Recessed brake pivot nut stuck in carbon fork
Please don't hammer it from the front. You risk rotating the nut and completely jamming it in the carbon. 

Keep at it for a few days with penetrating oil. If that doesn't help:

Try to remove the nut by pulling it out from the rear. 
I would suggest finding out what size bolt will fit through the entire nut (perhaps M4). Get a long bolt or piece of threaded rod in this size and slide it through the stuck nut. On the front side, thread on two nuts and a washer (the washer goes between the nuts and the stuck nut).Screw both nuts tightly together.

On the rear side, place a small plate of (ply)wood with a 5mm hole in it. Make sure the block is shaped such that it comfortably rests on the rear of the fork legs/fork crown. Take some time to shape the wood, depending on your fork geometry to avoid any damage.

Thread a washer and nut onto the wood block, and thread on two nuts at the end of the rod again.
Use a wrench to hold the the nut on the wood block, and another wrench to move the two rear nuts to pull out the whole assembly, including your stuck nut.