{"schema_version":"ocme-question-v0.1","id":"q-20261015-advance-20261115-r07-many-one-reduction-0001","batch_id":"batch-20261015-advance-20261115-r07-many-one-reduction-foundations","language":"zh-Hant","source_mko_ids":["mko-many-one-reduction"],"title_zh":"多對一歸約","stem_zh":"明示decision predicates與complete total map的雙向membership equivalence。操作=mreduction-total-map-qualification；資料={\"source_carrier\":[0,1,2],\"target_carrier\":[0,1,2],\"mapping\":[0,1,null]}。請依 exact_ordered_tuple_declared_by_interface 欄序回答。","answer":{"kind":"expression","value":"([0, 1, 2], [0, 1, 2], [[0, 0, 是], [1, 1, 是], [2, null, 否]], 否, [2, null, 否], many_one_reduction_requires_a_complete_total_map_before_membership_audit)","explanation_zh":"Wave6第九層核對=([0, 1, 2], [0, 1, 2], [[0, 0, 是], [1, 1, 是], [2, null, 否]], 否, [2, null, 否], many_one_reduction_requires_a_complete_total_map_before_membership_audit)；依完整明示資料獨立重算；composition與decider transfer保持A≤mB的方向；partial map與yes-only檢查無效；finite table只證finite domain instance，不證無限domain computability；不混同Turing reduction或反向decidability transfer。"},"difficulty":{"band":"undergraduate_core","level":1,"skills":["多對一歸約"]},"variant":{"family_id":"qf-mod46-mreduction-total-map-qualification","seed":202611157001,"parameters":{"source_carrier":[0,1,2],"target_carrier":[0,1,2],"mapping":[0,1,null],"domain":"Complete_finite_many_one_reduction","operation":"mreduction-total-map-qualification","semantic_template":"qf-mod46-mreduction-total-map-qualification/{\"mapping\":[0,1,null],\"source_carrier\":[0,1,2],\"target_carrier\":[0,1,2]}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_or_symbolic_model","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"候選須主端重算；不構成人工審定、一般第一同構／strong duality／max-flow-min-cut證明、class equation、consistency、integrality、König theorem、無限domain computability、Lean或Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-15","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261015-advance-20261115-r07-many-one-reduction-0002","batch_id":"batch-20261015-advance-20261115-r07-many-one-reduction-foundations","language":"zh-Hant","source_mko_ids":["mko-many-one-reduction"],"title_zh":"多對一歸約","stem_zh":"明示decision predicates與complete total map的雙向membership equivalence。操作=mreduction-total-map-qualification；資料={\"source_carrier\":[0,1,2,3],\"target_carrier\":[0,1,2],\"mapping\":[1,2,0,1]}。請依 exact_ordered_tuple_declared_by_interface 欄序回答。","answer":{"kind":"expression","value":"([0, 1, 2, 3], [0, 1, 2], [[0, 1, 是], [1, 2, 是], [2, 0, 是], [3, 1, 是]], 是, null, many_one_reduction_requires_a_complete_total_map_before_membership_audit)","explanation_zh":"Wave6第九層核對=([0, 1, 2, 3], [0, 1, 2], [[0, 1, 是], [1, 2, 是], [2, 0, 是], [3, 1, 是]], 是, null, many_one_reduction_requires_a_complete_total_map_before_membership_audit)；依完整明示資料獨立重算；composition與decider transfer保持A≤mB的方向；partial map與yes-only檢查無效；finite table只證finite domain instance，不證無限domain computability；不混同Turing reduction或反向decidability transfer。"},"difficulty":{"band":"undergraduate_core","level":1,"skills":["多對一歸約"]},"variant":{"family_id":"qf-mod46-mreduction-total-map-qualification","seed":202611157002,"parameters":{"source_carrier":[0,1,2,3],"target_carrier":[0,1,2],"mapping":[1,2,0,1],"domain":"Complete_finite_many_one_reduction","operation":"mreduction-total-map-qualification","semantic_template":"qf-mod46-mreduction-total-map-qualification/{\"mapping\":[1,2,0,1],\"source_carrier\":[0,1,2,3],\"target_carrier\":[0,1,2]}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_or_symbolic_model","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"候選須主端重算；不構成人工審定、一般第一同構／strong duality／max-flow-min-cut證明、class equation、consistency、integrality、König theorem、無限domain computability、Lean或Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-15","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261015-advance-20261115-r07-many-one-reduction-0003","batch_id":"batch-20261015-advance-20261115-r07-many-one-reduction-foundations","language":"zh-Hant","source_mko_ids":["mko-many-one-reduction"],"title_zh":"多對一歸約","stem_zh":"明示decision predicates與complete total map的雙向membership equivalence。操作=mreduction-total-map-qualification；資料={\"source_carrier\":[0,1,2,3,4],\"target_carrier\":[0,1,2],\"mapping\":[2,0,1,2,0]}。請依 exact_ordered_tuple_declared_by_interface 欄序回答。","answer":{"kind":"expression","value":"([0, 1, 2, 3, 4], [0, 1, 2], [[0, 2, 是], [1, 0, 是], [2, 1, 是], [3, 2, 是], [4, 0, 是]], 是, null, many_one_reduction_requires_a_complete_total_map_before_membership_audit)","explanation_zh":"Wave6第九層核對=([0, 1, 2, 3, 4], [0, 1, 2], [[0, 2, 是], [1, 0, 是], [2, 1, 是], [3, 2, 是], [4, 0, 是]], 是, null, many_one_reduction_requires_a_complete_total_map_before_membership_audit)；依完整明示資料獨立重算；composition與decider transfer保持A≤mB的方向；partial map與yes-only檢查無效；finite table只證finite domain instance，不證無限domain computability；不混同Turing reduction或反向decidability transfer。"},"difficulty":{"band":"undergraduate_core","level":1,"skills":["多對一歸約"]},"variant":{"family_id":"qf-mod46-mreduction-total-map-qualification","seed":202611157003,"parameters":{"source_carrier":[0,1,2,3,4],"target_carrier":[0,1,2],"mapping":[2,0,1,2,0],"domain":"Complete_finite_many_one_reduction","operation":"mreduction-total-map-qualification","semantic_template":"qf-mod46-mreduction-total-map-qualification/{\"mapping\":[2,0,1,2,0],\"source_carrier\":[0,1,2,3,4],\"target_carrier\":[0,1,2]}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_or_symbolic_model","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"候選須主端重算；不構成人工審定、一般第一同構／strong duality／max-flow-min-cut證明、class equation、consistency、integrality、König theorem、無限domain computability、Lean或Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-15","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261015-advance-20261115-r07-many-one-reduction-0004","batch_id":"batch-20261015-advance-20261115-r07-many-one-reduction-foundations","language":"zh-Hant","source_mko_ids":["mko-many-one-reduction"],"title_zh":"多對一歸約","stem_zh":"明示decision predicates與complete total map的雙向membership equivalence。操作=mreduction-total-map-qualification；資料={\"source_carrier\":[0,1,2,3,4,5],\"target_carrier\":[0,1,2],\"mapping\":[0,1,2,0,1,2]}。請依 exact_ordered_tuple_declared_by_interface 欄序回答。","answer":{"kind":"expression","value":"([0, 1, 2, 3, 4, 5], [0, 1, 2], [[0, 0, 是], [1, 1, 是], [2, 2, 是], [3, 0, 是], [4, 1, 是], [5, 2, 是]], 是, null, many_one_reduction_requires_a_complete_total_map_before_membership_audit)","explanation_zh":"Wave6第九層核對=([0, 1, 2, 3, 4, 5], [0, 1, 2], [[0, 0, 是], [1, 1, 是], [2, 2, 是], [3, 0, 是], [4, 1, 是], [5, 2, 是]], 是, null, many_one_reduction_requires_a_complete_total_map_before_membership_audit)；依完整明示資料獨立重算；composition與decider transfer保持A≤mB的方向；partial map與yes-only檢查無效；finite table只證finite domain instance，不證無限domain computability；不混同Turing reduction或反向decidability transfer。"},"difficulty":{"band":"undergraduate_core","level":1,"skills":["多對一歸約"]},"variant":{"family_id":"qf-mod46-mreduction-total-map-qualification","seed":202611157004,"parameters":{"source_carrier":[0,1,2,3,4,5],"target_carrier":[0,1,2],"mapping":[0,1,2,0,1,2],"domain":"Complete_finite_many_one_reduction","operation":"mreduction-total-map-qualification","semantic_template":"qf-mod46-mreduction-total-map-qualification/{\"mapping\":[0,1,2,0,1,2],\"source_carrier\":[0,1,2,3,4,5],\"target_carrier\":[0,1,2]}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_or_symbolic_model","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"候選須主端重算；不構成人工審定、一般第一同構／strong duality／max-flow-min-cut證明、class equation、consistency、integrality、König theorem、無限domain computability、Lean或Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-15","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261015-advance-20261115-r07-many-one-reduction-0005","batch_id":"batch-20261015-advance-20261115-r07-many-one-reduction-foundations","language":"zh-Hant","source_mko_ids":["mko-many-one-reduction"],"title_zh":"多對一歸約","stem_zh":"明示decision predicates與complete total map的雙向membership equivalence。操作=mreduction-total-map-qualification；資料={\"source_carrier\":[0,1,2,3,4,5,6],\"target_carrier\":[0,1,2],\"mapping\":[1,2,0,1,2,0,1]}。請依 exact_ordered_tuple_declared_by_interface 欄序回答。","answer":{"kind":"expression","value":"([0, 1, 2, 3, 4, 5, 6], [0, 1, 2], [[0, 1, 是], [1, 2, 是], [2, 0, 是], [3, 1, 是], [4, 2, 是], [5, 0, 是], [6, 1, 是]], 是, null, many_one_reduction_requires_a_complete_total_map_before_membership_audit)","explanation_zh":"Wave6第九層核對=([0, 1, 2, 3, 4, 5, 6], [0, 1, 2], [[0, 1, 是], [1, 2, 是], [2, 0, 是], [3, 1, 是], [4, 2, 是], [5, 0, 是], [6, 1, 是]], 是, null, many_one_reduction_requires_a_complete_total_map_before_membership_audit)；依完整明示資料獨立重算；composition與decider transfer保持A≤mB的方向；partial map與yes-only檢查無效；finite table只證finite domain instance，不證無限domain computability；不混同Turing reduction或反向decidability transfer。"},"difficulty":{"band":"undergraduate_core","level":1,"skills":["多對一歸約"]},"variant":{"family_id":"qf-mod46-mreduction-total-map-qualification","seed":202611157005,"parameters":{"source_carrier":[0,1,2,3,4,5,6],"target_carrier":[0,1,2],"mapping":[1,2,0,1,2,0,1],"domain":"Complete_finite_many_one_reduction","operation":"mreduction-total-map-qualification","semantic_template":"qf-mod46-mreduction-total-map-qualification/{\"mapping\":[1,2,0,1,2,0,1],\"source_carrier\":[0,1,2,3,4,5,6],\"target_carrier\":[0,1,2]}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_or_symbolic_model","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"候選須主端重算；不構成人工審定、一般第一同構／strong duality／max-flow-min-cut證明、class equation、consistency、integrality、König theorem、無限domain computability、Lean或Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-15","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261015-advance-20261115-r07-many-one-reduction-0006","batch_id":"batch-20261015-advance-20261115-r07-many-one-reduction-foundations","language":"zh-Hant","source_mko_ids":["mko-many-one-reduction"],"title_zh":"多對一歸約","stem_zh":"明示decision predicates與complete total map的雙向membership equivalence。操作=mreduction-total-map-qualification；資料={\"source_carrier\":[0,1,2,3,4,5,6,7],\"target_carrier\":[0,1,2],\"mapping\":[2,0,1,2,0,1,2,null]}。請依 exact_ordered_tuple_declared_by_interface 欄序回答。","answer":{"kind":"expression","value":"([0, 1, 2, 3, 4, 5, 6, 7], [0, 1, 2], [[0, 2, 是], [1, 0, 是], [2, 1, 是], [3, 2, 是], [4, 0, 是], [5, 1, 是], [6, 2, 是], [7, null, 否]], 否, [7, null, 否], many_one_reduction_requires_a_complete_total_map_before_membership_audit)","explanation_zh":"Wave6第九層核對=([0, 1, 2, 3, 4, 5, 6, 7], [0, 1, 2], [[0, 2, 是], [1, 0, 是], [2, 1, 是], [3, 2, 是], [4, 0, 是], [5, 1, 是], [6, 2, 是], [7, null, 否]], 否, [7, null, 否], many_one_reduction_requires_a_complete_total_map_before_membership_audit)；依完整明示資料獨立重算；composition與decider transfer保持A≤mB的方向；partial map與yes-only檢查無效；finite table只證finite domain instance，不證無限domain computability；不混同Turing reduction或反向decidability transfer。"},"difficulty":{"band":"undergraduate_core","level":1,"skills":["多對一歸約"]},"variant":{"family_id":"qf-mod46-mreduction-total-map-qualification","seed":202611157006,"parameters":{"source_carrier":[0,1,2,3,4,5,6,7],"target_carrier":[0,1,2],"mapping":[2,0,1,2,0,1,2,null],"domain":"Complete_finite_many_one_reduction","operation":"mreduction-total-map-qualification","semantic_template":"qf-mod46-mreduction-total-map-qualification/{\"mapping\":[2,0,1,2,0,1,2,null],\"source_carrier\":[0,1,2,3,4,5,6,7],\"target_carrier\":[0,1,2]}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_or_symbolic_model","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"候選須主端重算；不構成人工審定、一般第一同構／strong duality／max-flow-min-cut證明、class equation、consistency、integrality、König theorem、無限domain computability、Lean或Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-15","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261015-advance-20261115-r07-many-one-reduction-0007","batch_id":"batch-20261015-advance-20261115-r07-many-one-reduction-foundations","language":"zh-Hant","source_mko_ids":["mko-many-one-reduction"],"title_zh":"多對一歸約","stem_zh":"明示decision predicates與complete total map的雙向membership equivalence。操作=mreduction-total-map-qualification；資料={\"source_carrier\":[0,1,2,3,4,5,6,7,8],\"target_carrier\":[0,1,2],\"mapping\":[0,1,2,0,1,2,0,1,2]}。請依 exact_ordered_tuple_declared_by_interface 欄序回答。","answer":{"kind":"expression","value":"([0, 1, 2, 3, 4, 5, 6, 7, 8], [0, 1, 2], [[0, 0, 是], [1, 1, 是], [2, 2, 是], [3, 0, 是], [4, 1, 是], [5, 2, 是], [6, 0, 是], [7, 1, 是], [8, 2, 是]], 是, null, many_one_reduction_requires_a_complete_total_map_before_membership_audit)","explanation_zh":"Wave6第九層核對=([0, 1, 2, 3, 4, 5, 6, 7, 8], [0, 1, 2], [[0, 0, 是], [1, 1, 是], [2, 2, 是], [3, 0, 是], [4, 1, 是], [5, 2, 是], [6, 0, 是], [7, 1, 是], [8, 2, 是]], 是, null, many_one_reduction_requires_a_complete_total_map_before_membership_audit)；依完整明示資料獨立重算；composition與decider transfer保持A≤mB的方向；partial map與yes-only檢查無效；finite table只證finite domain instance，不證無限domain computability；不混同Turing reduction或反向decidability transfer。"},"difficulty":{"band":"undergraduate_core","level":1,"skills":["多對一歸約"]},"variant":{"family_id":"qf-mod46-mreduction-total-map-qualification","seed":202611157007,"parameters":{"source_carrier":[0,1,2,3,4,5,6,7,8],"target_carrier":[0,1,2],"mapping":[0,1,2,0,1,2,0,1,2],"domain":"Complete_finite_many_one_reduction","operation":"mreduction-total-map-qualification","semantic_template":"qf-mod46-mreduction-total-map-qualification/{\"mapping\":[0,1,2,0,1,2,0,1,2],\"source_carrier\":[0,1,2,3,4,5,6,7,8],\"target_carrier\":[0,1,2]}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_or_symbolic_model","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"候選須主端重算；不構成人工審定、一般第一同構／strong duality／max-flow-min-cut證明、class equation、consistency、integrality、König theorem、無限domain computability、Lean或Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-15","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261015-advance-20261115-r07-many-one-reduction-0008","batch_id":"batch-20261015-advance-20261115-r07-many-one-reduction-foundations","language":"zh-Hant","source_mko_ids":["mko-many-one-reduction"],"title_zh":"多對一歸約","stem_zh":"明示decision predicates與complete total map的雙向membership equivalence。操作=mreduction-total-map-qualification；資料={\"source_carrier\":[0,1,2,3,4,5,6,7,8,9],\"target_carrier\":[0,1,2],\"mapping\":[1,2,0,1,2,0,1,2,0,1]}。請依 exact_ordered_tuple_declared_by_interface 欄序回答。","answer":{"kind":"expression","value":"([0, 1, 2, 3, 4, 5, 6, 7, 8, 9], [0, 1, 2], [[0, 1, 是], [1, 2, 是], [2, 0, 是], [3, 1, 是], [4, 2, 是], [5, 0, 是], [6, 1, 是], [7, 2, 是], [8, 0, 是], [9, 1, 是]], 是, null, many_one_reduction_requires_a_complete_total_map_before_membership_audit)","explanation_zh":"Wave6第九層核對=([0, 1, 2, 3, 4, 5, 6, 7, 8, 9], [0, 1, 2], [[0, 1, 是], [1, 2, 是], [2, 0, 是], [3, 1, 是], [4, 2, 是], [5, 0, 是], [6, 1, 是], [7, 2, 是], [8, 0, 是], [9, 1, 是]], 是, null, many_one_reduction_requires_a_complete_total_map_before_membership_audit)；依完整明示資料獨立重算；composition與decider transfer保持A≤mB的方向；partial map與yes-only檢查無效；finite table只證finite domain instance，不證無限domain computability；不混同Turing reduction或反向decidability transfer。"},"difficulty":{"band":"undergraduate_core","level":1,"skills":["多對一歸約"]},"variant":{"family_id":"qf-mod46-mreduction-total-map-qualification","seed":202611157008,"parameters":{"source_carrier":[0,1,2,3,4,5,6,7,8,9],"target_carrier":[0,1,2],"mapping":[1,2,0,1,2,0,1,2,0,1],"domain":"Complete_finite_many_one_reduction","operation":"mreduction-total-map-qualification","semantic_template":"qf-mod46-mreduction-total-map-qualification/{\"mapping\":[1,2,0,1,2,0,1,2,0,1],\"source_carrier\":[0,1,2,3,4,5,6,7,8,9],\"target_carrier\":[0,1,2]}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_or_symbolic_model","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"候選須主端重算；不構成人工審定、一般第一同構／strong duality／max-flow-min-cut證明、class equation、consistency、integrality、König theorem、無限domain computability、Lean或Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-15","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261015-advance-20261115-r07-many-one-reduction-0009","batch_id":"batch-20261015-advance-20261115-r07-many-one-reduction-foundations","language":"zh-Hant","source_mko_ids":["mko-many-one-reduction"],"title_zh":"多對一歸約","stem_zh":"明示decision predicates與complete total map的雙向membership equivalence。操作=mreduction-total-map-qualification；資料={\"source_carrier\":[0,1,2,3,4,5,6,7,8,9,10],\"target_carrier\":[0,1,2],\"mapping\":[2,0,1,2,0,1,2,0,1,2,0]}。請依 exact_ordered_tuple_declared_by_interface 欄序回答。","answer":{"kind":"expression","value":"([0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10], [0, 1, 2], [[0, 2, 是], [1, 0, 是], [2, 1, 是], [3, 2, 是], [4, 0, 是], [5, 1, 是], [6, 2, 是], [7, 0, 是], [8, 1, 是], [9, 2, 是], [10, 0, 是]], 是, null, many_one_reduction_requires_a_complete_total_map_before_membership_audit)","explanation_zh":"Wave6第九層核對=([0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10], [0, 1, 2], [[0, 2, 是], [1, 0, 是], [2, 1, 是], [3, 2, 是], [4, 0, 是], [5, 1, 是], [6, 2, 是], [7, 0, 是], [8, 1, 是], [9, 2, 是], [10, 0, 是]], 是, null, many_one_reduction_requires_a_complete_total_map_before_membership_audit)；依完整明示資料獨立重算；composition與decider transfer保持A≤mB的方向；partial map與yes-only檢查無效；finite table只證finite domain instance，不證無限domain computability；不混同Turing reduction或反向decidability transfer。"},"difficulty":{"band":"undergraduate_core","level":2,"skills":["多對一歸約"]},"variant":{"family_id":"qf-mod46-mreduction-total-map-qualification","seed":202611157009,"parameters":{"source_carrier":[0,1,2,3,4,5,6,7,8,9,10],"target_carrier":[0,1,2],"mapping":[2,0,1,2,0,1,2,0,1,2,0],"domain":"Complete_finite_many_one_reduction","operation":"mreduction-total-map-qualification","semantic_template":"qf-mod46-mreduction-total-map-qualification/{\"mapping\":[2,0,1,2,0,1,2,0,1,2,0],\"source_carrier\":[0,1,2,3,4,5,6,7,8,9,10],\"target_carrier\":[0,1,2]}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_or_symbolic_model","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"候選須主端重算；不構成人工審定、一般第一同構／strong duality／max-flow-min-cut證明、class equation、consistency、integrality、König theorem、無限domain computability、Lean或Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-15","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261015-advance-20261115-r07-many-one-reduction-0010","batch_id":"batch-20261015-advance-20261115-r07-many-one-reduction-foundations","language":"zh-Hant","source_mko_ids":["mko-many-one-reduction"],"title_zh":"多對一歸約","stem_zh":"明示decision predicates與complete total map的雙向membership equivalence。操作=mreduction-total-map-qualification；資料={\"source_carrier\":[0,1,2,3,4,5,6,7,8,9,10,11],\"target_carrier\":[0,1,2],\"mapping\":[0,1,2,0,1,2,0,1,2,0,1,2]}。請依 exact_ordered_tuple_declared_by_interface 欄序回答。","answer":{"kind":"expression","value":"([0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11], [0, 1, 2], [[0, 0, 是], [1, 1, 是], [2, 2, 是], [3, 0, 是], [4, 1, 是], [5, 2, 是], [6, 0, 是], [7, 1, 是], [8, 2, 是], [9, 0, 是], [10, 1, 是], [11, 2, 是]], 是, null, many_one_reduction_requires_a_complete_total_map_before_membership_audit)","explanation_zh":"Wave6第九層核對=([0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11], [0, 1, 2], [[0, 0, 是], [1, 1, 是], [2, 2, 是], [3, 0, 是], [4, 1, 是], [5, 2, 是], [6, 0, 是], [7, 1, 是], [8, 2, 是], [9, 0, 是], [10, 1, 是], [11, 2, 是]], 是, null, many_one_reduction_requires_a_complete_total_map_before_membership_audit)；依完整明示資料獨立重算；composition與decider transfer保持A≤mB的方向；partial map與yes-only檢查無效；finite table只證finite domain instance，不證無限domain computability；不混同Turing reduction或反向decidability transfer。"},"difficulty":{"band":"undergraduate_core","level":2,"skills":["多對一歸約"]},"variant":{"family_id":"qf-mod46-mreduction-total-map-qualification","seed":202611157010,"parameters":{"source_carrier":[0,1,2,3,4,5,6,7,8,9,10,11],"target_carrier":[0,1,2],"mapping":[0,1,2,0,1,2,0,1,2,0,1,2],"domain":"Complete_finite_many_one_reduction","operation":"mreduction-total-map-qualification","semantic_template":"qf-mod46-mreduction-total-map-qualification/{\"mapping\":[0,1,2,0,1,2,0,1,2,0,1,2],\"source_carrier\":[0,1,2,3,4,5,6,7,8,9,10,11],\"target_carrier\":[0,1,2]}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_or_symbolic_model","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"候選須主端重算；不構成人工審定、一般第一同構／strong duality／max-flow-min-cut證明、class equation、consistency、integrality、König theorem、無限domain computability、Lean或Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-15","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261015-advance-20261115-r07-many-one-reduction-0011","batch_id":"batch-20261015-advance-20261115-r07-many-one-reduction-foundations","language":"zh-Hant","source_mko_ids":["mko-many-one-reduction"],"title_zh":"多對一歸約","stem_zh":"明示decision predicates與complete total map的雙向membership equivalence。操作=mreduction-total-map-qualification；資料={\"source_carrier\":[0,1,2,3,4,5,6,7,8,9,10,11,12],\"target_carrier\":[0,1,2],\"mapping\":[1,2,0,1,2,0,1,2,0,1,2,0,null]}。請依 exact_ordered_tuple_declared_by_interface 欄序回答。","answer":{"kind":"expression","value":"([0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12], [0, 1, 2], [[0, 1, 是], [1, 2, 是], [2, 0, 是], [3, 1, 是], [4, 2, 是], [5, 0, 是], [6, 1, 是], [7, 2, 是], [8, 0, 是], [9, 1, 是], [10, 2, 是], [11, 0, 是], [12, null, 否]], 否, [12, null, 否], many_one_reduction_requires_a_complete_total_map_before_membership_audit)","explanation_zh":"Wave6第九層核對=([0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12], [0, 1, 2], [[0, 1, 是], [1, 2, 是], [2, 0, 是], [3, 1, 是], [4, 2, 是], [5, 0, 是], [6, 1, 是], [7, 2, 是], [8, 0, 是], [9, 1, 是], [10, 2, 是], [11, 0, 是], [12, null, 否]], 否, [12, null, 否], many_one_reduction_requires_a_complete_total_map_before_membership_audit)；依完整明示資料獨立重算；composition與decider transfer保持A≤mB的方向；partial map與yes-only檢查無效；finite table只證finite domain instance，不證無限domain computability；不混同Turing reduction或反向decidability transfer。"},"difficulty":{"band":"undergraduate_core","level":2,"skills":["多對一歸約"]},"variant":{"family_id":"qf-mod46-mreduction-total-map-qualification","seed":202611157011,"parameters":{"source_carrier":[0,1,2,3,4,5,6,7,8,9,10,11,12],"target_carrier":[0,1,2],"mapping":[1,2,0,1,2,0,1,2,0,1,2,0,null],"domain":"Complete_finite_many_one_reduction","operation":"mreduction-total-map-qualification","semantic_template":"qf-mod46-mreduction-total-map-qualification/{\"mapping\":[1,2,0,1,2,0,1,2,0,1,2,0,null],\"source_carrier\":[0,1,2,3,4,5,6,7,8,9,10,11,12],\"target_carrier\":[0,1,2]}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_or_symbolic_model","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"候選須主端重算；不構成人工審定、一般第一同構／strong duality／max-flow-min-cut證明、class equation、consistency、integrality、König theorem、無限domain computability、Lean或Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-15","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261015-advance-20261115-r07-many-one-reduction-0012","batch_id":"batch-20261015-advance-20261115-r07-many-one-reduction-foundations","language":"zh-Hant","source_mko_ids":["mko-many-one-reduction"],"title_zh":"多對一歸約","stem_zh":"明示decision predicates與complete total map的雙向membership equivalence。操作=mreduction-total-map-qualification；資料={\"source_carrier\":[0,1,2,3,4,5,6,7,8,9,10,11,12,13],\"target_carrier\":[0,1,2],\"mapping\":[2,0,1,2,0,1,2,0,1,2,0,1,2,0]}。請依 exact_ordered_tuple_declared_by_interface 欄序回答。","answer":{"kind":"expression","value":"([0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13], [0, 1, 2], [[0, 2, 是], [1, 0, 是], [2, 1, 是], [3, 2, 是], [4, 0, 是], [5, 1, 是], [6, 2, 是], [7, 0, 是], [8, 1, 是], [9, 2, 是], [10, 0, 是], [11, 1, 是], [12, 2, 是], [13, 0, 是]], 是, null, many_one_reduction_requires_a_complete_total_map_before_membership_audit)","explanation_zh":"Wave6第九層核對=([0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13], [0, 1, 2], [[0, 2, 是], [1, 0, 是], [2, 1, 是], [3, 2, 是], [4, 0, 是], [5, 1, 是], [6, 2, 是], [7, 0, 是], [8, 1, 是], [9, 2, 是], [10, 0, 是], [11, 1, 是], [12, 2, 是], [13, 0, 是]], 是, null, many_one_reduction_requires_a_complete_total_map_before_membership_audit)；依完整明示資料獨立重算；composition與decider transfer保持A≤mB的方向；partial map與yes-only檢查無效；finite table只證finite domain instance，不證無限domain computability；不混同Turing reduction或反向decidability transfer。"},"difficulty":{"band":"undergraduate_core","level":2,"skills":["多對一歸約"]},"variant":{"family_id":"qf-mod46-mreduction-total-map-qualification","seed":202611157012,"parameters":{"source_carrier":[0,1,2,3,4,5,6,7,8,9,10,11,12,13],"target_carrier":[0,1,2],"mapping":[2,0,1,2,0,1,2,0,1,2,0,1,2,0],"domain":"Complete_finite_many_one_reduction","operation":"mreduction-total-map-qualification","semantic_template":"qf-mod46-mreduction-total-map-qualification/{\"mapping\":[2,0,1,2,0,1,2,0,1,2,0,1,2,0],\"source_carrier\":[0,1,2,3,4,5,6,7,8,9,10,11,12,13],\"target_carrier\":[0,1,2]}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_or_symbolic_model","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"候選須主端重算；不構成人工審定、一般第一同構／strong duality／max-flow-min-cut證明、class equation、consistency、integrality、König theorem、無限domain computability、Lean或Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-15","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261015-advance-20261115-r07-many-one-reduction-0013","batch_id":"batch-20261015-advance-20261115-r07-many-one-reduction-foundations","language":"zh-Hant","source_mko_ids":["mko-many-one-reduction"],"title_zh":"多對一歸約","stem_zh":"明示decision predicates與complete total map的雙向membership equivalence。操作=mreduction-total-map-qualification；資料={\"source_carrier\":[0,1,2,3,4,5,6,7,8,9,10,11,12,13,14],\"target_carrier\":[0,1,2],\"mapping\":[0,1,2,0,1,2,0,1,2,0,1,2,0,1,2]}。請依 exact_ordered_tuple_declared_by_interface 欄序回答。","answer":{"kind":"expression","value":"([0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14], [0, 1, 2], [[0, 0, 是], [1, 1, 是], [2, 2, 是], [3, 0, 是], [4, 1, 是], [5, 2, 是], [6, 0, 是], [7, 1, 是], [8, 2, 是], [9, 0, 是], [10, 1, 是], [11, 2, 是], [12, 0, 是], [13, 1, 是], [14, 2, 是]], 是, null, many_one_reduction_requires_a_complete_total_map_before_membership_audit)","explanation_zh":"Wave6第九層核對=([0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14], [0, 1, 2], [[0, 0, 是], [1, 1, 是], [2, 2, 是], [3, 0, 是], [4, 1, 是], [5, 2, 是], [6, 0, 是], [7, 1, 是], [8, 2, 是], [9, 0, 是], [10, 1, 是], [11, 2, 是], [12, 0, 是], [13, 1, 是], [14, 2, 是]], 是, null, many_one_reduction_requires_a_complete_total_map_before_membership_audit)；依完整明示資料獨立重算；composition與decider transfer保持A≤mB的方向；partial map與yes-only檢查無效；finite table只證finite domain instance，不證無限domain computability；不混同Turing reduction或反向decidability transfer。"},"difficulty":{"band":"undergraduate_core","level":2,"skills":["多對一歸約"]},"variant":{"family_id":"qf-mod46-mreduction-total-map-qualification","seed":202611157013,"parameters":{"source_carrier":[0,1,2,3,4,5,6,7,8,9,10,11,12,13,14],"target_carrier":[0,1,2],"mapping":[0,1,2,0,1,2,0,1,2,0,1,2,0,1,2],"domain":"Complete_finite_many_one_reduction","operation":"mreduction-total-map-qualification","semantic_template":"qf-mod46-mreduction-total-map-qualification/{\"mapping\":[0,1,2,0,1,2,0,1,2,0,1,2,0,1,2],\"source_carrier\":[0,1,2,3,4,5,6,7,8,9,10,11,12,13,14],\"target_carrier\":[0,1,2]}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_or_symbolic_model","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"候選須主端重算；不構成人工審定、一般第一同構／strong duality／max-flow-min-cut證明、class equation、consistency、integrality、König theorem、無限domain computability、Lean或Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-15","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261015-advance-20261115-r07-many-one-reduction-0014","batch_id":"batch-20261015-advance-20261115-r07-many-one-reduction-foundations","language":"zh-Hant","source_mko_ids":["mko-many-one-reduction"],"title_zh":"多對一歸約","stem_zh":"明示decision predicates與complete total map的雙向membership equivalence。操作=mreduction-total-map-qualification；資料={\"source_carrier\":[0,1,2,3,4,5,6,7,8,9,10,11,12,13,14,15],\"target_carrier\":[0,1,2],\"mapping\":[1,2,0,1,2,0,1,2,0,1,2,0,1,2,0,1]}。請依 exact_ordered_tuple_declared_by_interface 欄序回答。","answer":{"kind":"expression","value":"([0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15], [0, 1, 2], [[0, 1, 是], [1, 2, 是], [2, 0, 是], [3, 1, 是], [4, 2, 是], [5, 0, 是], [6, 1, 是], [7, 2, 是], [8, 0, 是], [9, 1, 是], [10, 2, 是], [11, 0, 是], [12, 1, 是], [13, 2, 是], [14, 0, 是], [15, 1, 是]], 是, null, many_one_reduction_requires_a_complete_total_map_before_membership_audit)","explanation_zh":"Wave6第九層核對=([0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15], [0, 1, 2], [[0, 1, 是], [1, 2, 是], [2, 0, 是], [3, 1, 是], [4, 2, 是], [5, 0, 是], [6, 1, 是], [7, 2, 是], [8, 0, 是], [9, 1, 是], [10, 2, 是], [11, 0, 是], [12, 1, 是], [13, 2, 是], [14, 0, 是], [15, 1, 是]], 是, null, many_one_reduction_requires_a_complete_total_map_before_membership_audit)；依完整明示資料獨立重算；composition與decider transfer保持A≤mB的方向；partial map與yes-only檢查無效；finite table只證finite domain instance，不證無限domain computability；不混同Turing reduction或反向decidability transfer。"},"difficulty":{"band":"undergraduate_core","level":2,"skills":["多對一歸約"]},"variant":{"family_id":"qf-mod46-mreduction-total-map-qualification","seed":202611157014,"parameters":{"source_carrier":[0,1,2,3,4,5,6,7,8,9,10,11,12,13,14,15],"target_carrier":[0,1,2],"mapping":[1,2,0,1,2,0,1,2,0,1,2,0,1,2,0,1],"domain":"Complete_finite_many_one_reduction","operation":"mreduction-total-map-qualification","semantic_template":"qf-mod46-mreduction-total-map-qualification/{\"mapping\":[1,2,0,1,2,0,1,2,0,1,2,0,1,2,0,1],\"source_carrier\":[0,1,2,3,4,5,6,7,8,9,10,11,12,13,14,15],\"target_carrier\":[0,1,2]}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_or_symbolic_model","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"候選須主端重算；不構成人工審定、一般第一同構／strong duality／max-flow-min-cut證明、class equation、consistency、integrality、König theorem、無限domain computability、Lean或Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-15","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261015-advance-20261115-r07-many-one-reduction-0015","batch_id":"batch-20261015-advance-20261115-r07-many-one-reduction-foundations","language":"zh-Hant","source_mko_ids":["mko-many-one-reduction"],"title_zh":"多對一歸約","stem_zh":"明示decision predicates與complete total map的雙向membership equivalence。操作=mreduction-total-map-qualification；資料={\"source_carrier\":[0,1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16],\"target_carrier\":[0,1,2],\"mapping\":[2,0,1,2,0,1,2,0,1,2,0,1,2,0,1,2,0]}。請依 exact_ordered_tuple_declared_by_interface 欄序回答。","answer":{"kind":"expression","value":"([0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16], [0, 1, 2], [[0, 2, 是], [1, 0, 是], [2, 1, 是], [3, 2, 是], [4, 0, 是], [5, 1, 是], [6, 2, 是], [7, 0, 是], [8, 1, 是], [9, 2, 是], [10, 0, 是], [11, 1, 是], [12, 2, 是], [13, 0, 是], [14, 1, 是], [15, 2, 是], [16, 0, 是]], 是, null, many_one_reduction_requires_a_complete_total_map_before_membership_audit)","explanation_zh":"Wave6第九層核對=([0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16], [0, 1, 2], [[0, 2, 是], [1, 0, 是], [2, 1, 是], [3, 2, 是], [4, 0, 是], [5, 1, 是], [6, 2, 是], [7, 0, 是], [8, 1, 是], [9, 2, 是], [10, 0, 是], [11, 1, 是], [12, 2, 是], [13, 0, 是], [14, 1, 是], [15, 2, 是], [16, 0, 是]], 是, null, many_one_reduction_requires_a_complete_total_map_before_membership_audit)；依完整明示資料獨立重算；composition與decider transfer保持A≤mB的方向；partial map與yes-only檢查無效；finite table只證finite domain instance，不證無限domain computability；不混同Turing reduction或反向decidability transfer。"},"difficulty":{"band":"undergraduate_core","level":2,"skills":["多對一歸約"]},"variant":{"family_id":"qf-mod46-mreduction-total-map-qualification","seed":202611157015,"parameters":{"source_carrier":[0,1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16],"target_carrier":[0,1,2],"mapping":[2,0,1,2,0,1,2,0,1,2,0,1,2,0,1,2,0],"domain":"Complete_finite_many_one_reduction","operation":"mreduction-total-map-qualification","semantic_template":"qf-mod46-mreduction-total-map-qualification/{\"mapping\":[2,0,1,2,0,1,2,0,1,2,0,1,2,0,1,2,0],\"source_carrier\":[0,1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16],\"target_carrier\":[0,1,2]}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_or_symbolic_model","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"候選須主端重算；不構成人工審定、一般第一同構／strong duality／max-flow-min-cut證明、class equation、consistency、integrality、König theorem、無限domain computability、Lean或Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-15","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261015-advance-20261115-r07-many-one-reduction-0016","batch_id":"batch-20261015-advance-20261115-r07-many-one-reduction-foundations","language":"zh-Hant","source_mko_ids":["mko-many-one-reduction"],"title_zh":"多對一歸約","stem_zh":"明示decision predicates與complete total map的雙向membership equivalence。操作=mreduction-total-map-qualification；資料={\"source_carrier\":[0,1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17],\"target_carrier\":[0,1,2],\"mapping\":[0,1,2,0,1,2,0,1,2,0,1,2,0,1,2,0,1,null]}。請依 exact_ordered_tuple_declared_by_interface 欄序回答。","answer":{"kind":"expression","value":"([0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17], [0, 1, 2], [[0, 0, 是], [1, 1, 是], [2, 2, 是], [3, 0, 是], [4, 1, 是], [5, 2, 是], [6, 0, 是], [7, 1, 是], [8, 2, 是], [9, 0, 是], [10, 1, 是], [11, 2, 是], [12, 0, 是], [13, 1, 是], [14, 2, 是], [15, 0, 是], [16, 1, 是], [17, null, 否]], 否, [17, null, 否], many_one_reduction_requires_a_complete_total_map_before_membership_audit)","explanation_zh":"Wave6第九層核對=([0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17], [0, 1, 2], [[0, 0, 是], [1, 1, 是], [2, 2, 是], [3, 0, 是], [4, 1, 是], [5, 2, 是], [6, 0, 是], [7, 1, 是], [8, 2, 是], [9, 0, 是], [10, 1, 是], [11, 2, 是], [12, 0, 是], [13, 1, 是], [14, 2, 是], [15, 0, 是], [16, 1, 是], [17, null, 否]], 否, [17, null, 否], many_one_reduction_requires_a_complete_total_map_before_membership_audit)；依完整明示資料獨立重算；composition與decider transfer保持A≤mB的方向；partial map與yes-only檢查無效；finite table只證finite domain instance，不證無限domain computability；不混同Turing reduction或反向decidability transfer。"},"difficulty":{"band":"undergraduate_core","level":2,"skills":["多對一歸約"]},"variant":{"family_id":"qf-mod46-mreduction-total-map-qualification","seed":202611157016,"parameters":{"source_carrier":[0,1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17],"target_carrier":[0,1,2],"mapping":[0,1,2,0,1,2,0,1,2,0,1,2,0,1,2,0,1,null],"domain":"Complete_finite_many_one_reduction","operation":"mreduction-total-map-qualification","semantic_template":"qf-mod46-mreduction-total-map-qualification/{\"mapping\":[0,1,2,0,1,2,0,1,2,0,1,2,0,1,2,0,1,null],\"source_carrier\":[0,1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17],\"target_carrier\":[0,1,2]}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_or_symbolic_model","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"候選須主端重算；不構成人工審定、一般第一同構／strong duality／max-flow-min-cut證明、class equation、consistency、integrality、König theorem、無限domain computability、Lean或Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-15","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261015-advance-20261115-r07-many-one-reduction-0017","batch_id":"batch-20261015-advance-20261115-r07-many-one-reduction-foundations","language":"zh-Hant","source_mko_ids":["mko-many-one-reduction"],"title_zh":"多對一歸約","stem_zh":"明示decision predicates與complete total map的雙向membership equivalence。操作=mreduction-total-map-qualification；資料={\"source_carrier\":[0,1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18],\"target_carrier\":[0,1,2],\"mapping\":[1,2,0,1,2,0,1,2,0,1,2,0,1,2,0,1,2,0,1]}。請依 exact_ordered_tuple_declared_by_interface 欄序回答。","answer":{"kind":"expression","value":"([0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18], [0, 1, 2], [[0, 1, 是], [1, 2, 是], [2, 0, 是], [3, 1, 是], [4, 2, 是], [5, 0, 是], [6, 1, 是], [7, 2, 是], [8, 0, 是], [9, 1, 是], [10, 2, 是], [11, 0, 是], [12, 1, 是], [13, 2, 是], [14, 0, 是], [15, 1, 是], [16, 2, 是], [17, 0, 是], [18, 1, 是]], 是, null, many_one_reduction_requires_a_complete_total_map_before_membership_audit)","explanation_zh":"Wave6第九層核對=([0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18], [0, 1, 2], [[0, 1, 是], [1, 2, 是], [2, 0, 是], [3, 1, 是], [4, 2, 是], [5, 0, 是], [6, 1, 是], [7, 2, 是], [8, 0, 是], [9, 1, 是], [10, 2, 是], [11, 0, 是], [12, 1, 是], [13, 2, 是], [14, 0, 是], [15, 1, 是], [16, 2, 是], [17, 0, 是], [18, 1, 是]], 是, null, many_one_reduction_requires_a_complete_total_map_before_membership_audit)；依完整明示資料獨立重算；composition與decider transfer保持A≤mB的方向；partial map與yes-only檢查無效；finite table只證finite domain instance，不證無限domain computability；不混同Turing reduction或反向decidability transfer。"},"difficulty":{"band":"undergraduate_core","level":2,"skills":["多對一歸約"]},"variant":{"family_id":"qf-mod46-mreduction-total-map-qualification","seed":202611157017,"parameters":{"source_carrier":[0,1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18],"target_carrier":[0,1,2],"mapping":[1,2,0,1,2,0,1,2,0,1,2,0,1,2,0,1,2,0,1],"domain":"Complete_finite_many_one_reduction","operation":"mreduction-total-map-qualification","semantic_template":"qf-mod46-mreduction-total-map-qualification/{\"mapping\":[1,2,0,1,2,0,1,2,0,1,2,0,1,2,0,1,2,0,1],\"source_carrier\":[0,1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18],\"target_carrier\":[0,1,2]}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_or_symbolic_model","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"候選須主端重算；不構成人工審定、一般第一同構／strong duality／max-flow-min-cut證明、class equation、consistency、integrality、König theorem、無限domain computability、Lean或Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-15","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261015-advance-20261115-r07-many-one-reduction-0018","batch_id":"batch-20261015-advance-20261115-r07-many-one-reduction-foundations","language":"zh-Hant","source_mko_ids":["mko-many-one-reduction"],"title_zh":"多對一歸約","stem_zh":"明示decision predicates與complete total map的雙向membership equivalence。操作=mreduction-total-map-qualification；資料={\"source_carrier\":[0,1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,19],\"target_carrier\":[0,1,2],\"mapping\":[2,0,1,2,0,1,2,0,1,2,0,1,2,0,1,2,0,1,2,0]}。請依 exact_ordered_tuple_declared_by_interface 欄序回答。","answer":{"kind":"expression","value":"([0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19], [0, 1, 2], [[0, 2, 是], [1, 0, 是], [2, 1, 是], [3, 2, 是], [4, 0, 是], [5, 1, 是], [6, 2, 是], [7, 0, 是], [8, 1, 是], [9, 2, 是], [10, 0, 是], [11, 1, 是], [12, 2, 是], [13, 0, 是], [14, 1, 是], [15, 2, 是], [16, 0, 是], [17, 1, 是], [18, 2, 是], [19, 0, 是]], 是, null, many_one_reduction_requires_a_complete_total_map_before_membership_audit)","explanation_zh":"Wave6第九層核對=([0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19], [0, 1, 2], [[0, 2, 是], [1, 0, 是], [2, 1, 是], [3, 2, 是], [4, 0, 是], [5, 1, 是], [6, 2, 是], [7, 0, 是], [8, 1, 是], [9, 2, 是], [10, 0, 是], [11, 1, 是], [12, 2, 是], [13, 0, 是], [14, 1, 是], [15, 2, 是], [16, 0, 是], [17, 1, 是], [18, 2, 是], [19, 0, 是]], 是, null, many_one_reduction_requires_a_complete_total_map_before_membership_audit)；依完整明示資料獨立重算；composition與decider transfer保持A≤mB的方向；partial map與yes-only檢查無效；finite table只證finite domain instance，不證無限domain computability；不混同Turing reduction或反向decidability transfer。"},"difficulty":{"band":"undergraduate_core","level":3,"skills":["多對一歸約"]},"variant":{"family_id":"qf-mod46-mreduction-total-map-qualification","seed":202611157018,"parameters":{"source_carrier":[0,1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,19],"target_carrier":[0,1,2],"mapping":[2,0,1,2,0,1,2,0,1,2,0,1,2,0,1,2,0,1,2,0],"domain":"Complete_finite_many_one_reduction","operation":"mreduction-total-map-qualification","semantic_template":"qf-mod46-mreduction-total-map-qualification/{\"mapping\":[2,0,1,2,0,1,2,0,1,2,0,1,2,0,1,2,0,1,2,0],\"source_carrier\":[0,1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,19],\"target_carrier\":[0,1,2]}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_or_symbolic_model","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"候選須主端重算；不構成人工審定、一般第一同構／strong duality／max-flow-min-cut證明、class equation、consistency、integrality、König theorem、無限domain computability、Lean或Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-15","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261015-advance-20261115-r07-many-one-reduction-0019","batch_id":"batch-20261015-advance-20261115-r07-many-one-reduction-foundations","language":"zh-Hant","source_mko_ids":["mko-many-one-reduction"],"title_zh":"多對一歸約","stem_zh":"明示decision predicates與complete total map的雙向membership equivalence。操作=mreduction-total-map-qualification；資料={\"source_carrier\":[0,1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,19,20],\"target_carrier\":[0,1,2],\"mapping\":[0,1,2,0,1,2,0,1,2,0,1,2,0,1,2,0,1,2,0,1,2]}。請依 exact_ordered_tuple_declared_by_interface 欄序回答。","answer":{"kind":"expression","value":"([0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20], [0, 1, 2], [[0, 0, 是], [1, 1, 是], [2, 2, 是], [3, 0, 是], [4, 1, 是], [5, 2, 是], [6, 0, 是], [7, 1, 是], [8, 2, 是], [9, 0, 是], [10, 1, 是], [11, 2, 是], [12, 0, 是], [13, 1, 是], [14, 2, 是], [15, 0, 是], [16, 1, 是], [17, 2, 是], [18, 0, 是], [19, 1, 是], [20, 2, 是]], 是, null, many_one_reduction_requires_a_complete_total_map_before_membership_audit)","explanation_zh":"Wave6第九層核對=([0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20], [0, 1, 2], [[0, 0, 是], [1, 1, 是], [2, 2, 是], [3, 0, 是], [4, 1, 是], [5, 2, 是], [6, 0, 是], [7, 1, 是], [8, 2, 是], [9, 0, 是], [10, 1, 是], [11, 2, 是], [12, 0, 是], [13, 1, 是], [14, 2, 是], [15, 0, 是], [16, 1, 是], [17, 2, 是], [18, 0, 是], [19, 1, 是], [20, 2, 是]], 是, null, many_one_reduction_requires_a_complete_total_map_before_membership_audit)；依完整明示資料獨立重算；composition與decider transfer保持A≤mB的方向；partial map與yes-only檢查無效；finite table只證finite domain instance，不證無限domain computability；不混同Turing reduction或反向decidability transfer。"},"difficulty":{"band":"undergraduate_core","level":3,"skills":["多對一歸約"]},"variant":{"family_id":"qf-mod46-mreduction-total-map-qualification","seed":202611157019,"parameters":{"source_carrier":[0,1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,19,20],"target_carrier":[0,1,2],"mapping":[0,1,2,0,1,2,0,1,2,0,1,2,0,1,2,0,1,2,0,1,2],"domain":"Complete_finite_many_one_reduction","operation":"mreduction-total-map-qualification","semantic_template":"qf-mod46-mreduction-total-map-qualification/{\"mapping\":[0,1,2,0,1,2,0,1,2,0,1,2,0,1,2,0,1,2,0,1,2],\"source_carrier\":[0,1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,19,20],\"target_carrier\":[0,1,2]}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_or_symbolic_model","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"候選須主端重算；不構成人工審定、一般第一同構／strong duality／max-flow-min-cut證明、class equation、consistency、integrality、König theorem、無限domain computability、Lean或Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-15","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261015-advance-20261115-r07-many-one-reduction-0020","batch_id":"batch-20261015-advance-20261115-r07-many-one-reduction-foundations","language":"zh-Hant","source_mko_ids":["mko-many-one-reduction"],"title_zh":"多對一歸約","stem_zh":"明示decision predicates與complete total map的雙向membership equivalence。操作=mreduction-total-map-qualification；資料={\"source_carrier\":[0,1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,19,20,21],\"target_carrier\":[0,1,2],\"mapping\":[1,2,0,1,2,0,1,2,0,1,2,0,1,2,0,1,2,0,1,2,0,1]}。請依 exact_ordered_tuple_declared_by_interface 欄序回答。","answer":{"kind":"expression","value":"([0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20, 21], [0, 1, 2], [[0, 1, 是], [1, 2, 是], [2, 0, 是], [3, 1, 是], [4, 2, 是], [5, 0, 是], [6, 1, 是], [7, 2, 是], [8, 0, 是], [9, 1, 是], [10, 2, 是], [11, 0, 是], [12, 1, 是], [13, 2, 是], [14, 0, 是], [15, 1, 是], [16, 2, 是], [17, 0, 是], [18, 1, 是], [19, 2, 是], [20, 0, 是], [21, 1, 是]], 是, null, many_one_reduction_requires_a_complete_total_map_before_membership_audit)","explanation_zh":"Wave6第九層核對=([0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20, 21], [0, 1, 2], [[0, 1, 是], [1, 2, 是], [2, 0, 是], [3, 1, 是], [4, 2, 是], [5, 0, 是], [6, 1, 是], [7, 2, 是], [8, 0, 是], [9, 1, 是], [10, 2, 是], [11, 0, 是], [12, 1, 是], [13, 2, 是], [14, 0, 是], [15, 1, 是], [16, 2, 是], [17, 0, 是], [18, 1, 是], [19, 2, 是], [20, 0, 是], [21, 1, 是]], 是, null, many_one_reduction_requires_a_complete_total_map_before_membership_audit)；依完整明示資料獨立重算；composition與decider transfer保持A≤mB的方向；partial map與yes-only檢查無效；finite table只證finite domain instance，不證無限domain computability；不混同Turing reduction或反向decidability transfer。"},"difficulty":{"band":"undergraduate_core","level":3,"skills":["多對一歸約"]},"variant":{"family_id":"qf-mod46-mreduction-total-map-qualification","seed":202611157020,"parameters":{"source_carrier":[0,1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,19,20,21],"target_carrier":[0,1,2],"mapping":[1,2,0,1,2,0,1,2,0,1,2,0,1,2,0,1,2,0,1,2,0,1],"domain":"Complete_finite_many_one_reduction","operation":"mreduction-total-map-qualification","semantic_template":"qf-mod46-mreduction-total-map-qualification/{\"mapping\":[1,2,0,1,2,0,1,2,0,1,2,0,1,2,0,1,2,0,1,2,0,1],\"source_carrier\":[0,1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,19,20,21],\"target_carrier\":[0,1,2]}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_or_symbolic_model","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"候選須主端重算；不構成人工審定、一般第一同構／strong duality／max-flow-min-cut證明、class equation、consistency、integrality、König theorem、無限domain computability、Lean或Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-15","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261015-advance-20261115-r07-many-one-reduction-0021","batch_id":"batch-20261015-advance-20261115-r07-many-one-reduction-foundations","language":"zh-Hant","source_mko_ids":["mko-many-one-reduction"],"title_zh":"多對一歸約","stem_zh":"明示decision predicates與complete total map的雙向membership equivalence。操作=mreduction-total-map-qualification；資料={\"source_carrier\":[0,1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,19,20,21,22],\"target_carrier\":[0,1,2],\"mapping\":[2,0,1,2,0,1,2,0,1,2,0,1,2,0,1,2,0,1,2,0,1,2,null]}。請依 exact_ordered_tuple_declared_by_interface 欄序回答。","answer":{"kind":"expression","value":"([0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20, 21, 22], [0, 1, 2], [[0, 2, 是], [1, 0, 是], [2, 1, 是], [3, 2, 是], [4, 0, 是], [5, 1, 是], [6, 2, 是], [7, 0, 是], [8, 1, 是], [9, 2, 是], [10, 0, 是], [11, 1, 是], [12, 2, 是], [13, 0, 是], [14, 1, 是], [15, 2, 是], [16, 0, 是], [17, 1, 是], [18, 2, 是], [19, 0, 是], [20, 1, 是], [21, 2, 是], [22, null, 否]], 否, [22, null, 否], many_one_reduction_requires_a_complete_total_map_before_membership_audit)","explanation_zh":"Wave6第九層核對=([0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20, 21, 22], [0, 1, 2], [[0, 2, 是], [1, 0, 是], [2, 1, 是], [3, 2, 是], [4, 0, 是], [5, 1, 是], [6, 2, 是], [7, 0, 是], [8, 1, 是], [9, 2, 是], [10, 0, 是], [11, 1, 是], [12, 2, 是], [13, 0, 是], [14, 1, 是], [15, 2, 是], [16, 0, 是], [17, 1, 是], [18, 2, 是], [19, 0, 是], [20, 1, 是], [21, 2, 是], [22, null, 否]], 否, [22, null, 否], many_one_reduction_requires_a_complete_total_map_before_membership_audit)；依完整明示資料獨立重算；composition與decider transfer保持A≤mB的方向；partial map與yes-only檢查無效；finite table只證finite domain instance，不證無限domain computability；不混同Turing reduction或反向decidability transfer。"},"difficulty":{"band":"undergraduate_core","level":3,"skills":["多對一歸約"]},"variant":{"family_id":"qf-mod46-mreduction-total-map-qualification","seed":202611157021,"parameters":{"source_carrier":[0,1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,19,20,21,22],"target_carrier":[0,1,2],"mapping":[2,0,1,2,0,1,2,0,1,2,0,1,2,0,1,2,0,1,2,0,1,2,null],"domain":"Complete_finite_many_one_reduction","operation":"mreduction-total-map-qualification","semantic_template":"qf-mod46-mreduction-total-map-qualification/{\"mapping\":[2,0,1,2,0,1,2,0,1,2,0,1,2,0,1,2,0,1,2,0,1,2,null],\"source_carrier\":[0,1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,19,20,21,22],\"target_carrier\":[0,1,2]}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_or_symbolic_model","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"候選須主端重算；不構成人工審定、一般第一同構／strong duality／max-flow-min-cut證明、class equation、consistency、integrality、König theorem、無限domain computability、Lean或Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-15","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261015-advance-20261115-r07-many-one-reduction-0022","batch_id":"batch-20261015-advance-20261115-r07-many-one-reduction-foundations","language":"zh-Hant","source_mko_ids":["mko-many-one-reduction"],"title_zh":"多對一歸約","stem_zh":"明示decision predicates與complete total map的雙向membership equivalence。操作=mreduction-total-map-qualification；資料={\"source_carrier\":[0,1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,19,20,21,22,23],\"target_carrier\":[0,1,2],\"mapping\":[0,1,2,0,1,2,0,1,2,0,1,2,0,1,2,0,1,2,0,1,2,0,1,2]}。請依 exact_ordered_tuple_declared_by_interface 欄序回答。","answer":{"kind":"expression","value":"([0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20, 21, 22, 23], [0, 1, 2], [[0, 0, 是], [1, 1, 是], [2, 2, 是], [3, 0, 是], [4, 1, 是], [5, 2, 是], [6, 0, 是], [7, 1, 是], [8, 2, 是], [9, 0, 是], [10, 1, 是], [11, 2, 是], [12, 0, 是], [13, 1, 是], [14, 2, 是], [15, 0, 是], [16, 1, 是], [17, 2, 是], [18, 0, 是], [19, 1, 是], [20, 2, 是], [21, 0, 是], [22, 1, 是], [23, 2, 是]], 是, null, many_one_reduction_requires_a_complete_total_map_before_membership_audit)","explanation_zh":"Wave6第九層核對=([0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20, 21, 22, 23], [0, 1, 2], [[0, 0, 是], [1, 1, 是], [2, 2, 是], [3, 0, 是], [4, 1, 是], [5, 2, 是], [6, 0, 是], [7, 1, 是], [8, 2, 是], [9, 0, 是], [10, 1, 是], [11, 2, 是], [12, 0, 是], [13, 1, 是], [14, 2, 是], [15, 0, 是], [16, 1, 是], [17, 2, 是], [18, 0, 是], [19, 1, 是], [20, 2, 是], [21, 0, 是], [22, 1, 是], [23, 2, 是]], 是, null, many_one_reduction_requires_a_complete_total_map_before_membership_audit)；依完整明示資料獨立重算；composition與decider transfer保持A≤mB的方向；partial map與yes-only檢查無效；finite table只證finite domain instance，不證無限domain computability；不混同Turing reduction或反向decidability transfer。"},"difficulty":{"band":"undergraduate_core","level":3,"skills":["多對一歸約"]},"variant":{"family_id":"qf-mod46-mreduction-total-map-qualification","seed":202611157022,"parameters":{"source_carrier":[0,1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,19,20,21,22,23],"target_carrier":[0,1,2],"mapping":[0,1,2,0,1,2,0,1,2,0,1,2,0,1,2,0,1,2,0,1,2,0,1,2],"domain":"Complete_finite_many_one_reduction","operation":"mreduction-total-map-qualification","semantic_template":"qf-mod46-mreduction-total-map-qualification/{\"mapping\":[0,1,2,0,1,2,0,1,2,0,1,2,0,1,2,0,1,2,0,1,2,0,1,2],\"source_carrier\":[0,1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,19,20,21,22,23],\"target_carrier\":[0,1,2]}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_or_symbolic_model","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"候選須主端重算；不構成人工審定、一般第一同構／strong duality／max-flow-min-cut證明、class equation、consistency、integrality、König theorem、無限domain computability、Lean或Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-15","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261015-advance-20261115-r07-many-one-reduction-0023","batch_id":"batch-20261015-advance-20261115-r07-many-one-reduction-foundations","language":"zh-Hant","source_mko_ids":["mko-many-one-reduction"],"title_zh":"多對一歸約","stem_zh":"明示decision predicates與complete total map的雙向membership equivalence。操作=mreduction-total-map-qualification；資料={\"source_carrier\":[0,1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,19,20,21,22,23,24],\"target_carrier\":[0,1,2],\"mapping\":[1,2,0,1,2,0,1,2,0,1,2,0,1,2,0,1,2,0,1,2,0,1,2,0,1]}。請依 exact_ordered_tuple_declared_by_interface 欄序回答。","answer":{"kind":"expression","value":"([0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20, 21, 22, 23, 24], [0, 1, 2], [[0, 1, 是], [1, 2, 是], [2, 0, 是], [3, 1, 是], [4, 2, 是], [5, 0, 是], [6, 1, 是], [7, 2, 是], [8, 0, 是], [9, 1, 是], [10, 2, 是], [11, 0, 是], [12, 1, 是], [13, 2, 是], [14, 0, 是], [15, 1, 是], [16, 2, 是], [17, 0, 是], [18, 1, 是], [19, 2, 是], [20, 0, 是], [21, 1, 是], [22, 2, 是], [23, 0, 是], [24, 1, 是]], 是, null, many_one_reduction_requires_a_complete_total_map_before_membership_audit)","explanation_zh":"Wave6第九層核對=([0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20, 21, 22, 23, 24], [0, 1, 2], [[0, 1, 是], [1, 2, 是], [2, 0, 是], [3, 1, 是], [4, 2, 是], [5, 0, 是], [6, 1, 是], [7, 2, 是], [8, 0, 是], [9, 1, 是], [10, 2, 是], [11, 0, 是], [12, 1, 是], [13, 2, 是], [14, 0, 是], [15, 1, 是], [16, 2, 是], [17, 0, 是], [18, 1, 是], [19, 2, 是], [20, 0, 是], [21, 1, 是], [22, 2, 是], [23, 0, 是], [24, 1, 是]], 是, null, many_one_reduction_requires_a_complete_total_map_before_membership_audit)；依完整明示資料獨立重算；composition與decider transfer保持A≤mB的方向；partial map與yes-only檢查無效；finite table只證finite domain instance，不證無限domain computability；不混同Turing reduction或反向decidability transfer。"},"difficulty":{"band":"undergraduate_core","level":3,"skills":["多對一歸約"]},"variant":{"family_id":"qf-mod46-mreduction-total-map-qualification","seed":202611157023,"parameters":{"source_carrier":[0,1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,19,20,21,22,23,24],"target_carrier":[0,1,2],"mapping":[1,2,0,1,2,0,1,2,0,1,2,0,1,2,0,1,2,0,1,2,0,1,2,0,1],"domain":"Complete_finite_many_one_reduction","operation":"mreduction-total-map-qualification","semantic_template":"qf-mod46-mreduction-total-map-qualification/{\"mapping\":[1,2,0,1,2,0,1,2,0,1,2,0,1,2,0,1,2,0,1,2,0,1,2,0,1],\"source_carrier\":[0,1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,19,20,21,22,23,24],\"target_carrier\":[0,1,2]}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_or_symbolic_model","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"候選須主端重算；不構成人工審定、一般第一同構／strong duality／max-flow-min-cut證明、class equation、consistency、integrality、König theorem、無限domain computability、Lean或Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-15","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261015-advance-20261115-r07-many-one-reduction-0024","batch_id":"batch-20261015-advance-20261115-r07-many-one-reduction-foundations","language":"zh-Hant","source_mko_ids":["mko-many-one-reduction"],"title_zh":"多對一歸約","stem_zh":"明示decision predicates與complete total map的雙向membership equivalence。操作=mreduction-total-map-qualification；資料={\"source_carrier\":[0,1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,19,20,21,22,23,24,25],\"target_carrier\":[0,1,2],\"mapping\":[2,0,1,2,0,1,2,0,1,2,0,1,2,0,1,2,0,1,2,0,1,2,0,1,2,0]}。請依 exact_ordered_tuple_declared_by_interface 欄序回答。","answer":{"kind":"expression","value":"([0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20, 21, 22, 23, 24, 25], [0, 1, 2], [[0, 2, 是], [1, 0, 是], [2, 1, 是], [3, 2, 是], [4, 0, 是], [5, 1, 是], [6, 2, 是], [7, 0, 是], [8, 1, 是], [9, 2, 是], [10, 0, 是], [11, 1, 是], [12, 2, 是], [13, 0, 是], [14, 1, 是], [15, 2, 是], [16, 0, 是], [17, 1, 是], [18, 2, 是], [19, 0, 是], [20, 1, 是], [21, 2, 是], [22, 0, 是], [23, 1, 是], [24, 2, 是], [25, 0, 是]], 是, null, many_one_reduction_requires_a_complete_total_map_before_membership_audit)","explanation_zh":"Wave6第九層核對=([0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20, 21, 22, 23, 24, 25], [0, 1, 2], [[0, 2, 是], [1, 0, 是], [2, 1, 是], [3, 2, 是], [4, 0, 是], [5, 1, 是], [6, 2, 是], [7, 0, 是], [8, 1, 是], [9, 2, 是], [10, 0, 是], [11, 1, 是], [12, 2, 是], [13, 0, 是], [14, 1, 是], [15, 2, 是], [16, 0, 是], [17, 1, 是], [18, 2, 是], [19, 0, 是], [20, 1, 是], [21, 2, 是], [22, 0, 是], [23, 1, 是], [24, 2, 是], [25, 0, 是]], 是, null, many_one_reduction_requires_a_complete_total_map_before_membership_audit)；依完整明示資料獨立重算；composition與decider transfer保持A≤mB的方向；partial map與yes-only檢查無效；finite table只證finite domain instance，不證無限domain computability；不混同Turing reduction或反向decidability transfer。"},"difficulty":{"band":"undergraduate_core","level":3,"skills":["多對一歸約"]},"variant":{"family_id":"qf-mod46-mreduction-total-map-qualification","seed":202611157024,"parameters":{"source_carrier":[0,1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,19,20,21,22,23,24,25],"target_carrier":[0,1,2],"mapping":[2,0,1,2,0,1,2,0,1,2,0,1,2,0,1,2,0,1,2,0,1,2,0,1,2,0],"domain":"Complete_finite_many_one_reduction","operation":"mreduction-total-map-qualification","semantic_template":"qf-mod46-mreduction-total-map-qualification/{\"mapping\":[2,0,1,2,0,1,2,0,1,2,0,1,2,0,1,2,0,1,2,0,1,2,0,1,2,0],\"source_carrier\":[0,1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,19,20,21,22,23,24,25],\"target_carrier\":[0,1,2]}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_or_symbolic_model","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"候選須主端重算；不構成人工審定、一般第一同構／strong duality／max-flow-min-cut證明、class equation、consistency、integrality、König theorem、無限domain computability、Lean或Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-15","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261015-advance-20261115-r07-many-one-reduction-0025","batch_id":"batch-20261015-advance-20261115-r07-many-one-reduction-foundations","language":"zh-Hant","source_mko_ids":["mko-many-one-reduction"],"title_zh":"多對一歸約","stem_zh":"明示decision predicates與complete total map的雙向membership equivalence。操作=mreduction-total-map-qualification；資料={\"source_carrier\":[0,1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,19,20,21,22,23,24,25,26],\"target_carrier\":[0,1,2],\"mapping\":[0,1,2,0,1,2,0,1,2,0,1,2,0,1,2,0,1,2,0,1,2,0,1,2,0,1,2]}。請依 exact_ordered_tuple_declared_by_interface 欄序回答。","answer":{"kind":"expression","value":"([0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20, 21, 22, 23, 24, 25, 26], [0, 1, 2], [[0, 0, 是], [1, 1, 是], [2, 2, 是], [3, 0, 是], [4, 1, 是], [5, 2, 是], [6, 0, 是], [7, 1, 是], [8, 2, 是], [9, 0, 是], [10, 1, 是], [11, 2, 是], [12, 0, 是], [13, 1, 是], [14, 2, 是], [15, 0, 是], [16, 1, 是], [17, 2, 是], [18, 0, 是], [19, 1, 是], [20, 2, 是], [21, 0, 是], [22, 1, 是], [23, 2, 是], [24, 0, 是], [25, 1, 是], [26, 2, 是]], 是, null, many_one_reduction_requires_a_complete_total_map_before_membership_audit)","explanation_zh":"Wave6第九層核對=([0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20, 21, 22, 23, 24, 25, 26], [0, 1, 2], [[0, 0, 是], [1, 1, 是], [2, 2, 是], [3, 0, 是], [4, 1, 是], [5, 2, 是], [6, 0, 是], [7, 1, 是], [8, 2, 是], [9, 0, 是], [10, 1, 是], [11, 2, 是], [12, 0, 是], [13, 1, 是], [14, 2, 是], [15, 0, 是], [16, 1, 是], [17, 2, 是], [18, 0, 是], [19, 1, 是], [20, 2, 是], [21, 0, 是], [22, 1, 是], [23, 2, 是], [24, 0, 是], [25, 1, 是], [26, 2, 是]], 是, null, many_one_reduction_requires_a_complete_total_map_before_membership_audit)；依完整明示資料獨立重算；composition與decider transfer保持A≤mB的方向；partial map與yes-only檢查無效；finite table只證finite domain instance，不證無限domain computability；不混同Turing reduction或反向decidability transfer。"},"difficulty":{"band":"undergraduate_core","level":3,"skills":["多對一歸約"]},"variant":{"family_id":"qf-mod46-mreduction-total-map-qualification","seed":202611157025,"parameters":{"source_carrier":[0,1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,19,20,21,22,23,24,25,26],"target_carrier":[0,1,2],"mapping":[0,1,2,0,1,2,0,1,2,0,1,2,0,1,2,0,1,2,0,1,2,0,1,2,0,1,2],"domain":"Complete_finite_many_one_reduction","operation":"mreduction-total-map-qualification","semantic_template":"qf-mod46-mreduction-total-map-qualification/{\"mapping\":[0,1,2,0,1,2,0,1,2,0,1,2,0,1,2,0,1,2,0,1,2,0,1,2,0,1,2],\"source_carrier\":[0,1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,19,20,21,22,23,24,25,26],\"target_carrier\":[0,1,2]}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_or_symbolic_model","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"候選須主端重算；不構成人工審定、一般第一同構／strong duality／max-flow-min-cut證明、class equation、consistency、integrality、König theorem、無限domain computability、Lean或Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-15","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261015-advance-20261115-r07-many-one-reduction-0026","batch_id":"batch-20261015-advance-20261115-r07-many-one-reduction-foundations","language":"zh-Hant","source_mko_ids":["mko-many-one-reduction"],"title_zh":"多對一歸約","stem_zh":"明示decision predicates與complete total map的雙向membership equivalence。操作=mreduction-iff-audit；資料={\"source_carrier\":[0,1,2],\"target_carrier\":[0,1],\"source_yes\":[1],\"target_yes\":[1],\"mapping\":[0,1,0]}。請依 exact_ordered_tuple_declared_by_interface 欄序回答。","answer":{"kind":"expression","value":"([1], [1], [[0, 否, 0, 否, 是], [1, 是, 1, 是, 是], [2, 否, 0, 否, 是]], 是, x_in_A_iff_f_x_in_B_requires_both_yes_and_no_directions)","explanation_zh":"Wave6第九層核對=([1], [1], [[0, 否, 0, 否, 是], [1, 是, 1, 是, 是], [2, 否, 0, 否, 是]], 是, x_in_A_iff_f_x_in_B_requires_both_yes_and_no_directions)；依完整明示資料獨立重算；composition與decider transfer保持A≤mB的方向；partial map與yes-only檢查無效；finite table只證finite domain instance，不證無限domain computability；不混同Turing reduction或反向decidability transfer。"},"difficulty":{"band":"undergraduate_core","level":1,"skills":["多對一歸約"]},"variant":{"family_id":"qf-mod46-mreduction-iff-audit","seed":202611157026,"parameters":{"source_carrier":[0,1,2],"target_carrier":[0,1],"source_yes":[1],"target_yes":[1],"mapping":[0,1,0],"domain":"Complete_finite_many_one_reduction","operation":"mreduction-iff-audit","semantic_template":"qf-mod46-mreduction-iff-audit/{\"mapping\":[0,1,0],\"source_carrier\":[0,1,2],\"source_yes\":[1],\"target_carrier\":[0,1],\"target_yes\":[1]}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_or_symbolic_model","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"候選須主端重算；不構成人工審定、一般第一同構／strong duality／max-flow-min-cut證明、class equation、consistency、integrality、König theorem、無限domain computability、Lean或Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-15","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261015-advance-20261115-r07-many-one-reduction-0027","batch_id":"batch-20261015-advance-20261115-r07-many-one-reduction-foundations","language":"zh-Hant","source_mko_ids":["mko-many-one-reduction"],"title_zh":"多對一歸約","stem_zh":"明示decision predicates與complete total map的雙向membership equivalence。操作=mreduction-iff-audit；資料={\"source_carrier\":[0,1,2,3],\"target_carrier\":[0,1],\"source_yes\":[1,3],\"target_yes\":[1],\"mapping\":[0,1,0,1]}。請依 exact_ordered_tuple_declared_by_interface 欄序回答。","answer":{"kind":"expression","value":"([1, 3], [1], [[0, 否, 0, 否, 是], [1, 是, 1, 是, 是], [2, 否, 0, 否, 是], [3, 是, 1, 是, 是]], 是, x_in_A_iff_f_x_in_B_requires_both_yes_and_no_directions)","explanation_zh":"Wave6第九層核對=([1, 3], [1], [[0, 否, 0, 否, 是], [1, 是, 1, 是, 是], [2, 否, 0, 否, 是], [3, 是, 1, 是, 是]], 是, x_in_A_iff_f_x_in_B_requires_both_yes_and_no_directions)；依完整明示資料獨立重算；composition與decider transfer保持A≤mB的方向；partial map與yes-only檢查無效；finite table只證finite domain instance，不證無限domain computability；不混同Turing reduction或反向decidability transfer。"},"difficulty":{"band":"undergraduate_core","level":1,"skills":["多對一歸約"]},"variant":{"family_id":"qf-mod46-mreduction-iff-audit","seed":202611157027,"parameters":{"source_carrier":[0,1,2,3],"target_carrier":[0,1],"source_yes":[1,3],"target_yes":[1],"mapping":[0,1,0,1],"domain":"Complete_finite_many_one_reduction","operation":"mreduction-iff-audit","semantic_template":"qf-mod46-mreduction-iff-audit/{\"mapping\":[0,1,0,1],\"source_carrier\":[0,1,2,3],\"source_yes\":[1,3],\"target_carrier\":[0,1],\"target_yes\":[1]}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_or_symbolic_model","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"候選須主端重算；不構成人工審定、一般第一同構／strong duality／max-flow-min-cut證明、class equation、consistency、integrality、König theorem、無限domain computability、Lean或Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-15","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261015-advance-20261115-r07-many-one-reduction-0028","batch_id":"batch-20261015-advance-20261115-r07-many-one-reduction-foundations","language":"zh-Hant","source_mko_ids":["mko-many-one-reduction"],"title_zh":"多對一歸約","stem_zh":"明示decision predicates與complete total map的雙向membership equivalence。操作=mreduction-iff-audit；資料={\"source_carrier\":[0,1,2,3,4],\"target_carrier\":[0,1],\"source_yes\":[1,3],\"target_yes\":[1],\"mapping\":[0,1,0,1,0]}。請依 exact_ordered_tuple_declared_by_interface 欄序回答。","answer":{"kind":"expression","value":"([1, 3], [1], [[0, 否, 0, 否, 是], [1, 是, 1, 是, 是], [2, 否, 0, 否, 是], [3, 是, 1, 是, 是], [4, 否, 0, 否, 是]], 是, x_in_A_iff_f_x_in_B_requires_both_yes_and_no_directions)","explanation_zh":"Wave6第九層核對=([1, 3], [1], [[0, 否, 0, 否, 是], [1, 是, 1, 是, 是], [2, 否, 0, 否, 是], [3, 是, 1, 是, 是], [4, 否, 0, 否, 是]], 是, x_in_A_iff_f_x_in_B_requires_both_yes_and_no_directions)；依完整明示資料獨立重算；composition與decider transfer保持A≤mB的方向；partial map與yes-only檢查無效；finite table只證finite domain instance，不證無限domain computability；不混同Turing reduction或反向decidability transfer。"},"difficulty":{"band":"undergraduate_core","level":1,"skills":["多對一歸約"]},"variant":{"family_id":"qf-mod46-mreduction-iff-audit","seed":202611157028,"parameters":{"source_carrier":[0,1,2,3,4],"target_carrier":[0,1],"source_yes":[1,3],"target_yes":[1],"mapping":[0,1,0,1,0],"domain":"Complete_finite_many_one_reduction","operation":"mreduction-iff-audit","semantic_template":"qf-mod46-mreduction-iff-audit/{\"mapping\":[0,1,0,1,0],\"source_carrier\":[0,1,2,3,4],\"source_yes\":[1,3],\"target_carrier\":[0,1],\"target_yes\":[1]}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_or_symbolic_model","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"候選須主端重算；不構成人工審定、一般第一同構／strong duality／max-flow-min-cut證明、class equation、consistency、integrality、König theorem、無限domain computability、Lean或Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-15","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261015-advance-20261115-r07-many-one-reduction-0029","batch_id":"batch-20261015-advance-20261115-r07-many-one-reduction-foundations","language":"zh-Hant","source_mko_ids":["mko-many-one-reduction"],"title_zh":"多對一歸約","stem_zh":"明示decision predicates與complete total map的雙向membership equivalence。操作=mreduction-iff-audit；資料={\"source_carrier\":[0,1,2,3,4,5],\"target_carrier\":[0,1],\"source_yes\":[1,3,5],\"target_yes\":[1],\"mapping\":[0,1,0,1,0,1]}。請依 exact_ordered_tuple_declared_by_interface 欄序回答。","answer":{"kind":"expression","value":"([1, 3, 5], [1], [[0, 否, 0, 否, 是], [1, 是, 1, 是, 是], [2, 否, 0, 否, 是], [3, 是, 1, 是, 是], [4, 否, 0, 否, 是], [5, 是, 1, 是, 是]], 是, x_in_A_iff_f_x_in_B_requires_both_yes_and_no_directions)","explanation_zh":"Wave6第九層核對=([1, 3, 5], [1], [[0, 否, 0, 否, 是], [1, 是, 1, 是, 是], [2, 否, 0, 否, 是], [3, 是, 1, 是, 是], [4, 否, 0, 否, 是], [5, 是, 1, 是, 是]], 是, x_in_A_iff_f_x_in_B_requires_both_yes_and_no_directions)；依完整明示資料獨立重算；composition與decider transfer保持A≤mB的方向；partial map與yes-only檢查無效；finite table只證finite domain instance，不證無限domain computability；不混同Turing reduction或反向decidability transfer。"},"difficulty":{"band":"undergraduate_core","level":1,"skills":["多對一歸約"]},"variant":{"family_id":"qf-mod46-mreduction-iff-audit","seed":202611157029,"parameters":{"source_carrier":[0,1,2,3,4,5],"target_carrier":[0,1],"source_yes":[1,3,5],"target_yes":[1],"mapping":[0,1,0,1,0,1],"domain":"Complete_finite_many_one_reduction","operation":"mreduction-iff-audit","semantic_template":"qf-mod46-mreduction-iff-audit/{\"mapping\":[0,1,0,1,0,1],\"source_carrier\":[0,1,2,3,4,5],\"source_yes\":[1,3,5],\"target_carrier\":[0,1],\"target_yes\":[1]}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_or_symbolic_model","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"候選須主端重算；不構成人工審定、一般第一同構／strong duality／max-flow-min-cut證明、class equation、consistency、integrality、König theorem、無限domain computability、Lean或Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-15","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261015-advance-20261115-r07-many-one-reduction-0030","batch_id":"batch-20261015-advance-20261115-r07-many-one-reduction-foundations","language":"zh-Hant","source_mko_ids":["mko-many-one-reduction"],"title_zh":"多對一歸約","stem_zh":"明示decision predicates與complete total map的雙向membership equivalence。操作=mreduction-iff-audit；資料={\"source_carrier\":[0,1,2,3,4,5,6],\"target_carrier\":[0,1],\"source_yes\":[1,3,5],\"target_yes\":[1],\"mapping\":[0,1,0,1,0,1,0]}。請依 exact_ordered_tuple_declared_by_interface 欄序回答。","answer":{"kind":"expression","value":"([1, 3, 5], [1], [[0, 否, 0, 否, 是], [1, 是, 1, 是, 是], [2, 否, 0, 否, 是], [3, 是, 1, 是, 是], [4, 否, 0, 否, 是], [5, 是, 1, 是, 是], [6, 否, 0, 否, 是]], 是, x_in_A_iff_f_x_in_B_requires_both_yes_and_no_directions)","explanation_zh":"Wave6第九層核對=([1, 3, 5], [1], [[0, 否, 0, 否, 是], [1, 是, 1, 是, 是], [2, 否, 0, 否, 是], [3, 是, 1, 是, 是], [4, 否, 0, 否, 是], [5, 是, 1, 是, 是], [6, 否, 0, 否, 是]], 是, x_in_A_iff_f_x_in_B_requires_both_yes_and_no_directions)；依完整明示資料獨立重算；composition與decider transfer保持A≤mB的方向；partial map與yes-only檢查無效；finite table只證finite domain instance，不證無限domain computability；不混同Turing reduction或反向decidability transfer。"},"difficulty":{"band":"undergraduate_core","level":1,"skills":["多對一歸約"]},"variant":{"family_id":"qf-mod46-mreduction-iff-audit","seed":202611157030,"parameters":{"source_carrier":[0,1,2,3,4,5,6],"target_carrier":[0,1],"source_yes":[1,3,5],"target_yes":[1],"mapping":[0,1,0,1,0,1,0],"domain":"Complete_finite_many_one_reduction","operation":"mreduction-iff-audit","semantic_template":"qf-mod46-mreduction-iff-audit/{\"mapping\":[0,1,0,1,0,1,0],\"source_carrier\":[0,1,2,3,4,5,6],\"source_yes\":[1,3,5],\"target_carrier\":[0,1],\"target_yes\":[1]}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_or_symbolic_model","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"候選須主端重算；不構成人工審定、一般第一同構／strong duality／max-flow-min-cut證明、class equation、consistency、integrality、König theorem、無限domain computability、Lean或Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-15","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261015-advance-20261115-r07-many-one-reduction-0031","batch_id":"batch-20261015-advance-20261115-r07-many-one-reduction-foundations","language":"zh-Hant","source_mko_ids":["mko-many-one-reduction"],"title_zh":"多對一歸約","stem_zh":"明示decision predicates與complete total map的雙向membership equivalence。操作=mreduction-iff-audit；資料={\"source_carrier\":[0,1,2,3,4,5,6,7],\"target_carrier\":[0,1],\"source_yes\":[1,3,5,7],\"target_yes\":[1],\"mapping\":[0,1,0,1,0,1,0,1]}。請依 exact_ordered_tuple_declared_by_interface 欄序回答。","answer":{"kind":"expression","value":"([1, 3, 5, 7], [1], [[0, 否, 0, 否, 是], [1, 是, 1, 是, 是], [2, 否, 0, 否, 是], [3, 是, 1, 是, 是], [4, 否, 0, 否, 是], [5, 是, 1, 是, 是], [6, 否, 0, 否, 是], [7, 是, 1, 是, 是]], 是, x_in_A_iff_f_x_in_B_requires_both_yes_and_no_directions)","explanation_zh":"Wave6第九層核對=([1, 3, 5, 7], [1], [[0, 否, 0, 否, 是], [1, 是, 1, 是, 是], [2, 否, 0, 否, 是], [3, 是, 1, 是, 是], [4, 否, 0, 否, 是], [5, 是, 1, 是, 是], [6, 否, 0, 否, 是], [7, 是, 1, 是, 是]], 是, x_in_A_iff_f_x_in_B_requires_both_yes_and_no_directions)；依完整明示資料獨立重算；composition與decider transfer保持A≤mB的方向；partial map與yes-only檢查無效；finite table只證finite domain instance，不證無限domain computability；不混同Turing reduction或反向decidability transfer。"},"difficulty":{"band":"undergraduate_core","level":1,"skills":["多對一歸約"]},"variant":{"family_id":"qf-mod46-mreduction-iff-audit","seed":202611157031,"parameters":{"source_carrier":[0,1,2,3,4,5,6,7],"target_carrier":[0,1],"source_yes":[1,3,5,7],"target_yes":[1],"mapping":[0,1,0,1,0,1,0,1],"domain":"Complete_finite_many_one_reduction","operation":"mreduction-iff-audit","semantic_template":"qf-mod46-mreduction-iff-audit/{\"mapping\":[0,1,0,1,0,1,0,1],\"source_carrier\":[0,1,2,3,4,5,6,7],\"source_yes\":[1,3,5,7],\"target_carrier\":[0,1],\"target_yes\":[1]}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_or_symbolic_model","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"候選須主端重算；不構成人工審定、一般第一同構／strong duality／max-flow-min-cut證明、class equation、consistency、integrality、König theorem、無限domain computability、Lean或Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-15","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261015-advance-20261115-r07-many-one-reduction-0032","batch_id":"batch-20261015-advance-20261115-r07-many-one-reduction-foundations","language":"zh-Hant","source_mko_ids":["mko-many-one-reduction"],"title_zh":"多對一歸約","stem_zh":"明示decision predicates與complete total map的雙向membership equivalence。操作=mreduction-iff-audit；資料={\"source_carrier\":[0,1,2,3,4,5,6,7,8],\"target_carrier\":[0,1],\"source_yes\":[1,3,5,7],\"target_yes\":[1],\"mapping\":[0,1,0,1,0,1,0,1,0]}。請依 exact_ordered_tuple_declared_by_interface 欄序回答。","answer":{"kind":"expression","value":"([1, 3, 5, 7], [1], [[0, 否, 0, 否, 是], [1, 是, 1, 是, 是], [2, 否, 0, 否, 是], [3, 是, 1, 是, 是], [4, 否, 0, 否, 是], [5, 是, 1, 是, 是], [6, 否, 0, 否, 是], [7, 是, 1, 是, 是], [8, 否, 0, 否, 是]], 是, x_in_A_iff_f_x_in_B_requires_both_yes_and_no_directions)","explanation_zh":"Wave6第九層核對=([1, 3, 5, 7], [1], [[0, 否, 0, 否, 是], [1, 是, 1, 是, 是], [2, 否, 0, 否, 是], [3, 是, 1, 是, 是], [4, 否, 0, 否, 是], [5, 是, 1, 是, 是], [6, 否, 0, 否, 是], [7, 是, 1, 是, 是], [8, 否, 0, 否, 是]], 是, x_in_A_iff_f_x_in_B_requires_both_yes_and_no_directions)；依完整明示資料獨立重算；composition與decider transfer保持A≤mB的方向；partial map與yes-only檢查無效；finite table只證finite domain instance，不證無限domain computability；不混同Turing reduction或反向decidability transfer。"},"difficulty":{"band":"undergraduate_core","level":1,"skills":["多對一歸約"]},"variant":{"family_id":"qf-mod46-mreduction-iff-audit","seed":202611157032,"parameters":{"source_carrier":[0,1,2,3,4,5,6,7,8],"target_carrier":[0,1],"source_yes":[1,3,5,7],"target_yes":[1],"mapping":[0,1,0,1,0,1,0,1,0],"domain":"Complete_finite_many_one_reduction","operation":"mreduction-iff-audit","semantic_template":"qf-mod46-mreduction-iff-audit/{\"mapping\":[0,1,0,1,0,1,0,1,0],\"source_carrier\":[0,1,2,3,4,5,6,7,8],\"source_yes\":[1,3,5,7],\"target_carrier\":[0,1],\"target_yes\":[1]}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_or_symbolic_model","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"候選須主端重算；不構成人工審定、一般第一同構／strong duality／max-flow-min-cut證明、class equation、consistency、integrality、König theorem、無限domain computability、Lean或Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-15","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261015-advance-20261115-r07-many-one-reduction-0033","batch_id":"batch-20261015-advance-20261115-r07-many-one-reduction-foundations","language":"zh-Hant","source_mko_ids":["mko-many-one-reduction"],"title_zh":"多對一歸約","stem_zh":"明示decision predicates與complete total map的雙向membership equivalence。操作=mreduction-iff-audit；資料={\"source_carrier\":[0,1,2,3,4,5,6,7,8,9],\"target_carrier\":[0,1],\"source_yes\":[1,3,5,7,9],\"target_yes\":[1],\"mapping\":[0,1,0,1,0,1,0,1,0,1]}。請依 exact_ordered_tuple_declared_by_interface 欄序回答。","answer":{"kind":"expression","value":"([1, 3, 5, 7, 9], [1], [[0, 否, 0, 否, 是], [1, 是, 1, 是, 是], [2, 否, 0, 否, 是], [3, 是, 1, 是, 是], [4, 否, 0, 否, 是], [5, 是, 1, 是, 是], [6, 否, 0, 否, 是], [7, 是, 1, 是, 是], [8, 否, 0, 否, 是], [9, 是, 1, 是, 是]], 是, x_in_A_iff_f_x_in_B_requires_both_yes_and_no_directions)","explanation_zh":"Wave6第九層核對=([1, 3, 5, 7, 9], [1], [[0, 否, 0, 否, 是], [1, 是, 1, 是, 是], [2, 否, 0, 否, 是], [3, 是, 1, 是, 是], [4, 否, 0, 否, 是], [5, 是, 1, 是, 是], [6, 否, 0, 否, 是], [7, 是, 1, 是, 是], [8, 否, 0, 否, 是], [9, 是, 1, 是, 是]], 是, x_in_A_iff_f_x_in_B_requires_both_yes_and_no_directions)；依完整明示資料獨立重算；composition與decider transfer保持A≤mB的方向；partial map與yes-only檢查無效；finite table只證finite domain instance，不證無限domain computability；不混同Turing reduction或反向decidability transfer。"},"difficulty":{"band":"undergraduate_core","level":1,"skills":["多對一歸約"]},"variant":{"family_id":"qf-mod46-mreduction-iff-audit","seed":202611157033,"parameters":{"source_carrier":[0,1,2,3,4,5,6,7,8,9],"target_carrier":[0,1],"source_yes":[1,3,5,7,9],"target_yes":[1],"mapping":[0,1,0,1,0,1,0,1,0,1],"domain":"Complete_finite_many_one_reduction","operation":"mreduction-iff-audit","semantic_template":"qf-mod46-mreduction-iff-audit/{\"mapping\":[0,1,0,1,0,1,0,1,0,1],\"source_carrier\":[0,1,2,3,4,5,6,7,8,9],\"source_yes\":[1,3,5,7,9],\"target_carrier\":[0,1],\"target_yes\":[1]}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_or_symbolic_model","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"候選須主端重算；不構成人工審定、一般第一同構／strong duality／max-flow-min-cut證明、class equation、consistency、integrality、König theorem、無限domain computability、Lean或Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-15","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261015-advance-20261115-r07-many-one-reduction-0034","batch_id":"batch-20261015-advance-20261115-r07-many-one-reduction-foundations","language":"zh-Hant","source_mko_ids":["mko-many-one-reduction"],"title_zh":"多對一歸約","stem_zh":"明示decision predicates與complete total map的雙向membership equivalence。操作=mreduction-iff-audit；資料={\"source_carrier\":[0,1,2,3,4,5,6,7,8,9,10],\"target_carrier\":[0,1],\"source_yes\":[1,3,5,7,9],\"target_yes\":[1],\"mapping\":[0,1,0,1,0,1,0,1,0,1,0]}。請依 exact_ordered_tuple_declared_by_interface 欄序回答。","answer":{"kind":"expression","value":"([1, 3, 5, 7, 9], [1], [[0, 否, 0, 否, 是], [1, 是, 1, 是, 是], [2, 否, 0, 否, 是], [3, 是, 1, 是, 是], [4, 否, 0, 否, 是], [5, 是, 1, 是, 是], [6, 否, 0, 否, 是], [7, 是, 1, 是, 是], [8, 否, 0, 否, 是], [9, 是, 1, 是, 是], [10, 否, 0, 否, 是]], 是, x_in_A_iff_f_x_in_B_requires_both_yes_and_no_directions)","explanation_zh":"Wave6第九層核對=([1, 3, 5, 7, 9], [1], [[0, 否, 0, 否, 是], [1, 是, 1, 是, 是], [2, 否, 0, 否, 是], [3, 是, 1, 是, 是], [4, 否, 0, 否, 是], [5, 是, 1, 是, 是], [6, 否, 0, 否, 是], [7, 是, 1, 是, 是], [8, 否, 0, 否, 是], [9, 是, 1, 是, 是], [10, 否, 0, 否, 是]], 是, x_in_A_iff_f_x_in_B_requires_both_yes_and_no_directions)；依完整明示資料獨立重算；composition與decider transfer保持A≤mB的方向；partial map與yes-only檢查無效；finite table只證finite domain instance，不證無限domain computability；不混同Turing reduction或反向decidability transfer。"},"difficulty":{"band":"undergraduate_core","level":2,"skills":["多對一歸約"]},"variant":{"family_id":"qf-mod46-mreduction-iff-audit","seed":202611157034,"parameters":{"source_carrier":[0,1,2,3,4,5,6,7,8,9,10],"target_carrier":[0,1],"source_yes":[1,3,5,7,9],"target_yes":[1],"mapping":[0,1,0,1,0,1,0,1,0,1,0],"domain":"Complete_finite_many_one_reduction","operation":"mreduction-iff-audit","semantic_template":"qf-mod46-mreduction-iff-audit/{\"mapping\":[0,1,0,1,0,1,0,1,0,1,0],\"source_carrier\":[0,1,2,3,4,5,6,7,8,9,10],\"source_yes\":[1,3,5,7,9],\"target_carrier\":[0,1],\"target_yes\":[1]}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_or_symbolic_model","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"候選須主端重算；不構成人工審定、一般第一同構／strong duality／max-flow-min-cut證明、class equation、consistency、integrality、König theorem、無限domain computability、Lean或Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-15","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261015-advance-20261115-r07-many-one-reduction-0035","batch_id":"batch-20261015-advance-20261115-r07-many-one-reduction-foundations","language":"zh-Hant","source_mko_ids":["mko-many-one-reduction"],"title_zh":"多對一歸約","stem_zh":"明示decision predicates與complete total map的雙向membership equivalence。操作=mreduction-iff-audit；資料={\"source_carrier\":[0,1,2,3,4,5,6,7,8,9,10,11],\"target_carrier\":[0,1],\"source_yes\":[1,3,5,7,9,11],\"target_yes\":[1],\"mapping\":[0,1,0,1,0,1,0,1,0,1,0,1]}。請依 exact_ordered_tuple_declared_by_interface 欄序回答。","answer":{"kind":"expression","value":"([1, 3, 5, 7, 9, 11], [1], [[0, 否, 0, 否, 是], [1, 是, 1, 是, 是], [2, 否, 0, 否, 是], [3, 是, 1, 是, 是], [4, 否, 0, 否, 是], [5, 是, 1, 是, 是], [6, 否, 0, 否, 是], [7, 是, 1, 是, 是], [8, 否, 0, 否, 是], [9, 是, 1, 是, 是], [10, 否, 0, 否, 是], [11, 是, 1, 是, 是]], 是, x_in_A_iff_f_x_in_B_requires_both_yes_and_no_directions)","explanation_zh":"Wave6第九層核對=([1, 3, 5, 7, 9, 11], [1], [[0, 否, 0, 否, 是], [1, 是, 1, 是, 是], [2, 否, 0, 否, 是], [3, 是, 1, 是, 是], [4, 否, 0, 否, 是], [5, 是, 1, 是, 是], [6, 否, 0, 否, 是], [7, 是, 1, 是, 是], [8, 否, 0, 否, 是], [9, 是, 1, 是, 是], [10, 否, 0, 否, 是], [11, 是, 1, 是, 是]], 是, x_in_A_iff_f_x_in_B_requires_both_yes_and_no_directions)；依完整明示資料獨立重算；composition與decider transfer保持A≤mB的方向；partial map與yes-only檢查無效；finite table只證finite domain instance，不證無限domain computability；不混同Turing reduction或反向decidability transfer。"},"difficulty":{"band":"undergraduate_core","level":2,"skills":["多對一歸約"]},"variant":{"family_id":"qf-mod46-mreduction-iff-audit","seed":202611157035,"parameters":{"source_carrier":[0,1,2,3,4,5,6,7,8,9,10,11],"target_carrier":[0,1],"source_yes":[1,3,5,7,9,11],"target_yes":[1],"mapping":[0,1,0,1,0,1,0,1,0,1,0,1],"domain":"Complete_finite_many_one_reduction","operation":"mreduction-iff-audit","semantic_template":"qf-mod46-mreduction-iff-audit/{\"mapping\":[0,1,0,1,0,1,0,1,0,1,0,1],\"source_carrier\":[0,1,2,3,4,5,6,7,8,9,10,11],\"source_yes\":[1,11,3,5,7,9],\"target_carrier\":[0,1],\"target_yes\":[1]}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_or_symbolic_model","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"候選須主端重算；不構成人工審定、一般第一同構／strong duality／max-flow-min-cut證明、class equation、consistency、integrality、König theorem、無限domain computability、Lean或Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-15","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261015-advance-20261115-r07-many-one-reduction-0036","batch_id":"batch-20261015-advance-20261115-r07-many-one-reduction-foundations","language":"zh-Hant","source_mko_ids":["mko-many-one-reduction"],"title_zh":"多對一歸約","stem_zh":"明示decision predicates與complete total map的雙向membership equivalence。操作=mreduction-iff-audit；資料={\"source_carrier\":[0,1,2,3,4,5,6,7,8,9,10,11,12],\"target_carrier\":[0,1],\"source_yes\":[1,3,5,7,9,11],\"target_yes\":[1],\"mapping\":[0,1,0,1,0,1,0,1,0,1,0,1,0]}。請依 exact_ordered_tuple_declared_by_interface 欄序回答。","answer":{"kind":"expression","value":"([1, 3, 5, 7, 9, 11], [1], [[0, 否, 0, 否, 是], [1, 是, 1, 是, 是], [2, 否, 0, 否, 是], [3, 是, 1, 是, 是], [4, 否, 0, 否, 是], [5, 是, 1, 是, 是], [6, 否, 0, 否, 是], [7, 是, 1, 是, 是], [8, 否, 0, 否, 是], [9, 是, 1, 是, 是], [10, 否, 0, 否, 是], [11, 是, 1, 是, 是], [12, 否, 0, 否, 是]], 是, x_in_A_iff_f_x_in_B_requires_both_yes_and_no_directions)","explanation_zh":"Wave6第九層核對=([1, 3, 5, 7, 9, 11], [1], [[0, 否, 0, 否, 是], [1, 是, 1, 是, 是], [2, 否, 0, 否, 是], [3, 是, 1, 是, 是], [4, 否, 0, 否, 是], [5, 是, 1, 是, 是], [6, 否, 0, 否, 是], [7, 是, 1, 是, 是], [8, 否, 0, 否, 是], [9, 是, 1, 是, 是], [10, 否, 0, 否, 是], [11, 是, 1, 是, 是], [12, 否, 0, 否, 是]], 是, x_in_A_iff_f_x_in_B_requires_both_yes_and_no_directions)；依完整明示資料獨立重算；composition與decider transfer保持A≤mB的方向；partial map與yes-only檢查無效；finite table只證finite domain instance，不證無限domain computability；不混同Turing reduction或反向decidability transfer。"},"difficulty":{"band":"undergraduate_core","level":2,"skills":["多對一歸約"]},"variant":{"family_id":"qf-mod46-mreduction-iff-audit","seed":202611157036,"parameters":{"source_carrier":[0,1,2,3,4,5,6,7,8,9,10,11,12],"target_carrier":[0,1],"source_yes":[1,3,5,7,9,11],"target_yes":[1],"mapping":[0,1,0,1,0,1,0,1,0,1,0,1,0],"domain":"Complete_finite_many_one_reduction","operation":"mreduction-iff-audit","semantic_template":"qf-mod46-mreduction-iff-audit/{\"mapping\":[0,1,0,1,0,1,0,1,0,1,0,1,0],\"source_carrier\":[0,1,2,3,4,5,6,7,8,9,10,11,12],\"source_yes\":[1,11,3,5,7,9],\"target_carrier\":[0,1],\"target_yes\":[1]}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_or_symbolic_model","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"候選須主端重算；不構成人工審定、一般第一同構／strong duality／max-flow-min-cut證明、class equation、consistency、integrality、König theorem、無限domain computability、Lean或Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-15","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261015-advance-20261115-r07-many-one-reduction-0037","batch_id":"batch-20261015-advance-20261115-r07-many-one-reduction-foundations","language":"zh-Hant","source_mko_ids":["mko-many-one-reduction"],"title_zh":"多對一歸約","stem_zh":"明示decision predicates與complete total map的雙向membership equivalence。操作=mreduction-iff-audit；資料={\"source_carrier\":[0,1,2,3,4,5,6,7,8,9,10,11,12,13],\"target_carrier\":[0,1],\"source_yes\":[1,3,5,7,9,11,13],\"target_yes\":[1],\"mapping\":[0,1,0,1,0,1,0,1,0,1,0,1,0,1]}。請依 exact_ordered_tuple_declared_by_interface 欄序回答。","answer":{"kind":"expression","value":"([1, 3, 5, 7, 9, 11, 13], [1], [[0, 否, 0, 否, 是], [1, 是, 1, 是, 是], [2, 否, 0, 否, 是], [3, 是, 1, 是, 是], [4, 否, 0, 否, 是], [5, 是, 1, 是, 是], [6, 否, 0, 否, 是], [7, 是, 1, 是, 是], [8, 否, 0, 否, 是], [9, 是, 1, 是, 是], [10, 否, 0, 否, 是], [11, 是, 1, 是, 是], [12, 否, 0, 否, 是], [13, 是, 1, 是, 是]], 是, x_in_A_iff_f_x_in_B_requires_both_yes_and_no_directions)","explanation_zh":"Wave6第九層核對=([1, 3, 5, 7, 9, 11, 13], [1], [[0, 否, 0, 否, 是], [1, 是, 1, 是, 是], [2, 否, 0, 否, 是], [3, 是, 1, 是, 是], [4, 否, 0, 否, 是], [5, 是, 1, 是, 是], [6, 否, 0, 否, 是], [7, 是, 1, 是, 是], [8, 否, 0, 否, 是], [9, 是, 1, 是, 是], [10, 否, 0, 否, 是], [11, 是, 1, 是, 是], [12, 否, 0, 否, 是], [13, 是, 1, 是, 是]], 是, x_in_A_iff_f_x_in_B_requires_both_yes_and_no_directions)；依完整明示資料獨立重算；composition與decider transfer保持A≤mB的方向；partial map與yes-only檢查無效；finite table只證finite domain instance，不證無限domain computability；不混同Turing reduction或反向decidability transfer。"},"difficulty":{"band":"undergraduate_core","level":2,"skills":["多對一歸約"]},"variant":{"family_id":"qf-mod46-mreduction-iff-audit","seed":202611157037,"parameters":{"source_carrier":[0,1,2,3,4,5,6,7,8,9,10,11,12,13],"target_carrier":[0,1],"source_yes":[1,3,5,7,9,11,13],"target_yes":[1],"mapping":[0,1,0,1,0,1,0,1,0,1,0,1,0,1],"domain":"Complete_finite_many_one_reduction","operation":"mreduction-iff-audit","semantic_template":"qf-mod46-mreduction-iff-audit/{\"mapping\":[0,1,0,1,0,1,0,1,0,1,0,1,0,1],\"source_carrier\":[0,1,2,3,4,5,6,7,8,9,10,11,12,13],\"source_yes\":[1,11,13,3,5,7,9],\"target_carrier\":[0,1],\"target_yes\":[1]}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_or_symbolic_model","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"候選須主端重算；不構成人工審定、一般第一同構／strong duality／max-flow-min-cut證明、class equation、consistency、integrality、König theorem、無限domain computability、Lean或Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-15","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261015-advance-20261115-r07-many-one-reduction-0038","batch_id":"batch-20261015-advance-20261115-r07-many-one-reduction-foundations","language":"zh-Hant","source_mko_ids":["mko-many-one-reduction"],"title_zh":"多對一歸約","stem_zh":"明示decision predicates與complete total map的雙向membership equivalence。操作=mreduction-iff-audit；資料={\"source_carrier\":[0,1,2,3,4,5,6,7,8,9,10,11,12,13,14],\"target_carrier\":[0,1],\"source_yes\":[1,3,5,7,9,11,13],\"target_yes\":[1],\"mapping\":[0,1,0,1,0,1,0,1,0,1,0,1,0,1,0]}。請依 exact_ordered_tuple_declared_by_interface 欄序回答。","answer":{"kind":"expression","value":"([1, 3, 5, 7, 9, 11, 13], [1], [[0, 否, 0, 否, 是], [1, 是, 1, 是, 是], [2, 否, 0, 否, 是], [3, 是, 1, 是, 是], [4, 否, 0, 否, 是], [5, 是, 1, 是, 是], [6, 否, 0, 否, 是], [7, 是, 1, 是, 是], [8, 否, 0, 否, 是], [9, 是, 1, 是, 是], [10, 否, 0, 否, 是], [11, 是, 1, 是, 是], [12, 否, 0, 否, 是], [13, 是, 1, 是, 是], [14, 否, 0, 否, 是]], 是, x_in_A_iff_f_x_in_B_requires_both_yes_and_no_directions)","explanation_zh":"Wave6第九層核對=([1, 3, 5, 7, 9, 11, 13], [1], [[0, 否, 0, 否, 是], [1, 是, 1, 是, 是], [2, 否, 0, 否, 是], [3, 是, 1, 是, 是], [4, 否, 0, 否, 是], [5, 是, 1, 是, 是], [6, 否, 0, 否, 是], [7, 是, 1, 是, 是], [8, 否, 0, 否, 是], [9, 是, 1, 是, 是], [10, 否, 0, 否, 是], [11, 是, 1, 是, 是], [12, 否, 0, 否, 是], [13, 是, 1, 是, 是], [14, 否, 0, 否, 是]], 是, x_in_A_iff_f_x_in_B_requires_both_yes_and_no_directions)；依完整明示資料獨立重算；composition與decider transfer保持A≤mB的方向；partial map與yes-only檢查無效；finite table只證finite domain instance，不證無限domain computability；不混同Turing reduction或反向decidability transfer。"},"difficulty":{"band":"undergraduate_core","level":2,"skills":["多對一歸約"]},"variant":{"family_id":"qf-mod46-mreduction-iff-audit","seed":202611157038,"parameters":{"source_carrier":[0,1,2,3,4,5,6,7,8,9,10,11,12,13,14],"target_carrier":[0,1],"source_yes":[1,3,5,7,9,11,13],"target_yes":[1],"mapping":[0,1,0,1,0,1,0,1,0,1,0,1,0,1,0],"domain":"Complete_finite_many_one_reduction","operation":"mreduction-iff-audit","semantic_template":"qf-mod46-mreduction-iff-audit/{\"mapping\":[0,1,0,1,0,1,0,1,0,1,0,1,0,1,0],\"source_carrier\":[0,1,2,3,4,5,6,7,8,9,10,11,12,13,14],\"source_yes\":[1,11,13,3,5,7,9],\"target_carrier\":[0,1],\"target_yes\":[1]}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_or_symbolic_model","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"候選須主端重算；不構成人工審定、一般第一同構／strong duality／max-flow-min-cut證明、class equation、consistency、integrality、König theorem、無限domain computability、Lean或Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-15","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261015-advance-20261115-r07-many-one-reduction-0039","batch_id":"batch-20261015-advance-20261115-r07-many-one-reduction-foundations","language":"zh-Hant","source_mko_ids":["mko-many-one-reduction"],"title_zh":"多對一歸約","stem_zh":"明示decision predicates與complete total map的雙向membership equivalence。操作=mreduction-iff-audit；資料={\"source_carrier\":[0,1,2,3,4,5,6,7,8,9,10,11,12,13,14,15],\"target_carrier\":[0,1],\"source_yes\":[1,3,5,7,9,11,13,15],\"target_yes\":[1],\"mapping\":[0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1]}。請依 exact_ordered_tuple_declared_by_interface 欄序回答。","answer":{"kind":"expression","value":"([1, 3, 5, 7, 9, 11, 13, 15], [1], [[0, 否, 0, 否, 是], [1, 是, 1, 是, 是], [2, 否, 0, 否, 是], [3, 是, 1, 是, 是], [4, 否, 0, 否, 是], [5, 是, 1, 是, 是], [6, 否, 0, 否, 是], [7, 是, 1, 是, 是], [8, 否, 0, 否, 是], [9, 是, 1, 是, 是], [10, 否, 0, 否, 是], [11, 是, 1, 是, 是], [12, 否, 0, 否, 是], [13, 是, 1, 是, 是], [14, 否, 0, 否, 是], [15, 是, 1, 是, 是]], 是, x_in_A_iff_f_x_in_B_requires_both_yes_and_no_directions)","explanation_zh":"Wave6第九層核對=([1, 3, 5, 7, 9, 11, 13, 15], [1], [[0, 否, 0, 否, 是], [1, 是, 1, 是, 是], [2, 否, 0, 否, 是], [3, 是, 1, 是, 是], [4, 否, 0, 否, 是], [5, 是, 1, 是, 是], [6, 否, 0, 否, 是], [7, 是, 1, 是, 是], [8, 否, 0, 否, 是], [9, 是, 1, 是, 是], [10, 否, 0, 否, 是], [11, 是, 1, 是, 是], [12, 否, 0, 否, 是], [13, 是, 1, 是, 是], [14, 否, 0, 否, 是], [15, 是, 1, 是, 是]], 是, x_in_A_iff_f_x_in_B_requires_both_yes_and_no_directions)；依完整明示資料獨立重算；composition與decider transfer保持A≤mB的方向；partial map與yes-only檢查無效；finite table只證finite domain instance，不證無限domain computability；不混同Turing reduction或反向decidability transfer。"},"difficulty":{"band":"undergraduate_core","level":2,"skills":["多對一歸約"]},"variant":{"family_id":"qf-mod46-mreduction-iff-audit","seed":202611157039,"parameters":{"source_carrier":[0,1,2,3,4,5,6,7,8,9,10,11,12,13,14,15],"target_carrier":[0,1],"source_yes":[1,3,5,7,9,11,13,15],"target_yes":[1],"mapping":[0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1],"domain":"Complete_finite_many_one_reduction","operation":"mreduction-iff-audit","semantic_template":"qf-mod46-mreduction-iff-audit/{\"mapping\":[0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1],\"source_carrier\":[0,1,2,3,4,5,6,7,8,9,10,11,12,13,14,15],\"source_yes\":[1,11,13,15,3,5,7,9],\"target_carrier\":[0,1],\"target_yes\":[1]}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_or_symbolic_model","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"候選須主端重算；不構成人工審定、一般第一同構／strong duality／max-flow-min-cut證明、class equation、consistency、integrality、König theorem、無限domain computability、Lean或Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-15","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261015-advance-20261115-r07-many-one-reduction-0040","batch_id":"batch-20261015-advance-20261115-r07-many-one-reduction-foundations","language":"zh-Hant","source_mko_ids":["mko-many-one-reduction"],"title_zh":"多對一歸約","stem_zh":"明示decision predicates與complete total map的雙向membership equivalence。操作=mreduction-iff-audit；資料={\"source_carrier\":[0,1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16],\"target_carrier\":[0,1],\"source_yes\":[1,3,5,7,9,11,13,15],\"target_yes\":[1],\"mapping\":[0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0]}。請依 exact_ordered_tuple_declared_by_interface 欄序回答。","answer":{"kind":"expression","value":"([1, 3, 5, 7, 9, 11, 13, 15], [1], [[0, 否, 0, 否, 是], [1, 是, 1, 是, 是], [2, 否, 0, 否, 是], [3, 是, 1, 是, 是], [4, 否, 0, 否, 是], [5, 是, 1, 是, 是], [6, 否, 0, 否, 是], [7, 是, 1, 是, 是], [8, 否, 0, 否, 是], [9, 是, 1, 是, 是], [10, 否, 0, 否, 是], [11, 是, 1, 是, 是], [12, 否, 0, 否, 是], [13, 是, 1, 是, 是], [14, 否, 0, 否, 是], [15, 是, 1, 是, 是], [16, 否, 0, 否, 是]], 是, x_in_A_iff_f_x_in_B_requires_both_yes_and_no_directions)","explanation_zh":"Wave6第九層核對=([1, 3, 5, 7, 9, 11, 13, 15], [1], [[0, 否, 0, 否, 是], [1, 是, 1, 是, 是], [2, 否, 0, 否, 是], [3, 是, 1, 是, 是], [4, 否, 0, 否, 是], [5, 是, 1, 是, 是], [6, 否, 0, 否, 是], [7, 是, 1, 是, 是], [8, 否, 0, 否, 是], [9, 是, 1, 是, 是], [10, 否, 0, 否, 是], [11, 是, 1, 是, 是], [12, 否, 0, 否, 是], [13, 是, 1, 是, 是], [14, 否, 0, 否, 是], [15, 是, 1, 是, 是], [16, 否, 0, 否, 是]], 是, x_in_A_iff_f_x_in_B_requires_both_yes_and_no_directions)；依完整明示資料獨立重算；composition與decider transfer保持A≤mB的方向；partial map與yes-only檢查無效；finite table只證finite domain instance，不證無限domain computability；不混同Turing reduction或反向decidability transfer。"},"difficulty":{"band":"undergraduate_core","level":2,"skills":["多對一歸約"]},"variant":{"family_id":"qf-mod46-mreduction-iff-audit","seed":202611157040,"parameters":{"source_carrier":[0,1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16],"target_carrier":[0,1],"source_yes":[1,3,5,7,9,11,13,15],"target_yes":[1],"mapping":[0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0],"domain":"Complete_finite_many_one_reduction","operation":"mreduction-iff-audit","semantic_template":"qf-mod46-mreduction-iff-audit/{\"mapping\":[0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0],\"source_carrier\":[0,1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16],\"source_yes\":[1,11,13,15,3,5,7,9],\"target_carrier\":[0,1],\"target_yes\":[1]}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_or_symbolic_model","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"候選須主端重算；不構成人工審定、一般第一同構／strong duality／max-flow-min-cut證明、class equation、consistency、integrality、König theorem、無限domain computability、Lean或Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-15","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261015-advance-20261115-r07-many-one-reduction-0041","batch_id":"batch-20261015-advance-20261115-r07-many-one-reduction-foundations","language":"zh-Hant","source_mko_ids":["mko-many-one-reduction"],"title_zh":"多對一歸約","stem_zh":"明示decision predicates與complete total map的雙向membership equivalence。操作=mreduction-iff-audit；資料={\"source_carrier\":[0,1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17],\"target_carrier\":[0,1],\"source_yes\":[1,3,5,7,9,11,13,15,17],\"target_yes\":[1],\"mapping\":[0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1]}。請依 exact_ordered_tuple_declared_by_interface 欄序回答。","answer":{"kind":"expression","value":"([1, 3, 5, 7, 9, 11, 13, 15, 17], [1], [[0, 否, 0, 否, 是], [1, 是, 1, 是, 是], [2, 否, 0, 否, 是], [3, 是, 1, 是, 是], [4, 否, 0, 否, 是], [5, 是, 1, 是, 是], [6, 否, 0, 否, 是], [7, 是, 1, 是, 是], [8, 否, 0, 否, 是], [9, 是, 1, 是, 是], [10, 否, 0, 否, 是], [11, 是, 1, 是, 是], [12, 否, 0, 否, 是], [13, 是, 1, 是, 是], [14, 否, 0, 否, 是], [15, 是, 1, 是, 是], [16, 否, 0, 否, 是], [17, 是, 1, 是, 是]], 是, x_in_A_iff_f_x_in_B_requires_both_yes_and_no_directions)","explanation_zh":"Wave6第九層核對=([1, 3, 5, 7, 9, 11, 13, 15, 17], [1], [[0, 否, 0, 否, 是], [1, 是, 1, 是, 是], [2, 否, 0, 否, 是], [3, 是, 1, 是, 是], [4, 否, 0, 否, 是], [5, 是, 1, 是, 是], [6, 否, 0, 否, 是], [7, 是, 1, 是, 是], [8, 否, 0, 否, 是], [9, 是, 1, 是, 是], [10, 否, 0, 否, 是], [11, 是, 1, 是, 是], [12, 否, 0, 否, 是], [13, 是, 1, 是, 是], [14, 否, 0, 否, 是], [15, 是, 1, 是, 是], [16, 否, 0, 否, 是], [17, 是, 1, 是, 是]], 是, x_in_A_iff_f_x_in_B_requires_both_yes_and_no_directions)；依完整明示資料獨立重算；composition與decider transfer保持A≤mB的方向；partial map與yes-only檢查無效；finite table只證finite domain instance，不證無限domain computability；不混同Turing reduction或反向decidability transfer。"},"difficulty":{"band":"undergraduate_core","level":2,"skills":["多對一歸約"]},"variant":{"family_id":"qf-mod46-mreduction-iff-audit","seed":202611157041,"parameters":{"source_carrier":[0,1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17],"target_carrier":[0,1],"source_yes":[1,3,5,7,9,11,13,15,17],"target_yes":[1],"mapping":[0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1],"domain":"Complete_finite_many_one_reduction","operation":"mreduction-iff-audit","semantic_template":"qf-mod46-mreduction-iff-audit/{\"mapping\":[0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1],\"source_carrier\":[0,1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17],\"source_yes\":[1,11,13,15,17,3,5,7,9],\"target_carrier\":[0,1],\"target_yes\":[1]}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_or_symbolic_model","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"候選須主端重算；不構成人工審定、一般第一同構／strong duality／max-flow-min-cut證明、class equation、consistency、integrality、König theorem、無限domain computability、Lean或Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-15","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261015-advance-20261115-r07-many-one-reduction-0042","batch_id":"batch-20261015-advance-20261115-r07-many-one-reduction-foundations","language":"zh-Hant","source_mko_ids":["mko-many-one-reduction"],"title_zh":"多對一歸約","stem_zh":"明示decision predicates與complete total map的雙向membership equivalence。操作=mreduction-iff-audit；資料={\"source_carrier\":[0,1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18],\"target_carrier\":[0,1],\"source_yes\":[1,3,5,7,9,11,13,15,17],\"target_yes\":[1],\"mapping\":[0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0]}。請依 exact_ordered_tuple_declared_by_interface 欄序回答。","answer":{"kind":"expression","value":"([1, 3, 5, 7, 9, 11, 13, 15, 17], [1], [[0, 否, 0, 否, 是], [1, 是, 1, 是, 是], [2, 否, 0, 否, 是], [3, 是, 1, 是, 是], [4, 否, 0, 否, 是], [5, 是, 1, 是, 是], [6, 否, 0, 否, 是], [7, 是, 1, 是, 是], [8, 否, 0, 否, 是], [9, 是, 1, 是, 是], [10, 否, 0, 否, 是], [11, 是, 1, 是, 是], [12, 否, 0, 否, 是], [13, 是, 1, 是, 是], [14, 否, 0, 否, 是], [15, 是, 1, 是, 是], [16, 否, 0, 否, 是], [17, 是, 1, 是, 是], [18, 否, 0, 否, 是]], 是, x_in_A_iff_f_x_in_B_requires_both_yes_and_no_directions)","explanation_zh":"Wave6第九層核對=([1, 3, 5, 7, 9, 11, 13, 15, 17], [1], [[0, 否, 0, 否, 是], [1, 是, 1, 是, 是], [2, 否, 0, 否, 是], [3, 是, 1, 是, 是], [4, 否, 0, 否, 是], [5, 是, 1, 是, 是], [6, 否, 0, 否, 是], [7, 是, 1, 是, 是], [8, 否, 0, 否, 是], [9, 是, 1, 是, 是], [10, 否, 0, 否, 是], [11, 是, 1, 是, 是], [12, 否, 0, 否, 是], [13, 是, 1, 是, 是], [14, 否, 0, 否, 是], [15, 是, 1, 是, 是], [16, 否, 0, 否, 是], [17, 是, 1, 是, 是], [18, 否, 0, 否, 是]], 是, x_in_A_iff_f_x_in_B_requires_both_yes_and_no_directions)；依完整明示資料獨立重算；composition與decider transfer保持A≤mB的方向；partial map與yes-only檢查無效；finite table只證finite domain instance，不證無限domain computability；不混同Turing reduction或反向decidability transfer。"},"difficulty":{"band":"undergraduate_core","level":2,"skills":["多對一歸約"]},"variant":{"family_id":"qf-mod46-mreduction-iff-audit","seed":202611157042,"parameters":{"source_carrier":[0,1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18],"target_carrier":[0,1],"source_yes":[1,3,5,7,9,11,13,15,17],"target_yes":[1],"mapping":[0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0],"domain":"Complete_finite_many_one_reduction","operation":"mreduction-iff-audit","semantic_template":"qf-mod46-mreduction-iff-audit/{\"mapping\":[0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0],\"source_carrier\":[0,1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18],\"source_yes\":[1,11,13,15,17,3,5,7,9],\"target_carrier\":[0,1],\"target_yes\":[1]}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_or_symbolic_model","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"候選須主端重算；不構成人工審定、一般第一同構／strong duality／max-flow-min-cut證明、class equation、consistency、integrality、König theorem、無限domain computability、Lean或Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-15","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261015-advance-20261115-r07-many-one-reduction-0043","batch_id":"batch-20261015-advance-20261115-r07-many-one-reduction-foundations","language":"zh-Hant","source_mko_ids":["mko-many-one-reduction"],"title_zh":"多對一歸約","stem_zh":"明示decision predicates與complete total map的雙向membership equivalence。操作=mreduction-iff-audit；資料={\"source_carrier\":[0,1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,19],\"target_carrier\":[0,1],\"source_yes\":[1,3,5,7,9,11,13,15,17,19],\"target_yes\":[1],\"mapping\":[0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1]}。請依 exact_ordered_tuple_declared_by_interface 欄序回答。","answer":{"kind":"expression","value":"([1, 3, 5, 7, 9, 11, 13, 15, 17, 19], [1], [[0, 否, 0, 否, 是], [1, 是, 1, 是, 是], [2, 否, 0, 否, 是], [3, 是, 1, 是, 是], [4, 否, 0, 否, 是], [5, 是, 1, 是, 是], [6, 否, 0, 否, 是], [7, 是, 1, 是, 是], [8, 否, 0, 否, 是], [9, 是, 1, 是, 是], [10, 否, 0, 否, 是], [11, 是, 1, 是, 是], [12, 否, 0, 否, 是], [13, 是, 1, 是, 是], [14, 否, 0, 否, 是], [15, 是, 1, 是, 是], [16, 否, 0, 否, 是], [17, 是, 1, 是, 是], [18, 否, 0, 否, 是], [19, 是, 1, 是, 是]], 是, x_in_A_iff_f_x_in_B_requires_both_yes_and_no_directions)","explanation_zh":"Wave6第九層核對=([1, 3, 5, 7, 9, 11, 13, 15, 17, 19], [1], [[0, 否, 0, 否, 是], [1, 是, 1, 是, 是], [2, 否, 0, 否, 是], [3, 是, 1, 是, 是], [4, 否, 0, 否, 是], [5, 是, 1, 是, 是], [6, 否, 0, 否, 是], [7, 是, 1, 是, 是], [8, 否, 0, 否, 是], [9, 是, 1, 是, 是], [10, 否, 0, 否, 是], [11, 是, 1, 是, 是], [12, 否, 0, 否, 是], [13, 是, 1, 是, 是], [14, 否, 0, 否, 是], [15, 是, 1, 是, 是], [16, 否, 0, 否, 是], [17, 是, 1, 是, 是], [18, 否, 0, 否, 是], [19, 是, 1, 是, 是]], 是, x_in_A_iff_f_x_in_B_requires_both_yes_and_no_directions)；依完整明示資料獨立重算；composition與decider transfer保持A≤mB的方向；partial map與yes-only檢查無效；finite table只證finite domain instance，不證無限domain computability；不混同Turing reduction或反向decidability transfer。"},"difficulty":{"band":"undergraduate_core","level":3,"skills":["多對一歸約"]},"variant":{"family_id":"qf-mod46-mreduction-iff-audit","seed":202611157043,"parameters":{"source_carrier":[0,1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,19],"target_carrier":[0,1],"source_yes":[1,3,5,7,9,11,13,15,17,19],"target_yes":[1],"mapping":[0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1],"domain":"Complete_finite_many_one_reduction","operation":"mreduction-iff-audit","semantic_template":"qf-mod46-mreduction-iff-audit/{\"mapping\":[0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1],\"source_carrier\":[0,1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,19],\"source_yes\":[1,11,13,15,17,19,3,5,7,9],\"target_carrier\":[0,1],\"target_yes\":[1]}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_or_symbolic_model","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"候選須主端重算；不構成人工審定、一般第一同構／strong duality／max-flow-min-cut證明、class equation、consistency、integrality、König theorem、無限domain computability、Lean或Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-15","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261015-advance-20261115-r07-many-one-reduction-0044","batch_id":"batch-20261015-advance-20261115-r07-many-one-reduction-foundations","language":"zh-Hant","source_mko_ids":["mko-many-one-reduction"],"title_zh":"多對一歸約","stem_zh":"明示decision predicates與complete total map的雙向membership equivalence。操作=mreduction-iff-audit；資料={\"source_carrier\":[0,1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,19,20],\"target_carrier\":[0,1],\"source_yes\":[1,3,5,7,9,11,13,15,17,19],\"target_yes\":[1],\"mapping\":[0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0]}。請依 exact_ordered_tuple_declared_by_interface 欄序回答。","answer":{"kind":"expression","value":"([1, 3, 5, 7, 9, 11, 13, 15, 17, 19], [1], [[0, 否, 0, 否, 是], [1, 是, 1, 是, 是], [2, 否, 0, 否, 是], [3, 是, 1, 是, 是], [4, 否, 0, 否, 是], [5, 是, 1, 是, 是], [6, 否, 0, 否, 是], [7, 是, 1, 是, 是], [8, 否, 0, 否, 是], [9, 是, 1, 是, 是], [10, 否, 0, 否, 是], [11, 是, 1, 是, 是], [12, 否, 0, 否, 是], [13, 是, 1, 是, 是], [14, 否, 0, 否, 是], [15, 是, 1, 是, 是], [16, 否, 0, 否, 是], [17, 是, 1, 是, 是], [18, 否, 0, 否, 是], [19, 是, 1, 是, 是], [20, 否, 0, 否, 是]], 是, x_in_A_iff_f_x_in_B_requires_both_yes_and_no_directions)","explanation_zh":"Wave6第九層核對=([1, 3, 5, 7, 9, 11, 13, 15, 17, 19], [1], [[0, 否, 0, 否, 是], [1, 是, 1, 是, 是], [2, 否, 0, 否, 是], [3, 是, 1, 是, 是], [4, 否, 0, 否, 是], [5, 是, 1, 是, 是], [6, 否, 0, 否, 是], [7, 是, 1, 是, 是], [8, 否, 0, 否, 是], [9, 是, 1, 是, 是], [10, 否, 0, 否, 是], [11, 是, 1, 是, 是], [12, 否, 0, 否, 是], [13, 是, 1, 是, 是], [14, 否, 0, 否, 是], [15, 是, 1, 是, 是], [16, 否, 0, 否, 是], [17, 是, 1, 是, 是], [18, 否, 0, 否, 是], [19, 是, 1, 是, 是], [20, 否, 0, 否, 是]], 是, x_in_A_iff_f_x_in_B_requires_both_yes_and_no_directions)；依完整明示資料獨立重算；composition與decider transfer保持A≤mB的方向；partial map與yes-only檢查無效；finite table只證finite domain instance，不證無限domain computability；不混同Turing reduction或反向decidability transfer。"},"difficulty":{"band":"undergraduate_core","level":3,"skills":["多對一歸約"]},"variant":{"family_id":"qf-mod46-mreduction-iff-audit","seed":202611157044,"parameters":{"source_carrier":[0,1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,19,20],"target_carrier":[0,1],"source_yes":[1,3,5,7,9,11,13,15,17,19],"target_yes":[1],"mapping":[0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0],"domain":"Complete_finite_many_one_reduction","operation":"mreduction-iff-audit","semantic_template":"qf-mod46-mreduction-iff-audit/{\"mapping\":[0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0],\"source_carrier\":[0,1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,19,20],\"source_yes\":[1,11,13,15,17,19,3,5,7,9],\"target_carrier\":[0,1],\"target_yes\":[1]}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_or_symbolic_model","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"候選須主端重算；不構成人工審定、一般第一同構／strong duality／max-flow-min-cut證明、class equation、consistency、integrality、König theorem、無限domain computability、Lean或Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-15","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261015-advance-20261115-r07-many-one-reduction-0045","batch_id":"batch-20261015-advance-20261115-r07-many-one-reduction-foundations","language":"zh-Hant","source_mko_ids":["mko-many-one-reduction"],"title_zh":"多對一歸約","stem_zh":"明示decision predicates與complete total map的雙向membership equivalence。操作=mreduction-iff-audit；資料={\"source_carrier\":[0,1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,19,20,21],\"target_carrier\":[0,1],\"source_yes\":[1,3,5,7,9,11,13,15,17,19,21],\"target_yes\":[1],\"mapping\":[0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1]}。請依 exact_ordered_tuple_declared_by_interface 欄序回答。","answer":{"kind":"expression","value":"([1, 3, 5, 7, 9, 11, 13, 15, 17, 19, 21], [1], [[0, 否, 0, 否, 是], [1, 是, 1, 是, 是], [2, 否, 0, 否, 是], [3, 是, 1, 是, 是], [4, 否, 0, 否, 是], [5, 是, 1, 是, 是], [6, 否, 0, 否, 是], [7, 是, 1, 是, 是], [8, 否, 0, 否, 是], [9, 是, 1, 是, 是], [10, 否, 0, 否, 是], [11, 是, 1, 是, 是], [12, 否, 0, 否, 是], [13, 是, 1, 是, 是], [14, 否, 0, 否, 是], [15, 是, 1, 是, 是], [16, 否, 0, 否, 是], [17, 是, 1, 是, 是], [18, 否, 0, 否, 是], [19, 是, 1, 是, 是], [20, 否, 0, 否, 是], [21, 是, 1, 是, 是]], 是, x_in_A_iff_f_x_in_B_requires_both_yes_and_no_directions)","explanation_zh":"Wave6第九層核對=([1, 3, 5, 7, 9, 11, 13, 15, 17, 19, 21], [1], [[0, 否, 0, 否, 是], [1, 是, 1, 是, 是], [2, 否, 0, 否, 是], [3, 是, 1, 是, 是], [4, 否, 0, 否, 是], [5, 是, 1, 是, 是], [6, 否, 0, 否, 是], [7, 是, 1, 是, 是], [8, 否, 0, 否, 是], [9, 是, 1, 是, 是], [10, 否, 0, 否, 是], [11, 是, 1, 是, 是], [12, 否, 0, 否, 是], [13, 是, 1, 是, 是], [14, 否, 0, 否, 是], [15, 是, 1, 是, 是], [16, 否, 0, 否, 是], [17, 是, 1, 是, 是], [18, 否, 0, 否, 是], [19, 是, 1, 是, 是], [20, 否, 0, 否, 是], [21, 是, 1, 是, 是]], 是, x_in_A_iff_f_x_in_B_requires_both_yes_and_no_directions)；依完整明示資料獨立重算；composition與decider transfer保持A≤mB的方向；partial map與yes-only檢查無效；finite table只證finite domain instance，不證無限domain computability；不混同Turing reduction或反向decidability transfer。"},"difficulty":{"band":"undergraduate_core","level":3,"skills":["多對一歸約"]},"variant":{"family_id":"qf-mod46-mreduction-iff-audit","seed":202611157045,"parameters":{"source_carrier":[0,1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,19,20,21],"target_carrier":[0,1],"source_yes":[1,3,5,7,9,11,13,15,17,19,21],"target_yes":[1],"mapping":[0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1],"domain":"Complete_finite_many_one_reduction","operation":"mreduction-iff-audit","semantic_template":"qf-mod46-mreduction-iff-audit/{\"mapping\":[0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1],\"source_carrier\":[0,1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,19,20,21],\"source_yes\":[1,11,13,15,17,19,21,3,5,7,9],\"target_carrier\":[0,1],\"target_yes\":[1]}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_or_symbolic_model","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"候選須主端重算；不構成人工審定、一般第一同構／strong duality／max-flow-min-cut證明、class equation、consistency、integrality、König theorem、無限domain computability、Lean或Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-15","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261015-advance-20261115-r07-many-one-reduction-0046","batch_id":"batch-20261015-advance-20261115-r07-many-one-reduction-foundations","language":"zh-Hant","source_mko_ids":["mko-many-one-reduction"],"title_zh":"多對一歸約","stem_zh":"明示decision predicates與complete total map的雙向membership equivalence。操作=mreduction-iff-audit；資料={\"source_carrier\":[0,1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,19,20,21,22],\"target_carrier\":[0,1],\"source_yes\":[1,3,5,7,9,11,13,15,17,19,21],\"target_yes\":[1],\"mapping\":[0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0]}。請依 exact_ordered_tuple_declared_by_interface 欄序回答。","answer":{"kind":"expression","value":"([1, 3, 5, 7, 9, 11, 13, 15, 17, 19, 21], [1], [[0, 否, 0, 否, 是], [1, 是, 1, 是, 是], [2, 否, 0, 否, 是], [3, 是, 1, 是, 是], [4, 否, 0, 否, 是], [5, 是, 1, 是, 是], [6, 否, 0, 否, 是], [7, 是, 1, 是, 是], [8, 否, 0, 否, 是], [9, 是, 1, 是, 是], [10, 否, 0, 否, 是], [11, 是, 1, 是, 是], [12, 否, 0, 否, 是], [13, 是, 1, 是, 是], [14, 否, 0, 否, 是], [15, 是, 1, 是, 是], [16, 否, 0, 否, 是], [17, 是, 1, 是, 是], [18, 否, 0, 否, 是], [19, 是, 1, 是, 是], [20, 否, 0, 否, 是], [21, 是, 1, 是, 是], [22, 否, 0, 否, 是]], 是, x_in_A_iff_f_x_in_B_requires_both_yes_and_no_directions)","explanation_zh":"Wave6第九層核對=([1, 3, 5, 7, 9, 11, 13, 15, 17, 19, 21], [1], [[0, 否, 0, 否, 是], [1, 是, 1, 是, 是], [2, 否, 0, 否, 是], [3, 是, 1, 是, 是], [4, 否, 0, 否, 是], [5, 是, 1, 是, 是], [6, 否, 0, 否, 是], [7, 是, 1, 是, 是], [8, 否, 0, 否, 是], [9, 是, 1, 是, 是], [10, 否, 0, 否, 是], [11, 是, 1, 是, 是], [12, 否, 0, 否, 是], [13, 是, 1, 是, 是], [14, 否, 0, 否, 是], [15, 是, 1, 是, 是], [16, 否, 0, 否, 是], [17, 是, 1, 是, 是], [18, 否, 0, 否, 是], [19, 是, 1, 是, 是], [20, 否, 0, 否, 是], [21, 是, 1, 是, 是], [22, 否, 0, 否, 是]], 是, x_in_A_iff_f_x_in_B_requires_both_yes_and_no_directions)；依完整明示資料獨立重算；composition與decider transfer保持A≤mB的方向；partial map與yes-only檢查無效；finite table只證finite domain instance，不證無限domain computability；不混同Turing reduction或反向decidability transfer。"},"difficulty":{"band":"undergraduate_core","level":3,"skills":["多對一歸約"]},"variant":{"family_id":"qf-mod46-mreduction-iff-audit","seed":202611157046,"parameters":{"source_carrier":[0,1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,19,20,21,22],"target_carrier":[0,1],"source_yes":[1,3,5,7,9,11,13,15,17,19,21],"target_yes":[1],"mapping":[0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0],"domain":"Complete_finite_many_one_reduction","operation":"mreduction-iff-audit","semantic_template":"qf-mod46-mreduction-iff-audit/{\"mapping\":[0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0],\"source_carrier\":[0,1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,19,20,21,22],\"source_yes\":[1,11,13,15,17,19,21,3,5,7,9],\"target_carrier\":[0,1],\"target_yes\":[1]}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_or_symbolic_model","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"候選須主端重算；不構成人工審定、一般第一同構／strong duality／max-flow-min-cut證明、class equation、consistency、integrality、König theorem、無限domain computability、Lean或Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-15","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261015-advance-20261115-r07-many-one-reduction-0047","batch_id":"batch-20261015-advance-20261115-r07-many-one-reduction-foundations","language":"zh-Hant","source_mko_ids":["mko-many-one-reduction"],"title_zh":"多對一歸約","stem_zh":"明示decision predicates與complete total map的雙向membership equivalence。操作=mreduction-iff-audit；資料={\"source_carrier\":[0,1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,19,20,21,22,23],\"target_carrier\":[0,1],\"source_yes\":[1,3,5,7,9,11,13,15,17,19,21,23],\"target_yes\":[1],\"mapping\":[0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1]}。請依 exact_ordered_tuple_declared_by_interface 欄序回答。","answer":{"kind":"expression","value":"([1, 3, 5, 7, 9, 11, 13, 15, 17, 19, 21, 23], [1], [[0, 否, 0, 否, 是], [1, 是, 1, 是, 是], [2, 否, 0, 否, 是], [3, 是, 1, 是, 是], [4, 否, 0, 否, 是], [5, 是, 1, 是, 是], [6, 否, 0, 否, 是], [7, 是, 1, 是, 是], [8, 否, 0, 否, 是], [9, 是, 1, 是, 是], [10, 否, 0, 否, 是], [11, 是, 1, 是, 是], [12, 否, 0, 否, 是], [13, 是, 1, 是, 是], [14, 否, 0, 否, 是], [15, 是, 1, 是, 是], [16, 否, 0, 否, 是], [17, 是, 1, 是, 是], [18, 否, 0, 否, 是], [19, 是, 1, 是, 是], [20, 否, 0, 否, 是], [21, 是, 1, 是, 是], [22, 否, 0, 否, 是], [23, 是, 1, 是, 是]], 是, x_in_A_iff_f_x_in_B_requires_both_yes_and_no_directions)","explanation_zh":"Wave6第九層核對=([1, 3, 5, 7, 9, 11, 13, 15, 17, 19, 21, 23], [1], [[0, 否, 0, 否, 是], [1, 是, 1, 是, 是], [2, 否, 0, 否, 是], [3, 是, 1, 是, 是], [4, 否, 0, 否, 是], [5, 是, 1, 是, 是], [6, 否, 0, 否, 是], [7, 是, 1, 是, 是], [8, 否, 0, 否, 是], [9, 是, 1, 是, 是], [10, 否, 0, 否, 是], [11, 是, 1, 是, 是], [12, 否, 0, 否, 是], [13, 是, 1, 是, 是], [14, 否, 0, 否, 是], [15, 是, 1, 是, 是], [16, 否, 0, 否, 是], [17, 是, 1, 是, 是], [18, 否, 0, 否, 是], [19, 是, 1, 是, 是], [20, 否, 0, 否, 是], [21, 是, 1, 是, 是], [22, 否, 0, 否, 是], [23, 是, 1, 是, 是]], 是, x_in_A_iff_f_x_in_B_requires_both_yes_and_no_directions)；依完整明示資料獨立重算；composition與decider transfer保持A≤mB的方向；partial map與yes-only檢查無效；finite table只證finite domain instance，不證無限domain computability；不混同Turing reduction或反向decidability transfer。"},"difficulty":{"band":"undergraduate_core","level":3,"skills":["多對一歸約"]},"variant":{"family_id":"qf-mod46-mreduction-iff-audit","seed":202611157047,"parameters":{"source_carrier":[0,1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,19,20,21,22,23],"target_carrier":[0,1],"source_yes":[1,3,5,7,9,11,13,15,17,19,21,23],"target_yes":[1],"mapping":[0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1],"domain":"Complete_finite_many_one_reduction","operation":"mreduction-iff-audit","semantic_template":"qf-mod46-mreduction-iff-audit/{\"mapping\":[0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1],\"source_carrier\":[0,1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,19,20,21,22,23],\"source_yes\":[1,11,13,15,17,19,21,23,3,5,7,9],\"target_carrier\":[0,1],\"target_yes\":[1]}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_or_symbolic_model","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"候選須主端重算；不構成人工審定、一般第一同構／strong duality／max-flow-min-cut證明、class equation、consistency、integrality、König theorem、無限domain computability、Lean或Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-15","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261015-advance-20261115-r07-many-one-reduction-0048","batch_id":"batch-20261015-advance-20261115-r07-many-one-reduction-foundations","language":"zh-Hant","source_mko_ids":["mko-many-one-reduction"],"title_zh":"多對一歸約","stem_zh":"明示decision predicates與complete total map的雙向membership equivalence。操作=mreduction-iff-audit；資料={\"source_carrier\":[0,1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,19,20,21,22,23,24],\"target_carrier\":[0,1],\"source_yes\":[1,3,5,7,9,11,13,15,17,19,21,23],\"target_yes\":[1],\"mapping\":[0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0]}。請依 exact_ordered_tuple_declared_by_interface 欄序回答。","answer":{"kind":"expression","value":"([1, 3, 5, 7, 9, 11, 13, 15, 17, 19, 21, 23], [1], [[0, 否, 0, 否, 是], [1, 是, 1, 是, 是], [2, 否, 0, 否, 是], [3, 是, 1, 是, 是], [4, 否, 0, 否, 是], [5, 是, 1, 是, 是], [6, 否, 0, 否, 是], [7, 是, 1, 是, 是], [8, 否, 0, 否, 是], [9, 是, 1, 是, 是], [10, 否, 0, 否, 是], [11, 是, 1, 是, 是], [12, 否, 0, 否, 是], [13, 是, 1, 是, 是], [14, 否, 0, 否, 是], [15, 是, 1, 是, 是], [16, 否, 0, 否, 是], [17, 是, 1, 是, 是], [18, 否, 0, 否, 是], [19, 是, 1, 是, 是], [20, 否, 0, 否, 是], [21, 是, 1, 是, 是], [22, 否, 0, 否, 是], [23, 是, 1, 是, 是], [24, 否, 0, 否, 是]], 是, x_in_A_iff_f_x_in_B_requires_both_yes_and_no_directions)","explanation_zh":"Wave6第九層核對=([1, 3, 5, 7, 9, 11, 13, 15, 17, 19, 21, 23], [1], [[0, 否, 0, 否, 是], [1, 是, 1, 是, 是], [2, 否, 0, 否, 是], [3, 是, 1, 是, 是], [4, 否, 0, 否, 是], [5, 是, 1, 是, 是], [6, 否, 0, 否, 是], [7, 是, 1, 是, 是], [8, 否, 0, 否, 是], [9, 是, 1, 是, 是], [10, 否, 0, 否, 是], [11, 是, 1, 是, 是], [12, 否, 0, 否, 是], [13, 是, 1, 是, 是], [14, 否, 0, 否, 是], [15, 是, 1, 是, 是], [16, 否, 0, 否, 是], [17, 是, 1, 是, 是], [18, 否, 0, 否, 是], [19, 是, 1, 是, 是], [20, 否, 0, 否, 是], [21, 是, 1, 是, 是], [22, 否, 0, 否, 是], [23, 是, 1, 是, 是], [24, 否, 0, 否, 是]], 是, x_in_A_iff_f_x_in_B_requires_both_yes_and_no_directions)；依完整明示資料獨立重算；composition與decider transfer保持A≤mB的方向；partial map與yes-only檢查無效；finite table只證finite domain instance，不證無限domain computability；不混同Turing reduction或反向decidability transfer。"},"difficulty":{"band":"undergraduate_core","level":3,"skills":["多對一歸約"]},"variant":{"family_id":"qf-mod46-mreduction-iff-audit","seed":202611157048,"parameters":{"source_carrier":[0,1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,19,20,21,22,23,24],"target_carrier":[0,1],"source_yes":[1,3,5,7,9,11,13,15,17,19,21,23],"target_yes":[1],"mapping":[0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0],"domain":"Complete_finite_many_one_reduction","operation":"mreduction-iff-audit","semantic_template":"qf-mod46-mreduction-iff-audit/{\"mapping\":[0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0],\"source_carrier\":[0,1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,19,20,21,22,23,24],\"source_yes\":[1,11,13,15,17,19,21,23,3,5,7,9],\"target_carrier\":[0,1],\"target_yes\":[1]}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_or_symbolic_model","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"候選須主端重算；不構成人工審定、一般第一同構／strong duality／max-flow-min-cut證明、class equation、consistency、integrality、König theorem、無限domain computability、Lean或Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-15","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261015-advance-20261115-r07-many-one-reduction-0049","batch_id":"batch-20261015-advance-20261115-r07-many-one-reduction-foundations","language":"zh-Hant","source_mko_ids":["mko-many-one-reduction"],"title_zh":"多對一歸約","stem_zh":"明示decision predicates與complete total map的雙向membership equivalence。操作=mreduction-iff-audit；資料={\"source_carrier\":[0,1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,19,20,21,22,23,24,25],\"target_carrier\":[0,1],\"source_yes\":[1,3,5,7,9,11,13,15,17,19,21,23,25],\"target_yes\":[1],\"mapping\":[0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1]}。請依 exact_ordered_tuple_declared_by_interface 欄序回答。","answer":{"kind":"expression","value":"([1, 3, 5, 7, 9, 11, 13, 15, 17, 19, 21, 23, 25], [1], [[0, 否, 0, 否, 是], [1, 是, 1, 是, 是], [2, 否, 0, 否, 是], [3, 是, 1, 是, 是], [4, 否, 0, 否, 是], [5, 是, 1, 是, 是], [6, 否, 0, 否, 是], [7, 是, 1, 是, 是], [8, 否, 0, 否, 是], [9, 是, 1, 是, 是], [10, 否, 0, 否, 是], [11, 是, 1, 是, 是], [12, 否, 0, 否, 是], [13, 是, 1, 是, 是], [14, 否, 0, 否, 是], [15, 是, 1, 是, 是], [16, 否, 0, 否, 是], [17, 是, 1, 是, 是], [18, 否, 0, 否, 是], [19, 是, 1, 是, 是], [20, 否, 0, 否, 是], [21, 是, 1, 是, 是], [22, 否, 0, 否, 是], [23, 是, 1, 是, 是], [24, 否, 0, 否, 是], [25, 是, 1, 是, 是]], 是, x_in_A_iff_f_x_in_B_requires_both_yes_and_no_directions)","explanation_zh":"Wave6第九層核對=([1, 3, 5, 7, 9, 11, 13, 15, 17, 19, 21, 23, 25], [1], [[0, 否, 0, 否, 是], [1, 是, 1, 是, 是], [2, 否, 0, 否, 是], [3, 是, 1, 是, 是], [4, 否, 0, 否, 是], [5, 是, 1, 是, 是], [6, 否, 0, 否, 是], [7, 是, 1, 是, 是], [8, 否, 0, 否, 是], [9, 是, 1, 是, 是], [10, 否, 0, 否, 是], [11, 是, 1, 是, 是], [12, 否, 0, 否, 是], [13, 是, 1, 是, 是], [14, 否, 0, 否, 是], [15, 是, 1, 是, 是], [16, 否, 0, 否, 是], [17, 是, 1, 是, 是], [18, 否, 0, 否, 是], [19, 是, 1, 是, 是], [20, 否, 0, 否, 是], [21, 是, 1, 是, 是], [22, 否, 0, 否, 是], [23, 是, 1, 是, 是], [24, 否, 0, 否, 是], [25, 是, 1, 是, 是]], 是, x_in_A_iff_f_x_in_B_requires_both_yes_and_no_directions)；依完整明示資料獨立重算；composition與decider transfer保持A≤mB的方向；partial map與yes-only檢查無效；finite table只證finite domain instance，不證無限domain computability；不混同Turing reduction或反向decidability transfer。"},"difficulty":{"band":"undergraduate_core","level":3,"skills":["多對一歸約"]},"variant":{"family_id":"qf-mod46-mreduction-iff-audit","seed":202611157049,"parameters":{"source_carrier":[0,1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,19,20,21,22,23,24,25],"target_carrier":[0,1],"source_yes":[1,3,5,7,9,11,13,15,17,19,21,23,25],"target_yes":[1],"mapping":[0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1],"domain":"Complete_finite_many_one_reduction","operation":"mreduction-iff-audit","semantic_template":"qf-mod46-mreduction-iff-audit/{\"mapping\":[0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1],\"source_carrier\":[0,1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,19,20,21,22,23,24,25],\"source_yes\":[1,11,13,15,17,19,21,23,25,3,5,7,9],\"target_carrier\":[0,1],\"target_yes\":[1]}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_or_symbolic_model","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"候選須主端重算；不構成人工審定、一般第一同構／strong duality／max-flow-min-cut證明、class equation、consistency、integrality、König theorem、無限domain computability、Lean或Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-15","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261015-advance-20261115-r07-many-one-reduction-0050","batch_id":"batch-20261015-advance-20261115-r07-many-one-reduction-foundations","language":"zh-Hant","source_mko_ids":["mko-many-one-reduction"],"title_zh":"多對一歸約","stem_zh":"明示decision predicates與complete total map的雙向membership equivalence。操作=mreduction-iff-audit；資料={\"source_carrier\":[0,1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,19,20,21,22,23,24,25,26],\"target_carrier\":[0,1],\"source_yes\":[1,3,5,7,9,11,13,15,17,19,21,23,25],\"target_yes\":[1],\"mapping\":[0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0]}。請依 exact_ordered_tuple_declared_by_interface 欄序回答。","answer":{"kind":"expression","value":"([1, 3, 5, 7, 9, 11, 13, 15, 17, 19, 21, 23, 25], [1], [[0, 否, 0, 否, 是], [1, 是, 1, 是, 是], [2, 否, 0, 否, 是], [3, 是, 1, 是, 是], [4, 否, 0, 否, 是], [5, 是, 1, 是, 是], [6, 否, 0, 否, 是], [7, 是, 1, 是, 是], [8, 否, 0, 否, 是], [9, 是, 1, 是, 是], [10, 否, 0, 否, 是], [11, 是, 1, 是, 是], [12, 否, 0, 否, 是], [13, 是, 1, 是, 是], [14, 否, 0, 否, 是], [15, 是, 1, 是, 是], [16, 否, 0, 否, 是], [17, 是, 1, 是, 是], [18, 否, 0, 否, 是], [19, 是, 1, 是, 是], [20, 否, 0, 否, 是], [21, 是, 1, 是, 是], [22, 否, 0, 否, 是], [23, 是, 1, 是, 是], [24, 否, 0, 否, 是], [25, 是, 1, 是, 是], [26, 否, 0, 否, 是]], 是, x_in_A_iff_f_x_in_B_requires_both_yes_and_no_directions)","explanation_zh":"Wave6第九層核對=([1, 3, 5, 7, 9, 11, 13, 15, 17, 19, 21, 23, 25], [1], [[0, 否, 0, 否, 是], [1, 是, 1, 是, 是], [2, 否, 0, 否, 是], [3, 是, 1, 是, 是], [4, 否, 0, 否, 是], [5, 是, 1, 是, 是], [6, 否, 0, 否, 是], [7, 是, 1, 是, 是], [8, 否, 0, 否, 是], [9, 是, 1, 是, 是], [10, 否, 0, 否, 是], [11, 是, 1, 是, 是], [12, 否, 0, 否, 是], [13, 是, 1, 是, 是], [14, 否, 0, 否, 是], [15, 是, 1, 是, 是], [16, 否, 0, 否, 是], [17, 是, 1, 是, 是], [18, 否, 0, 否, 是], [19, 是, 1, 是, 是], [20, 否, 0, 否, 是], [21, 是, 1, 是, 是], [22, 否, 0, 否, 是], [23, 是, 1, 是, 是], [24, 否, 0, 否, 是], [25, 是, 1, 是, 是], [26, 否, 0, 否, 是]], 是, x_in_A_iff_f_x_in_B_requires_both_yes_and_no_directions)；依完整明示資料獨立重算；composition與decider transfer保持A≤mB的方向；partial map與yes-only檢查無效；finite table只證finite domain instance，不證無限domain computability；不混同Turing reduction或反向decidability transfer。"},"difficulty":{"band":"undergraduate_core","level":3,"skills":["多對一歸約"]},"variant":{"family_id":"qf-mod46-mreduction-iff-audit","seed":202611157050,"parameters":{"source_carrier":[0,1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,19,20,21,22,23,24,25,26],"target_carrier":[0,1],"source_yes":[1,3,5,7,9,11,13,15,17,19,21,23,25],"target_yes":[1],"mapping":[0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0],"domain":"Complete_finite_many_one_reduction","operation":"mreduction-iff-audit","semantic_template":"qf-mod46-mreduction-iff-audit/{\"mapping\":[0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0],\"source_carrier\":[0,1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,19,20,21,22,23,24,25,26],\"source_yes\":[1,11,13,15,17,19,21,23,25,3,5,7,9],\"target_carrier\":[0,1],\"target_yes\":[1]}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_or_symbolic_model","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"候選須主端重算；不構成人工審定、一般第一同構／strong duality／max-flow-min-cut證明、class equation、consistency、integrality、König theorem、無限domain computability、Lean或Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-15","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261015-advance-20261115-r07-many-one-reduction-0051","batch_id":"batch-20261015-advance-20261115-r07-many-one-reduction-foundations","language":"zh-Hant","source_mko_ids":["mko-many-one-reduction"],"title_zh":"多對一歸約","stem_zh":"明示decision predicates與complete total map的雙向membership equivalence。操作=mreduction-composition-direction；資料={\"source_carrier\":[0,1,2],\"middle_carrier\":[0,1],\"target_carrier\":[10,11],\"source_yes\":[1],\"middle_yes\":[1],\"target_yes\":[11],\"mapping_ab\":[0,1,0],\"mapping_bc\":[10,11]}。請依 exact_ordered_tuple_declared_by_interface 欄序回答。","answer":{"kind":"expression","value":"([[0, 否, 0, 否, 是], [1, 是, 1, 是, 是], [2, 否, 0, 否, 是]], [[0, 否, 10, 否, 是], [1, 是, 11, 是, 是]], [10, 11, 10], [[0, 否, 10, 否, 是], [1, 是, 11, 是, 是], [2, 否, 10, 否, 是]], 是, A_le_m_B_and_B_le_m_C_imply_A_le_m_C_in_that_direction_only)","explanation_zh":"Wave6第九層核對=([[0, 否, 0, 否, 是], [1, 是, 1, 是, 是], [2, 否, 0, 否, 是]], [[0, 否, 10, 否, 是], [1, 是, 11, 是, 是]], [10, 11, 10], [[0, 否, 10, 否, 是], [1, 是, 11, 是, 是], [2, 否, 10, 否, 是]], 是, A_le_m_B_and_B_le_m_C_imply_A_le_m_C_in_that_direction_only)；依完整明示資料獨立重算；composition與decider transfer保持A≤mB的方向；partial map與yes-only檢查無效；finite table只證finite domain instance，不證無限domain computability；不混同Turing reduction或反向decidability transfer。"},"difficulty":{"band":"undergraduate_core","level":1,"skills":["多對一歸約"]},"variant":{"family_id":"qf-mod46-mreduction-composition-direction","seed":202611157051,"parameters":{"source_carrier":[0,1,2],"middle_carrier":[0,1],"target_carrier":[10,11],"source_yes":[1],"middle_yes":[1],"target_yes":[11],"mapping_ab":[0,1,0],"mapping_bc":[10,11],"domain":"Complete_finite_many_one_reduction","operation":"mreduction-composition-direction","semantic_template":"qf-mod46-mreduction-composition-direction/{\"mapping_ab\":[0,1,0],\"mapping_bc\":[10,11],\"middle_carrier\":[0,1],\"middle_yes\":[1],\"source_carrier\":[0,1,2],\"source_yes\":[1],\"target_carrier\":[10,11],\"target_yes\":[11]}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_or_symbolic_model","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"候選須主端重算；不構成人工審定、一般第一同構／strong duality／max-flow-min-cut證明、class equation、consistency、integrality、König theorem、無限domain computability、Lean或Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-15","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261015-advance-20261115-r07-many-one-reduction-0052","batch_id":"batch-20261015-advance-20261115-r07-many-one-reduction-foundations","language":"zh-Hant","source_mko_ids":["mko-many-one-reduction"],"title_zh":"多對一歸約","stem_zh":"明示decision predicates與complete total map的雙向membership equivalence。操作=mreduction-composition-direction；資料={\"source_carrier\":[0,1,2,3],\"middle_carrier\":[0,1],\"target_carrier\":[10,11],\"source_yes\":[1,3],\"middle_yes\":[1],\"target_yes\":[11],\"mapping_ab\":[0,1,0,1],\"mapping_bc\":[10,11]}。請依 exact_ordered_tuple_declared_by_interface 欄序回答。","answer":{"kind":"expression","value":"([[0, 否, 0, 否, 是], [1, 是, 1, 是, 是], [2, 否, 0, 否, 是], [3, 是, 1, 是, 是]], [[0, 否, 10, 否, 是], [1, 是, 11, 是, 是]], [10, 11, 10, 11], [[0, 否, 10, 否, 是], [1, 是, 11, 是, 是], [2, 否, 10, 否, 是], [3, 是, 11, 是, 是]], 是, A_le_m_B_and_B_le_m_C_imply_A_le_m_C_in_that_direction_only)","explanation_zh":"Wave6第九層核對=([[0, 否, 0, 否, 是], [1, 是, 1, 是, 是], [2, 否, 0, 否, 是], [3, 是, 1, 是, 是]], [[0, 否, 10, 否, 是], [1, 是, 11, 是, 是]], [10, 11, 10, 11], [[0, 否, 10, 否, 是], [1, 是, 11, 是, 是], [2, 否, 10, 否, 是], [3, 是, 11, 是, 是]], 是, A_le_m_B_and_B_le_m_C_imply_A_le_m_C_in_that_direction_only)；依完整明示資料獨立重算；composition與decider transfer保持A≤mB的方向；partial map與yes-only檢查無效；finite table只證finite domain instance，不證無限domain computability；不混同Turing reduction或反向decidability transfer。"},"difficulty":{"band":"undergraduate_core","level":1,"skills":["多對一歸約"]},"variant":{"family_id":"qf-mod46-mreduction-composition-direction","seed":202611157052,"parameters":{"source_carrier":[0,1,2,3],"middle_carrier":[0,1],"target_carrier":[10,11],"source_yes":[1,3],"middle_yes":[1],"target_yes":[11],"mapping_ab":[0,1,0,1],"mapping_bc":[10,11],"domain":"Complete_finite_many_one_reduction","operation":"mreduction-composition-direction","semantic_template":"qf-mod46-mreduction-composition-direction/{\"mapping_ab\":[0,1,0,1],\"mapping_bc\":[10,11],\"middle_carrier\":[0,1],\"middle_yes\":[1],\"source_carrier\":[0,1,2,3],\"source_yes\":[1,3],\"target_carrier\":[10,11],\"target_yes\":[11]}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_or_symbolic_model","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"候選須主端重算；不構成人工審定、一般第一同構／strong duality／max-flow-min-cut證明、class equation、consistency、integrality、König theorem、無限domain computability、Lean或Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-15","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261015-advance-20261115-r07-many-one-reduction-0053","batch_id":"batch-20261015-advance-20261115-r07-many-one-reduction-foundations","language":"zh-Hant","source_mko_ids":["mko-many-one-reduction"],"title_zh":"多對一歸約","stem_zh":"明示decision predicates與complete total map的雙向membership equivalence。操作=mreduction-composition-direction；資料={\"source_carrier\":[0,1,2,3,4],\"middle_carrier\":[0,1],\"target_carrier\":[10,11],\"source_yes\":[1,3],\"middle_yes\":[1],\"target_yes\":[11],\"mapping_ab\":[0,1,0,1,0],\"mapping_bc\":[10,11]}。請依 exact_ordered_tuple_declared_by_interface 欄序回答。","answer":{"kind":"expression","value":"([[0, 否, 0, 否, 是], [1, 是, 1, 是, 是], [2, 否, 0, 否, 是], [3, 是, 1, 是, 是], [4, 否, 0, 否, 是]], [[0, 否, 10, 否, 是], [1, 是, 11, 是, 是]], [10, 11, 10, 11, 10], [[0, 否, 10, 否, 是], [1, 是, 11, 是, 是], [2, 否, 10, 否, 是], [3, 是, 11, 是, 是], [4, 否, 10, 否, 是]], 是, A_le_m_B_and_B_le_m_C_imply_A_le_m_C_in_that_direction_only)","explanation_zh":"Wave6第九層核對=([[0, 否, 0, 否, 是], [1, 是, 1, 是, 是], [2, 否, 0, 否, 是], [3, 是, 1, 是, 是], [4, 否, 0, 否, 是]], [[0, 否, 10, 否, 是], [1, 是, 11, 是, 是]], [10, 11, 10, 11, 10], [[0, 否, 10, 否, 是], [1, 是, 11, 是, 是], [2, 否, 10, 否, 是], [3, 是, 11, 是, 是], [4, 否, 10, 否, 是]], 是, A_le_m_B_and_B_le_m_C_imply_A_le_m_C_in_that_direction_only)；依完整明示資料獨立重算；composition與decider transfer保持A≤mB的方向；partial map與yes-only檢查無效；finite table只證finite domain instance，不證無限domain computability；不混同Turing reduction或反向decidability transfer。"},"difficulty":{"band":"undergraduate_core","level":1,"skills":["多對一歸約"]},"variant":{"family_id":"qf-mod46-mreduction-composition-direction","seed":202611157053,"parameters":{"source_carrier":[0,1,2,3,4],"middle_carrier":[0,1],"target_carrier":[10,11],"source_yes":[1,3],"middle_yes":[1],"target_yes":[11],"mapping_ab":[0,1,0,1,0],"mapping_bc":[10,11],"domain":"Complete_finite_many_one_reduction","operation":"mreduction-composition-direction","semantic_template":"qf-mod46-mreduction-composition-direction/{\"mapping_ab\":[0,1,0,1,0],\"mapping_bc\":[10,11],\"middle_carrier\":[0,1],\"middle_yes\":[1],\"source_carrier\":[0,1,2,3,4],\"source_yes\":[1,3],\"target_carrier\":[10,11],\"target_yes\":[11]}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_or_symbolic_model","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"候選須主端重算；不構成人工審定、一般第一同構／strong duality／max-flow-min-cut證明、class equation、consistency、integrality、König theorem、無限domain computability、Lean或Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-15","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261015-advance-20261115-r07-many-one-reduction-0054","batch_id":"batch-20261015-advance-20261115-r07-many-one-reduction-foundations","language":"zh-Hant","source_mko_ids":["mko-many-one-reduction"],"title_zh":"多對一歸約","stem_zh":"明示decision predicates與complete total map的雙向membership equivalence。操作=mreduction-composition-direction；資料={\"source_carrier\":[0,1,2,3,4,5],\"middle_carrier\":[0,1],\"target_carrier\":[10,11],\"source_yes\":[1,3,5],\"middle_yes\":[1],\"target_yes\":[11],\"mapping_ab\":[0,1,0,1,0,1],\"mapping_bc\":[10,11]}。請依 exact_ordered_tuple_declared_by_interface 欄序回答。","answer":{"kind":"expression","value":"([[0, 否, 0, 否, 是], [1, 是, 1, 是, 是], [2, 否, 0, 否, 是], [3, 是, 1, 是, 是], [4, 否, 0, 否, 是], [5, 是, 1, 是, 是]], [[0, 否, 10, 否, 是], [1, 是, 11, 是, 是]], [10, 11, 10, 11, 10, 11], [[0, 否, 10, 否, 是], [1, 是, 11, 是, 是], [2, 否, 10, 否, 是], [3, 是, 11, 是, 是], [4, 否, 10, 否, 是], [5, 是, 11, 是, 是]], 是, A_le_m_B_and_B_le_m_C_imply_A_le_m_C_in_that_direction_only)","explanation_zh":"Wave6第九層核對=([[0, 否, 0, 否, 是], [1, 是, 1, 是, 是], [2, 否, 0, 否, 是], [3, 是, 1, 是, 是], [4, 否, 0, 否, 是], [5, 是, 1, 是, 是]], [[0, 否, 10, 否, 是], [1, 是, 11, 是, 是]], [10, 11, 10, 11, 10, 11], [[0, 否, 10, 否, 是], [1, 是, 11, 是, 是], [2, 否, 10, 否, 是], [3, 是, 11, 是, 是], [4, 否, 10, 否, 是], [5, 是, 11, 是, 是]], 是, A_le_m_B_and_B_le_m_C_imply_A_le_m_C_in_that_direction_only)；依完整明示資料獨立重算；composition與decider transfer保持A≤mB的方向；partial map與yes-only檢查無效；finite table只證finite domain instance，不證無限domain computability；不混同Turing reduction或反向decidability transfer。"},"difficulty":{"band":"undergraduate_core","level":1,"skills":["多對一歸約"]},"variant":{"family_id":"qf-mod46-mreduction-composition-direction","seed":202611157054,"parameters":{"source_carrier":[0,1,2,3,4,5],"middle_carrier":[0,1],"target_carrier":[10,11],"source_yes":[1,3,5],"middle_yes":[1],"target_yes":[11],"mapping_ab":[0,1,0,1,0,1],"mapping_bc":[10,11],"domain":"Complete_finite_many_one_reduction","operation":"mreduction-composition-direction","semantic_template":"qf-mod46-mreduction-composition-direction/{\"mapping_ab\":[0,1,0,1,0,1],\"mapping_bc\":[10,11],\"middle_carrier\":[0,1],\"middle_yes\":[1],\"source_carrier\":[0,1,2,3,4,5],\"source_yes\":[1,3,5],\"target_carrier\":[10,11],\"target_yes\":[11]}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_or_symbolic_model","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"候選須主端重算；不構成人工審定、一般第一同構／strong duality／max-flow-min-cut證明、class equation、consistency、integrality、König theorem、無限domain computability、Lean或Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-15","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261015-advance-20261115-r07-many-one-reduction-0055","batch_id":"batch-20261015-advance-20261115-r07-many-one-reduction-foundations","language":"zh-Hant","source_mko_ids":["mko-many-one-reduction"],"title_zh":"多對一歸約","stem_zh":"明示decision predicates與complete total map的雙向membership equivalence。操作=mreduction-composition-direction；資料={\"source_carrier\":[0,1,2,3,4,5,6],\"middle_carrier\":[0,1],\"target_carrier\":[10,11],\"source_yes\":[1,3,5],\"middle_yes\":[1],\"target_yes\":[11],\"mapping_ab\":[0,1,0,1,0,1,0],\"mapping_bc\":[10,11]}。請依 exact_ordered_tuple_declared_by_interface 欄序回答。","answer":{"kind":"expression","value":"([[0, 否, 0, 否, 是], [1, 是, 1, 是, 是], [2, 否, 0, 否, 是], [3, 是, 1, 是, 是], [4, 否, 0, 否, 是], [5, 是, 1, 是, 是], [6, 否, 0, 否, 是]], [[0, 否, 10, 否, 是], [1, 是, 11, 是, 是]], [10, 11, 10, 11, 10, 11, 10], [[0, 否, 10, 否, 是], [1, 是, 11, 是, 是], [2, 否, 10, 否, 是], [3, 是, 11, 是, 是], [4, 否, 10, 否, 是], [5, 是, 11, 是, 是], [6, 否, 10, 否, 是]], 是, A_le_m_B_and_B_le_m_C_imply_A_le_m_C_in_that_direction_only)","explanation_zh":"Wave6第九層核對=([[0, 否, 0, 否, 是], [1, 是, 1, 是, 是], [2, 否, 0, 否, 是], [3, 是, 1, 是, 是], [4, 否, 0, 否, 是], [5, 是, 1, 是, 是], [6, 否, 0, 否, 是]], [[0, 否, 10, 否, 是], [1, 是, 11, 是, 是]], [10, 11, 10, 11, 10, 11, 10], [[0, 否, 10, 否, 是], [1, 是, 11, 是, 是], [2, 否, 10, 否, 是], [3, 是, 11, 是, 是], [4, 否, 10, 否, 是], [5, 是, 11, 是, 是], [6, 否, 10, 否, 是]], 是, A_le_m_B_and_B_le_m_C_imply_A_le_m_C_in_that_direction_only)；依完整明示資料獨立重算；composition與decider transfer保持A≤mB的方向；partial map與yes-only檢查無效；finite table只證finite domain instance，不證無限domain computability；不混同Turing reduction或反向decidability transfer。"},"difficulty":{"band":"undergraduate_core","level":1,"skills":["多對一歸約"]},"variant":{"family_id":"qf-mod46-mreduction-composition-direction","seed":202611157055,"parameters":{"source_carrier":[0,1,2,3,4,5,6],"middle_carrier":[0,1],"target_carrier":[10,11],"source_yes":[1,3,5],"middle_yes":[1],"target_yes":[11],"mapping_ab":[0,1,0,1,0,1,0],"mapping_bc":[10,11],"domain":"Complete_finite_many_one_reduction","operation":"mreduction-composition-direction","semantic_template":"qf-mod46-mreduction-composition-direction/{\"mapping_ab\":[0,1,0,1,0,1,0],\"mapping_bc\":[10,11],\"middle_carrier\":[0,1],\"middle_yes\":[1],\"source_carrier\":[0,1,2,3,4,5,6],\"source_yes\":[1,3,5],\"target_carrier\":[10,11],\"target_yes\":[11]}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_or_symbolic_model","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"候選須主端重算；不構成人工審定、一般第一同構／strong duality／max-flow-min-cut證明、class equation、consistency、integrality、König theorem、無限domain computability、Lean或Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-15","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261015-advance-20261115-r07-many-one-reduction-0056","batch_id":"batch-20261015-advance-20261115-r07-many-one-reduction-foundations","language":"zh-Hant","source_mko_ids":["mko-many-one-reduction"],"title_zh":"多對一歸約","stem_zh":"明示decision predicates與complete total map的雙向membership equivalence。操作=mreduction-composition-direction；資料={\"source_carrier\":[0,1,2,3,4,5,6,7],\"middle_carrier\":[0,1],\"target_carrier\":[10,11],\"source_yes\":[1,3,5,7],\"middle_yes\":[1],\"target_yes\":[11],\"mapping_ab\":[0,1,0,1,0,1,0,1],\"mapping_bc\":[10,11]}。請依 exact_ordered_tuple_declared_by_interface 欄序回答。","answer":{"kind":"expression","value":"([[0, 否, 0, 否, 是], [1, 是, 1, 是, 是], [2, 否, 0, 否, 是], [3, 是, 1, 是, 是], [4, 否, 0, 否, 是], [5, 是, 1, 是, 是], [6, 否, 0, 否, 是], [7, 是, 1, 是, 是]], [[0, 否, 10, 否, 是], [1, 是, 11, 是, 是]], [10, 11, 10, 11, 10, 11, 10, 11], [[0, 否, 10, 否, 是], [1, 是, 11, 是, 是], [2, 否, 10, 否, 是], [3, 是, 11, 是, 是], [4, 否, 10, 否, 是], [5, 是, 11, 是, 是], [6, 否, 10, 否, 是], [7, 是, 11, 是, 是]], 是, A_le_m_B_and_B_le_m_C_imply_A_le_m_C_in_that_direction_only)","explanation_zh":"Wave6第九層核對=([[0, 否, 0, 否, 是], [1, 是, 1, 是, 是], [2, 否, 0, 否, 是], [3, 是, 1, 是, 是], [4, 否, 0, 否, 是], [5, 是, 1, 是, 是], [6, 否, 0, 否, 是], [7, 是, 1, 是, 是]], [[0, 否, 10, 否, 是], [1, 是, 11, 是, 是]], [10, 11, 10, 11, 10, 11, 10, 11], [[0, 否, 10, 否, 是], [1, 是, 11, 是, 是], [2, 否, 10, 否, 是], [3, 是, 11, 是, 是], [4, 否, 10, 否, 是], [5, 是, 11, 是, 是], [6, 否, 10, 否, 是], [7, 是, 11, 是, 是]], 是, A_le_m_B_and_B_le_m_C_imply_A_le_m_C_in_that_direction_only)；依完整明示資料獨立重算；composition與decider transfer保持A≤mB的方向；partial map與yes-only檢查無效；finite table只證finite domain instance，不證無限domain computability；不混同Turing reduction或反向decidability transfer。"},"difficulty":{"band":"undergraduate_core","level":1,"skills":["多對一歸約"]},"variant":{"family_id":"qf-mod46-mreduction-composition-direction","seed":202611157056,"parameters":{"source_carrier":[0,1,2,3,4,5,6,7],"middle_carrier":[0,1],"target_carrier":[10,11],"source_yes":[1,3,5,7],"middle_yes":[1],"target_yes":[11],"mapping_ab":[0,1,0,1,0,1,0,1],"mapping_bc":[10,11],"domain":"Complete_finite_many_one_reduction","operation":"mreduction-composition-direction","semantic_template":"qf-mod46-mreduction-composition-direction/{\"mapping_ab\":[0,1,0,1,0,1,0,1],\"mapping_bc\":[10,11],\"middle_carrier\":[0,1],\"middle_yes\":[1],\"source_carrier\":[0,1,2,3,4,5,6,7],\"source_yes\":[1,3,5,7],\"target_carrier\":[10,11],\"target_yes\":[11]}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_or_symbolic_model","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"候選須主端重算；不構成人工審定、一般第一同構／strong duality／max-flow-min-cut證明、class equation、consistency、integrality、König theorem、無限domain computability、Lean或Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-15","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261015-advance-20261115-r07-many-one-reduction-0057","batch_id":"batch-20261015-advance-20261115-r07-many-one-reduction-foundations","language":"zh-Hant","source_mko_ids":["mko-many-one-reduction"],"title_zh":"多對一歸約","stem_zh":"明示decision predicates與complete total map的雙向membership equivalence。操作=mreduction-composition-direction；資料={\"source_carrier\":[0,1,2,3,4,5,6,7,8],\"middle_carrier\":[0,1],\"target_carrier\":[10,11],\"source_yes\":[1,3,5,7],\"middle_yes\":[1],\"target_yes\":[11],\"mapping_ab\":[0,1,0,1,0,1,0,1,0],\"mapping_bc\":[10,11]}。請依 exact_ordered_tuple_declared_by_interface 欄序回答。","answer":{"kind":"expression","value":"([[0, 否, 0, 否, 是], [1, 是, 1, 是, 是], [2, 否, 0, 否, 是], [3, 是, 1, 是, 是], [4, 否, 0, 否, 是], [5, 是, 1, 是, 是], [6, 否, 0, 否, 是], [7, 是, 1, 是, 是], [8, 否, 0, 否, 是]], [[0, 否, 10, 否, 是], [1, 是, 11, 是, 是]], [10, 11, 10, 11, 10, 11, 10, 11, 10], [[0, 否, 10, 否, 是], [1, 是, 11, 是, 是], [2, 否, 10, 否, 是], [3, 是, 11, 是, 是], [4, 否, 10, 否, 是], [5, 是, 11, 是, 是], [6, 否, 10, 否, 是], [7, 是, 11, 是, 是], [8, 否, 10, 否, 是]], 是, A_le_m_B_and_B_le_m_C_imply_A_le_m_C_in_that_direction_only)","explanation_zh":"Wave6第九層核對=([[0, 否, 0, 否, 是], [1, 是, 1, 是, 是], [2, 否, 0, 否, 是], [3, 是, 1, 是, 是], [4, 否, 0, 否, 是], [5, 是, 1, 是, 是], [6, 否, 0, 否, 是], [7, 是, 1, 是, 是], [8, 否, 0, 否, 是]], [[0, 否, 10, 否, 是], [1, 是, 11, 是, 是]], [10, 11, 10, 11, 10, 11, 10, 11, 10], [[0, 否, 10, 否, 是], [1, 是, 11, 是, 是], [2, 否, 10, 否, 是], [3, 是, 11, 是, 是], [4, 否, 10, 否, 是], [5, 是, 11, 是, 是], [6, 否, 10, 否, 是], [7, 是, 11, 是, 是], [8, 否, 10, 否, 是]], 是, A_le_m_B_and_B_le_m_C_imply_A_le_m_C_in_that_direction_only)；依完整明示資料獨立重算；composition與decider transfer保持A≤mB的方向；partial map與yes-only檢查無效；finite table只證finite domain instance，不證無限domain computability；不混同Turing reduction或反向decidability transfer。"},"difficulty":{"band":"undergraduate_core","level":1,"skills":["多對一歸約"]},"variant":{"family_id":"qf-mod46-mreduction-composition-direction","seed":202611157057,"parameters":{"source_carrier":[0,1,2,3,4,5,6,7,8],"middle_carrier":[0,1],"target_carrier":[10,11],"source_yes":[1,3,5,7],"middle_yes":[1],"target_yes":[11],"mapping_ab":[0,1,0,1,0,1,0,1,0],"mapping_bc":[10,11],"domain":"Complete_finite_many_one_reduction","operation":"mreduction-composition-direction","semantic_template":"qf-mod46-mreduction-composition-direction/{\"mapping_ab\":[0,1,0,1,0,1,0,1,0],\"mapping_bc\":[10,11],\"middle_carrier\":[0,1],\"middle_yes\":[1],\"source_carrier\":[0,1,2,3,4,5,6,7,8],\"source_yes\":[1,3,5,7],\"target_carrier\":[10,11],\"target_yes\":[11]}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_or_symbolic_model","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"候選須主端重算；不構成人工審定、一般第一同構／strong duality／max-flow-min-cut證明、class equation、consistency、integrality、König theorem、無限domain computability、Lean或Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-15","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261015-advance-20261115-r07-many-one-reduction-0058","batch_id":"batch-20261015-advance-20261115-r07-many-one-reduction-foundations","language":"zh-Hant","source_mko_ids":["mko-many-one-reduction"],"title_zh":"多對一歸約","stem_zh":"明示decision predicates與complete total map的雙向membership equivalence。操作=mreduction-composition-direction；資料={\"source_carrier\":[0,1,2,3,4,5,6,7,8,9],\"middle_carrier\":[0,1],\"target_carrier\":[10,11],\"source_yes\":[1,3,5,7,9],\"middle_yes\":[1],\"target_yes\":[11],\"mapping_ab\":[0,1,0,1,0,1,0,1,0,1],\"mapping_bc\":[10,11]}。請依 exact_ordered_tuple_declared_by_interface 欄序回答。","answer":{"kind":"expression","value":"([[0, 否, 0, 否, 是], [1, 是, 1, 是, 是], [2, 否, 0, 否, 是], [3, 是, 1, 是, 是], [4, 否, 0, 否, 是], [5, 是, 1, 是, 是], [6, 否, 0, 否, 是], [7, 是, 1, 是, 是], [8, 否, 0, 否, 是], [9, 是, 1, 是, 是]], [[0, 否, 10, 否, 是], [1, 是, 11, 是, 是]], [10, 11, 10, 11, 10, 11, 10, 11, 10, 11], [[0, 否, 10, 否, 是], [1, 是, 11, 是, 是], [2, 否, 10, 否, 是], [3, 是, 11, 是, 是], [4, 否, 10, 否, 是], [5, 是, 11, 是, 是], [6, 否, 10, 否, 是], [7, 是, 11, 是, 是], [8, 否, 10, 否, 是], [9, 是, 11, 是, 是]], 是, A_le_m_B_and_B_le_m_C_imply_A_le_m_C_in_that_direction_only)","explanation_zh":"Wave6第九層核對=([[0, 否, 0, 否, 是], [1, 是, 1, 是, 是], [2, 否, 0, 否, 是], [3, 是, 1, 是, 是], [4, 否, 0, 否, 是], [5, 是, 1, 是, 是], [6, 否, 0, 否, 是], [7, 是, 1, 是, 是], [8, 否, 0, 否, 是], [9, 是, 1, 是, 是]], [[0, 否, 10, 否, 是], [1, 是, 11, 是, 是]], [10, 11, 10, 11, 10, 11, 10, 11, 10, 11], [[0, 否, 10, 否, 是], [1, 是, 11, 是, 是], [2, 否, 10, 否, 是], [3, 是, 11, 是, 是], [4, 否, 10, 否, 是], [5, 是, 11, 是, 是], [6, 否, 10, 否, 是], [7, 是, 11, 是, 是], [8, 否, 10, 否, 是], [9, 是, 11, 是, 是]], 是, A_le_m_B_and_B_le_m_C_imply_A_le_m_C_in_that_direction_only)；依完整明示資料獨立重算；composition與decider transfer保持A≤mB的方向；partial map與yes-only檢查無效；finite table只證finite domain instance，不證無限domain computability；不混同Turing reduction或反向decidability transfer。"},"difficulty":{"band":"undergraduate_core","level":1,"skills":["多對一歸約"]},"variant":{"family_id":"qf-mod46-mreduction-composition-direction","seed":202611157058,"parameters":{"source_carrier":[0,1,2,3,4,5,6,7,8,9],"middle_carrier":[0,1],"target_carrier":[10,11],"source_yes":[1,3,5,7,9],"middle_yes":[1],"target_yes":[11],"mapping_ab":[0,1,0,1,0,1,0,1,0,1],"mapping_bc":[10,11],"domain":"Complete_finite_many_one_reduction","operation":"mreduction-composition-direction","semantic_template":"qf-mod46-mreduction-composition-direction/{\"mapping_ab\":[0,1,0,1,0,1,0,1,0,1],\"mapping_bc\":[10,11],\"middle_carrier\":[0,1],\"middle_yes\":[1],\"source_carrier\":[0,1,2,3,4,5,6,7,8,9],\"source_yes\":[1,3,5,7,9],\"target_carrier\":[10,11],\"target_yes\":[11]}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_or_symbolic_model","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"候選須主端重算；不構成人工審定、一般第一同構／strong duality／max-flow-min-cut證明、class equation、consistency、integrality、König theorem、無限domain computability、Lean或Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-15","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261015-advance-20261115-r07-many-one-reduction-0059","batch_id":"batch-20261015-advance-20261115-r07-many-one-reduction-foundations","language":"zh-Hant","source_mko_ids":["mko-many-one-reduction"],"title_zh":"多對一歸約","stem_zh":"明示decision predicates與complete total map的雙向membership equivalence。操作=mreduction-composition-direction；資料={\"source_carrier\":[0,1,2,3,4,5,6,7,8,9,10],\"middle_carrier\":[0,1],\"target_carrier\":[10,11],\"source_yes\":[1,3,5,7,9],\"middle_yes\":[1],\"target_yes\":[11],\"mapping_ab\":[0,1,0,1,0,1,0,1,0,1,0],\"mapping_bc\":[10,11]}。請依 exact_ordered_tuple_declared_by_interface 欄序回答。","answer":{"kind":"expression","value":"([[0, 否, 0, 否, 是], [1, 是, 1, 是, 是], [2, 否, 0, 否, 是], [3, 是, 1, 是, 是], [4, 否, 0, 否, 是], [5, 是, 1, 是, 是], [6, 否, 0, 否, 是], [7, 是, 1, 是, 是], [8, 否, 0, 否, 是], [9, 是, 1, 是, 是], [10, 否, 0, 否, 是]], [[0, 否, 10, 否, 是], [1, 是, 11, 是, 是]], [10, 11, 10, 11, 10, 11, 10, 11, 10, 11, 10], [[0, 否, 10, 否, 是], [1, 是, 11, 是, 是], [2, 否, 10, 否, 是], [3, 是, 11, 是, 是], [4, 否, 10, 否, 是], [5, 是, 11, 是, 是], [6, 否, 10, 否, 是], [7, 是, 11, 是, 是], [8, 否, 10, 否, 是], [9, 是, 11, 是, 是], [10, 否, 10, 否, 是]], 是, A_le_m_B_and_B_le_m_C_imply_A_le_m_C_in_that_direction_only)","explanation_zh":"Wave6第九層核對=([[0, 否, 0, 否, 是], [1, 是, 1, 是, 是], [2, 否, 0, 否, 是], [3, 是, 1, 是, 是], [4, 否, 0, 否, 是], [5, 是, 1, 是, 是], [6, 否, 0, 否, 是], [7, 是, 1, 是, 是], [8, 否, 0, 否, 是], [9, 是, 1, 是, 是], [10, 否, 0, 否, 是]], [[0, 否, 10, 否, 是], [1, 是, 11, 是, 是]], [10, 11, 10, 11, 10, 11, 10, 11, 10, 11, 10], [[0, 否, 10, 否, 是], [1, 是, 11, 是, 是], [2, 否, 10, 否, 是], [3, 是, 11, 是, 是], [4, 否, 10, 否, 是], [5, 是, 11, 是, 是], [6, 否, 10, 否, 是], [7, 是, 11, 是, 是], [8, 否, 10, 否, 是], [9, 是, 11, 是, 是], [10, 否, 10, 否, 是]], 是, A_le_m_B_and_B_le_m_C_imply_A_le_m_C_in_that_direction_only)；依完整明示資料獨立重算；composition與decider transfer保持A≤mB的方向；partial map與yes-only檢查無效；finite table只證finite domain instance，不證無限domain computability；不混同Turing reduction或反向decidability transfer。"},"difficulty":{"band":"undergraduate_core","level":2,"skills":["多對一歸約"]},"variant":{"family_id":"qf-mod46-mreduction-composition-direction","seed":202611157059,"parameters":{"source_carrier":[0,1,2,3,4,5,6,7,8,9,10],"middle_carrier":[0,1],"target_carrier":[10,11],"source_yes":[1,3,5,7,9],"middle_yes":[1],"target_yes":[11],"mapping_ab":[0,1,0,1,0,1,0,1,0,1,0],"mapping_bc":[10,11],"domain":"Complete_finite_many_one_reduction","operation":"mreduction-composition-direction","semantic_template":"qf-mod46-mreduction-composition-direction/{\"mapping_ab\":[0,1,0,1,0,1,0,1,0,1,0],\"mapping_bc\":[10,11],\"middle_carrier\":[0,1],\"middle_yes\":[1],\"source_carrier\":[0,1,2,3,4,5,6,7,8,9,10],\"source_yes\":[1,3,5,7,9],\"target_carrier\":[10,11],\"target_yes\":[11]}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_or_symbolic_model","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"候選須主端重算；不構成人工審定、一般第一同構／strong duality／max-flow-min-cut證明、class equation、consistency、integrality、König theorem、無限domain computability、Lean或Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-15","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261015-advance-20261115-r07-many-one-reduction-0060","batch_id":"batch-20261015-advance-20261115-r07-many-one-reduction-foundations","language":"zh-Hant","source_mko_ids":["mko-many-one-reduction"],"title_zh":"多對一歸約","stem_zh":"明示decision predicates與complete total map的雙向membership equivalence。操作=mreduction-composition-direction；資料={\"source_carrier\":[0,1,2,3,4,5,6,7,8,9,10,11],\"middle_carrier\":[0,1],\"target_carrier\":[10,11],\"source_yes\":[1,3,5,7,9,11],\"middle_yes\":[1],\"target_yes\":[11],\"mapping_ab\":[0,1,0,1,0,1,0,1,0,1,0,1],\"mapping_bc\":[10,11]}。請依 exact_ordered_tuple_declared_by_interface 欄序回答。","answer":{"kind":"expression","value":"([[0, 否, 0, 否, 是], [1, 是, 1, 是, 是], [2, 否, 0, 否, 是], [3, 是, 1, 是, 是], [4, 否, 0, 否, 是], [5, 是, 1, 是, 是], [6, 否, 0, 否, 是], [7, 是, 1, 是, 是], [8, 否, 0, 否, 是], [9, 是, 1, 是, 是], [10, 否, 0, 否, 是], [11, 是, 1, 是, 是]], [[0, 否, 10, 否, 是], [1, 是, 11, 是, 是]], [10, 11, 10, 11, 10, 11, 10, 11, 10, 11, 10, 11], [[0, 否, 10, 否, 是], [1, 是, 11, 是, 是], [2, 否, 10, 否, 是], [3, 是, 11, 是, 是], [4, 否, 10, 否, 是], [5, 是, 11, 是, 是], [6, 否, 10, 否, 是], [7, 是, 11, 是, 是], [8, 否, 10, 否, 是], [9, 是, 11, 是, 是], [10, 否, 10, 否, 是], [11, 是, 11, 是, 是]], 是, A_le_m_B_and_B_le_m_C_imply_A_le_m_C_in_that_direction_only)","explanation_zh":"Wave6第九層核對=([[0, 否, 0, 否, 是], [1, 是, 1, 是, 是], [2, 否, 0, 否, 是], [3, 是, 1, 是, 是], [4, 否, 0, 否, 是], [5, 是, 1, 是, 是], [6, 否, 0, 否, 是], [7, 是, 1, 是, 是], [8, 否, 0, 否, 是], [9, 是, 1, 是, 是], [10, 否, 0, 否, 是], [11, 是, 1, 是, 是]], [[0, 否, 10, 否, 是], [1, 是, 11, 是, 是]], [10, 11, 10, 11, 10, 11, 10, 11, 10, 11, 10, 11], [[0, 否, 10, 否, 是], [1, 是, 11, 是, 是], [2, 否, 10, 否, 是], [3, 是, 11, 是, 是], [4, 否, 10, 否, 是], [5, 是, 11, 是, 是], [6, 否, 10, 否, 是], [7, 是, 11, 是, 是], [8, 否, 10, 否, 是], [9, 是, 11, 是, 是], [10, 否, 10, 否, 是], [11, 是, 11, 是, 是]], 是, A_le_m_B_and_B_le_m_C_imply_A_le_m_C_in_that_direction_only)；依完整明示資料獨立重算；composition與decider transfer保持A≤mB的方向；partial map與yes-only檢查無效；finite table只證finite domain instance，不證無限domain computability；不混同Turing reduction或反向decidability transfer。"},"difficulty":{"band":"undergraduate_core","level":2,"skills":["多對一歸約"]},"variant":{"family_id":"qf-mod46-mreduction-composition-direction","seed":202611157060,"parameters":{"source_carrier":[0,1,2,3,4,5,6,7,8,9,10,11],"middle_carrier":[0,1],"target_carrier":[10,11],"source_yes":[1,3,5,7,9,11],"middle_yes":[1],"target_yes":[11],"mapping_ab":[0,1,0,1,0,1,0,1,0,1,0,1],"mapping_bc":[10,11],"domain":"Complete_finite_many_one_reduction","operation":"mreduction-composition-direction","semantic_template":"qf-mod46-mreduction-composition-direction/{\"mapping_ab\":[0,1,0,1,0,1,0,1,0,1,0,1],\"mapping_bc\":[10,11],\"middle_carrier\":[0,1],\"middle_yes\":[1],\"source_carrier\":[0,1,2,3,4,5,6,7,8,9,10,11],\"source_yes\":[1,11,3,5,7,9],\"target_carrier\":[10,11],\"target_yes\":[11]}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_or_symbolic_model","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"候選須主端重算；不構成人工審定、一般第一同構／strong duality／max-flow-min-cut證明、class equation、consistency、integrality、König theorem、無限domain computability、Lean或Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-15","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261015-advance-20261115-r07-many-one-reduction-0061","batch_id":"batch-20261015-advance-20261115-r07-many-one-reduction-foundations","language":"zh-Hant","source_mko_ids":["mko-many-one-reduction"],"title_zh":"多對一歸約","stem_zh":"明示decision predicates與complete total map的雙向membership equivalence。操作=mreduction-composition-direction；資料={\"source_carrier\":[0,1,2,3,4,5,6,7,8,9,10,11,12],\"middle_carrier\":[0,1],\"target_carrier\":[10,11],\"source_yes\":[1,3,5,7,9,11],\"middle_yes\":[1],\"target_yes\":[11],\"mapping_ab\":[0,1,0,1,0,1,0,1,0,1,0,1,0],\"mapping_bc\":[10,11]}。請依 exact_ordered_tuple_declared_by_interface 欄序回答。","answer":{"kind":"expression","value":"([[0, 否, 0, 否, 是], [1, 是, 1, 是, 是], [2, 否, 0, 否, 是], [3, 是, 1, 是, 是], [4, 否, 0, 否, 是], [5, 是, 1, 是, 是], [6, 否, 0, 否, 是], [7, 是, 1, 是, 是], [8, 否, 0, 否, 是], [9, 是, 1, 是, 是], [10, 否, 0, 否, 是], [11, 是, 1, 是, 是], [12, 否, 0, 否, 是]], [[0, 否, 10, 否, 是], [1, 是, 11, 是, 是]], [10, 11, 10, 11, 10, 11, 10, 11, 10, 11, 10, 11, 10], [[0, 否, 10, 否, 是], [1, 是, 11, 是, 是], [2, 否, 10, 否, 是], [3, 是, 11, 是, 是], [4, 否, 10, 否, 是], [5, 是, 11, 是, 是], [6, 否, 10, 否, 是], [7, 是, 11, 是, 是], [8, 否, 10, 否, 是], [9, 是, 11, 是, 是], [10, 否, 10, 否, 是], [11, 是, 11, 是, 是], [12, 否, 10, 否, 是]], 是, A_le_m_B_and_B_le_m_C_imply_A_le_m_C_in_that_direction_only)","explanation_zh":"Wave6第九層核對=([[0, 否, 0, 否, 是], [1, 是, 1, 是, 是], [2, 否, 0, 否, 是], [3, 是, 1, 是, 是], [4, 否, 0, 否, 是], [5, 是, 1, 是, 是], [6, 否, 0, 否, 是], [7, 是, 1, 是, 是], [8, 否, 0, 否, 是], [9, 是, 1, 是, 是], [10, 否, 0, 否, 是], [11, 是, 1, 是, 是], [12, 否, 0, 否, 是]], [[0, 否, 10, 否, 是], [1, 是, 11, 是, 是]], [10, 11, 10, 11, 10, 11, 10, 11, 10, 11, 10, 11, 10], [[0, 否, 10, 否, 是], [1, 是, 11, 是, 是], [2, 否, 10, 否, 是], [3, 是, 11, 是, 是], [4, 否, 10, 否, 是], [5, 是, 11, 是, 是], [6, 否, 10, 否, 是], [7, 是, 11, 是, 是], [8, 否, 10, 否, 是], [9, 是, 11, 是, 是], [10, 否, 10, 否, 是], [11, 是, 11, 是, 是], [12, 否, 10, 否, 是]], 是, A_le_m_B_and_B_le_m_C_imply_A_le_m_C_in_that_direction_only)；依完整明示資料獨立重算；composition與decider transfer保持A≤mB的方向；partial map與yes-only檢查無效；finite table只證finite domain instance，不證無限domain computability；不混同Turing reduction或反向decidability transfer。"},"difficulty":{"band":"undergraduate_core","level":2,"skills":["多對一歸約"]},"variant":{"family_id":"qf-mod46-mreduction-composition-direction","seed":202611157061,"parameters":{"source_carrier":[0,1,2,3,4,5,6,7,8,9,10,11,12],"middle_carrier":[0,1],"target_carrier":[10,11],"source_yes":[1,3,5,7,9,11],"middle_yes":[1],"target_yes":[11],"mapping_ab":[0,1,0,1,0,1,0,1,0,1,0,1,0],"mapping_bc":[10,11],"domain":"Complete_finite_many_one_reduction","operation":"mreduction-composition-direction","semantic_template":"qf-mod46-mreduction-composition-direction/{\"mapping_ab\":[0,1,0,1,0,1,0,1,0,1,0,1,0],\"mapping_bc\":[10,11],\"middle_carrier\":[0,1],\"middle_yes\":[1],\"source_carrier\":[0,1,2,3,4,5,6,7,8,9,10,11,12],\"source_yes\":[1,11,3,5,7,9],\"target_carrier\":[10,11],\"target_yes\":[11]}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_or_symbolic_model","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"候選須主端重算；不構成人工審定、一般第一同構／strong duality／max-flow-min-cut證明、class equation、consistency、integrality、König theorem、無限domain computability、Lean或Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-15","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261015-advance-20261115-r07-many-one-reduction-0062","batch_id":"batch-20261015-advance-20261115-r07-many-one-reduction-foundations","language":"zh-Hant","source_mko_ids":["mko-many-one-reduction"],"title_zh":"多對一歸約","stem_zh":"明示decision predicates與complete total map的雙向membership equivalence。操作=mreduction-composition-direction；資料={\"source_carrier\":[0,1,2,3,4,5,6,7,8,9,10,11,12,13],\"middle_carrier\":[0,1],\"target_carrier\":[10,11],\"source_yes\":[1,3,5,7,9,11,13],\"middle_yes\":[1],\"target_yes\":[11],\"mapping_ab\":[0,1,0,1,0,1,0,1,0,1,0,1,0,1],\"mapping_bc\":[10,11]}。請依 exact_ordered_tuple_declared_by_interface 欄序回答。","answer":{"kind":"expression","value":"([[0, 否, 0, 否, 是], [1, 是, 1, 是, 是], [2, 否, 0, 否, 是], [3, 是, 1, 是, 是], [4, 否, 0, 否, 是], [5, 是, 1, 是, 是], [6, 否, 0, 否, 是], [7, 是, 1, 是, 是], [8, 否, 0, 否, 是], [9, 是, 1, 是, 是], [10, 否, 0, 否, 是], [11, 是, 1, 是, 是], [12, 否, 0, 否, 是], [13, 是, 1, 是, 是]], [[0, 否, 10, 否, 是], [1, 是, 11, 是, 是]], [10, 11, 10, 11, 10, 11, 10, 11, 10, 11, 10, 11, 10, 11], [[0, 否, 10, 否, 是], [1, 是, 11, 是, 是], [2, 否, 10, 否, 是], [3, 是, 11, 是, 是], [4, 否, 10, 否, 是], [5, 是, 11, 是, 是], [6, 否, 10, 否, 是], [7, 是, 11, 是, 是], [8, 否, 10, 否, 是], [9, 是, 11, 是, 是], [10, 否, 10, 否, 是], [11, 是, 11, 是, 是], [12, 否, 10, 否, 是], [13, 是, 11, 是, 是]], 是, A_le_m_B_and_B_le_m_C_imply_A_le_m_C_in_that_direction_only)","explanation_zh":"Wave6第九層核對=([[0, 否, 0, 否, 是], [1, 是, 1, 是, 是], [2, 否, 0, 否, 是], [3, 是, 1, 是, 是], [4, 否, 0, 否, 是], [5, 是, 1, 是, 是], [6, 否, 0, 否, 是], [7, 是, 1, 是, 是], [8, 否, 0, 否, 是], [9, 是, 1, 是, 是], [10, 否, 0, 否, 是], [11, 是, 1, 是, 是], [12, 否, 0, 否, 是], [13, 是, 1, 是, 是]], [[0, 否, 10, 否, 是], [1, 是, 11, 是, 是]], [10, 11, 10, 11, 10, 11, 10, 11, 10, 11, 10, 11, 10, 11], [[0, 否, 10, 否, 是], [1, 是, 11, 是, 是], [2, 否, 10, 否, 是], [3, 是, 11, 是, 是], [4, 否, 10, 否, 是], [5, 是, 11, 是, 是], [6, 否, 10, 否, 是], [7, 是, 11, 是, 是], [8, 否, 10, 否, 是], [9, 是, 11, 是, 是], [10, 否, 10, 否, 是], [11, 是, 11, 是, 是], [12, 否, 10, 否, 是], [13, 是, 11, 是, 是]], 是, A_le_m_B_and_B_le_m_C_imply_A_le_m_C_in_that_direction_only)；依完整明示資料獨立重算；composition與decider transfer保持A≤mB的方向；partial map與yes-only檢查無效；finite table只證finite domain instance，不證無限domain computability；不混同Turing reduction或反向decidability transfer。"},"difficulty":{"band":"undergraduate_core","level":2,"skills":["多對一歸約"]},"variant":{"family_id":"qf-mod46-mreduction-composition-direction","seed":202611157062,"parameters":{"source_carrier":[0,1,2,3,4,5,6,7,8,9,10,11,12,13],"middle_carrier":[0,1],"target_carrier":[10,11],"source_yes":[1,3,5,7,9,11,13],"middle_yes":[1],"target_yes":[11],"mapping_ab":[0,1,0,1,0,1,0,1,0,1,0,1,0,1],"mapping_bc":[10,11],"domain":"Complete_finite_many_one_reduction","operation":"mreduction-composition-direction","semantic_template":"qf-mod46-mreduction-composition-direction/{\"mapping_ab\":[0,1,0,1,0,1,0,1,0,1,0,1,0,1],\"mapping_bc\":[10,11],\"middle_carrier\":[0,1],\"middle_yes\":[1],\"source_carrier\":[0,1,2,3,4,5,6,7,8,9,10,11,12,13],\"source_yes\":[1,11,13,3,5,7,9],\"target_carrier\":[10,11],\"target_yes\":[11]}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_or_symbolic_model","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"候選須主端重算；不構成人工審定、一般第一同構／strong duality／max-flow-min-cut證明、class equation、consistency、integrality、König theorem、無限domain computability、Lean或Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-15","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261015-advance-20261115-r07-many-one-reduction-0063","batch_id":"batch-20261015-advance-20261115-r07-many-one-reduction-foundations","language":"zh-Hant","source_mko_ids":["mko-many-one-reduction"],"title_zh":"多對一歸約","stem_zh":"明示decision predicates與complete total map的雙向membership equivalence。操作=mreduction-composition-direction；資料={\"source_carrier\":[0,1,2,3,4,5,6,7,8,9,10,11,12,13,14],\"middle_carrier\":[0,1],\"target_carrier\":[10,11],\"source_yes\":[1,3,5,7,9,11,13],\"middle_yes\":[1],\"target_yes\":[11],\"mapping_ab\":[0,1,0,1,0,1,0,1,0,1,0,1,0,1,0],\"mapping_bc\":[10,11]}。請依 exact_ordered_tuple_declared_by_interface 欄序回答。","answer":{"kind":"expression","value":"([[0, 否, 0, 否, 是], [1, 是, 1, 是, 是], [2, 否, 0, 否, 是], [3, 是, 1, 是, 是], [4, 否, 0, 否, 是], [5, 是, 1, 是, 是], [6, 否, 0, 否, 是], [7, 是, 1, 是, 是], [8, 否, 0, 否, 是], [9, 是, 1, 是, 是], [10, 否, 0, 否, 是], [11, 是, 1, 是, 是], [12, 否, 0, 否, 是], [13, 是, 1, 是, 是], [14, 否, 0, 否, 是]], [[0, 否, 10, 否, 是], [1, 是, 11, 是, 是]], [10, 11, 10, 11, 10, 11, 10, 11, 10, 11, 10, 11, 10, 11, 10], [[0, 否, 10, 否, 是], [1, 是, 11, 是, 是], [2, 否, 10, 否, 是], [3, 是, 11, 是, 是], [4, 否, 10, 否, 是], [5, 是, 11, 是, 是], [6, 否, 10, 否, 是], [7, 是, 11, 是, 是], [8, 否, 10, 否, 是], [9, 是, 11, 是, 是], [10, 否, 10, 否, 是], [11, 是, 11, 是, 是], [12, 否, 10, 否, 是], [13, 是, 11, 是, 是], [14, 否, 10, 否, 是]], 是, A_le_m_B_and_B_le_m_C_imply_A_le_m_C_in_that_direction_only)","explanation_zh":"Wave6第九層核對=([[0, 否, 0, 否, 是], [1, 是, 1, 是, 是], [2, 否, 0, 否, 是], [3, 是, 1, 是, 是], [4, 否, 0, 否, 是], [5, 是, 1, 是, 是], [6, 否, 0, 否, 是], [7, 是, 1, 是, 是], [8, 否, 0, 否, 是], [9, 是, 1, 是, 是], [10, 否, 0, 否, 是], [11, 是, 1, 是, 是], [12, 否, 0, 否, 是], [13, 是, 1, 是, 是], [14, 否, 0, 否, 是]], [[0, 否, 10, 否, 是], [1, 是, 11, 是, 是]], [10, 11, 10, 11, 10, 11, 10, 11, 10, 11, 10, 11, 10, 11, 10], [[0, 否, 10, 否, 是], [1, 是, 11, 是, 是], [2, 否, 10, 否, 是], [3, 是, 11, 是, 是], [4, 否, 10, 否, 是], [5, 是, 11, 是, 是], [6, 否, 10, 否, 是], [7, 是, 11, 是, 是], [8, 否, 10, 否, 是], [9, 是, 11, 是, 是], [10, 否, 10, 否, 是], [11, 是, 11, 是, 是], [12, 否, 10, 否, 是], [13, 是, 11, 是, 是], [14, 否, 10, 否, 是]], 是, A_le_m_B_and_B_le_m_C_imply_A_le_m_C_in_that_direction_only)；依完整明示資料獨立重算；composition與decider transfer保持A≤mB的方向；partial map與yes-only檢查無效；finite table只證finite domain instance，不證無限domain computability；不混同Turing reduction或反向decidability transfer。"},"difficulty":{"band":"undergraduate_core","level":2,"skills":["多對一歸約"]},"variant":{"family_id":"qf-mod46-mreduction-composition-direction","seed":202611157063,"parameters":{"source_carrier":[0,1,2,3,4,5,6,7,8,9,10,11,12,13,14],"middle_carrier":[0,1],"target_carrier":[10,11],"source_yes":[1,3,5,7,9,11,13],"middle_yes":[1],"target_yes":[11],"mapping_ab":[0,1,0,1,0,1,0,1,0,1,0,1,0,1,0],"mapping_bc":[10,11],"domain":"Complete_finite_many_one_reduction","operation":"mreduction-composition-direction","semantic_template":"qf-mod46-mreduction-composition-direction/{\"mapping_ab\":[0,1,0,1,0,1,0,1,0,1,0,1,0,1,0],\"mapping_bc\":[10,11],\"middle_carrier\":[0,1],\"middle_yes\":[1],\"source_carrier\":[0,1,2,3,4,5,6,7,8,9,10,11,12,13,14],\"source_yes\":[1,11,13,3,5,7,9],\"target_carrier\":[10,11],\"target_yes\":[11]}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_or_symbolic_model","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"候選須主端重算；不構成人工審定、一般第一同構／strong duality／max-flow-min-cut證明、class equation、consistency、integrality、König theorem、無限domain computability、Lean或Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-15","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261015-advance-20261115-r07-many-one-reduction-0064","batch_id":"batch-20261015-advance-20261115-r07-many-one-reduction-foundations","language":"zh-Hant","source_mko_ids":["mko-many-one-reduction"],"title_zh":"多對一歸約","stem_zh":"明示decision predicates與complete total map的雙向membership equivalence。操作=mreduction-composition-direction；資料={\"source_carrier\":[0,1,2,3,4,5,6,7,8,9,10,11,12,13,14,15],\"middle_carrier\":[0,1],\"target_carrier\":[10,11],\"source_yes\":[1,3,5,7,9,11,13,15],\"middle_yes\":[1],\"target_yes\":[11],\"mapping_ab\":[0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1],\"mapping_bc\":[10,11]}。請依 exact_ordered_tuple_declared_by_interface 欄序回答。","answer":{"kind":"expression","value":"([[0, 否, 0, 否, 是], [1, 是, 1, 是, 是], [2, 否, 0, 否, 是], [3, 是, 1, 是, 是], [4, 否, 0, 否, 是], [5, 是, 1, 是, 是], [6, 否, 0, 否, 是], [7, 是, 1, 是, 是], [8, 否, 0, 否, 是], [9, 是, 1, 是, 是], [10, 否, 0, 否, 是], [11, 是, 1, 是, 是], [12, 否, 0, 否, 是], [13, 是, 1, 是, 是], [14, 否, 0, 否, 是], [15, 是, 1, 是, 是]], [[0, 否, 10, 否, 是], [1, 是, 11, 是, 是]], [10, 11, 10, 11, 10, 11, 10, 11, 10, 11, 10, 11, 10, 11, 10, 11], [[0, 否, 10, 否, 是], [1, 是, 11, 是, 是], [2, 否, 10, 否, 是], [3, 是, 11, 是, 是], [4, 否, 10, 否, 是], [5, 是, 11, 是, 是], [6, 否, 10, 否, 是], [7, 是, 11, 是, 是], [8, 否, 10, 否, 是], [9, 是, 11, 是, 是], [10, 否, 10, 否, 是], [11, 是, 11, 是, 是], [12, 否, 10, 否, 是], [13, 是, 11, 是, 是], [14, 否, 10, 否, 是], [15, 是, 11, 是, 是]], 是, A_le_m_B_and_B_le_m_C_imply_A_le_m_C_in_that_direction_only)","explanation_zh":"Wave6第九層核對=([[0, 否, 0, 否, 是], [1, 是, 1, 是, 是], [2, 否, 0, 否, 是], [3, 是, 1, 是, 是], [4, 否, 0, 否, 是], [5, 是, 1, 是, 是], [6, 否, 0, 否, 是], [7, 是, 1, 是, 是], [8, 否, 0, 否, 是], [9, 是, 1, 是, 是], [10, 否, 0, 否, 是], [11, 是, 1, 是, 是], [12, 否, 0, 否, 是], [13, 是, 1, 是, 是], [14, 否, 0, 否, 是], [15, 是, 1, 是, 是]], [[0, 否, 10, 否, 是], [1, 是, 11, 是, 是]], [10, 11, 10, 11, 10, 11, 10, 11, 10, 11, 10, 11, 10, 11, 10, 11], [[0, 否, 10, 否, 是], [1, 是, 11, 是, 是], [2, 否, 10, 否, 是], [3, 是, 11, 是, 是], [4, 否, 10, 否, 是], [5, 是, 11, 是, 是], [6, 否, 10, 否, 是], [7, 是, 11, 是, 是], [8, 否, 10, 否, 是], [9, 是, 11, 是, 是], [10, 否, 10, 否, 是], [11, 是, 11, 是, 是], [12, 否, 10, 否, 是], [13, 是, 11, 是, 是], [14, 否, 10, 否, 是], [15, 是, 11, 是, 是]], 是, A_le_m_B_and_B_le_m_C_imply_A_le_m_C_in_that_direction_only)；依完整明示資料獨立重算；composition與decider transfer保持A≤mB的方向；partial map與yes-only檢查無效；finite table只證finite domain instance，不證無限domain computability；不混同Turing reduction或反向decidability transfer。"},"difficulty":{"band":"undergraduate_core","level":2,"skills":["多對一歸約"]},"variant":{"family_id":"qf-mod46-mreduction-composition-direction","seed":202611157064,"parameters":{"source_carrier":[0,1,2,3,4,5,6,7,8,9,10,11,12,13,14,15],"middle_carrier":[0,1],"target_carrier":[10,11],"source_yes":[1,3,5,7,9,11,13,15],"middle_yes":[1],"target_yes":[11],"mapping_ab":[0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1],"mapping_bc":[10,11],"domain":"Complete_finite_many_one_reduction","operation":"mreduction-composition-direction","semantic_template":"qf-mod46-mreduction-composition-direction/{\"mapping_ab\":[0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1],\"mapping_bc\":[10,11],\"middle_carrier\":[0,1],\"middle_yes\":[1],\"source_carrier\":[0,1,2,3,4,5,6,7,8,9,10,11,12,13,14,15],\"source_yes\":[1,11,13,15,3,5,7,9],\"target_carrier\":[10,11],\"target_yes\":[11]}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_or_symbolic_model","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"候選須主端重算；不構成人工審定、一般第一同構／strong duality／max-flow-min-cut證明、class equation、consistency、integrality、König theorem、無限domain computability、Lean或Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-15","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261015-advance-20261115-r07-many-one-reduction-0065","batch_id":"batch-20261015-advance-20261115-r07-many-one-reduction-foundations","language":"zh-Hant","source_mko_ids":["mko-many-one-reduction"],"title_zh":"多對一歸約","stem_zh":"明示decision predicates與complete total map的雙向membership equivalence。操作=mreduction-composition-direction；資料={\"source_carrier\":[0,1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16],\"middle_carrier\":[0,1],\"target_carrier\":[10,11],\"source_yes\":[1,3,5,7,9,11,13,15],\"middle_yes\":[1],\"target_yes\":[11],\"mapping_ab\":[0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0],\"mapping_bc\":[10,11]}。請依 exact_ordered_tuple_declared_by_interface 欄序回答。","answer":{"kind":"expression","value":"([[0, 否, 0, 否, 是], [1, 是, 1, 是, 是], [2, 否, 0, 否, 是], [3, 是, 1, 是, 是], [4, 否, 0, 否, 是], [5, 是, 1, 是, 是], [6, 否, 0, 否, 是], [7, 是, 1, 是, 是], [8, 否, 0, 否, 是], [9, 是, 1, 是, 是], [10, 否, 0, 否, 是], [11, 是, 1, 是, 是], [12, 否, 0, 否, 是], [13, 是, 1, 是, 是], [14, 否, 0, 否, 是], [15, 是, 1, 是, 是], [16, 否, 0, 否, 是]], [[0, 否, 10, 否, 是], [1, 是, 11, 是, 是]], [10, 11, 10, 11, 10, 11, 10, 11, 10, 11, 10, 11, 10, 11, 10, 11, 10], [[0, 否, 10, 否, 是], [1, 是, 11, 是, 是], [2, 否, 10, 否, 是], [3, 是, 11, 是, 是], [4, 否, 10, 否, 是], [5, 是, 11, 是, 是], [6, 否, 10, 否, 是], [7, 是, 11, 是, 是], [8, 否, 10, 否, 是], [9, 是, 11, 是, 是], [10, 否, 10, 否, 是], [11, 是, 11, 是, 是], [12, 否, 10, 否, 是], [13, 是, 11, 是, 是], [14, 否, 10, 否, 是], [15, 是, 11, 是, 是], [16, 否, 10, 否, 是]], 是, A_le_m_B_and_B_le_m_C_imply_A_le_m_C_in_that_direction_only)","explanation_zh":"Wave6第九層核對=([[0, 否, 0, 否, 是], [1, 是, 1, 是, 是], [2, 否, 0, 否, 是], [3, 是, 1, 是, 是], [4, 否, 0, 否, 是], [5, 是, 1, 是, 是], [6, 否, 0, 否, 是], [7, 是, 1, 是, 是], [8, 否, 0, 否, 是], [9, 是, 1, 是, 是], [10, 否, 0, 否, 是], [11, 是, 1, 是, 是], [12, 否, 0, 否, 是], [13, 是, 1, 是, 是], [14, 否, 0, 否, 是], [15, 是, 1, 是, 是], [16, 否, 0, 否, 是]], [[0, 否, 10, 否, 是], [1, 是, 11, 是, 是]], [10, 11, 10, 11, 10, 11, 10, 11, 10, 11, 10, 11, 10, 11, 10, 11, 10], [[0, 否, 10, 否, 是], [1, 是, 11, 是, 是], [2, 否, 10, 否, 是], [3, 是, 11, 是, 是], [4, 否, 10, 否, 是], [5, 是, 11, 是, 是], [6, 否, 10, 否, 是], [7, 是, 11, 是, 是], [8, 否, 10, 否, 是], [9, 是, 11, 是, 是], [10, 否, 10, 否, 是], [11, 是, 11, 是, 是], [12, 否, 10, 否, 是], [13, 是, 11, 是, 是], [14, 否, 10, 否, 是], [15, 是, 11, 是, 是], [16, 否, 10, 否, 是]], 是, A_le_m_B_and_B_le_m_C_imply_A_le_m_C_in_that_direction_only)；依完整明示資料獨立重算；composition與decider transfer保持A≤mB的方向；partial map與yes-only檢查無效；finite table只證finite domain instance，不證無限domain computability；不混同Turing reduction或反向decidability transfer。"},"difficulty":{"band":"undergraduate_core","level":2,"skills":["多對一歸約"]},"variant":{"family_id":"qf-mod46-mreduction-composition-direction","seed":202611157065,"parameters":{"source_carrier":[0,1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16],"middle_carrier":[0,1],"target_carrier":[10,11],"source_yes":[1,3,5,7,9,11,13,15],"middle_yes":[1],"target_yes":[11],"mapping_ab":[0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0],"mapping_bc":[10,11],"domain":"Complete_finite_many_one_reduction","operation":"mreduction-composition-direction","semantic_template":"qf-mod46-mreduction-composition-direction/{\"mapping_ab\":[0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0],\"mapping_bc\":[10,11],\"middle_carrier\":[0,1],\"middle_yes\":[1],\"source_carrier\":[0,1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16],\"source_yes\":[1,11,13,15,3,5,7,9],\"target_carrier\":[10,11],\"target_yes\":[11]}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_or_symbolic_model","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"候選須主端重算；不構成人工審定、一般第一同構／strong duality／max-flow-min-cut證明、class equation、consistency、integrality、König theorem、無限domain computability、Lean或Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-15","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261015-advance-20261115-r07-many-one-reduction-0066","batch_id":"batch-20261015-advance-20261115-r07-many-one-reduction-foundations","language":"zh-Hant","source_mko_ids":["mko-many-one-reduction"],"title_zh":"多對一歸約","stem_zh":"明示decision predicates與complete total map的雙向membership equivalence。操作=mreduction-composition-direction；資料={\"source_carrier\":[0,1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17],\"middle_carrier\":[0,1],\"target_carrier\":[10,11],\"source_yes\":[1,3,5,7,9,11,13,15,17],\"middle_yes\":[1],\"target_yes\":[11],\"mapping_ab\":[0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1],\"mapping_bc\":[10,11]}。請依 exact_ordered_tuple_declared_by_interface 欄序回答。","answer":{"kind":"expression","value":"([[0, 否, 0, 否, 是], [1, 是, 1, 是, 是], [2, 否, 0, 否, 是], [3, 是, 1, 是, 是], [4, 否, 0, 否, 是], [5, 是, 1, 是, 是], [6, 否, 0, 否, 是], [7, 是, 1, 是, 是], [8, 否, 0, 否, 是], [9, 是, 1, 是, 是], [10, 否, 0, 否, 是], [11, 是, 1, 是, 是], [12, 否, 0, 否, 是], [13, 是, 1, 是, 是], [14, 否, 0, 否, 是], [15, 是, 1, 是, 是], [16, 否, 0, 否, 是], [17, 是, 1, 是, 是]], [[0, 否, 10, 否, 是], [1, 是, 11, 是, 是]], [10, 11, 10, 11, 10, 11, 10, 11, 10, 11, 10, 11, 10, 11, 10, 11, 10, 11], [[0, 否, 10, 否, 是], [1, 是, 11, 是, 是], [2, 否, 10, 否, 是], [3, 是, 11, 是, 是], [4, 否, 10, 否, 是], [5, 是, 11, 是, 是], [6, 否, 10, 否, 是], [7, 是, 11, 是, 是], [8, 否, 10, 否, 是], [9, 是, 11, 是, 是], [10, 否, 10, 否, 是], [11, 是, 11, 是, 是], [12, 否, 10, 否, 是], [13, 是, 11, 是, 是], [14, 否, 10, 否, 是], [15, 是, 11, 是, 是], [16, 否, 10, 否, 是], [17, 是, 11, 是, 是]], 是, A_le_m_B_and_B_le_m_C_imply_A_le_m_C_in_that_direction_only)","explanation_zh":"Wave6第九層核對=([[0, 否, 0, 否, 是], [1, 是, 1, 是, 是], [2, 否, 0, 否, 是], [3, 是, 1, 是, 是], [4, 否, 0, 否, 是], [5, 是, 1, 是, 是], [6, 否, 0, 否, 是], [7, 是, 1, 是, 是], [8, 否, 0, 否, 是], [9, 是, 1, 是, 是], [10, 否, 0, 否, 是], [11, 是, 1, 是, 是], [12, 否, 0, 否, 是], [13, 是, 1, 是, 是], [14, 否, 0, 否, 是], [15, 是, 1, 是, 是], [16, 否, 0, 否, 是], [17, 是, 1, 是, 是]], [[0, 否, 10, 否, 是], [1, 是, 11, 是, 是]], [10, 11, 10, 11, 10, 11, 10, 11, 10, 11, 10, 11, 10, 11, 10, 11, 10, 11], [[0, 否, 10, 否, 是], [1, 是, 11, 是, 是], [2, 否, 10, 否, 是], [3, 是, 11, 是, 是], [4, 否, 10, 否, 是], [5, 是, 11, 是, 是], [6, 否, 10, 否, 是], [7, 是, 11, 是, 是], [8, 否, 10, 否, 是], [9, 是, 11, 是, 是], [10, 否, 10, 否, 是], [11, 是, 11, 是, 是], [12, 否, 10, 否, 是], [13, 是, 11, 是, 是], [14, 否, 10, 否, 是], [15, 是, 11, 是, 是], [16, 否, 10, 否, 是], [17, 是, 11, 是, 是]], 是, A_le_m_B_and_B_le_m_C_imply_A_le_m_C_in_that_direction_only)；依完整明示資料獨立重算；composition與decider transfer保持A≤mB的方向；partial map與yes-only檢查無效；finite table只證finite domain instance，不證無限domain computability；不混同Turing reduction或反向decidability transfer。"},"difficulty":{"band":"undergraduate_core","level":2,"skills":["多對一歸約"]},"variant":{"family_id":"qf-mod46-mreduction-composition-direction","seed":202611157066,"parameters":{"source_carrier":[0,1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17],"middle_carrier":[0,1],"target_carrier":[10,11],"source_yes":[1,3,5,7,9,11,13,15,17],"middle_yes":[1],"target_yes":[11],"mapping_ab":[0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1],"mapping_bc":[10,11],"domain":"Complete_finite_many_one_reduction","operation":"mreduction-composition-direction","semantic_template":"qf-mod46-mreduction-composition-direction/{\"mapping_ab\":[0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1],\"mapping_bc\":[10,11],\"middle_carrier\":[0,1],\"middle_yes\":[1],\"source_carrier\":[0,1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17],\"source_yes\":[1,11,13,15,17,3,5,7,9],\"target_carrier\":[10,11],\"target_yes\":[11]}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_or_symbolic_model","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"候選須主端重算；不構成人工審定、一般第一同構／strong duality／max-flow-min-cut證明、class equation、consistency、integrality、König theorem、無限domain computability、Lean或Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-15","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261015-advance-20261115-r07-many-one-reduction-0067","batch_id":"batch-20261015-advance-20261115-r07-many-one-reduction-foundations","language":"zh-Hant","source_mko_ids":["mko-many-one-reduction"],"title_zh":"多對一歸約","stem_zh":"明示decision predicates與complete total map的雙向membership equivalence。操作=mreduction-composition-direction；資料={\"source_carrier\":[0,1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18],\"middle_carrier\":[0,1],\"target_carrier\":[10,11],\"source_yes\":[1,3,5,7,9,11,13,15,17],\"middle_yes\":[1],\"target_yes\":[11],\"mapping_ab\":[0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0],\"mapping_bc\":[10,11]}。請依 exact_ordered_tuple_declared_by_interface 欄序回答。","answer":{"kind":"expression","value":"([[0, 否, 0, 否, 是], [1, 是, 1, 是, 是], [2, 否, 0, 否, 是], [3, 是, 1, 是, 是], [4, 否, 0, 否, 是], [5, 是, 1, 是, 是], [6, 否, 0, 否, 是], [7, 是, 1, 是, 是], [8, 否, 0, 否, 是], [9, 是, 1, 是, 是], [10, 否, 0, 否, 是], [11, 是, 1, 是, 是], [12, 否, 0, 否, 是], [13, 是, 1, 是, 是], [14, 否, 0, 否, 是], [15, 是, 1, 是, 是], [16, 否, 0, 否, 是], [17, 是, 1, 是, 是], [18, 否, 0, 否, 是]], [[0, 否, 10, 否, 是], [1, 是, 11, 是, 是]], [10, 11, 10, 11, 10, 11, 10, 11, 10, 11, 10, 11, 10, 11, 10, 11, 10, 11, 10], [[0, 否, 10, 否, 是], [1, 是, 11, 是, 是], [2, 否, 10, 否, 是], [3, 是, 11, 是, 是], [4, 否, 10, 否, 是], [5, 是, 11, 是, 是], [6, 否, 10, 否, 是], [7, 是, 11, 是, 是], [8, 否, 10, 否, 是], [9, 是, 11, 是, 是], [10, 否, 10, 否, 是], [11, 是, 11, 是, 是], [12, 否, 10, 否, 是], [13, 是, 11, 是, 是], [14, 否, 10, 否, 是], [15, 是, 11, 是, 是], [16, 否, 10, 否, 是], [17, 是, 11, 是, 是], [18, 否, 10, 否, 是]], 是, A_le_m_B_and_B_le_m_C_imply_A_le_m_C_in_that_direction_only)","explanation_zh":"Wave6第九層核對=([[0, 否, 0, 否, 是], [1, 是, 1, 是, 是], [2, 否, 0, 否, 是], [3, 是, 1, 是, 是], [4, 否, 0, 否, 是], [5, 是, 1, 是, 是], [6, 否, 0, 否, 是], [7, 是, 1, 是, 是], [8, 否, 0, 否, 是], [9, 是, 1, 是, 是], [10, 否, 0, 否, 是], [11, 是, 1, 是, 是], [12, 否, 0, 否, 是], [13, 是, 1, 是, 是], [14, 否, 0, 否, 是], [15, 是, 1, 是, 是], [16, 否, 0, 否, 是], [17, 是, 1, 是, 是], [18, 否, 0, 否, 是]], [[0, 否, 10, 否, 是], [1, 是, 11, 是, 是]], [10, 11, 10, 11, 10, 11, 10, 11, 10, 11, 10, 11, 10, 11, 10, 11, 10, 11, 10], [[0, 否, 10, 否, 是], [1, 是, 11, 是, 是], [2, 否, 10, 否, 是], [3, 是, 11, 是, 是], [4, 否, 10, 否, 是], [5, 是, 11, 是, 是], [6, 否, 10, 否, 是], [7, 是, 11, 是, 是], [8, 否, 10, 否, 是], [9, 是, 11, 是, 是], [10, 否, 10, 否, 是], [11, 是, 11, 是, 是], [12, 否, 10, 否, 是], [13, 是, 11, 是, 是], [14, 否, 10, 否, 是], [15, 是, 11, 是, 是], [16, 否, 10, 否, 是], [17, 是, 11, 是, 是], [18, 否, 10, 否, 是]], 是, A_le_m_B_and_B_le_m_C_imply_A_le_m_C_in_that_direction_only)；依完整明示資料獨立重算；composition與decider transfer保持A≤mB的方向；partial map與yes-only檢查無效；finite table只證finite domain instance，不證無限domain computability；不混同Turing reduction或反向decidability transfer。"},"difficulty":{"band":"undergraduate_core","level":2,"skills":["多對一歸約"]},"variant":{"family_id":"qf-mod46-mreduction-composition-direction","seed":202611157067,"parameters":{"source_carrier":[0,1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18],"middle_carrier":[0,1],"target_carrier":[10,11],"source_yes":[1,3,5,7,9,11,13,15,17],"middle_yes":[1],"target_yes":[11],"mapping_ab":[0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0],"mapping_bc":[10,11],"domain":"Complete_finite_many_one_reduction","operation":"mreduction-composition-direction","semantic_template":"qf-mod46-mreduction-composition-direction/{\"mapping_ab\":[0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0],\"mapping_bc\":[10,11],\"middle_carrier\":[0,1],\"middle_yes\":[1],\"source_carrier\":[0,1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18],\"source_yes\":[1,11,13,15,17,3,5,7,9],\"target_carrier\":[10,11],\"target_yes\":[11]}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_or_symbolic_model","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"候選須主端重算；不構成人工審定、一般第一同構／strong duality／max-flow-min-cut證明、class equation、consistency、integrality、König theorem、無限domain computability、Lean或Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-15","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261015-advance-20261115-r07-many-one-reduction-0068","batch_id":"batch-20261015-advance-20261115-r07-many-one-reduction-foundations","language":"zh-Hant","source_mko_ids":["mko-many-one-reduction"],"title_zh":"多對一歸約","stem_zh":"明示decision predicates與complete total map的雙向membership equivalence。操作=mreduction-composition-direction；資料={\"source_carrier\":[0,1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,19],\"middle_carrier\":[0,1],\"target_carrier\":[10,11],\"source_yes\":[1,3,5,7,9,11,13,15,17,19],\"middle_yes\":[1],\"target_yes\":[11],\"mapping_ab\":[0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1],\"mapping_bc\":[10,11]}。請依 exact_ordered_tuple_declared_by_interface 欄序回答。","answer":{"kind":"expression","value":"([[0, 否, 0, 否, 是], [1, 是, 1, 是, 是], [2, 否, 0, 否, 是], [3, 是, 1, 是, 是], [4, 否, 0, 否, 是], [5, 是, 1, 是, 是], [6, 否, 0, 否, 是], [7, 是, 1, 是, 是], [8, 否, 0, 否, 是], [9, 是, 1, 是, 是], [10, 否, 0, 否, 是], [11, 是, 1, 是, 是], [12, 否, 0, 否, 是], [13, 是, 1, 是, 是], [14, 否, 0, 否, 是], [15, 是, 1, 是, 是], [16, 否, 0, 否, 是], [17, 是, 1, 是, 是], [18, 否, 0, 否, 是], [19, 是, 1, 是, 是]], [[0, 否, 10, 否, 是], [1, 是, 11, 是, 是]], [10, 11, 10, 11, 10, 11, 10, 11, 10, 11, 10, 11, 10, 11, 10, 11, 10, 11, 10, 11], [[0, 否, 10, 否, 是], [1, 是, 11, 是, 是], [2, 否, 10, 否, 是], [3, 是, 11, 是, 是], [4, 否, 10, 否, 是], [5, 是, 11, 是, 是], [6, 否, 10, 否, 是], [7, 是, 11, 是, 是], [8, 否, 10, 否, 是], [9, 是, 11, 是, 是], [10, 否, 10, 否, 是], [11, 是, 11, 是, 是], [12, 否, 10, 否, 是], [13, 是, 11, 是, 是], [14, 否, 10, 否, 是], [15, 是, 11, 是, 是], [16, 否, 10, 否, 是], [17, 是, 11, 是, 是], [18, 否, 10, 否, 是], [19, 是, 11, 是, 是]], 是, A_le_m_B_and_B_le_m_C_imply_A_le_m_C_in_that_direction_only)","explanation_zh":"Wave6第九層核對=([[0, 否, 0, 否, 是], [1, 是, 1, 是, 是], [2, 否, 0, 否, 是], [3, 是, 1, 是, 是], [4, 否, 0, 否, 是], [5, 是, 1, 是, 是], [6, 否, 0, 否, 是], [7, 是, 1, 是, 是], [8, 否, 0, 否, 是], [9, 是, 1, 是, 是], [10, 否, 0, 否, 是], [11, 是, 1, 是, 是], [12, 否, 0, 否, 是], [13, 是, 1, 是, 是], [14, 否, 0, 否, 是], [15, 是, 1, 是, 是], [16, 否, 0, 否, 是], [17, 是, 1, 是, 是], [18, 否, 0, 否, 是], [19, 是, 1, 是, 是]], [[0, 否, 10, 否, 是], [1, 是, 11, 是, 是]], [10, 11, 10, 11, 10, 11, 10, 11, 10, 11, 10, 11, 10, 11, 10, 11, 10, 11, 10, 11], [[0, 否, 10, 否, 是], [1, 是, 11, 是, 是], [2, 否, 10, 否, 是], [3, 是, 11, 是, 是], [4, 否, 10, 否, 是], [5, 是, 11, 是, 是], [6, 否, 10, 否, 是], [7, 是, 11, 是, 是], [8, 否, 10, 否, 是], [9, 是, 11, 是, 是], [10, 否, 10, 否, 是], [11, 是, 11, 是, 是], [12, 否, 10, 否, 是], [13, 是, 11, 是, 是], [14, 否, 10, 否, 是], [15, 是, 11, 是, 是], [16, 否, 10, 否, 是], [17, 是, 11, 是, 是], [18, 否, 10, 否, 是], [19, 是, 11, 是, 是]], 是, A_le_m_B_and_B_le_m_C_imply_A_le_m_C_in_that_direction_only)；依完整明示資料獨立重算；composition與decider transfer保持A≤mB的方向；partial map與yes-only檢查無效；finite table只證finite domain instance，不證無限domain computability；不混同Turing reduction或反向decidability transfer。"},"difficulty":{"band":"undergraduate_core","level":3,"skills":["多對一歸約"]},"variant":{"family_id":"qf-mod46-mreduction-composition-direction","seed":202611157068,"parameters":{"source_carrier":[0,1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,19],"middle_carrier":[0,1],"target_carrier":[10,11],"source_yes":[1,3,5,7,9,11,13,15,17,19],"middle_yes":[1],"target_yes":[11],"mapping_ab":[0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1],"mapping_bc":[10,11],"domain":"Complete_finite_many_one_reduction","operation":"mreduction-composition-direction","semantic_template":"qf-mod46-mreduction-composition-direction/{\"mapping_ab\":[0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1],\"mapping_bc\":[10,11],\"middle_carrier\":[0,1],\"middle_yes\":[1],\"source_carrier\":[0,1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,19],\"source_yes\":[1,11,13,15,17,19,3,5,7,9],\"target_carrier\":[10,11],\"target_yes\":[11]}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_or_symbolic_model","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"候選須主端重算；不構成人工審定、一般第一同構／strong duality／max-flow-min-cut證明、class equation、consistency、integrality、König theorem、無限domain computability、Lean或Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-15","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261015-advance-20261115-r07-many-one-reduction-0069","batch_id":"batch-20261015-advance-20261115-r07-many-one-reduction-foundations","language":"zh-Hant","source_mko_ids":["mko-many-one-reduction"],"title_zh":"多對一歸約","stem_zh":"明示decision predicates與complete total map的雙向membership equivalence。操作=mreduction-composition-direction；資料={\"source_carrier\":[0,1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,19,20],\"middle_carrier\":[0,1],\"target_carrier\":[10,11],\"source_yes\":[1,3,5,7,9,11,13,15,17,19],\"middle_yes\":[1],\"target_yes\":[11],\"mapping_ab\":[0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0],\"mapping_bc\":[10,11]}。請依 exact_ordered_tuple_declared_by_interface 欄序回答。","answer":{"kind":"expression","value":"([[0, 否, 0, 否, 是], [1, 是, 1, 是, 是], [2, 否, 0, 否, 是], [3, 是, 1, 是, 是], [4, 否, 0, 否, 是], [5, 是, 1, 是, 是], [6, 否, 0, 否, 是], [7, 是, 1, 是, 是], [8, 否, 0, 否, 是], [9, 是, 1, 是, 是], [10, 否, 0, 否, 是], [11, 是, 1, 是, 是], [12, 否, 0, 否, 是], [13, 是, 1, 是, 是], [14, 否, 0, 否, 是], [15, 是, 1, 是, 是], [16, 否, 0, 否, 是], [17, 是, 1, 是, 是], [18, 否, 0, 否, 是], [19, 是, 1, 是, 是], [20, 否, 0, 否, 是]], [[0, 否, 10, 否, 是], [1, 是, 11, 是, 是]], [10, 11, 10, 11, 10, 11, 10, 11, 10, 11, 10, 11, 10, 11, 10, 11, 10, 11, 10, 11, 10], [[0, 否, 10, 否, 是], [1, 是, 11, 是, 是], [2, 否, 10, 否, 是], [3, 是, 11, 是, 是], [4, 否, 10, 否, 是], [5, 是, 11, 是, 是], [6, 否, 10, 否, 是], [7, 是, 11, 是, 是], [8, 否, 10, 否, 是], [9, 是, 11, 是, 是], [10, 否, 10, 否, 是], [11, 是, 11, 是, 是], [12, 否, 10, 否, 是], [13, 是, 11, 是, 是], [14, 否, 10, 否, 是], [15, 是, 11, 是, 是], [16, 否, 10, 否, 是], [17, 是, 11, 是, 是], [18, 否, 10, 否, 是], [19, 是, 11, 是, 是], [20, 否, 10, 否, 是]], 是, A_le_m_B_and_B_le_m_C_imply_A_le_m_C_in_that_direction_only)","explanation_zh":"Wave6第九層核對=([[0, 否, 0, 否, 是], [1, 是, 1, 是, 是], [2, 否, 0, 否, 是], [3, 是, 1, 是, 是], [4, 否, 0, 否, 是], [5, 是, 1, 是, 是], [6, 否, 0, 否, 是], [7, 是, 1, 是, 是], [8, 否, 0, 否, 是], [9, 是, 1, 是, 是], [10, 否, 0, 否, 是], [11, 是, 1, 是, 是], [12, 否, 0, 否, 是], [13, 是, 1, 是, 是], [14, 否, 0, 否, 是], [15, 是, 1, 是, 是], [16, 否, 0, 否, 是], [17, 是, 1, 是, 是], [18, 否, 0, 否, 是], [19, 是, 1, 是, 是], [20, 否, 0, 否, 是]], [[0, 否, 10, 否, 是], [1, 是, 11, 是, 是]], [10, 11, 10, 11, 10, 11, 10, 11, 10, 11, 10, 11, 10, 11, 10, 11, 10, 11, 10, 11, 10], [[0, 否, 10, 否, 是], [1, 是, 11, 是, 是], [2, 否, 10, 否, 是], [3, 是, 11, 是, 是], [4, 否, 10, 否, 是], [5, 是, 11, 是, 是], [6, 否, 10, 否, 是], [7, 是, 11, 是, 是], [8, 否, 10, 否, 是], [9, 是, 11, 是, 是], [10, 否, 10, 否, 是], [11, 是, 11, 是, 是], [12, 否, 10, 否, 是], [13, 是, 11, 是, 是], [14, 否, 10, 否, 是], [15, 是, 11, 是, 是], [16, 否, 10, 否, 是], [17, 是, 11, 是, 是], [18, 否, 10, 否, 是], [19, 是, 11, 是, 是], [20, 否, 10, 否, 是]], 是, A_le_m_B_and_B_le_m_C_imply_A_le_m_C_in_that_direction_only)；依完整明示資料獨立重算；composition與decider transfer保持A≤mB的方向；partial map與yes-only檢查無效；finite table只證finite domain instance，不證無限domain computability；不混同Turing reduction或反向decidability transfer。"},"difficulty":{"band":"undergraduate_core","level":3,"skills":["多對一歸約"]},"variant":{"family_id":"qf-mod46-mreduction-composition-direction","seed":202611157069,"parameters":{"source_carrier":[0,1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,19,20],"middle_carrier":[0,1],"target_carrier":[10,11],"source_yes":[1,3,5,7,9,11,13,15,17,19],"middle_yes":[1],"target_yes":[11],"mapping_ab":[0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0],"mapping_bc":[10,11],"domain":"Complete_finite_many_one_reduction","operation":"mreduction-composition-direction","semantic_template":"qf-mod46-mreduction-composition-direction/{\"mapping_ab\":[0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0],\"mapping_bc\":[10,11],\"middle_carrier\":[0,1],\"middle_yes\":[1],\"source_carrier\":[0,1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,19,20],\"source_yes\":[1,11,13,15,17,19,3,5,7,9],\"target_carrier\":[10,11],\"target_yes\":[11]}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_or_symbolic_model","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"候選須主端重算；不構成人工審定、一般第一同構／strong duality／max-flow-min-cut證明、class equation、consistency、integrality、König theorem、無限domain computability、Lean或Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-15","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261015-advance-20261115-r07-many-one-reduction-0070","batch_id":"batch-20261015-advance-20261115-r07-many-one-reduction-foundations","language":"zh-Hant","source_mko_ids":["mko-many-one-reduction"],"title_zh":"多對一歸約","stem_zh":"明示decision predicates與complete total map的雙向membership equivalence。操作=mreduction-composition-direction；資料={\"source_carrier\":[0,1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,19,20,21],\"middle_carrier\":[0,1],\"target_carrier\":[10,11],\"source_yes\":[1,3,5,7,9,11,13,15,17,19,21],\"middle_yes\":[1],\"target_yes\":[11],\"mapping_ab\":[0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1],\"mapping_bc\":[10,11]}。請依 exact_ordered_tuple_declared_by_interface 欄序回答。","answer":{"kind":"expression","value":"([[0, 否, 0, 否, 是], [1, 是, 1, 是, 是], [2, 否, 0, 否, 是], [3, 是, 1, 是, 是], [4, 否, 0, 否, 是], [5, 是, 1, 是, 是], [6, 否, 0, 否, 是], [7, 是, 1, 是, 是], [8, 否, 0, 否, 是], [9, 是, 1, 是, 是], [10, 否, 0, 否, 是], [11, 是, 1, 是, 是], [12, 否, 0, 否, 是], [13, 是, 1, 是, 是], [14, 否, 0, 否, 是], [15, 是, 1, 是, 是], [16, 否, 0, 否, 是], [17, 是, 1, 是, 是], [18, 否, 0, 否, 是], [19, 是, 1, 是, 是], [20, 否, 0, 否, 是], [21, 是, 1, 是, 是]], [[0, 否, 10, 否, 是], [1, 是, 11, 是, 是]], [10, 11, 10, 11, 10, 11, 10, 11, 10, 11, 10, 11, 10, 11, 10, 11, 10, 11, 10, 11, 10, 11], [[0, 否, 10, 否, 是], [1, 是, 11, 是, 是], [2, 否, 10, 否, 是], [3, 是, 11, 是, 是], [4, 否, 10, 否, 是], [5, 是, 11, 是, 是], [6, 否, 10, 否, 是], [7, 是, 11, 是, 是], [8, 否, 10, 否, 是], [9, 是, 11, 是, 是], [10, 否, 10, 否, 是], [11, 是, 11, 是, 是], [12, 否, 10, 否, 是], [13, 是, 11, 是, 是], [14, 否, 10, 否, 是], [15, 是, 11, 是, 是], [16, 否, 10, 否, 是], [17, 是, 11, 是, 是], [18, 否, 10, 否, 是], [19, 是, 11, 是, 是], [20, 否, 10, 否, 是], [21, 是, 11, 是, 是]], 是, A_le_m_B_and_B_le_m_C_imply_A_le_m_C_in_that_direction_only)","explanation_zh":"Wave6第九層核對=([[0, 否, 0, 否, 是], [1, 是, 1, 是, 是], [2, 否, 0, 否, 是], [3, 是, 1, 是, 是], [4, 否, 0, 否, 是], [5, 是, 1, 是, 是], [6, 否, 0, 否, 是], [7, 是, 1, 是, 是], [8, 否, 0, 否, 是], [9, 是, 1, 是, 是], [10, 否, 0, 否, 是], [11, 是, 1, 是, 是], [12, 否, 0, 否, 是], [13, 是, 1, 是, 是], [14, 否, 0, 否, 是], [15, 是, 1, 是, 是], [16, 否, 0, 否, 是], [17, 是, 1, 是, 是], [18, 否, 0, 否, 是], [19, 是, 1, 是, 是], [20, 否, 0, 否, 是], [21, 是, 1, 是, 是]], [[0, 否, 10, 否, 是], [1, 是, 11, 是, 是]], [10, 11, 10, 11, 10, 11, 10, 11, 10, 11, 10, 11, 10, 11, 10, 11, 10, 11, 10, 11, 10, 11], [[0, 否, 10, 否, 是], [1, 是, 11, 是, 是], [2, 否, 10, 否, 是], [3, 是, 11, 是, 是], [4, 否, 10, 否, 是], [5, 是, 11, 是, 是], [6, 否, 10, 否, 是], [7, 是, 11, 是, 是], [8, 否, 10, 否, 是], [9, 是, 11, 是, 是], [10, 否, 10, 否, 是], [11, 是, 11, 是, 是], [12, 否, 10, 否, 是], [13, 是, 11, 是, 是], [14, 否, 10, 否, 是], [15, 是, 11, 是, 是], [16, 否, 10, 否, 是], [17, 是, 11, 是, 是], [18, 否, 10, 否, 是], [19, 是, 11, 是, 是], [20, 否, 10, 否, 是], [21, 是, 11, 是, 是]], 是, A_le_m_B_and_B_le_m_C_imply_A_le_m_C_in_that_direction_only)；依完整明示資料獨立重算；composition與decider transfer保持A≤mB的方向；partial map與yes-only檢查無效；finite table只證finite domain instance，不證無限domain computability；不混同Turing reduction或反向decidability transfer。"},"difficulty":{"band":"undergraduate_core","level":3,"skills":["多對一歸約"]},"variant":{"family_id":"qf-mod46-mreduction-composition-direction","seed":202611157070,"parameters":{"source_carrier":[0,1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,19,20,21],"middle_carrier":[0,1],"target_carrier":[10,11],"source_yes":[1,3,5,7,9,11,13,15,17,19,21],"middle_yes":[1],"target_yes":[11],"mapping_ab":[0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1],"mapping_bc":[10,11],"domain":"Complete_finite_many_one_reduction","operation":"mreduction-composition-direction","semantic_template":"qf-mod46-mreduction-composition-direction/{\"mapping_ab\":[0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1],\"mapping_bc\":[10,11],\"middle_carrier\":[0,1],\"middle_yes\":[1],\"source_carrier\":[0,1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,19,20,21],\"source_yes\":[1,11,13,15,17,19,21,3,5,7,9],\"target_carrier\":[10,11],\"target_yes\":[11]}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_or_symbolic_model","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"候選須主端重算；不構成人工審定、一般第一同構／strong duality／max-flow-min-cut證明、class equation、consistency、integrality、König theorem、無限domain computability、Lean或Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-15","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261015-advance-20261115-r07-many-one-reduction-0071","batch_id":"batch-20261015-advance-20261115-r07-many-one-reduction-foundations","language":"zh-Hant","source_mko_ids":["mko-many-one-reduction"],"title_zh":"多對一歸約","stem_zh":"明示decision predicates與complete total map的雙向membership equivalence。操作=mreduction-composition-direction；資料={\"source_carrier\":[0,1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,19,20,21,22],\"middle_carrier\":[0,1],\"target_carrier\":[10,11],\"source_yes\":[1,3,5,7,9,11,13,15,17,19,21],\"middle_yes\":[1],\"target_yes\":[11],\"mapping_ab\":[0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0],\"mapping_bc\":[10,11]}。請依 exact_ordered_tuple_declared_by_interface 欄序回答。","answer":{"kind":"expression","value":"([[0, 否, 0, 否, 是], [1, 是, 1, 是, 是], [2, 否, 0, 否, 是], [3, 是, 1, 是, 是], [4, 否, 0, 否, 是], [5, 是, 1, 是, 是], [6, 否, 0, 否, 是], [7, 是, 1, 是, 是], [8, 否, 0, 否, 是], [9, 是, 1, 是, 是], [10, 否, 0, 否, 是], [11, 是, 1, 是, 是], [12, 否, 0, 否, 是], [13, 是, 1, 是, 是], [14, 否, 0, 否, 是], [15, 是, 1, 是, 是], [16, 否, 0, 否, 是], [17, 是, 1, 是, 是], [18, 否, 0, 否, 是], [19, 是, 1, 是, 是], [20, 否, 0, 否, 是], [21, 是, 1, 是, 是], [22, 否, 0, 否, 是]], [[0, 否, 10, 否, 是], [1, 是, 11, 是, 是]], [10, 11, 10, 11, 10, 11, 10, 11, 10, 11, 10, 11, 10, 11, 10, 11, 10, 11, 10, 11, 10, 11, 10], [[0, 否, 10, 否, 是], [1, 是, 11, 是, 是], [2, 否, 10, 否, 是], [3, 是, 11, 是, 是], [4, 否, 10, 否, 是], [5, 是, 11, 是, 是], [6, 否, 10, 否, 是], [7, 是, 11, 是, 是], [8, 否, 10, 否, 是], [9, 是, 11, 是, 是], [10, 否, 10, 否, 是], [11, 是, 11, 是, 是], [12, 否, 10, 否, 是], [13, 是, 11, 是, 是], [14, 否, 10, 否, 是], [15, 是, 11, 是, 是], [16, 否, 10, 否, 是], [17, 是, 11, 是, 是], [18, 否, 10, 否, 是], [19, 是, 11, 是, 是], [20, 否, 10, 否, 是], [21, 是, 11, 是, 是], [22, 否, 10, 否, 是]], 是, A_le_m_B_and_B_le_m_C_imply_A_le_m_C_in_that_direction_only)","explanation_zh":"Wave6第九層核對=([[0, 否, 0, 否, 是], [1, 是, 1, 是, 是], [2, 否, 0, 否, 是], [3, 是, 1, 是, 是], [4, 否, 0, 否, 是], [5, 是, 1, 是, 是], [6, 否, 0, 否, 是], [7, 是, 1, 是, 是], [8, 否, 0, 否, 是], [9, 是, 1, 是, 是], [10, 否, 0, 否, 是], [11, 是, 1, 是, 是], [12, 否, 0, 否, 是], [13, 是, 1, 是, 是], [14, 否, 0, 否, 是], [15, 是, 1, 是, 是], [16, 否, 0, 否, 是], [17, 是, 1, 是, 是], [18, 否, 0, 否, 是], [19, 是, 1, 是, 是], [20, 否, 0, 否, 是], [21, 是, 1, 是, 是], [22, 否, 0, 否, 是]], [[0, 否, 10, 否, 是], [1, 是, 11, 是, 是]], [10, 11, 10, 11, 10, 11, 10, 11, 10, 11, 10, 11, 10, 11, 10, 11, 10, 11, 10, 11, 10, 11, 10], [[0, 否, 10, 否, 是], [1, 是, 11, 是, 是], [2, 否, 10, 否, 是], [3, 是, 11, 是, 是], [4, 否, 10, 否, 是], [5, 是, 11, 是, 是], [6, 否, 10, 否, 是], [7, 是, 11, 是, 是], [8, 否, 10, 否, 是], [9, 是, 11, 是, 是], [10, 否, 10, 否, 是], [11, 是, 11, 是, 是], [12, 否, 10, 否, 是], [13, 是, 11, 是, 是], [14, 否, 10, 否, 是], [15, 是, 11, 是, 是], [16, 否, 10, 否, 是], [17, 是, 11, 是, 是], [18, 否, 10, 否, 是], [19, 是, 11, 是, 是], [20, 否, 10, 否, 是], [21, 是, 11, 是, 是], [22, 否, 10, 否, 是]], 是, A_le_m_B_and_B_le_m_C_imply_A_le_m_C_in_that_direction_only)；依完整明示資料獨立重算；composition與decider transfer保持A≤mB的方向；partial map與yes-only檢查無效；finite table只證finite domain instance，不證無限domain computability；不混同Turing reduction或反向decidability transfer。"},"difficulty":{"band":"undergraduate_core","level":3,"skills":["多對一歸約"]},"variant":{"family_id":"qf-mod46-mreduction-composition-direction","seed":202611157071,"parameters":{"source_carrier":[0,1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,19,20,21,22],"middle_carrier":[0,1],"target_carrier":[10,11],"source_yes":[1,3,5,7,9,11,13,15,17,19,21],"middle_yes":[1],"target_yes":[11],"mapping_ab":[0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0],"mapping_bc":[10,11],"domain":"Complete_finite_many_one_reduction","operation":"mreduction-composition-direction","semantic_template":"qf-mod46-mreduction-composition-direction/{\"mapping_ab\":[0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0],\"mapping_bc\":[10,11],\"middle_carrier\":[0,1],\"middle_yes\":[1],\"source_carrier\":[0,1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,19,20,21,22],\"source_yes\":[1,11,13,15,17,19,21,3,5,7,9],\"target_carrier\":[10,11],\"target_yes\":[11]}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_or_symbolic_model","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"候選須主端重算；不構成人工審定、一般第一同構／strong duality／max-flow-min-cut證明、class equation、consistency、integrality、König theorem、無限domain computability、Lean或Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-15","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261015-advance-20261115-r07-many-one-reduction-0072","batch_id":"batch-20261015-advance-20261115-r07-many-one-reduction-foundations","language":"zh-Hant","source_mko_ids":["mko-many-one-reduction"],"title_zh":"多對一歸約","stem_zh":"明示decision predicates與complete total map的雙向membership equivalence。操作=mreduction-composition-direction；資料={\"source_carrier\":[0,1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,19,20,21,22,23],\"middle_carrier\":[0,1],\"target_carrier\":[10,11],\"source_yes\":[1,3,5,7,9,11,13,15,17,19,21,23],\"middle_yes\":[1],\"target_yes\":[11],\"mapping_ab\":[0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1],\"mapping_bc\":[10,11]}。請依 exact_ordered_tuple_declared_by_interface 欄序回答。","answer":{"kind":"expression","value":"([[0, 否, 0, 否, 是], [1, 是, 1, 是, 是], [2, 否, 0, 否, 是], [3, 是, 1, 是, 是], [4, 否, 0, 否, 是], [5, 是, 1, 是, 是], [6, 否, 0, 否, 是], [7, 是, 1, 是, 是], [8, 否, 0, 否, 是], [9, 是, 1, 是, 是], [10, 否, 0, 否, 是], [11, 是, 1, 是, 是], [12, 否, 0, 否, 是], [13, 是, 1, 是, 是], [14, 否, 0, 否, 是], [15, 是, 1, 是, 是], [16, 否, 0, 否, 是], [17, 是, 1, 是, 是], [18, 否, 0, 否, 是], [19, 是, 1, 是, 是], [20, 否, 0, 否, 是], [21, 是, 1, 是, 是], [22, 否, 0, 否, 是], [23, 是, 1, 是, 是]], [[0, 否, 10, 否, 是], [1, 是, 11, 是, 是]], [10, 11, 10, 11, 10, 11, 10, 11, 10, 11, 10, 11, 10, 11, 10, 11, 10, 11, 10, 11, 10, 11, 10, 11], [[0, 否, 10, 否, 是], [1, 是, 11, 是, 是], [2, 否, 10, 否, 是], [3, 是, 11, 是, 是], [4, 否, 10, 否, 是], [5, 是, 11, 是, 是], [6, 否, 10, 否, 是], [7, 是, 11, 是, 是], [8, 否, 10, 否, 是], [9, 是, 11, 是, 是], [10, 否, 10, 否, 是], [11, 是, 11, 是, 是], [12, 否, 10, 否, 是], [13, 是, 11, 是, 是], [14, 否, 10, 否, 是], [15, 是, 11, 是, 是], [16, 否, 10, 否, 是], [17, 是, 11, 是, 是], [18, 否, 10, 否, 是], [19, 是, 11, 是, 是], [20, 否, 10, 否, 是], [21, 是, 11, 是, 是], [22, 否, 10, 否, 是], [23, 是, 11, 是, 是]], 是, A_le_m_B_and_B_le_m_C_imply_A_le_m_C_in_that_direction_only)","explanation_zh":"Wave6第九層核對=([[0, 否, 0, 否, 是], [1, 是, 1, 是, 是], [2, 否, 0, 否, 是], [3, 是, 1, 是, 是], [4, 否, 0, 否, 是], [5, 是, 1, 是, 是], [6, 否, 0, 否, 是], [7, 是, 1, 是, 是], [8, 否, 0, 否, 是], [9, 是, 1, 是, 是], [10, 否, 0, 否, 是], [11, 是, 1, 是, 是], [12, 否, 0, 否, 是], [13, 是, 1, 是, 是], [14, 否, 0, 否, 是], [15, 是, 1, 是, 是], [16, 否, 0, 否, 是], [17, 是, 1, 是, 是], [18, 否, 0, 否, 是], [19, 是, 1, 是, 是], [20, 否, 0, 否, 是], [21, 是, 1, 是, 是], [22, 否, 0, 否, 是], [23, 是, 1, 是, 是]], [[0, 否, 10, 否, 是], [1, 是, 11, 是, 是]], [10, 11, 10, 11, 10, 11, 10, 11, 10, 11, 10, 11, 10, 11, 10, 11, 10, 11, 10, 11, 10, 11, 10, 11], [[0, 否, 10, 否, 是], [1, 是, 11, 是, 是], [2, 否, 10, 否, 是], [3, 是, 11, 是, 是], [4, 否, 10, 否, 是], [5, 是, 11, 是, 是], [6, 否, 10, 否, 是], [7, 是, 11, 是, 是], [8, 否, 10, 否, 是], [9, 是, 11, 是, 是], [10, 否, 10, 否, 是], [11, 是, 11, 是, 是], [12, 否, 10, 否, 是], [13, 是, 11, 是, 是], [14, 否, 10, 否, 是], [15, 是, 11, 是, 是], [16, 否, 10, 否, 是], [17, 是, 11, 是, 是], [18, 否, 10, 否, 是], [19, 是, 11, 是, 是], [20, 否, 10, 否, 是], [21, 是, 11, 是, 是], [22, 否, 10, 否, 是], [23, 是, 11, 是, 是]], 是, A_le_m_B_and_B_le_m_C_imply_A_le_m_C_in_that_direction_only)；依完整明示資料獨立重算；composition與decider transfer保持A≤mB的方向；partial map與yes-only檢查無效；finite table只證finite domain instance，不證無限domain computability；不混同Turing reduction或反向decidability transfer。"},"difficulty":{"band":"undergraduate_core","level":3,"skills":["多對一歸約"]},"variant":{"family_id":"qf-mod46-mreduction-composition-direction","seed":202611157072,"parameters":{"source_carrier":[0,1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,19,20,21,22,23],"middle_carrier":[0,1],"target_carrier":[10,11],"source_yes":[1,3,5,7,9,11,13,15,17,19,21,23],"middle_yes":[1],"target_yes":[11],"mapping_ab":[0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1],"mapping_bc":[10,11],"domain":"Complete_finite_many_one_reduction","operation":"mreduction-composition-direction","semantic_template":"qf-mod46-mreduction-composition-direction/{\"mapping_ab\":[0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1],\"mapping_bc\":[10,11],\"middle_carrier\":[0,1],\"middle_yes\":[1],\"source_carrier\":[0,1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,19,20,21,22,23],\"source_yes\":[1,11,13,15,17,19,21,23,3,5,7,9],\"target_carrier\":[10,11],\"target_yes\":[11]}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_or_symbolic_model","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"候選須主端重算；不構成人工審定、一般第一同構／strong duality／max-flow-min-cut證明、class equation、consistency、integrality、König theorem、無限domain computability、Lean或Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-15","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261015-advance-20261115-r07-many-one-reduction-0073","batch_id":"batch-20261015-advance-20261115-r07-many-one-reduction-foundations","language":"zh-Hant","source_mko_ids":["mko-many-one-reduction"],"title_zh":"多對一歸約","stem_zh":"明示decision predicates與complete total map的雙向membership equivalence。操作=mreduction-composition-direction；資料={\"source_carrier\":[0,1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,19,20,21,22,23,24],\"middle_carrier\":[0,1],\"target_carrier\":[10,11],\"source_yes\":[1,3,5,7,9,11,13,15,17,19,21,23],\"middle_yes\":[1],\"target_yes\":[11],\"mapping_ab\":[0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0],\"mapping_bc\":[10,11]}。請依 exact_ordered_tuple_declared_by_interface 欄序回答。","answer":{"kind":"expression","value":"([[0, 否, 0, 否, 是], [1, 是, 1, 是, 是], [2, 否, 0, 否, 是], [3, 是, 1, 是, 是], [4, 否, 0, 否, 是], [5, 是, 1, 是, 是], [6, 否, 0, 否, 是], [7, 是, 1, 是, 是], [8, 否, 0, 否, 是], [9, 是, 1, 是, 是], [10, 否, 0, 否, 是], [11, 是, 1, 是, 是], [12, 否, 0, 否, 是], [13, 是, 1, 是, 是], [14, 否, 0, 否, 是], [15, 是, 1, 是, 是], [16, 否, 0, 否, 是], [17, 是, 1, 是, 是], [18, 否, 0, 否, 是], [19, 是, 1, 是, 是], [20, 否, 0, 否, 是], [21, 是, 1, 是, 是], [22, 否, 0, 否, 是], [23, 是, 1, 是, 是], [24, 否, 0, 否, 是]], [[0, 否, 10, 否, 是], [1, 是, 11, 是, 是]], [10, 11, 10, 11, 10, 11, 10, 11, 10, 11, 10, 11, 10, 11, 10, 11, 10, 11, 10, 11, 10, 11, 10, 11, 10], [[0, 否, 10, 否, 是], [1, 是, 11, 是, 是], [2, 否, 10, 否, 是], [3, 是, 11, 是, 是], [4, 否, 10, 否, 是], [5, 是, 11, 是, 是], [6, 否, 10, 否, 是], [7, 是, 11, 是, 是], [8, 否, 10, 否, 是], [9, 是, 11, 是, 是], [10, 否, 10, 否, 是], [11, 是, 11, 是, 是], [12, 否, 10, 否, 是], [13, 是, 11, 是, 是], [14, 否, 10, 否, 是], [15, 是, 11, 是, 是], [16, 否, 10, 否, 是], [17, 是, 11, 是, 是], [18, 否, 10, 否, 是], [19, 是, 11, 是, 是], [20, 否, 10, 否, 是], [21, 是, 11, 是, 是], [22, 否, 10, 否, 是], [23, 是, 11, 是, 是], [24, 否, 10, 否, 是]], 是, A_le_m_B_and_B_le_m_C_imply_A_le_m_C_in_that_direction_only)","explanation_zh":"Wave6第九層核對=([[0, 否, 0, 否, 是], [1, 是, 1, 是, 是], [2, 否, 0, 否, 是], [3, 是, 1, 是, 是], [4, 否, 0, 否, 是], [5, 是, 1, 是, 是], [6, 否, 0, 否, 是], [7, 是, 1, 是, 是], [8, 否, 0, 否, 是], [9, 是, 1, 是, 是], [10, 否, 0, 否, 是], [11, 是, 1, 是, 是], [12, 否, 0, 否, 是], [13, 是, 1, 是, 是], [14, 否, 0, 否, 是], [15, 是, 1, 是, 是], [16, 否, 0, 否, 是], [17, 是, 1, 是, 是], [18, 否, 0, 否, 是], [19, 是, 1, 是, 是], [20, 否, 0, 否, 是], [21, 是, 1, 是, 是], [22, 否, 0, 否, 是], [23, 是, 1, 是, 是], [24, 否, 0, 否, 是]], [[0, 否, 10, 否, 是], [1, 是, 11, 是, 是]], [10, 11, 10, 11, 10, 11, 10, 11, 10, 11, 10, 11, 10, 11, 10, 11, 10, 11, 10, 11, 10, 11, 10, 11, 10], [[0, 否, 10, 否, 是], [1, 是, 11, 是, 是], [2, 否, 10, 否, 是], [3, 是, 11, 是, 是], [4, 否, 10, 否, 是], [5, 是, 11, 是, 是], [6, 否, 10, 否, 是], [7, 是, 11, 是, 是], [8, 否, 10, 否, 是], [9, 是, 11, 是, 是], [10, 否, 10, 否, 是], [11, 是, 11, 是, 是], [12, 否, 10, 否, 是], [13, 是, 11, 是, 是], [14, 否, 10, 否, 是], [15, 是, 11, 是, 是], [16, 否, 10, 否, 是], [17, 是, 11, 是, 是], [18, 否, 10, 否, 是], [19, 是, 11, 是, 是], [20, 否, 10, 否, 是], [21, 是, 11, 是, 是], [22, 否, 10, 否, 是], [23, 是, 11, 是, 是], [24, 否, 10, 否, 是]], 是, A_le_m_B_and_B_le_m_C_imply_A_le_m_C_in_that_direction_only)；依完整明示資料獨立重算；composition與decider transfer保持A≤mB的方向；partial map與yes-only檢查無效；finite table只證finite domain instance，不證無限domain computability；不混同Turing reduction或反向decidability transfer。"},"difficulty":{"band":"undergraduate_core","level":3,"skills":["多對一歸約"]},"variant":{"family_id":"qf-mod46-mreduction-composition-direction","seed":202611157073,"parameters":{"source_carrier":[0,1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,19,20,21,22,23,24],"middle_carrier":[0,1],"target_carrier":[10,11],"source_yes":[1,3,5,7,9,11,13,15,17,19,21,23],"middle_yes":[1],"target_yes":[11],"mapping_ab":[0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0],"mapping_bc":[10,11],"domain":"Complete_finite_many_one_reduction","operation":"mreduction-composition-direction","semantic_template":"qf-mod46-mreduction-composition-direction/{\"mapping_ab\":[0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0],\"mapping_bc\":[10,11],\"middle_carrier\":[0,1],\"middle_yes\":[1],\"source_carrier\":[0,1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,19,20,21,22,23,24],\"source_yes\":[1,11,13,15,17,19,21,23,3,5,7,9],\"target_carrier\":[10,11],\"target_yes\":[11]}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_or_symbolic_model","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"候選須主端重算；不構成人工審定、一般第一同構／strong duality／max-flow-min-cut證明、class equation、consistency、integrality、König theorem、無限domain computability、Lean或Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-15","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261015-advance-20261115-r07-many-one-reduction-0074","batch_id":"batch-20261015-advance-20261115-r07-many-one-reduction-foundations","language":"zh-Hant","source_mko_ids":["mko-many-one-reduction"],"title_zh":"多對一歸約","stem_zh":"明示decision predicates與complete total map的雙向membership equivalence。操作=mreduction-composition-direction；資料={\"source_carrier\":[0,1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,19,20,21,22,23,24,25],\"middle_carrier\":[0,1],\"target_carrier\":[10,11],\"source_yes\":[1,3,5,7,9,11,13,15,17,19,21,23,25],\"middle_yes\":[1],\"target_yes\":[11],\"mapping_ab\":[0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1],\"mapping_bc\":[10,11]}。請依 exact_ordered_tuple_declared_by_interface 欄序回答。","answer":{"kind":"expression","value":"([[0, 否, 0, 否, 是], [1, 是, 1, 是, 是], [2, 否, 0, 否, 是], [3, 是, 1, 是, 是], [4, 否, 0, 否, 是], [5, 是, 1, 是, 是], [6, 否, 0, 否, 是], [7, 是, 1, 是, 是], [8, 否, 0, 否, 是], [9, 是, 1, 是, 是], [10, 否, 0, 否, 是], [11, 是, 1, 是, 是], [12, 否, 0, 否, 是], [13, 是, 1, 是, 是], [14, 否, 0, 否, 是], [15, 是, 1, 是, 是], [16, 否, 0, 否, 是], [17, 是, 1, 是, 是], [18, 否, 0, 否, 是], [19, 是, 1, 是, 是], [20, 否, 0, 否, 是], [21, 是, 1, 是, 是], [22, 否, 0, 否, 是], [23, 是, 1, 是, 是], [24, 否, 0, 否, 是], [25, 是, 1, 是, 是]], [[0, 否, 10, 否, 是], [1, 是, 11, 是, 是]], [10, 11, 10, 11, 10, 11, 10, 11, 10, 11, 10, 11, 10, 11, 10, 11, 10, 11, 10, 11, 10, 11, 10, 11, 10, 11], [[0, 否, 10, 否, 是], [1, 是, 11, 是, 是], [2, 否, 10, 否, 是], [3, 是, 11, 是, 是], [4, 否, 10, 否, 是], [5, 是, 11, 是, 是], [6, 否, 10, 否, 是], [7, 是, 11, 是, 是], [8, 否, 10, 否, 是], [9, 是, 11, 是, 是], [10, 否, 10, 否, 是], [11, 是, 11, 是, 是], [12, 否, 10, 否, 是], [13, 是, 11, 是, 是], [14, 否, 10, 否, 是], [15, 是, 11, 是, 是], [16, 否, 10, 否, 是], [17, 是, 11, 是, 是], [18, 否, 10, 否, 是], [19, 是, 11, 是, 是], [20, 否, 10, 否, 是], [21, 是, 11, 是, 是], [22, 否, 10, 否, 是], [23, 是, 11, 是, 是], [24, 否, 10, 否, 是], [25, 是, 11, 是, 是]], 是, A_le_m_B_and_B_le_m_C_imply_A_le_m_C_in_that_direction_only)","explanation_zh":"Wave6第九層核對=([[0, 否, 0, 否, 是], [1, 是, 1, 是, 是], [2, 否, 0, 否, 是], [3, 是, 1, 是, 是], [4, 否, 0, 否, 是], [5, 是, 1, 是, 是], [6, 否, 0, 否, 是], [7, 是, 1, 是, 是], [8, 否, 0, 否, 是], [9, 是, 1, 是, 是], [10, 否, 0, 否, 是], [11, 是, 1, 是, 是], [12, 否, 0, 否, 是], [13, 是, 1, 是, 是], [14, 否, 0, 否, 是], [15, 是, 1, 是, 是], [16, 否, 0, 否, 是], [17, 是, 1, 是, 是], [18, 否, 0, 否, 是], [19, 是, 1, 是, 是], [20, 否, 0, 否, 是], [21, 是, 1, 是, 是], [22, 否, 0, 否, 是], [23, 是, 1, 是, 是], [24, 否, 0, 否, 是], [25, 是, 1, 是, 是]], [[0, 否, 10, 否, 是], [1, 是, 11, 是, 是]], [10, 11, 10, 11, 10, 11, 10, 11, 10, 11, 10, 11, 10, 11, 10, 11, 10, 11, 10, 11, 10, 11, 10, 11, 10, 11], [[0, 否, 10, 否, 是], [1, 是, 11, 是, 是], [2, 否, 10, 否, 是], [3, 是, 11, 是, 是], [4, 否, 10, 否, 是], [5, 是, 11, 是, 是], [6, 否, 10, 否, 是], [7, 是, 11, 是, 是], [8, 否, 10, 否, 是], [9, 是, 11, 是, 是], [10, 否, 10, 否, 是], [11, 是, 11, 是, 是], [12, 否, 10, 否, 是], [13, 是, 11, 是, 是], [14, 否, 10, 否, 是], [15, 是, 11, 是, 是], [16, 否, 10, 否, 是], [17, 是, 11, 是, 是], [18, 否, 10, 否, 是], [19, 是, 11, 是, 是], [20, 否, 10, 否, 是], [21, 是, 11, 是, 是], [22, 否, 10, 否, 是], [23, 是, 11, 是, 是], [24, 否, 10, 否, 是], [25, 是, 11, 是, 是]], 是, A_le_m_B_and_B_le_m_C_imply_A_le_m_C_in_that_direction_only)；依完整明示資料獨立重算；composition與decider transfer保持A≤mB的方向；partial map與yes-only檢查無效；finite table只證finite domain instance，不證無限domain computability；不混同Turing reduction或反向decidability transfer。"},"difficulty":{"band":"undergraduate_core","level":3,"skills":["多對一歸約"]},"variant":{"family_id":"qf-mod46-mreduction-composition-direction","seed":202611157074,"parameters":{"source_carrier":[0,1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,19,20,21,22,23,24,25],"middle_carrier":[0,1],"target_carrier":[10,11],"source_yes":[1,3,5,7,9,11,13,15,17,19,21,23,25],"middle_yes":[1],"target_yes":[11],"mapping_ab":[0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1],"mapping_bc":[10,11],"domain":"Complete_finite_many_one_reduction","operation":"mreduction-composition-direction","semantic_template":"qf-mod46-mreduction-composition-direction/{\"mapping_ab\":[0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1],\"mapping_bc\":[10,11],\"middle_carrier\":[0,1],\"middle_yes\":[1],\"source_carrier\":[0,1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,19,20,21,22,23,24,25],\"source_yes\":[1,11,13,15,17,19,21,23,25,3,5,7,9],\"target_carrier\":[10,11],\"target_yes\":[11]}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_or_symbolic_model","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"候選須主端重算；不構成人工審定、一般第一同構／strong duality／max-flow-min-cut證明、class equation、consistency、integrality、König theorem、無限domain computability、Lean或Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-15","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261015-advance-20261115-r07-many-one-reduction-0075","batch_id":"batch-20261015-advance-20261115-r07-many-one-reduction-foundations","language":"zh-Hant","source_mko_ids":["mko-many-one-reduction"],"title_zh":"多對一歸約","stem_zh":"明示decision predicates與complete total map的雙向membership equivalence。操作=mreduction-composition-direction；資料={\"source_carrier\":[0,1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,19,20,21,22,23,24,25,26],\"middle_carrier\":[0,1],\"target_carrier\":[10,11],\"source_yes\":[1,3,5,7,9,11,13,15,17,19,21,23,25],\"middle_yes\":[1],\"target_yes\":[11],\"mapping_ab\":[0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0],\"mapping_bc\":[10,11]}。請依 exact_ordered_tuple_declared_by_interface 欄序回答。","answer":{"kind":"expression","value":"([[0, 否, 0, 否, 是], [1, 是, 1, 是, 是], [2, 否, 0, 否, 是], [3, 是, 1, 是, 是], [4, 否, 0, 否, 是], [5, 是, 1, 是, 是], [6, 否, 0, 否, 是], [7, 是, 1, 是, 是], [8, 否, 0, 否, 是], [9, 是, 1, 是, 是], [10, 否, 0, 否, 是], [11, 是, 1, 是, 是], [12, 否, 0, 否, 是], [13, 是, 1, 是, 是], [14, 否, 0, 否, 是], [15, 是, 1, 是, 是], [16, 否, 0, 否, 是], [17, 是, 1, 是, 是], [18, 否, 0, 否, 是], [19, 是, 1, 是, 是], [20, 否, 0, 否, 是], [21, 是, 1, 是, 是], [22, 否, 0, 否, 是], [23, 是, 1, 是, 是], [24, 否, 0, 否, 是], [25, 是, 1, 是, 是], [26, 否, 0, 否, 是]], [[0, 否, 10, 否, 是], [1, 是, 11, 是, 是]], [10, 11, 10, 11, 10, 11, 10, 11, 10, 11, 10, 11, 10, 11, 10, 11, 10, 11, 10, 11, 10, 11, 10, 11, 10, 11, 10], [[0, 否, 10, 否, 是], [1, 是, 11, 是, 是], [2, 否, 10, 否, 是], [3, 是, 11, 是, 是], [4, 否, 10, 否, 是], [5, 是, 11, 是, 是], [6, 否, 10, 否, 是], [7, 是, 11, 是, 是], [8, 否, 10, 否, 是], [9, 是, 11, 是, 是], [10, 否, 10, 否, 是], [11, 是, 11, 是, 是], [12, 否, 10, 否, 是], [13, 是, 11, 是, 是], [14, 否, 10, 否, 是], [15, 是, 11, 是, 是], [16, 否, 10, 否, 是], [17, 是, 11, 是, 是], [18, 否, 10, 否, 是], [19, 是, 11, 是, 是], [20, 否, 10, 否, 是], [21, 是, 11, 是, 是], [22, 否, 10, 否, 是], [23, 是, 11, 是, 是], [24, 否, 10, 否, 是], [25, 是, 11, 是, 是], [26, 否, 10, 否, 是]], 是, A_le_m_B_and_B_le_m_C_imply_A_le_m_C_in_that_direction_only)","explanation_zh":"Wave6第九層核對=([[0, 否, 0, 否, 是], [1, 是, 1, 是, 是], [2, 否, 0, 否, 是], [3, 是, 1, 是, 是], [4, 否, 0, 否, 是], [5, 是, 1, 是, 是], [6, 否, 0, 否, 是], [7, 是, 1, 是, 是], [8, 否, 0, 否, 是], [9, 是, 1, 是, 是], [10, 否, 0, 否, 是], [11, 是, 1, 是, 是], [12, 否, 0, 否, 是], [13, 是, 1, 是, 是], [14, 否, 0, 否, 是], [15, 是, 1, 是, 是], [16, 否, 0, 否, 是], [17, 是, 1, 是, 是], [18, 否, 0, 否, 是], [19, 是, 1, 是, 是], [20, 否, 0, 否, 是], [21, 是, 1, 是, 是], [22, 否, 0, 否, 是], [23, 是, 1, 是, 是], [24, 否, 0, 否, 是], [25, 是, 1, 是, 是], [26, 否, 0, 否, 是]], [[0, 否, 10, 否, 是], [1, 是, 11, 是, 是]], [10, 11, 10, 11, 10, 11, 10, 11, 10, 11, 10, 11, 10, 11, 10, 11, 10, 11, 10, 11, 10, 11, 10, 11, 10, 11, 10], [[0, 否, 10, 否, 是], [1, 是, 11, 是, 是], [2, 否, 10, 否, 是], [3, 是, 11, 是, 是], [4, 否, 10, 否, 是], [5, 是, 11, 是, 是], [6, 否, 10, 否, 是], [7, 是, 11, 是, 是], [8, 否, 10, 否, 是], [9, 是, 11, 是, 是], [10, 否, 10, 否, 是], [11, 是, 11, 是, 是], [12, 否, 10, 否, 是], [13, 是, 11, 是, 是], [14, 否, 10, 否, 是], [15, 是, 11, 是, 是], [16, 否, 10, 否, 是], [17, 是, 11, 是, 是], [18, 否, 10, 否, 是], [19, 是, 11, 是, 是], [20, 否, 10, 否, 是], [21, 是, 11, 是, 是], [22, 否, 10, 否, 是], [23, 是, 11, 是, 是], [24, 否, 10, 否, 是], [25, 是, 11, 是, 是], [26, 否, 10, 否, 是]], 是, A_le_m_B_and_B_le_m_C_imply_A_le_m_C_in_that_direction_only)；依完整明示資料獨立重算；composition與decider transfer保持A≤mB的方向；partial map與yes-only檢查無效；finite table只證finite domain instance，不證無限domain computability；不混同Turing reduction或反向decidability transfer。"},"difficulty":{"band":"undergraduate_core","level":3,"skills":["多對一歸約"]},"variant":{"family_id":"qf-mod46-mreduction-composition-direction","seed":202611157075,"parameters":{"source_carrier":[0,1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,19,20,21,22,23,24,25,26],"middle_carrier":[0,1],"target_carrier":[10,11],"source_yes":[1,3,5,7,9,11,13,15,17,19,21,23,25],"middle_yes":[1],"target_yes":[11],"mapping_ab":[0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0],"mapping_bc":[10,11],"domain":"Complete_finite_many_one_reduction","operation":"mreduction-composition-direction","semantic_template":"qf-mod46-mreduction-composition-direction/{\"mapping_ab\":[0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0],\"mapping_bc\":[10,11],\"middle_carrier\":[0,1],\"middle_yes\":[1],\"source_carrier\":[0,1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,19,20,21,22,23,24,25,26],\"source_yes\":[1,11,13,15,17,19,21,23,25,3,5,7,9],\"target_carrier\":[10,11],\"target_yes\":[11]}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_or_symbolic_model","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"候選須主端重算；不構成人工審定、一般第一同構／strong duality／max-flow-min-cut證明、class equation、consistency、integrality、König theorem、無限domain computability、Lean或Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-15","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261015-advance-20261115-r07-many-one-reduction-0076","batch_id":"batch-20261015-advance-20261115-r07-many-one-reduction-foundations","language":"zh-Hant","source_mko_ids":["mko-many-one-reduction"],"title_zh":"多對一歸約","stem_zh":"明示decision predicates與complete total map的雙向membership equivalence。操作=mreduction-decider-transfer-boundary；資料={\"mode\":\"valid_transfer\",\"source_carrier\":[0,1,2],\"target_carrier\":[0,1],\"source_yes\":[1],\"target_yes\":[1],\"mapping\":[0,1,0],\"target_decider\":[false,true]}。請依 exact_ordered_tuple_declared_by_interface 欄序回答。","answer":{"kind":"expression","value":"(valid_transfer, [[0, 否, 0, 否, 是], [1, 是, 1, 是, 是], [2, 否, 0, 否, 是]], 是, 是, [否, 是], 是, [否, 是, 否], 是, 是, 否, A_le_m_B_plus_B_decidable_transfers_decidability_to_A_not_the_reverse_partial_maps_and_yes_only_checks_are_invalid_and_finite_tables_do_not_prove_infinite_computability)","explanation_zh":"Wave6第九層核對=(valid_transfer, [[0, 否, 0, 否, 是], [1, 是, 1, 是, 是], [2, 否, 0, 否, 是]], 是, 是, [否, 是], 是, [否, 是, 否], 是, 是, 否, A_le_m_B_plus_B_decidable_transfers_decidability_to_A_not_the_reverse_partial_maps_and_yes_only_checks_are_invalid_and_finite_tables_do_not_prove_infinite_computability)；依完整明示資料獨立重算；composition與decider transfer保持A≤mB的方向；partial map與yes-only檢查無效；finite table只證finite domain instance，不證無限domain computability；不混同Turing reduction或反向decidability transfer。"},"difficulty":{"band":"undergraduate_core","level":1,"skills":["多對一歸約"]},"variant":{"family_id":"qf-mod46-mreduction-decider-transfer-boundary","seed":202611157076,"parameters":{"mode":"valid_transfer","source_carrier":[0,1,2],"target_carrier":[0,1],"source_yes":[1],"target_yes":[1],"mapping":[0,1,0],"target_decider":[false,true],"domain":"Complete_finite_many_one_reduction","operation":"mreduction-decider-transfer-boundary","semantic_template":"qf-mod46-mreduction-decider-transfer-boundary/{\"mapping\":[0,1,0],\"mode\":\"valid_transfer\",\"source_carrier\":[0,1,2],\"source_yes\":[1],\"target_carrier\":[0,1],\"target_decider\":[false,true],\"target_yes\":[1]}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_or_symbolic_model","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"候選須主端重算；不構成人工審定、一般第一同構／strong duality／max-flow-min-cut證明、class equation、consistency、integrality、König theorem、無限domain computability、Lean或Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-15","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261015-advance-20261115-r07-many-one-reduction-0077","batch_id":"batch-20261015-advance-20261115-r07-many-one-reduction-foundations","language":"zh-Hant","source_mko_ids":["mko-many-one-reduction"],"title_zh":"多對一歸約","stem_zh":"明示decision predicates與complete total map的雙向membership equivalence。操作=mreduction-decider-transfer-boundary；資料={\"mode\":\"reverse_misuse\",\"source_carrier\":[0,1,2,3],\"target_carrier\":[0,1],\"source_yes\":[1,3],\"target_yes\":[1],\"mapping\":[0,1,0,1],\"target_decider\":[false,true]}。請依 exact_ordered_tuple_declared_by_interface 欄序回答。","answer":{"kind":"expression","value":"(reverse_misuse, [[0, 否, 0, 否, 是], [1, 是, 1, 是, 是], [2, 否, 0, 否, 是], [3, 是, 1, 是, 是]], 是, 是, [否, 是], 是, [否, 是, 否, 是], 是, 否, 否, A_le_m_B_plus_B_decidable_transfers_decidability_to_A_not_the_reverse_partial_maps_and_yes_only_checks_are_invalid_and_finite_tables_do_not_prove_infinite_computability)","explanation_zh":"Wave6第九層核對=(reverse_misuse, [[0, 否, 0, 否, 是], [1, 是, 1, 是, 是], [2, 否, 0, 否, 是], [3, 是, 1, 是, 是]], 是, 是, [否, 是], 是, [否, 是, 否, 是], 是, 否, 否, A_le_m_B_plus_B_decidable_transfers_decidability_to_A_not_the_reverse_partial_maps_and_yes_only_checks_are_invalid_and_finite_tables_do_not_prove_infinite_computability)；依完整明示資料獨立重算；composition與decider transfer保持A≤mB的方向；partial map與yes-only檢查無效；finite table只證finite domain instance，不證無限domain computability；不混同Turing reduction或反向decidability transfer。"},"difficulty":{"band":"undergraduate_core","level":1,"skills":["多對一歸約"]},"variant":{"family_id":"qf-mod46-mreduction-decider-transfer-boundary","seed":202611157077,"parameters":{"mode":"reverse_misuse","source_carrier":[0,1,2,3],"target_carrier":[0,1],"source_yes":[1,3],"target_yes":[1],"mapping":[0,1,0,1],"target_decider":[false,true],"domain":"Complete_finite_many_one_reduction","operation":"mreduction-decider-transfer-boundary","semantic_template":"qf-mod46-mreduction-decider-transfer-boundary/{\"mapping\":[0,1,0,1],\"mode\":\"reverse_misuse\",\"source_carrier\":[0,1,2,3],\"source_yes\":[1,3],\"target_carrier\":[0,1],\"target_decider\":[false,true],\"target_yes\":[1]}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_or_symbolic_model","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"候選須主端重算；不構成人工審定、一般第一同構／strong duality／max-flow-min-cut證明、class equation、consistency、integrality、König theorem、無限domain computability、Lean或Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-15","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261015-advance-20261115-r07-many-one-reduction-0078","batch_id":"batch-20261015-advance-20261115-r07-many-one-reduction-foundations","language":"zh-Hant","source_mko_ids":["mko-many-one-reduction"],"title_zh":"多對一歸約","stem_zh":"明示decision predicates與complete total map的雙向membership equivalence。操作=mreduction-decider-transfer-boundary；資料={\"mode\":\"partial_map\",\"source_carrier\":[0,1,2,3,4],\"target_carrier\":[0,1],\"source_yes\":[1,3],\"target_yes\":[1],\"mapping\":[0,1,0,1,null],\"target_decider\":[false,true]}。請依 exact_ordered_tuple_declared_by_interface 欄序回答。","answer":{"kind":"expression","value":"(partial_map, [[0, 否, 0, 否, 是], [1, 是, 1, 是, 是], [2, 否, 0, 否, 是], [3, 是, 1, 是, 是], [4, 否, null, null, 否]], 否, 否, [否, 是], 是, null, 否, 否, 否, A_le_m_B_plus_B_decidable_transfers_decidability_to_A_not_the_reverse_partial_maps_and_yes_only_checks_are_invalid_and_finite_tables_do_not_prove_infinite_computability)","explanation_zh":"Wave6第九層核對=(partial_map, [[0, 否, 0, 否, 是], [1, 是, 1, 是, 是], [2, 否, 0, 否, 是], [3, 是, 1, 是, 是], [4, 否, null, null, 否]], 否, 否, [否, 是], 是, null, 否, 否, 否, A_le_m_B_plus_B_decidable_transfers_decidability_to_A_not_the_reverse_partial_maps_and_yes_only_checks_are_invalid_and_finite_tables_do_not_prove_infinite_computability)；依完整明示資料獨立重算；composition與decider transfer保持A≤mB的方向；partial map與yes-only檢查無效；finite table只證finite domain instance，不證無限domain computability；不混同Turing reduction或反向decidability transfer。"},"difficulty":{"band":"undergraduate_core","level":1,"skills":["多對一歸約"]},"variant":{"family_id":"qf-mod46-mreduction-decider-transfer-boundary","seed":202611157078,"parameters":{"mode":"partial_map","source_carrier":[0,1,2,3,4],"target_carrier":[0,1],"source_yes":[1,3],"target_yes":[1],"mapping":[0,1,0,1,null],"target_decider":[false,true],"domain":"Complete_finite_many_one_reduction","operation":"mreduction-decider-transfer-boundary","semantic_template":"qf-mod46-mreduction-decider-transfer-boundary/{\"mapping\":[0,1,0,1,null],\"mode\":\"partial_map\",\"source_carrier\":[0,1,2,3,4],\"source_yes\":[1,3],\"target_carrier\":[0,1],\"target_decider\":[false,true],\"target_yes\":[1]}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_or_symbolic_model","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"候選須主端重算；不構成人工審定、一般第一同構／strong duality／max-flow-min-cut證明、class equation、consistency、integrality、König theorem、無限domain computability、Lean或Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-15","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261015-advance-20261115-r07-many-one-reduction-0079","batch_id":"batch-20261015-advance-20261115-r07-many-one-reduction-foundations","language":"zh-Hant","source_mko_ids":["mko-many-one-reduction"],"title_zh":"多對一歸約","stem_zh":"明示decision predicates與complete total map的雙向membership equivalence。操作=mreduction-decider-transfer-boundary；資料={\"mode\":\"one_way_yes_only\",\"source_carrier\":[0,1,2,3,4,5],\"target_carrier\":[0,1],\"source_yes\":[0],\"target_yes\":[0],\"mapping\":[0,0,0,0,0,0],\"target_decider\":[true,false]}。請依 exact_ordered_tuple_declared_by_interface 欄序回答。","answer":{"kind":"expression","value":"(one_way_yes_only, [[0, 是, 0, 是, 是], [1, 否, 0, 是, 否], [2, 否, 0, 是, 否], [3, 否, 0, 是, 否], [4, 否, 0, 是, 否], [5, 否, 0, 是, 否]], 是, 否, [是, 否], 是, [是, 是, 是, 是, 是, 是], 否, 否, 否, A_le_m_B_plus_B_decidable_transfers_decidability_to_A_not_the_reverse_partial_maps_and_yes_only_checks_are_invalid_and_finite_tables_do_not_prove_infinite_computability)","explanation_zh":"Wave6第九層核對=(one_way_yes_only, [[0, 是, 0, 是, 是], [1, 否, 0, 是, 否], [2, 否, 0, 是, 否], [3, 否, 0, 是, 否], [4, 否, 0, 是, 否], [5, 否, 0, 是, 否]], 是, 否, [是, 否], 是, [是, 是, 是, 是, 是, 是], 否, 否, 否, A_le_m_B_plus_B_decidable_transfers_decidability_to_A_not_the_reverse_partial_maps_and_yes_only_checks_are_invalid_and_finite_tables_do_not_prove_infinite_computability)；依完整明示資料獨立重算；composition與decider transfer保持A≤mB的方向；partial map與yes-only檢查無效；finite table只證finite domain instance，不證無限domain computability；不混同Turing reduction或反向decidability transfer。"},"difficulty":{"band":"undergraduate_core","level":1,"skills":["多對一歸約"]},"variant":{"family_id":"qf-mod46-mreduction-decider-transfer-boundary","seed":202611157079,"parameters":{"mode":"one_way_yes_only","source_carrier":[0,1,2,3,4,5],"target_carrier":[0,1],"source_yes":[0],"target_yes":[0],"mapping":[0,0,0,0,0,0],"target_decider":[true,false],"domain":"Complete_finite_many_one_reduction","operation":"mreduction-decider-transfer-boundary","semantic_template":"qf-mod46-mreduction-decider-transfer-boundary/{\"mapping\":[0,0,0,0,0,0],\"mode\":\"one_way_yes_only\",\"source_carrier\":[0,1,2,3,4,5],\"source_yes\":[0],\"target_carrier\":[0,1],\"target_decider\":[true,false],\"target_yes\":[0]}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_or_symbolic_model","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"候選須主端重算；不構成人工審定、一般第一同構／strong duality／max-flow-min-cut證明、class equation、consistency、integrality、König theorem、無限domain computability、Lean或Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-15","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261015-advance-20261115-r07-many-one-reduction-0080","batch_id":"batch-20261015-advance-20261115-r07-many-one-reduction-foundations","language":"zh-Hant","source_mko_ids":["mko-many-one-reduction"],"title_zh":"多對一歸約","stem_zh":"明示decision predicates與complete total map的雙向membership equivalence。操作=mreduction-decider-transfer-boundary；資料={\"mode\":\"valid_transfer\",\"source_carrier\":[0,1,2,3,4,5,6],\"target_carrier\":[0,1],\"source_yes\":[1,3,5],\"target_yes\":[1],\"mapping\":[0,1,0,1,0,1,0],\"target_decider\":[false,true]}。請依 exact_ordered_tuple_declared_by_interface 欄序回答。","answer":{"kind":"expression","value":"(valid_transfer, [[0, 否, 0, 否, 是], [1, 是, 1, 是, 是], [2, 否, 0, 否, 是], [3, 是, 1, 是, 是], [4, 否, 0, 否, 是], [5, 是, 1, 是, 是], [6, 否, 0, 否, 是]], 是, 是, [否, 是], 是, [否, 是, 否, 是, 否, 是, 否], 是, 是, 否, A_le_m_B_plus_B_decidable_transfers_decidability_to_A_not_the_reverse_partial_maps_and_yes_only_checks_are_invalid_and_finite_tables_do_not_prove_infinite_computability)","explanation_zh":"Wave6第九層核對=(valid_transfer, [[0, 否, 0, 否, 是], [1, 是, 1, 是, 是], [2, 否, 0, 否, 是], [3, 是, 1, 是, 是], [4, 否, 0, 否, 是], [5, 是, 1, 是, 是], [6, 否, 0, 否, 是]], 是, 是, [否, 是], 是, [否, 是, 否, 是, 否, 是, 否], 是, 是, 否, A_le_m_B_plus_B_decidable_transfers_decidability_to_A_not_the_reverse_partial_maps_and_yes_only_checks_are_invalid_and_finite_tables_do_not_prove_infinite_computability)；依完整明示資料獨立重算；composition與decider transfer保持A≤mB的方向；partial map與yes-only檢查無效；finite table只證finite domain instance，不證無限domain computability；不混同Turing reduction或反向decidability transfer。"},"difficulty":{"band":"undergraduate_core","level":1,"skills":["多對一歸約"]},"variant":{"family_id":"qf-mod46-mreduction-decider-transfer-boundary","seed":202611157080,"parameters":{"mode":"valid_transfer","source_carrier":[0,1,2,3,4,5,6],"target_carrier":[0,1],"source_yes":[1,3,5],"target_yes":[1],"mapping":[0,1,0,1,0,1,0],"target_decider":[false,true],"domain":"Complete_finite_many_one_reduction","operation":"mreduction-decider-transfer-boundary","semantic_template":"qf-mod46-mreduction-decider-transfer-boundary/{\"mapping\":[0,1,0,1,0,1,0],\"mode\":\"valid_transfer\",\"source_carrier\":[0,1,2,3,4,5,6],\"source_yes\":[1,3,5],\"target_carrier\":[0,1],\"target_decider\":[false,true],\"target_yes\":[1]}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_or_symbolic_model","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"候選須主端重算；不構成人工審定、一般第一同構／strong duality／max-flow-min-cut證明、class equation、consistency、integrality、König theorem、無限domain computability、Lean或Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-15","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261015-advance-20261115-r07-many-one-reduction-0081","batch_id":"batch-20261015-advance-20261115-r07-many-one-reduction-foundations","language":"zh-Hant","source_mko_ids":["mko-many-one-reduction"],"title_zh":"多對一歸約","stem_zh":"明示decision predicates與complete total map的雙向membership equivalence。操作=mreduction-decider-transfer-boundary；資料={\"mode\":\"reverse_misuse\",\"source_carrier\":[0,1,2,3,4,5,6,7],\"target_carrier\":[0,1],\"source_yes\":[1,3,5,7],\"target_yes\":[1],\"mapping\":[0,1,0,1,0,1,0,1],\"target_decider\":[false,true]}。請依 exact_ordered_tuple_declared_by_interface 欄序回答。","answer":{"kind":"expression","value":"(reverse_misuse, [[0, 否, 0, 否, 是], [1, 是, 1, 是, 是], [2, 否, 0, 否, 是], [3, 是, 1, 是, 是], [4, 否, 0, 否, 是], [5, 是, 1, 是, 是], [6, 否, 0, 否, 是], [7, 是, 1, 是, 是]], 是, 是, [否, 是], 是, [否, 是, 否, 是, 否, 是, 否, 是], 是, 否, 否, A_le_m_B_plus_B_decidable_transfers_decidability_to_A_not_the_reverse_partial_maps_and_yes_only_checks_are_invalid_and_finite_tables_do_not_prove_infinite_computability)","explanation_zh":"Wave6第九層核對=(reverse_misuse, [[0, 否, 0, 否, 是], [1, 是, 1, 是, 是], [2, 否, 0, 否, 是], [3, 是, 1, 是, 是], [4, 否, 0, 否, 是], [5, 是, 1, 是, 是], [6, 否, 0, 否, 是], [7, 是, 1, 是, 是]], 是, 是, [否, 是], 是, [否, 是, 否, 是, 否, 是, 否, 是], 是, 否, 否, A_le_m_B_plus_B_decidable_transfers_decidability_to_A_not_the_reverse_partial_maps_and_yes_only_checks_are_invalid_and_finite_tables_do_not_prove_infinite_computability)；依完整明示資料獨立重算；composition與decider transfer保持A≤mB的方向；partial map與yes-only檢查無效；finite table只證finite domain instance，不證無限domain computability；不混同Turing reduction或反向decidability transfer。"},"difficulty":{"band":"undergraduate_core","level":1,"skills":["多對一歸約"]},"variant":{"family_id":"qf-mod46-mreduction-decider-transfer-boundary","seed":202611157081,"parameters":{"mode":"reverse_misuse","source_carrier":[0,1,2,3,4,5,6,7],"target_carrier":[0,1],"source_yes":[1,3,5,7],"target_yes":[1],"mapping":[0,1,0,1,0,1,0,1],"target_decider":[false,true],"domain":"Complete_finite_many_one_reduction","operation":"mreduction-decider-transfer-boundary","semantic_template":"qf-mod46-mreduction-decider-transfer-boundary/{\"mapping\":[0,1,0,1,0,1,0,1],\"mode\":\"reverse_misuse\",\"source_carrier\":[0,1,2,3,4,5,6,7],\"source_yes\":[1,3,5,7],\"target_carrier\":[0,1],\"target_decider\":[false,true],\"target_yes\":[1]}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_or_symbolic_model","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"候選須主端重算；不構成人工審定、一般第一同構／strong duality／max-flow-min-cut證明、class equation、consistency、integrality、König theorem、無限domain computability、Lean或Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-15","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261015-advance-20261115-r07-many-one-reduction-0082","batch_id":"batch-20261015-advance-20261115-r07-many-one-reduction-foundations","language":"zh-Hant","source_mko_ids":["mko-many-one-reduction"],"title_zh":"多對一歸約","stem_zh":"明示decision predicates與complete total map的雙向membership equivalence。操作=mreduction-decider-transfer-boundary；資料={\"mode\":\"partial_map\",\"source_carrier\":[0,1,2,3,4,5,6,7,8],\"target_carrier\":[0,1],\"source_yes\":[1,3,5,7],\"target_yes\":[1],\"mapping\":[0,1,0,1,0,1,0,1,null],\"target_decider\":[false,true]}。請依 exact_ordered_tuple_declared_by_interface 欄序回答。","answer":{"kind":"expression","value":"(partial_map, [[0, 否, 0, 否, 是], [1, 是, 1, 是, 是], [2, 否, 0, 否, 是], [3, 是, 1, 是, 是], [4, 否, 0, 否, 是], [5, 是, 1, 是, 是], [6, 否, 0, 否, 是], [7, 是, 1, 是, 是], [8, 否, null, null, 否]], 否, 否, [否, 是], 是, null, 否, 否, 否, A_le_m_B_plus_B_decidable_transfers_decidability_to_A_not_the_reverse_partial_maps_and_yes_only_checks_are_invalid_and_finite_tables_do_not_prove_infinite_computability)","explanation_zh":"Wave6第九層核對=(partial_map, [[0, 否, 0, 否, 是], [1, 是, 1, 是, 是], [2, 否, 0, 否, 是], [3, 是, 1, 是, 是], [4, 否, 0, 否, 是], [5, 是, 1, 是, 是], [6, 否, 0, 否, 是], [7, 是, 1, 是, 是], [8, 否, null, null, 否]], 否, 否, [否, 是], 是, null, 否, 否, 否, A_le_m_B_plus_B_decidable_transfers_decidability_to_A_not_the_reverse_partial_maps_and_yes_only_checks_are_invalid_and_finite_tables_do_not_prove_infinite_computability)；依完整明示資料獨立重算；composition與decider transfer保持A≤mB的方向；partial map與yes-only檢查無效；finite table只證finite domain instance，不證無限domain computability；不混同Turing reduction或反向decidability transfer。"},"difficulty":{"band":"undergraduate_core","level":1,"skills":["多對一歸約"]},"variant":{"family_id":"qf-mod46-mreduction-decider-transfer-boundary","seed":202611157082,"parameters":{"mode":"partial_map","source_carrier":[0,1,2,3,4,5,6,7,8],"target_carrier":[0,1],"source_yes":[1,3,5,7],"target_yes":[1],"mapping":[0,1,0,1,0,1,0,1,null],"target_decider":[false,true],"domain":"Complete_finite_many_one_reduction","operation":"mreduction-decider-transfer-boundary","semantic_template":"qf-mod46-mreduction-decider-transfer-boundary/{\"mapping\":[0,1,0,1,0,1,0,1,null],\"mode\":\"partial_map\",\"source_carrier\":[0,1,2,3,4,5,6,7,8],\"source_yes\":[1,3,5,7],\"target_carrier\":[0,1],\"target_decider\":[false,true],\"target_yes\":[1]}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_or_symbolic_model","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"候選須主端重算；不構成人工審定、一般第一同構／strong duality／max-flow-min-cut證明、class equation、consistency、integrality、König theorem、無限domain computability、Lean或Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-15","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261015-advance-20261115-r07-many-one-reduction-0083","batch_id":"batch-20261015-advance-20261115-r07-many-one-reduction-foundations","language":"zh-Hant","source_mko_ids":["mko-many-one-reduction"],"title_zh":"多對一歸約","stem_zh":"明示decision predicates與complete total map的雙向membership equivalence。操作=mreduction-decider-transfer-boundary；資料={\"mode\":\"one_way_yes_only\",\"source_carrier\":[0,1,2,3,4,5,6,7,8,9],\"target_carrier\":[0,1],\"source_yes\":[0],\"target_yes\":[0],\"mapping\":[0,0,0,0,0,0,0,0,0,0],\"target_decider\":[true,false]}。請依 exact_ordered_tuple_declared_by_interface 欄序回答。","answer":{"kind":"expression","value":"(one_way_yes_only, [[0, 是, 0, 是, 是], [1, 否, 0, 是, 否], [2, 否, 0, 是, 否], [3, 否, 0, 是, 否], [4, 否, 0, 是, 否], [5, 否, 0, 是, 否], [6, 否, 0, 是, 否], [7, 否, 0, 是, 否], [8, 否, 0, 是, 否], [9, 否, 0, 是, 否]], 是, 否, [是, 否], 是, [是, 是, 是, 是, 是, 是, 是, 是, 是, 是], 否, 否, 否, A_le_m_B_plus_B_decidable_transfers_decidability_to_A_not_the_reverse_partial_maps_and_yes_only_checks_are_invalid_and_finite_tables_do_not_prove_infinite_computability)","explanation_zh":"Wave6第九層核對=(one_way_yes_only, [[0, 是, 0, 是, 是], [1, 否, 0, 是, 否], [2, 否, 0, 是, 否], [3, 否, 0, 是, 否], [4, 否, 0, 是, 否], [5, 否, 0, 是, 否], [6, 否, 0, 是, 否], [7, 否, 0, 是, 否], [8, 否, 0, 是, 否], [9, 否, 0, 是, 否]], 是, 否, [是, 否], 是, [是, 是, 是, 是, 是, 是, 是, 是, 是, 是], 否, 否, 否, A_le_m_B_plus_B_decidable_transfers_decidability_to_A_not_the_reverse_partial_maps_and_yes_only_checks_are_invalid_and_finite_tables_do_not_prove_infinite_computability)；依完整明示資料獨立重算；composition與decider transfer保持A≤mB的方向；partial map與yes-only檢查無效；finite table只證finite domain instance，不證無限domain computability；不混同Turing reduction或反向decidability transfer。"},"difficulty":{"band":"undergraduate_core","level":1,"skills":["多對一歸約"]},"variant":{"family_id":"qf-mod46-mreduction-decider-transfer-boundary","seed":202611157083,"parameters":{"mode":"one_way_yes_only","source_carrier":[0,1,2,3,4,5,6,7,8,9],"target_carrier":[0,1],"source_yes":[0],"target_yes":[0],"mapping":[0,0,0,0,0,0,0,0,0,0],"target_decider":[true,false],"domain":"Complete_finite_many_one_reduction","operation":"mreduction-decider-transfer-boundary","semantic_template":"qf-mod46-mreduction-decider-transfer-boundary/{\"mapping\":[0,0,0,0,0,0,0,0,0,0],\"mode\":\"one_way_yes_only\",\"source_carrier\":[0,1,2,3,4,5,6,7,8,9],\"source_yes\":[0],\"target_carrier\":[0,1],\"target_decider\":[true,false],\"target_yes\":[0]}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_or_symbolic_model","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"候選須主端重算；不構成人工審定、一般第一同構／strong duality／max-flow-min-cut證明、class equation、consistency、integrality、König theorem、無限domain computability、Lean或Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-15","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261015-advance-20261115-r07-many-one-reduction-0084","batch_id":"batch-20261015-advance-20261115-r07-many-one-reduction-foundations","language":"zh-Hant","source_mko_ids":["mko-many-one-reduction"],"title_zh":"多對一歸約","stem_zh":"明示decision predicates與complete total map的雙向membership equivalence。操作=mreduction-decider-transfer-boundary；資料={\"mode\":\"valid_transfer\",\"source_carrier\":[0,1,2,3,4,5,6,7,8,9,10],\"target_carrier\":[0,1],\"source_yes\":[1,3,5,7,9],\"target_yes\":[1],\"mapping\":[0,1,0,1,0,1,0,1,0,1,0],\"target_decider\":[false,true]}。請依 exact_ordered_tuple_declared_by_interface 欄序回答。","answer":{"kind":"expression","value":"(valid_transfer, [[0, 否, 0, 否, 是], [1, 是, 1, 是, 是], [2, 否, 0, 否, 是], [3, 是, 1, 是, 是], [4, 否, 0, 否, 是], [5, 是, 1, 是, 是], [6, 否, 0, 否, 是], [7, 是, 1, 是, 是], [8, 否, 0, 否, 是], [9, 是, 1, 是, 是], [10, 否, 0, 否, 是]], 是, 是, [否, 是], 是, [否, 是, 否, 是, 否, 是, 否, 是, 否, 是, 否], 是, 是, 否, A_le_m_B_plus_B_decidable_transfers_decidability_to_A_not_the_reverse_partial_maps_and_yes_only_checks_are_invalid_and_finite_tables_do_not_prove_infinite_computability)","explanation_zh":"Wave6第九層核對=(valid_transfer, [[0, 否, 0, 否, 是], [1, 是, 1, 是, 是], [2, 否, 0, 否, 是], [3, 是, 1, 是, 是], [4, 否, 0, 否, 是], [5, 是, 1, 是, 是], [6, 否, 0, 否, 是], [7, 是, 1, 是, 是], [8, 否, 0, 否, 是], [9, 是, 1, 是, 是], [10, 否, 0, 否, 是]], 是, 是, [否, 是], 是, [否, 是, 否, 是, 否, 是, 否, 是, 否, 是, 否], 是, 是, 否, A_le_m_B_plus_B_decidable_transfers_decidability_to_A_not_the_reverse_partial_maps_and_yes_only_checks_are_invalid_and_finite_tables_do_not_prove_infinite_computability)；依完整明示資料獨立重算；composition與decider transfer保持A≤mB的方向；partial map與yes-only檢查無效；finite table只證finite domain instance，不證無限domain computability；不混同Turing reduction或反向decidability transfer。"},"difficulty":{"band":"undergraduate_core","level":2,"skills":["多對一歸約"]},"variant":{"family_id":"qf-mod46-mreduction-decider-transfer-boundary","seed":202611157084,"parameters":{"mode":"valid_transfer","source_carrier":[0,1,2,3,4,5,6,7,8,9,10],"target_carrier":[0,1],"source_yes":[1,3,5,7,9],"target_yes":[1],"mapping":[0,1,0,1,0,1,0,1,0,1,0],"target_decider":[false,true],"domain":"Complete_finite_many_one_reduction","operation":"mreduction-decider-transfer-boundary","semantic_template":"qf-mod46-mreduction-decider-transfer-boundary/{\"mapping\":[0,1,0,1,0,1,0,1,0,1,0],\"mode\":\"valid_transfer\",\"source_carrier\":[0,1,2,3,4,5,6,7,8,9,10],\"source_yes\":[1,3,5,7,9],\"target_carrier\":[0,1],\"target_decider\":[false,true],\"target_yes\":[1]}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_or_symbolic_model","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"候選須主端重算；不構成人工審定、一般第一同構／strong duality／max-flow-min-cut證明、class equation、consistency、integrality、König theorem、無限domain computability、Lean或Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-15","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261015-advance-20261115-r07-many-one-reduction-0085","batch_id":"batch-20261015-advance-20261115-r07-many-one-reduction-foundations","language":"zh-Hant","source_mko_ids":["mko-many-one-reduction"],"title_zh":"多對一歸約","stem_zh":"明示decision predicates與complete total map的雙向membership equivalence。操作=mreduction-decider-transfer-boundary；資料={\"mode\":\"reverse_misuse\",\"source_carrier\":[0,1,2,3,4,5,6,7,8,9,10,11],\"target_carrier\":[0,1],\"source_yes\":[1,3,5,7,9,11],\"target_yes\":[1],\"mapping\":[0,1,0,1,0,1,0,1,0,1,0,1],\"target_decider\":[false,true]}。請依 exact_ordered_tuple_declared_by_interface 欄序回答。","answer":{"kind":"expression","value":"(reverse_misuse, [[0, 否, 0, 否, 是], [1, 是, 1, 是, 是], [2, 否, 0, 否, 是], [3, 是, 1, 是, 是], [4, 否, 0, 否, 是], [5, 是, 1, 是, 是], [6, 否, 0, 否, 是], [7, 是, 1, 是, 是], [8, 否, 0, 否, 是], [9, 是, 1, 是, 是], [10, 否, 0, 否, 是], [11, 是, 1, 是, 是]], 是, 是, [否, 是], 是, [否, 是, 否, 是, 否, 是, 否, 是, 否, 是, 否, 是], 是, 否, 否, A_le_m_B_plus_B_decidable_transfers_decidability_to_A_not_the_reverse_partial_maps_and_yes_only_checks_are_invalid_and_finite_tables_do_not_prove_infinite_computability)","explanation_zh":"Wave6第九層核對=(reverse_misuse, [[0, 否, 0, 否, 是], [1, 是, 1, 是, 是], [2, 否, 0, 否, 是], [3, 是, 1, 是, 是], [4, 否, 0, 否, 是], [5, 是, 1, 是, 是], [6, 否, 0, 否, 是], [7, 是, 1, 是, 是], [8, 否, 0, 否, 是], [9, 是, 1, 是, 是], [10, 否, 0, 否, 是], [11, 是, 1, 是, 是]], 是, 是, [否, 是], 是, [否, 是, 否, 是, 否, 是, 否, 是, 否, 是, 否, 是], 是, 否, 否, A_le_m_B_plus_B_decidable_transfers_decidability_to_A_not_the_reverse_partial_maps_and_yes_only_checks_are_invalid_and_finite_tables_do_not_prove_infinite_computability)；依完整明示資料獨立重算；composition與decider transfer保持A≤mB的方向；partial map與yes-only檢查無效；finite table只證finite domain instance，不證無限domain computability；不混同Turing reduction或反向decidability transfer。"},"difficulty":{"band":"undergraduate_core","level":2,"skills":["多對一歸約"]},"variant":{"family_id":"qf-mod46-mreduction-decider-transfer-boundary","seed":202611157085,"parameters":{"mode":"reverse_misuse","source_carrier":[0,1,2,3,4,5,6,7,8,9,10,11],"target_carrier":[0,1],"source_yes":[1,3,5,7,9,11],"target_yes":[1],"mapping":[0,1,0,1,0,1,0,1,0,1,0,1],"target_decider":[false,true],"domain":"Complete_finite_many_one_reduction","operation":"mreduction-decider-transfer-boundary","semantic_template":"qf-mod46-mreduction-decider-transfer-boundary/{\"mapping\":[0,1,0,1,0,1,0,1,0,1,0,1],\"mode\":\"reverse_misuse\",\"source_carrier\":[0,1,2,3,4,5,6,7,8,9,10,11],\"source_yes\":[1,11,3,5,7,9],\"target_carrier\":[0,1],\"target_decider\":[false,true],\"target_yes\":[1]}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_or_symbolic_model","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"候選須主端重算；不構成人工審定、一般第一同構／strong duality／max-flow-min-cut證明、class equation、consistency、integrality、König theorem、無限domain computability、Lean或Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-15","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261015-advance-20261115-r07-many-one-reduction-0086","batch_id":"batch-20261015-advance-20261115-r07-many-one-reduction-foundations","language":"zh-Hant","source_mko_ids":["mko-many-one-reduction"],"title_zh":"多對一歸約","stem_zh":"明示decision predicates與complete total map的雙向membership equivalence。操作=mreduction-decider-transfer-boundary；資料={\"mode\":\"partial_map\",\"source_carrier\":[0,1,2,3,4,5,6,7,8,9,10,11,12],\"target_carrier\":[0,1],\"source_yes\":[1,3,5,7,9,11],\"target_yes\":[1],\"mapping\":[0,1,0,1,0,1,0,1,0,1,0,1,null],\"target_decider\":[false,true]}。請依 exact_ordered_tuple_declared_by_interface 欄序回答。","answer":{"kind":"expression","value":"(partial_map, [[0, 否, 0, 否, 是], [1, 是, 1, 是, 是], [2, 否, 0, 否, 是], [3, 是, 1, 是, 是], [4, 否, 0, 否, 是], [5, 是, 1, 是, 是], [6, 否, 0, 否, 是], [7, 是, 1, 是, 是], [8, 否, 0, 否, 是], [9, 是, 1, 是, 是], [10, 否, 0, 否, 是], [11, 是, 1, 是, 是], [12, 否, null, null, 否]], 否, 否, [否, 是], 是, null, 否, 否, 否, A_le_m_B_plus_B_decidable_transfers_decidability_to_A_not_the_reverse_partial_maps_and_yes_only_checks_are_invalid_and_finite_tables_do_not_prove_infinite_computability)","explanation_zh":"Wave6第九層核對=(partial_map, [[0, 否, 0, 否, 是], [1, 是, 1, 是, 是], [2, 否, 0, 否, 是], [3, 是, 1, 是, 是], [4, 否, 0, 否, 是], [5, 是, 1, 是, 是], [6, 否, 0, 否, 是], [7, 是, 1, 是, 是], [8, 否, 0, 否, 是], [9, 是, 1, 是, 是], [10, 否, 0, 否, 是], [11, 是, 1, 是, 是], [12, 否, null, null, 否]], 否, 否, [否, 是], 是, null, 否, 否, 否, A_le_m_B_plus_B_decidable_transfers_decidability_to_A_not_the_reverse_partial_maps_and_yes_only_checks_are_invalid_and_finite_tables_do_not_prove_infinite_computability)；依完整明示資料獨立重算；composition與decider transfer保持A≤mB的方向；partial map與yes-only檢查無效；finite table只證finite domain instance，不證無限domain computability；不混同Turing reduction或反向decidability transfer。"},"difficulty":{"band":"undergraduate_core","level":2,"skills":["多對一歸約"]},"variant":{"family_id":"qf-mod46-mreduction-decider-transfer-boundary","seed":202611157086,"parameters":{"mode":"partial_map","source_carrier":[0,1,2,3,4,5,6,7,8,9,10,11,12],"target_carrier":[0,1],"source_yes":[1,3,5,7,9,11],"target_yes":[1],"mapping":[0,1,0,1,0,1,0,1,0,1,0,1,null],"target_decider":[false,true],"domain":"Complete_finite_many_one_reduction","operation":"mreduction-decider-transfer-boundary","semantic_template":"qf-mod46-mreduction-decider-transfer-boundary/{\"mapping\":[0,1,0,1,0,1,0,1,0,1,0,1,null],\"mode\":\"partial_map\",\"source_carrier\":[0,1,2,3,4,5,6,7,8,9,10,11,12],\"source_yes\":[1,11,3,5,7,9],\"target_carrier\":[0,1],\"target_decider\":[false,true],\"target_yes\":[1]}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_or_symbolic_model","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"候選須主端重算；不構成人工審定、一般第一同構／strong duality／max-flow-min-cut證明、class equation、consistency、integrality、König theorem、無限domain computability、Lean或Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-15","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261015-advance-20261115-r07-many-one-reduction-0087","batch_id":"batch-20261015-advance-20261115-r07-many-one-reduction-foundations","language":"zh-Hant","source_mko_ids":["mko-many-one-reduction"],"title_zh":"多對一歸約","stem_zh":"明示decision predicates與complete total map的雙向membership equivalence。操作=mreduction-decider-transfer-boundary；資料={\"mode\":\"one_way_yes_only\",\"source_carrier\":[0,1,2,3,4,5,6,7,8,9,10,11,12,13],\"target_carrier\":[0,1],\"source_yes\":[0],\"target_yes\":[0],\"mapping\":[0,0,0,0,0,0,0,0,0,0,0,0,0,0],\"target_decider\":[true,false]}。請依 exact_ordered_tuple_declared_by_interface 欄序回答。","answer":{"kind":"expression","value":"(one_way_yes_only, [[0, 是, 0, 是, 是], [1, 否, 0, 是, 否], [2, 否, 0, 是, 否], [3, 否, 0, 是, 否], [4, 否, 0, 是, 否], [5, 否, 0, 是, 否], [6, 否, 0, 是, 否], [7, 否, 0, 是, 否], [8, 否, 0, 是, 否], [9, 否, 0, 是, 否], [10, 否, 0, 是, 否], [11, 否, 0, 是, 否], [12, 否, 0, 是, 否], [13, 否, 0, 是, 否]], 是, 否, [是, 否], 是, [是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是], 否, 否, 否, A_le_m_B_plus_B_decidable_transfers_decidability_to_A_not_the_reverse_partial_maps_and_yes_only_checks_are_invalid_and_finite_tables_do_not_prove_infinite_computability)","explanation_zh":"Wave6第九層核對=(one_way_yes_only, [[0, 是, 0, 是, 是], [1, 否, 0, 是, 否], [2, 否, 0, 是, 否], [3, 否, 0, 是, 否], [4, 否, 0, 是, 否], [5, 否, 0, 是, 否], [6, 否, 0, 是, 否], [7, 否, 0, 是, 否], [8, 否, 0, 是, 否], [9, 否, 0, 是, 否], [10, 否, 0, 是, 否], [11, 否, 0, 是, 否], [12, 否, 0, 是, 否], [13, 否, 0, 是, 否]], 是, 否, [是, 否], 是, [是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是], 否, 否, 否, A_le_m_B_plus_B_decidable_transfers_decidability_to_A_not_the_reverse_partial_maps_and_yes_only_checks_are_invalid_and_finite_tables_do_not_prove_infinite_computability)；依完整明示資料獨立重算；composition與decider transfer保持A≤mB的方向；partial map與yes-only檢查無效；finite table只證finite domain instance，不證無限domain computability；不混同Turing reduction或反向decidability transfer。"},"difficulty":{"band":"undergraduate_core","level":2,"skills":["多對一歸約"]},"variant":{"family_id":"qf-mod46-mreduction-decider-transfer-boundary","seed":202611157087,"parameters":{"mode":"one_way_yes_only","source_carrier":[0,1,2,3,4,5,6,7,8,9,10,11,12,13],"target_carrier":[0,1],"source_yes":[0],"target_yes":[0],"mapping":[0,0,0,0,0,0,0,0,0,0,0,0,0,0],"target_decider":[true,false],"domain":"Complete_finite_many_one_reduction","operation":"mreduction-decider-transfer-boundary","semantic_template":"qf-mod46-mreduction-decider-transfer-boundary/{\"mapping\":[0,0,0,0,0,0,0,0,0,0,0,0,0,0],\"mode\":\"one_way_yes_only\",\"source_carrier\":[0,1,2,3,4,5,6,7,8,9,10,11,12,13],\"source_yes\":[0],\"target_carrier\":[0,1],\"target_decider\":[true,false],\"target_yes\":[0]}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_or_symbolic_model","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"候選須主端重算；不構成人工審定、一般第一同構／strong duality／max-flow-min-cut證明、class equation、consistency、integrality、König theorem、無限domain computability、Lean或Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-15","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261015-advance-20261115-r07-many-one-reduction-0088","batch_id":"batch-20261015-advance-20261115-r07-many-one-reduction-foundations","language":"zh-Hant","source_mko_ids":["mko-many-one-reduction"],"title_zh":"多對一歸約","stem_zh":"明示decision predicates與complete total map的雙向membership equivalence。操作=mreduction-decider-transfer-boundary；資料={\"mode\":\"valid_transfer\",\"source_carrier\":[0,1,2,3,4,5,6,7,8,9,10,11,12,13,14],\"target_carrier\":[0,1],\"source_yes\":[1,3,5,7,9,11,13],\"target_yes\":[1],\"mapping\":[0,1,0,1,0,1,0,1,0,1,0,1,0,1,0],\"target_decider\":[false,true]}。請依 exact_ordered_tuple_declared_by_interface 欄序回答。","answer":{"kind":"expression","value":"(valid_transfer, [[0, 否, 0, 否, 是], [1, 是, 1, 是, 是], [2, 否, 0, 否, 是], [3, 是, 1, 是, 是], [4, 否, 0, 否, 是], [5, 是, 1, 是, 是], [6, 否, 0, 否, 是], [7, 是, 1, 是, 是], [8, 否, 0, 否, 是], [9, 是, 1, 是, 是], [10, 否, 0, 否, 是], [11, 是, 1, 是, 是], [12, 否, 0, 否, 是], [13, 是, 1, 是, 是], [14, 否, 0, 否, 是]], 是, 是, [否, 是], 是, [否, 是, 否, 是, 否, 是, 否, 是, 否, 是, 否, 是, 否, 是, 否], 是, 是, 否, A_le_m_B_plus_B_decidable_transfers_decidability_to_A_not_the_reverse_partial_maps_and_yes_only_checks_are_invalid_and_finite_tables_do_not_prove_infinite_computability)","explanation_zh":"Wave6第九層核對=(valid_transfer, [[0, 否, 0, 否, 是], [1, 是, 1, 是, 是], [2, 否, 0, 否, 是], [3, 是, 1, 是, 是], [4, 否, 0, 否, 是], [5, 是, 1, 是, 是], [6, 否, 0, 否, 是], [7, 是, 1, 是, 是], [8, 否, 0, 否, 是], [9, 是, 1, 是, 是], [10, 否, 0, 否, 是], [11, 是, 1, 是, 是], [12, 否, 0, 否, 是], [13, 是, 1, 是, 是], [14, 否, 0, 否, 是]], 是, 是, [否, 是], 是, [否, 是, 否, 是, 否, 是, 否, 是, 否, 是, 否, 是, 否, 是, 否], 是, 是, 否, A_le_m_B_plus_B_decidable_transfers_decidability_to_A_not_the_reverse_partial_maps_and_yes_only_checks_are_invalid_and_finite_tables_do_not_prove_infinite_computability)；依完整明示資料獨立重算；composition與decider transfer保持A≤mB的方向；partial map與yes-only檢查無效；finite table只證finite domain instance，不證無限domain computability；不混同Turing reduction或反向decidability transfer。"},"difficulty":{"band":"undergraduate_core","level":2,"skills":["多對一歸約"]},"variant":{"family_id":"qf-mod46-mreduction-decider-transfer-boundary","seed":202611157088,"parameters":{"mode":"valid_transfer","source_carrier":[0,1,2,3,4,5,6,7,8,9,10,11,12,13,14],"target_carrier":[0,1],"source_yes":[1,3,5,7,9,11,13],"target_yes":[1],"mapping":[0,1,0,1,0,1,0,1,0,1,0,1,0,1,0],"target_decider":[false,true],"domain":"Complete_finite_many_one_reduction","operation":"mreduction-decider-transfer-boundary","semantic_template":"qf-mod46-mreduction-decider-transfer-boundary/{\"mapping\":[0,1,0,1,0,1,0,1,0,1,0,1,0,1,0],\"mode\":\"valid_transfer\",\"source_carrier\":[0,1,2,3,4,5,6,7,8,9,10,11,12,13,14],\"source_yes\":[1,11,13,3,5,7,9],\"target_carrier\":[0,1],\"target_decider\":[false,true],\"target_yes\":[1]}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_or_symbolic_model","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"候選須主端重算；不構成人工審定、一般第一同構／strong duality／max-flow-min-cut證明、class equation、consistency、integrality、König theorem、無限domain computability、Lean或Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-15","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261015-advance-20261115-r07-many-one-reduction-0089","batch_id":"batch-20261015-advance-20261115-r07-many-one-reduction-foundations","language":"zh-Hant","source_mko_ids":["mko-many-one-reduction"],"title_zh":"多對一歸約","stem_zh":"明示decision predicates與complete total map的雙向membership equivalence。操作=mreduction-decider-transfer-boundary；資料={\"mode\":\"reverse_misuse\",\"source_carrier\":[0,1,2,3,4,5,6,7,8,9,10,11,12,13,14,15],\"target_carrier\":[0,1],\"source_yes\":[1,3,5,7,9,11,13,15],\"target_yes\":[1],\"mapping\":[0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1],\"target_decider\":[false,true]}。請依 exact_ordered_tuple_declared_by_interface 欄序回答。","answer":{"kind":"expression","value":"(reverse_misuse, [[0, 否, 0, 否, 是], [1, 是, 1, 是, 是], [2, 否, 0, 否, 是], [3, 是, 1, 是, 是], [4, 否, 0, 否, 是], [5, 是, 1, 是, 是], [6, 否, 0, 否, 是], [7, 是, 1, 是, 是], [8, 否, 0, 否, 是], [9, 是, 1, 是, 是], [10, 否, 0, 否, 是], [11, 是, 1, 是, 是], [12, 否, 0, 否, 是], [13, 是, 1, 是, 是], [14, 否, 0, 否, 是], [15, 是, 1, 是, 是]], 是, 是, [否, 是], 是, [否, 是, 否, 是, 否, 是, 否, 是, 否, 是, 否, 是, 否, 是, 否, 是], 是, 否, 否, A_le_m_B_plus_B_decidable_transfers_decidability_to_A_not_the_reverse_partial_maps_and_yes_only_checks_are_invalid_and_finite_tables_do_not_prove_infinite_computability)","explanation_zh":"Wave6第九層核對=(reverse_misuse, [[0, 否, 0, 否, 是], [1, 是, 1, 是, 是], [2, 否, 0, 否, 是], [3, 是, 1, 是, 是], [4, 否, 0, 否, 是], [5, 是, 1, 是, 是], [6, 否, 0, 否, 是], [7, 是, 1, 是, 是], [8, 否, 0, 否, 是], [9, 是, 1, 是, 是], [10, 否, 0, 否, 是], [11, 是, 1, 是, 是], [12, 否, 0, 否, 是], [13, 是, 1, 是, 是], [14, 否, 0, 否, 是], [15, 是, 1, 是, 是]], 是, 是, [否, 是], 是, [否, 是, 否, 是, 否, 是, 否, 是, 否, 是, 否, 是, 否, 是, 否, 是], 是, 否, 否, A_le_m_B_plus_B_decidable_transfers_decidability_to_A_not_the_reverse_partial_maps_and_yes_only_checks_are_invalid_and_finite_tables_do_not_prove_infinite_computability)；依完整明示資料獨立重算；composition與decider transfer保持A≤mB的方向；partial map與yes-only檢查無效；finite table只證finite domain instance，不證無限domain computability；不混同Turing reduction或反向decidability transfer。"},"difficulty":{"band":"undergraduate_core","level":2,"skills":["多對一歸約"]},"variant":{"family_id":"qf-mod46-mreduction-decider-transfer-boundary","seed":202611157089,"parameters":{"mode":"reverse_misuse","source_carrier":[0,1,2,3,4,5,6,7,8,9,10,11,12,13,14,15],"target_carrier":[0,1],"source_yes":[1,3,5,7,9,11,13,15],"target_yes":[1],"mapping":[0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1],"target_decider":[false,true],"domain":"Complete_finite_many_one_reduction","operation":"mreduction-decider-transfer-boundary","semantic_template":"qf-mod46-mreduction-decider-transfer-boundary/{\"mapping\":[0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1],\"mode\":\"reverse_misuse\",\"source_carrier\":[0,1,2,3,4,5,6,7,8,9,10,11,12,13,14,15],\"source_yes\":[1,11,13,15,3,5,7,9],\"target_carrier\":[0,1],\"target_decider\":[false,true],\"target_yes\":[1]}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_or_symbolic_model","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"候選須主端重算；不構成人工審定、一般第一同構／strong duality／max-flow-min-cut證明、class equation、consistency、integrality、König theorem、無限domain computability、Lean或Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-15","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261015-advance-20261115-r07-many-one-reduction-0090","batch_id":"batch-20261015-advance-20261115-r07-many-one-reduction-foundations","language":"zh-Hant","source_mko_ids":["mko-many-one-reduction"],"title_zh":"多對一歸約","stem_zh":"明示decision predicates與complete total map的雙向membership equivalence。操作=mreduction-decider-transfer-boundary；資料={\"mode\":\"partial_map\",\"source_carrier\":[0,1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16],\"target_carrier\":[0,1],\"source_yes\":[1,3,5,7,9,11,13,15],\"target_yes\":[1],\"mapping\":[0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,null],\"target_decider\":[false,true]}。請依 exact_ordered_tuple_declared_by_interface 欄序回答。","answer":{"kind":"expression","value":"(partial_map, [[0, 否, 0, 否, 是], [1, 是, 1, 是, 是], [2, 否, 0, 否, 是], [3, 是, 1, 是, 是], [4, 否, 0, 否, 是], [5, 是, 1, 是, 是], [6, 否, 0, 否, 是], [7, 是, 1, 是, 是], [8, 否, 0, 否, 是], [9, 是, 1, 是, 是], [10, 否, 0, 否, 是], [11, 是, 1, 是, 是], [12, 否, 0, 否, 是], [13, 是, 1, 是, 是], [14, 否, 0, 否, 是], [15, 是, 1, 是, 是], [16, 否, null, null, 否]], 否, 否, [否, 是], 是, null, 否, 否, 否, A_le_m_B_plus_B_decidable_transfers_decidability_to_A_not_the_reverse_partial_maps_and_yes_only_checks_are_invalid_and_finite_tables_do_not_prove_infinite_computability)","explanation_zh":"Wave6第九層核對=(partial_map, [[0, 否, 0, 否, 是], [1, 是, 1, 是, 是], [2, 否, 0, 否, 是], [3, 是, 1, 是, 是], [4, 否, 0, 否, 是], [5, 是, 1, 是, 是], [6, 否, 0, 否, 是], [7, 是, 1, 是, 是], [8, 否, 0, 否, 是], [9, 是, 1, 是, 是], [10, 否, 0, 否, 是], [11, 是, 1, 是, 是], [12, 否, 0, 否, 是], [13, 是, 1, 是, 是], [14, 否, 0, 否, 是], [15, 是, 1, 是, 是], [16, 否, null, null, 否]], 否, 否, [否, 是], 是, null, 否, 否, 否, A_le_m_B_plus_B_decidable_transfers_decidability_to_A_not_the_reverse_partial_maps_and_yes_only_checks_are_invalid_and_finite_tables_do_not_prove_infinite_computability)；依完整明示資料獨立重算；composition與decider transfer保持A≤mB的方向；partial map與yes-only檢查無效；finite table只證finite domain instance，不證無限domain computability；不混同Turing reduction或反向decidability transfer。"},"difficulty":{"band":"undergraduate_core","level":2,"skills":["多對一歸約"]},"variant":{"family_id":"qf-mod46-mreduction-decider-transfer-boundary","seed":202611157090,"parameters":{"mode":"partial_map","source_carrier":[0,1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16],"target_carrier":[0,1],"source_yes":[1,3,5,7,9,11,13,15],"target_yes":[1],"mapping":[0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,null],"target_decider":[false,true],"domain":"Complete_finite_many_one_reduction","operation":"mreduction-decider-transfer-boundary","semantic_template":"qf-mod46-mreduction-decider-transfer-boundary/{\"mapping\":[0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,null],\"mode\":\"partial_map\",\"source_carrier\":[0,1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16],\"source_yes\":[1,11,13,15,3,5,7,9],\"target_carrier\":[0,1],\"target_decider\":[false,true],\"target_yes\":[1]}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_or_symbolic_model","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"候選須主端重算；不構成人工審定、一般第一同構／strong duality／max-flow-min-cut證明、class equation、consistency、integrality、König theorem、無限domain computability、Lean或Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-15","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261015-advance-20261115-r07-many-one-reduction-0091","batch_id":"batch-20261015-advance-20261115-r07-many-one-reduction-foundations","language":"zh-Hant","source_mko_ids":["mko-many-one-reduction"],"title_zh":"多對一歸約","stem_zh":"明示decision predicates與complete total map的雙向membership equivalence。操作=mreduction-decider-transfer-boundary；資料={\"mode\":\"one_way_yes_only\",\"source_carrier\":[0,1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17],\"target_carrier\":[0,1],\"source_yes\":[0],\"target_yes\":[0],\"mapping\":[0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0],\"target_decider\":[true,false]}。請依 exact_ordered_tuple_declared_by_interface 欄序回答。","answer":{"kind":"expression","value":"(one_way_yes_only, [[0, 是, 0, 是, 是], [1, 否, 0, 是, 否], [2, 否, 0, 是, 否], [3, 否, 0, 是, 否], [4, 否, 0, 是, 否], [5, 否, 0, 是, 否], [6, 否, 0, 是, 否], [7, 否, 0, 是, 否], [8, 否, 0, 是, 否], [9, 否, 0, 是, 否], [10, 否, 0, 是, 否], [11, 否, 0, 是, 否], [12, 否, 0, 是, 否], [13, 否, 0, 是, 否], [14, 否, 0, 是, 否], [15, 否, 0, 是, 否], [16, 否, 0, 是, 否], [17, 否, 0, 是, 否]], 是, 否, [是, 否], 是, [是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是], 否, 否, 否, A_le_m_B_plus_B_decidable_transfers_decidability_to_A_not_the_reverse_partial_maps_and_yes_only_checks_are_invalid_and_finite_tables_do_not_prove_infinite_computability)","explanation_zh":"Wave6第九層核對=(one_way_yes_only, [[0, 是, 0, 是, 是], [1, 否, 0, 是, 否], [2, 否, 0, 是, 否], [3, 否, 0, 是, 否], [4, 否, 0, 是, 否], [5, 否, 0, 是, 否], [6, 否, 0, 是, 否], [7, 否, 0, 是, 否], [8, 否, 0, 是, 否], [9, 否, 0, 是, 否], [10, 否, 0, 是, 否], [11, 否, 0, 是, 否], [12, 否, 0, 是, 否], [13, 否, 0, 是, 否], [14, 否, 0, 是, 否], [15, 否, 0, 是, 否], [16, 否, 0, 是, 否], [17, 否, 0, 是, 否]], 是, 否, [是, 否], 是, [是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是], 否, 否, 否, A_le_m_B_plus_B_decidable_transfers_decidability_to_A_not_the_reverse_partial_maps_and_yes_only_checks_are_invalid_and_finite_tables_do_not_prove_infinite_computability)；依完整明示資料獨立重算；composition與decider transfer保持A≤mB的方向；partial map與yes-only檢查無效；finite table只證finite domain instance，不證無限domain computability；不混同Turing reduction或反向decidability transfer。"},"difficulty":{"band":"undergraduate_core","level":2,"skills":["多對一歸約"]},"variant":{"family_id":"qf-mod46-mreduction-decider-transfer-boundary","seed":202611157091,"parameters":{"mode":"one_way_yes_only","source_carrier":[0,1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17],"target_carrier":[0,1],"source_yes":[0],"target_yes":[0],"mapping":[0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0],"target_decider":[true,false],"domain":"Complete_finite_many_one_reduction","operation":"mreduction-decider-transfer-boundary","semantic_template":"qf-mod46-mreduction-decider-transfer-boundary/{\"mapping\":[0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0],\"mode\":\"one_way_yes_only\",\"source_carrier\":[0,1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17],\"source_yes\":[0],\"target_carrier\":[0,1],\"target_decider\":[true,false],\"target_yes\":[0]}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_or_symbolic_model","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"候選須主端重算；不構成人工審定、一般第一同構／strong duality／max-flow-min-cut證明、class equation、consistency、integrality、König theorem、無限domain computability、Lean或Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-15","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261015-advance-20261115-r07-many-one-reduction-0092","batch_id":"batch-20261015-advance-20261115-r07-many-one-reduction-foundations","language":"zh-Hant","source_mko_ids":["mko-many-one-reduction"],"title_zh":"多對一歸約","stem_zh":"明示decision predicates與complete total map的雙向membership equivalence。操作=mreduction-decider-transfer-boundary；資料={\"mode\":\"valid_transfer\",\"source_carrier\":[0,1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18],\"target_carrier\":[0,1],\"source_yes\":[1,3,5,7,9,11,13,15,17],\"target_yes\":[1],\"mapping\":[0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0],\"target_decider\":[false,true]}。請依 exact_ordered_tuple_declared_by_interface 欄序回答。","answer":{"kind":"expression","value":"(valid_transfer, [[0, 否, 0, 否, 是], [1, 是, 1, 是, 是], [2, 否, 0, 否, 是], [3, 是, 1, 是, 是], [4, 否, 0, 否, 是], [5, 是, 1, 是, 是], [6, 否, 0, 否, 是], [7, 是, 1, 是, 是], [8, 否, 0, 否, 是], [9, 是, 1, 是, 是], [10, 否, 0, 否, 是], [11, 是, 1, 是, 是], [12, 否, 0, 否, 是], [13, 是, 1, 是, 是], [14, 否, 0, 否, 是], [15, 是, 1, 是, 是], [16, 否, 0, 否, 是], [17, 是, 1, 是, 是], [18, 否, 0, 否, 是]], 是, 是, [否, 是], 是, [否, 是, 否, 是, 否, 是, 否, 是, 否, 是, 否, 是, 否, 是, 否, 是, 否, 是, 否], 是, 是, 否, A_le_m_B_plus_B_decidable_transfers_decidability_to_A_not_the_reverse_partial_maps_and_yes_only_checks_are_invalid_and_finite_tables_do_not_prove_infinite_computability)","explanation_zh":"Wave6第九層核對=(valid_transfer, [[0, 否, 0, 否, 是], [1, 是, 1, 是, 是], [2, 否, 0, 否, 是], [3, 是, 1, 是, 是], [4, 否, 0, 否, 是], [5, 是, 1, 是, 是], [6, 否, 0, 否, 是], [7, 是, 1, 是, 是], [8, 否, 0, 否, 是], [9, 是, 1, 是, 是], [10, 否, 0, 否, 是], [11, 是, 1, 是, 是], [12, 否, 0, 否, 是], [13, 是, 1, 是, 是], [14, 否, 0, 否, 是], [15, 是, 1, 是, 是], [16, 否, 0, 否, 是], [17, 是, 1, 是, 是], [18, 否, 0, 否, 是]], 是, 是, [否, 是], 是, [否, 是, 否, 是, 否, 是, 否, 是, 否, 是, 否, 是, 否, 是, 否, 是, 否, 是, 否], 是, 是, 否, A_le_m_B_plus_B_decidable_transfers_decidability_to_A_not_the_reverse_partial_maps_and_yes_only_checks_are_invalid_and_finite_tables_do_not_prove_infinite_computability)；依完整明示資料獨立重算；composition與decider transfer保持A≤mB的方向；partial map與yes-only檢查無效；finite table只證finite domain instance，不證無限domain computability；不混同Turing reduction或反向decidability transfer。"},"difficulty":{"band":"undergraduate_core","level":2,"skills":["多對一歸約"]},"variant":{"family_id":"qf-mod46-mreduction-decider-transfer-boundary","seed":202611157092,"parameters":{"mode":"valid_transfer","source_carrier":[0,1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18],"target_carrier":[0,1],"source_yes":[1,3,5,7,9,11,13,15,17],"target_yes":[1],"mapping":[0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0],"target_decider":[false,true],"domain":"Complete_finite_many_one_reduction","operation":"mreduction-decider-transfer-boundary","semantic_template":"qf-mod46-mreduction-decider-transfer-boundary/{\"mapping\":[0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0],\"mode\":\"valid_transfer\",\"source_carrier\":[0,1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18],\"source_yes\":[1,11,13,15,17,3,5,7,9],\"target_carrier\":[0,1],\"target_decider\":[false,true],\"target_yes\":[1]}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_or_symbolic_model","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"候選須主端重算；不構成人工審定、一般第一同構／strong duality／max-flow-min-cut證明、class equation、consistency、integrality、König theorem、無限domain computability、Lean或Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-15","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261015-advance-20261115-r07-many-one-reduction-0093","batch_id":"batch-20261015-advance-20261115-r07-many-one-reduction-foundations","language":"zh-Hant","source_mko_ids":["mko-many-one-reduction"],"title_zh":"多對一歸約","stem_zh":"明示decision predicates與complete total map的雙向membership equivalence。操作=mreduction-decider-transfer-boundary；資料={\"mode\":\"reverse_misuse\",\"source_carrier\":[0,1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,19],\"target_carrier\":[0,1],\"source_yes\":[1,3,5,7,9,11,13,15,17,19],\"target_yes\":[1],\"mapping\":[0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1],\"target_decider\":[false,true]}。請依 exact_ordered_tuple_declared_by_interface 欄序回答。","answer":{"kind":"expression","value":"(reverse_misuse, [[0, 否, 0, 否, 是], [1, 是, 1, 是, 是], [2, 否, 0, 否, 是], [3, 是, 1, 是, 是], [4, 否, 0, 否, 是], [5, 是, 1, 是, 是], [6, 否, 0, 否, 是], [7, 是, 1, 是, 是], [8, 否, 0, 否, 是], [9, 是, 1, 是, 是], [10, 否, 0, 否, 是], [11, 是, 1, 是, 是], [12, 否, 0, 否, 是], [13, 是, 1, 是, 是], [14, 否, 0, 否, 是], [15, 是, 1, 是, 是], [16, 否, 0, 否, 是], [17, 是, 1, 是, 是], [18, 否, 0, 否, 是], [19, 是, 1, 是, 是]], 是, 是, [否, 是], 是, [否, 是, 否, 是, 否, 是, 否, 是, 否, 是, 否, 是, 否, 是, 否, 是, 否, 是, 否, 是], 是, 否, 否, A_le_m_B_plus_B_decidable_transfers_decidability_to_A_not_the_reverse_partial_maps_and_yes_only_checks_are_invalid_and_finite_tables_do_not_prove_infinite_computability)","explanation_zh":"Wave6第九層核對=(reverse_misuse, [[0, 否, 0, 否, 是], [1, 是, 1, 是, 是], [2, 否, 0, 否, 是], [3, 是, 1, 是, 是], [4, 否, 0, 否, 是], [5, 是, 1, 是, 是], [6, 否, 0, 否, 是], [7, 是, 1, 是, 是], [8, 否, 0, 否, 是], [9, 是, 1, 是, 是], [10, 否, 0, 否, 是], [11, 是, 1, 是, 是], [12, 否, 0, 否, 是], [13, 是, 1, 是, 是], [14, 否, 0, 否, 是], [15, 是, 1, 是, 是], [16, 否, 0, 否, 是], [17, 是, 1, 是, 是], [18, 否, 0, 否, 是], [19, 是, 1, 是, 是]], 是, 是, [否, 是], 是, [否, 是, 否, 是, 否, 是, 否, 是, 否, 是, 否, 是, 否, 是, 否, 是, 否, 是, 否, 是], 是, 否, 否, A_le_m_B_plus_B_decidable_transfers_decidability_to_A_not_the_reverse_partial_maps_and_yes_only_checks_are_invalid_and_finite_tables_do_not_prove_infinite_computability)；依完整明示資料獨立重算；composition與decider transfer保持A≤mB的方向；partial map與yes-only檢查無效；finite table只證finite domain instance，不證無限domain computability；不混同Turing reduction或反向decidability transfer。"},"difficulty":{"band":"undergraduate_core","level":3,"skills":["多對一歸約"]},"variant":{"family_id":"qf-mod46-mreduction-decider-transfer-boundary","seed":202611157093,"parameters":{"mode":"reverse_misuse","source_carrier":[0,1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,19],"target_carrier":[0,1],"source_yes":[1,3,5,7,9,11,13,15,17,19],"target_yes":[1],"mapping":[0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1],"target_decider":[false,true],"domain":"Complete_finite_many_one_reduction","operation":"mreduction-decider-transfer-boundary","semantic_template":"qf-mod46-mreduction-decider-transfer-boundary/{\"mapping\":[0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1],\"mode\":\"reverse_misuse\",\"source_carrier\":[0,1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,19],\"source_yes\":[1,11,13,15,17,19,3,5,7,9],\"target_carrier\":[0,1],\"target_decider\":[false,true],\"target_yes\":[1]}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_or_symbolic_model","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"候選須主端重算；不構成人工審定、一般第一同構／strong duality／max-flow-min-cut證明、class equation、consistency、integrality、König theorem、無限domain computability、Lean或Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-15","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261015-advance-20261115-r07-many-one-reduction-0094","batch_id":"batch-20261015-advance-20261115-r07-many-one-reduction-foundations","language":"zh-Hant","source_mko_ids":["mko-many-one-reduction"],"title_zh":"多對一歸約","stem_zh":"明示decision predicates與complete total map的雙向membership equivalence。操作=mreduction-decider-transfer-boundary；資料={\"mode\":\"partial_map\",\"source_carrier\":[0,1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,19,20],\"target_carrier\":[0,1],\"source_yes\":[1,3,5,7,9,11,13,15,17,19],\"target_yes\":[1],\"mapping\":[0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,null],\"target_decider\":[false,true]}。請依 exact_ordered_tuple_declared_by_interface 欄序回答。","answer":{"kind":"expression","value":"(partial_map, [[0, 否, 0, 否, 是], [1, 是, 1, 是, 是], [2, 否, 0, 否, 是], [3, 是, 1, 是, 是], [4, 否, 0, 否, 是], [5, 是, 1, 是, 是], [6, 否, 0, 否, 是], [7, 是, 1, 是, 是], [8, 否, 0, 否, 是], [9, 是, 1, 是, 是], [10, 否, 0, 否, 是], [11, 是, 1, 是, 是], [12, 否, 0, 否, 是], [13, 是, 1, 是, 是], [14, 否, 0, 否, 是], [15, 是, 1, 是, 是], [16, 否, 0, 否, 是], [17, 是, 1, 是, 是], [18, 否, 0, 否, 是], [19, 是, 1, 是, 是], [20, 否, null, null, 否]], 否, 否, [否, 是], 是, null, 否, 否, 否, A_le_m_B_plus_B_decidable_transfers_decidability_to_A_not_the_reverse_partial_maps_and_yes_only_checks_are_invalid_and_finite_tables_do_not_prove_infinite_computability)","explanation_zh":"Wave6第九層核對=(partial_map, [[0, 否, 0, 否, 是], [1, 是, 1, 是, 是], [2, 否, 0, 否, 是], [3, 是, 1, 是, 是], [4, 否, 0, 否, 是], [5, 是, 1, 是, 是], [6, 否, 0, 否, 是], [7, 是, 1, 是, 是], [8, 否, 0, 否, 是], [9, 是, 1, 是, 是], [10, 否, 0, 否, 是], [11, 是, 1, 是, 是], [12, 否, 0, 否, 是], [13, 是, 1, 是, 是], [14, 否, 0, 否, 是], [15, 是, 1, 是, 是], [16, 否, 0, 否, 是], [17, 是, 1, 是, 是], [18, 否, 0, 否, 是], [19, 是, 1, 是, 是], [20, 否, null, null, 否]], 否, 否, [否, 是], 是, null, 否, 否, 否, A_le_m_B_plus_B_decidable_transfers_decidability_to_A_not_the_reverse_partial_maps_and_yes_only_checks_are_invalid_and_finite_tables_do_not_prove_infinite_computability)；依完整明示資料獨立重算；composition與decider transfer保持A≤mB的方向；partial map與yes-only檢查無效；finite table只證finite domain instance，不證無限domain computability；不混同Turing reduction或反向decidability transfer。"},"difficulty":{"band":"undergraduate_core","level":3,"skills":["多對一歸約"]},"variant":{"family_id":"qf-mod46-mreduction-decider-transfer-boundary","seed":202611157094,"parameters":{"mode":"partial_map","source_carrier":[0,1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,19,20],"target_carrier":[0,1],"source_yes":[1,3,5,7,9,11,13,15,17,19],"target_yes":[1],"mapping":[0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,null],"target_decider":[false,true],"domain":"Complete_finite_many_one_reduction","operation":"mreduction-decider-transfer-boundary","semantic_template":"qf-mod46-mreduction-decider-transfer-boundary/{\"mapping\":[0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,null],\"mode\":\"partial_map\",\"source_carrier\":[0,1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,19,20],\"source_yes\":[1,11,13,15,17,19,3,5,7,9],\"target_carrier\":[0,1],\"target_decider\":[false,true],\"target_yes\":[1]}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_or_symbolic_model","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"候選須主端重算；不構成人工審定、一般第一同構／strong duality／max-flow-min-cut證明、class equation、consistency、integrality、König theorem、無限domain computability、Lean或Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-15","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261015-advance-20261115-r07-many-one-reduction-0095","batch_id":"batch-20261015-advance-20261115-r07-many-one-reduction-foundations","language":"zh-Hant","source_mko_ids":["mko-many-one-reduction"],"title_zh":"多對一歸約","stem_zh":"明示decision predicates與complete total map的雙向membership equivalence。操作=mreduction-decider-transfer-boundary；資料={\"mode\":\"one_way_yes_only\",\"source_carrier\":[0,1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,19,20,21],\"target_carrier\":[0,1],\"source_yes\":[0],\"target_yes\":[0],\"mapping\":[0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0],\"target_decider\":[true,false]}。請依 exact_ordered_tuple_declared_by_interface 欄序回答。","answer":{"kind":"expression","value":"(one_way_yes_only, [[0, 是, 0, 是, 是], [1, 否, 0, 是, 否], [2, 否, 0, 是, 否], [3, 否, 0, 是, 否], [4, 否, 0, 是, 否], [5, 否, 0, 是, 否], [6, 否, 0, 是, 否], [7, 否, 0, 是, 否], [8, 否, 0, 是, 否], [9, 否, 0, 是, 否], [10, 否, 0, 是, 否], [11, 否, 0, 是, 否], [12, 否, 0, 是, 否], [13, 否, 0, 是, 否], [14, 否, 0, 是, 否], [15, 否, 0, 是, 否], [16, 否, 0, 是, 否], [17, 否, 0, 是, 否], [18, 否, 0, 是, 否], [19, 否, 0, 是, 否], [20, 否, 0, 是, 否], [21, 否, 0, 是, 否]], 是, 否, [是, 否], 是, [是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是], 否, 否, 否, A_le_m_B_plus_B_decidable_transfers_decidability_to_A_not_the_reverse_partial_maps_and_yes_only_checks_are_invalid_and_finite_tables_do_not_prove_infinite_computability)","explanation_zh":"Wave6第九層核對=(one_way_yes_only, [[0, 是, 0, 是, 是], [1, 否, 0, 是, 否], [2, 否, 0, 是, 否], [3, 否, 0, 是, 否], [4, 否, 0, 是, 否], [5, 否, 0, 是, 否], [6, 否, 0, 是, 否], [7, 否, 0, 是, 否], [8, 否, 0, 是, 否], [9, 否, 0, 是, 否], [10, 否, 0, 是, 否], [11, 否, 0, 是, 否], [12, 否, 0, 是, 否], [13, 否, 0, 是, 否], [14, 否, 0, 是, 否], [15, 否, 0, 是, 否], [16, 否, 0, 是, 否], [17, 否, 0, 是, 否], [18, 否, 0, 是, 否], [19, 否, 0, 是, 否], [20, 否, 0, 是, 否], [21, 否, 0, 是, 否]], 是, 否, [是, 否], 是, [是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是], 否, 否, 否, A_le_m_B_plus_B_decidable_transfers_decidability_to_A_not_the_reverse_partial_maps_and_yes_only_checks_are_invalid_and_finite_tables_do_not_prove_infinite_computability)；依完整明示資料獨立重算；composition與decider transfer保持A≤mB的方向；partial map與yes-only檢查無效；finite table只證finite domain instance，不證無限domain computability；不混同Turing reduction或反向decidability transfer。"},"difficulty":{"band":"undergraduate_core","level":3,"skills":["多對一歸約"]},"variant":{"family_id":"qf-mod46-mreduction-decider-transfer-boundary","seed":202611157095,"parameters":{"mode":"one_way_yes_only","source_carrier":[0,1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,19,20,21],"target_carrier":[0,1],"source_yes":[0],"target_yes":[0],"mapping":[0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0],"target_decider":[true,false],"domain":"Complete_finite_many_one_reduction","operation":"mreduction-decider-transfer-boundary","semantic_template":"qf-mod46-mreduction-decider-transfer-boundary/{\"mapping\":[0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0],\"mode\":\"one_way_yes_only\",\"source_carrier\":[0,1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,19,20,21],\"source_yes\":[0],\"target_carrier\":[0,1],\"target_decider\":[true,false],\"target_yes\":[0]}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_or_symbolic_model","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"候選須主端重算；不構成人工審定、一般第一同構／strong duality／max-flow-min-cut證明、class equation、consistency、integrality、König theorem、無限domain computability、Lean或Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-15","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261015-advance-20261115-r07-many-one-reduction-0096","batch_id":"batch-20261015-advance-20261115-r07-many-one-reduction-foundations","language":"zh-Hant","source_mko_ids":["mko-many-one-reduction"],"title_zh":"多對一歸約","stem_zh":"明示decision predicates與complete total map的雙向membership equivalence。操作=mreduction-decider-transfer-boundary；資料={\"mode\":\"valid_transfer\",\"source_carrier\":[0,1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,19,20,21,22],\"target_carrier\":[0,1],\"source_yes\":[1,3,5,7,9,11,13,15,17,19,21],\"target_yes\":[1],\"mapping\":[0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0],\"target_decider\":[false,true]}。請依 exact_ordered_tuple_declared_by_interface 欄序回答。","answer":{"kind":"expression","value":"(valid_transfer, [[0, 否, 0, 否, 是], [1, 是, 1, 是, 是], [2, 否, 0, 否, 是], [3, 是, 1, 是, 是], [4, 否, 0, 否, 是], [5, 是, 1, 是, 是], [6, 否, 0, 否, 是], [7, 是, 1, 是, 是], [8, 否, 0, 否, 是], [9, 是, 1, 是, 是], [10, 否, 0, 否, 是], [11, 是, 1, 是, 是], [12, 否, 0, 否, 是], [13, 是, 1, 是, 是], [14, 否, 0, 否, 是], [15, 是, 1, 是, 是], [16, 否, 0, 否, 是], [17, 是, 1, 是, 是], [18, 否, 0, 否, 是], [19, 是, 1, 是, 是], [20, 否, 0, 否, 是], [21, 是, 1, 是, 是], [22, 否, 0, 否, 是]], 是, 是, [否, 是], 是, [否, 是, 否, 是, 否, 是, 否, 是, 否, 是, 否, 是, 否, 是, 否, 是, 否, 是, 否, 是, 否, 是, 否], 是, 是, 否, A_le_m_B_plus_B_decidable_transfers_decidability_to_A_not_the_reverse_partial_maps_and_yes_only_checks_are_invalid_and_finite_tables_do_not_prove_infinite_computability)","explanation_zh":"Wave6第九層核對=(valid_transfer, [[0, 否, 0, 否, 是], [1, 是, 1, 是, 是], [2, 否, 0, 否, 是], [3, 是, 1, 是, 是], [4, 否, 0, 否, 是], [5, 是, 1, 是, 是], [6, 否, 0, 否, 是], [7, 是, 1, 是, 是], [8, 否, 0, 否, 是], [9, 是, 1, 是, 是], [10, 否, 0, 否, 是], [11, 是, 1, 是, 是], [12, 否, 0, 否, 是], [13, 是, 1, 是, 是], [14, 否, 0, 否, 是], [15, 是, 1, 是, 是], [16, 否, 0, 否, 是], [17, 是, 1, 是, 是], [18, 否, 0, 否, 是], [19, 是, 1, 是, 是], [20, 否, 0, 否, 是], [21, 是, 1, 是, 是], [22, 否, 0, 否, 是]], 是, 是, [否, 是], 是, [否, 是, 否, 是, 否, 是, 否, 是, 否, 是, 否, 是, 否, 是, 否, 是, 否, 是, 否, 是, 否, 是, 否], 是, 是, 否, A_le_m_B_plus_B_decidable_transfers_decidability_to_A_not_the_reverse_partial_maps_and_yes_only_checks_are_invalid_and_finite_tables_do_not_prove_infinite_computability)；依完整明示資料獨立重算；composition與decider transfer保持A≤mB的方向；partial map與yes-only檢查無效；finite table只證finite domain instance，不證無限domain computability；不混同Turing reduction或反向decidability transfer。"},"difficulty":{"band":"undergraduate_core","level":3,"skills":["多對一歸約"]},"variant":{"family_id":"qf-mod46-mreduction-decider-transfer-boundary","seed":202611157096,"parameters":{"mode":"valid_transfer","source_carrier":[0,1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,19,20,21,22],"target_carrier":[0,1],"source_yes":[1,3,5,7,9,11,13,15,17,19,21],"target_yes":[1],"mapping":[0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0],"target_decider":[false,true],"domain":"Complete_finite_many_one_reduction","operation":"mreduction-decider-transfer-boundary","semantic_template":"qf-mod46-mreduction-decider-transfer-boundary/{\"mapping\":[0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0],\"mode\":\"valid_transfer\",\"source_carrier\":[0,1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,19,20,21,22],\"source_yes\":[1,11,13,15,17,19,21,3,5,7,9],\"target_carrier\":[0,1],\"target_decider\":[false,true],\"target_yes\":[1]}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_or_symbolic_model","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"候選須主端重算；不構成人工審定、一般第一同構／strong duality／max-flow-min-cut證明、class equation、consistency、integrality、König theorem、無限domain computability、Lean或Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-15","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261015-advance-20261115-r07-many-one-reduction-0097","batch_id":"batch-20261015-advance-20261115-r07-many-one-reduction-foundations","language":"zh-Hant","source_mko_ids":["mko-many-one-reduction"],"title_zh":"多對一歸約","stem_zh":"明示decision predicates與complete total map的雙向membership equivalence。操作=mreduction-decider-transfer-boundary；資料={\"mode\":\"reverse_misuse\",\"source_carrier\":[0,1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,19,20,21,22,23],\"target_carrier\":[0,1],\"source_yes\":[1,3,5,7,9,11,13,15,17,19,21,23],\"target_yes\":[1],\"mapping\":[0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1],\"target_decider\":[false,true]}。請依 exact_ordered_tuple_declared_by_interface 欄序回答。","answer":{"kind":"expression","value":"(reverse_misuse, [[0, 否, 0, 否, 是], [1, 是, 1, 是, 是], [2, 否, 0, 否, 是], [3, 是, 1, 是, 是], [4, 否, 0, 否, 是], [5, 是, 1, 是, 是], [6, 否, 0, 否, 是], [7, 是, 1, 是, 是], [8, 否, 0, 否, 是], [9, 是, 1, 是, 是], [10, 否, 0, 否, 是], [11, 是, 1, 是, 是], [12, 否, 0, 否, 是], [13, 是, 1, 是, 是], [14, 否, 0, 否, 是], [15, 是, 1, 是, 是], [16, 否, 0, 否, 是], [17, 是, 1, 是, 是], [18, 否, 0, 否, 是], [19, 是, 1, 是, 是], [20, 否, 0, 否, 是], [21, 是, 1, 是, 是], [22, 否, 0, 否, 是], [23, 是, 1, 是, 是]], 是, 是, [否, 是], 是, [否, 是, 否, 是, 否, 是, 否, 是, 否, 是, 否, 是, 否, 是, 否, 是, 否, 是, 否, 是, 否, 是, 否, 是], 是, 否, 否, A_le_m_B_plus_B_decidable_transfers_decidability_to_A_not_the_reverse_partial_maps_and_yes_only_checks_are_invalid_and_finite_tables_do_not_prove_infinite_computability)","explanation_zh":"Wave6第九層核對=(reverse_misuse, [[0, 否, 0, 否, 是], [1, 是, 1, 是, 是], [2, 否, 0, 否, 是], [3, 是, 1, 是, 是], [4, 否, 0, 否, 是], [5, 是, 1, 是, 是], [6, 否, 0, 否, 是], [7, 是, 1, 是, 是], [8, 否, 0, 否, 是], [9, 是, 1, 是, 是], [10, 否, 0, 否, 是], [11, 是, 1, 是, 是], [12, 否, 0, 否, 是], [13, 是, 1, 是, 是], [14, 否, 0, 否, 是], [15, 是, 1, 是, 是], [16, 否, 0, 否, 是], [17, 是, 1, 是, 是], [18, 否, 0, 否, 是], [19, 是, 1, 是, 是], [20, 否, 0, 否, 是], [21, 是, 1, 是, 是], [22, 否, 0, 否, 是], [23, 是, 1, 是, 是]], 是, 是, [否, 是], 是, [否, 是, 否, 是, 否, 是, 否, 是, 否, 是, 否, 是, 否, 是, 否, 是, 否, 是, 否, 是, 否, 是, 否, 是], 是, 否, 否, A_le_m_B_plus_B_decidable_transfers_decidability_to_A_not_the_reverse_partial_maps_and_yes_only_checks_are_invalid_and_finite_tables_do_not_prove_infinite_computability)；依完整明示資料獨立重算；composition與decider transfer保持A≤mB的方向；partial map與yes-only檢查無效；finite table只證finite domain instance，不證無限domain computability；不混同Turing reduction或反向decidability transfer。"},"difficulty":{"band":"undergraduate_core","level":3,"skills":["多對一歸約"]},"variant":{"family_id":"qf-mod46-mreduction-decider-transfer-boundary","seed":202611157097,"parameters":{"mode":"reverse_misuse","source_carrier":[0,1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,19,20,21,22,23],"target_carrier":[0,1],"source_yes":[1,3,5,7,9,11,13,15,17,19,21,23],"target_yes":[1],"mapping":[0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1],"target_decider":[false,true],"domain":"Complete_finite_many_one_reduction","operation":"mreduction-decider-transfer-boundary","semantic_template":"qf-mod46-mreduction-decider-transfer-boundary/{\"mapping\":[0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1],\"mode\":\"reverse_misuse\",\"source_carrier\":[0,1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,19,20,21,22,23],\"source_yes\":[1,11,13,15,17,19,21,23,3,5,7,9],\"target_carrier\":[0,1],\"target_decider\":[false,true],\"target_yes\":[1]}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_or_symbolic_model","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"候選須主端重算；不構成人工審定、一般第一同構／strong duality／max-flow-min-cut證明、class equation、consistency、integrality、König theorem、無限domain computability、Lean或Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-15","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261015-advance-20261115-r07-many-one-reduction-0098","batch_id":"batch-20261015-advance-20261115-r07-many-one-reduction-foundations","language":"zh-Hant","source_mko_ids":["mko-many-one-reduction"],"title_zh":"多對一歸約","stem_zh":"明示decision predicates與complete total map的雙向membership equivalence。操作=mreduction-decider-transfer-boundary；資料={\"mode\":\"partial_map\",\"source_carrier\":[0,1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,19,20,21,22,23,24],\"target_carrier\":[0,1],\"source_yes\":[1,3,5,7,9,11,13,15,17,19,21,23],\"target_yes\":[1],\"mapping\":[0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,null],\"target_decider\":[false,true]}。請依 exact_ordered_tuple_declared_by_interface 欄序回答。","answer":{"kind":"expression","value":"(partial_map, [[0, 否, 0, 否, 是], [1, 是, 1, 是, 是], [2, 否, 0, 否, 是], [3, 是, 1, 是, 是], [4, 否, 0, 否, 是], [5, 是, 1, 是, 是], [6, 否, 0, 否, 是], [7, 是, 1, 是, 是], [8, 否, 0, 否, 是], [9, 是, 1, 是, 是], [10, 否, 0, 否, 是], [11, 是, 1, 是, 是], [12, 否, 0, 否, 是], [13, 是, 1, 是, 是], [14, 否, 0, 否, 是], [15, 是, 1, 是, 是], [16, 否, 0, 否, 是], [17, 是, 1, 是, 是], [18, 否, 0, 否, 是], [19, 是, 1, 是, 是], [20, 否, 0, 否, 是], [21, 是, 1, 是, 是], [22, 否, 0, 否, 是], [23, 是, 1, 是, 是], [24, 否, null, null, 否]], 否, 否, [否, 是], 是, null, 否, 否, 否, A_le_m_B_plus_B_decidable_transfers_decidability_to_A_not_the_reverse_partial_maps_and_yes_only_checks_are_invalid_and_finite_tables_do_not_prove_infinite_computability)","explanation_zh":"Wave6第九層核對=(partial_map, [[0, 否, 0, 否, 是], [1, 是, 1, 是, 是], [2, 否, 0, 否, 是], [3, 是, 1, 是, 是], [4, 否, 0, 否, 是], [5, 是, 1, 是, 是], [6, 否, 0, 否, 是], [7, 是, 1, 是, 是], [8, 否, 0, 否, 是], [9, 是, 1, 是, 是], [10, 否, 0, 否, 是], [11, 是, 1, 是, 是], [12, 否, 0, 否, 是], [13, 是, 1, 是, 是], [14, 否, 0, 否, 是], [15, 是, 1, 是, 是], [16, 否, 0, 否, 是], [17, 是, 1, 是, 是], [18, 否, 0, 否, 是], [19, 是, 1, 是, 是], [20, 否, 0, 否, 是], [21, 是, 1, 是, 是], [22, 否, 0, 否, 是], [23, 是, 1, 是, 是], [24, 否, null, null, 否]], 否, 否, [否, 是], 是, null, 否, 否, 否, A_le_m_B_plus_B_decidable_transfers_decidability_to_A_not_the_reverse_partial_maps_and_yes_only_checks_are_invalid_and_finite_tables_do_not_prove_infinite_computability)；依完整明示資料獨立重算；composition與decider transfer保持A≤mB的方向；partial map與yes-only檢查無效；finite table只證finite domain instance，不證無限domain computability；不混同Turing reduction或反向decidability transfer。"},"difficulty":{"band":"undergraduate_core","level":3,"skills":["多對一歸約"]},"variant":{"family_id":"qf-mod46-mreduction-decider-transfer-boundary","seed":202611157098,"parameters":{"mode":"partial_map","source_carrier":[0,1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,19,20,21,22,23,24],"target_carrier":[0,1],"source_yes":[1,3,5,7,9,11,13,15,17,19,21,23],"target_yes":[1],"mapping":[0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,null],"target_decider":[false,true],"domain":"Complete_finite_many_one_reduction","operation":"mreduction-decider-transfer-boundary","semantic_template":"qf-mod46-mreduction-decider-transfer-boundary/{\"mapping\":[0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,null],\"mode\":\"partial_map\",\"source_carrier\":[0,1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,19,20,21,22,23,24],\"source_yes\":[1,11,13,15,17,19,21,23,3,5,7,9],\"target_carrier\":[0,1],\"target_decider\":[false,true],\"target_yes\":[1]}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_or_symbolic_model","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"候選須主端重算；不構成人工審定、一般第一同構／strong duality／max-flow-min-cut證明、class equation、consistency、integrality、König theorem、無限domain computability、Lean或Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-15","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261015-advance-20261115-r07-many-one-reduction-0099","batch_id":"batch-20261015-advance-20261115-r07-many-one-reduction-foundations","language":"zh-Hant","source_mko_ids":["mko-many-one-reduction"],"title_zh":"多對一歸約","stem_zh":"明示decision predicates與complete total map的雙向membership equivalence。操作=mreduction-decider-transfer-boundary；資料={\"mode\":\"one_way_yes_only\",\"source_carrier\":[0,1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,19,20,21,22,23,24,25],\"target_carrier\":[0,1],\"source_yes\":[0],\"target_yes\":[0],\"mapping\":[0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0],\"target_decider\":[true,false]}。請依 exact_ordered_tuple_declared_by_interface 欄序回答。","answer":{"kind":"expression","value":"(one_way_yes_only, [[0, 是, 0, 是, 是], [1, 否, 0, 是, 否], [2, 否, 0, 是, 否], [3, 否, 0, 是, 否], [4, 否, 0, 是, 否], [5, 否, 0, 是, 否], [6, 否, 0, 是, 否], [7, 否, 0, 是, 否], [8, 否, 0, 是, 否], [9, 否, 0, 是, 否], [10, 否, 0, 是, 否], [11, 否, 0, 是, 否], [12, 否, 0, 是, 否], [13, 否, 0, 是, 否], [14, 否, 0, 是, 否], [15, 否, 0, 是, 否], [16, 否, 0, 是, 否], [17, 否, 0, 是, 否], [18, 否, 0, 是, 否], [19, 否, 0, 是, 否], [20, 否, 0, 是, 否], [21, 否, 0, 是, 否], [22, 否, 0, 是, 否], [23, 否, 0, 是, 否], [24, 否, 0, 是, 否], [25, 否, 0, 是, 否]], 是, 否, [是, 否], 是, [是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是], 否, 否, 否, A_le_m_B_plus_B_decidable_transfers_decidability_to_A_not_the_reverse_partial_maps_and_yes_only_checks_are_invalid_and_finite_tables_do_not_prove_infinite_computability)","explanation_zh":"Wave6第九層核對=(one_way_yes_only, [[0, 是, 0, 是, 是], [1, 否, 0, 是, 否], [2, 否, 0, 是, 否], [3, 否, 0, 是, 否], [4, 否, 0, 是, 否], [5, 否, 0, 是, 否], [6, 否, 0, 是, 否], [7, 否, 0, 是, 否], [8, 否, 0, 是, 否], [9, 否, 0, 是, 否], [10, 否, 0, 是, 否], [11, 否, 0, 是, 否], [12, 否, 0, 是, 否], [13, 否, 0, 是, 否], [14, 否, 0, 是, 否], [15, 否, 0, 是, 否], [16, 否, 0, 是, 否], [17, 否, 0, 是, 否], [18, 否, 0, 是, 否], [19, 否, 0, 是, 否], [20, 否, 0, 是, 否], [21, 否, 0, 是, 否], [22, 否, 0, 是, 否], [23, 否, 0, 是, 否], [24, 否, 0, 是, 否], [25, 否, 0, 是, 否]], 是, 否, [是, 否], 是, [是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是], 否, 否, 否, A_le_m_B_plus_B_decidable_transfers_decidability_to_A_not_the_reverse_partial_maps_and_yes_only_checks_are_invalid_and_finite_tables_do_not_prove_infinite_computability)；依完整明示資料獨立重算；composition與decider transfer保持A≤mB的方向；partial map與yes-only檢查無效；finite table只證finite domain instance，不證無限domain computability；不混同Turing reduction或反向decidability transfer。"},"difficulty":{"band":"undergraduate_core","level":3,"skills":["多對一歸約"]},"variant":{"family_id":"qf-mod46-mreduction-decider-transfer-boundary","seed":202611157099,"parameters":{"mode":"one_way_yes_only","source_carrier":[0,1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,19,20,21,22,23,24,25],"target_carrier":[0,1],"source_yes":[0],"target_yes":[0],"mapping":[0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0],"target_decider":[true,false],"domain":"Complete_finite_many_one_reduction","operation":"mreduction-decider-transfer-boundary","semantic_template":"qf-mod46-mreduction-decider-transfer-boundary/{\"mapping\":[0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0,0],\"mode\":\"one_way_yes_only\",\"source_carrier\":[0,1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,19,20,21,22,23,24,25],\"source_yes\":[0],\"target_carrier\":[0,1],\"target_decider\":[true,false],\"target_yes\":[0]}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_or_symbolic_model","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"候選須主端重算；不構成人工審定、一般第一同構／strong duality／max-flow-min-cut證明、class equation、consistency、integrality、König theorem、無限domain computability、Lean或Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-15","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261015-advance-20261115-r07-many-one-reduction-0100","batch_id":"batch-20261015-advance-20261115-r07-many-one-reduction-foundations","language":"zh-Hant","source_mko_ids":["mko-many-one-reduction"],"title_zh":"多對一歸約","stem_zh":"明示decision predicates與complete total map的雙向membership equivalence。操作=mreduction-decider-transfer-boundary；資料={\"mode\":\"valid_transfer\",\"source_carrier\":[0,1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,19,20,21,22,23,24,25,26],\"target_carrier\":[0,1],\"source_yes\":[1,3,5,7,9,11,13,15,17,19,21,23,25],\"target_yes\":[1],\"mapping\":[0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0],\"target_decider\":[false,true]}。請依 exact_ordered_tuple_declared_by_interface 欄序回答。","answer":{"kind":"expression","value":"(valid_transfer, [[0, 否, 0, 否, 是], [1, 是, 1, 是, 是], [2, 否, 0, 否, 是], [3, 是, 1, 是, 是], [4, 否, 0, 否, 是], [5, 是, 1, 是, 是], [6, 否, 0, 否, 是], [7, 是, 1, 是, 是], [8, 否, 0, 否, 是], [9, 是, 1, 是, 是], [10, 否, 0, 否, 是], [11, 是, 1, 是, 是], [12, 否, 0, 否, 是], [13, 是, 1, 是, 是], [14, 否, 0, 否, 是], [15, 是, 1, 是, 是], [16, 否, 0, 否, 是], [17, 是, 1, 是, 是], [18, 否, 0, 否, 是], [19, 是, 1, 是, 是], [20, 否, 0, 否, 是], [21, 是, 1, 是, 是], [22, 否, 0, 否, 是], [23, 是, 1, 是, 是], [24, 否, 0, 否, 是], [25, 是, 1, 是, 是], [26, 否, 0, 否, 是]], 是, 是, [否, 是], 是, [否, 是, 否, 是, 否, 是, 否, 是, 否, 是, 否, 是, 否, 是, 否, 是, 否, 是, 否, 是, 否, 是, 否, 是, 否, 是, 否], 是, 是, 否, A_le_m_B_plus_B_decidable_transfers_decidability_to_A_not_the_reverse_partial_maps_and_yes_only_checks_are_invalid_and_finite_tables_do_not_prove_infinite_computability)","explanation_zh":"Wave6第九層核對=(valid_transfer, [[0, 否, 0, 否, 是], [1, 是, 1, 是, 是], [2, 否, 0, 否, 是], [3, 是, 1, 是, 是], [4, 否, 0, 否, 是], [5, 是, 1, 是, 是], [6, 否, 0, 否, 是], [7, 是, 1, 是, 是], [8, 否, 0, 否, 是], [9, 是, 1, 是, 是], [10, 否, 0, 否, 是], [11, 是, 1, 是, 是], [12, 否, 0, 否, 是], [13, 是, 1, 是, 是], [14, 否, 0, 否, 是], [15, 是, 1, 是, 是], [16, 否, 0, 否, 是], [17, 是, 1, 是, 是], [18, 否, 0, 否, 是], [19, 是, 1, 是, 是], [20, 否, 0, 否, 是], [21, 是, 1, 是, 是], [22, 否, 0, 否, 是], [23, 是, 1, 是, 是], [24, 否, 0, 否, 是], [25, 是, 1, 是, 是], [26, 否, 0, 否, 是]], 是, 是, [否, 是], 是, [否, 是, 否, 是, 否, 是, 否, 是, 否, 是, 否, 是, 否, 是, 否, 是, 否, 是, 否, 是, 否, 是, 否, 是, 否, 是, 否], 是, 是, 否, A_le_m_B_plus_B_decidable_transfers_decidability_to_A_not_the_reverse_partial_maps_and_yes_only_checks_are_invalid_and_finite_tables_do_not_prove_infinite_computability)；依完整明示資料獨立重算；composition與decider transfer保持A≤mB的方向；partial map與yes-only檢查無效；finite table只證finite domain instance，不證無限domain computability；不混同Turing reduction或反向decidability transfer。"},"difficulty":{"band":"undergraduate_core","level":3,"skills":["多對一歸約"]},"variant":{"family_id":"qf-mod46-mreduction-decider-transfer-boundary","seed":202611157100,"parameters":{"mode":"valid_transfer","source_carrier":[0,1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,19,20,21,22,23,24,25,26],"target_carrier":[0,1],"source_yes":[1,3,5,7,9,11,13,15,17,19,21,23,25],"target_yes":[1],"mapping":[0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0],"target_decider":[false,true],"domain":"Complete_finite_many_one_reduction","operation":"mreduction-decider-transfer-boundary","semantic_template":"qf-mod46-mreduction-decider-transfer-boundary/{\"mapping\":[0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0],\"mode\":\"valid_transfer\",\"source_carrier\":[0,1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,19,20,21,22,23,24,25,26],\"source_yes\":[1,11,13,15,17,19,21,23,25,3,5,7,9],\"target_carrier\":[0,1],\"target_decider\":[false,true],\"target_yes\":[1]}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_or_symbolic_model","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"候選須主端重算；不構成人工審定、一般第一同構／strong duality／max-flow-min-cut證明、class equation、consistency、integrality、König theorem、無限domain computability、Lean或Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-15","contract_version":"ocme-question-factory-v0.1"}}