{
  "schema_version": 1,
  "id": "evt-2026-magenta",
  "slug": "magenta-lean-verification-loop",
  "title": {
    "en": "Magenta closes the loop between informal mathematical reasoning and Lean verification",
    "zh-CN": "Magenta 打通非形式数学推理与 Lean 验证闭环"
  },
  "dates": {
    "event": "2026-09-10",
    "first_public_claim": "2026-09-10",
    "paper_release": "2026-09-10",
    "artifact_release": null,
    "independently_verified": null,
    "added_to_chronicle": "2026-09-14",
    "last_updated": "2026-09-14"
  },
  "event_types": [
    "system",
    "formalization"
  ],
  "significance": {
    "tier": "H2",
    "rationale": {
      "en": "Magenta is a field-level milestone in verifier-guided mathematical agents because it integrates informal problem solving, Lean statement construction, statement-faithfulness judging, proof search and error attribution into one feedback loop instead of treating formalization and proving as isolated stages.",
      "zh-CN": "Magenta 是验证器引导数学 Agent 路线上的领域级里程碑：它把非形式解题、Lean 命题构造、命题忠实性判断、证明搜索与错误归因整合为同一反馈闭环，而不是把形式化和证明视为彼此孤立的阶段。"
    }
  },
  "mathematical_novelty": {
    "type": "tooling_only"
  },
  "interfaces": [
    "informal",
    "formal",
    "hybrid"
  ],
  "claim": {
    "en": "The Magenta paper introduced a training-free agentic pipeline that starts from a natural-language problem, derives an answer, formalizes the statement in Lean 4 and constructs a machine-checked proof; the authors report 100% accuracy on their evaluated Olympiad benchmarks and, with K2-Horizon-7B as the reasoner, successful proofs for all six IMO 2026 problems.",
    "zh-CN": "Magenta 论文提出一个无需额外训练的 Agent 管线：从自然语言问题出发，先得到答案，再将命题形式化为 Lean 4，并构造机器检查证明；作者报告该系统在其评测的奥赛基准上达到 100% 准确率，并在使用 K2-Horizon-7B 作为推理模型时完成 IMO 2026 全部 6 道题的证明。"
  },
  "summary": {
    "en": "Magenta uses a statement judge to check whether a generated Lean statement preserves the original informal problem and an error-attribution judge to decide whether a failed attempt should return to mathematical re-derivation or local Lean repair. The paper reports that this feedback-guided correction loop outperforms independent resampling on difficult problems.",
    "zh-CN": "Magenta 使用 statement judge 检查生成的 Lean 命题是否保持原始非形式问题的含义，并使用 error-attribution judge 判断失败尝试应回到数学推导还是进行局部 Lean 修复。论文报告称，这种基于反馈的纠错闭环在困难问题上优于独立重采样。"
  },
  "why_it_matters": {
    "en": "The work makes formal verification an active part of mathematical reasoning rather than only a final certificate. In particular, it addresses a central failure mode of end-to-end autoformalization systems: a prover can certify the wrong formal statement unless the pipeline also checks whether that statement faithfully represents the human problem.",
    "zh-CN": "该工作把形式验证变成数学推理过程中的主动反馈，而不只是最终证书。尤其是，它直接处理端到端自动形式化的核心失效模式：如果系统不检查形式命题是否忠实表达原始人类问题，那么证明器可能只是正确证明了错误的形式化目标。"
  },
  "ai_role": {
    "level": "autonomous_primary",
    "description": {
      "en": "Language-model agents perform the mathematical derivation, translate the result into Lean, construct proofs, judge statement fidelity and route failures between mathematical re-reasoning and Lean repair inside the evaluated pipeline.",
      "zh-CN": "在评测管线中，语言模型 Agent 承担数学推导、Lean 形式化、证明构造、命题忠实性判断，并在失败时决定进入重新数学推理还是 Lean 修复。"
    }
  },
  "human_contribution": {
    "description": {
      "en": "Researchers designed the multi-stage pipeline, judges, routing logic and evaluation protocol, selected the underlying reasoners and benchmarks, and analyzed the failure and correction behavior.",
      "zh-CN": "研究者设计多阶段管线、判断器、错误路由逻辑与评测协议，选择底层推理模型和基准，并分析系统的失败与纠错行为。"
    }
  },
  "systems": [
    "magenta",
    "lean",
    "k2-horizon-7b"
  ],
  "organizations": [],
  "people": [],
  "problems": [
    "olympiad-mathematics",
    "imo-2026"
  ],
  "methods": [
    "agentic-theorem-proving",
    "autoformalization",
    "statement-verification",
    "error-attribution",
    "lean-feedback"
  ],
  "verification": {
    "evidence_level": "E2",
    "status": "paper_released",
    "formal_assurance": "machine_checked",
    "history": [
      {
        "date": "2026-09-10",
        "status": "paper_released",
        "evidence_level": "E2",
        "note": {
          "en": "The arXiv research record describes the Magenta pipeline and reports the benchmark and IMO 2026 results. The paper states that successful outputs are checked in Lean 4; no independent replay or public proof artifact is recorded by the Chronicle at this stage.",
          "zh-CN": "arXiv 研究记录描述了 Magenta 管线，并报告其基准与 IMO 2026 结果。论文称成功输出由 Lean 4 检查；Chronicle 当前尚未记录独立重放或公开证明产物。"
        }
      }
    ]
  },
  "sources": [
    {
      "id": "arxiv-magenta-2609.11319",
      "tier": "S1",
      "type": "paper",
      "title": "Magenta: Closing the Loop Between Mathematical Reasoning and Lean Verification",
      "url": "https://arxiv.org/abs/2609.11319",
      "primary": true,
      "published_date": "2026-09-10",
      "accessed_at": "2026-09-14"
    }
  ],
  "artifacts": [],
  "relationships": {
    "predecessors": [
      "evt-2025-mathesis"
    ],
    "successors": [],
    "related": [
      "evt-2026-aimo-proof-pilot"
    ]
  },
  "timeline": {
    "featured": true,
    "significance": "primary"
  },
  "tags": [
    "magenta",
    "lean",
    "autoformalization",
    "theorem-proving",
    "agent",
    "olympiad",
    "imo-2026"
  ],
  "editorial": {
    "created_at": "2026-09-14",
    "last_reviewed": "2026-09-14",
    "reviewers": [
      "Charlie-Wang-03"
    ]
  },
  "corrections": []
}