{
  "schema_version": "1.0.0",
  "source": "vibemath",
  "problem_id": "vibemathed:connes-rigidity-icc-property-t",
  "title": "Connes' Rigidity Conjecture for ICC Property (T) Groups",
  "canonical_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 $L(\\Gamma_1) \\cong L(\\Gamma_2)$.",
  "plain_summary": "VibeMathed reports this item as resolved. VibeMath preserves that report as a source assertion and has not independently authored a plain-language mathematical explanation.",
  "current_status": "resolved",
  "solution_events": [
    {
      "id": "vibemathed:connes-rigidity-icc-property-t:event",
      "problem_id": "vibemathed:connes-rigidity-icc-property-t",
      "type": "disproved",
      "status": "resolved",
      "occurred_at": "2026-08-03T00:00:00.000Z",
      "title": "arXiv:2608.02327 - ICC property(T) groups without W*-superrigidity",
      "summary": "Settles the ICC property (T) case. The paper records that the result was obtained independently of and concurrently with work by OpenAI.",
      "ai_contribution": "ai_discovered",
      "attempt_ids": [
        "vibemathed:connes-rigidity-icc-property-t:attempt"
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      "problem_id": "vibemathed:connes-rigidity-icc-property-t",
      "model": "GPT-5.6 Sol; Codex; Danus",
      "provider": "OpenAI",
      "attempted_at": "2026-08-03T00:00:00.000Z",
      "human_collaborators": [
        "Shuoxing Zhou"
      ],
      "exposure": "unknown",
      "prompt_public": null,
      "outcome": "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.",
      "failed_routes": [],
      "artifacts": [],
      "sources": [
        {
          "label": "arXiv:2608.02327 - ICC property(T) groups without W*-superrigidity",
          "url": "https://arxiv.org/abs/2608.02327",
          "kind": "primary-mathematical-source",
          "license": null
        },
        {
          "label": "VibeMathed: Connes' Rigidity Conjecture for ICC Property (T) Groups",
          "url": "https://vibemathed.com/problem/connes-rigidity-icc-property-t",
          "kind": "source-assertion",
          "license": "https://vibemathed.com/data-license"
        }
      ],
      "cost_usd": null,
      "independence": "unknown"
    }
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    {
      "id": "vibemathed:connes-rigidity-icc-property-t:verification",
      "problem_id": "vibemathed:connes-rigidity-icc-property-t",
      "solution_event_id": "vibemathed:connes-rigidity-icc-property-t:event",
      "level": "unreviewed",
      "mathematical_correctness": "unknown",
      "statement_fidelity": "unaudited",
      "peer_review": "none",
      "verifier": "VibeMathed (source-reported label)",
      "verified_at": null,
      "note": "arXiv preprint, not yet peer-reviewed. The paper reports Lean 4.32.1 used during the work; the site has not checked that development.",
      "sources": [
        {
          "label": "VibeMathed: Connes' Rigidity Conjecture for ICC Property (T) Groups",
          "url": "https://vibemathed.com/problem/connes-rigidity-icc-property-t",
          "kind": "source-assertion",
          "license": "https://vibemathed.com/data-license"
        },
        {
          "label": "arXiv:2608.02327 - ICC property(T) groups without W*-superrigidity",
          "url": "https://arxiv.org/abs/2608.02327",
          "kind": "primary-mathematical-source",
          "license": null
        }
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  "sources": [
    {
      "label": "arXiv:2608.02327 - ICC property(T) groups without W*-superrigidity",
      "url": "https://arxiv.org/abs/2608.02327",
      "kind": "primary-mathematical-source",
      "license": null
    },
    {
      "label": "VibeMathed: Connes' Rigidity Conjecture for ICC Property (T) Groups",
      "url": "https://vibemathed.com/problem/connes-rigidity-icc-property-t",
      "kind": "source-assertion",
      "license": "https://vibemathed.com/data-license"
    }
  ],
  "recommended_mode": "verify",
  "recommended_exposure": "result_only",
  "opportunity_signals": [
    {
      "id": "vibemathed:connes-rigidity-icc-property-t:signal:watch_only",
      "problem_id": "vibemathed:connes-rigidity-icc-property-t",
      "kind": "watch_only",
      "reason": "Current public evidence does not meet the default replay threshold.",
      "generated_at": "2026-09-13T16:28:40.178Z"
    }
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  "uncertainties": [
    "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."
  ],
  "generated_at": "2026-09-13T16:28:40.178Z"
}