It is hard to prove non-existence, but as far as my research goes, there is no carbon frame available for belt drive systems like Gates. My guess is that this is due to the requirement to be able to open and close the frame during belt installation. However, at the same time, carbon frame manufacturers claim that they can tailor a frame's lateral & etc. stiffness by layer density, fibre orientation and the like.
So my question is what is the exact reason why belt drive systems are not available on carbon frames?

...of course, I'd also be happy if my research turns out to be incomplete...