Coupled-soliton decomposition conjecture for affine general linear Lie superalgebra cellular automata

Let $v$ be a coupled soliton. A coupled-soliton decomposition conjecture asserts that there exist positive integers $d$ and $\widetilde{t}$ such that, whenever $w$ is an uncoupled soliton of length at least $d$ and $t>\widetilde{t}$, the state $(T_{\infty})^t(w\otimes u_1^{\otimes d}\otimes v\otimes u_1^{\otimes\infty})$ has the displayed decomposition into uncoupled solitons $\widetilde{v}_1,\ldots,\widetilde{v}_D,\widetilde{w}$ with the stated linear separations and speeds $d_1,\ldots,d_D,d$, and

$$\left\lvert \{\widetilde{v}_j\mid d_j=\ell\}\right\rvert=N_{\ell}(w\otimes u_1^{\otimes d}\otimes v\otimes u_1^{\otimes\infty}).$$

Here $C_j(t)=c_j+(d_j-d_{j-1})(t-\widetilde{t})$, with $d_0=0$ and $d_{D+1}=d$. This formalizes the idea that a coupled soliton separates into uncoupled solitons after collision with a sufficiently long uncoupled soliton.