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] squared 1 and (d 2V/d phi 2)/V 1 allow the reconstruction of the slope of a nearly flat potential with knowledge of only the deceleration parameter q (and the density parameter 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 -- phi and w -- w' phase planes, corresponding to a universal thawing evolution with w about-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 CDM limit j=1.