Braided tangent vector-field equations for quantum orbits

Let $A_{0,q}^c$ be the braided coordinate algebra, with braided coadjoint vector fields $U_i^q$ and quadratic basis elements $f_{\beta,i}(q)$ as defined above. The corresponding relations are obtained from the classical equations by replacing each $U_i$ with $U_i^q$ and each $f_{\beta,i}$ with $f_{\beta,i}(q)$.

Braided tangent-field conjecture. Equations (4) hold if we replace $U_i$ by $U_i^q$ and $f_{\beta,i}$ by $f_{\beta,i}(q)$.

This statement is presented as the assertion that must be proved in order to justify the definition of braided tangent vector fields. The supplied text gives no resolution, proof, or counterexample.