Paper gamut check with ColorThink

[francescogola]

Dear friends,
I have a question regarding paper gamut and I'm pretty sure that thanks to your incredible experience I'll finally solve this lack of knowledge.
Please refer to the attached image.
I'm having a bit of fun with ColorThink Pro an I'm analyzing on the 3D Lab space the decomposition of an image already converted in AdobeRGB color space (small square dots) inside the gamut volume of a specific paper (the red volume).
Well, here my probably stupid questions:

1) The pixels outside the red volume are still inside the gamut 2D projection. Does it mean that the paper is able to reproduce that specific color but not at his luminosity?
2) Most of these out of volume pixels are at a very low level of Luminosity. What information is giving to me about the final output? Is telling me that the blacks can't be reproduced so "deep"?
3) According to the colorimetric rendering intent, these pixels should be translated in something inside the red volume..is it right?
4) If yes, why if on ColorThink I use the rendering intent simulation the red volume is somehow deformed/shifted but at the end some pixels remains out of it?

I really hope you can help me!
All the best,

[digitaldog]

Without being able to see the 3D gamut at any angle, it's difficult to answer totally but yes, it appears the colors are out of gamut which is the big issue. Working spaces have vastly different shapes than output color spaces (one's defined using light and is additive, the other subtractive and the paper white plays a role of course. I'd plot this against ProPhoto RGB too. But in the end, you're dealing with the issue of round holes fitting into square pegs. Plus, NO printer can output all of even sRGB (or any RGB working space).
Either rendering intent will move the out of gamut colors into the final destination but differently (clip to boundaries or move other colors as well into the boundaries). What mattes is how the images appear with either kind of rendering intent. ICC profiles don't know anything about images or color in context. You simply need to soft proof each RI and pick the one you visually prefer!

[francescogola]

Thank you very much!
Yes I’m sure the soft proof of RInis the best way in real world..that was more a question from the nerdy side of the moon 
Best!