The Vassiliev degree bound for far combinatorial cohomology classes of long knots

Let $H_{d,\text{far}}^i$ denote the submodule of $i$-th cohomology classes in degree $d$ represented by cocycles in the far subcomplex, and let $H^i(\mathcal{K}\setminus\Sigma)$ be the cohomology of the complement of the discriminant in the space of long knots. Vassiliev degree-bound conjecture. The image of the map

$$H_{d,\text{far}}^i \rightarrow H^i(\mathcal{K}\setminus \Sigma)$$

consists of Vassiliev cohomology classes of degree at most $d$. This would relate the combinatorial cochain complex to the Vassiliev filtration on the cohomology of the long-knot space; the supplied text does not state whether the claim has been proved or disproved.