Equality cases in the sharp one-dimensional matrix Lieb–Thirring inequality

We classify all equality cases in the sharp one-dimensional Lieb–Thirring inequality for every finite matrix size and $1/2<\gamma <3/2$. For measurable Hermitian positive semidefinite potentials W with ${\int }_{\mathbb{R}}\mathrm{tr}(W^{\gamma +1/2})<\infty$, equality holds precisely for direct sums, in one constant unitary basis, of scalar one-bound-state solitons and zero channels. The nonzero solitons may have independent scales and centers.