{
  "schema_version": "1.0.0",
  "source": "vibemath",
  "problem_id": "vibemathed:non-sofic-groups-exist",
  "title": "Gromov and Weiss's Question on Sofic Groups",
  "canonical_statement": "Is every group sofic - does every group admit approximate finite permutation representations? A central open question of geometric group theory since Gromov introduced soficity: soficity implies Gottschalk's surjunctivity conjecture, Kaplansky's stable finiteness and more, and no non-sofic group was known. An explicit construction now establishes that non-sofic groups exist.",
  "plain_summary": "VibeMathed reports this item as candidate. VibeMath preserves that report as a source assertion and has not independently authored a plain-language mathematical explanation.",
  "current_status": "candidate",
  "solution_events": [
    {
      "id": "vibemathed:non-sofic-groups-exist:event",
      "problem_id": "vibemathed:non-sofic-groups-exist",
      "type": "disproved",
      "status": "candidate",
      "occurred_at": "2026-08-01T00:00:00.000Z",
      "title": "OpenAI: Ten advances in mathematics and theoretical computer science",
      "summary": "answered no: non-sofic groups exist",
      "ai_contribution": "ai_discovered",
      "attempt_ids": [
        "vibemathed:non-sofic-groups-exist:attempt"
      ],
      "method_family_ids": [
        "vibemathed:non-sofic-groups-exist:method"
      ],
      "source_assertion_ids": [
        "vibemathed:non-sofic-groups-exist:assertion"
      ]
    }
  ],
  "attempts": [
    {
      "id": "vibemathed:non-sofic-groups-exist:attempt",
      "problem_id": "vibemathed:non-sofic-groups-exist",
      "model": "Astra (internal preview)",
      "provider": "OpenAI",
      "attempted_at": "2026-08-01T00:00:00.000Z",
      "human_collaborators": [],
      "exposure": "unknown",
      "prompt_public": null,
      "outcome": "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.",
      "failed_routes": [],
      "artifacts": [
        {
          "label": "Manuscripts (ten-proofs paper, PDF)",
          "url": "https://cdn.openai.com/pdf/ten-proofs-oai.pdf",
          "kind": "paper",
          "license": null
        },
        {
          "label": "Lean certificate (NonSoficGroup.lean)",
          "url": "https://github.com/openai/ten-proofs/blob/main/NonSoficGroup.lean",
          "kind": "lean-proof",
          "license": null
        },
        {
          "label": "Reasoning walkthroughs (PDF)",
          "url": "https://cdn.openai.com/pdf/reasoning-walkthroughs.pdf",
          "kind": "transcript",
          "license": null
        }
      ],
      "sources": [
        {
          "label": "OpenAI: Ten advances in mathematics and theoretical computer science",
          "url": "https://openai.com/index/ten-advances-in-mathematics/",
          "kind": "primary-mathematical-source",
          "license": null
        },
        {
          "label": "VibeMathed: Gromov and Weiss's Question on Sofic Groups",
          "url": "https://vibemathed.com/problem/non-sofic-groups-exist",
          "kind": "source-assertion",
          "license": "https://vibemathed.com/data-license"
        }
      ],
      "cost_usd": 182,
      "independence": "unknown"
    }
  ],
  "verifications": [
    {
      "id": "vibemathed:non-sofic-groups-exist:verification",
      "problem_id": "vibemathed:non-sofic-groups-exist",
      "solution_event_id": "vibemathed:non-sofic-groups-exist:event",
      "level": "lean_verified_statement_audited",
      "mathematical_correctness": "supported",
      "statement_fidelity": "audited",
      "peer_review": "none",
      "verifier": "VibeMathed (source-reported label)",
      "verified_at": null,
      "note": "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": [
        {
          "label": "VibeMathed: Gromov and Weiss's Question on Sofic Groups",
          "url": "https://vibemathed.com/problem/non-sofic-groups-exist",
          "kind": "source-assertion",
          "license": "https://vibemathed.com/data-license"
        },
        {
          "label": "OpenAI: Ten advances in mathematics and theoretical computer science",
          "url": "https://openai.com/index/ten-advances-in-mathematics/",
          "kind": "primary-mathematical-source",
          "license": null
        }
      ]
    }
  ],
  "sources": [
    {
      "label": "OpenAI: Ten advances in mathematics and theoretical computer science",
      "url": "https://openai.com/index/ten-advances-in-mathematics/",
      "kind": "primary-mathematical-source",
      "license": null
    },
    {
      "label": "VibeMathed: Gromov and Weiss's Question on Sofic Groups",
      "url": "https://vibemathed.com/problem/non-sofic-groups-exist",
      "kind": "source-assertion",
      "license": "https://vibemathed.com/data-license"
    }
  ],
  "recommended_mode": "verify",
  "recommended_exposure": "result_only",
  "opportunity_signals": [
    {
      "id": "vibemathed:non-sofic-groups-exist:signal:verify_now",
      "problem_id": "vibemathed:non-sofic-groups-exist",
      "kind": "verify_now",
      "reason": "The source labels this result as a candidate; verification should precede reuse.",
      "generated_at": "2026-09-13T16:28:40.178Z"
    }
  ],
  "uncertainties": [
    "The source status is candidate and must not be represented as solved.",
    "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"
}