OK, well I’ve devised a test that does demonstrate at least to some extent the issue we’ve been discussing.
I took a file with a sort of Granger Rainbow that I constructed myself in sRGB in 16-bit mode.
I then converted this to ProPhoto.
I then converted both images to a destination profile (I used a Canson profile so it’s entirely 3rd-party and out of my control). The conversion was perceptual with BPC on in both cases. This is the data that would be sent to the printer: the job of the CMM is done.
I then placed one image above the other as layers in Photoshop and set the upper layer to Difference. I applied a Levels adjustment above the two layers to make the difference more apparent. This is what it looks like:
The test is not conclusive as the differences could be due to rounding errors … or they could be due to the compression of the ProPhoto space to the smaller printer space.
The only conclusive way of doing this, to my mind, is to look at the mapping algorithm … or at the profile mapping using GamutVision or Chromix. This is a bit like asking to see a Black Hole … you can show the maths, you can show the stars twirling around seemingly nothing … but you can’t show the Black Hole. Or at least I can’t for this particular black hole