Uniqueness conjecture for the submodule series of the Weyl module

Let $G=\operatorname{SO}(2n+1,\mathbb{F})$ over a field $\mathbb{F}$ of characteristic $2$, and let $V_\mathbb{F}(\lambda_k^\circ)$ be the Weyl module containing the submodules

$$0\subset M_0\subset M_1\subset\cdots\subset M_k=V_\mathbb{F}(\lambda_k^\circ),$$

where $M_i=Y_{u_{i+1}}Y_{u_{i+2}}\cdots Y_{u_k}(v^+)$ as in, and where $M_{-1}:=0$. The series satisfies $M_i\cong V_\mathbb{F}(\lambda_i^\circ)$ for $i=0,1,\ldots,k$ and $M_i/M_{i-2}\cong W_i^\circ(\mathbb{F})$ for $i=1,2,\ldots,k$. Uniqueness conjecture. The series of submodules defined as in is the unique series of $G$-submodules of $V_\mathbb{F}(\lambda_k^\circ)$ satisfying these two conditions. The conjecture concerns the uniqueness of the submodule structure established in the paper; it remains open because the authors do not know whether $V_\mathbb{F}(\lambda_k^\circ)$ is rigid as a $G$-module.