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Sorry for the necroposting, but I spent this month trying to reread everything possible to understand what I was missing, and unfortunately the situation has improved very little. I realized that actually the missing part in my mind is contained in...
Thanks a lot, this was exactly the problematic point I was trying to explain. It is not a trivial procedure but is overlooked as taken for granted in the papers, causing many problems of understanding.
> 16-cell honeycomb that provides you with coordinates How? If there is an arbitrariness to obtain the coordinates, and it is not possible to obtain it directly from the topology, it is a huge problem. I believe that the use of lattice...
If I understand correctly this goes to think of spin as a quantum measurement already, but there are spin measurements with a certain result (for example a $\hat{\sigma}_z$ on an electron with spin status $\left| \frac{1}{2}, \pm \frac{1}{2}\right>$....