{
  "schema_version": "ocme-reviewed-question-reader-v1",
  "question_id": "q-20261008-advance-20261011-r07-tends-to-relation-0088",
  "pilot_number": "R0009-05238",
  "number": 5238,
  "family_id": "qf-density11-tends-principal-composition-images",
  "title": {
    "zh-Hant": "第 5238 題：兩條有限主濾子合成像",
    "en": "Question 5238: Two Finite Principal-Filter Composition Images"
  },
  "original_question": {
    "schema_version": "ocme-question-v0.1",
    "id": "q-20261008-advance-20261011-r07-tends-to-relation-0088",
    "batch_id": "batch-20261008-advance-20261011-r07-tends-to-relation-foundations",
    "language": "zh-Hant",
    "source_mko_ids": [
      "mko-tends-to-relation"
    ],
    "title_zh": "兩條有限主濾子合成像",
    "stem_zh": "有限主濾子；完整總映射 f:Fin(8)→Fin(8) 的表=[7, 6, 5, 4, 3, 2, 1, 0]，S=[2, 3]；principal(S)由包含S的所有來源子集構成，允許空生成集且不加入NeBot。完整總映射 g:Fin(8)→Fin(8) 的表=[7, 6, 5, 4, 3, 2, 1, 0]。依序列 ((g∘f)(S), g(f(S)))，兩條路各以完整遞增集表示。",
    "answer": {
      "kind": "expression",
      "value": "([2, 3], [2, 3])",
      "explanation_zh": "兩路主濾子合成像=([2, 3], [2, 3])。第一條逐來源合成，第二條先去重中間像再映射；所有F/G表項仍須總合法，非一般數列或點極限。"
    },
    "difficulty": {
      "band": "undergraduate_core",
      "level": 2,
      "skills": [
        "兩條有限主濾子合成像"
      ]
    },
    "variant": {
      "family_id": "qf-density11-tends-principal-composition-images",
      "seed": 202610117088,
      "parameters": {
        "n": 8,
        "m": 8,
        "l": 8,
        "images": [
          7,
          6,
          5,
          4,
          3,
          2,
          1,
          0
        ],
        "after": [
          7,
          6,
          5,
          4,
          3,
          2,
          1,
          0
        ],
        "S": [
          2,
          3
        ],
        "filter_model": "principal_generators",
        "operation": "density11_tends_principal_composition_images",
        "domain": "finite_principal_filter_model",
        "semantic_template": "qf-density11-tends-principal-composition-images/[2,3]"
      }
    },
    "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": "2026-10-08",
      "contract_version": "ocme-question-factory-v0.1"
    }
  },
  "original_english_edition": {
    "schema_version": "ocme-question-localization-v0.1",
    "question_id": "q-20261008-advance-20261011-r07-tends-to-relation-0088",
    "batch_id": "batch-20261008-advance-20261011-r07-tends-to-relation-foundations",
    "locale": "en",
    "translation_state": "ai_candidate",
    "source": {
      "question_sha256": "f566b2e889ac450fa4f19493421c357394f51eec7476ebc0571e548fa0640b88",
      "family_id": "qf-density11-tends-principal-composition-images",
      "seed": 202610117088,
      "semantic_template": "qf-density11-tends-principal-composition-images/[2,3]"
    },
    "fields": {
      "title": "Two Finite Principal-Filter Composition Images",
      "stem": "The complete total map f:Fin(8)→Fin(8) has images=[7, 6, 5, 4, 3, 2, 1, 0] indexed from 0; Fin(8)={0,…,7}. Every table entry must lie in the target type. S=[2, 3]. principal(S) contains all source subsets containing S; the empty generator is allowed, and no NeBot premise is added. The complete map g:Fin(8)→Fin(8) has after=[7, 6, 5, 4, 3, 2, 1, 0]. Give ((g∘f)(S), g(f(S))) as complete increasing sets.",
      "answer": {
        "kind": "expression",
        "value": "([2, 3], [2, 3])",
        "explanation": "Evaluate the composition sourcewise for one route and first deduplicate the intermediate image for the other; all f/g entries must remain total and typed. This is a finite principal-filter model, not a general sequence or point-limit claim. The exact result, retaining the requested order, is ([2, 3], [2, 3])."
      },
      "skills": [
        "Two Finite Principal-Filter Composition Images"
      ],
      "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": "有限主濾子；完整總映射 f:Fin(8)→Fin(8) 的表=[7, 6, 5, 4, 3, 2, 1, 0]，S=[2, 3]；principal(S)由包含S的所有來源子集構成，允許空生成集且不加入NeBot。完整總映射 g:Fin(8)→Fin(8) 的表=[7, 6, 5, 4, 3, 2, 1, 0]。依序列 ((g∘f)(S), g(f(S)))，兩條路各以完整遞增集表示。",
        "en": "The complete total map f:Fin(8)→Fin(8) has images=[7, 6, 5, 4, 3, 2, 1, 0] indexed from 0; Fin(8)={0,…,7}. Every table entry must lie in the target type. S=[2, 3]. principal(S) contains all source subsets containing S; the empty generator is allowed, and no NeBot premise is added. The complete map g:Fin(8)→Fin(8) has after=[7, 6, 5, 4, 3, 2, 1, 0]. Give ((g∘f)(S), g(f(S))) as complete increasing sets."
      }
    }
  ],
  "steps": [
    {
      "id": "S001",
      "uses": [
        "G001"
      ],
      "before": "source index=0∈Fin(8)",
      "after": "image=7∈Fin(8)",
      "relation": "implies",
      "rule_id": "complete_principal_map_row",
      "conditions": [],
      "explanation": {
        "zh-Hant": "完整表的每項都要合法，不能只因稍後未使用某項就略過總映射前提。",
        "en": "Every entry of the complete table must be legal;an entry being unused later does not waive total-map typing."
      },
      "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": "source index=1∈Fin(8)",
      "after": "image=6∈Fin(8)",
      "relation": "implies",
      "rule_id": "complete_principal_map_row",
      "conditions": [],
      "explanation": {
        "zh-Hant": "完整表的每項都要合法，不能只因稍後未使用某項就略過總映射前提。",
        "en": "Every entry of the complete table must be legal;an entry being unused later does not waive total-map typing."
      },
      "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": "source index=2∈Fin(8)",
      "after": "image=5∈Fin(8)",
      "relation": "implies",
      "rule_id": "complete_principal_map_row",
      "conditions": [],
      "explanation": {
        "zh-Hant": "完整表的每項都要合法，不能只因稍後未使用某項就略過總映射前提。",
        "en": "Every entry of the complete table must be legal;an entry being unused later does not waive total-map typing."
      },
      "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": "source index=3∈Fin(8)",
      "after": "image=4∈Fin(8)",
      "relation": "implies",
      "rule_id": "complete_principal_map_row",
      "conditions": [],
      "explanation": {
        "zh-Hant": "完整表的每項都要合法，不能只因稍後未使用某項就略過總映射前提。",
        "en": "Every entry of the complete table must be legal;an entry being unused later does not waive total-map typing."
      },
      "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": "source index=4∈Fin(8)",
      "after": "image=3∈Fin(8)",
      "relation": "implies",
      "rule_id": "complete_principal_map_row",
      "conditions": [],
      "explanation": {
        "zh-Hant": "完整表的每項都要合法，不能只因稍後未使用某項就略過總映射前提。",
        "en": "Every entry of the complete table must be legal;an entry being unused later does not waive total-map typing."
      },
      "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": "source index=5∈Fin(8)",
      "after": "image=2∈Fin(8)",
      "relation": "implies",
      "rule_id": "complete_principal_map_row",
      "conditions": [],
      "explanation": {
        "zh-Hant": "完整表的每項都要合法，不能只因稍後未使用某項就略過總映射前提。",
        "en": "Every entry of the complete table must be legal;an entry being unused later does not waive total-map typing."
      },
      "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": "source index=6∈Fin(8)",
      "after": "image=1∈Fin(8)",
      "relation": "implies",
      "rule_id": "complete_principal_map_row",
      "conditions": [],
      "explanation": {
        "zh-Hant": "完整表的每項都要合法，不能只因稍後未使用某項就略過總映射前提。",
        "en": "Every entry of the complete table must be legal;an entry being unused later does not waive total-map typing."
      },
      "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": "source index=7∈Fin(8)",
      "after": "image=0∈Fin(8)",
      "relation": "implies",
      "rule_id": "complete_principal_map_row",
      "conditions": [],
      "explanation": {
        "zh-Hant": "完整表的每項都要合法，不能只因稍後未使用某項就略過總映射前提。",
        "en": "Every entry of the complete table must be legal;an entry being unused later does not waive total-map typing."
      },
      "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": "Fin(8)→Fin(8);S=[2, 3];full map=[7, 6, 5, 4, 3, 2, 1, 0]",
      "after": "principal(S)={A:S⊆A};empty generators allowed,no NeBot",
      "relation": "implies",
      "rule_id": "finite_principal_generator_convention",
      "conditions": [],
      "explanation": {
        "zh-Hant": "依明示約定允許S空；此時包含S的族含空集，不另加真濾子或NeBot條件。這是有限主生成集模型，不是假定一般數列或點極限。",
        "en": "The declared convention allows empty S;its family of supersets then contains the empty set,and no proper-filter or NeBot condition is added.This is a finite principal-generator model,not a general sequence or point limit."
      },
      "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": "source index=0∈Fin(8)",
      "after": "image=7∈Fin(8)",
      "relation": "implies",
      "rule_id": "complete_after_map_row",
      "conditions": [],
      "explanation": {
        "zh-Hant": "完整表的每項都要合法，不能只因稍後未使用某項就略過總映射前提。",
        "en": "Every entry of the complete table must be legal;an entry being unused later does not waive total-map typing."
      },
      "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": "source index=1∈Fin(8)",
      "after": "image=6∈Fin(8)",
      "relation": "implies",
      "rule_id": "complete_after_map_row",
      "conditions": [],
      "explanation": {
        "zh-Hant": "完整表的每項都要合法，不能只因稍後未使用某項就略過總映射前提。",
        "en": "Every entry of the complete table must be legal;an entry being unused later does not waive total-map typing."
      },
      "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": "source index=2∈Fin(8)",
      "after": "image=5∈Fin(8)",
      "relation": "implies",
      "rule_id": "complete_after_map_row",
      "conditions": [],
      "explanation": {
        "zh-Hant": "完整表的每項都要合法，不能只因稍後未使用某項就略過總映射前提。",
        "en": "Every entry of the complete table must be legal;an entry being unused later does not waive total-map typing."
      },
      "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": "source index=3∈Fin(8)",
      "after": "image=4∈Fin(8)",
      "relation": "implies",
      "rule_id": "complete_after_map_row",
      "conditions": [],
      "explanation": {
        "zh-Hant": "完整表的每項都要合法，不能只因稍後未使用某項就略過總映射前提。",
        "en": "Every entry of the complete table must be legal;an entry being unused later does not waive total-map typing."
      },
      "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": "S014",
      "uses": [
        "G001",
        "S013"
      ],
      "before": "source index=4∈Fin(8)",
      "after": "image=3∈Fin(8)",
      "relation": "implies",
      "rule_id": "complete_after_map_row",
      "conditions": [],
      "explanation": {
        "zh-Hant": "完整表的每項都要合法，不能只因稍後未使用某項就略過總映射前提。",
        "en": "Every entry of the complete table must be legal;an entry being unused later does not waive total-map typing."
      },
      "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": "S015",
      "uses": [
        "G001",
        "S014"
      ],
      "before": "source index=5∈Fin(8)",
      "after": "image=2∈Fin(8)",
      "relation": "implies",
      "rule_id": "complete_after_map_row",
      "conditions": [],
      "explanation": {
        "zh-Hant": "完整表的每項都要合法，不能只因稍後未使用某項就略過總映射前提。",
        "en": "Every entry of the complete table must be legal;an entry being unused later does not waive total-map typing."
      },
      "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": "S016",
      "uses": [
        "G001",
        "S015"
      ],
      "before": "source index=6∈Fin(8)",
      "after": "image=1∈Fin(8)",
      "relation": "implies",
      "rule_id": "complete_after_map_row",
      "conditions": [],
      "explanation": {
        "zh-Hant": "完整表的每項都要合法，不能只因稍後未使用某項就略過總映射前提。",
        "en": "Every entry of the complete table must be legal;an entry being unused later does not waive total-map typing."
      },
      "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": "S017",
      "uses": [
        "G001",
        "S016"
      ],
      "before": "source index=7∈Fin(8)",
      "after": "image=0∈Fin(8)",
      "relation": "implies",
      "rule_id": "complete_after_map_row",
      "conditions": [],
      "explanation": {
        "zh-Hant": "完整表的每項都要合法，不能只因稍後未使用某項就略過總映射前提。",
        "en": "Every entry of the complete table must be legal;an entry being unused later does not waive total-map typing."
      },
      "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": "S018",
      "uses": [
        "G001",
        "S017"
      ],
      "before": "x=2;f(x)=5",
      "after": "g(f(x))=2",
      "relation": "implies",
      "rule_id": "principal_direct_composition_row",
      "conditions": [],
      "explanation": {
        "zh-Hant": "第一條路按來源元素逐一合成，保持兩個映射方向。",
        "en": "The first route composes at each source element,retaining the direction of both maps."
      },
      "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": "S019",
      "uses": [
        "G001",
        "S018"
      ],
      "before": "x=3;f(x)=4",
      "after": "g(f(x))=3",
      "relation": "implies",
      "rule_id": "principal_direct_composition_row",
      "conditions": [],
      "explanation": {
        "zh-Hant": "第一條路按來源元素逐一合成，保持兩個映射方向。",
        "en": "The first route composes at each source element,retaining the direction of both maps."
      },
      "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": "S020",
      "uses": [
        "G001",
        "S019"
      ],
      "before": "distinct intermediate image=4",
      "after": "g(y)=3",
      "relation": "implies",
      "rule_id": "principal_image_then_map_row",
      "conditions": [],
      "explanation": {
        "zh-Hant": "第二條路先去重f(S)再映射；總映射對相同中間值給同一後繼，所以去重不漏掉終像。",
        "en": "The second route deduplicates f(S) before applying g;a total function assigns the same successor to the same intermediate value,so deduplication loses no final image."
      },
      "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": "S021",
      "uses": [
        "G001",
        "S020"
      ],
      "before": "distinct intermediate image=5",
      "after": "g(y)=2",
      "relation": "implies",
      "rule_id": "principal_image_then_map_row",
      "conditions": [],
      "explanation": {
        "zh-Hant": "第二條路先去重f(S)再映射；總映射對相同中間值給同一後繼，所以去重不漏掉終像。",
        "en": "The second route deduplicates f(S) before applying g;a total function assigns the same successor to the same intermediate value,so deduplication loses no final image."
      },
      "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": "S022",
      "uses": [
        "G001",
        "S021"
      ],
      "before": "direct composite image=[2, 3];image then map=[2, 3]",
      "after": "(g∘f)(S)=g(f(S)) in this complete finite model",
      "relation": "implies",
      "rule_id": "principal_composition_image_identity",
      "conditions": [],
      "explanation": {
        "zh-Hant": "兩路列出相同終像；空S兩路都空。此核對不引入一般解析極限或額外非空前提。",
        "en": "Both routes give the same final image;empty S gives empty images on both routes.No general analytic limit or additional nonemptiness premise is introduced."
      },
      "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
    }
  ],
  "math_model": {
    "result": [
      [
        2,
        3
      ],
      [
        2,
        3
      ]
    ],
    "direct_rows": [
      [
        2,
        5,
        2
      ],
      [
        3,
        4,
        3
      ]
    ],
    "intermediate_image": [
      4,
      5
    ]
  },
  "conclusion": {
    "canonical_value": "([2, 3], [2, 3])",
    "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-20261008-advance-20261011-r07-tends-to-relation-foundations",
      "batch_path": "public/data/questions/batches/batch-20261008-advance-20261011-r07-tends-to-relation-foundations/questions.jsonl",
      "batch_sha256": "3ca90336b05f08a7567b56044185bef7fc4f4f8286e5afeac67e950f7c74bfde",
      "original_line": 88,
      "original_line_sha256": "f2baaae56c217134f19a6b98f774496b9ac5edab2500fbd31f1a40d92859b422",
      "question_compact_sha256": "f566b2e889ac450fa4f19493421c357394f51eec7476ebc0571e548fa0640b88",
      "english_row_compact_sha256": "ba3af60f715f09a90c6ee7dd68af42afab8447119cac284fd3a673f495245acd",
      "english_manifest_path": "public/data/i18n/editions/batch-20261008-advance-20261011-r07-tends-to-relation-foundations.en.json",
      "english_rows_path": "public/data/i18n/questions/batch-20261008-advance-20261011-r07-tends-to-relation-foundations.en.jsonl"
    },
    "mko_bindings": {
      "mko-tends-to-relation": {
        "sha256": "2fbb3c700378e80e68833bcada18866ed6439803d8b639e304fe76d31903f70e",
        "english_sha256": "bed5d2c178f726aeda66b8705697852f39ce93b2d1a6807b7acbb3c97dfd4ac4",
        "original_path": "public/data/mko/tends-to-relation.json",
        "english_path": "public/data/i18n/editions/mko-tends-to-relation.en.json"
      }
    },
    "selected_manifest_sha256": "5233edba9654a6cffd8b6b2d83c932f82ded15f9c0b7c733bd049943e672acff",
    "selected_part_sha256": "3132b1200be7a5de38191badc52fb1727d4dd9d4c2f26818de2e8a76426d2d3f",
    "original_candidate_sha256": "ccfe92d2f23e6cf7595fa8bbe7134c89eabcd1f388de009e2aadd4e80c5f1449",
    "original_candidate_line_sha256": "ccfe92d2f23e6cf7595fa8bbe7134c89eabcd1f388de009e2aadd4e80c5f1449"
  },
  "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-p10",
    "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": "71e7db519df31f3a164533e472e293cb64f001b475a8d002b4a5c2740a237b56",
      "question_first_witness_sha256": "5a43f4f81b6256281f8d139a4010bbde127be803c528e5878857269c8f854462"
    },
    "status": "second_context_reviewed",
    "mathematical_semantics": true,
    "bilingual_semantics": true,
    "steps_reviewed": 22,
    "method": "family_template_semantic_review_plus_independent_per_instance_reconstruction",
    "exact_question_first_check": {
      "model_sha256": "024364e1165c02e00b9c3be209c9eeaa2b00411a5c06e8ccce8fd7798658ca41",
      "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."
  }
}