angular momentum - Mathematical reference about spin

I am looking for a reference about a mathematical rigourous treatment of spin. I do not know if what I'm looking for actually exists, so let me get into details.

More precisely, I would like an exposition of spin starting from assumptions, or axioms (for example, of experimental nature) for the behavior of spin (not just $\frac{1}{2}$, but any $m \in \frac{1}{2}\mathbb{N}$) and then a detailed presentation of the model (observables and symmetries) and, if possible (and true), a proof that the model is unique (I am sure that this problem can be formulated as a problem of isomorphism of $SU(2,\mathbb{C})$ representations).

In other words, I would like to find something like this: "in such and such experiments, such thing is supposed to behave like that; we can model it by such Pauli matrices; Theorem: Any such representation is of the form this and this.".