  A central question in science of science concerns how time affects citations.
Despite the long-standing interests and its broad impact, we lack systematic
answers to this simple yet fundamental question. By reviewing and classifying
prior studies for the past 50 years, we find a significant lack of consensus in
the literature, primarily due to the coexistence of retrospective and
prospective approaches to measuring citation age distributions. These two
approaches have been pursued in parallel, lacking any known connections between
the two. Here we developed a new theoretical framework that not only allows us
to connect the two approaches through precise mathematical relationships, it
also helps us reconcile the interplay between temporal decay of citations and
the growth of science, helping us uncover new functional forms characterizing
citation age distributions. We find retrospective distribution follows a
lognormal distribution with exponential cutoff, while prospective distribution
is governed by the interplay between a lognormal distribution and the growth in
the number of references. Most interestingly, the two approaches can be
connected once rescaled by the growth of publications and citations. We further
validate our framework using both large-scale citation datasets and analytical
models capturing citation dynamics. Together this paper presents a
comprehensive analysis of the time dimension of science, representing a new
empirical and theoretical basis for all future studies in this area.
