The generalized oscillating tableaux–sl(n) web bijection conjecture

Let a generalized oscillating tableau have length $k$ and $n$ parts, with final component $(m,\ldots,m)$ for some $m\in\mathbb{Z}$. Consider $\operatorname{sl}(n)$ webs with $k$ boundary vertices. The generalized oscillating tableaux–sl$(n)$ web bijection conjecture. There is a bijection between these generalized oscillating tableaux and $\operatorname{sl}(n)$ webs with $k$ boundary vertices. This would extend the tableau–web correspondence beyond the $\operatorname{sl}(3)$ setting, where the relevant notions of irreducible and rotation-invariant web bases are not yet available for general $n>3$.