In my previous post, i gave some details of the dng/dcp white balance and color calibration process. It's been a while since I looked at the DNG spec but I just revisited it and need to mention a couple of points of clarification on what I said earlier in relation to dng processing in Adobe software:-
after white balance,the Forward matrices are used to convert the camera RGB values to the XYZ space (the Profile Connection Space). These values are then converted to linear RGB Prophoto space which is the working color space if you like.
The LUT I mentioned is based on HSV rather than L*a*b* as I previously indicated. If there is an LUT to be applied, the RGB values are converted to HSV, the LUT is applied and then the values are converted back to linear Prophoto RGB.
It's covered in Sect 6 of the DNG spec document 1.4.0.0.
If L*a*b* editing is set up in Photoshop, I assume the working color space is changed from linear Prophoto to L*a*b* for this function but I don't really know the details of this process.
Dave