Color Science differences

Don't :) After few unsuccessful attempts I at last began to understand your 'infinite dimensional spectral densities' (as an infinite set of all possible spectral density functions over entire visible spectrum) - and now you turn my understanding upside down again :(
🙃

The uncertainty principal limits the number of distinguishable measurements that we can make of photons of a given momentum (and thus energy/wavelength) within a locational constraint (such as a pixel). So in fact the spectral density is only infinite if the sensor is infinitely large.

The question is the number of distinguishable data points, which is indeed theoretically limited by the uncertainty principle - and makes the ultimate dimensionality not infinite. In practice, there are plenty on other limits (such as read and shot noise) which come into play well before the uncertainty principle.

IMO Heisenberg uncertainly principle (HUP) does not change anything here - set of visible wavelengths (interval on ℝ) is uncountably infnite and set of overlapping intervals on it (assuming HUP changes points to intervals) is uncountably infinite too.

You thought I'd accept it just because you say so? No chance. It seems I'll have to take you through this.
OK, the uncertainty principle says that we cannot know a both a quantum's location and its momentum to an arbitrary precision. I'm sure that you know the formula, 𝜎𝑥*𝜎𝑝 ≥ ℎ/4𝜋. 𝜎𝑥 is the standard deviation of position, 𝜎𝑝 is the standard deviation of the momentum. The momentum of a photon is 𝑝 = ℎ * 𝜆. Substitute that into the uncertainty equation and we get 𝜎𝑥*𝜎𝜆 = 1/4𝜋. So, what this means is that if we know the location of a photon to some precision (for instance, the space defined by the size of a pixel), then there is a limit to the precision with which we can know its wavelength. So, if there is a fundamental limit to the precision of measurement, there is also a limit to the the range of observations (samples) which can be differentiated. What this means is the the 'space' of observed wavelengths is not in fact infinite as you were suggesting. It is under a classical model, but not under a quantum mechanical model - which is the observable reality. It's the divergence of abstract mathematics from reality.
Not that it really matters, since as I said, more practical considerations limit the range of independent observations which we can make far more than the quantum limits do.

No, it is not. As every observation is probablistical, then probability distributions of single measurements can be imagined as intervals and like I said, there are uncountably many different subintervals on any interval of ℝ. You can't just split wavelengths from 400 to 800nm to fixed set of intervals (say 1nm wide) and say that there are now 401 of possible different resulting values.
Moreover, spectral density is statistical property of big amount of 'incoming' photons, which is not related to observer (sensor). Sure we can record different densities as identical ones, but this doesn't tell that there is only finite or even countable amount of them.

OK, I prefer your mode of discussion (to actually argue your case) to his (just make pronouncements in a kind of argumentum ad sui verecundiam). I missed your earlier reply to this. Yes, I think you're right on the statistics of it. But we've got to the point of dancing angels. The real point is that in any real case we do not need an infinite data set to describe the incoming spectral density functions, because the reality is determined by ability to actually measure something.

Deciding which colour to render each of the three columns is an 'interpretation', and amounts to 'development', albeit a very simplistic one.

I'm getting really pissed off with all this accusing me of sophistry, from you and other people. Neither of those things. The rendering you see on the screen doesn't just happen. Somewhere in the guts of your computer a piece of software decides what will be the hue of each of your 'red', 'blue' and 'green' columns, that's if you don't explicitly do it yourself by assigning RGB values. That's an 'interpretation', even if not yours. The 'method' of arranging the raw data in three columns (a very crude demosaicking) and then going through the aforementioned process of assigning RGB values is 'development'.

This I can agree. In reality we don't need any abstract math at all :)

But to discuss general concepts some kind of abstraction is needed. Like in current talk of metamerism - in light of understanding metamerism in general and possible sources of metameric failures problems with observations uncertainty or sensor technology are largely irrelevant.
Even CFA filters technology related questions are not relevant on first approximation - but to analyse reasons of real metameric failures this becomes important.

What I'm often attempting to do is to create suitable model of real system - model has to be as simple as possible and not principially wrong (this usually means that we can ignore second order or minor effects, but should not redefine first order formulas and concepts). Also I'm aware that my understanding of things may be wrong and it certainly is incomplete, thereby to discuss them I have to present my point and substantiate it - if anyone can refute it on basis of strong arguments, then I see no problem with it.

Unintentional, and I value the feedback. I don't intend to 'put people down' by simply disagreeing with them. If I stop unintentionally making people grumpy it will be a good thing. That's also why I gave feedback about me feeling grumpy. Now you know you can avoid.