Response: Commentary: Is the moon there if nobody looks? Bell inequalities and physical reality

Abstract: We reject unjustified criticism of our published article [2209.07992] by Gill and Lambare [arXiv:2211.02481, arXiv:2208.09930]. They completely misinterpret the content and conclusions of this article. They construct a counterfactual probabilistic model in which random variables representing outcomes of four experiments performed using incompatible experimental settings are jointly distributed. Thus, CHSH inequalities trivially hold for all finite samples generated by their model. Their model defines a probabilistic coupling for our model describing only the raw data from Bell tests. The existence of this coupling does not invalidate the derivation of the contextual probabilistic model describing the final data from Bell tests. Only these final data are used to test Bell inequalities. Inequalities cannot be derived because our model violates statistical independence. Our contextual model allows to explain in a local and causal way the violation of inequalities and the apparent violation of no-signaling reported in these experiments.