arXiv:2607.21798v1 Announce Type: new Abstract: The mean-field Heisenberg ferromagnet is a quantum spin model on the complete graph with isotropic spin-1/2 interactions. This non-commuting Hamiltonian is permutation and $\mathsf{SU}(2)$ invariant, and its Gibbs states undergo an $\mathsf{SU}(2)$ sy