The CAT(0) conjecture for Artin groups

Theorem 1.1: there is an explicit Artin matrix on 116 generators, with off-diagonal labels in $\{2,3,\infty\}$, whose Artin group admits no proper cocompact isometric action on any nonempty proper CAT(0) space, in any dimension. The group contains the triangle Artin group $T$ with three braid relations, extended by three 40-strand braid blocks and two commuting generators making $T$ a simultaneous centralizer; stable translation lengths force six Euclidean sectors of angle less than $\pi/3$ around a cycle, which a winding-number argument rules out. It does not decide which Artin groups are CAT(0).

Theorem 1.1: there is an explicit Artin matrix on 116 generators, with off-diagonal labels in $\{2,3,\infty\}$, whose Artin group admits no proper cocompact isometric action on any nonempty proper CAT(0) space, in any dimension. The group contains the triangle Artin group $T$ with three braid relations, extended by three 40-strand braid blocks and two commuting generators making $T$ a simultaneous centralizer; stable translation lengths force six Euclidean sectors of angle less than $\pi/3$ around a cycle, which a winding-number argument rules out. It does not decide which Artin groups are CAT(0).