Polynomial growth conjecture for Vassiliev invariants

A Vassiliev invariant of order $k$ is a knot invariant that vanishes on higher-order differences of knots. Let $v_k$ be any Vassiliev invariant of order $k$, let $K$ be a knot with $n$ crossings, and let $C$ be a constant. Polynomial growth conjecture. There is a constant $C$ such that

$$|v_k(K)|<Cn^k.$$

This conjecture predicts that every finite-type invariant has polynomial growth of degree at most its order as a function of crossing number. The preceding discussion establishes the analogous quadratic bound for the order-two invariant $v_2$ and notes that a similar bound follows for order three from a combinatorial formula; the general assertion remains open in the supplied source.