I haven’t read through the whole thing (28 pages is an awfully long paper, especially for a supposed “smoking gun”), but that last pair of figures comparing their data to both a Newtonian and a MOND model shows the data not particularly fitting either. The data might fit the MOND model slightly better, but then, an extra fitting parameter will always improve a fit. The fact that neither one is particularly close, though, leads me to suspect that there’s some fundamental problem with their modeling.
I realize this is an old post, but both complex numbers and quaternions are associative. Complex numbers are commutative, but quaternions are not. Octonions are neither commutative nor associative.
Late to the party here, and I haven’t had a chance to read the paper in detail, but my initial take is to be highly skeptical. The original raw data is very far from actually being a telltale source of information on MOND, so they must send the data through some serious meat grinders. Some of the many, many grindy steps along the way are… bold, and I would expect to see more tests showing that the methodology is even robust. Of note, this same original data set has been analyzed by others with the same goal (MOND v. Newton), and when they use their own particular sequence of meat grinders, they end up seeing no tension with Newtonian gravity.
If you know what “code smell” means in computing, then I would borrow that concept here and say that there’s way more “method smell” present here than I would want to see in a paper suggesting something as fundamental as “our understanding of gravity is broken”.