Scientific impact emerges from citation networks shaped by nonlinear and out-of-equilibrium dynamics. By analyzing over 30 million scientific papers and 1 billion references across disciplines, we uncover a two-phase correlation structure: a long-term assortative regime, where highly cited works reinforce each other, and a short-term antiassortative regime, where transformative papers tend to draw upon under-recognized ideas. To reconcile this paradox, we introduce a single state variable—capacity—which quantifies the residual “originality budget” of prior knowledge. We demonstrate that capacity governs a universal double-exponential relationship with long-term impact, consistent across biology, chemistry, and physics. Building on this empirical regularity, we formulate a stochastic dynamical model coupling novelty erosion with capacity-driven attachment. The model accurately reproduces the observed dual-phase correlations and predicts a critical capacity that maximizes future impact. Furthermore, we show that capacity serves as a robust early indicator of scientific breakthroughs, effectively distinguishing Nobel-Prize-winning papers from the rest. Our results provide a unified theoretical framework for correlated impact dynamics, advancing our understanding of knowledge diffusion and breakthrough emergence in complex evolving networks.

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• Social networks
• Stochastic networks
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