Good evening!

Recently I have found this article: https://arxiv.org/abs/1610.00022

It tells about a no-go theorem which is considered to rule out several forms of macrorealism. The description of the theorem is on the page 9. As authors say, it implies contradiction between macrorealism and predictions of quantum mechanics.

I had some troubles in understanding of mathematical sense of this theorem. However, I don't ask for explaining the steps of it formulation. But it would be great if someone told me whether this theorem is sufficient to falsify macrorealism or it just provides some conditions where macroscopic objects cannot be considered as classical objects?

My question appeared because I thought that we can rule out macrorealism only empirically, for example, by violating Leggett-Garg inequalities. Also we can put the parallel to Bell's inequalities and their violation ruling out local hidden variables. But the authors of this paper seem to tell that macrorealism is already falsified only by their theoretical assumptions. That is why I was confused. I am sure that I missed something in this theorem, that is why I make wrong conclusions.

So, rephrasing my initial question metaphorically:"Does this theorem really prove that, for example, the moon or the table have not macroscopically definable state while one is not observing them?"

I should mention that my question is not about decoherence, measurement problem etc. it is about concrete theorem.

Thank you in advance!