If in one collection, one has different mixes of 4 fixed dyes or pigments which each respond to the light in a particular way, then, the way the result responds to different light sources should be in a particular 4d space, while more generally pigments could have the lighting->appearance function be a point in a larger space which that 4D space is a subset of, right?

I don’t particularly know what I’m talking about in this comment, but it seems to me like it should be right..

Though, even if what I said is right, there’s still the question of whether a person could reasonably learn to recognize whether such a response function (“response function” is not some technical term that I know. If it is a technical term, it is likely I’m using it wrong. I’m just using it as a description of the function from lighting to apparent color.) is from such a 4D subspace or not.

Based on a video I saw, I suspect that in some cases, yes, but in general idk. How often would the function be very close to something that is in the 4d subspace but isn’t quite?

I imagine a machine could do it easily.

Assuming you have a cheap way of producing light of a variable wavelength? Do we have such a thing? I think electron vibrating lasers (Idr the proper name for them) have a tunable wavelength, but I imagine those are expensive, and also probably something that isn’t a laser would be preferable.

However, as you say, a pigment colour has high dimensional properties - the spectral response. As others have mentioned this determines how it impacts on the observed/perceived colour, depending in the spectral response of the light it reflects.