The spherical-generator characterization of Gelfand and weak Gelfand type

Let $Z_S$ be the additive monoid of highest-weight-vector weights for an irreducible quantum flag manifold $\mathcal{O}_q(G/L_S)$. Say that $Z_S$ is generated by $r$ elements if its minimal generating set has cardinality $r$. Spherical-generator conjecture. For non-exceptional irreducible quantum flag manifolds, $\mathcal{O}_q(G/L_S)$ is of Gelfand type exactly when $Z_S$ is generated by one element, and it is of weak Gelfand type exactly when $Z_S$ is generated by two elements. This reformulates the proposed classification in terms of spherical weights. The source presents it as an alternative conjectural formulation and gives no resolution.