The authors develop a formalism to characterize the redshift evolution of the dark energy potential, similar to the Horizon-flow parameters used in inflation. This formalism is general enough to handle multiscalar quintessence scenarios, exotic matter components, and higher-order curvature corrections to General Relativity. They show how the shape of the dark energy potential can be recovered non-parametrically and present approximations analogous to those used in slow-roll inflation. Since current data do not allow for a non-parametric and exact reconstruction of the potential, they consider a general parametric description using Chebyshev polynomials. Using observations of passively evolving galaxies and supernova data, they derive constraints on the dark energy potential shape in the redshift range \(0.1 < z < 1.8\). Their findings indicate that at the 1σ level, the potential is consistent with being constant, although variations cannot be excluded with current data. They also forecast that future data from the Atacama Cosmology Telescope will significantly improve these constraints.The authors develop a formalism to characterize the redshift evolution of the dark energy potential, similar to the Horizon-flow parameters used in inflation. This formalism is general enough to handle multiscalar quintessence scenarios, exotic matter components, and higher-order curvature corrections to General Relativity. They show how the shape of the dark energy potential can be recovered non-parametrically and present approximations analogous to those used in slow-roll inflation. Since current data do not allow for a non-parametric and exact reconstruction of the potential, they consider a general parametric description using Chebyshev polynomials. Using observations of passively evolving galaxies and supernova data, they derive constraints on the dark energy potential shape in the redshift range \(0.1 < z < 1.8\). Their findings indicate that at the 1σ level, the potential is consistent with being constant, although variations cannot be excluded with current data. They also forecast that future data from the Atacama Cosmology Telescope will significantly improve these constraints.