{
  "schema_version": "1.0.0",
  "source": "vibemath",
  "problem_id": "vibemathed:fgg-qaoa-ring-of-disagrees",
  "title": "FGG Conjecture for QAOA on the Ring of Disagrees",
  "canonical_statement": "For an even cycle of size $N$ and depth $p$ with $2p + 2 \\le N$, is the optimal QAOA approximation ratio for MaxCut exactly $\\frac{2p+1}{2p+2}$, as Farhi, Goldstone and Gutmann conjectured?",
  "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:fgg-qaoa-ring-of-disagrees:event",
      "problem_id": "vibemathed:fgg-qaoa-ring-of-disagrees",
      "type": "proved",
      "status": "resolved",
      "occurred_at": "2026-06-29T00:00:00.000Z",
      "title": "arXiv:2606.29687 - A machine-verified proof of a quantum-optimization conjecture",
      "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",
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        "vibemathed:fgg-qaoa-ring-of-disagrees:attempt"
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      "id": "vibemathed:fgg-qaoa-ring-of-disagrees:attempt",
      "problem_id": "vibemathed:fgg-qaoa-ring-of-disagrees",
      "model": "Claude Fable 5",
      "provider": "Anthropic",
      "attempted_at": "2026-06-29T00:00:00.000Z",
      "human_collaborators": [],
      "exposure": "unknown",
      "prompt_public": null,
      "outcome": "Claude Fable 5 found a dynamical-symmetry and quantum-signal-processing argument; the complete proof is checked by the Lean 4 kernel. An independent group proved the same result simultaneously via Laurent-polynomial optimization (arXiv:2606.29562).",
      "failed_routes": [],
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          "kind": "primary-mathematical-source",
          "license": null
        },
        {
          "label": "VibeMathed: FGG Conjecture for QAOA on the Ring of Disagrees",
          "url": "https://vibemathed.com/problem/fgg-qaoa-ring-of-disagrees",
          "kind": "source-assertion",
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  "verifications": [
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      "mathematical_correctness": "supported",
      "statement_fidelity": "audited",
      "peer_review": "none",
      "verifier": "VibeMathed (source-reported label)",
      "verified_at": null,
      "note": "Machine-verified end to end in Lean 4, with an independent simultaneous human proof of the same theorem.",
      "sources": [
        {
          "label": "VibeMathed: FGG Conjecture for QAOA on the Ring of Disagrees",
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          "label": "arXiv:2606.29687 - A machine-verified proof of a quantum-optimization conjecture",
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  "sources": [
    {
      "label": "arXiv:2606.29687 - A machine-verified proof of a quantum-optimization conjecture",
      "url": "https://arxiv.org/abs/2606.29687",
      "kind": "primary-mathematical-source",
      "license": null
    },
    {
      "label": "VibeMathed: FGG Conjecture for QAOA on the Ring of Disagrees",
      "url": "https://vibemathed.com/problem/fgg-qaoa-ring-of-disagrees",
      "kind": "source-assertion",
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  "recommended_exposure": "method_aware",
  "opportunity_signals": [
    {
      "id": "vibemathed:fgg-qaoa-ring-of-disagrees:signal:replay_ready",
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      "kind": "replay_ready",
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      "generated_at": "2026-09-13T16:28:40.178Z"
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  "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"
}