Connes' Rigidity Conjecture for ICC Property (T) Groups

Precise statement

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 $\Gamma_1$ and $\Gamma_2$, both ICC and property (T), are non-isomorphic as groups while $L(\Gamma_1) \cong L(\Gamma_2)$.

The source statement is reproduced for indexing with attribution. Mathematical correctness requires domain-expert or mechanical review. VibeMath has not independently audited statement fidelity, correctness, priority, or novelty.

What AI did

GPT-5.6 Sol; Codex; Danus

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.

Provider: OpenAI · Prompt public: unknown · Independence: unknown

Verification boundary

unreviewed

arXiv preprint, not yet peer-reviewed. The paper reports Lean 4.32.1 used during the work; the site has not checked that development.

Correctness: unknown · statement fidelity: unaudited · peer review: none

Timeline

1. 2026-08-03

   arXiv:2608.02327 - ICC property(T) groups without W*-superrigidity

   Settles the ICC property (T) case. The paper records that the result was obtained independently of and concurrently with work by OpenAI.

Known method families

construction (source-reported)

Source-reported tools: construction.

Independent: unknown · difference confidence: 0

What remains uncertain

VibeMath has not independently audited the mathematical statement, proof, or novelty claim.

• VibeMath has not independently verified the mathematical claim.
• AI-attempt independence and training-data exposure are unknown unless explicitly documented.
• VibeMath has not independently audited the mathematical statement, proof, or novelty claim.