Classifying spaces and geometric obstructions for Artin groups

What OpenAI claims

The Salvetti complex of every finite-rank Artin group is aspherical, proving the Artin K(π,1) conjecture. Arbitrary intersections of its parabolic subgroups are parabolic, proving the Parabolic Intersection Conjecture. An explicit Artin group admits no proper cocompact isometric action on any nonempty proper CAT(0) space. (Lean)

Papers (3)

1. Harmonic heights and the Artin K(pi,1) conjecture

   23 September 2026 · Preprint, not peer reviewed · PDF

   We prove that the standard Salvetti complex of every Artin group with finitely many standard generators is aspherical. This resolves the Artin K(π,1) conjecture in finite rank.

2. An Artin group with no geometric CAT(0) action

   23 September 2026 · Preprint, not peer reviewed · PDF

   We construct an Artin group on 116 generators that admits no proper, cocompact isometric action on a nonempty proper CAT(0) space. This refutes the CAT(0) conjecture for Artin groups.

3. Parabolic intersections in Artin groups

   23 September 2026 · Preprint, not peer reviewed · PDF

   We prove that every intersection of parabolic subgroups of any finite-rank Artin group, with arbitrary finite or infinite Coxeter labels, is parabolic. This resolves the Parabolic Intersection Conjecture affirmatively.

Status

Preprint. The papers have not been independently reviewed. Treat the result as OpenAI's claim until other mathematicians have checked it. If a video exists, it illustrates the statement; it is not the proof.