> the spin matrices were built to deal with three spatial axes If I understand correctly, it kinda happened the other way around. First the Pauli matrices were

> the spin matrices were built to deal with three spatial axes If I understand correctly, it kinda happened the other way around. First the Pauli matrices were introduced to explain unexpected degrees of freedom in experimental observations; then the term "spin" was proposed because the operators related to each other in the same way as classical angular momentum operators. See e.g. https://www.sciencedirect.com/science/article/abs/pii/S1355219808000269 https://www.sciencedirect.com/science/article/abs/pii/S13552...