{
  "schema_version": "ocme-reviewed-question-reader-v1",
  "question_id": "q-20261015-advance-20261117-r05-quotient-topology-0066",
  "pilot_number": "R0052-26841",
  "number": 26841,
  "family_id": "qf-mod48-quotient-final-continuity",
  "title": {
    "zh-Hant": "第 26841 題：商拓撲",
    "en": "Question 26841: The Final-Topology Criterion Compares h with Its Composite with q"
  },
  "original_question": {
    "schema_version": "ocme-question-v0.1",
    "id": "q-20261015-advance-20261117-r05-quotient-topology-0066",
    "batch_id": "batch-20261015-advance-20261117-r05-quotient-topology-foundations",
    "language": "zh-Hant",
    "source_mko_ids": [
      "mko-quotient-topology"
    ],
    "title_zh": "商拓撲",
    "stem_zh": "finite total surjection、fibers與U open iff q-preimage(U) open責任。操作=quotient-final-continuity；資料={\"x_points\":[0,1,2,3,4,5],\"x_topology\":[[],[0,1,2,3,4,5],[0,5]],\"y_points\":[\"a\",\"b\"],\"q_map\":[\"a\",\"b\",\"b\",\"b\",\"b\",\"a\"],\"z_points\":[0,1],\"z_topology\":[[],[1],[0,1]],\"h_map\":[0,1]}。請依 exact_ordered_tuple_declared_by_interface 欄序回答。",
    "answer": {
      "kind": "expression",
      "value": "(否, 否, 是, [[a, 0], [b, 1]], [[0, 0], [1, 1], [2, 1], [3, 1], [4, 1], [5, 0]], quotient_final_property_for_surjective_q)",
      "explanation_zh": "Wave6第十一層核對=(否, 否, 是, [[a, 0], [b, 1]], [[0, 0], [1, 1], [2, 1], [3, 1], [4, 1], [5, 0]], quotient_final_property_for_surjective_q)；依完整明示資料獨立重算；只由saturated opens對應quotient opens，final continuity需完整preimage audit；open images、非滿射或任意coarser topology不等於quotient topology。"
    },
    "difficulty": {
      "band": "undergraduate_core",
      "level": 2,
      "skills": [
        "商拓撲"
      ]
    },
    "variant": {
      "family_id": "qf-mod48-quotient-final-continuity",
      "seed": 202611175066,
      "parameters": {
        "x_points": [
          0,
          1,
          2,
          3,
          4,
          5
        ],
        "x_topology": [
          [],
          [
            0,
            1,
            2,
            3,
            4,
            5
          ],
          [
            0,
            5
          ]
        ],
        "y_points": [
          "a",
          "b"
        ],
        "q_map": [
          "a",
          "b",
          "b",
          "b",
          "b",
          "a"
        ],
        "z_points": [
          0,
          1
        ],
        "z_topology": [
          [],
          [
            1
          ],
          [
            0,
            1
          ]
        ],
        "h_map": [
          0,
          1
        ],
        "domain": "Complete_finite_quotient_topology",
        "operation": "quotient-final-continuity",
        "semantic_template": "quotient-final-continuity|{h_map:[[\"a\",0],[\"b\",1]],q_map:[[0,\"a\"],[1,\"b\"],[2,\"b\"],[3,\"b\"],[4,\"b\"],[5,\"a\"]],x_points:[0,1,2,3,4,5],x_topology:[[],[0,1,2,3,4,5],[0,5]],y_points:[\"a\",\"b\"],z_points:[0,1],z_topology:[[],[0,1],[1]]}"
      }
    },
    "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；不構成一般series、uniform-limit或topology定理證明、人工審定、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-20261117-r05-quotient-topology-0066",
    "batch_id": "batch-20261015-advance-20261117-r05-quotient-topology-foundations",
    "locale": "en",
    "translation_state": "ai_candidate",
    "source": {
      "question_sha256": "43ad0f4a17e08cd27f138807067d89da2d0f3be24dd63ea3811907e819f42f23",
      "family_id": "qf-mod48-quotient-final-continuity",
      "seed": 202611175066,
      "semantic_template": "quotient-final-continuity|{h_map:[[\"a\",0],[\"b\",1]],q_map:[[0,\"a\"],[1,\"b\"],[2,\"b\"],[3,\"b\"],[4,\"b\"],[5,\"a\"]],x_points:[0,1,2,3,4,5],x_topology:[[],[0,1,2,3,4,5],[0,5]],y_points:[\"a\",\"b\"],z_points:[0,1],z_topology:[[],[0,1],[1]]}"
    },
    "fields": {
      "title": "The Final-Topology Criterion Compares h with Its Composite with q",
      "stem": "Use complete source points=[0, 1, 2, 3, 4, 5], topology=[[], [0, 1, 2, 3, 4, 5], [0, 5]], target carrier=[a, b] and aligned total q=[a, b, b, b, b, a]. Normal quotient families require q surjective. Target opens are exactly the subsets with open full preimage; continuity alone is weaker. Target Z=[0, 1], topology=[[], [1], [0, 1]], aligned h=[0, 1]. Give (h_continuous, composite_continuous, criterion_equivalence, h_rows, composite_rows, certificate).",
      "answer": {
        "kind": "expression",
        "value": "(No, No, Yes, [[a, 0], [b, 1]], [[0, 0], [1, 1], [2, 1], [3, 1], [4, 1], [5, 0]], quotient_final_property_for_surjective_q)",
        "explanation": "Audit every target-open preimage for h and h∘q with their complete aligned tables. Both maps can be discontinuous while the equivalence holds. The qualified surjection and full final topology precede this criterion. The exact result, retaining the requested order, is (No, No, Yes, [[a, 0], [b, 1]], [[0, 0], [1, 1], [2, 1], [3, 1], [4, 1], [5, 0]], quotient_final_property_for_surjective_q)."
      },
      "skills": [
        "The Final-Topology Criterion Compares h with Its Composite with q"
      ],
      "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 total surjection、fibers與U open iff q-preimage(U) open責任。操作=quotient-final-continuity；資料={\"x_points\":[0,1,2,3,4,5],\"x_topology\":[[],[0,1,2,3,4,5],[0,5]],\"y_points\":[\"a\",\"b\"],\"q_map\":[\"a\",\"b\",\"b\",\"b\",\"b\",\"a\"],\"z_points\":[0,1],\"z_topology\":[[],[1],[0,1]],\"h_map\":[0,1]}。請依 exact_ordered_tuple_declared_by_interface 欄序回答。",
        "en": "Use complete source points=[0, 1, 2, 3, 4, 5], topology=[[], [0, 1, 2, 3, 4, 5], [0, 5]], target carrier=[a, b] and aligned total q=[a, b, b, b, b, a]. Normal quotient families require q surjective. Target opens are exactly the subsets with open full preimage; continuity alone is weaker. Target Z=[0, 1], topology=[[], [1], [0, 1]], aligned h=[0, 1]. Give (h_continuous, composite_continuous, criterion_equivalence, h_rows, composite_rows, certificate)."
      }
    }
  ],
  "steps": [
    {
      "id": "S001",
      "uses": [
        "G001"
      ],
      "before": "source roles = [quotient-final-continuity]",
      "after": "derived = [[h_continuous, composite_continuous, equivalence, h_rows, composite_rows, certificate]]",
      "relation": "implies",
      "rule_id": "source_ordered_fields_without_JS",
      "conditions": [],
      "explanation": {
        "zh-Hant": "直接列出此操作及mode的完整來源欄序，不需JavaScript；布林、字串與null角色保持區別，不補欄或以答案形狀猜介面。",
        "en": "List this operation/mode exact source field order without JavaScript.Keep Boolean,string and null roles distinct;do not pad fields or infer the interface from answer shape."
      },
      "reverse_audit": {
        "kind": "premise_and_result_audit",
        "explanation": {
          "zh-Hant": "反查原題的完整資料、型別、欄序與本步條件；有限核對不升格為無限定理的形式證明。",
          "en": "Reverse-check the complete original data,types,field order and premises;finite audits are not formal proofs of infinite theorems."
        }
      },
      "arithmetic": null
    },
    {
      "id": "S002",
      "uses": [
        "G001",
        "S001"
      ],
      "before": "source roles = [quotient ORIGINAL X, [0, 1, 2, 3, 4, 5], [[], [0, 1, 2, 3, 4, 5], [0, 5]], 否]",
      "after": "derived = [[0, 1, 2, 3, 4, 5], [[], [0, 1, 2, 3, 4, 5], [0, 5]], [[0, 0, 0, 0, 是, 是], [0, 1, 63, 0, 是, 是], [0, 2, 33, 0, 是, 是], [1, 0, 63, 0, 是, 是], [1, 1, 63, 63, 是, 是], [1, 2, 63, 33, 是, 是], [2, 0, 33, 0, 是, 是], [2, 1, 63, 33, 是, 是], [2, 2, 33, 33, 是, 是]]]",
      "relation": "implies",
      "rule_id": "Topology_full_typed_carrier_and_ALL_pair_axioms",
      "conditions": [],
      "explanation": {
        "zh-Hant": "保留JSON型別，set與open族依來源English序。逐全部open pair驗union及intersection，含空集與全集；有限族的二元閉包給任意union閉包，不由抽樣認定topology。",
        "en": "Retain JSON types and English source ordering of sets and open families.Check union/intersection for every open pair and empty/full sets;in a finite family binary closure gives arbitrary-union closure,not sampled qualification."
      },
      "reverse_audit": {
        "kind": "premise_and_result_audit",
        "explanation": {
          "zh-Hant": "反查原題的完整資料、型別、欄序與本步條件；有限核對不升格為無限定理的形式證明。",
          "en": "Reverse-check the complete original data,types,field order and premises;finite audits are not formal proofs of infinite theorems."
        }
      },
      "arithmetic": null
    },
    {
      "id": "S003",
      "uses": [
        "G001",
        "S002"
      ],
      "before": "source roles = [[0, 1, 2, 3, 4, 5], [a, b], [a, b, b, b, b, a]]",
      "after": "derived = [[[0, a], [1, b], [2, b], [3, b], [4, b], [5, a]], [[a, [0, 5]], [b, [1, 2, 3, 4]]], 是]",
      "relation": "implies",
      "rule_id": "Quotient_ORIGINAL_domain_alignment_ALL_fibers",
      "conditions": [],
      "explanation": {
        "zh-Hant": "依原始X次序綁定q再排序，對每個typed Y點取完整fiber。total map保每個x恰屬一fiber；surjective才保每fiber非空。",
        "en": "Bind q to the ORIGINAL X order before sorting and compute the full fiber of every typed Y point.Totality gives exactly one fiber per x;surjectivity additionally makes every fiber nonempty."
      },
      "reverse_audit": {
        "kind": "premise_and_result_audit",
        "explanation": {
          "zh-Hant": "反查原題的完整資料、型別、欄序與本步條件；有限核對不升格為無限定理的形式證明。",
          "en": "Reverse-check the complete original data,types,field order and premises;finite audits are not formal proofs of infinite theorems."
        }
      },
      "arithmetic": null
    },
    {
      "id": "S004",
      "uses": [
        "G001",
        "S003"
      ],
      "before": "source roles = [[0, 1, 2, 3, 4, 5], [[], [0, 1, 2, 3, 4, 5], [0, 5]], [a, b], [[0, a], [1, b], [2, b], [3, b], [4, b], [5, a]]]",
      "after": "derived = [[[0, [], [], 是], [1, [a], [0, 5], 是], [2, [b], [1, 2, 3, 4], 否], [3, [a, b], [0, 1, 2, 3, 4, 5], 是]], [[a, b], [a], []]]",
      "relation": "implies",
      "rule_id": "Quotient_ALL_target_subsets_PREIMAGE_IFF_unique_final_topology",
      "conditions": [],
      "explanation": {
        "zh-Hant": "逐Y的所有subsets，以完整反像在X是否open定義IFF。反像保空、全集、任意union與有限intersection，故生成topology且此IFF逐subset唯一決定它；此唯一性不需要surjection。",
        "en": "For every subset of Y use openness of its full X preimage as an IFF.Preimages preserve empty/full sets,arbitrary unions and finite intersections,hence define a topology.The IFF uniquely determines each subset status even without surjectivity."
      },
      "reverse_audit": {
        "kind": "premise_and_result_audit",
        "explanation": {
          "zh-Hant": "反查原題的完整資料、型別、欄序與本步條件；有限核對不升格為無限定理的形式證明。",
          "en": "Reverse-check the complete original data,types,field order and premises;finite audits are not formal proofs of infinite theorems."
        }
      },
      "arithmetic": null
    },
    {
      "id": "S005",
      "uses": [
        "G001",
        "S004"
      ],
      "before": "source roles = [quotient GENERATED final topology, [a, b], [[a, b], [a], []], 否]",
      "after": "derived = [[a, b], [[a, b], [a], []], [[0, 0, 3, 3, 是, 是], [0, 1, 3, 1, 是, 是], [0, 2, 3, 0, 是, 是], [1, 0, 3, 1, 是, 是], [1, 1, 1, 1, 是, 是], [1, 2, 1, 0, 是, 是], [2, 0, 3, 0, 是, 是], [2, 1, 1, 0, 是, 是], [2, 2, 0, 0, 是, 是]]]",
      "relation": "implies",
      "rule_id": "Topology_full_typed_carrier_and_ALL_pair_axioms",
      "conditions": [],
      "explanation": {
        "zh-Hant": "保留JSON型別，set與open族依來源English序。逐全部open pair驗union及intersection，含空集與全集；有限族的二元閉包給任意union閉包，不由抽樣認定topology。",
        "en": "Retain JSON types and English source ordering of sets and open families.Check union/intersection for every open pair and empty/full sets;in a finite family binary closure gives arbitrary-union closure,not sampled qualification."
      },
      "reverse_audit": {
        "kind": "premise_and_result_audit",
        "explanation": {
          "zh-Hant": "反查原題的完整資料、型別、欄序與本步條件；有限核對不升格為無限定理的形式證明。",
          "en": "Reverse-check the complete original data,types,field order and premises;finite audits are not formal proofs of infinite theorems."
        }
      },
      "arithmetic": null
    },
    {
      "id": "S006",
      "uses": [
        "G001",
        "S005"
      ],
      "before": "source roles = [[[], [0, 1, 2, 3, 4, 5], [0, 5]], [[0, a], [1, b], [2, b], [3, b], [4, b], [5, a]]]",
      "after": "derived = [[[], [0, 1, 2, 3, 4, 5], [0, 5]], 是]",
      "relation": "implies",
      "rule_id": "Quotient_ALL_source_open_saturation_correspondence",
      "conditions": [],
      "explanation": {
        "zh-Hant": "source opens依原canonical序逐一核A=q^-1(q(A))；只有saturated opens才對應完整fiber聯集。surjective時q^-1在Y subsets上單射，與這些opens互逆，不能把所有source opens當商開集。",
        "en": "Audit A=q^-1(q(A)) for every source open in original canonical order.Only saturated opens are full unions of fibers.For surjective q,preimage is injective on Y subsets and gives the correspondence;not every source open is a quotient open."
      },
      "reverse_audit": {
        "kind": "premise_and_result_audit",
        "explanation": {
          "zh-Hant": "反查原題的完整資料、型別、欄序與本步條件；有限核對不升格為無限定理的形式證明。",
          "en": "Reverse-check the complete original data,types,field order and premises;finite audits are not formal proofs of infinite theorems."
        }
      },
      "arithmetic": null
    },
    {
      "id": "S007",
      "uses": [
        "G001",
        "S006"
      ],
      "before": "source roles = [quotient ORIGINAL Z, [0, 1], [[], [1], [0, 1]], 否]",
      "after": "derived = [[0, 1], [[], [0, 1], [1]], [[0, 0, 0, 0, 是, 是], [0, 1, 3, 0, 是, 是], [0, 2, 2, 0, 是, 是], [1, 0, 3, 0, 是, 是], [1, 1, 3, 3, 是, 是], [1, 2, 3, 2, 是, 是], [2, 0, 2, 0, 是, 是], [2, 1, 3, 2, 是, 是], [2, 2, 2, 2, 是, 是]]]",
      "relation": "implies",
      "rule_id": "Topology_full_typed_carrier_and_ALL_pair_axioms",
      "conditions": [],
      "explanation": {
        "zh-Hant": "保留JSON型別，set與open族依來源English序。逐全部open pair驗union及intersection，含空集與全集；有限族的二元閉包給任意union閉包，不由抽樣認定topology。",
        "en": "Retain JSON types and English source ordering of sets and open families.Check union/intersection for every open pair and empty/full sets;in a finite family binary closure gives arbitrary-union closure,not sampled qualification."
      },
      "reverse_audit": {
        "kind": "premise_and_result_audit",
        "explanation": {
          "zh-Hant": "反查原題的完整資料、型別、欄序與本步條件；有限核對不升格為無限定理的形式證明。",
          "en": "Reverse-check the complete original data,types,field order and premises;finite audits are not formal proofs of infinite theorems."
        }
      },
      "arithmetic": null
    },
    {
      "id": "S008",
      "uses": [
        "G001",
        "S007"
      ],
      "before": "source roles = [quotient ORIGINAL h, [a, b], [[a, b], [a], []], [0, 1], [[], [0, 1], [1]], [[a, 0], [b, 1]]]",
      "after": "derived = [[[[], [], 是], [[0, 1], [a, b], 是], [[1], [b], 否]], 否]",
      "relation": "implies",
      "rule_id": "Continuity_ALL_target_open_preimages",
      "conditions": [],
      "explanation": {
        "zh-Hant": "連續性逐所有target開集的完整反像驗證，不是只看單點、image開集或有限samples。map先依原始domain對齊image，再連同image排序。",
        "en": "Test full preimages of every target open,not just points,open images or samples.Align images with the ORIGINAL domain before sorting the rows."
      },
      "reverse_audit": {
        "kind": "premise_and_result_audit",
        "explanation": {
          "zh-Hant": "反查原題的完整資料、型別、欄序與本步條件；有限核對不升格為無限定理的形式證明。",
          "en": "Reverse-check the complete original data,types,field order and premises;finite audits are not formal proofs of infinite theorems."
        }
      },
      "arithmetic": null
    },
    {
      "id": "S009",
      "uses": [
        "G001",
        "S008"
      ],
      "before": "source roles = [quotient ACTUAL h-after-q, [0, 1, 2, 3, 4, 5], [[], [0, 1, 2, 3, 4, 5], [0, 5]], [0, 1], [[], [0, 1], [1]], [[0, 0], [1, 1], [2, 1], [3, 1], [4, 1], [5, 0]]]",
      "after": "derived = [[[[], [], 是], [[0, 1], [0, 1, 2, 3, 4, 5], 是], [[1], [1, 2, 3, 4], 否]], 否]",
      "relation": "implies",
      "rule_id": "Continuity_ALL_target_open_preimages",
      "conditions": [],
      "explanation": {
        "zh-Hant": "連續性逐所有target開集的完整反像驗證，不是只看單點、image開集或有限samples。map先依原始domain對齊image，再連同image排序。",
        "en": "Test full preimages of every target open,not just points,open images or samples.Align images with the ORIGINAL domain before sorting the rows."
      },
      "reverse_audit": {
        "kind": "premise_and_result_audit",
        "explanation": {
          "zh-Hant": "反查原題的完整資料、型別、欄序與本步條件；有限核對不升格為無限定理的形式證明。",
          "en": "Reverse-check the complete original data,types,field order and premises;finite audits are not formal proofs of infinite theorems."
        }
      },
      "arithmetic": null
    },
    {
      "id": "S010",
      "uses": [
        "G001",
        "S009"
      ],
      "before": "source roles = [[[0, a], [1, b], [2, b], [3, b], [4, b], [5, a]], [[a, 0], [b, 1]], [[0, 0], [1, 1], [2, 1], [3, 1], [4, 1], [5, 0]], [[a, b], [a], []]]",
      "after": "derived = [否, 否, 是]",
      "relation": "implies",
      "rule_id": "Quotient_final_UNIVERSAL_IFF_not_bare_q_continuity",
      "conditions": [],
      "explanation": {
        "zh-Hant": "對每個Z開集W，(h∘q)^-1(W)=q^-1(h^-1(W))；final IFF使右側在X開當且僅當h^-1(W)在Y開。合取全部W便得等價；兩者都False也不破壞IFF。",
        "en": "For each Z open W,(h after q)^-1(W)=q^-1(h^-1(W)).The final-topology IFF says the right side is X-open exactly when h^-1(W) is Y-open.Conjoin over all W;both maps can be noncontinuous while the equivalence is true."
      },
      "reverse_audit": {
        "kind": "premise_and_result_audit",
        "explanation": {
          "zh-Hant": "反查原題的完整資料、型別、欄序與本步條件；有限核對不升格為無限定理的形式證明。",
          "en": "Reverse-check the complete original data,types,field order and premises;finite audits are not formal proofs of infinite theorems."
        }
      },
      "arithmetic": null
    }
  ],
  "math_model": {
    "result": [
      false,
      false,
      true,
      [
        [
          "a",
          0
        ],
        [
          "b",
          1
        ]
      ],
      [
        [
          0,
          0
        ],
        [
          1,
          1
        ],
        [
          2,
          1
        ],
        [
          3,
          1
        ],
        [
          4,
          1
        ],
        [
          5,
          0
        ]
      ],
      "quotient_final_property_for_surjective_q"
    ]
  },
  "conclusion": {
    "canonical_value": "(否, 否, 是, [[a, 0], [b, 1]], [[0, 0], [1, 1], [2, 1], [3, 1], [4, 1], [5, 0]], quotient_final_property_for_surjective_q)",
    "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-20261015-advance-20261117-r05-quotient-topology-foundations",
      "batch_path": "public/data/questions/batches/batch-20261015-advance-20261117-r05-quotient-topology-foundations/questions.jsonl",
      "batch_sha256": "c9c0a3659f4c4afd1218cc04b05fb9742a3e1d7f4d60af5e0c0ef47bf0069fdb",
      "original_line": 66,
      "original_line_sha256": "3ce349e6514413d4416d58a01c98a3b959be01cfdfbdb2d5e3f36002e054c331",
      "question_compact_sha256": "43ad0f4a17e08cd27f138807067d89da2d0f3be24dd63ea3811907e819f42f23",
      "english_row_compact_sha256": "7bdb37bb2cf62d9096090957206a6a8720f01964ba95b7e6c6656bb2ed7f9d25",
      "english_manifest_path": "public/data/i18n/editions/batch-20261015-advance-20261117-r05-quotient-topology-foundations.en.json",
      "english_rows_path": "public/data/i18n/questions/batch-20261015-advance-20261117-r05-quotient-topology-foundations.en.jsonl"
    },
    "mko_bindings": {
      "mko-quotient-topology": {
        "sha256": "6d39ac6c71e17262644cf9f224ea59cf647428b87cbb6eaf46dc2b3cdd563097",
        "english_sha256": "23927e8ec4e21af1c3c25981e6764a705877f07d698217deb5e780c1f756269e",
        "original_path": "public/data/mko/source13-20261018-quotient-topology.json",
        "english_path": "public/data/i18n/editions/mko-quotient-topology.en.json"
      }
    },
    "selected_manifest_sha256": "5233edba9654a6cffd8b6b2d83c932f82ded15f9c0b7c733bd049943e672acff",
    "selected_part_sha256": "a3def7368821a4d3dc7757fefd3c4a099713f8de8fb8e6f3434025e9d7b5a6d0",
    "original_candidate_sha256": "ffa7a834023d91bf03025da50edbfdbe59c444fbc9410815448a924886c0848f",
    "original_candidate_line_sha256": "ffa7a834023d91bf03025da50edbfdbe59c444fbc9410815448a924886c0848f"
  },
  "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-20261026-010-p53",
    "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": "729b25cbf6bf5cb1d07a21a511ae216ec5fdd54a4a7aa2f7c21156b81ff37252",
      "question_first_witness_sha256": "d1ab788770eaad04f986986e65afb0d55791e8a8c0d747e9a2b499f79fe78df2"
    },
    "status": "second_context_reviewed",
    "mathematical_semantics": true,
    "bilingual_semantics": true,
    "steps_reviewed": 10,
    "method": "family_template_semantic_review_plus_independent_per_instance_reconstruction",
    "exact_question_first_check": {
      "model_sha256": "9fc108e000ad620d634a2c4a7c4923a75f2de923b709a58dedf8e67902998de1",
      "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."
  }
}