Soliton content identity conjecture for affine general linear Lie superalgebra cellular automata

Let $v=v_1\otimes v_2\otimes\cdots\otimes v_{\mathfrak{d}}\in(B^{r,1})^{\otimes\mathfrak{d}}$ be a soliton. For each factor $v_j$, let $k_j$ be the value of $k$ assigned by the preceding speed theorem. A soliton content identity conjecture asserts that

$$\sum_{j=1}^{\mathfrak{d}}(r+1-k_j)=\sum_{\ell=1}^{\infty}\ell N_{\ell}(v\otimes u^{\otimes\infty}).$$

The identity proposes that the sum of the factor contributions $r+1-k_j$ equals the weighted total soliton content measured by the conserved quantities $N_{\ell}$. It is stated as a generalization of the preceding proposition and is not proved in the supplied text.