Based on some analytic structural properties of the Gini and Kolkata indices for social inequality, as obtained from a generic form of the Lorenz function, we make a conjecture that the limiting (effective saturation) value of the above-mentioned indices is about 0.865. This, together with some more new observations on the citation statistics of individual authors (including Nobel laureates), suggests that about $14\%$ of people or papers or social conflicts tend to earn or attract or cause about $86\%$ of wealth or citations or deaths respectively in very competitive situations in markets, universities or wars. This is a modified form of the (more than a) century old $80-20$ law of Pareto in economy (not visible today because of various welfare and other strategies) and gives an universal value ($0.86$) of social (inequality) constant or number.Comment: Accepted for publication in Physica A