Universality or near-universality of citation distributions was found empirically a decade ago but its theoretical justification has been lacking so far. Here, we systematically study citation distributions for different disciplines in order to characterize this putative universality and to understand it theoretically. Using our calibrated model of citation dynamics, we find microscopic explanation of the universality of citation distributions and explain deviations therefrom. We demonstrate that citation count of the paper is determined, on the one hand, by its fitness -- the attribute which, for most papers, is set at the moment of publication. The fitness distributions for different disciplines are very similar and can be approximated by the log-normal distribution. On another hand, citation dynamics of a paper is related to the mechanism by which the knowledge about it spreads in the scientific community. This viral propagation is non-universal and discipline-specific. Thus, universality of citation distributions traces its origin to the fitness distribution, while deviations from universality are associated with the discipline-specific citation dynamics of papers.
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