These authors argue that consciousness should be based on lossless integration, otherwise the memory traces would be affected each time we remember something. Problem is, this is exactly what happens.

- Jay

As with most papers in this genre, the trouble probably won't be the math. The trouble will be in the interface between the math and the thing it's supposed to be describing.

This is the kind of thing that when I take the outside view about my response, it looks bad. There is a scholarly paper refuting one of my strongly-held beliefs, a belief I arrived at due to armchair reasoning. And without reading it, or even trying to understand their argument indirectly, I'm going to brush it off as wrong. Merely based on the kind of bad argument (Bad philosophy doing all the work, wrapped in a little bit of correct math to prove some minor point once you've made the bad assumptions) I expect it to be, because this is what I think it would take to make a mathematical argument against my strongly-held belief, and because other people who share my strongly-held belief are saying that that's the mistake they make.

Still not wasting my time on this though.

As Douglas_Knight's link points out, the lossless integration model has been falsified experimentally, so the "formulation of consciousness as a lossless integration of information" does not apply to the actual observed consciousness. The math may or may not be interesting in itself, but it has no bearing on whether "sentient robots" are possible. Fortunately, the authors' conclusion is suitably qualified (emphasis mine):

This result implies that if unitary consciousness exists, it cannot be modelled computationally.

This is terrible even by New Scientist standards. I do wish they'd stop writing up random arXiv ramblings as if they'd even passed basic peer review. (Conference proceedings generally haven't.)