Here you go – don’t know if this is the distance out you want to go…
10745_proximalshader2.c4d.zip
with the proximal as a layer mask it needs to go in between the two shaders it’s masking (really it’s only masking the bottom shader out close to the source).
The settings in the proximal all make a massive difference – to see what’s happening turn off the other two layers (stripes and color) and set the proximal to Normal.
Try different Functions Linear and Smooth seem the best here but Square and Cubic could be good (the others don’t make any sense in this application but try them).
Blend mode in here doesn’t make much difference as long as it’s not Exclusion.
Distance – says % but it’s actually units (they keep it % because in polygon radius mode it does mean % – the help says 100% means 100m but that’s old and in your case where the scene scale is in centimeters it means 100cm). So your End distance needs to be pretty big.
Intensity will force more whiteness close to the object (camera in this case) but will also shorten the ramp from white to black (which when used as a Layer Mask shortens the blend distance).
Function, Start/End distance, Intensity values are where you are going to get results with this set up, just adjust them until you get the fade you need.