Polynomial-growth conjecture for Khovanov homology of torus links

Fix an integer $m\geq 2$, a field $\mathbb F$, and let $T(m,n)$ be the $m$-strand torus link. Write $\operatorname{Kh}_{\text{odd/even}}^{k,l}(T(m,n);\mathbb F)$ for its odd or even Khovanov homology in bidegree $(k,l)$.

Polynomial-growth conjecture. The total dimension satisfies

$$\dim_{\mathbb F}\left(\bigoplus_{k,l\in\mathbb Z}\operatorname{Kh}_{\text{odd/even}}^{k,l}(T(m,n);\mathbb F)\right)\leq O\left(n^{\left\lfloor\frac m2\right\rfloor}\right).$$

The paper obtains quadratic bounds in the 4-strand case, motivating the predicted degree $\lfloor m/2\rfloor$ for fixed strand number. Establishing this growth rate for all $m\geq2$ remains open in the supplied text.