Conversion both ways CMYK<-->RGB and color profiles

[Test Screen Name]

There are no formula for ICC profiles. Each profile contains up to six lookup tables, entirely specific to the profile (and rendering intent). They are usually derived from measurements with colour reading equipment and don't follow any other rules.

[ceyhun_akgun]

There is a logic error here. When CMYK returns RGB again, the COLOR RANGE returns collapsed. Lost vivid colors don't come back. For this reason, it will not work correctly even if there is a Profile.

[TheDigitalDog]

What's the question? 

There are no formula for ICC profiles?

When you convert from RGB to CMYK or back again, there's a Profile Connection Space, usually Lab in 'the middle'. So by the time CMYK comes into play, anything about RGB is gone. Or to put it another way, if you convert CMYK to anything, it's at one point in the conversion (PCS), Lab and anything about black generation is long gone. It's why we have and use Device Link Profiles to convert CMYK to CMYK and black gen can be honored in that process. No PCS. 

Indeed, if you convert RGB to CMYK and back again, colors that may be clipped the first time are indeed gone and nothing can bring that back. 

[D Fosse]

This looks like it has been branched/moved from somewhere else. For what reason is entirely unclear, and I suggest it is moved back to where it came from.

[Test Screen Name]

Certainly, the first post in the thread as it currently stands "There are no formula for ICC profiles. " was a reply, not a question! I think this may be the original: https://community.adobe.com/t5/illustrator/conversion-both-ways-cmyk-lt-gt-rgb-and-color-profiles/td...  The first reply there begins "Hmmmm, and I am guessing there is no simple viewer for those lookup tables?" which seems to be a reply to my reply, now separate and here.