Then, select ‘Links and Images’ in the menu on the left to see a list of files or objects that are using RGB colours. Images will need to be opened in an image editor like Adobe Photoshop, converted to CMYK and then saved. Any imported files will also need opening in their original software, changing to CMYK and resaving. As a "test", I copied the AI RGB file and pasted it into a Photoshop Adobe RGB document, On-screen the AI file matched the PSD file side-by-side (so far). In Photoshop, I went to Mode>CMYK and the colors "slightly" shifted to a less saturated version (as expected), but totally usable for print (perceptually the same for most people without

Testing on command line shows me that convert src.jpg -colorspace srgb out.jpg produces an image with bad colours, but convert src.jpg -profile AdobeRGB1998.icc -colorspace srgb out.jpg produces an image with good colours, and an 'icc' profile visible in identify -verbose output. I'm still playing with different ImageMagick versions, and cmd

No, none of this makes any sense. CMYK is a device-dependent color space and arbitrarily converting CMYK colors to RGB serves no purpose, as even if they were created with a specific color profile/ output device in mind, a different device (printer or whatever) would still interpret it differently and mix up the inks. that is the whole point.
When you convert to sRGB, Photoshop maps all of the out-of-gamut colors to the closest in-gamut colors. This can result in a loss of color saturation and may increase contrast. You can convert an image to sRGB in Photoshop by going to Edit > Convert to Profile and choosing sRGB from the drop-down menu. You can also choose Convert to Profile
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convert rgb to cmyk without losing color photoshop