Quantization of Angular Momentum Under Boosts

[strangerep]

Then remove the D SO(3) rotation?? You're applying the rotation AND its inverse, so of course you end up at the same pauli matrix. This seems like a completely trivial issue of passive vs. active transformations..

You miss the point. The pauli matrices are objects of composite type: each has 1 vector index, and 2 spinor indices. The correct representations of any given physical rotation must be applied to the respective indices simultaneously. The net effect is that, for a single physical rotation, the Pauli matrices remain unchanged.

I am just baffled how this thread became about something so irrelevant..

Well, when understood properly, the point is not irrelevant. Without understanding it correctly, one cannot understand non-relativistic QM with spin.

In any case, it's your thread. You asked questions, then tended to contradict the answers by making incorrect or ill-informed statements -- which others then felt obliged to correct, and so it continued. A number of people have tried to help you in this thread. Those people have helped lots of others here on PF. The common factor in this thread is you, not them.

Which textbook(s) are you working from anyway?