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：研究者的成功指数现今大多通过Hirsch指数（$h$）来衡量。我们最近的精确论证表明，在统计上$h \sim \sqrt {N_c} \sim \sqrt {N_p}$，其中$N_p$和$N_c$分别代表研究者的论文总数和总被引次数。这一结果暗示，每篇论文的平均被引次数（$N_c/N_p$）以及$h$本身，都是依赖于研究者所属社群或网络的统计数值（邓巴数）。在此，我们扩展先前的观察，表明成功的迹象并非由总被引次数$N_c$反映，而是由论文间被引次数的差异程度体现。具体而言，我们揭示：对于非常成功的作者，其Gini指数（$g$，衡量各论文被引次数的平均不均衡性）和Kolkata指数（$k$，表示前$1 - k$比例的论文所获得的总被引次数占比；$k = 0.80$对应帕累托80/20法则）的年际变化会彼此趋近，达到$g = k \simeq 0.82$。这一数值标志着其论文统计特性进入（或脱离）自组织临界（SOC）状态的前兆。通过分析三十位成功科学家在谷歌学术中完整记录的全部论文被引统计数据，我们发现：其中极为成功者（主要为诺贝尔奖得主、斯坦福高被引排名学者等）的$g$与$k$会达到并徘徊在$g = k \simeq 0.82$这一基准附近（先略高于，后略低于该值）；而其他研究者的$g$与$k$则始终低于该基准。此外，我们还发现，对于所有低于SOC基准值（0.82）的$k$和$g$，它们满足线性关系$k = 1/2 + cg$，其中$c = 0.39$。