Description
We present a likelihood-guided framework to interpret tomographic Alcock--Paczy\'{n}ski (AP) measurements in physically motivated quintessence dark-energy models. Rather than constraining scalar-field potentials directly from data, we map external constraints on the Chevallier--Polarski--Linder (CPL) parametrization—derived from tomographic AP measurements, Type~Ia supernovae, and DESI baryon acoustic oscillation data—onto quintessence parameter spaces. For each scalar-field realization, we solve the background dynamics and fit the equation-of-state history with an effective CPL form, $(w_0^{\rm eff}, w_a^{\rm eff})$. Statistical weights are assigned using an externally reconstructed likelihood in $(\Omega_m, w_0, w_a)$, enabling efficient identification of viable models. Applying this method to several representative potentials, we find that statistically favored models cluster around $w_0 \simeq -0.9$ with mild redshift evolution, consistent with tomographic AP constraints.