The critical role of persistent disruption in advancing science.

Disruptive innovation is an important feature of scientific research. However, increasing evidence in recent years shows that highly disruptive papers are not necessarily milestone works in science and may even receive very few citations. To understand the mechanisms leading to such phenomena, we develop a link disruption metric that quantifies the disruptiveness of each citation link. This metric allows us to investigate disruption at both the reference and citation levels, enabling the development of a two-dimensional framework to evaluate the persistence of disruption caused by a given paper. Surprisingly, we find that papers with high reference disruption can have high citation disruption, meaning that a paper that disrupts previous papers may itself be further disrupted by its later citing papers. We find that persistently disruptive papers (disruptive papers that are not disrupted by citing papers) are more likely to be recognized as award-winning papers and receive high numbers of citations. Finally, we find that papers of larger teams and papers in recent years, though found to have weaker disruption, are more likely to have stronger persistent disruption once they disrupt previous papers.