A globally correct potential energy surface (PES) for the hp molecular ion is presented. The Born-Oppenheimer (BO) ai grid points of Pavanello et. al. [textit{J. Chem. Phys.} {bf 136}, 184303 (2012)] are refitted as BOPES75K, which reproduces the energies below dissociation with a root mean square deviation of 0.05~cm; points between dissociation and 75,000 cm are reproduced with the average accuracy of a few wavenumbers. The new PES75K+ potential combines BOPES75K with adiabatic, relativistic and quantum electrodynamics (QED) surfaces to provide the most accurate representation of the hp global potential to date, overcoming the limitations on previous high accuracy H$_3^+$ PESs near and above dissociation. PES75K+ can be used to provide predictions of bound rovibrational energy levels with an accuracy of approaching 0.1~cm. Calculation of rovibrational energy levels within PES75K+ suggests that the non-adiabatic correction remains a limiting factor. The PES is also constructed to give the correct asymptotic limit making it suitable for use in studies of the H$^+$,+,H$_2$ prototypical chemical reaction. An improved dissociation energy for H$_3^+$ is derived as $D_0,=,$35,076,$pm,2,$cm$^{-1}$.
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