{
  "schema_version": "1.0.0",
  "source": "vibemath",
  "problem_id": "vibemathed:jacobian-conjecture",
  "title": "Jacobian Conjecture",
  "canonical_statement": "Every polynomial map $\\mathbb{C}^n \\to \\mathbb{C}^n$ with constant nonzero Jacobian determinant is invertible, with a polynomial inverse.",
  "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:jacobian-conjecture:event",
      "problem_id": "vibemathed:jacobian-conjecture",
      "type": "disproved",
      "status": "resolved",
      "occurred_at": "2026-07-20T00:00:00.000Z",
      "title": "OfficeChai",
      "summary": "n ≥ 3; plane case open",
      "ai_contribution": "ai_discovered",
      "attempt_ids": [
        "vibemathed:jacobian-conjecture:attempt"
      ],
      "method_family_ids": [
        "vibemathed:jacobian-conjecture:method"
      ],
      "source_assertion_ids": [
        "vibemathed:jacobian-conjecture:assertion"
      ]
    }
  ],
  "attempts": [
    {
      "id": "vibemathed:jacobian-conjecture:attempt",
      "problem_id": "vibemathed:jacobian-conjecture",
      "model": "Claude Fable 5",
      "provider": "Anthropic",
      "attempted_at": "2026-07-20T00:00:00.000Z",
      "human_collaborators": [
        "Levent Alpöge"
      ],
      "exposure": "unknown",
      "prompt_public": null,
      "outcome": "Alpöge used Fable 5 as a research collaborator to hunt down an explicit counterexample map in three variables, rather than running a generic formal-proof search. The two-variable (plane) case of the conjecture remains open.",
      "failed_routes": [],
      "artifacts": [
        {
          "label": "Gao's self-contained account, generalizing the tangent-sweep mechanism",
          "url": "https://arxiv.org/abs/2608.00222",
          "kind": "paper",
          "license": null
        }
      ],
      "sources": [
        {
          "label": "OfficeChai",
          "url": "https://officechai.com/ai/an-anthropic-researcher-says-fable-just-helped-him-disprove-the-85-year-old-jacobian-conjecture/",
          "kind": "primary-mathematical-source",
          "license": null
        },
        {
          "label": "VibeMathed: Jacobian Conjecture",
          "url": "https://vibemathed.com/problem/jacobian-conjecture",
          "kind": "source-assertion",
          "license": "https://vibemathed.com/data-license"
        }
      ],
      "cost_usd": null,
      "independence": "unknown"
    }
  ],
  "verifications": [
    {
      "id": "vibemathed:jacobian-conjecture:verification",
      "problem_id": "vibemathed:jacobian-conjecture",
      "solution_event_id": "vibemathed:jacobian-conjecture:event",
      "level": "independent_expert_verified",
      "mathematical_correctness": "supported",
      "statement_fidelity": "unaudited",
      "peer_review": "none",
      "verifier": "VibeMathed (source-reported label)",
      "verified_at": null,
      "note": "The counterexample is hand-checkable by direct substitution and was independently confirmed by outside mathematicians within hours of posting. Briefly caught in a Wikipedia edit war over whether to record it. No formal peer-reviewed publication yet.",
      "sources": [
        {
          "label": "VibeMathed: Jacobian Conjecture",
          "url": "https://vibemathed.com/problem/jacobian-conjecture",
          "kind": "source-assertion",
          "license": "https://vibemathed.com/data-license"
        },
        {
          "label": "OfficeChai",
          "url": "https://officechai.com/ai/an-anthropic-researcher-says-fable-just-helped-him-disprove-the-85-year-old-jacobian-conjecture/",
          "kind": "primary-mathematical-source",
          "license": null
        }
      ]
    }
  ],
  "sources": [
    {
      "label": "OfficeChai",
      "url": "https://officechai.com/ai/an-anthropic-researcher-says-fable-just-helped-him-disprove-the-85-year-old-jacobian-conjecture/",
      "kind": "primary-mathematical-source",
      "license": null
    },
    {
      "label": "VibeMathed: Jacobian Conjecture",
      "url": "https://vibemathed.com/problem/jacobian-conjecture",
      "kind": "source-assertion",
      "license": "https://vibemathed.com/data-license"
    }
  ],
  "recommended_mode": "replay",
  "recommended_exposure": "method_aware",
  "opportunity_signals": [
    {
      "id": "vibemathed:jacobian-conjecture:signal:replay_ready",
      "problem_id": "vibemathed:jacobian-conjecture",
      "kind": "replay_ready",
      "reason": "A public source and a non-unreviewed verification label support replay triage.",
      "generated_at": "2026-09-13T16:28:40.178Z"
    }
  ],
  "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"
}