{
  "schema_version": "1.0.0",
  "source": "vibemath",
  "problem_id": "vibemathed:huang-jiang-oblomkov-a3-layer",
  "title": "The Huang-Jiang-Oblomkov Conjecture at a = 3",
  "canonical_statement": "Huang, Jiang and Oblomkov conjectured that the Eulerian $q$-series counting commuting pairs of nilpotent matrices with $X^a = Y^b$ equals an explicit theta-and-eta product, making the point count essentially modular. The conjecture is layered in $a$; the $a = 2$ layer is classical, including Rogers-Ramanujan and Andrews-Gordon. Nothing was known for $a = 3$. That layer is now proved in full, yielding a new infinite family of Rogers-Ramanujan identities and a geometric origin for Warnaar's products.",
  "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:huang-jiang-oblomkov-a3-layer:event",
      "problem_id": "vibemathed:huang-jiang-oblomkov-a3-layer",
      "type": "proved",
      "status": "partial",
      "occurred_at": "2026-08-06T00:00:00.000Z",
      "title": "arXiv",
      "summary": "Proves the a = 3 layer; the conjecture is layered in a and remains open for larger a.",
      "ai_contribution": "ai_assisted",
      "attempt_ids": [
        "vibemathed:huang-jiang-oblomkov-a3-layer:attempt"
      ],
      "method_family_ids": [
        "vibemathed:huang-jiang-oblomkov-a3-layer:method"
      ],
      "source_assertion_ids": [
        "vibemathed:huang-jiang-oblomkov-a3-layer:assertion"
      ]
    }
  ],
  "attempts": [
    {
      "id": "vibemathed:huang-jiang-oblomkov-a3-layer:attempt",
      "problem_id": "vibemathed:huang-jiang-oblomkov-a3-layer",
      "model": "AxiomProver",
      "provider": "Axiom Math",
      "attempted_at": "2026-08-06T00:00:00.000Z",
      "human_collaborators": [
        "Kenny Lau",
        "Ken Ono"
      ],
      "exposure": "unknown",
      "prompt_public": null,
      "outcome": "The mathematics is the authors'; AxiomProver supplied the formal certificate. \"AxiomProver, an AI system currently under development, was used to generate this certificate. The system verified these results in Lean assuming existing literature.\"",
      "failed_routes": [],
      "artifacts": [
        {
          "label": "AxiomProver Lean certificate",
          "url": "https://github.com/AxiomMath/RR_a3",
          "kind": "lean-proof",
          "license": null
        }
      ],
      "sources": [
        {
          "label": "arXiv",
          "url": "https://arxiv.org/abs/2608.05480",
          "kind": "primary-mathematical-source",
          "license": null
        },
        {
          "label": "VibeMathed: The Huang-Jiang-Oblomkov Conjecture at a = 3",
          "url": "https://vibemathed.com/problem/huang-jiang-oblomkov-a3-layer",
          "kind": "source-assertion",
          "license": "https://vibemathed.com/data-license"
        }
      ],
      "cost_usd": null,
      "independence": "unknown"
    }
  ],
  "verifications": [
    {
      "id": "vibemathed:huang-jiang-oblomkov-a3-layer:verification",
      "problem_id": "vibemathed:huang-jiang-oblomkov-a3-layer",
      "solution_event_id": "vibemathed:huang-jiang-oblomkov-a3-layer:event",
      "level": "lean_checked_statement_unaudited",
      "mathematical_correctness": "supported",
      "statement_fidelity": "unaudited",
      "peer_review": "none",
      "verifier": "VibeMathed (source-reported label)",
      "verified_at": null,
      "note": "The Lean certificate is explicitly conditional, verifying the new identities assuming results from the existing literature rather than from first principles, and the system that produced it also produced the formal statements. Public at the AxiomMath repository.",
      "sources": [
        {
          "label": "VibeMathed: The Huang-Jiang-Oblomkov Conjecture at a = 3",
          "url": "https://vibemathed.com/problem/huang-jiang-oblomkov-a3-layer",
          "kind": "source-assertion",
          "license": "https://vibemathed.com/data-license"
        },
        {
          "label": "arXiv",
          "url": "https://arxiv.org/abs/2608.05480",
          "kind": "primary-mathematical-source",
          "license": null
        }
      ]
    }
  ],
  "sources": [
    {
      "label": "arXiv",
      "url": "https://arxiv.org/abs/2608.05480",
      "kind": "primary-mathematical-source",
      "license": null
    },
    {
      "label": "VibeMathed: The Huang-Jiang-Oblomkov Conjecture at a = 3",
      "url": "https://vibemathed.com/problem/huang-jiang-oblomkov-a3-layer",
      "kind": "source-assertion",
      "license": "https://vibemathed.com/data-license"
    }
  ],
  "recommended_mode": "verify",
  "recommended_exposure": "result_only",
  "opportunity_signals": [
    {
      "id": "vibemathed:huang-jiang-oblomkov-a3-layer:signal:recent_partial_result",
      "problem_id": "vibemathed:huang-jiang-oblomkov-a3-layer",
      "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"
}