Why would you tag a jpeg with ARGB? Jpegs should always be sRGB, because the sRGB gamma curve is better suited to an 8 bit image for general viewing. The ARGB colour space is irrelevant in todays photo workflow, and really should be ignored. Colour spaces in Lightroom are FIXED at Linear ProPhoto in the background, and Melissa RGB in the front GUI. You can NOT change them. Only exports from LrC/ACR can be changed to a smaller colour space. So, in LrC/ACR you ARE working in ProPhoto. If you move an image over to Ps from LrC, Ps needs to be set to ProPhoto as the working space, but you need to switch the Grey Gamma to 1.8 an set that as the default. Working this way, if you save the image in Ps, it looks the same when you view it in LrC, because it's in the LrC working space. Once you finish the image processing, simply export it as a jpeg, converting to sRGB as the output space, and the ACE colour engine will do the conversion for you. The result will be a jpeg in sRGB that looks the same as it did in LrC or Ps. Just forget about ARGB as a working space. As a measure of calbrated monitor colour space it's fine, but you monitor profile has nothing to do with Adobe Internal CM - unless you are softproofing for print.
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