{
  "schema_version": "1.0.0",
  "source": "vibemath",
  "problem_id": "vibemathed:generalized-vanishing-conjecture-five-variables",
  "title": "The Generalized Vanishing Conjecture",
  "canonical_statement": "Zhao's Generalized Vanishing Conjecture asks whether, for a differential operator with constant coefficients, $\\Lambda^m(P^m) = 0$ for all large $m$ forces $\\Lambda^m(P^m Q) = 0$ for all large $m$.",
  "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:generalized-vanishing-conjecture-five-variables:event",
      "problem_id": "vibemathed:generalized-vanishing-conjecture-five-variables",
      "type": "disproved",
      "status": "resolved",
      "occurred_at": "2026-08-05T00:00:00.000Z",
      "title": "The Generalized Vanishing Conjecture: The Two-Variable Theorem and the First Failing Dimension",
      "summary": "For n <= 2, we proof that the Generalized Vanishing Conjecture holds, and we have a failure at dimension 3 (including a counter-example).\n\nThis improves the original failure at dimension 5.",
      "ai_contribution": "ai_assisted",
      "attempt_ids": [
        "vibemathed:generalized-vanishing-conjecture-five-variables:attempt"
      ],
      "method_family_ids": [
        "vibemathed:generalized-vanishing-conjecture-five-variables:method"
      ],
      "source_assertion_ids": [
        "vibemathed:generalized-vanishing-conjecture-five-variables:assertion"
      ]
    }
  ],
  "attempts": [
    {
      "id": "vibemathed:generalized-vanishing-conjecture-five-variables:attempt",
      "problem_id": "vibemathed:generalized-vanishing-conjecture-five-variables",
      "model": "GPT-5.6 Sol",
      "provider": "OpenAI",
      "attempted_at": "2026-08-05T00:00:00.000Z",
      "human_collaborators": [
        "Alexander Dvorsky",
        "Roy van Rijn"
      ],
      "exposure": "unknown",
      "prompt_public": null,
      "outcome": "The initial paper (Alexander Dvorsky) used \"as an interactive research assistant\": the paper credits it with testing the homogenized five-variable construction, generating computational verification code and locating relevant literature, with all computations and references independently verified afterwards.\n\nA second paper (Roy van Rijn) used OpenAI's Codex to close the conjecture completely. It proofs that the conjecture holds for n <= 2 and fails at dimension 3 (counter-example provided in the paper). Codex monitored/ran several experiments and the human steered the experiments.",
      "failed_routes": [],
      "artifacts": [
        {
          "label": "An Explicit Five-Variable Counterexample to the Generalized Vanishing Conjecture",
          "url": "https://arxiv.org/abs/2608.07338",
          "kind": "paper",
          "license": null
        }
      ],
      "sources": [
        {
          "label": "The Generalized Vanishing Conjecture: The Two-Variable Theorem and the First Failing Dimension",
          "url": "https://zenodo.org/records/21803325",
          "kind": "primary-mathematical-source",
          "license": null
        },
        {
          "label": "VibeMathed: The Generalized Vanishing Conjecture",
          "url": "https://vibemathed.com/problem/generalized-vanishing-conjecture-five-variables",
          "kind": "source-assertion",
          "license": "https://vibemathed.com/data-license"
        }
      ],
      "cost_usd": null,
      "independence": "unknown"
    }
  ],
  "verifications": [
    {
      "id": "vibemathed:generalized-vanishing-conjecture-five-variables:verification",
      "problem_id": "vibemathed:generalized-vanishing-conjecture-five-variables",
      "solution_event_id": "vibemathed:generalized-vanishing-conjecture-five-variables:event",
      "level": "lean_verified_statement_audited",
      "mathematical_correctness": "supported",
      "statement_fidelity": "audited",
      "peer_review": "none",
      "verifier": "VibeMathed (source-reported label)",
      "verified_at": null,
      "note": "The preprints have (as of yet) no independent review. The counterexample can be checked directly, the proof has additional Python calculations and Lean verification.",
      "sources": [
        {
          "label": "VibeMathed: The Generalized Vanishing Conjecture",
          "url": "https://vibemathed.com/problem/generalized-vanishing-conjecture-five-variables",
          "kind": "source-assertion",
          "license": "https://vibemathed.com/data-license"
        },
        {
          "label": "The Generalized Vanishing Conjecture: The Two-Variable Theorem and the First Failing Dimension",
          "url": "https://zenodo.org/records/21803325",
          "kind": "primary-mathematical-source",
          "license": null
        }
      ]
    }
  ],
  "sources": [
    {
      "label": "The Generalized Vanishing Conjecture: The Two-Variable Theorem and the First Failing Dimension",
      "url": "https://zenodo.org/records/21803325",
      "kind": "primary-mathematical-source",
      "license": null
    },
    {
      "label": "VibeMathed: The Generalized Vanishing Conjecture",
      "url": "https://vibemathed.com/problem/generalized-vanishing-conjecture-five-variables",
      "kind": "source-assertion",
      "license": "https://vibemathed.com/data-license"
    }
  ],
  "recommended_mode": "replay",
  "recommended_exposure": "method_aware",
  "opportunity_signals": [
    {
      "id": "vibemathed:generalized-vanishing-conjecture-five-variables:signal:replay_ready",
      "problem_id": "vibemathed:generalized-vanishing-conjecture-five-variables",
      "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"
}