Flatness conjecture for braided symmetric algebras

Let $\mathfrak{g}$ be a reductive Lie algebra, let $V^q$ be a finite-dimensional $U_q(\mathfrak{g})$-module, and let $V$ be its classical limit. The reduced symmetric algebra is $\overline{S(V,r^-)}$. Flatness conjecture. The braided symmetric algebra $S_\sigma(V^q)$ is a flat deformation of $\overline{S(V,r^-)}$. This conjecture would provide a broad class of flat deformations and could help address the quantization of reduced symmetric algebras and other commutative Poisson algebras. The source presents it as an open conjecture; the supplied text gives no resolution.