The self-conjugate nucleus ${}^{164}\mathrm{Pb}$, with equal neutron and proton numbers ($N=Z=82$), lies far beyond the proton dripline and at a traditional magic number. Its possible doubly magic nature is investigated based on the state-of-the-art deformed relativistic Hartree-Bogoliubov theory in continuum (DRHBc), which incorporates nuclear deformation, pairing correlations, and continuum effects in a fully self-consistent framework. The experimentally known binding energies of neutron-deficient $Z=82$ isotopes and $N=82$ isotones are well reproduced. Pronounced two-neutron and two-proton gaps, together with sizable single-particle shell gaps, support the persistence of the $N=Z=82$ shell closures and point to mutually enhanced magicity in ${}^{164}\mathrm{Pb}$. Potential decay modes, including one-proton, two-proton, and multiproton emissions, are analyzed using the direct decay model with quantified uncertainties, predicting a dominant one-proton emission with a half-life ranging from $22\mathrm{ps}$ to $1.8\mu \mathrm{s}$. These results suggest that ${}^{164}\mathrm{Pb}$ may define the outermost reach of experimentally accessible nuclei beyond the proton dripline, making it a compelling target for future experiments.

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• Binding energy & masses
• Nuclear binding
• Nuclear structure & decays
• Proton emission
• 150 ≤ A ≤ 189
• Nuclear density functional theory
• Nuclear many-body theory