{
  "schema_version": "1.0.0",
  "source": "vibemath",
  "problem_id": "vibemathed:chen-gendron-spin-parity",
  "title": "Chen-Gendron Spin-Parity Identity for k-Differentials",
  "canonical_statement": "For odd $k$ with $\\gcd(n,k) = \\gcd(n+1,k) = 1$, is $N_k(n) \\equiv \\lfloor (k+1)/4 \\rfloor \\pmod 2$, where $N_k(n)$ counts pairs $1 \\le b_i \\le (k-1)/2$ with $b_1 + b_2 \\ge (k+1)/2$ and $b_2 \\equiv n b_1 \\pmod k$? Conjectured by Chen and Gendron; its proof removes a conditional step in the genus-zero and genus-one spin-parity classification.",
  "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:chen-gendron-spin-parity:event",
      "problem_id": "vibemathed:chen-gendron-spin-parity",
      "type": "proved",
      "status": "resolved",
      "occurred_at": "2026-02-03T00:00:00.000Z",
      "title": "arXiv:2602.03722 - Parity of k-differentials in genus zero and one",
      "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.",
      "ai_contribution": "ai_discovered",
      "attempt_ids": [
        "vibemathed:chen-gendron-spin-parity:attempt"
      ],
      "method_family_ids": [
        "vibemathed:chen-gendron-spin-parity:method"
      ],
      "source_assertion_ids": [
        "vibemathed:chen-gendron-spin-parity:assertion"
      ]
    }
  ],
  "attempts": [
    {
      "id": "vibemathed:chen-gendron-spin-parity:attempt",
      "problem_id": "vibemathed:chen-gendron-spin-parity",
      "model": "AxiomProver",
      "provider": null,
      "attempted_at": "2026-02-03T00:00:00.000Z",
      "human_collaborators": [],
      "exposure": "unknown",
      "prompt_public": null,
      "outcome": "Proved by the AxiomProver system with a Lean-checked core.",
      "failed_routes": [],
      "artifacts": [],
      "sources": [
        {
          "label": "arXiv:2602.03722 - Parity of k-differentials in genus zero and one",
          "url": "https://arxiv.org/abs/2602.03722",
          "kind": "primary-mathematical-source",
          "license": null
        },
        {
          "label": "VibeMathed: Chen-Gendron Spin-Parity Identity for k-Differentials",
          "url": "https://vibemathed.com/problem/chen-gendron-spin-parity",
          "kind": "source-assertion",
          "license": "https://vibemathed.com/data-license"
        }
      ],
      "cost_usd": null,
      "independence": "unknown"
    }
  ],
  "verifications": [
    {
      "id": "vibemathed:chen-gendron-spin-parity:verification",
      "problem_id": "vibemathed:chen-gendron-spin-parity",
      "solution_event_id": "vibemathed:chen-gendron-spin-parity:event",
      "level": "lean_checked_statement_unaudited",
      "mathematical_correctness": "supported",
      "statement_fidelity": "unaudited",
      "peer_review": "none",
      "verifier": "VibeMathed (source-reported label)",
      "verified_at": null,
      "note": "Core argument Lean-checked, with an expert-written exposition. Tier: the Lean-checked core comes from the proving system itself; the statement correspondence is not independently audited.",
      "sources": [
        {
          "label": "VibeMathed: Chen-Gendron Spin-Parity Identity for k-Differentials",
          "url": "https://vibemathed.com/problem/chen-gendron-spin-parity",
          "kind": "source-assertion",
          "license": "https://vibemathed.com/data-license"
        },
        {
          "label": "arXiv:2602.03722 - Parity of k-differentials in genus zero and one",
          "url": "https://arxiv.org/abs/2602.03722",
          "kind": "primary-mathematical-source",
          "license": null
        }
      ]
    }
  ],
  "sources": [
    {
      "label": "arXiv:2602.03722 - Parity of k-differentials in genus zero and one",
      "url": "https://arxiv.org/abs/2602.03722",
      "kind": "primary-mathematical-source",
      "license": null
    },
    {
      "label": "VibeMathed: Chen-Gendron Spin-Parity Identity for k-Differentials",
      "url": "https://vibemathed.com/problem/chen-gendron-spin-parity",
      "kind": "source-assertion",
      "license": "https://vibemathed.com/data-license"
    }
  ],
  "recommended_mode": "verify",
  "recommended_exposure": "result_only",
  "opportunity_signals": [
    {
      "id": "vibemathed:chen-gendron-spin-parity:signal:replay_ready",
      "problem_id": "vibemathed:chen-gendron-spin-parity",
      "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"
}