Symmetric spectral state-space conjecture for formally real Jordan algebras

Let a state space be a convex set whose states admit spectral decompositions, and call it symmetric when any $n$-frame can be transformed into any other $n$-frame by an affine map of the state space into itself. Symmetric spectral state-space conjecture. Every symmetric spectral state space is either a simplex or can be represented as the set of density elements of a formally real Jordan algebra. The source records a rank-two representation theorem for spin factors and presents this broader classification claim without evidence of resolution.