Koraks - it is simply impossible to make or dispense any of those inkjet systems on the premise of actual pigments alone. Not only is it impossible to achieve all the specific colorant hues involved without resorting to organic dyes, but even less would it be possible to get them through those tiny inkjet nozzles. It's hell to do it even with architectural pigments. Inkjet systems don't use
CMYK process colors at all, but a quantity of colorants which involve complex blends. Your allegedly definitive test that dyes aren't present is technically incorrect because you don't sufficiently admit how those dyes are bound to the colorant particles themselves; that's part of the whole R&D process behind it. No dyes come out by themselves, or else the system wouldn't consistently work.
Lakes are indeed a complex topic (the term is derived from lac), but should be differentiated from true pigments. Permanence is a whole other layer to the topic; but as an example, a yellow mono-azo lake like Charles Berger of Richard Kaufman chose might be more permanent than a yellow azo dye, but not as permanent as a true cadmium yellow pigment. Nearly all the most permanent red pigments are toxic; hence nearly all the commercially sold true red colorants are some kind of quinacridone lake. The purest most permanent blues and greens are extremely expensive and somewhat toxic, so the next best thing is thalo colorants, which aren't as pure-hued.
Another problems with inkjet is blacks themselves. Lampblack is not a neutral black at all, and trends purplish if lightened. Mineral blacks, on the other hand, trend greenish. Hence the need for more than one black - the darkest essentially being equivalent to a K printer, and the others deep gray. And this is one of real kinks still needing to be worked out in inkjet, because these often dry at mismatched sheens.
But I can do without your condescending attitude. I've been involved with this for half a century, and was in contact with those in the forefront of advancing pigment technology both in the US and EU right up till the time I retired (most of them are now retired too). The whole question of a true process set of nano-pigments is the still undiscovered holy grail, but there are people working on it on an entirely different premise than anything currently inkjet-oriented.
You are actually way way behind the curve by referring to the kind of pigments used by Ultrastable (Charles Berger) or Galvin Grier. All kinds of R&D is going on, mainly for sake of auto and industrial coatings, but with spinoff potential to other applications as well like color printing is the right colorants can be developed. And yes, pigments are highly ground for sake of dispersion in automatic programmable systems. They have to be. I had accounts with the finest grinders in the world. That's something done on industrial scale, not by mortar and pestle. And you don't find those products in art stores. I made an ultra-fine process set myself simply for experimental testing, but with true pigment printing in mind, not inkjet. But I don't have the time to undertake that kind of printing myself.
Pigment dispersion technology itself can be proprietary and hush-hush in some cases. The kinds of companies are multi-billion dollar enterprises with massive R&D labs. Their job is to come up with endless "what if" formulations, with only a small percentage of those ever likely to see the light of day commercially. But all it can take is one really big home run, just like in all the Biotech and Pharmaceutical R&D around here. Some grad student up at the University gets an idea, then a couple decades later he's a billionaire. And if there is another big seismic change in color printing, taking the place of inkjet in due turn, it will be due to research with something else in its sights all along, as a spinoff of that.
But please don't keep asking me to prove this or that to you, when if you took the time to dig more deeply into all of this, you could find out for yourself. Photrio isn't really the kind of place these things are discussed anyway. And I haven't stated a single thing that isn't common knowledge to the industry itself. I've actually given classes concerning the usage of nano-pigments, and don't see the need to given any longer sermons than I already have simply to convince web jockeys unwilling to do their own homework. There are mountains of patents out there relative to inkjet printing, with only a few of those themselves having actually seen the light of day commercially. The fact is, the mere fact so many mismatched colorants are used in inkjet systems mean that one of its weak points
is inevitable difference fading. At least with Cibachrome, all three of the azo dyes involved faded at the same rate, so no color shift was apparent, until almost the whole print finally crashed.