  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 author's 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 paper's 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
person's 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 paper's
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.
