Garaschuk's conjecture on fractional triangle decompositions

Let $G$ be a graph with $n$ vertices and minimum degree at least $\frac{3}{4}n$. Garaschuk's conjecture. If $n$ is large enough, then $G$ is fractionally $K_3$-decomposable. Fractional triangle decomposability is a relaxation of an actual triangle decomposition, and this conjecture would provide the fractional decomposition threshold needed in approaches to Nash-Williams' conjecture. The source presents it as a conjecture and identifies Garaschuk's result as the best known result towards Nash-Williams' conjecture, so its resolution status should be checked against the cited work.