Connes' Rigidity Conjecture for ICC Property (T) Groups
Connes' rigidity conjecture asks whether an ICC group with Kazhdan's property (T) is determined by its group von Neumann algebra. Disproved for this class: two explicit countable discrete groups and , both ICC and property (T), are non-isomorphic as groups while .
- Result
- Disproved(see note)
- Status
- Resolved
- AI contribution
- AI-discovered
- Method
- Construction
- Field
- Operator algebras
- Posed by
- Alain Connes
- Year posed
- —
- Years open
- —
- Solved
- 2026-08-03
- Model
- GPT-5.6 Sol; Codex; Danus
- Vendor
- OpenAI
- Collaborators
- Shuoxing Zhou
- Verification
- Unreviewed
- Publication
- Preprint
- Significance
- 35 / 100
- Disclosed cost
- —
- Wikipedia
- No dedicated article
What was actually shown
Settles the ICC property (T) case. The paper records that the result was obtained independently of and concurrently with work by OpenAI.
What the AI did
The AI use statement says the construction underlying the main result was found mainly by GPT-5.6 Sol, Codex and the Danus multi-agent research system, under the author's mathematical guidance, with Lean 4.32.1 used alongside.
Verification
arXiv preprint, not yet peer-reviewed. The paper reports Lean 4.32.1 used during the work; the site has not checked that development.
Source
arXiv:2608.02327 - ICC property(T) groups without W*-superrigidity