Strong twist conjecture for Artin generating sets

Let $(A,S)$ be an Artin system, with defining graph $\Gamma_S$. Let $R_S$ be the reflection set of $(A,S)$, namely the union of the conjugacy classes of the elements of $S$ in $A$. An Artin generating set $U\subseteq A$ has defining graph $\Gamma_U$, and $S$ and $U$ are twist equivalent when they are related by a sequence of elementary twists.

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

This is presented as a stronger version of the weak twist conjecture and is intended to address the rigidity of Artin generating sets with the same reflection set. The supplied text gives no evidence that the strong version has been proved or disproved, so its status remains open.