8 problems

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 pre…

Let $p$ be any state, and let $T_{\infty}$ be the time-evolution map. A soliton separation conjecture asserts that there exist a positive integer $\widetilde{t}$, solitons…

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…

Let a box-ball system have $n$ blocks, with $Q_k$ balls in the $k$-th block, and suppose the blocks are separated sufficiently so that the asymptotic soliton structure can be ident…

Let $\Phi(n,k)$ have initial configuration $(\mathbf{Y}_i^0)_i$ consisting only of positive solitons. Interchange space and time so that $\mathbf{Y}_i^t$ and $\mathbf{Z}_i^t$ are r…

Finite-carrier conjecture. When only positive solitons occur in $\Phi(n,k)$, the carriers $\mathbf{Z}_i^t$ take values in the finite set $M$. This is intended to express the observ…

Positive solitons are configurations of the cellular automaton $\Phi(n,k)$ in their minimal forms, and a multi-soliton solution is a configuration consisting of several such positi…

Soliton characterization conjecture. The state $p$ corresponds to a soliton of length $\ell$ if and only if