The index of success of the researchers are 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 for 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：研究人员的成功指数现在主要使用Hirsch指数（$h$）来衡量。我们最近的精确论证表明，统计上$h \sim \sqrt{N_c} \sim \sqrt{N_p}$（其中$N_p$和$N_c$分别表示研究人员的论文总数和总被引次数），这意味着每篇论文的平均被引次数（$N_c/N_p$）以及由此推得的$h$是取决于研究人员所属社群或网络的统计数（邓巴数）。我们在此延伸先前观察指出，成功的迹象并非通过总被引次数$N_c$反映，而是体现在论文间被引次数的不平等性上。具体而言，我们发现对于非常成功的作者，其吉尼指数（$g$，衡量论文被引次数的平均不平等程度）和加尔各答指数（$k$，表示前$1-k$比例论文所获总被引次数的比例；$k=0.80$对应帕累托80/20定律）的年度波动会趋近于$g=k\simeq0.82$，这预示着其发表统计特征即将进入（或脱离）自组织临界状态前兆。通过分析三十位成功科学家（来自谷歌学术）整个发表生涯的引文统计数据，我们发现其中极为成功者（多为诺贝尔奖得主、斯坦福最高分引用榜单入选者及少数其他学者）的$g$和$k$值会达到并在$g=k\simeq0.82$阈值附近（先略高于后略低于）波动，而其他人则始终低于该阈值。我们还发现所有低于自组织临界阈值（0.82）的$k$和$g$值均满足线性关系$k=1/2+cg$，其中$c=0.39$。