LittleCMS color correction not matching Adobe Acrobat values

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Background

I’m trying to use the littleCMS library to apply an ICC profile color correction in a custom application. I seem to have everything working, but when I try to use adobe acrobat to double-check my color correction the values don’t match and aren’t even all that close.

Test setup:
I have a PDF created in Adobe illustrator that contains a box filled with 100% pure cyan in CMYK color space. No ICC profile is embedded. I use an internal PDF value extraction tool to grab a pixel from this box in the sRGB color space.

Test #1:
My application produces RGB color code: red: 0, green: 176, blue: 240
This perfectly matches Adobe Acrobat’s view of this file when simulating sRGB output (I use the Windows Power Toys color picker to grab the RGB value of a pixel in the box).

Test #2:
In my application, I convert this RGB value to CMYK using the littleCMS library; from the sRGB color space to ICC profile USWebCoatedSWOP.icc (obtained from Adobe here). From this conversion I get the CMYK value: (72%, 13%, 0%, 0%). When I set adobe acrobat to simulate output “US Web Coated (SWOP) v2”, I get the CMYK value: (100%, 27%, 0%, 6%) with the color picker.

Test #3:
Repeated for ICC profile EuroscaleCoated.icc. From littleCMS I get the CMYK value: (78%, 10%, 0%, 0%). When I set adobe acrobat to simulate output “Euroscale Coated v2”, I get the CMYK value: (100%, 29%, 0%, 8%) with the color picker.

I have tried the same test with other ICC profiles as well and they are also not matching each other.

Questions:

Should I expect these two tools to match their color outputs, or am I basing this test on faulty assumptions? Is there a different way I can verify my application’s color correction is properly applying the ICC profile for a particular RGB value?

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