{
  "schema_version": "1.0.0",
  "source": "vibemath",
  "problem_id": "vibemathed:quantum-parallel-repetition",
  "title": "Quantum Parallel Repetition",
  "canonical_statement": "Does the value of a two-player quantum game decay exponentially under parallel repetition, as Raz's theorem gives for classical games? Yes: an exponential parallel repetition theorem holds for arbitrary finite two-player quantum games.",
  "plain_summary": "VibeMathed reports this item as candidate. VibeMath preserves that report as a source assertion and has not independently authored a plain-language mathematical explanation.",
  "current_status": "candidate",
  "solution_events": [
    {
      "id": "vibemathed:quantum-parallel-repetition:event",
      "problem_id": "vibemathed:quantum-parallel-repetition",
      "type": "proved",
      "status": "candidate",
      "occurred_at": "2026-08-01T00:00:00.000Z",
      "title": "OpenAI: Ten advances in mathematics and theoretical computer science",
      "summary": "VibeMathed reports this item as candidate. 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:quantum-parallel-repetition:attempt"
      ],
      "method_family_ids": [
        "vibemathed:quantum-parallel-repetition:method"
      ],
      "source_assertion_ids": [
        "vibemathed:quantum-parallel-repetition:assertion"
      ]
    }
  ],
  "attempts": [
    {
      "id": "vibemathed:quantum-parallel-repetition:attempt",
      "problem_id": "vibemathed:quantum-parallel-repetition",
      "model": "Astra (internal preview)",
      "provider": "OpenAI",
      "attempted_at": "2026-08-01T00:00:00.000Z",
      "human_collaborators": [],
      "exposure": "unknown",
      "prompt_public": null,
      "outcome": "Generated by an internal version of OpenAI's Astra: per the announcement, the mathematical arguments were produced by the system (roughly 2,000 dollars of compute at Sol API rates across all ten results), humans prepared the manuscripts with the same model, and the model then formalized the argument in Lean. A narrated reasoning walkthrough is published for each result.",
      "failed_routes": [],
      "artifacts": [
        {
          "label": "Manuscripts (ten-proofs paper, PDF)",
          "url": "https://cdn.openai.com/pdf/ten-proofs-oai.pdf",
          "kind": "paper",
          "license": null
        },
        {
          "label": "Lean certificate (QuantumParallelRepetition.lean)",
          "url": "https://github.com/openai/ten-proofs/blob/main/QuantumParallelRepetition.lean",
          "kind": "lean-proof",
          "license": null
        },
        {
          "label": "Reasoning walkthroughs (PDF)",
          "url": "https://cdn.openai.com/pdf/reasoning-walkthroughs.pdf",
          "kind": "transcript",
          "license": null
        }
      ],
      "sources": [
        {
          "label": "OpenAI: Ten advances in mathematics and theoretical computer science",
          "url": "https://openai.com/index/ten-advances-in-mathematics/",
          "kind": "primary-mathematical-source",
          "license": null
        },
        {
          "label": "VibeMathed: Quantum Parallel Repetition",
          "url": "https://vibemathed.com/problem/quantum-parallel-repetition",
          "kind": "source-assertion",
          "license": "https://vibemathed.com/data-license"
        }
      ],
      "cost_usd": 182,
      "independence": "unknown"
    }
  ],
  "verifications": [
    {
      "id": "vibemathed:quantum-parallel-repetition:verification",
      "problem_id": "vibemathed:quantum-parallel-repetition",
      "solution_event_id": "vibemathed:quantum-parallel-repetition:event",
      "level": "lean_verified_statement_audited",
      "mathematical_correctness": "supported",
      "statement_fidelity": "audited",
      "peer_review": "none",
      "verifier": "VibeMathed (source-reported label)",
      "verified_at": null,
      "note": "Kernel-checked Lean 4 certificate in OpenAI's public ten-proofs repository (Lean 4.32, mathlib, `lake build All`), with an independent Comparator checking route. Statement fidelity and community review of the day-old company announcement remain pending, hence candidate status.",
      "sources": [
        {
          "label": "VibeMathed: Quantum Parallel Repetition",
          "url": "https://vibemathed.com/problem/quantum-parallel-repetition",
          "kind": "source-assertion",
          "license": "https://vibemathed.com/data-license"
        },
        {
          "label": "OpenAI: Ten advances in mathematics and theoretical computer science",
          "url": "https://openai.com/index/ten-advances-in-mathematics/",
          "kind": "primary-mathematical-source",
          "license": null
        }
      ]
    }
  ],
  "sources": [
    {
      "label": "OpenAI: Ten advances in mathematics and theoretical computer science",
      "url": "https://openai.com/index/ten-advances-in-mathematics/",
      "kind": "primary-mathematical-source",
      "license": null
    },
    {
      "label": "VibeMathed: Quantum Parallel Repetition",
      "url": "https://vibemathed.com/problem/quantum-parallel-repetition",
      "kind": "source-assertion",
      "license": "https://vibemathed.com/data-license"
    }
  ],
  "recommended_mode": "verify",
  "recommended_exposure": "result_only",
  "opportunity_signals": [
    {
      "id": "vibemathed:quantum-parallel-repetition:signal:verify_now",
      "problem_id": "vibemathed:quantum-parallel-repetition",
      "kind": "verify_now",
      "reason": "The source labels this result as a candidate; verification should precede reuse.",
      "generated_at": "2026-09-13T16:28:40.178Z"
    }
  ],
  "uncertainties": [
    "The source status is candidate and must not be represented as solved.",
    "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"
}