sRGB profile comparison

sRGB has bugged me from the start, since it's not even clear to me which actual matrix to use to convert between linear sRGB colors and XYZ colors. I count at least 3 different matrices in IEC 61966-2-1, each of which I have seen different people ascribe to as the true version:

1. The matrix implied by the reference primaries in Table 1: [X; Y; Z] = [506752/1228815, 87098/409605, 7918/409605; 87881/245763, 175762/245763, 87881/737289; 12673/70218, 12673/175545, 1001167/1053270]*[R; G; B].

2. The matrix in section 5.2: [X; Y; Z] = [1031/2500, 447/1250, 361/2000; 1063/5000, 447/625, 361/5000; 193/10000, 149/1250, 1901/2000]*[R; G; B].

3. The inverse of the matrix in section 5.3: [X; Y; Z] = [248898325000/603542646087, 71938950000/201180882029, 36311670000/201180882029; 128304856250/603542646087, 143878592500/201180882029, 14525360000/201180882029; 11646692500/603542646087, 23977515000/201180882029, 191221850000/201180882029]*[R; G; B].

The distinction starts to matter for 16-bit color. The CSS people seem to take the position that the matrix implied by primaries is the true version, but meanwhile, the same document's Annex F (in Amd. 1) seems to suggest that the 5.2 matrix is the true version, and that the 5.3 matrix should be rederived to the increased precision. There's no easy way to decide, as far as I can tell.

Meanwhile, I agree with the author that the ICC's black-point finagling in their published profiles has not helped with the confusion over what exactly sRGB colors are supposed to map to.

It is a rabbit hole. I just checked the latest release of GiMP (3.2.4). The "GiMP built-in sRGB" profile is supposed to be a functional match to the ArgyllCMS sRGB color space – the true sRGB profile according to the addendum in the above profile comparison.

But if I embed it in a photo and then open the photo in GraphicConverter, it shows up as "sRGB IEC61966-2.1", which to my understanding is identical to Apple’s sRGB Color Space Profile.icm.

But that's an sRGB v2 profile. Should I download and use a v4 profile instead? Or download the ArgyllCMS sRGB.icm [1] and convert all photos to it? Or just select the Apple default sRGB profile everywhere?

I'm not a pro and don't have a calibrated display, but it annoys me when photos I upload online look vastly different in my browser than they look in my editing software on the same display.

[1] https://argyllcms.com/icclibsrc.html

I would have loved to have found this page back when I was adapting some PDF-generating program to conform to PDF/A (which requires a colour profile in some cases). I found several sRGB profiles and could see that they were different, but knowing almost nothing about them I just chose the one that seemed to be from the most authoritative source (I forgot which). This page must have existed then, actually.

From 2012, updated 2015 it says. Would have been interesting with a recent update to compare.

Wow I'm glad I'm not a graphic designer. My head hurts just trying to understand this. I just pick the colours that look good to me