Decidability of the word problem for general Artin groups

Establish whether the word problem is decidable for arbitrary Artin groups A(Γ); specifically, determine whether there exists an algorithm that, given a word over the standard generators of A(Γ), decides whether it represents the identity element for every Artin group.

Background

Artin groups form a broad class that includes braid groups and right-angled Artin groups. While many specific families (e.g., finite type Artin groups) have positive algorithmic results, a general decision procedure for the word problem across all Artin groups is not known. The paper situates this as a longstanding foundational question that remains unresolved even after decades of paper and despite progress for important subclasses.