Let $\mathbb{Z} \mathcal{K}$ be the free abelian group generated by isotopy class of (framed,) oriented knots in $S^3$. Write $$\mathbb{Z} \mathcal{K} = \mathcal{F}_0 \supset \mathcal{F}_1 \supset\mathcal{F}_2 \supset \cdots $$ for the Vassiliev-Goussarov filtration, ie, $\mathcal{F}_n$ is the subgroup generated by Vassiliev resolutions of singular knots with $\geq n$ crossings.
Question. Are the quotient groups $\mathbb{Z} \mathcal{K}/\mathcal{F}_n$ torsion-free?
Related question. Say that $ \mathbb{Z} \mathcal{C}_n$ is the free abelian group generated by chord diagrams on the circle, and let $4T$ be the subgroup generated by the four-term relation. Are the quotient groups $\mathbb{Z} \mathcal{C}_n/4T$ torsion-free?