The index of success of the researchers is now mostly measured using the Hirsch index ($h$). Our recent precise demonstration, that statistically $h \sim \sqrt {N_c} \sim \sqrt {N_p}$, where $N_p$ and $N_c$ denote respectively the total number of publications and total citations for the researcher, suggests that average number of citations per paper ($N_c/N_p$), and hence $h$, are statistical numbers (Dunbar numbers) depending on the community or network to which the researcher belongs. We show here, extending our earlier observations, that the indications of success are not reflected by the total citations $N_c$, rather by the inequalities among citations from publications to publications. Specifically, we show that for very successful authors, the yearly variations in the Gini index ($g$, giving the average inequality of citations for the publications) and the Kolkata index ($k$, giving the fraction of total citations received by the top $1 - k$ fraction of publications; $k = 0.80$ corresponds to Pareto's 80/20 law) approach each other to $g = k \simeq 0.82$, signaling a precursor for the arrival of (or departure from) the Self-Organized Critical (SOC) state of his/her publication statistics. Analyzing the citation statistics (from Google Scholar) of thirty successful scientists throughout their recorded publication history, we find that the $g$ and $k$ for very successful among them (mostly Nobel Laureates, highest rank Stanford Cite-Scorers, and a few others) reach and hover just above (and then) below that $g = k \simeq 0.82$ mark, while for others they remain below that mark. We also find that all the lower (than the SOC mark 0.82) values of $k$ and $g$ fit a linear relationship $k = 1/2 + cg$, with $c = 0.39$.

翻译：研究者成功的指标现已主要通过赫希指数（$h$）来衡量。我们近期精确论证，统计学上$h \sim \sqrt {N_c} \sim \sqrt {N_p}$（其中$N_p$和$N_c$分别表示研究者的论文总数和总被引次数），这表明每篇论文的平均被引次数（$N_c/N_p$）及因此的$h$值都是统计量（邓巴数），取决于研究者所属的社群或网络。我们在此扩展先前观察结果，表明成功的迹象并不反映在总被引次数$N_c$上，而是体现在不同论文被引次数的不平等性中。具体而言，对于非常成功的研究者，其基尼指数（$g$，衡量论文被引次数的平均不平等性）和加尔各答指数（$k$，表示被引次数最高的$1 - k$比例论文所获得的总被引占比；$k = 0.80$对应于帕累托80/20法则）的年度变化会趋近于$g = k \simeq 0.82$，这预示着其论文统计达到（或偏离）自组织临界（SOC）状态的前兆。通过分析三十位成功科学家在Google Scholar上完整出版历史中的被引统计数据，我们发现其中非常成功者（多为诺贝尔奖得主、斯坦福高被引学者榜单前列者及少数其他人）的$g$和$k$值会达到并在该$g = k \simeq 0.82$标记附近徘徊（先略高于后略低于），而其他人的$g$和$k$值则始终低于该标记。我们还发现，所有低于SOC标记（0.82）的$k$和$g$值均符合线性关系$k = 1/2 + cg$，其中$c = 0.39$。