Connes' Rigidity Conjecture
Are ICC property (T) groups remembered by their von Neumann algebras - if for such groups, must ? A counterexample refutes Connes' conjecture that these groups are uniquely determined by their group von Neumann algebras.
- Result
- Disproved
- Status
- Candidate (review pending)
- AI contribution
- AI-discovered
- Method
- Construction
- Field
- Operator algebras
- Posed by
- Alain Connes
- Year posed
- 1980
- Years open
- 46y
- Solved
- 2026-08-01
- Model
- Astra (internal preview)
- Vendor
- OpenAI
- Collaborators
- —
- Verification
- Lean-verified
- Publication
- Announced
- Significance
- 45 / 100
- Disclosed cost
- $182
- Wikipedia
- No dedicated article
What the AI did
Generated by an internal version of OpenAI's Astra: per the announcement, the mathematical arguments were produced by the system (roughly 2,000 dollars of compute at Sol API rates across all ten results), humans prepared the manuscripts with the same model, and the model then formalized the argument in Lean. A narrated reasoning walkthrough is published for each result.
Verification
No independent mathematician has checked this yet. Kernel-checked Lean 4 certificate in OpenAI's public ten-proofs repository (Lean 4.32, mathlib, `lake build All`), with an independent Comparator checking route. Statement fidelity and community review of the day-old company announcement remain pending, hence candidate status.
Sources
Related entries
- GeneralizesConnes rigidity (ICC, T)