Personally, I contested that with no carbs at all you would get sick pretty quickly.
In the sense of side effects of your body being in a particular state, rather than the classic 'deficiency disease' (scurvy, rickets etc.).
I'd be interested in any decently detailed evidence involving someone's experience of a diet with zero carbs for an extended period.
As opposed to ones like
this where the writer is still eating a lot of carbs, just cutting out bread, pasta and the usual stuff. And then got kinda sick, but that's by the by.
* - going with the mathematical definition of the term