early times. We also derive the corresponding relation in the cosmographic $q$--$j$ plane and show that different cosmological expansion histories can produce the same thawing evolution. Nevertheless, all viable trajectories remain close to the $\Lambda$CDM limit $j=1$.