{
  "schema_version": "1.0.0",
  "source": "vibemath",
  "problem_id": "vibemathed:davenport-constant-heisenberg-125",
  "title": "The Small Davenport Constant of the Heisenberg Group of Order 125",
  "canonical_statement": "Godara and Sarkar proved $\\mathsf{d}(H_{27})=6$ for the exponent-$p$ Heisenberg group and posed $\\mathsf{d}(H_{p^3})=3p-3$ for every odd prime $p$, leaving $p\\ge5$ open. The paper settles the first open case, $\\mathsf{d}(H_{125})=12$, the upper bound reducing to a finite spread bound verified by exhaustive search and independently reproduced.",
  "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:davenport-constant-heisenberg-125:event",
      "problem_id": "vibemathed:davenport-constant-heisenberg-125",
      "type": "proved",
      "status": "resolved",
      "occurred_at": "2026-07-15T00:00:00.000Z",
      "title": "arXiv",
      "summary": "Settles the case p=5. The posed formula for every odd prime remains open.",
      "ai_contribution": "ai_discovered",
      "attempt_ids": [
        "vibemathed:davenport-constant-heisenberg-125:attempt"
      ],
      "method_family_ids": [
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      ],
      "source_assertion_ids": [
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  "attempts": [
    {
      "id": "vibemathed:davenport-constant-heisenberg-125:attempt",
      "problem_id": "vibemathed:davenport-constant-heisenberg-125",
      "model": "Claude + GPT-5",
      "provider": null,
      "attempted_at": "2026-07-15T00:00:00.000Z",
      "human_collaborators": [
        "Patrick White"
      ],
      "exposure": "unknown",
      "prompt_public": null,
      "outcome": "An attribution note states the results were obtained by an AI research collaboration in which an AI system occupied the principal research seat under human direction. Claude produced the search implementations, the independent reproduction of the load-bearing computation and the write-up; a tool-free GPT-5 produced the reduction to the lemma chain and the corrected hypotheses of several lemmas.",
      "failed_routes": [],
      "artifacts": [],
      "sources": [
        {
          "label": "arXiv",
          "url": "https://arxiv.org/abs/2607.14379",
          "kind": "primary-mathematical-source",
          "license": null
        },
        {
          "label": "VibeMathed: The Small Davenport Constant of the Heisenberg Group of Order 125",
          "url": "https://vibemathed.com/problem/davenport-constant-heisenberg-125",
          "kind": "source-assertion",
          "license": "https://vibemathed.com/data-license"
        }
      ],
      "cost_usd": null,
      "independence": "unknown"
    }
  ],
  "verifications": [
    {
      "id": "vibemathed:davenport-constant-heisenberg-125:verification",
      "problem_id": "vibemathed:davenport-constant-heisenberg-125",
      "solution_event_id": "vibemathed:davenport-constant-heisenberg-125:event",
      "level": "unreviewed",
      "mathematical_correctness": "unknown",
      "statement_fidelity": "unaudited",
      "peer_review": "none",
      "verifier": "VibeMathed (source-reported label)",
      "verified_at": null,
      "note": "No independent review, though the load-bearing computation was reproduced by a second search with a different pruning strategy. Preprint, not refereed.",
      "sources": [
        {
          "label": "VibeMathed: The Small Davenport Constant of the Heisenberg Group of Order 125",
          "url": "https://vibemathed.com/problem/davenport-constant-heisenberg-125",
          "kind": "source-assertion",
          "license": "https://vibemathed.com/data-license"
        },
        {
          "label": "arXiv",
          "url": "https://arxiv.org/abs/2607.14379",
          "kind": "primary-mathematical-source",
          "license": null
        }
      ]
    }
  ],
  "sources": [
    {
      "label": "arXiv",
      "url": "https://arxiv.org/abs/2607.14379",
      "kind": "primary-mathematical-source",
      "license": null
    },
    {
      "label": "VibeMathed: The Small Davenport Constant of the Heisenberg Group of Order 125",
      "url": "https://vibemathed.com/problem/davenport-constant-heisenberg-125",
      "kind": "source-assertion",
      "license": "https://vibemathed.com/data-license"
    }
  ],
  "recommended_mode": "verify",
  "recommended_exposure": "result_only",
  "opportunity_signals": [
    {
      "id": "vibemathed:davenport-constant-heisenberg-125:signal:watch_only",
      "problem_id": "vibemathed:davenport-constant-heisenberg-125",
      "kind": "watch_only",
      "reason": "Current public evidence does not meet the default replay threshold.",
      "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"
}