A fair assignment of credit for multi-authored publications is a long-standing issue in scientometrics. In the calculation of the $h$-index, for instance, all co-authors receive equal credit for a given publication, independent of a given authors contribution to the work or of the total number of co-authors. Several attempts have been made to distribute the credit in a more appropriate manner. In a recent paper, Hirsch has suggested a new way of credit assignment that is fundamentally different from the previous ones: All credit for a multi-author paper goes to a single author, the called ``$alpha$-author, defined as the person with the highest current $h$-index not the highest $h$-index at the time of the papers publication) (J. E. Hirsch, Scientometrics 118, 673 (2019)). The collection of papers this author has received credit for as $alpha$-author is then used to calculate a new index, $h_{alpha}$, following the same recipe as for the usual $h$ index. The objective of this new assignment is not a fairer distribution of credit, but rather the determination of an altogether different property, the degree of a persons scientific leadership. We show that given the complex time dependence of $h$ for individual scientists, the approach of using the current $h$ value instead of the historic one is problematic, and we argue that it would be feasible to determine the $alpha$-author at the time of the papers publication instead. On the other hand, there are other practical considerations that make the calculation of the proposed $h_{alpha}$ very difficult. As an alternative, we explore other ways of crediting papers to a single author in order to test early career achievement or scientific leadership.
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