Universal characteristic-zero quasi-isomorphism conjecture for plumbing DG-algebras

Let $\Gamma$ be any tree, let $\mathscr{B}_\Gamma$ be the DG-algebra arising from the plumbing construction, and let $\mathscr{G}_\Gamma$ be the corresponding Ginzburg DG-algebra. Universal quasi-isomorphism conjecture. If $\mathbb{K}$ is a field of characteristic zero, then there is a quasi-isomorphism of DG-algebras

$$\mathscr{B}_\Gamma \simeq \mathscr{G}_\Gamma.$$

For Dynkin trees of types $A_n$ and $D_n$, the relevant quasi-isomorphism is established under the characteristic conditions described in the paper; the assertion for arbitrary trees, including non-Dynkin cases, remains open.