Is there proof that the exact exchange correlation functional is an analytic function? Mathematics show that some problems cannot be solved analytically. Could this be true for the exact exchange correlation functional?

Most textbooks state that the form of the exact exchange correlation functional is unknown. It is said to be an unknown mathematical object. Does this mean that said functional is an analytical function? And if so, what is the proof that shows that the functional is analytical?
See my colleagues work, it seems to be the answer you want.

http://journals.aps.org/pra/abstract/10.1103/PhysRevA.93.042511