>> Any color perception that we can register is a combination of these three signals.
> Only approximately.
No. That is precise, because three color sensors is all we (well most of us) have available[1].
>> Hence a three-dimensional space.
> Only approximately.
There was no claim of precision or precise matching for the space, only of dimensionality. The point was that it is a three dimensional space, and that's because there are three basic components that span it, the three color signals coming from the three types of cones. And once you have three base vectors, they will span a 3d space (unless co-planar).
So quite the opposite of what the poster I was replying to claimed, which was that the idea of representing human color perception as a "space" is somehow "comical".
> So there are color percepts such as responses to pure wavelengths that can’t be reproduced as combinations of real primaries.
Sure, which is one of the reasons why the matching functions can have negative coefficients for some colors / colorspaces, something that is, er, more difficult with real RGB monitors. Or, as you also noted, you invent primaries that cover the space but go outside of reality. The spaces are mathematical constructs, after all. However they are not arbitrary mathematical constructs. The fact that they are 3d spaces is rooted heavily in reality. And mathematically they are actually all the same space (as distinct from specific regions in that space if you constrain the vector components, for example to range [0,1]).
> In any case, the whole point of TFA is that a space is not an adequate characterization of color percepts, because there is no Riemannian geometry that matches the psychophysical data.
Not really. The article is a bit fuzzy on some of the terminology, but if you read even the abstract closely, it is clear that they are talking about perceptually-uniform color spaces that make a claim about color differences in that space matching perceived color differences, our good old friend ΔE.
https://en.wikipedia.org/wiki/Color_difference
I don't see the paper making such a claim for the more general concept of a color space that does not claim to be perceptually uniform. CIE XYZ for example, does not claim to be perceptually uniform. And isn't.
And once again, it is well-known that "perceptually-uniform" color spaces are only approximate. Always have been. ΔE varies in different regions of the space. It also varies depending on the area of the color swatches[2]. It also varies depending on whether the color is a light source or reflected. (IIRC, CIE Luv performs better for light sources). That these distances don't add is an interesting additional wrinkle, but not surprising, given all the other oddities and also the fact that the color spaces were never intended for having the distances add.
[1] Some people have reduced function in one or more of the cone types, they are color-blind, and some apparently have four types of cones.
https://en.wikipedia.org/wiki/Tetrachromacy
[2] The way those color spaces are tested is to give people swatches with colors that, I think, they are allowed to put next to each other. If they can tell they are different, the ΔE is greater than 1.