As you would know, the arxiv sees several papers every month claiming to have finally explained quantum theory. I would have seen yours in the daily listings and not even read it, expecting that it is based on some sort of fallacy, or on a "smuggled premise" - I mean that the usual interpretation of QM will be implicitly reintroduced (smuggled into the argument) in how the author talks about the mathematical objects, even while claiming to be doing without the Born rule. For example, it is very easy for this to happen when talking about density matrices.

It is a tedious thing to go through a paper full of mathematics and locate the place where the author makes a conceptual mistake. It means you have to do their thinking for them. I have had another look at your paper, and seen a little more of how it works. Since you are here and wanting to promote your idea, I hope you will engage with me even if I am somewhat "lazy", in the sense that I haven't gone through the whole thing and understood it.

So first of all, a very simple issue that you could comment on, not just for my benefit but for the benefit of anyone who wants to know what you're saying. An "observer" is a physical being who is part of the universe. The universe is described by a quantum state vector. The evolution of the state vector is deterministic. How do you get nondeterministic evolution of the observer's state, which ought to be just a part of the overall state of the universe? How do you get nondeterminism of the part, from determinism of the whole?

We know how this works in the many-worlds interpretation: the observer splits into several copies that exist in parallel, and the "nondeterminism" is just an individual copy wondering why it sees one eigenvalue rather than another. The copy in the universe next door is thinking the same thing but with a different eigenvalue, and the determinism applies at the multiverse level, where both copies were deterministically produced at the same time. That's the many-worlds story.

But you have explicitly said that only one branch exists. So how do you reconcile nondeterminism in the part with determinism in the whole?

Second, a slightly more technical issue. I see you writing about the observer as confined to a finite local region of space, into which particles unpredictably enter and scatter. But shouldn't the overall state vector be a superposition of such events? That is, it will be a superposition of "branches" where different particles enter the region at different times, or not at all. Are you implicitly supposing that the state vector outside the small region of space is already "reduced" to some very classical-looking basis?