Oh, you're good, no problem. I just needed some breakfast. :)

I agree with everything you've said. There is definitely an element of frustration at not being able to formulate a decent refutation to the content in the paper without it costing me the next year of my life. But yes, this type of legwork is necessary to unlock the next tier of secrets of the universe. It's just likely that only one direction will prove fruitful, when we've already embarked on so many different paths. That need not diminish from the endeavor though.

Here is my problem: if adding more and more particles that will produce a higher number of degrees of freedom should make it more and more localized, how would that work for something like contained electron gas, plasma etc. Where does 'boundary' of one particle set/macroscopic object ends and a new one starts, for the purpose of judging what constitutes as this localized system?

The closest thing I've encountered to this is group renormalization theory. It takes a semi-classical approach, and it's still a nightmare that I never want to revisit. Tying in relativity? Aw, hell no!

Still can't believe you're only 17, dude.