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The key here is the embedded document profile. Numbers are specific to color space. The same visual color will yield different numbers with different document profiles.
In a given file, the embedded profile overrides your working space. But when there is no embedded profile to use, the working space is used.
This means that the info readout uses your working spaces to calculate other modes. So the CMYK readout for an RGB file will be according to your working CMYK.
These will be the same i
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I can see that Photoshop CMYK values are still the same as the original.
Say what? How would that be possible?
Please set the Status Bar to »Document Profile« and post screenshots with the pertinent Panels (Toolbar, Layers, Options Bar, Info, …) visible.
Did you close the file since converting?
Unless the CMYK version is still available (in the History or a back-up) a conversion to those same CMYK-values is close to impossible.
Multiple combinations of CMYK values in a CMYK Color Space can share the same appearance.
Which one is the result of the conversion of the corresponding color in a profiled RGB-image is determined by TAC, GCR (or UCR), Render Intent etc.
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The key here is the embedded document profile. Numbers are specific to color space. The same visual color will yield different numbers with different document profiles.
In a given file, the embedded profile overrides your working space. But when there is no embedded profile to use, the working space is used.
This means that the info readout uses your working spaces to calculate other modes. So the CMYK readout for an RGB file will be according to your working CMYK.
These will be the same if, and only if, the profile you want is the same as your working space for that mode. If not, they won't match.
One more thing: If you have special content in the K channel that is not part of the image, like overprinting text or graphic elements, this will be integrated into RGB data and you need to recreate it from scratch.
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And a CMYK color like 70/0/70/30 will likely come out changed and »dirty«, meaning with a magenta-component in this case, when taking the »round-trip« through an RGB Color Space.