Existence of formal twist quantizations for modified dynamical r-matrices

Let $({\mathfrak{g}},t)$ be a finite-dimensional Lie algebra with an invariant tensor $t\in S^2({\mathfrak{g}})^{\mathfrak{g}}$, and let a modified dynamical $r$-matrix mean a solution of the modified classical dynamical Yang–Baxter equation for the relevant base and invariant element. A formal twist quantization is a formal dynamical twist whose classical limit is the given modified dynamical $r$-matrix.

Existence conjecture. Any modified dynamical $r$-matrix admits a formal twist quantization.

This conjecture asserts existence of quantizations beyond the cases established earlier in the paper, including the triangular and abelian-base settings. The supplied text gives no resolution, so its status remains open.