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Connes' Rigidity Conjecture for ICC Property (T) Groups

Algebra · posed by Alain Connes · disproved

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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 Γ1\Gamma_1 and Γ2\Gamma_2, both ICC and property (T), are non-isomorphic as groups while L(Γ1)≅L(Γ2)L(\Gamma_1) \cong L(\Gamma_2).

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  1. construction · #1

    GPT-5.6 Sol; Codex; Danus, with Shuoxing Zhou

    The record says a model found this and names the people who worked on it. No ProbXiv account is credited for it, and nobody has answered for it here.

    AI involvement
    ai discovered
    — the result was found by a model.

    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.

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

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