Unsolvability of deciding a spectral mass gap.

Question

Has anyone read this paper in detail?

https://arxiv.org/abs/1502.04573

I believe that it's indeed unsolvable, but do we have here a genuine mathematical proof?

Comments

I changed the title to remove a misunderstanding in your interpretation of the results. The results are proved mathematically.

But I didn't check all details of the proof. The main reason is that decidability questions of physical problems are without physical interest. Physicists work with real numbers which contain infinite amount of information, though only a few digits are physically certain. Significant gaps are observable and decidable.