  In all of science, the authors of publications depend on the knowledge
presented by the previous publications. Thus they "stand on the shoulders of
giants" and there is a flow of knowledge from previous publications to more
recent ones. The dominating paradigm for tracking this flow of knowledge is to
count the number of direct citations, but this neglects the fact that beneath
the first layer of citations there is a full body of literature. In this study,
we go underneath the "shoulders" by investigating the cumulative knowledge
creation process in a citation network of around 35 million publications. In
particular, we study stylized models of persistent influence and diffusion that
take into account all the possible chains of citations. When we study the
persistent influence values of publications and their citation counts, we find
that the publications related to Nobel Prizes i.e. Nobel papers have higher
ranks in terms of persistent influence than that due to citations, and that the
most outperforming publications are typically early works leading to hot
research topics of their time. The diffusion model reveals a significant
variation in the rates at which different fields of research share knowledge.
We find that these rates have been increasing systematically for several
decades, which can be explained by the increase in the publication volumes.
Overall, our results suggest that analyzing cumulative knowledge creation on a
global scale can be useful in estimating the type and scale of scientific
influence of individual publications and entire research areas as well as
yielding insights which could not be discovered by using only the direct
citation counts.

Physics and Society;Digital Libraries;Social and Information Networks