Strikes me as being very tautological. New names for old.
If something has real, physical existence, it is part of the invariant set. (As I define the invariant set).
I could just as well say so-and-so is a purple people eater (if in fact he/she was) and be equally correct.
Unless the theory can be used to predict a heretofore unknown QM effect (like a new kind of tunneling or whatever), then it’s not covering new ground.
Eddington discussed this type of reasoning in his “The Domain of Physical Science” in which he kind of admits that at some point tautology is all that’s left. An electron is a particle that acts like x,y, and z. So when you see a particle that acts like x, y, and z, then it’s an electron. Not by discovery. By definition!
As you stated above, Bell’s theorem is a rigorous mathematical model. But Bell also responded to Einstein, in as far as Einstein speculated that we simply might not “know enough” to have QM give us a complete answer.
Bells answer was that there is no local hidden variable theory that is compatible with QM. (when he talks “local” he means a theory that fits with relativity). And the proof here is just as rigorous.
I’ll have to wade through “Speakable and Unspeakable in Quantum Mechanics” again and see if I can absorb any more than the last time!
He quotes Penrose's 1989 The Emperor's New Mind extensively. This is an excellent book and full of many good ideas, and Penrose is certainly much smarter than I am, but this is a popular source, and not a peer reviewed article. I highly recommend Penrose over this paper if you want to read something that will make you think.
The essence of the sense in which this theory departs from conventional thinking can be described by this statement, which the author explicitly rejects:
't Hooft says: ‘... we must demand that our model (of nature) gives credible scenarios for a universe for any choice of the initial conditions’.
Unfortunately, I must agree with Nobel Laureate 't Hooft that this is a reasonable expectation, and although I am accused of a "withering scorn" for people who don't sit in "my little holes," I will hazard a guess that there is no physicist living or dead who would disagree with this requirement, except the author of the paper himself.
If you read the paper, pay particular attention to the section on page 9 discussing ontology and also the section on page 16 concerning non-locality, where the rabbit comes fully out of the hat. What the author ultimately wants us to believe is that all reality is embedded in a nowhere dense subset of phase space (think the Cantor Dust.) All of the details of the theory actually developed to a point to be thought-provoking are hidden in a leap of faith that any state constructed that contradicts his theory "probably" aren't in this set because it has measure zero. This is not proved, and he brushes aside the severe constraints that physics already places on admissible states in phase space without comment. Unfortunately for his thesis, these restrictions would make it highly likely that any physically realizable state is indeed in this set. Therefore he can dismiss the consequences of Belle's theorem or any other counter-intuitive result in QM because thought experiments aren't even admissible in his perverse ontology.
As an aside: the Invariance in "Invariant Set" comes about as a result of the fact that this nowhere-dense fractal set has is postulated to have physical invariance under a set of dynamical laws -- which are not specified. Until they are, there is really no "there, there."