A manuscript produced by an AI model, released on 1 August 2026 with nine others, claims to disprove Connes's rigidity conjecture, which holds that an ICC group with Kazhdan's property (T) is determined by its group von Neumann algebra. It constructs an infinite family of pairwise non-isomorphic ICC property (T) groups whose group von Neumann algebras are all isomorphic. A Lean certificate accompanies the principal theorem, and the manuscript was prepared by people with the model's help.
Feynman
The message reports a refutation without any of its steps: the isomorphism of algebras is not built, the Lean certificate is unaudited, and the packet holds only rigidity results in which the algebra remembers the group.
06 claims /08 objections /03 of 4 sources cited / lenses: Mechanism, Operational test, Formal model
Each square is an objection. Larger means heavier. Every claim was challenged by at least one lens.
01Every group in the constructed family has Kazhdan's property (T).
02Every group in the family is ICC, so its group von Neumann algebra is a II_1 factor.
03The family is infinite and its groups are pairwise non-isomorphic as abstract groups.
04The group von Neumann algebras of all members are isomorphic to one another as von Neumann algebras, by genuine isomorphisms rather than stable isomorphism, amplification, finite-index passage or a cocycle twist.
05Any two members meet every hypothesis of the conjecture as posed and so refute it, which requires the family to be countable and to avoid every class of property (T) groups already proved determined by its von Neumann algebra.
06The Lean certificate proves the principal theorem as stated, using the standard definitions of property (T), ICC, group von Neumann algebra and isomorphism, with no added axioms, unproved lemmas or extra hypotheses.