{
  "schema_version": "ocme-reviewed-question-reader-v1",
  "question_id": "q-20261015-advance-20261116-r06-topological-ordering-dag-0067",
  "pilot_number": "P1000-0817",
  "number": 817,
  "family_id": "qf-mod47-toposort-kahn-trace",
  "title": {
    "zh-Hant": "第 817 題：有向無環圖的拓撲排序",
    "en": "Question 817: Remove the Lexically First Zero-Indegree Source at Each Kahn Step"
  },
  "original_question": {
    "schema_version": "ocme-question-v0.1",
    "id": "q-20261015-advance-20261116-r06-topological-ordering-dag-0067",
    "batch_id": "batch-20261015-advance-20261116-r06-topological-ordering-dag-foundations",
    "language": "zh-Hant",
    "source_mko_ids": [
      "mko-topological-ordering-dag"
    ],
    "title_zh": "有向無環圖的拓撲排序",
    "stem_zh": "finite digraph、完整vertex permutation與all-edge order責任。操作=toposort-kahn-trace；資料={\"vertices\":[\"v0\",\"v1\",\"v2\",\"v3\",\"v4\",\"v5\"],\"edges\":[[\"v0\",\"v1\"],[\"v0\",\"v5\"]]}。請依 exact_ordered_tuple_declared_by_interface 欄序回答。",
    "answer": {
      "kind": "expression",
      "value": "([[[v0, v1, v2, v3, v4, v5], [v0, v2, v3, v4], v0], [[v1, v2, v3, v4, v5], [v1, v2, v3, v4, v5], v1], [[v2, v3, v4, v5], [v2, v3, v4, v5], v2], [[v3, v4, v5], [v3, v4, v5], v3], [[v4, v5], [v4, v5], v4], [[v5], [v5], v5]], [v0, v1, v2, v3, v4, v5], 否, 是, each_step_removes_lexicographically_first_zero_indegree_source)",
      "explanation_zh": "Wave6第十層核對=([[[v0, v1, v2, v3, v4, v5], [v0, v2, v3, v4], v0], [[v1, v2, v3, v4, v5], [v1, v2, v3, v4, v5], v1], [[v2, v3, v4, v5], [v2, v3, v4, v5], v2], [[v3, v4, v5], [v3, v4, v5], v3], [[v4, v5], [v4, v5], v4], [[v5], [v5], v5]], [v0, v1, v2, v3, v4, v5], 否, 是, each_step_removes_lexicographically_first_zero_indegree_source)；依完整明示資料獨立重算；全部orders、Kahn source-removal trace與cycle witness交叉核對；invalid candidate不等於cycle；multiple orders與empty-edge graph允許且不混同topological space。"
    },
    "difficulty": {
      "band": "undergraduate_core",
      "level": 2,
      "skills": [
        "有向無環圖的拓撲排序"
      ]
    },
    "variant": {
      "family_id": "qf-mod47-toposort-kahn-trace",
      "seed": 202611166067,
      "parameters": {
        "vertices": [
          "v0",
          "v1",
          "v2",
          "v3",
          "v4",
          "v5"
        ],
        "edges": [
          [
            "v0",
            "v1"
          ],
          [
            "v0",
            "v5"
          ]
        ],
        "domain": "Complete_finite_topological_ordering",
        "operation": "toposort-kahn-trace",
        "semantic_template": "qf-mod47-toposort-kahn-trace/{\"edges\":[[\"v0\",\"v1\"],[\"v0\",\"v5\"]],\"vertices\":[\"v0\",\"v1\",\"v2\",\"v3\",\"v4\",\"v5\"]}"
      }
    },
    "verification": {
      "status": "candidate",
      "checks": [
        "producer_exact_finite_or_symbolic_model",
        "producer_source_snapshot_check",
        "producer_substantive_template_deduplication",
        "producer_json_schema"
      ],
      "warning_zh": "候選須主端重算；不構成人工審定、一般Banach／IVT／Taylor證明、MLE漸近性、factorization theorem、一般DAG iff或primitive-root主張、Lean或Evidence。"
    },
    "provenance": {
      "generator_role": "question_producer",
      "generator_model": "model_unknown",
      "generated_at": "2026-10-15",
      "contract_version": "ocme-question-factory-v0.1"
    }
  },
  "original_english_edition": {
    "schema_version": "ocme-question-localization-v0.1",
    "question_id": "q-20261015-advance-20261116-r06-topological-ordering-dag-0067",
    "batch_id": "batch-20261015-advance-20261116-r06-topological-ordering-dag-foundations",
    "locale": "en",
    "translation_state": "ai_candidate",
    "source": {
      "question_sha256": "4a5670dfc11c353892eb6fc4d669aac93c5a1ba5de655a99a0c46e43a2f435cf",
      "family_id": "qf-mod47-toposort-kahn-trace",
      "seed": 202611166067,
      "semantic_template": "qf-mod47-toposort-kahn-trace/{\"edges\":[[\"v0\",\"v1\"],[\"v0\",\"v5\"]],\"vertices\":[\"v0\",\"v1\",\"v2\",\"v3\",\"v4\",\"v5\"]}"
    },
    "fields": {
      "title": "Remove the Lexically First Zero-Indegree Source at Each Kahn Step",
      "stem": "Use unique vertices=[v0, v1, v2, v3, v4, v5] and loop-free duplicate-free directed edges=[[v0, v1], [v0, v5]]. Every edge u→v needs position(u)<position(v) in a complete vertex permutation; labels use source lexical order. Give (source_removal_trace, output_order, cycle_detected, valid_completed_order, certificate).",
      "answer": {
        "kind": "expression",
        "value": "([[[v0, v1, v2, v3, v4, v5], [v0, v2, v3, v4], v0], [[v1, v2, v3, v4, v5], [v1, v2, v3, v4, v5], v1], [[v2, v3, v4, v5], [v2, v3, v4, v5], v2], [[v3, v4, v5], [v3, v4, v5], v3], [[v4, v5], [v4, v5], v4], [[v5], [v5], v5]], [v0, v1, v2, v3, v4, v5], No, Yes, each_step_removes_lexicographically_first_zero_indegree_source)",
        "explanation": "Retain remaining vertices, every available source and the selected first source at each step, then the output and cycle/completion flags. No available source with vertices remaining is a cycle condition. A finite trace is not the general induction proof. The exact result, retaining the requested order, is ([[[v0, v1, v2, v3, v4, v5], [v0, v2, v3, v4], v0], [[v1, v2, v3, v4, v5], [v1, v2, v3, v4, v5], v1], [[v2, v3, v4, v5], [v2, v3, v4, v5], v2], [[v3, v4, v5], [v3, v4, v5], v3], [[v4, v5], [v4, v5], v4], [[v5], [v5], v5]], [v0, v1, v2, v3, v4, v5], No, Yes, each_step_removes_lexicographically_first_zero_indegree_source)."
      },
      "skills": [
        "Remove the Lexically First Zero-Indegree Source at Each Kahn Step"
      ],
      "verification_warning": "This is a candidate exercise. Mechanical recomputation checks only the stated conditions and this instance; it is neither a formal proof nor human review."
    }
  },
  "givens": [
    {
      "id": "G001",
      "text": {
        "zh-Hant": "finite digraph、完整vertex permutation與all-edge order責任。操作=toposort-kahn-trace；資料={\"vertices\":[\"v0\",\"v1\",\"v2\",\"v3\",\"v4\",\"v5\"],\"edges\":[[\"v0\",\"v1\"],[\"v0\",\"v5\"]]}。請依 exact_ordered_tuple_declared_by_interface 欄序回答。",
        "en": "Use unique vertices=[v0, v1, v2, v3, v4, v5] and loop-free duplicate-free directed edges=[[v0, v1], [v0, v5]]. Every edge u→v needs position(u)<position(v) in a complete vertex permutation; labels use source lexical order. Give (source_removal_trace, output_order, cycle_detected, valid_completed_order, certificate)."
      }
    }
  ],
  "steps": [
    {
      "id": "S001",
      "uses": [
        "G001"
      ],
      "before": "V=[v0, v1, v2, v3, v4, v5]",
      "after": "all directed edges=[[v0, v1], [v0, v5]]",
      "relation": "implies",
      "rule_id": "full_directed_graph",
      "conditions": [],
      "explanation": {
        "zh-Hant": "這是完整指定的有限有向圖，不是圖論術語的完全圖。",
        "en": "This is a fully specified finite digraph, not necessarily a complete digraph."
      },
      "reverse_audit": {
        "kind": "premise_and_result_audit",
        "explanation": {
          "zh-Hant": "核對完整頂點與邊；一個失敗次序不等於有環，全部合法分支不能漏列。",
          "en": "Audit all vertices and edges; one failed order is not a cycle proof, and no legal branch may be omitted."
        }
      },
      "arithmetic": null
    },
    {
      "id": "S002",
      "uses": [
        "G001",
        "S001"
      ],
      "before": "remaining=[v0, v1, v2, v3, v4, v5]; active edges=[[v0, v1], [v0, v5]]",
      "after": "indegrees=[[v0, 0], [v1, 1], [v2, 0], [v3, 0], [v4, 0], [v5, 1]]; sources=[v0, v2, v3, v4]",
      "relation": "implies",
      "rule_id": "remaining_indegree",
      "conditions": [],
      "explanation": {
        "zh-Hant": "每次都以尚未移除的邊重新計算入度，不以原始入度硬套全部步驟。",
        "en": "Recompute indegrees from remaining edges at every stage, rather than reusing original indegrees."
      },
      "reverse_audit": {
        "kind": "premise_and_result_audit",
        "explanation": {
          "zh-Hant": "核對完整頂點與邊；一個失敗次序不等於有環，全部合法分支不能漏列。",
          "en": "Audit all vertices and edges; one failed order is not a cycle proof, and no legal branch may be omitted."
        }
      },
      "arithmetic": null
    },
    {
      "id": "S003",
      "uses": [
        "G001",
        "S002"
      ],
      "before": "zero-indegree choices=[v0, v2, v3, v4]",
      "after": "choose=v0; new prefix=[v0]",
      "relation": "implies",
      "rule_id": "lexicographic_kahn_choice",
      "conditions": [],
      "explanation": {
        "zh-Hant": "按已宣告的字典序挑第一個零入度點，並移除它發出的邊。",
        "en": "Choose the lexicographically first source and remove its outgoing edges."
      },
      "reverse_audit": {
        "kind": "premise_and_result_audit",
        "explanation": {
          "zh-Hant": "核對完整頂點與邊；一個失敗次序不等於有環，全部合法分支不能漏列。",
          "en": "Audit all vertices and edges; one failed order is not a cycle proof, and no legal branch may be omitted."
        }
      },
      "arithmetic": null
    },
    {
      "id": "S004",
      "uses": [
        "G001",
        "S003"
      ],
      "before": "remaining=[v1, v2, v3, v4, v5]; active edges=[]",
      "after": "indegrees=[[v1, 0], [v2, 0], [v3, 0], [v4, 0], [v5, 0]]; sources=[v1, v2, v3, v4, v5]",
      "relation": "implies",
      "rule_id": "remaining_indegree",
      "conditions": [],
      "explanation": {
        "zh-Hant": "每次都以尚未移除的邊重新計算入度，不以原始入度硬套全部步驟。",
        "en": "Recompute indegrees from remaining edges at every stage, rather than reusing original indegrees."
      },
      "reverse_audit": {
        "kind": "premise_and_result_audit",
        "explanation": {
          "zh-Hant": "核對完整頂點與邊；一個失敗次序不等於有環，全部合法分支不能漏列。",
          "en": "Audit all vertices and edges; one failed order is not a cycle proof, and no legal branch may be omitted."
        }
      },
      "arithmetic": null
    },
    {
      "id": "S005",
      "uses": [
        "G001",
        "S004"
      ],
      "before": "zero-indegree choices=[v1, v2, v3, v4, v5]",
      "after": "choose=v1; new prefix=[v0, v1]",
      "relation": "implies",
      "rule_id": "lexicographic_kahn_choice",
      "conditions": [],
      "explanation": {
        "zh-Hant": "按已宣告的字典序挑第一個零入度點，並移除它發出的邊。",
        "en": "Choose the lexicographically first source and remove its outgoing edges."
      },
      "reverse_audit": {
        "kind": "premise_and_result_audit",
        "explanation": {
          "zh-Hant": "核對完整頂點與邊；一個失敗次序不等於有環，全部合法分支不能漏列。",
          "en": "Audit all vertices and edges; one failed order is not a cycle proof, and no legal branch may be omitted."
        }
      },
      "arithmetic": null
    },
    {
      "id": "S006",
      "uses": [
        "G001",
        "S005"
      ],
      "before": "remaining=[v2, v3, v4, v5]; active edges=[]",
      "after": "indegrees=[[v2, 0], [v3, 0], [v4, 0], [v5, 0]]; sources=[v2, v3, v4, v5]",
      "relation": "implies",
      "rule_id": "remaining_indegree",
      "conditions": [],
      "explanation": {
        "zh-Hant": "每次都以尚未移除的邊重新計算入度，不以原始入度硬套全部步驟。",
        "en": "Recompute indegrees from remaining edges at every stage, rather than reusing original indegrees."
      },
      "reverse_audit": {
        "kind": "premise_and_result_audit",
        "explanation": {
          "zh-Hant": "核對完整頂點與邊；一個失敗次序不等於有環，全部合法分支不能漏列。",
          "en": "Audit all vertices and edges; one failed order is not a cycle proof, and no legal branch may be omitted."
        }
      },
      "arithmetic": null
    },
    {
      "id": "S007",
      "uses": [
        "G001",
        "S006"
      ],
      "before": "zero-indegree choices=[v2, v3, v4, v5]",
      "after": "choose=v2; new prefix=[v0, v1, v2]",
      "relation": "implies",
      "rule_id": "lexicographic_kahn_choice",
      "conditions": [],
      "explanation": {
        "zh-Hant": "按已宣告的字典序挑第一個零入度點，並移除它發出的邊。",
        "en": "Choose the lexicographically first source and remove its outgoing edges."
      },
      "reverse_audit": {
        "kind": "premise_and_result_audit",
        "explanation": {
          "zh-Hant": "核對完整頂點與邊；一個失敗次序不等於有環，全部合法分支不能漏列。",
          "en": "Audit all vertices and edges; one failed order is not a cycle proof, and no legal branch may be omitted."
        }
      },
      "arithmetic": null
    },
    {
      "id": "S008",
      "uses": [
        "G001",
        "S007"
      ],
      "before": "remaining=[v3, v4, v5]; active edges=[]",
      "after": "indegrees=[[v3, 0], [v4, 0], [v5, 0]]; sources=[v3, v4, v5]",
      "relation": "implies",
      "rule_id": "remaining_indegree",
      "conditions": [],
      "explanation": {
        "zh-Hant": "每次都以尚未移除的邊重新計算入度，不以原始入度硬套全部步驟。",
        "en": "Recompute indegrees from remaining edges at every stage, rather than reusing original indegrees."
      },
      "reverse_audit": {
        "kind": "premise_and_result_audit",
        "explanation": {
          "zh-Hant": "核對完整頂點與邊；一個失敗次序不等於有環，全部合法分支不能漏列。",
          "en": "Audit all vertices and edges; one failed order is not a cycle proof, and no legal branch may be omitted."
        }
      },
      "arithmetic": null
    },
    {
      "id": "S009",
      "uses": [
        "G001",
        "S008"
      ],
      "before": "zero-indegree choices=[v3, v4, v5]",
      "after": "choose=v3; new prefix=[v0, v1, v2, v3]",
      "relation": "implies",
      "rule_id": "lexicographic_kahn_choice",
      "conditions": [],
      "explanation": {
        "zh-Hant": "按已宣告的字典序挑第一個零入度點，並移除它發出的邊。",
        "en": "Choose the lexicographically first source and remove its outgoing edges."
      },
      "reverse_audit": {
        "kind": "premise_and_result_audit",
        "explanation": {
          "zh-Hant": "核對完整頂點與邊；一個失敗次序不等於有環，全部合法分支不能漏列。",
          "en": "Audit all vertices and edges; one failed order is not a cycle proof, and no legal branch may be omitted."
        }
      },
      "arithmetic": null
    },
    {
      "id": "S010",
      "uses": [
        "G001",
        "S009"
      ],
      "before": "remaining=[v4, v5]; active edges=[]",
      "after": "indegrees=[[v4, 0], [v5, 0]]; sources=[v4, v5]",
      "relation": "implies",
      "rule_id": "remaining_indegree",
      "conditions": [],
      "explanation": {
        "zh-Hant": "每次都以尚未移除的邊重新計算入度，不以原始入度硬套全部步驟。",
        "en": "Recompute indegrees from remaining edges at every stage, rather than reusing original indegrees."
      },
      "reverse_audit": {
        "kind": "premise_and_result_audit",
        "explanation": {
          "zh-Hant": "核對完整頂點與邊；一個失敗次序不等於有環，全部合法分支不能漏列。",
          "en": "Audit all vertices and edges; one failed order is not a cycle proof, and no legal branch may be omitted."
        }
      },
      "arithmetic": null
    },
    {
      "id": "S011",
      "uses": [
        "G001",
        "S010"
      ],
      "before": "zero-indegree choices=[v4, v5]",
      "after": "choose=v4; new prefix=[v0, v1, v2, v3, v4]",
      "relation": "implies",
      "rule_id": "lexicographic_kahn_choice",
      "conditions": [],
      "explanation": {
        "zh-Hant": "按已宣告的字典序挑第一個零入度點，並移除它發出的邊。",
        "en": "Choose the lexicographically first source and remove its outgoing edges."
      },
      "reverse_audit": {
        "kind": "premise_and_result_audit",
        "explanation": {
          "zh-Hant": "核對完整頂點與邊；一個失敗次序不等於有環，全部合法分支不能漏列。",
          "en": "Audit all vertices and edges; one failed order is not a cycle proof, and no legal branch may be omitted."
        }
      },
      "arithmetic": null
    },
    {
      "id": "S012",
      "uses": [
        "G001",
        "S011"
      ],
      "before": "remaining=[v5]; active edges=[]",
      "after": "indegrees=[[v5, 0]]; sources=[v5]",
      "relation": "implies",
      "rule_id": "remaining_indegree",
      "conditions": [],
      "explanation": {
        "zh-Hant": "每次都以尚未移除的邊重新計算入度，不以原始入度硬套全部步驟。",
        "en": "Recompute indegrees from remaining edges at every stage, rather than reusing original indegrees."
      },
      "reverse_audit": {
        "kind": "premise_and_result_audit",
        "explanation": {
          "zh-Hant": "核對完整頂點與邊；一個失敗次序不等於有環，全部合法分支不能漏列。",
          "en": "Audit all vertices and edges; one failed order is not a cycle proof, and no legal branch may be omitted."
        }
      },
      "arithmetic": null
    },
    {
      "id": "S013",
      "uses": [
        "G001",
        "S012"
      ],
      "before": "zero-indegree choices=[v5]",
      "after": "choose=v5; new prefix=[v0, v1, v2, v3, v4, v5]",
      "relation": "implies",
      "rule_id": "lexicographic_kahn_choice",
      "conditions": [],
      "explanation": {
        "zh-Hant": "按已宣告的字典序挑第一個零入度點，並移除它發出的邊。",
        "en": "Choose the lexicographically first source and remove its outgoing edges."
      },
      "reverse_audit": {
        "kind": "premise_and_result_audit",
        "explanation": {
          "zh-Hant": "核對完整頂點與邊；一個失敗次序不等於有環，全部合法分支不能漏列。",
          "en": "Audit all vertices and edges; one failed order is not a cycle proof, and no legal branch may be omitted."
        }
      },
      "arithmetic": null
    },
    {
      "id": "S014",
      "uses": [
        "G001",
        "S013"
      ],
      "before": "output=[v0, v1, v2, v3, v4, v5]; remaining=[]",
      "after": "blocked=否; complete valid order=是",
      "relation": "implies",
      "rule_id": "kahn_final_audit",
      "conditions": [],
      "explanation": {
        "zh-Hant": "完成後仍逐邊檢查最終排列；停住與成功用不同旗標保留。",
        "en": "Audit the final permutation edge by edge, retaining separate blocked and success flags."
      },
      "reverse_audit": {
        "kind": "premise_and_result_audit",
        "explanation": {
          "zh-Hant": "核對完整頂點與邊；一個失敗次序不等於有環，全部合法分支不能漏列。",
          "en": "Audit all vertices and edges; one failed order is not a cycle proof, and no legal branch may be omitted."
        }
      },
      "arithmetic": null
    }
  ],
  "math_model": {
    "result": [
      [
        [
          [
            "v0",
            "v1",
            "v2",
            "v3",
            "v4",
            "v5"
          ],
          [
            "v0",
            "v2",
            "v3",
            "v4"
          ],
          "v0"
        ],
        [
          [
            "v1",
            "v2",
            "v3",
            "v4",
            "v5"
          ],
          [
            "v1",
            "v2",
            "v3",
            "v4",
            "v5"
          ],
          "v1"
        ],
        [
          [
            "v2",
            "v3",
            "v4",
            "v5"
          ],
          [
            "v2",
            "v3",
            "v4",
            "v5"
          ],
          "v2"
        ],
        [
          [
            "v3",
            "v4",
            "v5"
          ],
          [
            "v3",
            "v4",
            "v5"
          ],
          "v3"
        ],
        [
          [
            "v4",
            "v5"
          ],
          [
            "v4",
            "v5"
          ],
          "v4"
        ],
        [
          [
            "v5"
          ],
          [
            "v5"
          ],
          "v5"
        ]
      ],
      [
        "v0",
        "v1",
        "v2",
        "v3",
        "v4",
        "v5"
      ],
      false,
      true,
      "each_step_removes_lexicographically_first_zero_indegree_source"
    ]
  },
  "conclusion": {
    "canonical_value": "([[[v0, v1, v2, v3, v4, v5], [v0, v2, v3, v4], v0], [[v1, v2, v3, v4, v5], [v1, v2, v3, v4, v5], v1], [[v2, v3, v4, v5], [v2, v3, v4, v5], v2], [[v3, v4, v5], [v3, v4, v5], v3], [[v4, v5], [v4, v5], v4], [[v5], [v5], v5]], [v0, v1, v2, v3, v4, v5], 否, 是, each_step_removes_lexicographically_first_zero_indegree_source)",
    "explanation": {
      "zh-Hant": "上述完整代值與條件核對得到原題答案；欄位次序及真假標記保持原始合約。",
      "en": "The full substitutions and premise audits recover the original answer, retaining its field order and verdict meanings."
    }
  },
  "definition_note": {
    "zh-Hant": "每輪以剩餘邊重算入度，取字典序第一個零入度點並刪除其出邊。",
    "en": "Each round recomputes indegrees from the remaining edges and removes the lexicographically first zero-indegree vertex."
  },
  "source": {
    "input_commit": "0f7be61e2c22317a4075561dc822c87d881a50db",
    "question_binding": {
      "batch_id": "batch-20261015-advance-20261116-r06-topological-ordering-dag-foundations",
      "batch_path": "public/data/questions/batches/batch-20261015-advance-20261116-r06-topological-ordering-dag-foundations/questions.jsonl",
      "batch_sha256": "d93ad638d602b169ce66fdacb2c40107b89c1577baa28a2b3fc1b46f2b105460",
      "original_line": 67,
      "original_line_sha256": "9382a6102aeecdb63e5fb3bdae69ca231daf626d65c17346890da6f28c73cdae",
      "question_compact_sha256": "4a5670dfc11c353892eb6fc4d669aac93c5a1ba5de655a99a0c46e43a2f435cf",
      "english_manifest_path": "public/data/i18n/editions/batch-20261015-advance-20261116-r06-topological-ordering-dag-foundations.en.json",
      "english_rows_path": "public/data/i18n/questions/batch-20261015-advance-20261116-r06-topological-ordering-dag-foundations.en.jsonl",
      "english_row_compact_sha256": "e2f912c5e65f986e09c6bb412ab86148a2f3473fae4bffdf17ebc53bd7ab0491"
    },
    "mko_bindings": {
      "mko-topological-ordering-dag": {
        "original_path": "public/data/mko/source13-20261018-topological-ordering-dag.json",
        "english_path": "public/data/i18n/editions/mko-topological-ordering-dag.en.json",
        "sha256": "826499909e9a38a23996ab91062cdf86e73a350078b0b11c2a5fb8828d12e5f9",
        "english_sha256": "3063e85d7b49e8d03329c2cbf2fe9c9b69db6122f1ad297fcebacdb7df784a96"
      }
    },
    "selected_manifest_sha256": "5233edba9654a6cffd8b6b2d83c932f82ded15f9c0b7c733bd049943e672acff",
    "selected_part_sha256": "afa7c0e9f7084cc5929124dcffe9929d5db7def32e40047056d19ea25535873e",
    "original_candidate_sha256": "42143e7b7d502277664834f84bd55b31371f54a27206ef9fa5eb0f6a72693bd0",
    "original_candidate_line_sha256": "42143e7b7d502277664834f84bd55b31371f54a27206ef9fa5eb0f6a72693bd0"
  },
  "historical_source_state": {
    "review_state": {
      "derivation": "candidate_authored_and_locally_checked",
      "source_question_state": "candidate",
      "independent_AI_or_human_review": "NOT_PERFORMED",
      "formalization": "not_formalized",
      "Lean": "NOT_RUN"
    },
    "scope_note": {
      "zh-Hant": "來源綁定的教學推導候選；精確算術及有限列舉不是獨立AI審查或一般形式化證明。原題、答案、MKO、公式、AST及歷史保持不變。",
      "en": "Source-bound pedagogical derivation candidate: exact arithmetic and finite enumeration are not independent AI review or general formal proof. Original questions, answers, MKOs, formulas, ASTs and history remain unchanged."
    },
    "label": "Frozen producer metadata; current per-question review is separate below."
  },
  "revision": {
    "id": "review-20261026-003-03",
    "review_date": "2026-10-26",
    "owner_authorized_reader_publication": true,
    "scope": "Thirty family prototypes and their mathematical/bilingual reasoning variants, stems, boundary statements and every distinct sentence shape were reviewed in a context independent of the producer; parameter substitutions, source bindings, full answer tuples, model results and every arithmetic step were independently reconstructed per question from the original parameters only, with negative controls. This grouped method does not claim a separate literal AI reading of every repeated sentence or an extra AI voter.",
    "review_receipts": {
      "semantic_review_sha256": "6c2c6d46aded7582a11ac41a8c0b3bdde2669a53bdb6e796eea2039994a02772",
      "question_first_witness_sha256": "77e43898df9efdbf8094ad81fe4ab91cf4b4bd82f481eb9b4699b73cb4da612b"
    },
    "status": "second_context_reviewed",
    "mathematical_semantics": true,
    "bilingual_semantics": true,
    "steps_reviewed": 14,
    "method": "family_template_semantic_review_plus_independent_per_instance_reconstruction",
    "exact_question_first_check": {
      "model_sha256": "8531042cf3028a16989302ef03a8db09a144e36ee7fc93035b0489192dd6ba41",
      "arithmetic_steps": 0
    },
    "uses_answer_as_premise": false,
    "human_review": "NOT_PERFORMED",
    "formalization": "not_formalized",
    "Lean": "NOT_RUN",
    "Canonical_truth_promotion": false,
    "authority": "Owner-authorized reviewed reader publication; original question/candidate states remain historical and unchanged."
  }
}