Weak twist conjecture for Artin generating sets

Let $(A,S)$ be an Artin system, with defining graphs $cGamma_S$ and $cGamma_U$ associated to Artin generating sets $S$ and $U$. For an Artin generating set $T$, let $R_T$ denote the reflection set of $(A,T)$, namely the union of the conjugacy classes of the elements of $T$ in $A$. Two defining graphs are twist equivalent when they arise from twist equivalent Artin generating sets.

Weak twist conjecture. If $U\subseteq A$ is an Artin generating set with $R_S=R_U$, then $\Gamma_S$ and $\Gamma_U$ are twist equivalent.

The conjecture is a first step toward the question of whether isomorphic Artin groups necessarily arise from twist-equivalent labelled graphs. The analogous conjecture for Coxeter groups has been disproved, while the Artin-group version remains a proposed rigidity statement; the supplied source does not establish its resolution.