Quasi-isometric rigidity conjecture for large-type Artin groups

Let $A_\Gamma$ be a large-type Artin group with $\Gamma\neq\Delta_{333}$. A self quasi-isometry of $A_\Gamma$ is a quasi-isometry from $A_\Gamma$ to itself, and $C_\Gamma$ denotes its Cayley complex. A defining graph is star rigid when it has the star-rigidity property used in the source.

Quasi-isometric rigidity conjecture.

1. Every self quasi-isometry of $A_\Gamma$ is at bounded distance from an automorphism of the Cayley complex $C_\Gamma$ if and only if $\Gamma$ is connected and twistless.
2. Every self quasi-isometry of $A_\Gamma$ is at bounded distance from an automorphism of $A_\Gamma$ if and only if $\Gamma$ is connected, twistless and star rigid.

The conjecture seeks a complete description of quasi-isometric rigidity for large-type Artin groups. The source proves the corresponding assertions for substantial classes, including groups admitting suitable twistless hierarchies, but leaves the general case open.