The $\alpha$-core structure has been constructed to successfully interpret the band spectra of a series of nuclei above the double shell closure, plus the extension to the heavier cluster structure in the actinide region. By refining the binary cluster model, we show that such kind of picture can be applicable to more heavy nuclei, implying that there can exist cluster states in any heavy nuclei. As for superheavy nuclei, the involved cluster, analogous to the heavy particle radioactivity, is allowed to be above $Z>28$ plus the core ${}^{208}\mathrm{Pb}$. In this sense, besides some predictions on energy spectra of cluster states in superheavy nuclei, the very recently reported $2^{+}$ state of ${}^{282}\mathrm{Cn}$ is diagnosed to be not in the ground state rotational band via the present method. During the whole procedure, the uncertainty of the cluster model is determined for the first time, by the nonparametric resampling strategy, to make the whole theoretical results reliable and complete.

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• Cluster models
• Energy levels
• Nuclear structure & decays