{
  "schema_version": "ocme-reviewed-question-reader-v1",
  "question_id": "q-20261004-advance-20261005-r02-surjective-0098",
  "pilot_number": "R0069-35323",
  "number": 35323,
  "family_id": "qf-surjective-codomain-change",
  "title": {
    "zh-Hant": "第 35323 題：合法更換陪域後的覆蓋",
    "en": "Question 35323: Coverage after a Valid Codomain Change"
  },
  "original_question": {
    "schema_version": "ocme-question-v0.1",
    "id": "q-20261004-advance-20261005-r02-surjective-0098",
    "batch_id": "batch-20261004-advance-20261005-r02-surjective-foundations",
    "language": "zh-Hant",
    "source_mko_ids": [
      "mko-surjective"
    ],
    "title_zh": "合法更換陪域後的覆蓋",
    "stem_zh": "明示總函數 f:A→B，A={-6, -5, -4, -3, -2, -1, 0}、B={1, 3, 5, 7, 9, 11, 13, 15}，函數表為 {(-6, 1), (-5, 3), (-4, 5), (-3, 7), (-2, 9), (-1, 11), (0, 13)}。新陪域 B2={1, 3, 5, 7, 9, 11, 13} 包含全部既有輸出；同一輸出表視為 A→B2 時是否滿射？",
    "answer": {
      "kind": "short_text",
      "value": "是",
      "explanation_zh": "新陪域未覆蓋=∅。值域包含於 B2 先保證總函數宣告合法，再比較是否等於 B2；不能為求滿射而丟掉既有輸出。"
    },
    "difficulty": {
      "band": "undergraduate_core",
      "level": 3,
      "skills": [
        "合法更換陪域後的覆蓋"
      ]
    },
    "variant": {
      "family_id": "qf-surjective-codomain-change",
      "seed": 202610052098,
      "parameters": {
        "A": [
          -6,
          -5,
          -4,
          -3,
          -2,
          -1,
          0
        ],
        "B": [
          1,
          3,
          5,
          7,
          9,
          11,
          13,
          15
        ],
        "pairs": [
          [
            -6,
            1
          ],
          [
            -5,
            3
          ],
          [
            -4,
            5
          ],
          [
            -3,
            7
          ],
          [
            -2,
            9
          ],
          [
            -1,
            11
          ],
          [
            0,
            13
          ]
        ],
        "B2": [
          1,
          3,
          5,
          7,
          9,
          11,
          13
        ],
        "operation": "changed_codomain",
        "semantic_template": "qf-surjective-codomain-change/{\"A\":[-6,-5,-4,-3,-2,-1,0],\"B2\":[1,3,5,7,9,11,13],\"operation\":\"changed_codomain\",\"pairs\":[[-6,1],[-5,3],[-4,5],[-3,7],[-2,9],[-1,11],[0,13]]}"
      }
    },
    "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": "Codex independent producer (inherited model; exact runtime model not exposed)",
      "generated_at": "2026-10-04",
      "contract_version": "ocme-question-factory-v0.1"
    }
  },
  "original_english_edition": {
    "schema_version": "ocme-question-localization-v0.1",
    "question_id": "q-20261004-advance-20261005-r02-surjective-0098",
    "batch_id": "batch-20261004-advance-20261005-r02-surjective-foundations",
    "locale": "en",
    "translation_state": "ai_candidate",
    "source": {
      "question_sha256": "38590ee82c42fded0004a4e21fd268350227c47ad61aaa08d0331a5b9ca43421",
      "family_id": "qf-surjective-codomain-change",
      "seed": 202610052098,
      "semantic_template": "qf-surjective-codomain-change/{\"A\":[-6,-5,-4,-3,-2,-1,0],\"B2\":[1,3,5,7,9,11,13],\"operation\":\"changed_codomain\",\"pairs\":[[-6,1],[-5,3],[-4,5],[-3,7],[-2,9],[-1,11],[0,13]]}"
    },
    "fields": {
      "title": "Coverage after a Valid Codomain Change",
      "stem": "The declared total function f:A→B has A={-6, -5, -4, -3, -2, -1, 0}, B={1, 3, 5, 7, 9, 11, 13, 15}, and table {(-6, 1), (-5, 3), (-4, 5), (-3, 7), (-2, 9), (-1, 11), (0, 13)}. The new codomain B2={1, 3, 5, 7, 9, 11, 13} contains every attained output. Is the same output table surjective as A→B2?",
      "answer": {
        "kind": "short_text",
        "value": "Yes",
        "explanation": "Containing the range first makes the new total-function declaration valid. Compare that range with B2 to obtain Yes; no existing output may be discarded to force surjectivity."
      },
      "skills": [
        "Coverage after a Valid Codomain Change"
      ],
      "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": "明示總函數 f:A→B，A={-6, -5, -4, -3, -2, -1, 0}、B={1, 3, 5, 7, 9, 11, 13, 15}，函數表為 {(-6, 1), (-5, 3), (-4, 5), (-3, 7), (-2, 9), (-1, 11), (0, 13)}。新陪域 B2={1, 3, 5, 7, 9, 11, 13} 包含全部既有輸出；同一輸出表視為 A→B2 時是否滿射？",
        "en": "The declared total function f:A→B has A={-6, -5, -4, -3, -2, -1, 0}, B={1, 3, 5, 7, 9, 11, 13, 15}, and table {(-6, 1), (-5, 3), (-4, 5), (-3, 7), (-2, 9), (-1, 11), (0, 13)}. The new codomain B2={1, 3, 5, 7, 9, 11, 13} contains every attained output. Is the same output table surjective as A→B2?"
      }
    }
  ],
  "steps": [
    {
      "id": "S001",
      "uses": [
        "G001"
      ],
      "before": "source roles = [qf-surjective-codomain-change, [A, B, B2, operation, pairs]]",
      "after": "derived = [changed_codomain, no-invented-domain]",
      "relation": "implies",
      "rule_id": "R69_SOURCE_specific_keys_operation_domain_AND_binary_contract",
      "conditions": [],
      "explanation": {
        "zh-Hant": "各bank的keys/operation/domain獨立：LDL/PULSE/function legacy為表內underscore，TREE是完整tree_*與明定domain，BASE signed較寬不偷加op/domain。所有算術保持binary primitive契約。",
        "en": "Keep EACH bank’s keys/operation/domain distinct:LDL/PULSE/function legacy table underscores,TREE full tree_* with its declared domain,and permissive BASE signed without invented op/domain.All arithmetic respects the binary-primitive contract."
      },
      "reverse_audit": {
        "kind": "premise_and_result_audit",
        "explanation": {
          "zh-Hant": "反查本題原資料、型別、角色、完整前提與欄序；單向推論不倒當等價，有限表核對不冒充無限論域/形式證明。原題/英文/MKO/AST/狀態不變。",
          "en": "Reverse-audit THIS question’s ORIGINAL data,types,roles,complete premises and field order.Do not invert implication or turn finite-table checks into infinite-domain/formal proof.Original Q/English/MKO/AST/status remain unchanged."
        }
      },
      "arithmetic": null
    },
    {
      "id": "S002",
      "uses": [
        "G001",
        "S001"
      ],
      "before": "source roles = [function ORIGINAL A, 100, [-6, -5, -4, -3, -2, -1, 0]]",
      "after": "derived = [[-6, -5, -4, -3, -2, -1, 0]]",
      "relation": "implies",
      "rule_id": "Finite_RAW_ALL_SAFE_distinct_labels_then_derived_sort",
      "conditions": [],
      "explanation": {
        "zh-Hant": "先驗全部raw SAFE元素、不重複及此bank個數界，空集合法；只把衍生表示排序，原JSON不修改。TREE與LDL的上限不可互搬。",
        "en": "Type EVERY RAW SAFE label,distinctness and THIS bank’s cardinality bound;empty is allowed.Sort ONLY the derived representation,not original JSON.Do not exchange TREE and LDL limits."
      },
      "reverse_audit": {
        "kind": "premise_and_result_audit",
        "explanation": {
          "zh-Hant": "反查本題原資料、型別、角色、完整前提與欄序；單向推論不倒當等價，有限表核對不冒充無限論域/形式證明。原題/英文/MKO/AST/狀態不變。",
          "en": "Reverse-audit THIS question’s ORIGINAL data,types,roles,complete premises and field order.Do not invert implication or turn finite-table checks into infinite-domain/formal proof.Original Q/English/MKO/AST/status remain unchanged."
        }
      },
      "arithmetic": null
    },
    {
      "id": "S003",
      "uses": [
        "G001",
        "S002"
      ],
      "before": "source roles = [function ORIGINAL B, 100, [1, 3, 5, 7, 9, 11, 13, 15]]",
      "after": "derived = [[1, 3, 5, 7, 9, 11, 13, 15]]",
      "relation": "implies",
      "rule_id": "Finite_RAW_ALL_SAFE_distinct_labels_then_derived_sort",
      "conditions": [],
      "explanation": {
        "zh-Hant": "先驗全部raw SAFE元素、不重複及此bank個數界，空集合法；只把衍生表示排序，原JSON不修改。TREE與LDL的上限不可互搬。",
        "en": "Type EVERY RAW SAFE label,distinctness and THIS bank’s cardinality bound;empty is allowed.Sort ONLY the derived representation,not original JSON.Do not exchange TREE and LDL limits."
      },
      "reverse_audit": {
        "kind": "premise_and_result_audit",
        "explanation": {
          "zh-Hant": "反查本題原資料、型別、角色、完整前提與欄序；單向推論不倒當等價，有限表核對不冒充無限論域/形式證明。原題/英文/MKO/AST/狀態不變。",
          "en": "Reverse-audit THIS question’s ORIGINAL data,types,roles,complete premises and field order.Do not invert implication or turn finite-table checks into infinite-domain/formal proof.Original Q/English/MKO/AST/status remain unchanged."
        }
      },
      "arithmetic": null
    },
    {
      "id": "S004",
      "uses": [
        "G001",
        "S003"
      ],
      "before": "source roles = [function ORIGINAL table, 0, [-6, 1]]",
      "after": "derived = [[-6, 1]]",
      "relation": "implies",
      "rule_id": "Pairs_EVERY_RAW_two_SAFE_cells_BEFORE_any_dedup",
      "conditions": [],
      "explanation": {
        "zh-Hant": "去重之前逐raw pair驗恰兩個SAFE分量；相同row可作表示重複，但不能先丟掉未驗欄位。",
        "en": "BEFORE deduplication,type EACH RAW pair as EXACTLY TWO SAFE components.Identical rows may be representation duplicates,but no unvalidated cell may be silently discarded."
      },
      "reverse_audit": {
        "kind": "premise_and_result_audit",
        "explanation": {
          "zh-Hant": "反查本題原資料、型別、角色、完整前提與欄序；單向推論不倒當等價，有限表核對不冒充無限論域/形式證明。原題/英文/MKO/AST/狀態不變。",
          "en": "Reverse-audit THIS question’s ORIGINAL data,types,roles,complete premises and field order.Do not invert implication or turn finite-table checks into infinite-domain/formal proof.Original Q/English/MKO/AST/status remain unchanged."
        }
      },
      "arithmetic": null
    },
    {
      "id": "S005",
      "uses": [
        "G001",
        "S004"
      ],
      "before": "source roles = [function ORIGINAL table, 1, [-5, 3]]",
      "after": "derived = [[-5, 3]]",
      "relation": "implies",
      "rule_id": "Pairs_EVERY_RAW_two_SAFE_cells_BEFORE_any_dedup",
      "conditions": [],
      "explanation": {
        "zh-Hant": "去重之前逐raw pair驗恰兩個SAFE分量；相同row可作表示重複，但不能先丟掉未驗欄位。",
        "en": "BEFORE deduplication,type EACH RAW pair as EXACTLY TWO SAFE components.Identical rows may be representation duplicates,but no unvalidated cell may be silently discarded."
      },
      "reverse_audit": {
        "kind": "premise_and_result_audit",
        "explanation": {
          "zh-Hant": "反查本題原資料、型別、角色、完整前提與欄序；單向推論不倒當等價，有限表核對不冒充無限論域/形式證明。原題/英文/MKO/AST/狀態不變。",
          "en": "Reverse-audit THIS question’s ORIGINAL data,types,roles,complete premises and field order.Do not invert implication or turn finite-table checks into infinite-domain/formal proof.Original Q/English/MKO/AST/status remain unchanged."
        }
      },
      "arithmetic": null
    },
    {
      "id": "S006",
      "uses": [
        "G001",
        "S005"
      ],
      "before": "source roles = [function ORIGINAL table, 2, [-4, 5]]",
      "after": "derived = [[-4, 5]]",
      "relation": "implies",
      "rule_id": "Pairs_EVERY_RAW_two_SAFE_cells_BEFORE_any_dedup",
      "conditions": [],
      "explanation": {
        "zh-Hant": "去重之前逐raw pair驗恰兩個SAFE分量；相同row可作表示重複，但不能先丟掉未驗欄位。",
        "en": "BEFORE deduplication,type EACH RAW pair as EXACTLY TWO SAFE components.Identical rows may be representation duplicates,but no unvalidated cell may be silently discarded."
      },
      "reverse_audit": {
        "kind": "premise_and_result_audit",
        "explanation": {
          "zh-Hant": "反查本題原資料、型別、角色、完整前提與欄序；單向推論不倒當等價，有限表核對不冒充無限論域/形式證明。原題/英文/MKO/AST/狀態不變。",
          "en": "Reverse-audit THIS question’s ORIGINAL data,types,roles,complete premises and field order.Do not invert implication or turn finite-table checks into infinite-domain/formal proof.Original Q/English/MKO/AST/status remain unchanged."
        }
      },
      "arithmetic": null
    },
    {
      "id": "S007",
      "uses": [
        "G001",
        "S006"
      ],
      "before": "source roles = [function ORIGINAL table, 3, [-3, 7]]",
      "after": "derived = [[-3, 7]]",
      "relation": "implies",
      "rule_id": "Pairs_EVERY_RAW_two_SAFE_cells_BEFORE_any_dedup",
      "conditions": [],
      "explanation": {
        "zh-Hant": "去重之前逐raw pair驗恰兩個SAFE分量；相同row可作表示重複，但不能先丟掉未驗欄位。",
        "en": "BEFORE deduplication,type EACH RAW pair as EXACTLY TWO SAFE components.Identical rows may be representation duplicates,but no unvalidated cell may be silently discarded."
      },
      "reverse_audit": {
        "kind": "premise_and_result_audit",
        "explanation": {
          "zh-Hant": "反查本題原資料、型別、角色、完整前提與欄序；單向推論不倒當等價，有限表核對不冒充無限論域/形式證明。原題/英文/MKO/AST/狀態不變。",
          "en": "Reverse-audit THIS question’s ORIGINAL data,types,roles,complete premises and field order.Do not invert implication or turn finite-table checks into infinite-domain/formal proof.Original Q/English/MKO/AST/status remain unchanged."
        }
      },
      "arithmetic": null
    },
    {
      "id": "S008",
      "uses": [
        "G001",
        "S007"
      ],
      "before": "source roles = [function ORIGINAL table, 4, [-2, 9]]",
      "after": "derived = [[-2, 9]]",
      "relation": "implies",
      "rule_id": "Pairs_EVERY_RAW_two_SAFE_cells_BEFORE_any_dedup",
      "conditions": [],
      "explanation": {
        "zh-Hant": "去重之前逐raw pair驗恰兩個SAFE分量；相同row可作表示重複，但不能先丟掉未驗欄位。",
        "en": "BEFORE deduplication,type EACH RAW pair as EXACTLY TWO SAFE components.Identical rows may be representation duplicates,but no unvalidated cell may be silently discarded."
      },
      "reverse_audit": {
        "kind": "premise_and_result_audit",
        "explanation": {
          "zh-Hant": "反查本題原資料、型別、角色、完整前提與欄序；單向推論不倒當等價，有限表核對不冒充無限論域/形式證明。原題/英文/MKO/AST/狀態不變。",
          "en": "Reverse-audit THIS question’s ORIGINAL data,types,roles,complete premises and field order.Do not invert implication or turn finite-table checks into infinite-domain/formal proof.Original Q/English/MKO/AST/status remain unchanged."
        }
      },
      "arithmetic": null
    },
    {
      "id": "S009",
      "uses": [
        "G001",
        "S008"
      ],
      "before": "source roles = [function ORIGINAL table, 5, [-1, 11]]",
      "after": "derived = [[-1, 11]]",
      "relation": "implies",
      "rule_id": "Pairs_EVERY_RAW_two_SAFE_cells_BEFORE_any_dedup",
      "conditions": [],
      "explanation": {
        "zh-Hant": "去重之前逐raw pair驗恰兩個SAFE分量；相同row可作表示重複，但不能先丟掉未驗欄位。",
        "en": "BEFORE deduplication,type EACH RAW pair as EXACTLY TWO SAFE components.Identical rows may be representation duplicates,but no unvalidated cell may be silently discarded."
      },
      "reverse_audit": {
        "kind": "premise_and_result_audit",
        "explanation": {
          "zh-Hant": "反查本題原資料、型別、角色、完整前提與欄序；單向推論不倒當等價，有限表核對不冒充無限論域/形式證明。原題/英文/MKO/AST/狀態不變。",
          "en": "Reverse-audit THIS question’s ORIGINAL data,types,roles,complete premises and field order.Do not invert implication or turn finite-table checks into infinite-domain/formal proof.Original Q/English/MKO/AST/status remain unchanged."
        }
      },
      "arithmetic": null
    },
    {
      "id": "S010",
      "uses": [
        "G001",
        "S009"
      ],
      "before": "source roles = [function ORIGINAL table, 6, [0, 13]]",
      "after": "derived = [[0, 13]]",
      "relation": "implies",
      "rule_id": "Pairs_EVERY_RAW_two_SAFE_cells_BEFORE_any_dedup",
      "conditions": [],
      "explanation": {
        "zh-Hant": "去重之前逐raw pair驗恰兩個SAFE分量；相同row可作表示重複，但不能先丟掉未驗欄位。",
        "en": "BEFORE deduplication,type EACH RAW pair as EXACTLY TWO SAFE components.Identical rows may be representation duplicates,but no unvalidated cell may be silently discarded."
      },
      "reverse_audit": {
        "kind": "premise_and_result_audit",
        "explanation": {
          "zh-Hant": "反查本題原資料、型別、角色、完整前提與欄序；單向推論不倒當等價，有限表核對不冒充無限論域/形式證明。原題/英文/MKO/AST/狀態不變。",
          "en": "Reverse-audit THIS question’s ORIGINAL data,types,roles,complete premises and field order.Do not invert implication or turn finite-table checks into infinite-domain/formal proof.Original Q/English/MKO/AST/status remain unchanged."
        }
      },
      "arithmetic": null
    },
    {
      "id": "S011",
      "uses": [
        "G001",
        "S010"
      ],
      "before": "source roles = [[-6, -5, -4, -3, -2, -1, 0], [1, 3, 5, 7, 9, 11, 13, 15], [[-6, 1], [-5, 3], [-4, 5], [-3, 7], [-2, 9], [-1, 11], [0, 13]]]",
      "after": "derived = [是]",
      "relation": "implies",
      "rule_id": "Function_WHOLE_qualified_total_AtoB_before_SURJECTIVE_claim",
      "conditions": [],
      "explanation": {
        "zh-Hant": "先驗完整表是A→B total function：每個A恰一output、所有pair在A×B；本legacy同pair重複可去重，別搬PULSE另一table的拒重複規則。B即使後續改陪域也先驗。",
        "en": "FIRST qualify the WHOLE total function A→B:EXACTLY one output for EVERY A and all pairs in A×B.Identical repeated rows normalize in THIS legacy bank,unlike a different PULSE table rule.Qualify ORIGINAL B even for later codomain changes."
      },
      "reverse_audit": {
        "kind": "premise_and_result_audit",
        "explanation": {
          "zh-Hant": "反查本題原資料、型別、角色、完整前提與欄序；單向推論不倒當等價，有限表核對不冒充無限論域/形式證明。原題/英文/MKO/AST/狀態不變。",
          "en": "Reverse-audit THIS question’s ORIGINAL data,types,roles,complete premises and field order.Do not invert implication or turn finite-table checks into infinite-domain/formal proof.Original Q/English/MKO/AST/status remain unchanged."
        }
      },
      "arithmetic": null
    },
    {
      "id": "S012",
      "uses": [
        "G001",
        "S011"
      ],
      "before": "source roles = [function NEW codomain B2, 100, [1, 3, 5, 7, 9, 11, 13]]",
      "after": "derived = [[1, 3, 5, 7, 9, 11, 13]]",
      "relation": "implies",
      "rule_id": "Finite_RAW_ALL_SAFE_distinct_labels_then_derived_sort",
      "conditions": [],
      "explanation": {
        "zh-Hant": "先驗全部raw SAFE元素、不重複及此bank個數界，空集合法；只把衍生表示排序，原JSON不修改。TREE與LDL的上限不可互搬。",
        "en": "Type EVERY RAW SAFE label,distinctness and THIS bank’s cardinality bound;empty is allowed.Sort ONLY the derived representation,not original JSON.Do not exchange TREE and LDL limits."
      },
      "reverse_audit": {
        "kind": "premise_and_result_audit",
        "explanation": {
          "zh-Hant": "反查本題原資料、型別、角色、完整前提與欄序；單向推論不倒當等價，有限表核對不冒充無限論域/形式證明。原題/英文/MKO/AST/狀態不變。",
          "en": "Reverse-audit THIS question’s ORIGINAL data,types,roles,complete premises and field order.Do not invert implication or turn finite-table checks into infinite-domain/formal proof.Original Q/English/MKO/AST/status remain unchanged."
        }
      },
      "arithmetic": null
    },
    {
      "id": "S013",
      "uses": [
        "G001",
        "S012"
      ],
      "before": "source roles = [[1, 3, 5, 7, 9, 11, 13, 15], [1, 3, 5, 7, 9, 11, 13], [[-6, 1], [-5, 3], [-4, 5], [-3, 7], [-2, 9], [-1, 11], [0, 13]]]",
      "after": "derived = [是]",
      "relation": "implies",
      "rule_id": "Surjective_NEW_codomain_contains_WHOLE_range_not_oldB_required",
      "conditions": [],
      "explanation": {
        "zh-Hant": "B2先包含全部已達output才是同一表的新total function；可增/減未達元素，不要求B2包含整個舊B，也不能丟掉實際output硬說滿射。",
        "en": "FIRST require B2 to contain the ENTIRE attained range for the same table to remain a total function.It may add/remove unattained targets and need not contain ALL old B.Never discard an actual output to force surjectivity."
      },
      "reverse_audit": {
        "kind": "premise_and_result_audit",
        "explanation": {
          "zh-Hant": "反查本題原資料、型別、角色、完整前提與欄序；單向推論不倒當等價，有限表核對不冒充無限論域/形式證明。原題/英文/MKO/AST/狀態不變。",
          "en": "Reverse-audit THIS question’s ORIGINAL data,types,roles,complete premises and field order.Do not invert implication or turn finite-table checks into infinite-domain/formal proof.Original Q/English/MKO/AST/status remain unchanged."
        }
      },
      "arithmetic": null
    },
    {
      "id": "S014",
      "uses": [
        "G001",
        "S013"
      ],
      "before": "source roles = [NEW B2, -6, 1, 1]",
      "after": "derived = [是]",
      "relation": "implies",
      "rule_id": "Surjective_EVERY_source_target_fiber_comparison",
      "conditions": [],
      "explanation": {
        "zh-Hant": "逐全部允許input核其output是否此target；每個fiber都完整列出，不把target當input或以集合大小猜滿射。",
        "en": "Compare EVERY permitted input’s output with THIS target.List EACH fiber completely;do not confuse target/input or infer surjectivity from cardinalities alone."
      },
      "reverse_audit": {
        "kind": "premise_and_result_audit",
        "explanation": {
          "zh-Hant": "反查本題原資料、型別、角色、完整前提與欄序；單向推論不倒當等價，有限表核對不冒充無限論域/形式證明。原題/英文/MKO/AST/狀態不變。",
          "en": "Reverse-audit THIS question’s ORIGINAL data,types,roles,complete premises and field order.Do not invert implication or turn finite-table checks into infinite-domain/formal proof.Original Q/English/MKO/AST/status remain unchanged."
        }
      },
      "arithmetic": null
    },
    {
      "id": "S015",
      "uses": [
        "G001",
        "S014"
      ],
      "before": "source roles = [NEW B2, -5, 3, 1]",
      "after": "derived = [否]",
      "relation": "implies",
      "rule_id": "Surjective_EVERY_source_target_fiber_comparison",
      "conditions": [],
      "explanation": {
        "zh-Hant": "逐全部允許input核其output是否此target；每個fiber都完整列出，不把target當input或以集合大小猜滿射。",
        "en": "Compare EVERY permitted input’s output with THIS target.List EACH fiber completely;do not confuse target/input or infer surjectivity from cardinalities alone."
      },
      "reverse_audit": {
        "kind": "premise_and_result_audit",
        "explanation": {
          "zh-Hant": "反查本題原資料、型別、角色、完整前提與欄序；單向推論不倒當等價，有限表核對不冒充無限論域/形式證明。原題/英文/MKO/AST/狀態不變。",
          "en": "Reverse-audit THIS question’s ORIGINAL data,types,roles,complete premises and field order.Do not invert implication or turn finite-table checks into infinite-domain/formal proof.Original Q/English/MKO/AST/status remain unchanged."
        }
      },
      "arithmetic": null
    },
    {
      "id": "S016",
      "uses": [
        "G001",
        "S015"
      ],
      "before": "source roles = [NEW B2, -4, 5, 1]",
      "after": "derived = [否]",
      "relation": "implies",
      "rule_id": "Surjective_EVERY_source_target_fiber_comparison",
      "conditions": [],
      "explanation": {
        "zh-Hant": "逐全部允許input核其output是否此target；每個fiber都完整列出，不把target當input或以集合大小猜滿射。",
        "en": "Compare EVERY permitted input’s output with THIS target.List EACH fiber completely;do not confuse target/input or infer surjectivity from cardinalities alone."
      },
      "reverse_audit": {
        "kind": "premise_and_result_audit",
        "explanation": {
          "zh-Hant": "反查本題原資料、型別、角色、完整前提與欄序；單向推論不倒當等價，有限表核對不冒充無限論域/形式證明。原題/英文/MKO/AST/狀態不變。",
          "en": "Reverse-audit THIS question’s ORIGINAL data,types,roles,complete premises and field order.Do not invert implication or turn finite-table checks into infinite-domain/formal proof.Original Q/English/MKO/AST/status remain unchanged."
        }
      },
      "arithmetic": null
    },
    {
      "id": "S017",
      "uses": [
        "G001",
        "S016"
      ],
      "before": "source roles = [NEW B2, -3, 7, 1]",
      "after": "derived = [否]",
      "relation": "implies",
      "rule_id": "Surjective_EVERY_source_target_fiber_comparison",
      "conditions": [],
      "explanation": {
        "zh-Hant": "逐全部允許input核其output是否此target；每個fiber都完整列出，不把target當input或以集合大小猜滿射。",
        "en": "Compare EVERY permitted input’s output with THIS target.List EACH fiber completely;do not confuse target/input or infer surjectivity from cardinalities alone."
      },
      "reverse_audit": {
        "kind": "premise_and_result_audit",
        "explanation": {
          "zh-Hant": "反查本題原資料、型別、角色、完整前提與欄序；單向推論不倒當等價，有限表核對不冒充無限論域/形式證明。原題/英文/MKO/AST/狀態不變。",
          "en": "Reverse-audit THIS question’s ORIGINAL data,types,roles,complete premises and field order.Do not invert implication or turn finite-table checks into infinite-domain/formal proof.Original Q/English/MKO/AST/status remain unchanged."
        }
      },
      "arithmetic": null
    },
    {
      "id": "S018",
      "uses": [
        "G001",
        "S017"
      ],
      "before": "source roles = [NEW B2, -2, 9, 1]",
      "after": "derived = [否]",
      "relation": "implies",
      "rule_id": "Surjective_EVERY_source_target_fiber_comparison",
      "conditions": [],
      "explanation": {
        "zh-Hant": "逐全部允許input核其output是否此target；每個fiber都完整列出，不把target當input或以集合大小猜滿射。",
        "en": "Compare EVERY permitted input’s output with THIS target.List EACH fiber completely;do not confuse target/input or infer surjectivity from cardinalities alone."
      },
      "reverse_audit": {
        "kind": "premise_and_result_audit",
        "explanation": {
          "zh-Hant": "反查本題原資料、型別、角色、完整前提與欄序；單向推論不倒當等價，有限表核對不冒充無限論域/形式證明。原題/英文/MKO/AST/狀態不變。",
          "en": "Reverse-audit THIS question’s ORIGINAL data,types,roles,complete premises and field order.Do not invert implication or turn finite-table checks into infinite-domain/formal proof.Original Q/English/MKO/AST/status remain unchanged."
        }
      },
      "arithmetic": null
    },
    {
      "id": "S019",
      "uses": [
        "G001",
        "S018"
      ],
      "before": "source roles = [NEW B2, -1, 11, 1]",
      "after": "derived = [否]",
      "relation": "implies",
      "rule_id": "Surjective_EVERY_source_target_fiber_comparison",
      "conditions": [],
      "explanation": {
        "zh-Hant": "逐全部允許input核其output是否此target；每個fiber都完整列出，不把target當input或以集合大小猜滿射。",
        "en": "Compare EVERY permitted input’s output with THIS target.List EACH fiber completely;do not confuse target/input or infer surjectivity from cardinalities alone."
      },
      "reverse_audit": {
        "kind": "premise_and_result_audit",
        "explanation": {
          "zh-Hant": "反查本題原資料、型別、角色、完整前提與欄序；單向推論不倒當等價，有限表核對不冒充無限論域/形式證明。原題/英文/MKO/AST/狀態不變。",
          "en": "Reverse-audit THIS question’s ORIGINAL data,types,roles,complete premises and field order.Do not invert implication or turn finite-table checks into infinite-domain/formal proof.Original Q/English/MKO/AST/status remain unchanged."
        }
      },
      "arithmetic": null
    },
    {
      "id": "S020",
      "uses": [
        "G001",
        "S019"
      ],
      "before": "source roles = [NEW B2, 0, 13, 1]",
      "after": "derived = [否]",
      "relation": "implies",
      "rule_id": "Surjective_EVERY_source_target_fiber_comparison",
      "conditions": [],
      "explanation": {
        "zh-Hant": "逐全部允許input核其output是否此target；每個fiber都完整列出，不把target當input或以集合大小猜滿射。",
        "en": "Compare EVERY permitted input’s output with THIS target.List EACH fiber completely;do not confuse target/input or infer surjectivity from cardinalities alone."
      },
      "reverse_audit": {
        "kind": "premise_and_result_audit",
        "explanation": {
          "zh-Hant": "反查本題原資料、型別、角色、完整前提與欄序；單向推論不倒當等價，有限表核對不冒充無限論域/形式證明。原題/英文/MKO/AST/狀態不變。",
          "en": "Reverse-audit THIS question’s ORIGINAL data,types,roles,complete premises and field order.Do not invert implication or turn finite-table checks into infinite-domain/formal proof.Original Q/English/MKO/AST/status remain unchanged."
        }
      },
      "arithmetic": null
    },
    {
      "id": "S021",
      "uses": [
        "G001",
        "S020"
      ],
      "before": "source roles = [NEW B2, -6, 1, 3]",
      "after": "derived = [否]",
      "relation": "implies",
      "rule_id": "Surjective_EVERY_source_target_fiber_comparison",
      "conditions": [],
      "explanation": {
        "zh-Hant": "逐全部允許input核其output是否此target；每個fiber都完整列出，不把target當input或以集合大小猜滿射。",
        "en": "Compare EVERY permitted input’s output with THIS target.List EACH fiber completely;do not confuse target/input or infer surjectivity from cardinalities alone."
      },
      "reverse_audit": {
        "kind": "premise_and_result_audit",
        "explanation": {
          "zh-Hant": "反查本題原資料、型別、角色、完整前提與欄序；單向推論不倒當等價，有限表核對不冒充無限論域/形式證明。原題/英文/MKO/AST/狀態不變。",
          "en": "Reverse-audit THIS question’s ORIGINAL data,types,roles,complete premises and field order.Do not invert implication or turn finite-table checks into infinite-domain/formal proof.Original Q/English/MKO/AST/status remain unchanged."
        }
      },
      "arithmetic": null
    },
    {
      "id": "S022",
      "uses": [
        "G001",
        "S021"
      ],
      "before": "source roles = [NEW B2, -5, 3, 3]",
      "after": "derived = [是]",
      "relation": "implies",
      "rule_id": "Surjective_EVERY_source_target_fiber_comparison",
      "conditions": [],
      "explanation": {
        "zh-Hant": "逐全部允許input核其output是否此target；每個fiber都完整列出，不把target當input或以集合大小猜滿射。",
        "en": "Compare EVERY permitted input’s output with THIS target.List EACH fiber completely;do not confuse target/input or infer surjectivity from cardinalities alone."
      },
      "reverse_audit": {
        "kind": "premise_and_result_audit",
        "explanation": {
          "zh-Hant": "反查本題原資料、型別、角色、完整前提與欄序；單向推論不倒當等價，有限表核對不冒充無限論域/形式證明。原題/英文/MKO/AST/狀態不變。",
          "en": "Reverse-audit THIS question’s ORIGINAL data,types,roles,complete premises and field order.Do not invert implication or turn finite-table checks into infinite-domain/formal proof.Original Q/English/MKO/AST/status remain unchanged."
        }
      },
      "arithmetic": null
    },
    {
      "id": "S023",
      "uses": [
        "G001",
        "S022"
      ],
      "before": "source roles = [NEW B2, -4, 5, 3]",
      "after": "derived = [否]",
      "relation": "implies",
      "rule_id": "Surjective_EVERY_source_target_fiber_comparison",
      "conditions": [],
      "explanation": {
        "zh-Hant": "逐全部允許input核其output是否此target；每個fiber都完整列出，不把target當input或以集合大小猜滿射。",
        "en": "Compare EVERY permitted input’s output with THIS target.List EACH fiber completely;do not confuse target/input or infer surjectivity from cardinalities alone."
      },
      "reverse_audit": {
        "kind": "premise_and_result_audit",
        "explanation": {
          "zh-Hant": "反查本題原資料、型別、角色、完整前提與欄序；單向推論不倒當等價，有限表核對不冒充無限論域/形式證明。原題/英文/MKO/AST/狀態不變。",
          "en": "Reverse-audit THIS question’s ORIGINAL data,types,roles,complete premises and field order.Do not invert implication or turn finite-table checks into infinite-domain/formal proof.Original Q/English/MKO/AST/status remain unchanged."
        }
      },
      "arithmetic": null
    },
    {
      "id": "S024",
      "uses": [
        "G001",
        "S023"
      ],
      "before": "source roles = [NEW B2, -3, 7, 3]",
      "after": "derived = [否]",
      "relation": "implies",
      "rule_id": "Surjective_EVERY_source_target_fiber_comparison",
      "conditions": [],
      "explanation": {
        "zh-Hant": "逐全部允許input核其output是否此target；每個fiber都完整列出，不把target當input或以集合大小猜滿射。",
        "en": "Compare EVERY permitted input’s output with THIS target.List EACH fiber completely;do not confuse target/input or infer surjectivity from cardinalities alone."
      },
      "reverse_audit": {
        "kind": "premise_and_result_audit",
        "explanation": {
          "zh-Hant": "反查本題原資料、型別、角色、完整前提與欄序；單向推論不倒當等價，有限表核對不冒充無限論域/形式證明。原題/英文/MKO/AST/狀態不變。",
          "en": "Reverse-audit THIS question’s ORIGINAL data,types,roles,complete premises and field order.Do not invert implication or turn finite-table checks into infinite-domain/formal proof.Original Q/English/MKO/AST/status remain unchanged."
        }
      },
      "arithmetic": null
    },
    {
      "id": "S025",
      "uses": [
        "G001",
        "S024"
      ],
      "before": "source roles = [NEW B2, -2, 9, 3]",
      "after": "derived = [否]",
      "relation": "implies",
      "rule_id": "Surjective_EVERY_source_target_fiber_comparison",
      "conditions": [],
      "explanation": {
        "zh-Hant": "逐全部允許input核其output是否此target；每個fiber都完整列出，不把target當input或以集合大小猜滿射。",
        "en": "Compare EVERY permitted input’s output with THIS target.List EACH fiber completely;do not confuse target/input or infer surjectivity from cardinalities alone."
      },
      "reverse_audit": {
        "kind": "premise_and_result_audit",
        "explanation": {
          "zh-Hant": "反查本題原資料、型別、角色、完整前提與欄序；單向推論不倒當等價，有限表核對不冒充無限論域/形式證明。原題/英文/MKO/AST/狀態不變。",
          "en": "Reverse-audit THIS question’s ORIGINAL data,types,roles,complete premises and field order.Do not invert implication or turn finite-table checks into infinite-domain/formal proof.Original Q/English/MKO/AST/status remain unchanged."
        }
      },
      "arithmetic": null
    },
    {
      "id": "S026",
      "uses": [
        "G001",
        "S025"
      ],
      "before": "source roles = [NEW B2, -1, 11, 3]",
      "after": "derived = [否]",
      "relation": "implies",
      "rule_id": "Surjective_EVERY_source_target_fiber_comparison",
      "conditions": [],
      "explanation": {
        "zh-Hant": "逐全部允許input核其output是否此target；每個fiber都完整列出，不把target當input或以集合大小猜滿射。",
        "en": "Compare EVERY permitted input’s output with THIS target.List EACH fiber completely;do not confuse target/input or infer surjectivity from cardinalities alone."
      },
      "reverse_audit": {
        "kind": "premise_and_result_audit",
        "explanation": {
          "zh-Hant": "反查本題原資料、型別、角色、完整前提與欄序；單向推論不倒當等價，有限表核對不冒充無限論域/形式證明。原題/英文/MKO/AST/狀態不變。",
          "en": "Reverse-audit THIS question’s ORIGINAL data,types,roles,complete premises and field order.Do not invert implication or turn finite-table checks into infinite-domain/formal proof.Original Q/English/MKO/AST/status remain unchanged."
        }
      },
      "arithmetic": null
    },
    {
      "id": "S027",
      "uses": [
        "G001",
        "S026"
      ],
      "before": "source roles = [NEW B2, 0, 13, 3]",
      "after": "derived = [否]",
      "relation": "implies",
      "rule_id": "Surjective_EVERY_source_target_fiber_comparison",
      "conditions": [],
      "explanation": {
        "zh-Hant": "逐全部允許input核其output是否此target；每個fiber都完整列出，不把target當input或以集合大小猜滿射。",
        "en": "Compare EVERY permitted input’s output with THIS target.List EACH fiber completely;do not confuse target/input or infer surjectivity from cardinalities alone."
      },
      "reverse_audit": {
        "kind": "premise_and_result_audit",
        "explanation": {
          "zh-Hant": "反查本題原資料、型別、角色、完整前提與欄序；單向推論不倒當等價，有限表核對不冒充無限論域/形式證明。原題/英文/MKO/AST/狀態不變。",
          "en": "Reverse-audit THIS question’s ORIGINAL data,types,roles,complete premises and field order.Do not invert implication or turn finite-table checks into infinite-domain/formal proof.Original Q/English/MKO/AST/status remain unchanged."
        }
      },
      "arithmetic": null
    },
    {
      "id": "S028",
      "uses": [
        "G001",
        "S027"
      ],
      "before": "source roles = [NEW B2, -6, 1, 5]",
      "after": "derived = [否]",
      "relation": "implies",
      "rule_id": "Surjective_EVERY_source_target_fiber_comparison",
      "conditions": [],
      "explanation": {
        "zh-Hant": "逐全部允許input核其output是否此target；每個fiber都完整列出，不把target當input或以集合大小猜滿射。",
        "en": "Compare EVERY permitted input’s output with THIS target.List EACH fiber completely;do not confuse target/input or infer surjectivity from cardinalities alone."
      },
      "reverse_audit": {
        "kind": "premise_and_result_audit",
        "explanation": {
          "zh-Hant": "反查本題原資料、型別、角色、完整前提與欄序；單向推論不倒當等價，有限表核對不冒充無限論域/形式證明。原題/英文/MKO/AST/狀態不變。",
          "en": "Reverse-audit THIS question’s ORIGINAL data,types,roles,complete premises and field order.Do not invert implication or turn finite-table checks into infinite-domain/formal proof.Original Q/English/MKO/AST/status remain unchanged."
        }
      },
      "arithmetic": null
    },
    {
      "id": "S029",
      "uses": [
        "G001",
        "S028"
      ],
      "before": "source roles = [NEW B2, -5, 3, 5]",
      "after": "derived = [否]",
      "relation": "implies",
      "rule_id": "Surjective_EVERY_source_target_fiber_comparison",
      "conditions": [],
      "explanation": {
        "zh-Hant": "逐全部允許input核其output是否此target；每個fiber都完整列出，不把target當input或以集合大小猜滿射。",
        "en": "Compare EVERY permitted input’s output with THIS target.List EACH fiber completely;do not confuse target/input or infer surjectivity from cardinalities alone."
      },
      "reverse_audit": {
        "kind": "premise_and_result_audit",
        "explanation": {
          "zh-Hant": "反查本題原資料、型別、角色、完整前提與欄序；單向推論不倒當等價，有限表核對不冒充無限論域/形式證明。原題/英文/MKO/AST/狀態不變。",
          "en": "Reverse-audit THIS question’s ORIGINAL data,types,roles,complete premises and field order.Do not invert implication or turn finite-table checks into infinite-domain/formal proof.Original Q/English/MKO/AST/status remain unchanged."
        }
      },
      "arithmetic": null
    },
    {
      "id": "S030",
      "uses": [
        "G001",
        "S029"
      ],
      "before": "source roles = [NEW B2, -4, 5, 5]",
      "after": "derived = [是]",
      "relation": "implies",
      "rule_id": "Surjective_EVERY_source_target_fiber_comparison",
      "conditions": [],
      "explanation": {
        "zh-Hant": "逐全部允許input核其output是否此target；每個fiber都完整列出，不把target當input或以集合大小猜滿射。",
        "en": "Compare EVERY permitted input’s output with THIS target.List EACH fiber completely;do not confuse target/input or infer surjectivity from cardinalities alone."
      },
      "reverse_audit": {
        "kind": "premise_and_result_audit",
        "explanation": {
          "zh-Hant": "反查本題原資料、型別、角色、完整前提與欄序；單向推論不倒當等價，有限表核對不冒充無限論域/形式證明。原題/英文/MKO/AST/狀態不變。",
          "en": "Reverse-audit THIS question’s ORIGINAL data,types,roles,complete premises and field order.Do not invert implication or turn finite-table checks into infinite-domain/formal proof.Original Q/English/MKO/AST/status remain unchanged."
        }
      },
      "arithmetic": null
    },
    {
      "id": "S031",
      "uses": [
        "G001",
        "S030"
      ],
      "before": "source roles = [NEW B2, -3, 7, 5]",
      "after": "derived = [否]",
      "relation": "implies",
      "rule_id": "Surjective_EVERY_source_target_fiber_comparison",
      "conditions": [],
      "explanation": {
        "zh-Hant": "逐全部允許input核其output是否此target；每個fiber都完整列出，不把target當input或以集合大小猜滿射。",
        "en": "Compare EVERY permitted input’s output with THIS target.List EACH fiber completely;do not confuse target/input or infer surjectivity from cardinalities alone."
      },
      "reverse_audit": {
        "kind": "premise_and_result_audit",
        "explanation": {
          "zh-Hant": "反查本題原資料、型別、角色、完整前提與欄序；單向推論不倒當等價，有限表核對不冒充無限論域/形式證明。原題/英文/MKO/AST/狀態不變。",
          "en": "Reverse-audit THIS question’s ORIGINAL data,types,roles,complete premises and field order.Do not invert implication or turn finite-table checks into infinite-domain/formal proof.Original Q/English/MKO/AST/status remain unchanged."
        }
      },
      "arithmetic": null
    },
    {
      "id": "S032",
      "uses": [
        "G001",
        "S031"
      ],
      "before": "source roles = [NEW B2, -2, 9, 5]",
      "after": "derived = [否]",
      "relation": "implies",
      "rule_id": "Surjective_EVERY_source_target_fiber_comparison",
      "conditions": [],
      "explanation": {
        "zh-Hant": "逐全部允許input核其output是否此target；每個fiber都完整列出，不把target當input或以集合大小猜滿射。",
        "en": "Compare EVERY permitted input’s output with THIS target.List EACH fiber completely;do not confuse target/input or infer surjectivity from cardinalities alone."
      },
      "reverse_audit": {
        "kind": "premise_and_result_audit",
        "explanation": {
          "zh-Hant": "反查本題原資料、型別、角色、完整前提與欄序；單向推論不倒當等價，有限表核對不冒充無限論域/形式證明。原題/英文/MKO/AST/狀態不變。",
          "en": "Reverse-audit THIS question’s ORIGINAL data,types,roles,complete premises and field order.Do not invert implication or turn finite-table checks into infinite-domain/formal proof.Original Q/English/MKO/AST/status remain unchanged."
        }
      },
      "arithmetic": null
    },
    {
      "id": "S033",
      "uses": [
        "G001",
        "S032"
      ],
      "before": "source roles = [NEW B2, -1, 11, 5]",
      "after": "derived = [否]",
      "relation": "implies",
      "rule_id": "Surjective_EVERY_source_target_fiber_comparison",
      "conditions": [],
      "explanation": {
        "zh-Hant": "逐全部允許input核其output是否此target；每個fiber都完整列出，不把target當input或以集合大小猜滿射。",
        "en": "Compare EVERY permitted input’s output with THIS target.List EACH fiber completely;do not confuse target/input or infer surjectivity from cardinalities alone."
      },
      "reverse_audit": {
        "kind": "premise_and_result_audit",
        "explanation": {
          "zh-Hant": "反查本題原資料、型別、角色、完整前提與欄序；單向推論不倒當等價，有限表核對不冒充無限論域/形式證明。原題/英文/MKO/AST/狀態不變。",
          "en": "Reverse-audit THIS question’s ORIGINAL data,types,roles,complete premises and field order.Do not invert implication or turn finite-table checks into infinite-domain/formal proof.Original Q/English/MKO/AST/status remain unchanged."
        }
      },
      "arithmetic": null
    },
    {
      "id": "S034",
      "uses": [
        "G001",
        "S033"
      ],
      "before": "source roles = [NEW B2, 0, 13, 5]",
      "after": "derived = [否]",
      "relation": "implies",
      "rule_id": "Surjective_EVERY_source_target_fiber_comparison",
      "conditions": [],
      "explanation": {
        "zh-Hant": "逐全部允許input核其output是否此target；每個fiber都完整列出，不把target當input或以集合大小猜滿射。",
        "en": "Compare EVERY permitted input’s output with THIS target.List EACH fiber completely;do not confuse target/input or infer surjectivity from cardinalities alone."
      },
      "reverse_audit": {
        "kind": "premise_and_result_audit",
        "explanation": {
          "zh-Hant": "反查本題原資料、型別、角色、完整前提與欄序；單向推論不倒當等價，有限表核對不冒充無限論域/形式證明。原題/英文/MKO/AST/狀態不變。",
          "en": "Reverse-audit THIS question’s ORIGINAL data,types,roles,complete premises and field order.Do not invert implication or turn finite-table checks into infinite-domain/formal proof.Original Q/English/MKO/AST/status remain unchanged."
        }
      },
      "arithmetic": null
    },
    {
      "id": "S035",
      "uses": [
        "G001",
        "S034"
      ],
      "before": "source roles = [NEW B2, -6, 1, 7]",
      "after": "derived = [否]",
      "relation": "implies",
      "rule_id": "Surjective_EVERY_source_target_fiber_comparison",
      "conditions": [],
      "explanation": {
        "zh-Hant": "逐全部允許input核其output是否此target；每個fiber都完整列出，不把target當input或以集合大小猜滿射。",
        "en": "Compare EVERY permitted input’s output with THIS target.List EACH fiber completely;do not confuse target/input or infer surjectivity from cardinalities alone."
      },
      "reverse_audit": {
        "kind": "premise_and_result_audit",
        "explanation": {
          "zh-Hant": "反查本題原資料、型別、角色、完整前提與欄序；單向推論不倒當等價，有限表核對不冒充無限論域/形式證明。原題/英文/MKO/AST/狀態不變。",
          "en": "Reverse-audit THIS question’s ORIGINAL data,types,roles,complete premises and field order.Do not invert implication or turn finite-table checks into infinite-domain/formal proof.Original Q/English/MKO/AST/status remain unchanged."
        }
      },
      "arithmetic": null
    },
    {
      "id": "S036",
      "uses": [
        "G001",
        "S035"
      ],
      "before": "source roles = [NEW B2, -5, 3, 7]",
      "after": "derived = [否]",
      "relation": "implies",
      "rule_id": "Surjective_EVERY_source_target_fiber_comparison",
      "conditions": [],
      "explanation": {
        "zh-Hant": "逐全部允許input核其output是否此target；每個fiber都完整列出，不把target當input或以集合大小猜滿射。",
        "en": "Compare EVERY permitted input’s output with THIS target.List EACH fiber completely;do not confuse target/input or infer surjectivity from cardinalities alone."
      },
      "reverse_audit": {
        "kind": "premise_and_result_audit",
        "explanation": {
          "zh-Hant": "反查本題原資料、型別、角色、完整前提與欄序；單向推論不倒當等價，有限表核對不冒充無限論域/形式證明。原題/英文/MKO/AST/狀態不變。",
          "en": "Reverse-audit THIS question’s ORIGINAL data,types,roles,complete premises and field order.Do not invert implication or turn finite-table checks into infinite-domain/formal proof.Original Q/English/MKO/AST/status remain unchanged."
        }
      },
      "arithmetic": null
    },
    {
      "id": "S037",
      "uses": [
        "G001",
        "S036"
      ],
      "before": "source roles = [NEW B2, -4, 5, 7]",
      "after": "derived = [否]",
      "relation": "implies",
      "rule_id": "Surjective_EVERY_source_target_fiber_comparison",
      "conditions": [],
      "explanation": {
        "zh-Hant": "逐全部允許input核其output是否此target；每個fiber都完整列出，不把target當input或以集合大小猜滿射。",
        "en": "Compare EVERY permitted input’s output with THIS target.List EACH fiber completely;do not confuse target/input or infer surjectivity from cardinalities alone."
      },
      "reverse_audit": {
        "kind": "premise_and_result_audit",
        "explanation": {
          "zh-Hant": "反查本題原資料、型別、角色、完整前提與欄序；單向推論不倒當等價，有限表核對不冒充無限論域/形式證明。原題/英文/MKO/AST/狀態不變。",
          "en": "Reverse-audit THIS question’s ORIGINAL data,types,roles,complete premises and field order.Do not invert implication or turn finite-table checks into infinite-domain/formal proof.Original Q/English/MKO/AST/status remain unchanged."
        }
      },
      "arithmetic": null
    },
    {
      "id": "S038",
      "uses": [
        "G001",
        "S037"
      ],
      "before": "source roles = [NEW B2, -3, 7, 7]",
      "after": "derived = [是]",
      "relation": "implies",
      "rule_id": "Surjective_EVERY_source_target_fiber_comparison",
      "conditions": [],
      "explanation": {
        "zh-Hant": "逐全部允許input核其output是否此target；每個fiber都完整列出，不把target當input或以集合大小猜滿射。",
        "en": "Compare EVERY permitted input’s output with THIS target.List EACH fiber completely;do not confuse target/input or infer surjectivity from cardinalities alone."
      },
      "reverse_audit": {
        "kind": "premise_and_result_audit",
        "explanation": {
          "zh-Hant": "反查本題原資料、型別、角色、完整前提與欄序；單向推論不倒當等價，有限表核對不冒充無限論域/形式證明。原題/英文/MKO/AST/狀態不變。",
          "en": "Reverse-audit THIS question’s ORIGINAL data,types,roles,complete premises and field order.Do not invert implication or turn finite-table checks into infinite-domain/formal proof.Original Q/English/MKO/AST/status remain unchanged."
        }
      },
      "arithmetic": null
    },
    {
      "id": "S039",
      "uses": [
        "G001",
        "S038"
      ],
      "before": "source roles = [NEW B2, -2, 9, 7]",
      "after": "derived = [否]",
      "relation": "implies",
      "rule_id": "Surjective_EVERY_source_target_fiber_comparison",
      "conditions": [],
      "explanation": {
        "zh-Hant": "逐全部允許input核其output是否此target；每個fiber都完整列出，不把target當input或以集合大小猜滿射。",
        "en": "Compare EVERY permitted input’s output with THIS target.List EACH fiber completely;do not confuse target/input or infer surjectivity from cardinalities alone."
      },
      "reverse_audit": {
        "kind": "premise_and_result_audit",
        "explanation": {
          "zh-Hant": "反查本題原資料、型別、角色、完整前提與欄序；單向推論不倒當等價，有限表核對不冒充無限論域/形式證明。原題/英文/MKO/AST/狀態不變。",
          "en": "Reverse-audit THIS question’s ORIGINAL data,types,roles,complete premises and field order.Do not invert implication or turn finite-table checks into infinite-domain/formal proof.Original Q/English/MKO/AST/status remain unchanged."
        }
      },
      "arithmetic": null
    },
    {
      "id": "S040",
      "uses": [
        "G001",
        "S039"
      ],
      "before": "source roles = [NEW B2, -1, 11, 7]",
      "after": "derived = [否]",
      "relation": "implies",
      "rule_id": "Surjective_EVERY_source_target_fiber_comparison",
      "conditions": [],
      "explanation": {
        "zh-Hant": "逐全部允許input核其output是否此target；每個fiber都完整列出，不把target當input或以集合大小猜滿射。",
        "en": "Compare EVERY permitted input’s output with THIS target.List EACH fiber completely;do not confuse target/input or infer surjectivity from cardinalities alone."
      },
      "reverse_audit": {
        "kind": "premise_and_result_audit",
        "explanation": {
          "zh-Hant": "反查本題原資料、型別、角色、完整前提與欄序；單向推論不倒當等價，有限表核對不冒充無限論域/形式證明。原題/英文/MKO/AST/狀態不變。",
          "en": "Reverse-audit THIS question’s ORIGINAL data,types,roles,complete premises and field order.Do not invert implication or turn finite-table checks into infinite-domain/formal proof.Original Q/English/MKO/AST/status remain unchanged."
        }
      },
      "arithmetic": null
    },
    {
      "id": "S041",
      "uses": [
        "G001",
        "S040"
      ],
      "before": "source roles = [NEW B2, 0, 13, 7]",
      "after": "derived = [否]",
      "relation": "implies",
      "rule_id": "Surjective_EVERY_source_target_fiber_comparison",
      "conditions": [],
      "explanation": {
        "zh-Hant": "逐全部允許input核其output是否此target；每個fiber都完整列出，不把target當input或以集合大小猜滿射。",
        "en": "Compare EVERY permitted input’s output with THIS target.List EACH fiber completely;do not confuse target/input or infer surjectivity from cardinalities alone."
      },
      "reverse_audit": {
        "kind": "premise_and_result_audit",
        "explanation": {
          "zh-Hant": "反查本題原資料、型別、角色、完整前提與欄序；單向推論不倒當等價，有限表核對不冒充無限論域/形式證明。原題/英文/MKO/AST/狀態不變。",
          "en": "Reverse-audit THIS question’s ORIGINAL data,types,roles,complete premises and field order.Do not invert implication or turn finite-table checks into infinite-domain/formal proof.Original Q/English/MKO/AST/status remain unchanged."
        }
      },
      "arithmetic": null
    },
    {
      "id": "S042",
      "uses": [
        "G001",
        "S041"
      ],
      "before": "source roles = [NEW B2, -6, 1, 9]",
      "after": "derived = [否]",
      "relation": "implies",
      "rule_id": "Surjective_EVERY_source_target_fiber_comparison",
      "conditions": [],
      "explanation": {
        "zh-Hant": "逐全部允許input核其output是否此target；每個fiber都完整列出，不把target當input或以集合大小猜滿射。",
        "en": "Compare EVERY permitted input’s output with THIS target.List EACH fiber completely;do not confuse target/input or infer surjectivity from cardinalities alone."
      },
      "reverse_audit": {
        "kind": "premise_and_result_audit",
        "explanation": {
          "zh-Hant": "反查本題原資料、型別、角色、完整前提與欄序；單向推論不倒當等價，有限表核對不冒充無限論域/形式證明。原題/英文/MKO/AST/狀態不變。",
          "en": "Reverse-audit THIS question’s ORIGINAL data,types,roles,complete premises and field order.Do not invert implication or turn finite-table checks into infinite-domain/formal proof.Original Q/English/MKO/AST/status remain unchanged."
        }
      },
      "arithmetic": null
    },
    {
      "id": "S043",
      "uses": [
        "G001",
        "S042"
      ],
      "before": "source roles = [NEW B2, -5, 3, 9]",
      "after": "derived = [否]",
      "relation": "implies",
      "rule_id": "Surjective_EVERY_source_target_fiber_comparison",
      "conditions": [],
      "explanation": {
        "zh-Hant": "逐全部允許input核其output是否此target；每個fiber都完整列出，不把target當input或以集合大小猜滿射。",
        "en": "Compare EVERY permitted input’s output with THIS target.List EACH fiber completely;do not confuse target/input or infer surjectivity from cardinalities alone."
      },
      "reverse_audit": {
        "kind": "premise_and_result_audit",
        "explanation": {
          "zh-Hant": "反查本題原資料、型別、角色、完整前提與欄序；單向推論不倒當等價，有限表核對不冒充無限論域/形式證明。原題/英文/MKO/AST/狀態不變。",
          "en": "Reverse-audit THIS question’s ORIGINAL data,types,roles,complete premises and field order.Do not invert implication or turn finite-table checks into infinite-domain/formal proof.Original Q/English/MKO/AST/status remain unchanged."
        }
      },
      "arithmetic": null
    },
    {
      "id": "S044",
      "uses": [
        "G001",
        "S043"
      ],
      "before": "source roles = [NEW B2, -4, 5, 9]",
      "after": "derived = [否]",
      "relation": "implies",
      "rule_id": "Surjective_EVERY_source_target_fiber_comparison",
      "conditions": [],
      "explanation": {
        "zh-Hant": "逐全部允許input核其output是否此target；每個fiber都完整列出，不把target當input或以集合大小猜滿射。",
        "en": "Compare EVERY permitted input’s output with THIS target.List EACH fiber completely;do not confuse target/input or infer surjectivity from cardinalities alone."
      },
      "reverse_audit": {
        "kind": "premise_and_result_audit",
        "explanation": {
          "zh-Hant": "反查本題原資料、型別、角色、完整前提與欄序；單向推論不倒當等價，有限表核對不冒充無限論域/形式證明。原題/英文/MKO/AST/狀態不變。",
          "en": "Reverse-audit THIS question’s ORIGINAL data,types,roles,complete premises and field order.Do not invert implication or turn finite-table checks into infinite-domain/formal proof.Original Q/English/MKO/AST/status remain unchanged."
        }
      },
      "arithmetic": null
    },
    {
      "id": "S045",
      "uses": [
        "G001",
        "S044"
      ],
      "before": "source roles = [NEW B2, -3, 7, 9]",
      "after": "derived = [否]",
      "relation": "implies",
      "rule_id": "Surjective_EVERY_source_target_fiber_comparison",
      "conditions": [],
      "explanation": {
        "zh-Hant": "逐全部允許input核其output是否此target；每個fiber都完整列出，不把target當input或以集合大小猜滿射。",
        "en": "Compare EVERY permitted input’s output with THIS target.List EACH fiber completely;do not confuse target/input or infer surjectivity from cardinalities alone."
      },
      "reverse_audit": {
        "kind": "premise_and_result_audit",
        "explanation": {
          "zh-Hant": "反查本題原資料、型別、角色、完整前提與欄序；單向推論不倒當等價，有限表核對不冒充無限論域/形式證明。原題/英文/MKO/AST/狀態不變。",
          "en": "Reverse-audit THIS question’s ORIGINAL data,types,roles,complete premises and field order.Do not invert implication or turn finite-table checks into infinite-domain/formal proof.Original Q/English/MKO/AST/status remain unchanged."
        }
      },
      "arithmetic": null
    },
    {
      "id": "S046",
      "uses": [
        "G001",
        "S045"
      ],
      "before": "source roles = [NEW B2, -2, 9, 9]",
      "after": "derived = [是]",
      "relation": "implies",
      "rule_id": "Surjective_EVERY_source_target_fiber_comparison",
      "conditions": [],
      "explanation": {
        "zh-Hant": "逐全部允許input核其output是否此target；每個fiber都完整列出，不把target當input或以集合大小猜滿射。",
        "en": "Compare EVERY permitted input’s output with THIS target.List EACH fiber completely;do not confuse target/input or infer surjectivity from cardinalities alone."
      },
      "reverse_audit": {
        "kind": "premise_and_result_audit",
        "explanation": {
          "zh-Hant": "反查本題原資料、型別、角色、完整前提與欄序；單向推論不倒當等價，有限表核對不冒充無限論域/形式證明。原題/英文/MKO/AST/狀態不變。",
          "en": "Reverse-audit THIS question’s ORIGINAL data,types,roles,complete premises and field order.Do not invert implication or turn finite-table checks into infinite-domain/formal proof.Original Q/English/MKO/AST/status remain unchanged."
        }
      },
      "arithmetic": null
    },
    {
      "id": "S047",
      "uses": [
        "G001",
        "S046"
      ],
      "before": "source roles = [NEW B2, -1, 11, 9]",
      "after": "derived = [否]",
      "relation": "implies",
      "rule_id": "Surjective_EVERY_source_target_fiber_comparison",
      "conditions": [],
      "explanation": {
        "zh-Hant": "逐全部允許input核其output是否此target；每個fiber都完整列出，不把target當input或以集合大小猜滿射。",
        "en": "Compare EVERY permitted input’s output with THIS target.List EACH fiber completely;do not confuse target/input or infer surjectivity from cardinalities alone."
      },
      "reverse_audit": {
        "kind": "premise_and_result_audit",
        "explanation": {
          "zh-Hant": "反查本題原資料、型別、角色、完整前提與欄序；單向推論不倒當等價，有限表核對不冒充無限論域/形式證明。原題/英文/MKO/AST/狀態不變。",
          "en": "Reverse-audit THIS question’s ORIGINAL data,types,roles,complete premises and field order.Do not invert implication or turn finite-table checks into infinite-domain/formal proof.Original Q/English/MKO/AST/status remain unchanged."
        }
      },
      "arithmetic": null
    },
    {
      "id": "S048",
      "uses": [
        "G001",
        "S047"
      ],
      "before": "source roles = [NEW B2, 0, 13, 9]",
      "after": "derived = [否]",
      "relation": "implies",
      "rule_id": "Surjective_EVERY_source_target_fiber_comparison",
      "conditions": [],
      "explanation": {
        "zh-Hant": "逐全部允許input核其output是否此target；每個fiber都完整列出，不把target當input或以集合大小猜滿射。",
        "en": "Compare EVERY permitted input’s output with THIS target.List EACH fiber completely;do not confuse target/input or infer surjectivity from cardinalities alone."
      },
      "reverse_audit": {
        "kind": "premise_and_result_audit",
        "explanation": {
          "zh-Hant": "反查本題原資料、型別、角色、完整前提與欄序；單向推論不倒當等價，有限表核對不冒充無限論域/形式證明。原題/英文/MKO/AST/狀態不變。",
          "en": "Reverse-audit THIS question’s ORIGINAL data,types,roles,complete premises and field order.Do not invert implication or turn finite-table checks into infinite-domain/formal proof.Original Q/English/MKO/AST/status remain unchanged."
        }
      },
      "arithmetic": null
    },
    {
      "id": "S049",
      "uses": [
        "G001",
        "S048"
      ],
      "before": "source roles = [NEW B2, -6, 1, 11]",
      "after": "derived = [否]",
      "relation": "implies",
      "rule_id": "Surjective_EVERY_source_target_fiber_comparison",
      "conditions": [],
      "explanation": {
        "zh-Hant": "逐全部允許input核其output是否此target；每個fiber都完整列出，不把target當input或以集合大小猜滿射。",
        "en": "Compare EVERY permitted input’s output with THIS target.List EACH fiber completely;do not confuse target/input or infer surjectivity from cardinalities alone."
      },
      "reverse_audit": {
        "kind": "premise_and_result_audit",
        "explanation": {
          "zh-Hant": "反查本題原資料、型別、角色、完整前提與欄序；單向推論不倒當等價，有限表核對不冒充無限論域/形式證明。原題/英文/MKO/AST/狀態不變。",
          "en": "Reverse-audit THIS question’s ORIGINAL data,types,roles,complete premises and field order.Do not invert implication or turn finite-table checks into infinite-domain/formal proof.Original Q/English/MKO/AST/status remain unchanged."
        }
      },
      "arithmetic": null
    },
    {
      "id": "S050",
      "uses": [
        "G001",
        "S049"
      ],
      "before": "source roles = [NEW B2, -5, 3, 11]",
      "after": "derived = [否]",
      "relation": "implies",
      "rule_id": "Surjective_EVERY_source_target_fiber_comparison",
      "conditions": [],
      "explanation": {
        "zh-Hant": "逐全部允許input核其output是否此target；每個fiber都完整列出，不把target當input或以集合大小猜滿射。",
        "en": "Compare EVERY permitted input’s output with THIS target.List EACH fiber completely;do not confuse target/input or infer surjectivity from cardinalities alone."
      },
      "reverse_audit": {
        "kind": "premise_and_result_audit",
        "explanation": {
          "zh-Hant": "反查本題原資料、型別、角色、完整前提與欄序；單向推論不倒當等價，有限表核對不冒充無限論域/形式證明。原題/英文/MKO/AST/狀態不變。",
          "en": "Reverse-audit THIS question’s ORIGINAL data,types,roles,complete premises and field order.Do not invert implication or turn finite-table checks into infinite-domain/formal proof.Original Q/English/MKO/AST/status remain unchanged."
        }
      },
      "arithmetic": null
    },
    {
      "id": "S051",
      "uses": [
        "G001",
        "S050"
      ],
      "before": "source roles = [NEW B2, -4, 5, 11]",
      "after": "derived = [否]",
      "relation": "implies",
      "rule_id": "Surjective_EVERY_source_target_fiber_comparison",
      "conditions": [],
      "explanation": {
        "zh-Hant": "逐全部允許input核其output是否此target；每個fiber都完整列出，不把target當input或以集合大小猜滿射。",
        "en": "Compare EVERY permitted input’s output with THIS target.List EACH fiber completely;do not confuse target/input or infer surjectivity from cardinalities alone."
      },
      "reverse_audit": {
        "kind": "premise_and_result_audit",
        "explanation": {
          "zh-Hant": "反查本題原資料、型別、角色、完整前提與欄序；單向推論不倒當等價，有限表核對不冒充無限論域/形式證明。原題/英文/MKO/AST/狀態不變。",
          "en": "Reverse-audit THIS question’s ORIGINAL data,types,roles,complete premises and field order.Do not invert implication or turn finite-table checks into infinite-domain/formal proof.Original Q/English/MKO/AST/status remain unchanged."
        }
      },
      "arithmetic": null
    },
    {
      "id": "S052",
      "uses": [
        "G001",
        "S051"
      ],
      "before": "source roles = [NEW B2, -3, 7, 11]",
      "after": "derived = [否]",
      "relation": "implies",
      "rule_id": "Surjective_EVERY_source_target_fiber_comparison",
      "conditions": [],
      "explanation": {
        "zh-Hant": "逐全部允許input核其output是否此target；每個fiber都完整列出，不把target當input或以集合大小猜滿射。",
        "en": "Compare EVERY permitted input’s output with THIS target.List EACH fiber completely;do not confuse target/input or infer surjectivity from cardinalities alone."
      },
      "reverse_audit": {
        "kind": "premise_and_result_audit",
        "explanation": {
          "zh-Hant": "反查本題原資料、型別、角色、完整前提與欄序；單向推論不倒當等價，有限表核對不冒充無限論域/形式證明。原題/英文/MKO/AST/狀態不變。",
          "en": "Reverse-audit THIS question’s ORIGINAL data,types,roles,complete premises and field order.Do not invert implication or turn finite-table checks into infinite-domain/formal proof.Original Q/English/MKO/AST/status remain unchanged."
        }
      },
      "arithmetic": null
    },
    {
      "id": "S053",
      "uses": [
        "G001",
        "S052"
      ],
      "before": "source roles = [NEW B2, -2, 9, 11]",
      "after": "derived = [否]",
      "relation": "implies",
      "rule_id": "Surjective_EVERY_source_target_fiber_comparison",
      "conditions": [],
      "explanation": {
        "zh-Hant": "逐全部允許input核其output是否此target；每個fiber都完整列出，不把target當input或以集合大小猜滿射。",
        "en": "Compare EVERY permitted input’s output with THIS target.List EACH fiber completely;do not confuse target/input or infer surjectivity from cardinalities alone."
      },
      "reverse_audit": {
        "kind": "premise_and_result_audit",
        "explanation": {
          "zh-Hant": "反查本題原資料、型別、角色、完整前提與欄序；單向推論不倒當等價，有限表核對不冒充無限論域/形式證明。原題/英文/MKO/AST/狀態不變。",
          "en": "Reverse-audit THIS question’s ORIGINAL data,types,roles,complete premises and field order.Do not invert implication or turn finite-table checks into infinite-domain/formal proof.Original Q/English/MKO/AST/status remain unchanged."
        }
      },
      "arithmetic": null
    },
    {
      "id": "S054",
      "uses": [
        "G001",
        "S053"
      ],
      "before": "source roles = [NEW B2, -1, 11, 11]",
      "after": "derived = [是]",
      "relation": "implies",
      "rule_id": "Surjective_EVERY_source_target_fiber_comparison",
      "conditions": [],
      "explanation": {
        "zh-Hant": "逐全部允許input核其output是否此target；每個fiber都完整列出，不把target當input或以集合大小猜滿射。",
        "en": "Compare EVERY permitted input’s output with THIS target.List EACH fiber completely;do not confuse target/input or infer surjectivity from cardinalities alone."
      },
      "reverse_audit": {
        "kind": "premise_and_result_audit",
        "explanation": {
          "zh-Hant": "反查本題原資料、型別、角色、完整前提與欄序；單向推論不倒當等價，有限表核對不冒充無限論域/形式證明。原題/英文/MKO/AST/狀態不變。",
          "en": "Reverse-audit THIS question’s ORIGINAL data,types,roles,complete premises and field order.Do not invert implication or turn finite-table checks into infinite-domain/formal proof.Original Q/English/MKO/AST/status remain unchanged."
        }
      },
      "arithmetic": null
    },
    {
      "id": "S055",
      "uses": [
        "G001",
        "S054"
      ],
      "before": "source roles = [NEW B2, 0, 13, 11]",
      "after": "derived = [否]",
      "relation": "implies",
      "rule_id": "Surjective_EVERY_source_target_fiber_comparison",
      "conditions": [],
      "explanation": {
        "zh-Hant": "逐全部允許input核其output是否此target；每個fiber都完整列出，不把target當input或以集合大小猜滿射。",
        "en": "Compare EVERY permitted input’s output with THIS target.List EACH fiber completely;do not confuse target/input or infer surjectivity from cardinalities alone."
      },
      "reverse_audit": {
        "kind": "premise_and_result_audit",
        "explanation": {
          "zh-Hant": "反查本題原資料、型別、角色、完整前提與欄序；單向推論不倒當等價，有限表核對不冒充無限論域/形式證明。原題/英文/MKO/AST/狀態不變。",
          "en": "Reverse-audit THIS question’s ORIGINAL data,types,roles,complete premises and field order.Do not invert implication or turn finite-table checks into infinite-domain/formal proof.Original Q/English/MKO/AST/status remain unchanged."
        }
      },
      "arithmetic": null
    },
    {
      "id": "S056",
      "uses": [
        "G001",
        "S055"
      ],
      "before": "source roles = [NEW B2, -6, 1, 13]",
      "after": "derived = [否]",
      "relation": "implies",
      "rule_id": "Surjective_EVERY_source_target_fiber_comparison",
      "conditions": [],
      "explanation": {
        "zh-Hant": "逐全部允許input核其output是否此target；每個fiber都完整列出，不把target當input或以集合大小猜滿射。",
        "en": "Compare EVERY permitted input’s output with THIS target.List EACH fiber completely;do not confuse target/input or infer surjectivity from cardinalities alone."
      },
      "reverse_audit": {
        "kind": "premise_and_result_audit",
        "explanation": {
          "zh-Hant": "反查本題原資料、型別、角色、完整前提與欄序；單向推論不倒當等價，有限表核對不冒充無限論域/形式證明。原題/英文/MKO/AST/狀態不變。",
          "en": "Reverse-audit THIS question’s ORIGINAL data,types,roles,complete premises and field order.Do not invert implication or turn finite-table checks into infinite-domain/formal proof.Original Q/English/MKO/AST/status remain unchanged."
        }
      },
      "arithmetic": null
    },
    {
      "id": "S057",
      "uses": [
        "G001",
        "S056"
      ],
      "before": "source roles = [NEW B2, -5, 3, 13]",
      "after": "derived = [否]",
      "relation": "implies",
      "rule_id": "Surjective_EVERY_source_target_fiber_comparison",
      "conditions": [],
      "explanation": {
        "zh-Hant": "逐全部允許input核其output是否此target；每個fiber都完整列出，不把target當input或以集合大小猜滿射。",
        "en": "Compare EVERY permitted input’s output with THIS target.List EACH fiber completely;do not confuse target/input or infer surjectivity from cardinalities alone."
      },
      "reverse_audit": {
        "kind": "premise_and_result_audit",
        "explanation": {
          "zh-Hant": "反查本題原資料、型別、角色、完整前提與欄序；單向推論不倒當等價，有限表核對不冒充無限論域/形式證明。原題/英文/MKO/AST/狀態不變。",
          "en": "Reverse-audit THIS question’s ORIGINAL data,types,roles,complete premises and field order.Do not invert implication or turn finite-table checks into infinite-domain/formal proof.Original Q/English/MKO/AST/status remain unchanged."
        }
      },
      "arithmetic": null
    },
    {
      "id": "S058",
      "uses": [
        "G001",
        "S057"
      ],
      "before": "source roles = [NEW B2, -4, 5, 13]",
      "after": "derived = [否]",
      "relation": "implies",
      "rule_id": "Surjective_EVERY_source_target_fiber_comparison",
      "conditions": [],
      "explanation": {
        "zh-Hant": "逐全部允許input核其output是否此target；每個fiber都完整列出，不把target當input或以集合大小猜滿射。",
        "en": "Compare EVERY permitted input’s output with THIS target.List EACH fiber completely;do not confuse target/input or infer surjectivity from cardinalities alone."
      },
      "reverse_audit": {
        "kind": "premise_and_result_audit",
        "explanation": {
          "zh-Hant": "反查本題原資料、型別、角色、完整前提與欄序；單向推論不倒當等價，有限表核對不冒充無限論域/形式證明。原題/英文/MKO/AST/狀態不變。",
          "en": "Reverse-audit THIS question’s ORIGINAL data,types,roles,complete premises and field order.Do not invert implication or turn finite-table checks into infinite-domain/formal proof.Original Q/English/MKO/AST/status remain unchanged."
        }
      },
      "arithmetic": null
    },
    {
      "id": "S059",
      "uses": [
        "G001",
        "S058"
      ],
      "before": "source roles = [NEW B2, -3, 7, 13]",
      "after": "derived = [否]",
      "relation": "implies",
      "rule_id": "Surjective_EVERY_source_target_fiber_comparison",
      "conditions": [],
      "explanation": {
        "zh-Hant": "逐全部允許input核其output是否此target；每個fiber都完整列出，不把target當input或以集合大小猜滿射。",
        "en": "Compare EVERY permitted input’s output with THIS target.List EACH fiber completely;do not confuse target/input or infer surjectivity from cardinalities alone."
      },
      "reverse_audit": {
        "kind": "premise_and_result_audit",
        "explanation": {
          "zh-Hant": "反查本題原資料、型別、角色、完整前提與欄序；單向推論不倒當等價，有限表核對不冒充無限論域/形式證明。原題/英文/MKO/AST/狀態不變。",
          "en": "Reverse-audit THIS question’s ORIGINAL data,types,roles,complete premises and field order.Do not invert implication or turn finite-table checks into infinite-domain/formal proof.Original Q/English/MKO/AST/status remain unchanged."
        }
      },
      "arithmetic": null
    },
    {
      "id": "S060",
      "uses": [
        "G001",
        "S059"
      ],
      "before": "source roles = [NEW B2, -2, 9, 13]",
      "after": "derived = [否]",
      "relation": "implies",
      "rule_id": "Surjective_EVERY_source_target_fiber_comparison",
      "conditions": [],
      "explanation": {
        "zh-Hant": "逐全部允許input核其output是否此target；每個fiber都完整列出，不把target當input或以集合大小猜滿射。",
        "en": "Compare EVERY permitted input’s output with THIS target.List EACH fiber completely;do not confuse target/input or infer surjectivity from cardinalities alone."
      },
      "reverse_audit": {
        "kind": "premise_and_result_audit",
        "explanation": {
          "zh-Hant": "反查本題原資料、型別、角色、完整前提與欄序；單向推論不倒當等價，有限表核對不冒充無限論域/形式證明。原題/英文/MKO/AST/狀態不變。",
          "en": "Reverse-audit THIS question’s ORIGINAL data,types,roles,complete premises and field order.Do not invert implication or turn finite-table checks into infinite-domain/formal proof.Original Q/English/MKO/AST/status remain unchanged."
        }
      },
      "arithmetic": null
    },
    {
      "id": "S061",
      "uses": [
        "G001",
        "S060"
      ],
      "before": "source roles = [NEW B2, -1, 11, 13]",
      "after": "derived = [否]",
      "relation": "implies",
      "rule_id": "Surjective_EVERY_source_target_fiber_comparison",
      "conditions": [],
      "explanation": {
        "zh-Hant": "逐全部允許input核其output是否此target；每個fiber都完整列出，不把target當input或以集合大小猜滿射。",
        "en": "Compare EVERY permitted input’s output with THIS target.List EACH fiber completely;do not confuse target/input or infer surjectivity from cardinalities alone."
      },
      "reverse_audit": {
        "kind": "premise_and_result_audit",
        "explanation": {
          "zh-Hant": "反查本題原資料、型別、角色、完整前提與欄序；單向推論不倒當等價，有限表核對不冒充無限論域/形式證明。原題/英文/MKO/AST/狀態不變。",
          "en": "Reverse-audit THIS question’s ORIGINAL data,types,roles,complete premises and field order.Do not invert implication or turn finite-table checks into infinite-domain/formal proof.Original Q/English/MKO/AST/status remain unchanged."
        }
      },
      "arithmetic": null
    },
    {
      "id": "S062",
      "uses": [
        "G001",
        "S061"
      ],
      "before": "source roles = [NEW B2, 0, 13, 13]",
      "after": "derived = [是]",
      "relation": "implies",
      "rule_id": "Surjective_EVERY_source_target_fiber_comparison",
      "conditions": [],
      "explanation": {
        "zh-Hant": "逐全部允許input核其output是否此target；每個fiber都完整列出，不把target當input或以集合大小猜滿射。",
        "en": "Compare EVERY permitted input’s output with THIS target.List EACH fiber completely;do not confuse target/input or infer surjectivity from cardinalities alone."
      },
      "reverse_audit": {
        "kind": "premise_and_result_audit",
        "explanation": {
          "zh-Hant": "反查本題原資料、型別、角色、完整前提與欄序；單向推論不倒當等價，有限表核對不冒充無限論域/形式證明。原題/英文/MKO/AST/狀態不變。",
          "en": "Reverse-audit THIS question’s ORIGINAL data,types,roles,complete premises and field order.Do not invert implication or turn finite-table checks into infinite-domain/formal proof.Original Q/English/MKO/AST/status remain unchanged."
        }
      },
      "arithmetic": null
    },
    {
      "id": "S063",
      "uses": [
        "G001",
        "S062"
      ],
      "before": "source roles = [[-6, -5, -4, -3, -2, -1, 0], [1, 3, 5, 7, 9, 11, 13], [[1, [-6]], [3, [-5]], [5, [-4]], [7, [-3]], [9, [-2]], [11, [-1]], [13, [0]]]]",
      "after": "derived = [[], 是]",
      "relation": "implies",
      "rule_id": "Surjective_ALL_codomain_targets_covered_including_EMPTY_vacuity",
      "conditions": [],
      "explanation": {
        "zh-Hant": "滿射需每個宣告target都有preimage，可有多個；空陪域在已合格empty function下條件空真。缺少target集合為B(或B2)減range，不把range直接當原陪域。",
        "en": "Surjectivity requires a preimage for EVERY declared target;multiple preimages are allowed.For a QUALIFIED empty function,the empty-codomain condition is vacuous.The missing set is B(or B2)minus range,not a replacement of the ORIGINAL codomain."
      },
      "reverse_audit": {
        "kind": "premise_and_result_audit",
        "explanation": {
          "zh-Hant": "反查本題原資料、型別、角色、完整前提與欄序；單向推論不倒當等價，有限表核對不冒充無限論域/形式證明。原題/英文/MKO/AST/狀態不變。",
          "en": "Reverse-audit THIS question’s ORIGINAL data,types,roles,complete premises and field order.Do not invert implication or turn finite-table checks into infinite-domain/formal proof.Original Q/English/MKO/AST/status remain unchanged."
        }
      },
      "arithmetic": null
    }
  ],
  "math_model": {
    "result": "是"
  },
  "conclusion": {
    "canonical_value": "是",
    "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-20261004-advance-20261005-r02-surjective-foundations",
      "batch_path": "public/data/questions/batches/batch-20261004-advance-20261005-r02-surjective-foundations/questions.jsonl",
      "batch_sha256": "2fd9a60abb39ad7c085cadea1e6e706edf88b02dbeae3cab1b4a6ae2f62fea65",
      "original_line": 98,
      "original_line_sha256": "a0ac7d0000be819926257ec0006edb90b1c107947cbdd6d0b004a8326f5019b6",
      "question_compact_sha256": "38590ee82c42fded0004a4e21fd268350227c47ad61aaa08d0331a5b9ca43421",
      "english_row_compact_sha256": "bd013e0f7f35ccbdc7b6c5a3e63c3e15e0ecdc14e0bb75190a4d76d0be6a85de",
      "english_manifest_path": "public/data/i18n/editions/batch-20261004-advance-20261005-r02-surjective-foundations.en.json",
      "english_rows_path": "public/data/i18n/questions/batch-20261004-advance-20261005-r02-surjective-foundations.en.jsonl"
    },
    "mko_bindings": {
      "mko-surjective": {
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        "english_sha256": "dc93237b8c19a6b091095797c7bb5b1ffc1e339f1c4437a9a8fecc626775520a",
        "original_path": "public/data/mko/surjective.json",
        "english_path": "public/data/i18n/editions/mko-surjective.en.json"
      }
    },
    "selected_manifest_sha256": "5233edba9654a6cffd8b6b2d83c932f82ded15f9c0b7c733bd049943e672acff",
    "selected_part_sha256": "63155b87d4994521b4a60f8f179750f57cbbd094e66cc42652608d1bbab47a9f",
    "original_candidate_sha256": "6cc72790ae0dc0833b45ce0e26e298edb11f07e5e1d627bc0f11ea71fe37a63e",
    "original_candidate_line_sha256": "6cc72790ae0dc0833b45ce0e26e298edb11f07e5e1d627bc0f11ea71fe37a63e"
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  "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-20261026-012-p70",
    "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": "ccf93c72638d6abf6a412514da5838d55ecb09b71d0e4fdec2b559dc9fdee14b",
      "question_first_witness_sha256": "11af9a338b5a610342b2cfb2ee295683131b3139ac402dd19b1ba1725976d518"
    },
    "status": "second_context_reviewed",
    "mathematical_semantics": true,
    "bilingual_semantics": true,
    "steps_reviewed": 63,
    "method": "family_template_semantic_review_plus_independent_per_instance_reconstruction",
    "exact_question_first_check": {
      "model_sha256": "04d3f7b1b53a2175e0fd8707acf3c0dbdc2b84c660bca89bf8f716e25f5ad050",
      "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."
  }
}