Systematic Evidence for Hyperonic Shell Closures from Pairing Correlations in Multi-Λ Hypernuclei

We present a systematic investigation of [Formula: see text] pairing correlations in multi-strange hypernuclei within the self-consistent coordinate-space Hartree-Fock-Bogoliubov (HFB) framework. Calculations are performed for even-even Ni ([Formula: see text], [Formula: see text]–[Formula: see text]) and Sn ([Formula: see text], [Formula: see text]–[Formula: see text]) isotopic chains with [Formula: see text] hyperons added pairwise up to strangeness [Formula: see text] and [Formula: see text], respectively. The SLy5 Skyrme functional is adopted for nucleons, while the DF-NSC97a and EmpC functionals describe the hyperonic sector. The hyperon pairing gap [Formula: see text] exhibits a pronounced oscillatory behavior with strangeness. For Ni isotopes, complete suppression occurs at [Formula: see text] and [Formula: see text], while the higher-shell closures at [Formula: see text] and [Formula: see text] are observed only in isotopes where a sufficient number of bound [Formula: see text] single-particle states is available. For Sn isotopes, complete suppression is observed at [Formula: see text] and [Formula: see text], while an additional closure appears at [Formula: see text] in isotopes where a sufficient number of bound [Formula: see text] single-particle states is available. These quenching points coincide with hyperonic shell and subshell closures, providing consistent evidence for the corresponding spherical hyperonic magic numbers. The persistence of these shell closures across both isotopic chains supports the use of [Formula: see text] as a sensitive probe of shell structure in multi-[Formula: see text] systems. Changes in neutron pairing, density distributions, and single-particle spectra further demonstrate the coupling between hyperon shell filling and nuclear structure.