that we propose to implement to improve the quality of the paper, based on the four reviews

We first would like to thank the reviewers for their insightful comments and suggestions. F oreword: This paper is framed as a methodological and theoretical contribution, with simple experimental validation. There is in particular no specific ethical concern with this paper - something we will add in a "Broader Impact" section. The uniqueness is only proven for the linear system. We will add one sentence along this line.