Difference between colors with a same rgb value in sRGB space and CIE RGB space

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Could someone tell me why colors with a same rgb value (for example 127, 127, 127) look the exactly same in an image using sRGB space and one using CIE RGB space? Since one is non-linear (with gamma correction) and the other one is linear (without gamma correction), I think they should look kinda different. But image I've created looks exactly the same (I used Photoshop to create the former and for the latter, I tried Photoshop, OpenGL and OpenCV).

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István Ujj-Mészáros On BEST ANSWER

The difference is coming when you are manipulating an image or a color (changing the brightness or the saturation of an image). This is most visible when lowering the saturation of yellow. Try it in Photoshop with RGB and with Lab mode. Do not switch to grayscale mode, because it is using luminance correction, but the saturation slider in the Adjustment>Hue/Saturation menu.

You can also see the difference when playing with my color picker (just scroll down to the full-blown example), which represents colors in the CIE Lch space (it is using CIE Lab in the background).