Cracking the Stanford top 2%: The mathematical advantage of single-authored papers

The c -index, introduced by Ioannidis and coworkers, is a ubiquitous composite metric for identifying top-cited scientists. In this article, we demonstrate that for an independent researcher, the c -index simplifies into a function of two fundamental variables, the total accumulated citations and the Hirsch index. By applying the fundamental inequality between them, we calculate the minimum requirements to reach a specific c -index threshold, corresponding for example to the value needed to enter the prestigious Stanford top 2% list of a particular scientific subfield. We also derive analytical approximations for the threshold conditions and utilize the 2019–2024 global datasets to reveal a persistent temporal inflation of these baseline requirements. Furthermore, we extend our analysis to incorporate the more realistic macroscopic Hirsch scaling law and also derive threshold conditions for collaborative networks. Ultimately, in this paper we quantify the mathematical penalty on team science compared to the single-author baseline, imposed by the structural architecture of the metric.