Well, it's theory, which is not my strong suit; these are just first impressions on casual perusal. It is not obvious nonsense. It is not completely clear to me what is the advantage over plain Copenhagen-style collapse. It makes no mention of even special relativity - it uses the Schrodinger rather than Dirac equation; but usually extending to Dirac is not very difficult. The approach of letting phases have significance appeals to me on the intuitive level that finds elegance in theories; having this unphysical variable hanging about has always annoyed me. In Theorem 3 it is shown that only the pointer states can maintain a perfect correlation, which is all very well, but why assume perfect correlation? If it's one-minus-epsilon, then presumably nobody would notice for sufficiently small epsilon. Overall, it's interesting but not obviously revolutionary. But really, you want a theorist for this sort of thing.