Evolution of scaling behaviors embedded in sentence series from A Story of the Stone

The novel entitled A Story of the Stone provides us precise details of life and social structure of the 18th century China. Its writing lasted a long duration of about 10 years, in which the author's habit may change significantly. It had been published anonymously up to the beginning of the 20th century, which left a mystery of the author's attribution. In the present work we focus our attention on scaling behavior embedded in the sentence series from this novel, hope to find how the ideas are organized from single sentences to the whole text. Especially we are interested in the evolution of scale invariance to monitor the changes of the author's language habit and to find some clues on the author's attribution. The sentence series are separated into a total of 69 non-overlapping segments with a length of 500 sentences each. The correlation dependent balanced estimation of diffusion entropy (cBEDE) is employed to evaluate the scaling behaviors embedded in the short segments. It is found that the total, the part attributed currently to Xueqin Cao (X-part), and the other part attributed to E Gao (E-part), display scale invariance in a large scale up to 103 sentences, while their scaling exponents are almost identical. All the segments behave scale invariant in considerable wide scales, most of which reach one third of the length. In the curve of scaling exponent versus segment number, the X-part has rich patterns with averagely larger values, while the E-part has a U-shape with a significant low bottom. This finding is a new clue to support the attribution of the E-part to E Gao.