Theoretical predictions of α- and cluster-decay modes in superheavy nuclei with Z=125

We investigate the [Formula: see text]-decay and spontaneous fission (SF) half-lives of several superheavy nuclei (SHN) with [Formula: see text], spanning the mass range [Formula: see text]. We employed the double-folding model (DFM) and other empirical formulas to compute [Formula: see text]-decay half-lives, validated against experimental data for [Formula: see text] (standard deviation [Formula: see text]). By comparing [Formula: see text]-decay and SF half-lives, we found that isotopes [Formula: see text] survive fission and exhibit predictable [Formula: see text]-decay chains, whereas [Formula: see text] favor fission due to shorter SF half-lives compared to [Formula: see text]-decay. Cluster emissions with atomic numbers [Formula: see text] from 18 SHN isotopes ([Formula: see text]) are examined. The most likely cluster decays, characterized by a lower [Formula: see text] relative to [Formula: see text]-decay, involve isotopes of the elements Cs, I, Sb, Rh, and Ag. These clusters and their daughters exhibit magic or semi-magic neutron/proton numbers, with [Formula: see text] ratios closely aligned to the parent isotope, enhancing decay probability. The DFM excels for [Formula: see text]-decay but struggles with heavy clusters ([Formula: see text]), where Universal Decay Law (UDL) provides more reliable predictions. This work deepens our understanding of SHN stability, offering critical insights into decay modes and nuclear structure, and paving the way for future experimental synthesis of exotic nuclei at the periodic table’s frontier.