Fig. 1.

Quantifying cumulative reputation measures and citation dynamics. (A and B) Growth trajectories of the cumulative publications $N\prime \left(t\right)$ and citations $C\prime \left(t\right)$, appropriately rescaled to start from unity in each ordinate. The characteristic $\overline{\alpha }$ and $\overline{\zeta }$ exponents shown in each legend are calculated over the growth phase of the career. The mathematicians [E] have distinct career trajectories, with $\overline{\alpha }\approx 1$ because collaboration spillovers via division of labor likely play a smaller role in publication rate growth. See SI Appendix, Tables S1–S9, for ${\alpha }_i$ and ${\zeta }_i$ values calculated for individual careers. (C) Relation between ${\tau }_{1/2}$ and cumulative citations $c_p$. (D) PA dynamics with $\pi \approx 1$ break down for $c<c_{\times }$. The reputation effect provides a citation boost above the baseline PA citation rate attributable to $c_p\left(t\right)$ only.