Scientometric engineering: Revealing spatiotemporal citation dynamics via open eprints

With the ever-increasing speed and volume of knowledge production and consumption, scholarly communication systems have been rapidly transformed into digitised and networked open ecosystems, where preprint servers have played a pivotal role. However, evidence is scarce regarding how this paradigm shift has affected the dynamics of collective attention on scientific knowledge. Herein, we address this issue by investigating the citation dynamics of more than 1.5 million eprints on arXiv, the most prominent and oldest eprint archive. The discipline-average citation history curves are estimated by applying a nonlinear regression model to the long-term citation data. The revealed spatiotemporal characteristics, including the growth and obsolescence patterns, are shown to vary across disciplines, reflecting the different publication and citation practices. The results are used to develop a spatiotemporally normalised citation index, called the $\gamma$-index, with an approximately normal distribution. It can be used to compare the citational impact of individual papers across disciplines and time periods, providing a less biased measure of research impact than those widely used in the literature and in practice. Further, a stochastic model for the observed spatiotemporal citation dynamics is derived, reproducing both the Lognormal Law for the cumulative citation distribution and the time trajectory of average citations in a unified formalism.