Understanding the statistical laws governing citation dynamics remains a fundamental challenge in network theory and the science of science. Citation networks typically exhibit in-degree distributions well approximated by log-normal distributions, yet also display power-law behavior in the high-citation regime—an apparent contradiction lacking a unified explanation. Here we identify a previously unrecognized phenomenon: The variance of the logarithm of citation counts per unit time follows a power law with respect to time ($t$) since publication, scaling as $t^H$, with $H$ constant. This discovery introduces a new challenge while simultaneously offering a crucial clue to resolving this discrepancy. We develop a stochastic model in which latent attention to publications evolves through a memory-driven process with cumulative advantage, modeled as fractional Brownian motion with Hurst parameter $H$ and volatility. We show that antipersistent fluctuations in attention ($H<1/2$) yield log-normal citation distributions, whereas persistent attention dynamics ($H>1/2$) favor heavy-tailed power laws, thus resolving the log-normal–power-law contradiction. Numerical simulations confirm both the $t^H$ law and the transition between regimes. Empirical analysis of arXiv e-prints indicates that the latent attention process is intrinsically antipersistent ($H\approx 0.13$). By linking memory effects and stochastic fluctuations in attention to broader network dynamics, our findings provide a unifying framework for understanding the evolution of collective attention in science and other attention-driven processes.

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• Collective behavior in networks
• Degree distributions
• Evolving networks
• Network evolution
• Preferential attachment
• Networks & random structures
• Scale free & inhomogeneous networks
• Social networks
• Stochastic networks
• Diffusion & random walks
• Evolving network models
• Preferential attachment models