We graphically illustrate the derivation of the characteristic

*c*_{i}(

*r*) crossover values that locate the two tail regimes of

*c*_{i}(

*r*), in particular, the distinguished “peak” paper regime corresponding to paper ranks

*r* ≤

*r** (shaded region). The crossover between two scaling regimes suggests a complex reinforcement relation between the impact of a scientist's most famous papers and the impact of his/her other papers. (a) The

*c*_{i}(

*r*) plotted on log-log axes with

*N* = 278,

*β* = 0.83 and

*γ* = 0.67, corresponding to the average values of the Dataset [A] scientists. The hatched magenta curve is the

*H*_{1}(

*z*) line on the log-linear scale with corresponding

*h*-index value

*h* = 104. The

*r** value for

*c*_{i}(

*r*) is not visibly obvious. (b) We plot on log-linear axes the centered citation profile

*c*_{i}(

*z*) (solid black curve) given by the symmetric rank transformation

*z* =

*r* −

*z*_{0} in Eq. [7]. This representation better highlights the peak paper regime, but fails to highlight the power-law

*β* scaling. (c) We plot the corresponding logarithmic derivative

*χ*(

*z*) of

*c*(

*z*) (solid black curve), which represents the relative change in

*c*(

*z*). The dashed red line corresponds to

, where

is the average value of

*χ*(

*z*) given by Eq. [12]. The values of

, indicated by the solid vertical green lines, are defined as the intersection of

with

*χ*(

*z*) given by Eq. [13]. The regime

corresponds to the best papers of a given author. The hatched blue line corresponds to

which marks the crossover between the

*β* and

*γ* scaling regimes.

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