{
  "schema_version": "ocme-reviewed-question-reader-v1",
  "question_id": "q-20261012-advance-20261017-r05-graph-0057",
  "pilot_number": "R0015-08057",
  "number": 8057,
  "family_id": "qf-density17-graph-edge-toggle-delta",
  "title": {
    "zh-Hant": "第 8057 題：切換一條邊的有號度差",
    "en": "Question 8057: Toggle a Typed Nonloop Edge and Compute Degree Changes"
  },
  "original_question": {
    "schema_version": "ocme-question-v0.1",
    "id": "q-20261012-advance-20261017-r05-graph-0057",
    "batch_id": "batch-20261012-advance-20261017-r05-graph-foundations",
    "language": "zh-Hant",
    "source_mko_ids": [
      "mko-graph"
    ],
    "title_zh": "切換一條邊的有號度差",
    "stem_zh": "簡單無向圖，Fin頂點從0起。V=Fin(5)=[0, 1, 2, 3, 4]，無向邊列項=[[0, 1], [0, 2]]；各邊兩端皆合法且相異。候選邊=[0, 4]。已存在則移除，未存在則新增。答 (原邊集, 排序候選邊, 新增或移除, 新邊集, 原度數, 新度數, 有號度數差, 度差總和)。",
    "answer": {
      "kind": "expression",
      "value": "([[0, 1], [0, 2]], [0, 4], 新增, [[0, 1], [0, 2], [0, 4]], [2, 1, 1, 0, 0], [3, 1, 1, 0, 1], [1, 0, 0, 0, 1], 2)",
      "explanation_zh": "離散結構核對=([[0, 1], [0, 2]], [0, 4], 新增, [[0, 1], [0, 2], [0, 4]], [2, 1, 1, 0, 0], [3, 1, 1, 0, 1], [1, 0, 0, 0, 1], 2)；先判是否原有此無向邊，再改一條邊並逐頂點計新度數。；有限精確核對不是一般形式證明；無自環端點已合型；反向或重複邊不增加邊；不由畫法推相鄰。"
    },
    "difficulty": {
      "band": "undergraduate_core",
      "level": 1,
      "skills": [
        "切換一條邊的有號度差"
      ]
    },
    "variant": {
      "family_id": "qf-density17-graph-edge-toggle-delta",
      "seed": 202610175057,
      "parameters": {
        "n": 5,
        "edges": [
          [
            0,
            1
          ],
          [
            0,
            2
          ]
        ],
        "edge": [
          0,
          4
        ],
        "domain": "Fin_simple_undirected_graph",
        "operation": "graph-edge-toggle-delta",
        "semantic_template": "qf-density17-graph-edge-toggle-delta/{\"edge\":[0,4],\"edges\":[[0,1],[0,2]],\"n\":5}"
      }
    },
    "verification": {
      "status": "candidate",
      "checks": [
        "producer_exact_integer_rational_arithmetic",
        "producer_finite_enumeration",
        "producer_source_snapshot_check",
        "producer_substantive_template_deduplication",
        "producer_json_schema"
      ],
      "warning_zh": "僅為產生端候選及自檢；主端須另做獨立驗收，不構成人工審定、普遍證明或形式 Evidence。"
    },
    "provenance": {
      "generator_role": "question_producer",
      "generator_model": "model_unknown",
      "generated_at": "2026-10-12",
      "contract_version": "ocme-question-factory-v0.1"
    }
  },
  "original_english_edition": {
    "schema_version": "ocme-question-localization-v0.1",
    "question_id": "q-20261012-advance-20261017-r05-graph-0057",
    "batch_id": "batch-20261012-advance-20261017-r05-graph-foundations",
    "locale": "en",
    "translation_state": "ai_candidate",
    "source": {
      "question_sha256": "944d5620bf8f51826c9288a10dc83fb0efcb1f099566dd18af480b0b195dc71a",
      "family_id": "qf-density17-graph-edge-toggle-delta",
      "seed": 202610175057,
      "semantic_template": "qf-density17-graph-edge-toggle-delta/{\"edge\":[0,4],\"edges\":[[0,1],[0,2]],\"n\":5}"
    },
    "fields": {
      "title": "Toggle a Typed Nonloop Edge and Compute Degree Changes",
      "stem": "Use a complete simple undirected graph on Fin(5)={0,…,4} with raw edges=[[0, 1], [0, 2]]. Endpoints are typed and loops are prohibited. Reversed or repeated edges count once; normalize endpoints and edge order. Do not infer adjacency from a drawing. Toggle edge=[0, 4]. Give (original normalized edges, normalized toggled edge, removed/added action, new edges, old degrees, new degrees, degree differences, degree-sum difference).",
      "answer": {
        "kind": "expression",
        "value": "([[0, 1], [0, 2]], [0, 4], added, [[0, 1], [0, 2], [0, 4]], [2, 1, 1, 0, 0], [3, 1, 1, 0, 1], [1, 0, 0, 0, 1], 2)",
        "explanation": "Remove an existing edge or insert an absent one, then independently count both degree lists; no loop or invalid endpoint is admitted. These exact finite checks are not new general formal Evidence. The exact result, retaining the requested order, is ([[0, 1], [0, 2]], [0, 4], added, [[0, 1], [0, 2], [0, 4]], [2, 1, 1, 0, 0], [3, 1, 1, 0, 1], [1, 0, 0, 0, 1], 2)."
      },
      "skills": [
        "Toggle a Typed Nonloop Edge and Compute Degree Changes"
      ],
      "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": "簡單無向圖，Fin頂點從0起。V=Fin(5)=[0, 1, 2, 3, 4]，無向邊列項=[[0, 1], [0, 2]]；各邊兩端皆合法且相異。候選邊=[0, 4]。已存在則移除，未存在則新增。答 (原邊集, 排序候選邊, 新增或移除, 新邊集, 原度數, 新度數, 有號度數差, 度差總和)。",
        "en": "Use a complete simple undirected graph on Fin(5)={0,…,4} with raw edges=[[0, 1], [0, 2]]. Endpoints are typed and loops are prohibited. Reversed or repeated edges count once; normalize endpoints and edge order. Do not infer adjacency from a drawing. Toggle edge=[0, 4]. Give (original normalized edges, normalized toggled edge, removed/added action, new edges, old degrees, new degrees, degree differences, degree-sum difference)."
      }
    }
  ],
  "steps": [
    {
      "id": "S001",
      "uses": [
        "G001"
      ],
      "before": "n=5;raw edges=[[0, 1], [0, 2]]",
      "after": "canonical edges=[[0, 1], [0, 2]]",
      "relation": "implies",
      "rule_id": "simple_graph_edge_normalization",
      "conditions": [],
      "explanation": {
        "zh-Hant": "整張簡單無向圖先查端點合型且無自環；邊兩端排序、反向與重複邊只算一次，不以畫法猜相鄰。",
        "en": "Validate every simple undirected edge for typed distinct endpoints.Sort endpoints and count reversed or repeated edges once;do not infer adjacency from a drawing."
      },
      "reverse_audit": {
        "kind": "premise_and_result_audit",
        "explanation": {
          "zh-Hant": "回到原始資料與本步條件核對，不把單向推論誤稱等價。",
          "en": "Check against the original data and this step's premises; a one-way implication is not an equivalence."
        }
      },
      "arithmetic": null
    },
    {
      "id": "S002",
      "uses": [
        "G001",
        "S001"
      ],
      "before": "phase=original;vertex=0;all edges=[[0, 1], [0, 2]]",
      "after": "neighbors=[1, 2];degree=2",
      "relation": "implies",
      "rule_id": "complete_graph_neighbor_inventory",
      "conditions": [],
      "explanation": {
        "zh-Hant": "掃描所有正規邊，只有以本頂點為端點的邊才給一個不同鄰居；原頂點標籤保留。",
        "en": "Scan all canonical edges.An incident edge contributes its other endpoint as a distinct neighbor.Keep original vertex labels."
      },
      "reverse_audit": {
        "kind": "premise_and_result_audit",
        "explanation": {
          "zh-Hant": "回到原始資料與本步條件核對，不把單向推論誤稱等價。",
          "en": "Check against the original data and this step's premises; a one-way implication is not an equivalence."
        }
      },
      "arithmetic": null
    },
    {
      "id": "S003",
      "uses": [
        "G001",
        "S002"
      ],
      "before": "phase=original;vertex=1;all edges=[[0, 1], [0, 2]]",
      "after": "neighbors=[0];degree=1",
      "relation": "implies",
      "rule_id": "complete_graph_neighbor_inventory",
      "conditions": [],
      "explanation": {
        "zh-Hant": "掃描所有正規邊，只有以本頂點為端點的邊才給一個不同鄰居；原頂點標籤保留。",
        "en": "Scan all canonical edges.An incident edge contributes its other endpoint as a distinct neighbor.Keep original vertex labels."
      },
      "reverse_audit": {
        "kind": "premise_and_result_audit",
        "explanation": {
          "zh-Hant": "回到原始資料與本步條件核對，不把單向推論誤稱等價。",
          "en": "Check against the original data and this step's premises; a one-way implication is not an equivalence."
        }
      },
      "arithmetic": null
    },
    {
      "id": "S004",
      "uses": [
        "G001",
        "S003"
      ],
      "before": "phase=original;vertex=2;all edges=[[0, 1], [0, 2]]",
      "after": "neighbors=[0];degree=1",
      "relation": "implies",
      "rule_id": "complete_graph_neighbor_inventory",
      "conditions": [],
      "explanation": {
        "zh-Hant": "掃描所有正規邊，只有以本頂點為端點的邊才給一個不同鄰居；原頂點標籤保留。",
        "en": "Scan all canonical edges.An incident edge contributes its other endpoint as a distinct neighbor.Keep original vertex labels."
      },
      "reverse_audit": {
        "kind": "premise_and_result_audit",
        "explanation": {
          "zh-Hant": "回到原始資料與本步條件核對，不把單向推論誤稱等價。",
          "en": "Check against the original data and this step's premises; a one-way implication is not an equivalence."
        }
      },
      "arithmetic": null
    },
    {
      "id": "S005",
      "uses": [
        "G001",
        "S004"
      ],
      "before": "phase=original;vertex=3;all edges=[[0, 1], [0, 2]]",
      "after": "neighbors=[];degree=0",
      "relation": "implies",
      "rule_id": "complete_graph_neighbor_inventory",
      "conditions": [],
      "explanation": {
        "zh-Hant": "掃描所有正規邊，只有以本頂點為端點的邊才給一個不同鄰居；原頂點標籤保留。",
        "en": "Scan all canonical edges.An incident edge contributes its other endpoint as a distinct neighbor.Keep original vertex labels."
      },
      "reverse_audit": {
        "kind": "premise_and_result_audit",
        "explanation": {
          "zh-Hant": "回到原始資料與本步條件核對，不把單向推論誤稱等價。",
          "en": "Check against the original data and this step's premises; a one-way implication is not an equivalence."
        }
      },
      "arithmetic": null
    },
    {
      "id": "S006",
      "uses": [
        "G001",
        "S005"
      ],
      "before": "phase=original;vertex=4;all edges=[[0, 1], [0, 2]]",
      "after": "neighbors=[];degree=0",
      "relation": "implies",
      "rule_id": "complete_graph_neighbor_inventory",
      "conditions": [],
      "explanation": {
        "zh-Hant": "掃描所有正規邊，只有以本頂點為端點的邊才給一個不同鄰居；原頂點標籤保留。",
        "en": "Scan all canonical edges.An incident edge contributes its other endpoint as a distinct neighbor.Keep original vertex labels."
      },
      "reverse_audit": {
        "kind": "premise_and_result_audit",
        "explanation": {
          "zh-Hant": "回到原始資料與本步條件核對，不把單向推論誤稱等價。",
          "en": "Check against the original data and this step's premises; a one-way implication is not an equivalence."
        }
      },
      "arithmetic": null
    },
    {
      "id": "S007",
      "uses": [
        "G001",
        "S006"
      ],
      "before": "typed candidate=[0, 4];old edges=[[0, 1], [0, 2]]",
      "after": "action=新增;new edges=[[0, 1], [0, 2], [0, 4]]",
      "relation": "implies",
      "rule_id": "toggle_one_undirected_nonloop_edge",
      "conditions": [],
      "explanation": {
        "zh-Hant": "反向候選先正規化，再由原邊集決定新增或移除，恰改一條無向邊。",
        "en": "Normalize a reversed candidate first,then decide addition/removal from the original edge set.Exactly one undirected edge changes."
      },
      "reverse_audit": {
        "kind": "premise_and_result_audit",
        "explanation": {
          "zh-Hant": "回到原始資料與本步條件核對，不把單向推論誤稱等價。",
          "en": "Check against the original data and this step's premises; a one-way implication is not an equivalence."
        }
      },
      "arithmetic": null
    },
    {
      "id": "S008",
      "uses": [
        "G001",
        "S007"
      ],
      "before": "phase=toggled;vertex=0;all edges=[[0, 1], [0, 2], [0, 4]]",
      "after": "neighbors=[1, 2, 4];degree=3",
      "relation": "implies",
      "rule_id": "complete_graph_neighbor_inventory",
      "conditions": [],
      "explanation": {
        "zh-Hant": "掃描所有正規邊，只有以本頂點為端點的邊才給一個不同鄰居；原頂點標籤保留。",
        "en": "Scan all canonical edges.An incident edge contributes its other endpoint as a distinct neighbor.Keep original vertex labels."
      },
      "reverse_audit": {
        "kind": "premise_and_result_audit",
        "explanation": {
          "zh-Hant": "回到原始資料與本步條件核對，不把單向推論誤稱等價。",
          "en": "Check against the original data and this step's premises; a one-way implication is not an equivalence."
        }
      },
      "arithmetic": null
    },
    {
      "id": "S009",
      "uses": [
        "G001",
        "S008"
      ],
      "before": "phase=toggled;vertex=1;all edges=[[0, 1], [0, 2], [0, 4]]",
      "after": "neighbors=[0];degree=1",
      "relation": "implies",
      "rule_id": "complete_graph_neighbor_inventory",
      "conditions": [],
      "explanation": {
        "zh-Hant": "掃描所有正規邊，只有以本頂點為端點的邊才給一個不同鄰居；原頂點標籤保留。",
        "en": "Scan all canonical edges.An incident edge contributes its other endpoint as a distinct neighbor.Keep original vertex labels."
      },
      "reverse_audit": {
        "kind": "premise_and_result_audit",
        "explanation": {
          "zh-Hant": "回到原始資料與本步條件核對，不把單向推論誤稱等價。",
          "en": "Check against the original data and this step's premises; a one-way implication is not an equivalence."
        }
      },
      "arithmetic": null
    },
    {
      "id": "S010",
      "uses": [
        "G001",
        "S009"
      ],
      "before": "phase=toggled;vertex=2;all edges=[[0, 1], [0, 2], [0, 4]]",
      "after": "neighbors=[0];degree=1",
      "relation": "implies",
      "rule_id": "complete_graph_neighbor_inventory",
      "conditions": [],
      "explanation": {
        "zh-Hant": "掃描所有正規邊，只有以本頂點為端點的邊才給一個不同鄰居；原頂點標籤保留。",
        "en": "Scan all canonical edges.An incident edge contributes its other endpoint as a distinct neighbor.Keep original vertex labels."
      },
      "reverse_audit": {
        "kind": "premise_and_result_audit",
        "explanation": {
          "zh-Hant": "回到原始資料與本步條件核對，不把單向推論誤稱等價。",
          "en": "Check against the original data and this step's premises; a one-way implication is not an equivalence."
        }
      },
      "arithmetic": null
    },
    {
      "id": "S011",
      "uses": [
        "G001",
        "S010"
      ],
      "before": "phase=toggled;vertex=3;all edges=[[0, 1], [0, 2], [0, 4]]",
      "after": "neighbors=[];degree=0",
      "relation": "implies",
      "rule_id": "complete_graph_neighbor_inventory",
      "conditions": [],
      "explanation": {
        "zh-Hant": "掃描所有正規邊，只有以本頂點為端點的邊才給一個不同鄰居；原頂點標籤保留。",
        "en": "Scan all canonical edges.An incident edge contributes its other endpoint as a distinct neighbor.Keep original vertex labels."
      },
      "reverse_audit": {
        "kind": "premise_and_result_audit",
        "explanation": {
          "zh-Hant": "回到原始資料與本步條件核對，不把單向推論誤稱等價。",
          "en": "Check against the original data and this step's premises; a one-way implication is not an equivalence."
        }
      },
      "arithmetic": null
    },
    {
      "id": "S012",
      "uses": [
        "G001",
        "S011"
      ],
      "before": "phase=toggled;vertex=4;all edges=[[0, 1], [0, 2], [0, 4]]",
      "after": "neighbors=[0];degree=1",
      "relation": "implies",
      "rule_id": "complete_graph_neighbor_inventory",
      "conditions": [],
      "explanation": {
        "zh-Hant": "掃描所有正規邊，只有以本頂點為端點的邊才給一個不同鄰居；原頂點標籤保留。",
        "en": "Scan all canonical edges.An incident edge contributes its other endpoint as a distinct neighbor.Keep original vertex labels."
      },
      "reverse_audit": {
        "kind": "premise_and_result_audit",
        "explanation": {
          "zh-Hant": "回到原始資料與本步條件核對，不把單向推論誤稱等價。",
          "en": "Check against the original data and this step's premises; a one-way implication is not an equivalence."
        }
      },
      "arithmetic": null
    },
    {
      "id": "S013",
      "uses": [
        "G001",
        "S012"
      ],
      "before": "degree delta0 := sub(3, 2)",
      "after": "degree delta0 = 1",
      "relation": "calculation",
      "rule_id": "exact_rational_arithmetic",
      "conditions": [],
      "explanation": {
        "zh-Hant": "按本步指定順序精確代入原數據，分母非零才允許除法。",
        "en": "Substitute the source data exactly in the stated operand order;division requires a nonzero denominator."
      },
      "reverse_audit": {
        "kind": "premise_and_result_audit",
        "explanation": {
          "zh-Hant": "以精確有理數重算 degree delta0，不以小數近似替代。",
          "en": "Recompute degree delta0 with exact rational arithmetic, not rounded decimals."
        }
      },
      "arithmetic": {
        "operation": "sub",
        "inputs": [
          "3",
          "2"
        ],
        "output": "1",
        "label": "degree delta0"
      }
    },
    {
      "id": "S014",
      "uses": [
        "G001",
        "S013"
      ],
      "before": "degree delta1 := sub(1, 1)",
      "after": "degree delta1 = 0",
      "relation": "calculation",
      "rule_id": "exact_rational_arithmetic",
      "conditions": [],
      "explanation": {
        "zh-Hant": "按本步指定順序精確代入原數據，分母非零才允許除法。",
        "en": "Substitute the source data exactly in the stated operand order;division requires a nonzero denominator."
      },
      "reverse_audit": {
        "kind": "premise_and_result_audit",
        "explanation": {
          "zh-Hant": "以精確有理數重算 degree delta1，不以小數近似替代。",
          "en": "Recompute degree delta1 with exact rational arithmetic, not rounded decimals."
        }
      },
      "arithmetic": {
        "operation": "sub",
        "inputs": [
          "1",
          "1"
        ],
        "output": "0",
        "label": "degree delta1"
      }
    },
    {
      "id": "S015",
      "uses": [
        "G001",
        "S014"
      ],
      "before": "degree delta2 := sub(1, 1)",
      "after": "degree delta2 = 0",
      "relation": "calculation",
      "rule_id": "exact_rational_arithmetic",
      "conditions": [],
      "explanation": {
        "zh-Hant": "按本步指定順序精確代入原數據，分母非零才允許除法。",
        "en": "Substitute the source data exactly in the stated operand order;division requires a nonzero denominator."
      },
      "reverse_audit": {
        "kind": "premise_and_result_audit",
        "explanation": {
          "zh-Hant": "以精確有理數重算 degree delta2，不以小數近似替代。",
          "en": "Recompute degree delta2 with exact rational arithmetic, not rounded decimals."
        }
      },
      "arithmetic": {
        "operation": "sub",
        "inputs": [
          "1",
          "1"
        ],
        "output": "0",
        "label": "degree delta2"
      }
    },
    {
      "id": "S016",
      "uses": [
        "G001",
        "S015"
      ],
      "before": "degree delta3 := sub(0, 0)",
      "after": "degree delta3 = 0",
      "relation": "calculation",
      "rule_id": "exact_rational_arithmetic",
      "conditions": [],
      "explanation": {
        "zh-Hant": "按本步指定順序精確代入原數據，分母非零才允許除法。",
        "en": "Substitute the source data exactly in the stated operand order;division requires a nonzero denominator."
      },
      "reverse_audit": {
        "kind": "premise_and_result_audit",
        "explanation": {
          "zh-Hant": "以精確有理數重算 degree delta3，不以小數近似替代。",
          "en": "Recompute degree delta3 with exact rational arithmetic, not rounded decimals."
        }
      },
      "arithmetic": {
        "operation": "sub",
        "inputs": [
          "0",
          "0"
        ],
        "output": "0",
        "label": "degree delta3"
      }
    },
    {
      "id": "S017",
      "uses": [
        "G001",
        "S016"
      ],
      "before": "degree delta4 := sub(1, 0)",
      "after": "degree delta4 = 1",
      "relation": "calculation",
      "rule_id": "exact_rational_arithmetic",
      "conditions": [],
      "explanation": {
        "zh-Hant": "按本步指定順序精確代入原數據，分母非零才允許除法。",
        "en": "Substitute the source data exactly in the stated operand order;division requires a nonzero denominator."
      },
      "reverse_audit": {
        "kind": "premise_and_result_audit",
        "explanation": {
          "zh-Hant": "以精確有理數重算 degree delta4，不以小數近似替代。",
          "en": "Recompute degree delta4 with exact rational arithmetic, not rounded decimals."
        }
      },
      "arithmetic": {
        "operation": "sub",
        "inputs": [
          "1",
          "0"
        ],
        "output": "1",
        "label": "degree delta4"
      }
    },
    {
      "id": "S018",
      "uses": [
        "G001",
        "S017"
      ],
      "before": "degree delta sum := sum(1, 0, 0, 0, 1)",
      "after": "degree delta sum = 2",
      "relation": "calculation",
      "rule_id": "exact_rational_arithmetic",
      "conditions": [],
      "explanation": {
        "zh-Hant": "按本步指定順序精確代入原數據，分母非零才允許除法。",
        "en": "Substitute the source data exactly in the stated operand order;division requires a nonzero denominator."
      },
      "reverse_audit": {
        "kind": "premise_and_result_audit",
        "explanation": {
          "zh-Hant": "以精確有理數重算 degree delta sum，不以小數近似替代。",
          "en": "Recompute degree delta sum with exact rational arithmetic, not rounded decimals."
        }
      },
      "arithmetic": {
        "operation": "sum",
        "inputs": [
          "1",
          "0",
          "0",
          "0",
          "1"
        ],
        "output": "2",
        "label": "degree delta sum"
      }
    }
  ],
  "math_model": {
    "result": [
      [
        [
          0,
          1
        ],
        [
          0,
          2
        ]
      ],
      [
        0,
        4
      ],
      "新增",
      [
        [
          0,
          1
        ],
        [
          0,
          2
        ],
        [
          0,
          4
        ]
      ],
      [
        2,
        1,
        1,
        0,
        0
      ],
      [
        3,
        1,
        1,
        0,
        1
      ],
      [
        "1",
        "0",
        "0",
        "0",
        "1"
      ],
      "2"
    ]
  },
  "conclusion": {
    "canonical_value": "([[0, 1], [0, 2]], [0, 4], 新增, [[0, 1], [0, 2], [0, 4]], [2, 1, 1, 0, 0], [3, 1, 1, 0, 1], [1, 0, 0, 0, 1], 2)",
    "explanation": {
      "zh-Hant": "依上列完整代值及條件核對得到原題答案；原題編號、格式與狀態保持不變。",
      "en": "The full substitutions and premise checks give the original answer; source identity,format and status are unchanged."
    }
  },
  "definition_note": {
    "zh-Hant": "沿用原題明示的論域、假設與來源 MKO 定義。本題已完成第二對話數理與中英語義覆核，並由原始參數逐題獨立重算模型、答案與每個算術步驟；原題仍為 candidate。",
    "en": "Use the original question domain, assumptions and cited MKO definitions. This item has second-context mathematical and bilingual review, with the model, answer and every arithmetic step independently recomputed from the original parameters; the source question remains a candidate."
  },
  "source": {
    "input_commit": "0f7be61e2c22317a4075561dc822c87d881a50db",
    "question_binding": {
      "batch_id": "batch-20261012-advance-20261017-r05-graph-foundations",
      "batch_path": "public/data/questions/batches/batch-20261012-advance-20261017-r05-graph-foundations/questions.jsonl",
      "batch_sha256": "a86da678771d2977669cd5e9bbbbc7d4a9dde189d293af5c1f2efa0ba35b82ce",
      "original_line": 57,
      "original_line_sha256": "af9425d4789a2407d0dcf0a10d94a0ce68d6912e604f978a81a86c624c6c6601",
      "question_compact_sha256": "944d5620bf8f51826c9288a10dc83fb0efcb1f099566dd18af480b0b195dc71a",
      "english_row_compact_sha256": "eae791bbfee4fb70e2c233917f5729d1eb3c99b95ee6d330b03e5fd30c035f1b",
      "english_manifest_path": "public/data/i18n/editions/batch-20261012-advance-20261017-r05-graph-foundations.en.json",
      "english_rows_path": "public/data/i18n/questions/batch-20261012-advance-20261017-r05-graph-foundations.en.jsonl"
    },
    "mko_bindings": {
      "mko-graph": {
        "sha256": "47d40107cd3836bb878ae46e5c4766288abb1b91e480c38ed14f61f749d27d55",
        "english_sha256": "985d93ed708f51da0e885228658ca76c7075f5bf67bb09b35d10745db33dc847",
        "original_path": "public/data/mko/graph.json",
        "english_path": "public/data/i18n/editions/mko-graph.en.json"
      }
    },
    "selected_manifest_sha256": "5233edba9654a6cffd8b6b2d83c932f82ded15f9c0b7c733bd049943e672acff",
    "selected_part_sha256": "ca1078dc467a0f3769865919aadc46c87712d098f1dfbde90f787471e22bcfec",
    "original_candidate_sha256": "18055b4a4cf046064530e6db64a3585e02614cf2db2ab6658f0a26220adb4854",
    "original_candidate_line_sha256": "18055b4a4cf046064530e6db64a3585e02614cf2db2ab6658f0a26220adb4854"
  },
  "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": "來源綁定教學推導候選；精確核對不等於獨立AI／人工審查或一般形式證明。原題、答案、MKO、公式、AST與歷史不變。",
      "en": "Source-bound pedagogical derivation candidate.Exact checking is not independent AI/human 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-20261026-005-p16",
    "review_date": "2026-10-26",
    "owner_authorized_reader_publication": true,
    "scope": "One hundred sixty family prototypes and their mathematical/bilingual reasoning variants, stems, boundary statements and every distinct explanation shape were reviewed in a context independent of the producer; parameter substitutions, source bindings, full math models, both answer strings 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": "6ecad9d909199221a07e923f87425e80b3bdec3eed46fe5910d04fca694cae18",
      "question_first_witness_sha256": "e8f00458977a09493b5f9f05ab9e6feec72debaf4c7d1c609d1fc95900a35a1b"
    },
    "status": "second_context_reviewed",
    "mathematical_semantics": true,
    "bilingual_semantics": true,
    "steps_reviewed": 18,
    "method": "family_template_semantic_review_plus_independent_per_instance_reconstruction",
    "exact_question_first_check": {
      "model_sha256": "3ddef56433cd8da1d102d5f062b7d64476bbc95a0b7b955d15db0ca3ba88f67f",
      "arithmetic_steps": 6
    },
    "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."
  }
}