  The phase diagram of the cuprate superconductors continues to pose formidable
scientific challenges. While these materials are typically viewed as doped Mott
insulators, it is well known that they are Fermi liquids at high hole-dopant
concentrations. It was recently demonstrated that at moderate doping, in the
pseudogap region of the phase diagram, the charge carriers are also best
described as Fermi liquid. Nevertheless, the relationship between the two
Fermi-liquid regions and the nature of the strange-metal state at intermediate
doping have remained unsolved. Here we show in the case of the model cuprate
superconductor HgBa2CuO4+{\delta} that the scattering rate measured by the
cotangent of the Hall angle remains quadratic in temperature across the
pseudogap temperature, upon entering the strange-metal state, and that it is
doping-independent below optimal doping. Analysis of the published results for
other cuprates reveals that this behavior is universal throughout the entire
phase diagram and points to a pervasive Fermi-liquid transport scattering rate.
We argue that these observations can be reconciled with other data upon
considering the possibility that the pseudogap phenomenon signifies the
completion of the gradual, non-uniform localization of one hole per planar CuO2
unit upon cooling.
