As for the Introduction, it would have been more pertinent to go into depth on issues strongly related to the focus of the paper.
- Generally, the manuscript contains several stylistic, grammatical, and typographical issues and would benefit from thorough editing and proofreading, with attention to the syntactic structure and lexical choice. The author writes well in general, but there are some issues with grammar and word choice, which need revision.
- The Corollaries 1-3 are very interesting and the proofs straightforward, but it is not evident how they should be considered from an interpretative and applied point of view. As a matter of fact, the useful results achieved by the author in Section 2.1 are poorly discussed.
- I would suggest to collect the proofs in an Appendix at the end of the paper and to expand the description of Sinha et al.’s (2006) KM statistic.
- In Section 4 I got lost among results, often unclearly described.
- The discussion seems lacking in explanation and incomplete. Overall, the discussion section would benefit from conceptual / theoretical expansion and a greater emphasis on why the outcomes of this research are particularly new and important.