We may disagree about how much progress the results to date represent regarding finite approximations. I’d say they contain conceptual ideas that may be important in a finite setting, but I also expect most of the work will lie in turning those ideas into non-trivial statements about finite settings. In contrast, most of your writing suggests to me that a large part of the theoretical work has been done (not sure to what extent this is a disagreement about the state of the theory or about communication).
Perhaps your instincts here are better than mine! Going to the finite case has indeed turned out to be more difficult than I expected at the time of writing most of the posts you reviewed.
Perhaps your instincts here are better than mine! Going to the finite case has indeed turned out to be more difficult than I expected at the time of writing most of the posts you reviewed.