{
  "schema_version": "1.0.0",
  "source": "vibemath",
  "problem_id": "vibemathed:hypergeometric-monodromy-arithmeticity",
  "title": "Arithmeticity of Degree-Six Symplectic Hypergeometric Monodromy Groups",
  "canonical_statement": "Bajpai, Dona and Nitsche left three degree-six symplectic hypergeometric monodromy groups unclassified as arithmetic or thin. Two of the three, C-47 and C-55, are arithmetic.",
  "plain_summary": "VibeMathed reports this item as partial. VibeMath preserves that report as a source assertion and has not independently authored a plain-language mathematical explanation.",
  "current_status": "partial",
  "solution_events": [
    {
      "id": "vibemathed:hypergeometric-monodromy-arithmeticity:event",
      "problem_id": "vibemathed:hypergeometric-monodromy-arithmeticity",
      "type": "proved",
      "status": "partial",
      "occurred_at": "2026-05-25T00:00:00.000Z",
      "title": "arXiv:2605.25935 - Certifying Arithmeticity for Two Degree-Six Symplectic Hypergeometric Monodromy Groups",
      "summary": "two of the three remaining cases; one is still unclassified",
      "ai_contribution": "ai_discovered",
      "attempt_ids": [
        "vibemathed:hypergeometric-monodromy-arithmeticity:attempt"
      ],
      "method_family_ids": [
        "vibemathed:hypergeometric-monodromy-arithmeticity:method"
      ],
      "source_assertion_ids": [
        "vibemathed:hypergeometric-monodromy-arithmeticity:assertion"
      ]
    }
  ],
  "attempts": [
    {
      "id": "vibemathed:hypergeometric-monodromy-arithmeticity:attempt",
      "problem_id": "vibemathed:hypergeometric-monodromy-arithmeticity",
      "model": "AlphaEvolve",
      "provider": "Google DeepMind",
      "attempted_at": "2026-05-25T00:00:00.000Z",
      "human_collaborators": [
        "J. Maxwell Riestenberg",
        "Diaaeldin Taha",
        "Steve Trettel"
      ],
      "exposure": "unknown",
      "prompt_public": null,
      "outcome": "The arithmeticity certificates were found with AlphaEvolve and then independently verified with exact matrix arithmetic over the rationals, so the search was the model's and the verification was exact rather than trusting.",
      "failed_routes": [],
      "artifacts": [],
      "sources": [
        {
          "label": "arXiv:2605.25935 - Certifying Arithmeticity for Two Degree-Six Symplectic Hypergeometric Monodromy Groups",
          "url": "https://arxiv.org/abs/2605.25935",
          "kind": "primary-mathematical-source",
          "license": null
        },
        {
          "label": "VibeMathed: Arithmeticity of Degree-Six Symplectic Hypergeometric Monodromy Groups",
          "url": "https://vibemathed.com/problem/hypergeometric-monodromy-arithmeticity",
          "kind": "source-assertion",
          "license": "https://vibemathed.com/data-license"
        }
      ],
      "cost_usd": null,
      "independence": "unknown"
    }
  ],
  "verifications": [
    {
      "id": "vibemathed:hypergeometric-monodromy-arithmeticity:verification",
      "problem_id": "vibemathed:hypergeometric-monodromy-arithmeticity",
      "solution_event_id": "vibemathed:hypergeometric-monodromy-arithmeticity:event",
      "level": "unreviewed",
      "mathematical_correctness": "unknown",
      "statement_fidelity": "unaudited",
      "peer_review": "none",
      "verifier": "VibeMathed (source-reported label)",
      "verified_at": null,
      "note": "The certificates are exact objects verified by exact rational matrix arithmetic, which is the right kind of check for a search result. arXiv preprint, not peer-reviewed.",
      "sources": [
        {
          "label": "VibeMathed: Arithmeticity of Degree-Six Symplectic Hypergeometric Monodromy Groups",
          "url": "https://vibemathed.com/problem/hypergeometric-monodromy-arithmeticity",
          "kind": "source-assertion",
          "license": "https://vibemathed.com/data-license"
        },
        {
          "label": "arXiv:2605.25935 - Certifying Arithmeticity for Two Degree-Six Symplectic Hypergeometric Monodromy Groups",
          "url": "https://arxiv.org/abs/2605.25935",
          "kind": "primary-mathematical-source",
          "license": null
        }
      ]
    }
  ],
  "sources": [
    {
      "label": "arXiv:2605.25935 - Certifying Arithmeticity for Two Degree-Six Symplectic Hypergeometric Monodromy Groups",
      "url": "https://arxiv.org/abs/2605.25935",
      "kind": "primary-mathematical-source",
      "license": null
    },
    {
      "label": "VibeMathed: Arithmeticity of Degree-Six Symplectic Hypergeometric Monodromy Groups",
      "url": "https://vibemathed.com/problem/hypergeometric-monodromy-arithmeticity",
      "kind": "source-assertion",
      "license": "https://vibemathed.com/data-license"
    }
  ],
  "recommended_mode": "expand",
  "recommended_exposure": "result_only",
  "opportunity_signals": [
    {
      "id": "vibemathed:hypergeometric-monodromy-arithmeticity:signal:recent_partial_result",
      "problem_id": "vibemathed:hypergeometric-monodromy-arithmeticity",
      "kind": "recent_partial_result",
      "reason": "A source-reported partial result may support bounded expansion.",
      "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"
}