Noncollinear boost obstruction from Pauli products ($A^{\prime }A-(A^{\prime }A{)}^{†}=2i{s}^{\prime }s({\mathbf{n}}^{\prime }\times \mathbf{n})\cdot \mathbf{\sigma }$)

For boost matrices $A=cI+s\mathbf{n}\cdot \mathbf{\sigma }$ and $A^{\prime }=c^{\prime }I+s^{\prime }{\mathbf{n}}^{\prime }\cdot \mathbf{\sigma }$, the Pauli matrix multiplication law gives the displayed anti-Hermitian part. If both rapidities are nonzero and the axes are noncollinear, it cannot vanish, while either lift of a pure boost is Hermitian. Thus an additional Wigner rotation is necessary. A zero boost is a degenerate exception.