Quantization conjecture for formal classical dynamical r-matrices

Let $cmathfrak h\to eqcmathfrak g$ be an inclusion of Lie algebras, let $Z\to eq(cmathop{\wedge}^3cmathfrak g)^{cmathfrak g}$, and let a formal classical dynamical $r$-matrix mean a formal $cmathfrak h$-equivariant map $crho:cmathfrak h^*\to eqcmathop{\wedge}^2cmathfrak g$ satisfying the modified classical dynamical Yang--Baxter equation associated to $Z$. A dynamical twist quantization is a formal dynamical twist $J=1+O(chbar)$ satisfying the modified dynamical twist equation for an associator quantizing $Z$ and whose first-order antisymmetrization is $crho$. Quantization conjecture. Any modified formal classical dynamical $r$-matrix admits a dynamical twist quantization. This is the paper's central quantization problem; the source does not provide evidence resolving the conjecture, so its status is left open.