Abstract The neutron shell gap at $N=152$ has been experimentally confirmed through high-precision mass measurements on nobelium ($Z=102$) and lawrencium ($Z=103$) isotopes. The experimental measurements on $\alpha$-decay properties suggest the deformed doubly-magic nature of $^{270}$Hs. However, the magic gaps in the superheavy region are generally expected to be fragile. In this study, we test the robustness of the $N=152$ shell closure in $N=152$ isotones and $Z=108$ shell closure in Hs isotopes by employing an alternative approach where both theoretical analysis and available experimental data are required. Combined with existing experimental measurements on $\alpha$-decay energies, it is found that the robust $N=152$ neutron shell persists at least in
$Z=101-105$ isotopes, and the robust $Z=108$ proton shell persists in Hs isotopes with $N=159, 160$. These results provide crucial benchmarks for constraining effective interactions suitable for superheavy nuclei in nuclear energy-density functional theory.
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