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{"schema_version":"ocme-question-v0.1","id":"q-20261013-advance-20261018-r06-decision-problem-0021","batch_id":"batch-20261013-advance-20261018-r06-decision-problem-foundations","language":"zh-Hant","source_mko_ids":["mko-decision-problem"],"title_zh":"有限決定問題","stem_zh":"明示有限輸入域。操作=decision-yes-set-table；資料={\"n\":6,\"yes\":[2,4]}。請依 [n,yes_set,full_truth_table] 的欄序回答。","answer":{"kind":"expression","value":"(6, [2, 4], [[0, 否], [1, 否], [2, 是], [3, 否], [4, 是], [5, 否]])","explanation_zh":"擴展基礎核對=(6, [2, 4], [[0, 否], [1, 否], [2, 是], [3, 否], [4, 是], [5, 否]])；依完整明示資料逐欄精確重算；有限／合成資料核對不是一般形式證明；規格與decider分離；有限完整表不外推無限可判定性。"},"difficulty":{"band":"undergraduate_core","level":3,"skills":["有限決定問題"]},"variant":{"family_id":"qf-ext18-decision-yes-set-table","seed":202610186021,"parameters":{"n":6,"yes":[2,4],"domain":"Fin_decision_problem","operation":"decision-yes-set-table","semantic_template":"qf-ext18-decision-yes-set-table/{\"n\":6,\"yes\":[2,4]}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_arithmetic","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"僅為產生端候選及自檢；主端須另做驗收，不構成人工審定、普遍證明、Lean執行或形式Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-13","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261013-advance-20261018-r06-decision-problem-0022","batch_id":"batch-20261013-advance-20261018-r06-decision-problem-foundations","language":"zh-Hant","source_mko_ids":["mko-decision-problem"],"title_zh":"有限決定問題","stem_zh":"明示有限輸入域。操作=decision-yes-set-table；資料={\"n\":6,\"yes\":[0,2,4]}。請依 [n,yes_set,full_truth_table] 的欄序回答。","answer":{"kind":"expression","value":"(6, [0, 2, 4], [[0, 是], [1, 否], [2, 是], [3, 否], [4, 是], [5, 否]])","explanation_zh":"擴展基礎核對=(6, [0, 2, 4], [[0, 是], [1, 否], [2, 是], [3, 否], [4, 是], [5, 否]])；依完整明示資料逐欄精確重算；有限／合成資料核對不是一般形式證明；規格與decider分離；有限完整表不外推無限可判定性。"},"difficulty":{"band":"undergraduate_core","level":3,"skills":["有限決定問題"]},"variant":{"family_id":"qf-ext18-decision-yes-set-table","seed":202610186022,"parameters":{"n":6,"yes":[0,2,4],"domain":"Fin_decision_problem","operation":"decision-yes-set-table","semantic_template":"qf-ext18-decision-yes-set-table/{\"n\":6,\"yes\":[0,2,4]}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_arithmetic","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"僅為產生端候選及自檢；主端須另做驗收，不構成人工審定、普遍證明、Lean執行或形式Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-13","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261013-advance-20261018-r06-decision-problem-0023","batch_id":"batch-20261013-advance-20261018-r06-decision-problem-foundations","language":"zh-Hant","source_mko_ids":["mko-decision-problem"],"title_zh":"有限決定問題","stem_zh":"明示有限輸入域。操作=decision-yes-set-table；資料={\"n\":6,\"yes\":[1,2,4]}。請依 [n,yes_set,full_truth_table] 的欄序回答。","answer":{"kind":"expression","value":"(6, [1, 2, 4], [[0, 否], [1, 是], [2, 是], [3, 否], [4, 是], [5, 否]])","explanation_zh":"擴展基礎核對=(6, [1, 2, 4], [[0, 否], [1, 是], [2, 是], [3, 否], [4, 是], [5, 否]])；依完整明示資料逐欄精確重算；有限／合成資料核對不是一般形式證明；規格與decider分離；有限完整表不外推無限可判定性。"},"difficulty":{"band":"undergraduate_core","level":3,"skills":["有限決定問題"]},"variant":{"family_id":"qf-ext18-decision-yes-set-table","seed":202610186023,"parameters":{"n":6,"yes":[1,2,4],"domain":"Fin_decision_problem","operation":"decision-yes-set-table","semantic_template":"qf-ext18-decision-yes-set-table/{\"n\":6,\"yes\":[1,2,4]}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_arithmetic","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"僅為產生端候選及自檢；主端須另做驗收，不構成人工審定、普遍證明、Lean執行或形式Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-13","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261013-advance-20261018-r06-decision-problem-0024","batch_id":"batch-20261013-advance-20261018-r06-decision-problem-foundations","language":"zh-Hant","source_mko_ids":["mko-decision-problem"],"title_zh":"有限決定問題","stem_zh":"明示有限輸入域。操作=decision-yes-set-table；資料={\"n\":6,\"yes\":[0,1,2,4]}。請依 [n,yes_set,full_truth_table] 的欄序回答。","answer":{"kind":"expression","value":"(6, [0, 1, 2, 4], [[0, 是], [1, 是], [2, 是], [3, 否], [4, 是], [5, 否]])","explanation_zh":"擴展基礎核對=(6, [0, 1, 2, 4], [[0, 是], [1, 是], [2, 是], [3, 否], [4, 是], [5, 否]])；依完整明示資料逐欄精確重算；有限／合成資料核對不是一般形式證明；規格與decider分離；有限完整表不外推無限可判定性。"},"difficulty":{"band":"undergraduate_core","level":3,"skills":["有限決定問題"]},"variant":{"family_id":"qf-ext18-decision-yes-set-table","seed":202610186024,"parameters":{"n":6,"yes":[0,1,2,4],"domain":"Fin_decision_problem","operation":"decision-yes-set-table","semantic_template":"qf-ext18-decision-yes-set-table/{\"n\":6,\"yes\":[0,1,2,4]}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_arithmetic","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"僅為產生端候選及自檢；主端須另做驗收，不構成人工審定、普遍證明、Lean執行或形式Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-13","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261013-advance-20261018-r06-decision-problem-0025","batch_id":"batch-20261013-advance-20261018-r06-decision-problem-foundations","language":"zh-Hant","source_mko_ids":["mko-decision-problem"],"title_zh":"有限決定問題","stem_zh":"明示有限輸入域。操作=decision-yes-set-table；資料={\"n\":6,\"yes\":[3,4]}。請依 [n,yes_set,full_truth_table] 的欄序回答。","answer":{"kind":"expression","value":"(6, [3, 4], [[0, 否], [1, 否], [2, 否], [3, 是], [4, 是], [5, 否]])","explanation_zh":"擴展基礎核對=(6, [3, 4], [[0, 否], [1, 否], [2, 否], [3, 是], [4, 是], [5, 否]])；依完整明示資料逐欄精確重算；有限／合成資料核對不是一般形式證明；規格與decider分離；有限完整表不外推無限可判定性。"},"difficulty":{"band":"undergraduate_core","level":3,"skills":["有限決定問題"]},"variant":{"family_id":"qf-ext18-decision-yes-set-table","seed":202610186025,"parameters":{"n":6,"yes":[3,4],"domain":"Fin_decision_problem","operation":"decision-yes-set-table","semantic_template":"qf-ext18-decision-yes-set-table/{\"n\":6,\"yes\":[3,4]}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_arithmetic","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"僅為產生端候選及自檢；主端須另做驗收，不構成人工審定、普遍證明、Lean執行或形式Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-13","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261013-advance-20261018-r06-decision-problem-0026","batch_id":"batch-20261013-advance-20261018-r06-decision-problem-foundations","language":"zh-Hant","source_mko_ids":["mko-decision-problem"],"title_zh":"有限決定問題","stem_zh":"明示有限輸入域。操作=decision-decider-agreement；資料={\"n\":6,\"yes\":[],\"decider\":[false,false,false,false,false,false]}。請依 [n,yes_set,decider,mismatches,agrees] 的欄序回答。","answer":{"kind":"expression","value":"(6, [], [否, 否, 否, 否, 否, 否], [], 是)","explanation_zh":"擴展基礎核對=(6, [], [否, 否, 否, 否, 否, 否], [], 是)；依完整明示資料逐欄精確重算；有限／合成資料核對不是一般形式證明；規格與decider分離；有限完整表不外推無限可判定性。"},"difficulty":{"band":"undergraduate_core","level":1,"skills":["有限決定問題"]},"variant":{"family_id":"qf-ext18-decision-decider-agreement","seed":202610186026,"parameters":{"n":6,"yes":[],"decider":[false,false,false,false,false,false],"domain":"Fin_decision_problem","operation":"decision-decider-agreement","semantic_template":"qf-ext18-decision-decider-agreement/{\"decider\":[false,false,false,false,false,false],\"n\":6,\"yes\":[]}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_arithmetic","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"僅為產生端候選及自檢；主端須另做驗收，不構成人工審定、普遍證明、Lean執行或形式Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-13","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261013-advance-20261018-r06-decision-problem-0027","batch_id":"batch-20261013-advance-20261018-r06-decision-problem-foundations","language":"zh-Hant","source_mko_ids":["mko-decision-problem"],"title_zh":"有限決定問題","stem_zh":"明示有限輸入域。操作=decision-decider-agreement；資料={\"n\":6,\"yes\":[0],\"decider\":[true,true,false,false,false,false]}。請依 [n,yes_set,decider,mismatches,agrees] 的欄序回答。","answer":{"kind":"expression","value":"(6, [0], [是, 是, 否, 否, 否, 否], [1], 否)","explanation_zh":"擴展基礎核對=(6, [0], [是, 是, 否, 否, 否, 否], [1], 否)；依完整明示資料逐欄精確重算；有限／合成資料核對不是一般形式證明；規格與decider分離；有限完整表不外推無限可判定性。"},"difficulty":{"band":"undergraduate_core","level":1,"skills":["有限決定問題"]},"variant":{"family_id":"qf-ext18-decision-decider-agreement","seed":202610186027,"parameters":{"n":6,"yes":[0],"decider":[true,true,false,false,false,false],"domain":"Fin_decision_problem","operation":"decision-decider-agreement","semantic_template":"qf-ext18-decision-decider-agreement/{\"decider\":[true,true,false,false,false,false],\"n\":6,\"yes\":[0]}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_arithmetic","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"僅為產生端候選及自檢；主端須另做驗收，不構成人工審定、普遍證明、Lean執行或形式Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-13","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261013-advance-20261018-r06-decision-problem-0028","batch_id":"batch-20261013-advance-20261018-r06-decision-problem-foundations","language":"zh-Hant","source_mko_ids":["mko-decision-problem"],"title_zh":"有限決定問題","stem_zh":"明示有限輸入域。操作=decision-decider-agreement；資料={\"n\":6,\"yes\":[1],\"decider\":[false,true,false,false,false,false]}。請依 [n,yes_set,decider,mismatches,agrees] 的欄序回答。","answer":{"kind":"expression","value":"(6, [1], [否, 是, 否, 否, 否, 否], [], 是)","explanation_zh":"擴展基礎核對=(6, [1], [否, 是, 否, 否, 否, 否], [], 是)；依完整明示資料逐欄精確重算；有限／合成資料核對不是一般形式證明；規格與decider分離；有限完整表不外推無限可判定性。"},"difficulty":{"band":"undergraduate_core","level":1,"skills":["有限決定問題"]},"variant":{"family_id":"qf-ext18-decision-decider-agreement","seed":202610186028,"parameters":{"n":6,"yes":[1],"decider":[false,true,false,false,false,false],"domain":"Fin_decision_problem","operation":"decision-decider-agreement","semantic_template":"qf-ext18-decision-decider-agreement/{\"decider\":[false,true,false,false,false,false],\"n\":6,\"yes\":[1]}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_arithmetic","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"僅為產生端候選及自檢；主端須另做驗收，不構成人工審定、普遍證明、Lean執行或形式Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-13","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261013-advance-20261018-r06-decision-problem-0029","batch_id":"batch-20261013-advance-20261018-r06-decision-problem-foundations","language":"zh-Hant","source_mko_ids":["mko-decision-problem"],"title_zh":"有限決定問題","stem_zh":"明示有限輸入域。操作=decision-decider-agreement；資料={\"n\":6,\"yes\":[0,1],\"decider\":[true,true,false,true,false,false]}。請依 [n,yes_set,decider,mismatches,agrees] 的欄序回答。","answer":{"kind":"expression","value":"(6, [0, 1], [是, 是, 否, 是, 否, 否], [3], 否)","explanation_zh":"擴展基礎核對=(6, [0, 1], [是, 是, 否, 是, 否, 否], [3], 否)；依完整明示資料逐欄精確重算；有限／合成資料核對不是一般形式證明；規格與decider分離；有限完整表不外推無限可判定性。"},"difficulty":{"band":"undergraduate_core","level":1,"skills":["有限決定問題"]},"variant":{"family_id":"qf-ext18-decision-decider-agreement","seed":202610186029,"parameters":{"n":6,"yes":[0,1],"decider":[true,true,false,true,false,false],"domain":"Fin_decision_problem","operation":"decision-decider-agreement","semantic_template":"qf-ext18-decision-decider-agreement/{\"decider\":[true,true,false,true,false,false],\"n\":6,\"yes\":[0,1]}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_arithmetic","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"僅為產生端候選及自檢；主端須另做驗收，不構成人工審定、普遍證明、Lean執行或形式Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-13","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261013-advance-20261018-r06-decision-problem-0030","batch_id":"batch-20261013-advance-20261018-r06-decision-problem-foundations","language":"zh-Hant","source_mko_ids":["mko-decision-problem"],"title_zh":"有限決定問題","stem_zh":"明示有限輸入域。操作=decision-decider-agreement；資料={\"n\":6,\"yes\":[2],\"decider\":[false,false,true,false,false,false]}。請依 [n,yes_set,decider,mismatches,agrees] 的欄序回答。","answer":{"kind":"expression","value":"(6, [2], [否, 否, 是, 否, 否, 否], [], 是)","explanation_zh":"擴展基礎核對=(6, [2], [否, 否, 是, 否, 否, 否], [], 是)；依完整明示資料逐欄精確重算；有限／合成資料核對不是一般形式證明；規格與decider分離；有限完整表不外推無限可判定性。"},"difficulty":{"band":"undergraduate_core","level":1,"skills":["有限決定問題"]},"variant":{"family_id":"qf-ext18-decision-decider-agreement","seed":202610186030,"parameters":{"n":6,"yes":[2],"decider":[false,false,true,false,false,false],"domain":"Fin_decision_problem","operation":"decision-decider-agreement","semantic_template":"qf-ext18-decision-decider-agreement/{\"decider\":[false,false,true,false,false,false],\"n\":6,\"yes\":[2]}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_arithmetic","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"僅為產生端候選及自檢；主端須另做驗收，不構成人工審定、普遍證明、Lean執行或形式Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-13","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261013-advance-20261018-r06-decision-problem-0031","batch_id":"batch-20261013-advance-20261018-r06-decision-problem-foundations","language":"zh-Hant","source_mko_ids":["mko-decision-problem"],"title_zh":"有限決定問題","stem_zh":"明示有限輸入域。操作=decision-decider-agreement；資料={\"n\":6,\"yes\":[0,2],\"decider\":[true,false,true,false,false,true]}。請依 [n,yes_set,decider,mismatches,agrees] 的欄序回答。","answer":{"kind":"expression","value":"(6, [0, 2], [是, 否, 是, 否, 否, 是], [5], 否)","explanation_zh":"擴展基礎核對=(6, [0, 2], [是, 否, 是, 否, 否, 是], [5], 否)；依完整明示資料逐欄精確重算；有限／合成資料核對不是一般形式證明；規格與decider分離；有限完整表不外推無限可判定性。"},"difficulty":{"band":"undergraduate_core","level":1,"skills":["有限決定問題"]},"variant":{"family_id":"qf-ext18-decision-decider-agreement","seed":202610186031,"parameters":{"n":6,"yes":[0,2],"decider":[true,false,true,false,false,true],"domain":"Fin_decision_problem","operation":"decision-decider-agreement","semantic_template":"qf-ext18-decision-decider-agreement/{\"decider\":[true,false,true,false,false,true],\"n\":6,\"yes\":[0,2]}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_arithmetic","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"僅為產生端候選及自檢；主端須另做驗收，不構成人工審定、普遍證明、Lean執行或形式Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-13","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261013-advance-20261018-r06-decision-problem-0032","batch_id":"batch-20261013-advance-20261018-r06-decision-problem-foundations","language":"zh-Hant","source_mko_ids":["mko-decision-problem"],"title_zh":"有限決定問題","stem_zh":"明示有限輸入域。操作=decision-decider-agreement；資料={\"n\":6,\"yes\":[1,2],\"decider\":[false,true,true,false,false,false]}。請依 [n,yes_set,decider,mismatches,agrees] 的欄序回答。","answer":{"kind":"expression","value":"(6, [1, 2], [否, 是, 是, 否, 否, 否], [], 是)","explanation_zh":"擴展基礎核對=(6, [1, 2], [否, 是, 是, 否, 否, 否], [], 是)；依完整明示資料逐欄精確重算；有限／合成資料核對不是一般形式證明；規格與decider分離；有限完整表不外推無限可判定性。"},"difficulty":{"band":"undergraduate_core","level":1,"skills":["有限決定問題"]},"variant":{"family_id":"qf-ext18-decision-decider-agreement","seed":202610186032,"parameters":{"n":6,"yes":[1,2],"decider":[false,true,true,false,false,false],"domain":"Fin_decision_problem","operation":"decision-decider-agreement","semantic_template":"qf-ext18-decision-decider-agreement/{\"decider\":[false,true,true,false,false,false],\"n\":6,\"yes\":[1,2]}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_arithmetic","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"僅為產生端候選及自檢；主端須另做驗收，不構成人工審定、普遍證明、Lean執行或形式Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-13","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261013-advance-20261018-r06-decision-problem-0033","batch_id":"batch-20261013-advance-20261018-r06-decision-problem-foundations","language":"zh-Hant","source_mko_ids":["mko-decision-problem"],"title_zh":"有限決定問題","stem_zh":"明示有限輸入域。操作=decision-decider-agreement；資料={\"n\":6,\"yes\":[0,1,2],\"decider\":[true,false,true,false,false,false]}。請依 [n,yes_set,decider,mismatches,agrees] 的欄序回答。","answer":{"kind":"expression","value":"(6, [0, 1, 2], [是, 否, 是, 否, 否, 否], [1], 否)","explanation_zh":"擴展基礎核對=(6, [0, 1, 2], [是, 否, 是, 否, 否, 否], [1], 否)；依完整明示資料逐欄精確重算；有限／合成資料核對不是一般形式證明；規格與decider分離；有限完整表不外推無限可判定性。"},"difficulty":{"band":"undergraduate_core","level":1,"skills":["有限決定問題"]},"variant":{"family_id":"qf-ext18-decision-decider-agreement","seed":202610186033,"parameters":{"n":6,"yes":[0,1,2],"decider":[true,false,true,false,false,false],"domain":"Fin_decision_problem","operation":"decision-decider-agreement","semantic_template":"qf-ext18-decision-decider-agreement/{\"decider\":[true,false,true,false,false,false],\"n\":6,\"yes\":[0,1,2]}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_arithmetic","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"僅為產生端候選及自檢；主端須另做驗收，不構成人工審定、普遍證明、Lean執行或形式Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-13","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261013-advance-20261018-r06-decision-problem-0034","batch_id":"batch-20261013-advance-20261018-r06-decision-problem-foundations","language":"zh-Hant","source_mko_ids":["mko-decision-problem"],"title_zh":"有限決定問題","stem_zh":"明示有限輸入域。操作=decision-decider-agreement；資料={\"n\":6,\"yes\":[3],\"decider\":[false,false,false,true,false,false]}。請依 [n,yes_set,decider,mismatches,agrees] 的欄序回答。","answer":{"kind":"expression","value":"(6, [3], [否, 否, 否, 是, 否, 否], [], 是)","explanation_zh":"擴展基礎核對=(6, [3], [否, 否, 否, 是, 否, 否], [], 是)；依完整明示資料逐欄精確重算；有限／合成資料核對不是一般形式證明；規格與decider分離；有限完整表不外推無限可判定性。"},"difficulty":{"band":"undergraduate_core","level":2,"skills":["有限決定問題"]},"variant":{"family_id":"qf-ext18-decision-decider-agreement","seed":202610186034,"parameters":{"n":6,"yes":[3],"decider":[false,false,false,true,false,false],"domain":"Fin_decision_problem","operation":"decision-decider-agreement","semantic_template":"qf-ext18-decision-decider-agreement/{\"decider\":[false,false,false,true,false,false],\"n\":6,\"yes\":[3]}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_arithmetic","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"僅為產生端候選及自檢；主端須另做驗收，不構成人工審定、普遍證明、Lean執行或形式Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-13","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261013-advance-20261018-r06-decision-problem-0035","batch_id":"batch-20261013-advance-20261018-r06-decision-problem-foundations","language":"zh-Hant","source_mko_ids":["mko-decision-problem"],"title_zh":"有限決定問題","stem_zh":"明示有限輸入域。操作=decision-decider-agreement；資料={\"n\":6,\"yes\":[0,3],\"decider\":[true,false,false,false,false,false]}。請依 [n,yes_set,decider,mismatches,agrees] 的欄序回答。","answer":{"kind":"expression","value":"(6, [0, 3], [是, 否, 否, 否, 否, 否], [3], 否)","explanation_zh":"擴展基礎核對=(6, [0, 3], [是, 否, 否, 否, 否, 否], [3], 否)；依完整明示資料逐欄精確重算；有限／合成資料核對不是一般形式證明；規格與decider分離；有限完整表不外推無限可判定性。"},"difficulty":{"band":"undergraduate_core","level":2,"skills":["有限決定問題"]},"variant":{"family_id":"qf-ext18-decision-decider-agreement","seed":202610186035,"parameters":{"n":6,"yes":[0,3],"decider":[true,false,false,false,false,false],"domain":"Fin_decision_problem","operation":"decision-decider-agreement","semantic_template":"qf-ext18-decision-decider-agreement/{\"decider\":[true,false,false,false,false,false],\"n\":6,\"yes\":[0,3]}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_arithmetic","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"僅為產生端候選及自檢；主端須另做驗收，不構成人工審定、普遍證明、Lean執行或形式Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-13","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261013-advance-20261018-r06-decision-problem-0036","batch_id":"batch-20261013-advance-20261018-r06-decision-problem-foundations","language":"zh-Hant","source_mko_ids":["mko-decision-problem"],"title_zh":"有限決定問題","stem_zh":"明示有限輸入域。操作=decision-decider-agreement；資料={\"n\":6,\"yes\":[1,3],\"decider\":[false,true,false,true,false,false]}。請依 [n,yes_set,decider,mismatches,agrees] 的欄序回答。","answer":{"kind":"expression","value":"(6, [1, 3], [否, 是, 否, 是, 否, 否], [], 是)","explanation_zh":"擴展基礎核對=(6, [1, 3], [否, 是, 否, 是, 否, 否], [], 是)；依完整明示資料逐欄精確重算；有限／合成資料核對不是一般形式證明；規格與decider分離；有限完整表不外推無限可判定性。"},"difficulty":{"band":"undergraduate_core","level":2,"skills":["有限決定問題"]},"variant":{"family_id":"qf-ext18-decision-decider-agreement","seed":202610186036,"parameters":{"n":6,"yes":[1,3],"decider":[false,true,false,true,false,false],"domain":"Fin_decision_problem","operation":"decision-decider-agreement","semantic_template":"qf-ext18-decision-decider-agreement/{\"decider\":[false,true,false,true,false,false],\"n\":6,\"yes\":[1,3]}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_arithmetic","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"僅為產生端候選及自檢；主端須另做驗收，不構成人工審定、普遍證明、Lean執行或形式Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-13","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261013-advance-20261018-r06-decision-problem-0037","batch_id":"batch-20261013-advance-20261018-r06-decision-problem-foundations","language":"zh-Hant","source_mko_ids":["mko-decision-problem"],"title_zh":"有限決定問題","stem_zh":"明示有限輸入域。操作=decision-decider-agreement；資料={\"n\":6,\"yes\":[0,1,3],\"decider\":[true,true,false,true,false,true]}。請依 [n,yes_set,decider,mismatches,agrees] 的欄序回答。","answer":{"kind":"expression","value":"(6, [0, 1, 3], [是, 是, 否, 是, 否, 是], [5], 否)","explanation_zh":"擴展基礎核對=(6, [0, 1, 3], [是, 是, 否, 是, 否, 是], [5], 否)；依完整明示資料逐欄精確重算；有限／合成資料核對不是一般形式證明；規格與decider分離；有限完整表不外推無限可判定性。"},"difficulty":{"band":"undergraduate_core","level":2,"skills":["有限決定問題"]},"variant":{"family_id":"qf-ext18-decision-decider-agreement","seed":202610186037,"parameters":{"n":6,"yes":[0,1,3],"decider":[true,true,false,true,false,true],"domain":"Fin_decision_problem","operation":"decision-decider-agreement","semantic_template":"qf-ext18-decision-decider-agreement/{\"decider\":[true,true,false,true,false,true],\"n\":6,\"yes\":[0,1,3]}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_arithmetic","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"僅為產生端候選及自檢；主端須另做驗收，不構成人工審定、普遍證明、Lean執行或形式Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-13","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261013-advance-20261018-r06-decision-problem-0038","batch_id":"batch-20261013-advance-20261018-r06-decision-problem-foundations","language":"zh-Hant","source_mko_ids":["mko-decision-problem"],"title_zh":"有限決定問題","stem_zh":"明示有限輸入域。操作=decision-decider-agreement；資料={\"n\":6,\"yes\":[2,3],\"decider\":[false,false,true,true,false,false]}。請依 [n,yes_set,decider,mismatches,agrees] 的欄序回答。","answer":{"kind":"expression","value":"(6, [2, 3], [否, 否, 是, 是, 否, 否], [], 是)","explanation_zh":"擴展基礎核對=(6, [2, 3], [否, 否, 是, 是, 否, 否], [], 是)；依完整明示資料逐欄精確重算；有限／合成資料核對不是一般形式證明；規格與decider分離；有限完整表不外推無限可判定性。"},"difficulty":{"band":"undergraduate_core","level":2,"skills":["有限決定問題"]},"variant":{"family_id":"qf-ext18-decision-decider-agreement","seed":202610186038,"parameters":{"n":6,"yes":[2,3],"decider":[false,false,true,true,false,false],"domain":"Fin_decision_problem","operation":"decision-decider-agreement","semantic_template":"qf-ext18-decision-decider-agreement/{\"decider\":[false,false,true,true,false,false],\"n\":6,\"yes\":[2,3]}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_arithmetic","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"僅為產生端候選及自檢；主端須另做驗收，不構成人工審定、普遍證明、Lean執行或形式Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-13","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261013-advance-20261018-r06-decision-problem-0039","batch_id":"batch-20261013-advance-20261018-r06-decision-problem-foundations","language":"zh-Hant","source_mko_ids":["mko-decision-problem"],"title_zh":"有限決定問題","stem_zh":"明示有限輸入域。操作=decision-decider-agreement；資料={\"n\":6,\"yes\":[0,2,3],\"decider\":[true,true,true,true,false,false]}。請依 [n,yes_set,decider,mismatches,agrees] 的欄序回答。","answer":{"kind":"expression","value":"(6, [0, 2, 3], [是, 是, 是, 是, 否, 否], [1], 否)","explanation_zh":"擴展基礎核對=(6, [0, 2, 3], [是, 是, 是, 是, 否, 否], [1], 否)；依完整明示資料逐欄精確重算；有限／合成資料核對不是一般形式證明；規格與decider分離；有限完整表不外推無限可判定性。"},"difficulty":{"band":"undergraduate_core","level":2,"skills":["有限決定問題"]},"variant":{"family_id":"qf-ext18-decision-decider-agreement","seed":202610186039,"parameters":{"n":6,"yes":[0,2,3],"decider":[true,true,true,true,false,false],"domain":"Fin_decision_problem","operation":"decision-decider-agreement","semantic_template":"qf-ext18-decision-decider-agreement/{\"decider\":[true,true,true,true,false,false],\"n\":6,\"yes\":[0,2,3]}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_arithmetic","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"僅為產生端候選及自檢；主端須另做驗收，不構成人工審定、普遍證明、Lean執行或形式Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-13","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261013-advance-20261018-r06-decision-problem-0040","batch_id":"batch-20261013-advance-20261018-r06-decision-problem-foundations","language":"zh-Hant","source_mko_ids":["mko-decision-problem"],"title_zh":"有限決定問題","stem_zh":"明示有限輸入域。操作=decision-decider-agreement；資料={\"n\":6,\"yes\":[1,2,3],\"decider\":[false,true,true,true,false,false]}。請依 [n,yes_set,decider,mismatches,agrees] 的欄序回答。","answer":{"kind":"expression","value":"(6, [1, 2, 3], [否, 是, 是, 是, 否, 否], [], 是)","explanation_zh":"擴展基礎核對=(6, [1, 2, 3], [否, 是, 是, 是, 否, 否], [], 是)；依完整明示資料逐欄精確重算；有限／合成資料核對不是一般形式證明；規格與decider分離；有限完整表不外推無限可判定性。"},"difficulty":{"band":"undergraduate_core","level":2,"skills":["有限決定問題"]},"variant":{"family_id":"qf-ext18-decision-decider-agreement","seed":202610186040,"parameters":{"n":6,"yes":[1,2,3],"decider":[false,true,true,true,false,false],"domain":"Fin_decision_problem","operation":"decision-decider-agreement","semantic_template":"qf-ext18-decision-decider-agreement/{\"decider\":[false,true,true,true,false,false],\"n\":6,\"yes\":[1,2,3]}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_arithmetic","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"僅為產生端候選及自檢；主端須另做驗收，不構成人工審定、普遍證明、Lean執行或形式Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-13","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261013-advance-20261018-r06-decision-problem-0041","batch_id":"batch-20261013-advance-20261018-r06-decision-problem-foundations","language":"zh-Hant","source_mko_ids":["mko-decision-problem"],"title_zh":"有限決定問題","stem_zh":"明示有限輸入域。操作=decision-decider-agreement；資料={\"n\":6,\"yes\":[0,1,2,3],\"decider\":[true,true,true,false,false,false]}。請依 [n,yes_set,decider,mismatches,agrees] 的欄序回答。","answer":{"kind":"expression","value":"(6, [0, 1, 2, 3], [是, 是, 是, 否, 否, 否], [3], 否)","explanation_zh":"擴展基礎核對=(6, [0, 1, 2, 3], [是, 是, 是, 否, 否, 否], [3], 否)；依完整明示資料逐欄精確重算；有限／合成資料核對不是一般形式證明；規格與decider分離；有限完整表不外推無限可判定性。"},"difficulty":{"band":"undergraduate_core","level":2,"skills":["有限決定問題"]},"variant":{"family_id":"qf-ext18-decision-decider-agreement","seed":202610186041,"parameters":{"n":6,"yes":[0,1,2,3],"decider":[true,true,true,false,false,false],"domain":"Fin_decision_problem","operation":"decision-decider-agreement","semantic_template":"qf-ext18-decision-decider-agreement/{\"decider\":[true,true,true,false,false,false],\"n\":6,\"yes\":[0,1,2,3]}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_arithmetic","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"僅為產生端候選及自檢；主端須另做驗收，不構成人工審定、普遍證明、Lean執行或形式Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-13","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261013-advance-20261018-r06-decision-problem-0042","batch_id":"batch-20261013-advance-20261018-r06-decision-problem-foundations","language":"zh-Hant","source_mko_ids":["mko-decision-problem"],"title_zh":"有限決定問題","stem_zh":"明示有限輸入域。操作=decision-decider-agreement；資料={\"n\":6,\"yes\":[4],\"decider\":[false,false,false,false,true,false]}。請依 [n,yes_set,decider,mismatches,agrees] 的欄序回答。","answer":{"kind":"expression","value":"(6, [4], [否, 否, 否, 否, 是, 否], [], 是)","explanation_zh":"擴展基礎核對=(6, [4], [否, 否, 否, 否, 是, 否], [], 是)；依完整明示資料逐欄精確重算；有限／合成資料核對不是一般形式證明；規格與decider分離；有限完整表不外推無限可判定性。"},"difficulty":{"band":"undergraduate_core","level":2,"skills":["有限決定問題"]},"variant":{"family_id":"qf-ext18-decision-decider-agreement","seed":202610186042,"parameters":{"n":6,"yes":[4],"decider":[false,false,false,false,true,false],"domain":"Fin_decision_problem","operation":"decision-decider-agreement","semantic_template":"qf-ext18-decision-decider-agreement/{\"decider\":[false,false,false,false,true,false],\"n\":6,\"yes\":[4]}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_arithmetic","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"僅為產生端候選及自檢；主端須另做驗收，不構成人工審定、普遍證明、Lean執行或形式Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-13","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261013-advance-20261018-r06-decision-problem-0043","batch_id":"batch-20261013-advance-20261018-r06-decision-problem-foundations","language":"zh-Hant","source_mko_ids":["mko-decision-problem"],"title_zh":"有限決定問題","stem_zh":"明示有限輸入域。操作=decision-decider-agreement；資料={\"n\":6,\"yes\":[0,4],\"decider\":[true,false,false,false,true,true]}。請依 [n,yes_set,decider,mismatches,agrees] 的欄序回答。","answer":{"kind":"expression","value":"(6, [0, 4], [是, 否, 否, 否, 是, 是], [5], 否)","explanation_zh":"擴展基礎核對=(6, [0, 4], [是, 否, 否, 否, 是, 是], [5], 否)；依完整明示資料逐欄精確重算；有限／合成資料核對不是一般形式證明；規格與decider分離；有限完整表不外推無限可判定性。"},"difficulty":{"band":"undergraduate_core","level":3,"skills":["有限決定問題"]},"variant":{"family_id":"qf-ext18-decision-decider-agreement","seed":202610186043,"parameters":{"n":6,"yes":[0,4],"decider":[true,false,false,false,true,true],"domain":"Fin_decision_problem","operation":"decision-decider-agreement","semantic_template":"qf-ext18-decision-decider-agreement/{\"decider\":[true,false,false,false,true,true],\"n\":6,\"yes\":[0,4]}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_arithmetic","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"僅為產生端候選及自檢；主端須另做驗收，不構成人工審定、普遍證明、Lean執行或形式Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-13","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261013-advance-20261018-r06-decision-problem-0044","batch_id":"batch-20261013-advance-20261018-r06-decision-problem-foundations","language":"zh-Hant","source_mko_ids":["mko-decision-problem"],"title_zh":"有限決定問題","stem_zh":"明示有限輸入域。操作=decision-decider-agreement；資料={\"n\":6,\"yes\":[1,4],\"decider\":[false,true,false,false,true,false]}。請依 [n,yes_set,decider,mismatches,agrees] 的欄序回答。","answer":{"kind":"expression","value":"(6, [1, 4], [否, 是, 否, 否, 是, 否], [], 是)","explanation_zh":"擴展基礎核對=(6, [1, 4], [否, 是, 否, 否, 是, 否], [], 是)；依完整明示資料逐欄精確重算；有限／合成資料核對不是一般形式證明；規格與decider分離；有限完整表不外推無限可判定性。"},"difficulty":{"band":"undergraduate_core","level":3,"skills":["有限決定問題"]},"variant":{"family_id":"qf-ext18-decision-decider-agreement","seed":202610186044,"parameters":{"n":6,"yes":[1,4],"decider":[false,true,false,false,true,false],"domain":"Fin_decision_problem","operation":"decision-decider-agreement","semantic_template":"qf-ext18-decision-decider-agreement/{\"decider\":[false,true,false,false,true,false],\"n\":6,\"yes\":[1,4]}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_arithmetic","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"僅為產生端候選及自檢；主端須另做驗收，不構成人工審定、普遍證明、Lean執行或形式Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-13","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261013-advance-20261018-r06-decision-problem-0045","batch_id":"batch-20261013-advance-20261018-r06-decision-problem-foundations","language":"zh-Hant","source_mko_ids":["mko-decision-problem"],"title_zh":"有限決定問題","stem_zh":"明示有限輸入域。操作=decision-decider-agreement；資料={\"n\":6,\"yes\":[0,1,4],\"decider\":[true,false,false,false,true,false]}。請依 [n,yes_set,decider,mismatches,agrees] 的欄序回答。","answer":{"kind":"expression","value":"(6, [0, 1, 4], [是, 否, 否, 否, 是, 否], [1], 否)","explanation_zh":"擴展基礎核對=(6, [0, 1, 4], [是, 否, 否, 否, 是, 否], [1], 否)；依完整明示資料逐欄精確重算；有限／合成資料核對不是一般形式證明；規格與decider分離；有限完整表不外推無限可判定性。"},"difficulty":{"band":"undergraduate_core","level":3,"skills":["有限決定問題"]},"variant":{"family_id":"qf-ext18-decision-decider-agreement","seed":202610186045,"parameters":{"n":6,"yes":[0,1,4],"decider":[true,false,false,false,true,false],"domain":"Fin_decision_problem","operation":"decision-decider-agreement","semantic_template":"qf-ext18-decision-decider-agreement/{\"decider\":[true,false,false,false,true,false],\"n\":6,\"yes\":[0,1,4]}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_arithmetic","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"僅為產生端候選及自檢；主端須另做驗收，不構成人工審定、普遍證明、Lean執行或形式Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-13","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261013-advance-20261018-r06-decision-problem-0046","batch_id":"batch-20261013-advance-20261018-r06-decision-problem-foundations","language":"zh-Hant","source_mko_ids":["mko-decision-problem"],"title_zh":"有限決定問題","stem_zh":"明示有限輸入域。操作=decision-decider-agreement；資料={\"n\":6,\"yes\":[2,4],\"decider\":[false,false,true,false,true,false]}。請依 [n,yes_set,decider,mismatches,agrees] 的欄序回答。","answer":{"kind":"expression","value":"(6, [2, 4], [否, 否, 是, 否, 是, 否], [], 是)","explanation_zh":"擴展基礎核對=(6, [2, 4], [否, 否, 是, 否, 是, 否], [], 是)；依完整明示資料逐欄精確重算；有限／合成資料核對不是一般形式證明；規格與decider分離；有限完整表不外推無限可判定性。"},"difficulty":{"band":"undergraduate_core","level":3,"skills":["有限決定問題"]},"variant":{"family_id":"qf-ext18-decision-decider-agreement","seed":202610186046,"parameters":{"n":6,"yes":[2,4],"decider":[false,false,true,false,true,false],"domain":"Fin_decision_problem","operation":"decision-decider-agreement","semantic_template":"qf-ext18-decision-decider-agreement/{\"decider\":[false,false,true,false,true,false],\"n\":6,\"yes\":[2,4]}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_arithmetic","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"僅為產生端候選及自檢；主端須另做驗收，不構成人工審定、普遍證明、Lean執行或形式Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-13","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261013-advance-20261018-r06-decision-problem-0047","batch_id":"batch-20261013-advance-20261018-r06-decision-problem-foundations","language":"zh-Hant","source_mko_ids":["mko-decision-problem"],"title_zh":"有限決定問題","stem_zh":"明示有限輸入域。操作=decision-decider-agreement；資料={\"n\":6,\"yes\":[0,2,4],\"decider\":[true,false,true,true,true,false]}。請依 [n,yes_set,decider,mismatches,agrees] 的欄序回答。","answer":{"kind":"expression","value":"(6, [0, 2, 4], [是, 否, 是, 是, 是, 否], [3], 否)","explanation_zh":"擴展基礎核對=(6, [0, 2, 4], [是, 否, 是, 是, 是, 否], [3], 否)；依完整明示資料逐欄精確重算；有限／合成資料核對不是一般形式證明；規格與decider分離；有限完整表不外推無限可判定性。"},"difficulty":{"band":"undergraduate_core","level":3,"skills":["有限決定問題"]},"variant":{"family_id":"qf-ext18-decision-decider-agreement","seed":202610186047,"parameters":{"n":6,"yes":[0,2,4],"decider":[true,false,true,true,true,false],"domain":"Fin_decision_problem","operation":"decision-decider-agreement","semantic_template":"qf-ext18-decision-decider-agreement/{\"decider\":[true,false,true,true,true,false],\"n\":6,\"yes\":[0,2,4]}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_arithmetic","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"僅為產生端候選及自檢；主端須另做驗收，不構成人工審定、普遍證明、Lean執行或形式Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-13","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261013-advance-20261018-r06-decision-problem-0048","batch_id":"batch-20261013-advance-20261018-r06-decision-problem-foundations","language":"zh-Hant","source_mko_ids":["mko-decision-problem"],"title_zh":"有限決定問題","stem_zh":"明示有限輸入域。操作=decision-decider-agreement；資料={\"n\":6,\"yes\":[1,2,4],\"decider\":[false,true,true,false,true,false]}。請依 [n,yes_set,decider,mismatches,agrees] 的欄序回答。","answer":{"kind":"expression","value":"(6, [1, 2, 4], [否, 是, 是, 否, 是, 否], [], 是)","explanation_zh":"擴展基礎核對=(6, [1, 2, 4], [否, 是, 是, 否, 是, 否], [], 是)；依完整明示資料逐欄精確重算；有限／合成資料核對不是一般形式證明；規格與decider分離；有限完整表不外推無限可判定性。"},"difficulty":{"band":"undergraduate_core","level":3,"skills":["有限決定問題"]},"variant":{"family_id":"qf-ext18-decision-decider-agreement","seed":202610186048,"parameters":{"n":6,"yes":[1,2,4],"decider":[false,true,true,false,true,false],"domain":"Fin_decision_problem","operation":"decision-decider-agreement","semantic_template":"qf-ext18-decision-decider-agreement/{\"decider\":[false,true,true,false,true,false],\"n\":6,\"yes\":[1,2,4]}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_arithmetic","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"僅為產生端候選及自檢；主端須另做驗收，不構成人工審定、普遍證明、Lean執行或形式Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-13","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261013-advance-20261018-r06-decision-problem-0049","batch_id":"batch-20261013-advance-20261018-r06-decision-problem-foundations","language":"zh-Hant","source_mko_ids":["mko-decision-problem"],"title_zh":"有限決定問題","stem_zh":"明示有限輸入域。操作=decision-decider-agreement；資料={\"n\":6,\"yes\":[0,1,2,4],\"decider\":[true,true,true,false,true,true]}。請依 [n,yes_set,decider,mismatches,agrees] 的欄序回答。","answer":{"kind":"expression","value":"(6, [0, 1, 2, 4], [是, 是, 是, 否, 是, 是], [5], 否)","explanation_zh":"擴展基礎核對=(6, [0, 1, 2, 4], [是, 是, 是, 否, 是, 是], [5], 否)；依完整明示資料逐欄精確重算；有限／合成資料核對不是一般形式證明；規格與decider分離；有限完整表不外推無限可判定性。"},"difficulty":{"band":"undergraduate_core","level":3,"skills":["有限決定問題"]},"variant":{"family_id":"qf-ext18-decision-decider-agreement","seed":202610186049,"parameters":{"n":6,"yes":[0,1,2,4],"decider":[true,true,true,false,true,true],"domain":"Fin_decision_problem","operation":"decision-decider-agreement","semantic_template":"qf-ext18-decision-decider-agreement/{\"decider\":[true,true,true,false,true,true],\"n\":6,\"yes\":[0,1,2,4]}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_arithmetic","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"僅為產生端候選及自檢；主端須另做驗收，不構成人工審定、普遍證明、Lean執行或形式Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-13","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261013-advance-20261018-r06-decision-problem-0050","batch_id":"batch-20261013-advance-20261018-r06-decision-problem-foundations","language":"zh-Hant","source_mko_ids":["mko-decision-problem"],"title_zh":"有限決定問題","stem_zh":"明示有限輸入域。操作=decision-decider-agreement；資料={\"n\":6,\"yes\":[3,4],\"decider\":[false,false,false,true,true,false]}。請依 [n,yes_set,decider,mismatches,agrees] 的欄序回答。","answer":{"kind":"expression","value":"(6, [3, 4], [否, 否, 否, 是, 是, 否], [], 是)","explanation_zh":"擴展基礎核對=(6, [3, 4], [否, 否, 否, 是, 是, 否], [], 是)；依完整明示資料逐欄精確重算；有限／合成資料核對不是一般形式證明；規格與decider分離；有限完整表不外推無限可判定性。"},"difficulty":{"band":"undergraduate_core","level":3,"skills":["有限決定問題"]},"variant":{"family_id":"qf-ext18-decision-decider-agreement","seed":202610186050,"parameters":{"n":6,"yes":[3,4],"decider":[false,false,false,true,true,false],"domain":"Fin_decision_problem","operation":"decision-decider-agreement","semantic_template":"qf-ext18-decision-decider-agreement/{\"decider\":[false,false,false,true,true,false],\"n\":6,\"yes\":[3,4]}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_arithmetic","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"僅為產生端候選及自檢；主端須另做驗收，不構成人工審定、普遍證明、Lean執行或形式Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-13","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261013-advance-20261018-r06-decision-problem-0051","batch_id":"batch-20261013-advance-20261018-r06-decision-problem-foundations","language":"zh-Hant","source_mko_ids":["mko-decision-problem"],"title_zh":"有限決定問題","stem_zh":"明示有限輸入域。操作=decision-domain-restriction；資料={\"n\":6,\"yes\":[],\"decider\":[false,false,true,false,false,false],\"subset\":[0,1,3]}。請依 [n,subset,restricted_yes,restricted_mismatches,agrees] 的欄序回答。","answer":{"kind":"expression","value":"(6, [0, 1, 3], [], [], 是)","explanation_zh":"擴展基礎核對=(6, [0, 1, 3], [], [], 是)；依完整明示資料逐欄精確重算；有限／合成資料核對不是一般形式證明；規格與decider分離；有限完整表不外推無限可判定性。"},"difficulty":{"band":"undergraduate_core","level":1,"skills":["有限決定問題"]},"variant":{"family_id":"qf-ext18-decision-domain-restriction","seed":202610186051,"parameters":{"n":6,"yes":[],"decider":[false,false,true,false,false,false],"subset":[0,1,3],"domain":"Fin_decision_problem","operation":"decision-domain-restriction","semantic_template":"qf-ext18-decision-domain-restriction/{\"decider\":[false,false,true,false,false,false],\"n\":6,\"subset\":[0,1,3],\"yes\":[]}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_arithmetic","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"僅為產生端候選及自檢；主端須另做驗收，不構成人工審定、普遍證明、Lean執行或形式Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-13","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261013-advance-20261018-r06-decision-problem-0052","batch_id":"batch-20261013-advance-20261018-r06-decision-problem-foundations","language":"zh-Hant","source_mko_ids":["mko-decision-problem"],"title_zh":"有限決定問題","stem_zh":"明示有限輸入域。操作=decision-domain-restriction；資料={\"n\":6,\"yes\":[0],\"decider\":[true,false,false,true,false,false],\"subset\":[1,2,4]}。請依 [n,subset,restricted_yes,restricted_mismatches,agrees] 的欄序回答。","answer":{"kind":"expression","value":"(6, [1, 2, 4], [], [], 是)","explanation_zh":"擴展基礎核對=(6, [1, 2, 4], [], [], 是)；依完整明示資料逐欄精確重算；有限／合成資料核對不是一般形式證明；規格與decider分離；有限完整表不外推無限可判定性。"},"difficulty":{"band":"undergraduate_core","level":1,"skills":["有限決定問題"]},"variant":{"family_id":"qf-ext18-decision-domain-restriction","seed":202610186052,"parameters":{"n":6,"yes":[0],"decider":[true,false,false,true,false,false],"subset":[1,2,4],"domain":"Fin_decision_problem","operation":"decision-domain-restriction","semantic_template":"qf-ext18-decision-domain-restriction/{\"decider\":[true,false,false,true,false,false],\"n\":6,\"subset\":[1,2,4],\"yes\":[0]}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_arithmetic","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"僅為產生端候選及自檢；主端須另做驗收，不構成人工審定、普遍證明、Lean執行或形式Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-13","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261013-advance-20261018-r06-decision-problem-0053","batch_id":"batch-20261013-advance-20261018-r06-decision-problem-foundations","language":"zh-Hant","source_mko_ids":["mko-decision-problem"],"title_zh":"有限決定問題","stem_zh":"明示有限輸入域。操作=decision-domain-restriction；資料={\"n\":6,\"yes\":[1],\"decider\":[false,true,false,false,true,false],\"subset\":[2,3,5]}。請依 [n,subset,restricted_yes,restricted_mismatches,agrees] 的欄序回答。","answer":{"kind":"expression","value":"(6, [2, 3, 5], [], [], 是)","explanation_zh":"擴展基礎核對=(6, [2, 3, 5], [], [], 是)；依完整明示資料逐欄精確重算；有限／合成資料核對不是一般形式證明；規格與decider分離；有限完整表不外推無限可判定性。"},"difficulty":{"band":"undergraduate_core","level":1,"skills":["有限決定問題"]},"variant":{"family_id":"qf-ext18-decision-domain-restriction","seed":202610186053,"parameters":{"n":6,"yes":[1],"decider":[false,true,false,false,true,false],"subset":[2,3,5],"domain":"Fin_decision_problem","operation":"decision-domain-restriction","semantic_template":"qf-ext18-decision-domain-restriction/{\"decider\":[false,true,false,false,true,false],\"n\":6,\"subset\":[2,3,5],\"yes\":[1]}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_arithmetic","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"僅為產生端候選及自檢；主端須另做驗收，不構成人工審定、普遍證明、Lean執行或形式Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-13","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261013-advance-20261018-r06-decision-problem-0054","batch_id":"batch-20261013-advance-20261018-r06-decision-problem-foundations","language":"zh-Hant","source_mko_ids":["mko-decision-problem"],"title_zh":"有限決定問題","stem_zh":"明示有限輸入域。操作=decision-domain-restriction；資料={\"n\":6,\"yes\":[0,1],\"decider\":[true,true,false,false,false,true],\"subset\":[0,3,4]}。請依 [n,subset,restricted_yes,restricted_mismatches,agrees] 的欄序回答。","answer":{"kind":"expression","value":"(6, [0, 3, 4], [0], [], 是)","explanation_zh":"擴展基礎核對=(6, [0, 3, 4], [0], [], 是)；依完整明示資料逐欄精確重算；有限／合成資料核對不是一般形式證明；規格與decider分離；有限完整表不外推無限可判定性。"},"difficulty":{"band":"undergraduate_core","level":1,"skills":["有限決定問題"]},"variant":{"family_id":"qf-ext18-decision-domain-restriction","seed":202610186054,"parameters":{"n":6,"yes":[0,1],"decider":[true,true,false,false,false,true],"subset":[0,3,4],"domain":"Fin_decision_problem","operation":"decision-domain-restriction","semantic_template":"qf-ext18-decision-domain-restriction/{\"decider\":[true,true,false,false,false,true],\"n\":6,\"subset\":[0,3,4],\"yes\":[0,1]}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_arithmetic","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"僅為產生端候選及自檢；主端須另做驗收，不構成人工審定、普遍證明、Lean執行或形式Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-13","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261013-advance-20261018-r06-decision-problem-0055","batch_id":"batch-20261013-advance-20261018-r06-decision-problem-foundations","language":"zh-Hant","source_mko_ids":["mko-decision-problem"],"title_zh":"有限決定問題","stem_zh":"明示有限輸入域。操作=decision-domain-restriction；資料={\"n\":6,\"yes\":[2],\"decider\":[true,false,true,false,false,false],\"subset\":[1,4,5]}。請依 [n,subset,restricted_yes,restricted_mismatches,agrees] 的欄序回答。","answer":{"kind":"expression","value":"(6, [1, 4, 5], [], [], 是)","explanation_zh":"擴展基礎核對=(6, [1, 4, 5], [], [], 是)；依完整明示資料逐欄精確重算；有限／合成資料核對不是一般形式證明；規格與decider分離；有限完整表不外推無限可判定性。"},"difficulty":{"band":"undergraduate_core","level":1,"skills":["有限決定問題"]},"variant":{"family_id":"qf-ext18-decision-domain-restriction","seed":202610186055,"parameters":{"n":6,"yes":[2],"decider":[true,false,true,false,false,false],"subset":[1,4,5],"domain":"Fin_decision_problem","operation":"decision-domain-restriction","semantic_template":"qf-ext18-decision-domain-restriction/{\"decider\":[true,false,true,false,false,false],\"n\":6,\"subset\":[1,4,5],\"yes\":[2]}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_arithmetic","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"僅為產生端候選及自檢；主端須另做驗收，不構成人工審定、普遍證明、Lean執行或形式Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-13","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261013-advance-20261018-r06-decision-problem-0056","batch_id":"batch-20261013-advance-20261018-r06-decision-problem-foundations","language":"zh-Hant","source_mko_ids":["mko-decision-problem"],"title_zh":"有限決定問題","stem_zh":"明示有限輸入域。操作=decision-domain-restriction；資料={\"n\":6,\"yes\":[0,2],\"decider\":[true,true,true,false,false,false],\"subset\":[0,2,5]}。請依 [n,subset,restricted_yes,restricted_mismatches,agrees] 的欄序回答。","answer":{"kind":"expression","value":"(6, [0, 2, 5], [0, 2], [], 是)","explanation_zh":"擴展基礎核對=(6, [0, 2, 5], [0, 2], [], 是)；依完整明示資料逐欄精確重算；有限／合成資料核對不是一般形式證明；規格與decider分離；有限完整表不外推無限可判定性。"},"difficulty":{"band":"undergraduate_core","level":1,"skills":["有限決定問題"]},"variant":{"family_id":"qf-ext18-decision-domain-restriction","seed":202610186056,"parameters":{"n":6,"yes":[0,2],"decider":[true,true,true,false,false,false],"subset":[0,2,5],"domain":"Fin_decision_problem","operation":"decision-domain-restriction","semantic_template":"qf-ext18-decision-domain-restriction/{\"decider\":[true,true,true,false,false,false],\"n\":6,\"subset\":[0,2,5],\"yes\":[0,2]}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_arithmetic","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"僅為產生端候選及自檢；主端須另做驗收，不構成人工審定、普遍證明、Lean執行或形式Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-13","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261013-advance-20261018-r06-decision-problem-0057","batch_id":"batch-20261013-advance-20261018-r06-decision-problem-foundations","language":"zh-Hant","source_mko_ids":["mko-decision-problem"],"title_zh":"有限決定問題","stem_zh":"明示有限輸入域。操作=decision-domain-restriction；資料={\"n\":6,\"yes\":[1,2],\"decider\":[false,true,false,false,false,false],\"subset\":[0,1,3]}。請依 [n,subset,restricted_yes,restricted_mismatches,agrees] 的欄序回答。","answer":{"kind":"expression","value":"(6, [0, 1, 3], [1], [], 是)","explanation_zh":"擴展基礎核對=(6, [0, 1, 3], [1], [], 是)；依完整明示資料逐欄精確重算；有限／合成資料核對不是一般形式證明；規格與decider分離；有限完整表不外推無限可判定性。"},"difficulty":{"band":"undergraduate_core","level":1,"skills":["有限決定問題"]},"variant":{"family_id":"qf-ext18-decision-domain-restriction","seed":202610186057,"parameters":{"n":6,"yes":[1,2],"decider":[false,true,false,false,false,false],"subset":[0,1,3],"domain":"Fin_decision_problem","operation":"decision-domain-restriction","semantic_template":"qf-ext18-decision-domain-restriction/{\"decider\":[false,true,false,false,false,false],\"n\":6,\"subset\":[0,1,3],\"yes\":[1,2]}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_arithmetic","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"僅為產生端候選及自檢；主端須另做驗收，不構成人工審定、普遍證明、Lean執行或形式Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-13","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261013-advance-20261018-r06-decision-problem-0058","batch_id":"batch-20261013-advance-20261018-r06-decision-problem-foundations","language":"zh-Hant","source_mko_ids":["mko-decision-problem"],"title_zh":"有限決定問題","stem_zh":"明示有限輸入域。操作=decision-domain-restriction；資料={\"n\":6,\"yes\":[0,1,2],\"decider\":[true,true,true,true,false,false],\"subset\":[1,2,4]}。請依 [n,subset,restricted_yes,restricted_mismatches,agrees] 的欄序回答。","answer":{"kind":"expression","value":"(6, [1, 2, 4], [1, 2], [], 是)","explanation_zh":"擴展基礎核對=(6, [1, 2, 4], [1, 2], [], 是)；依完整明示資料逐欄精確重算；有限／合成資料核對不是一般形式證明；規格與decider分離；有限完整表不外推無限可判定性。"},"difficulty":{"band":"undergraduate_core","level":1,"skills":["有限決定問題"]},"variant":{"family_id":"qf-ext18-decision-domain-restriction","seed":202610186058,"parameters":{"n":6,"yes":[0,1,2],"decider":[true,true,true,true,false,false],"subset":[1,2,4],"domain":"Fin_decision_problem","operation":"decision-domain-restriction","semantic_template":"qf-ext18-decision-domain-restriction/{\"decider\":[true,true,true,true,false,false],\"n\":6,\"subset\":[1,2,4],\"yes\":[0,1,2]}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_arithmetic","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"僅為產生端候選及自檢；主端須另做驗收，不構成人工審定、普遍證明、Lean執行或形式Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-13","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261013-advance-20261018-r06-decision-problem-0059","batch_id":"batch-20261013-advance-20261018-r06-decision-problem-foundations","language":"zh-Hant","source_mko_ids":["mko-decision-problem"],"title_zh":"有限決定問題","stem_zh":"明示有限輸入域。操作=decision-domain-restriction；資料={\"n\":6,\"yes\":[3],\"decider\":[false,false,false,true,true,false],\"subset\":[2,3,5]}。請依 [n,subset,restricted_yes,restricted_mismatches,agrees] 的欄序回答。","answer":{"kind":"expression","value":"(6, [2, 3, 5], [3], [], 是)","explanation_zh":"擴展基礎核對=(6, [2, 3, 5], [3], [], 是)；依完整明示資料逐欄精確重算；有限／合成資料核對不是一般形式證明；規格與decider分離；有限完整表不外推無限可判定性。"},"difficulty":{"band":"undergraduate_core","level":2,"skills":["有限決定問題"]},"variant":{"family_id":"qf-ext18-decision-domain-restriction","seed":202610186059,"parameters":{"n":6,"yes":[3],"decider":[false,false,false,true,true,false],"subset":[2,3,5],"domain":"Fin_decision_problem","operation":"decision-domain-restriction","semantic_template":"qf-ext18-decision-domain-restriction/{\"decider\":[false,false,false,true,true,false],\"n\":6,\"subset\":[2,3,5],\"yes\":[3]}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_arithmetic","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"僅為產生端候選及自檢；主端須另做驗收，不構成人工審定、普遍證明、Lean執行或形式Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-13","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261013-advance-20261018-r06-decision-problem-0060","batch_id":"batch-20261013-advance-20261018-r06-decision-problem-foundations","language":"zh-Hant","source_mko_ids":["mko-decision-problem"],"title_zh":"有限決定問題","stem_zh":"明示有限輸入域。操作=decision-domain-restriction；資料={\"n\":6,\"yes\":[0,3],\"decider\":[true,false,false,true,false,true],\"subset\":[0,3,4]}。請依 [n,subset,restricted_yes,restricted_mismatches,agrees] 的欄序回答。","answer":{"kind":"expression","value":"(6, [0, 3, 4], [0, 3], [], 是)","explanation_zh":"擴展基礎核對=(6, [0, 3, 4], [0, 3], [], 是)；依完整明示資料逐欄精確重算；有限／合成資料核對不是一般形式證明；規格與decider分離；有限完整表不外推無限可判定性。"},"difficulty":{"band":"undergraduate_core","level":2,"skills":["有限決定問題"]},"variant":{"family_id":"qf-ext18-decision-domain-restriction","seed":202610186060,"parameters":{"n":6,"yes":[0,3],"decider":[true,false,false,true,false,true],"subset":[0,3,4],"domain":"Fin_decision_problem","operation":"decision-domain-restriction","semantic_template":"qf-ext18-decision-domain-restriction/{\"decider\":[true,false,false,true,false,true],\"n\":6,\"subset\":[0,3,4],\"yes\":[0,3]}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_arithmetic","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"僅為產生端候選及自檢；主端須另做驗收，不構成人工審定、普遍證明、Lean執行或形式Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-13","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261013-advance-20261018-r06-decision-problem-0061","batch_id":"batch-20261013-advance-20261018-r06-decision-problem-foundations","language":"zh-Hant","source_mko_ids":["mko-decision-problem"],"title_zh":"有限決定問題","stem_zh":"明示有限輸入域。操作=decision-domain-restriction；資料={\"n\":6,\"yes\":[1,3],\"decider\":[true,true,false,true,false,false],\"subset\":[1,4,5]}。請依 [n,subset,restricted_yes,restricted_mismatches,agrees] 的欄序回答。","answer":{"kind":"expression","value":"(6, [1, 4, 5], [1], [], 是)","explanation_zh":"擴展基礎核對=(6, [1, 4, 5], [1], [], 是)；依完整明示資料逐欄精確重算；有限／合成資料核對不是一般形式證明；規格與decider分離；有限完整表不外推無限可判定性。"},"difficulty":{"band":"undergraduate_core","level":2,"skills":["有限決定問題"]},"variant":{"family_id":"qf-ext18-decision-domain-restriction","seed":202610186061,"parameters":{"n":6,"yes":[1,3],"decider":[true,true,false,true,false,false],"subset":[1,4,5],"domain":"Fin_decision_problem","operation":"decision-domain-restriction","semantic_template":"qf-ext18-decision-domain-restriction/{\"decider\":[true,true,false,true,false,false],\"n\":6,\"subset\":[1,4,5],\"yes\":[1,3]}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_arithmetic","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"僅為產生端候選及自檢；主端須另做驗收，不構成人工審定、普遍證明、Lean執行或形式Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-13","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261013-advance-20261018-r06-decision-problem-0062","batch_id":"batch-20261013-advance-20261018-r06-decision-problem-foundations","language":"zh-Hant","source_mko_ids":["mko-decision-problem"],"title_zh":"有限決定問題","stem_zh":"明示有限輸入域。操作=decision-domain-restriction；資料={\"n\":6,\"yes\":[0,1,3],\"decider\":[true,false,false,true,false,false],\"subset\":[0,2,5]}。請依 [n,subset,restricted_yes,restricted_mismatches,agrees] 的欄序回答。","answer":{"kind":"expression","value":"(6, [0, 2, 5], [0], [], 是)","explanation_zh":"擴展基礎核對=(6, [0, 2, 5], [0], [], 是)；依完整明示資料逐欄精確重算；有限／合成資料核對不是一般形式證明；規格與decider分離；有限完整表不外推無限可判定性。"},"difficulty":{"band":"undergraduate_core","level":2,"skills":["有限決定問題"]},"variant":{"family_id":"qf-ext18-decision-domain-restriction","seed":202610186062,"parameters":{"n":6,"yes":[0,1,3],"decider":[true,false,false,true,false,false],"subset":[0,2,5],"domain":"Fin_decision_problem","operation":"decision-domain-restriction","semantic_template":"qf-ext18-decision-domain-restriction/{\"decider\":[true,false,false,true,false,false],\"n\":6,\"subset\":[0,2,5],\"yes\":[0,1,3]}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_arithmetic","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"僅為產生端候選及自檢；主端須另做驗收，不構成人工審定、普遍證明、Lean執行或形式Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-13","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261013-advance-20261018-r06-decision-problem-0063","batch_id":"batch-20261013-advance-20261018-r06-decision-problem-foundations","language":"zh-Hant","source_mko_ids":["mko-decision-problem"],"title_zh":"有限決定問題","stem_zh":"明示有限輸入域。操作=decision-domain-restriction；資料={\"n\":6,\"yes\":[2,3],\"decider\":[false,false,false,true,false,false],\"subset\":[0,1,3]}。請依 [n,subset,restricted_yes,restricted_mismatches,agrees] 的欄序回答。","answer":{"kind":"expression","value":"(6, [0, 1, 3], [3], [], 是)","explanation_zh":"擴展基礎核對=(6, [0, 1, 3], [3], [], 是)；依完整明示資料逐欄精確重算；有限／合成資料核對不是一般形式證明；規格與decider分離；有限完整表不外推無限可判定性。"},"difficulty":{"band":"undergraduate_core","level":2,"skills":["有限決定問題"]},"variant":{"family_id":"qf-ext18-decision-domain-restriction","seed":202610186063,"parameters":{"n":6,"yes":[2,3],"decider":[false,false,false,true,false,false],"subset":[0,1,3],"domain":"Fin_decision_problem","operation":"decision-domain-restriction","semantic_template":"qf-ext18-decision-domain-restriction/{\"decider\":[false,false,false,true,false,false],\"n\":6,\"subset\":[0,1,3],\"yes\":[2,3]}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_arithmetic","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"僅為產生端候選及自檢；主端須另做驗收，不構成人工審定、普遍證明、Lean執行或形式Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-13","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261013-advance-20261018-r06-decision-problem-0064","batch_id":"batch-20261013-advance-20261018-r06-decision-problem-foundations","language":"zh-Hant","source_mko_ids":["mko-decision-problem"],"title_zh":"有限決定問題","stem_zh":"明示有限輸入域。操作=decision-domain-restriction；資料={\"n\":6,\"yes\":[0,2,3],\"decider\":[true,false,true,false,false,false],\"subset\":[1,2,4]}。請依 [n,subset,restricted_yes,restricted_mismatches,agrees] 的欄序回答。","answer":{"kind":"expression","value":"(6, [1, 2, 4], [2], [], 是)","explanation_zh":"擴展基礎核對=(6, [1, 2, 4], [2], [], 是)；依完整明示資料逐欄精確重算；有限／合成資料核對不是一般形式證明；規格與decider分離；有限完整表不外推無限可判定性。"},"difficulty":{"band":"undergraduate_core","level":2,"skills":["有限決定問題"]},"variant":{"family_id":"qf-ext18-decision-domain-restriction","seed":202610186064,"parameters":{"n":6,"yes":[0,2,3],"decider":[true,false,true,false,false,false],"subset":[1,2,4],"domain":"Fin_decision_problem","operation":"decision-domain-restriction","semantic_template":"qf-ext18-decision-domain-restriction/{\"decider\":[true,false,true,false,false,false],\"n\":6,\"subset\":[1,2,4],\"yes\":[0,2,3]}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_arithmetic","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"僅為產生端候選及自檢；主端須另做驗收，不構成人工審定、普遍證明、Lean執行或形式Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-13","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261013-advance-20261018-r06-decision-problem-0065","batch_id":"batch-20261013-advance-20261018-r06-decision-problem-foundations","language":"zh-Hant","source_mko_ids":["mko-decision-problem"],"title_zh":"有限決定問題","stem_zh":"明示有限輸入域。操作=decision-domain-restriction；資料={\"n\":6,\"yes\":[1,2,3],\"decider\":[false,true,true,true,true,false],\"subset\":[2,3,5]}。請依 [n,subset,restricted_yes,restricted_mismatches,agrees] 的欄序回答。","answer":{"kind":"expression","value":"(6, [2, 3, 5], [2, 3], [], 是)","explanation_zh":"擴展基礎核對=(6, [2, 3, 5], [2, 3], [], 是)；依完整明示資料逐欄精確重算；有限／合成資料核對不是一般形式證明；規格與decider分離；有限完整表不外推無限可判定性。"},"difficulty":{"band":"undergraduate_core","level":2,"skills":["有限決定問題"]},"variant":{"family_id":"qf-ext18-decision-domain-restriction","seed":202610186065,"parameters":{"n":6,"yes":[1,2,3],"decider":[false,true,true,true,true,false],"subset":[2,3,5],"domain":"Fin_decision_problem","operation":"decision-domain-restriction","semantic_template":"qf-ext18-decision-domain-restriction/{\"decider\":[false,true,true,true,true,false],\"n\":6,\"subset\":[2,3,5],\"yes\":[1,2,3]}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_arithmetic","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"僅為產生端候選及自檢；主端須另做驗收，不構成人工審定、普遍證明、Lean執行或形式Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-13","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261013-advance-20261018-r06-decision-problem-0066","batch_id":"batch-20261013-advance-20261018-r06-decision-problem-foundations","language":"zh-Hant","source_mko_ids":["mko-decision-problem"],"title_zh":"有限決定問題","stem_zh":"明示有限輸入域。操作=decision-domain-restriction；資料={\"n\":6,\"yes\":[0,1,2,3],\"decider\":[true,true,true,true,false,true],\"subset\":[0,3,4]}。請依 [n,subset,restricted_yes,restricted_mismatches,agrees] 的欄序回答。","answer":{"kind":"expression","value":"(6, [0, 3, 4], [0, 3], [], 是)","explanation_zh":"擴展基礎核對=(6, [0, 3, 4], [0, 3], [], 是)；依完整明示資料逐欄精確重算；有限／合成資料核對不是一般形式證明；規格與decider分離；有限完整表不外推無限可判定性。"},"difficulty":{"band":"undergraduate_core","level":2,"skills":["有限決定問題"]},"variant":{"family_id":"qf-ext18-decision-domain-restriction","seed":202610186066,"parameters":{"n":6,"yes":[0,1,2,3],"decider":[true,true,true,true,false,true],"subset":[0,3,4],"domain":"Fin_decision_problem","operation":"decision-domain-restriction","semantic_template":"qf-ext18-decision-domain-restriction/{\"decider\":[true,true,true,true,false,true],\"n\":6,\"subset\":[0,3,4],\"yes\":[0,1,2,3]}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_arithmetic","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"僅為產生端候選及自檢；主端須另做驗收，不構成人工審定、普遍證明、Lean執行或形式Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-13","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261013-advance-20261018-r06-decision-problem-0067","batch_id":"batch-20261013-advance-20261018-r06-decision-problem-foundations","language":"zh-Hant","source_mko_ids":["mko-decision-problem"],"title_zh":"有限決定問題","stem_zh":"明示有限輸入域。操作=decision-domain-restriction；資料={\"n\":6,\"yes\":[4],\"decider\":[true,false,false,false,true,false],\"subset\":[1,4,5]}。請依 [n,subset,restricted_yes,restricted_mismatches,agrees] 的欄序回答。","answer":{"kind":"expression","value":"(6, [1, 4, 5], [4], [], 是)","explanation_zh":"擴展基礎核對=(6, [1, 4, 5], [4], [], 是)；依完整明示資料逐欄精確重算；有限／合成資料核對不是一般形式證明；規格與decider分離；有限完整表不外推無限可判定性。"},"difficulty":{"band":"undergraduate_core","level":2,"skills":["有限決定問題"]},"variant":{"family_id":"qf-ext18-decision-domain-restriction","seed":202610186067,"parameters":{"n":6,"yes":[4],"decider":[true,false,false,false,true,false],"subset":[1,4,5],"domain":"Fin_decision_problem","operation":"decision-domain-restriction","semantic_template":"qf-ext18-decision-domain-restriction/{\"decider\":[true,false,false,false,true,false],\"n\":6,\"subset\":[1,4,5],\"yes\":[4]}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_arithmetic","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"僅為產生端候選及自檢；主端須另做驗收，不構成人工審定、普遍證明、Lean執行或形式Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-13","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261013-advance-20261018-r06-decision-problem-0068","batch_id":"batch-20261013-advance-20261018-r06-decision-problem-foundations","language":"zh-Hant","source_mko_ids":["mko-decision-problem"],"title_zh":"有限決定問題","stem_zh":"明示有限輸入域。操作=decision-domain-restriction；資料={\"n\":6,\"yes\":[0,4],\"decider\":[true,true,false,false,true,false],\"subset\":[0,2,5]}。請依 [n,subset,restricted_yes,restricted_mismatches,agrees] 的欄序回答。","answer":{"kind":"expression","value":"(6, [0, 2, 5], [0], [], 是)","explanation_zh":"擴展基礎核對=(6, [0, 2, 5], [0], [], 是)；依完整明示資料逐欄精確重算；有限／合成資料核對不是一般形式證明；規格與decider分離；有限完整表不外推無限可判定性。"},"difficulty":{"band":"undergraduate_core","level":3,"skills":["有限決定問題"]},"variant":{"family_id":"qf-ext18-decision-domain-restriction","seed":202610186068,"parameters":{"n":6,"yes":[0,4],"decider":[true,true,false,false,true,false],"subset":[0,2,5],"domain":"Fin_decision_problem","operation":"decision-domain-restriction","semantic_template":"qf-ext18-decision-domain-restriction/{\"decider\":[true,true,false,false,true,false],\"n\":6,\"subset\":[0,2,5],\"yes\":[0,4]}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_arithmetic","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"僅為產生端候選及自檢；主端須另做驗收，不構成人工審定、普遍證明、Lean執行或形式Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-13","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261013-advance-20261018-r06-decision-problem-0069","batch_id":"batch-20261013-advance-20261018-r06-decision-problem-foundations","language":"zh-Hant","source_mko_ids":["mko-decision-problem"],"title_zh":"有限決定問題","stem_zh":"明示有限輸入域。操作=decision-domain-restriction；資料={\"n\":6,\"yes\":[1,4],\"decider\":[false,true,true,false,true,false],\"subset\":[0,1,3]}。請依 [n,subset,restricted_yes,restricted_mismatches,agrees] 的欄序回答。","answer":{"kind":"expression","value":"(6, [0, 1, 3], [1], [], 是)","explanation_zh":"擴展基礎核對=(6, [0, 1, 3], [1], [], 是)；依完整明示資料逐欄精確重算；有限／合成資料核對不是一般形式證明；規格與decider分離；有限完整表不外推無限可判定性。"},"difficulty":{"band":"undergraduate_core","level":3,"skills":["有限決定問題"]},"variant":{"family_id":"qf-ext18-decision-domain-restriction","seed":202610186069,"parameters":{"n":6,"yes":[1,4],"decider":[false,true,true,false,true,false],"subset":[0,1,3],"domain":"Fin_decision_problem","operation":"decision-domain-restriction","semantic_template":"qf-ext18-decision-domain-restriction/{\"decider\":[false,true,true,false,true,false],\"n\":6,\"subset\":[0,1,3],\"yes\":[1,4]}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_arithmetic","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"僅為產生端候選及自檢；主端須另做驗收，不構成人工審定、普遍證明、Lean執行或形式Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-13","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261013-advance-20261018-r06-decision-problem-0070","batch_id":"batch-20261013-advance-20261018-r06-decision-problem-foundations","language":"zh-Hant","source_mko_ids":["mko-decision-problem"],"title_zh":"有限決定問題","stem_zh":"明示有限輸入域。操作=decision-domain-restriction；資料={\"n\":6,\"yes\":[0,1,4],\"decider\":[true,true,false,true,true,false],\"subset\":[1,2,4]}。請依 [n,subset,restricted_yes,restricted_mismatches,agrees] 的欄序回答。","answer":{"kind":"expression","value":"(6, [1, 2, 4], [1, 4], [], 是)","explanation_zh":"擴展基礎核對=(6, [1, 2, 4], [1, 4], [], 是)；依完整明示資料逐欄精確重算；有限／合成資料核對不是一般形式證明；規格與decider分離；有限完整表不外推無限可判定性。"},"difficulty":{"band":"undergraduate_core","level":3,"skills":["有限決定問題"]},"variant":{"family_id":"qf-ext18-decision-domain-restriction","seed":202610186070,"parameters":{"n":6,"yes":[0,1,4],"decider":[true,true,false,true,true,false],"subset":[1,2,4],"domain":"Fin_decision_problem","operation":"decision-domain-restriction","semantic_template":"qf-ext18-decision-domain-restriction/{\"decider\":[true,true,false,true,true,false],\"n\":6,\"subset\":[1,2,4],\"yes\":[0,1,4]}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_arithmetic","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"僅為產生端候選及自檢；主端須另做驗收，不構成人工審定、普遍證明、Lean執行或形式Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-13","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261013-advance-20261018-r06-decision-problem-0071","batch_id":"batch-20261013-advance-20261018-r06-decision-problem-foundations","language":"zh-Hant","source_mko_ids":["mko-decision-problem"],"title_zh":"有限決定問題","stem_zh":"明示有限輸入域。操作=decision-domain-restriction；資料={\"n\":6,\"yes\":[2,4],\"decider\":[false,false,true,false,false,false],\"subset\":[2,3,5]}。請依 [n,subset,restricted_yes,restricted_mismatches,agrees] 的欄序回答。","answer":{"kind":"expression","value":"(6, [2, 3, 5], [2], [], 是)","explanation_zh":"擴展基礎核對=(6, [2, 3, 5], [2], [], 是)；依完整明示資料逐欄精確重算；有限／合成資料核對不是一般形式證明；規格與decider分離；有限完整表不外推無限可判定性。"},"difficulty":{"band":"undergraduate_core","level":3,"skills":["有限決定問題"]},"variant":{"family_id":"qf-ext18-decision-domain-restriction","seed":202610186071,"parameters":{"n":6,"yes":[2,4],"decider":[false,false,true,false,false,false],"subset":[2,3,5],"domain":"Fin_decision_problem","operation":"decision-domain-restriction","semantic_template":"qf-ext18-decision-domain-restriction/{\"decider\":[false,false,true,false,false,false],\"n\":6,\"subset\":[2,3,5],\"yes\":[2,4]}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_arithmetic","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"僅為產生端候選及自檢；主端須另做驗收，不構成人工審定、普遍證明、Lean執行或形式Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-13","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261013-advance-20261018-r06-decision-problem-0072","batch_id":"batch-20261013-advance-20261018-r06-decision-problem-foundations","language":"zh-Hant","source_mko_ids":["mko-decision-problem"],"title_zh":"有限決定問題","stem_zh":"明示有限輸入域。操作=decision-domain-restriction；資料={\"n\":6,\"yes\":[0,2,4],\"decider\":[true,false,true,false,true,true],\"subset\":[0,3,4]}。請依 [n,subset,restricted_yes,restricted_mismatches,agrees] 的欄序回答。","answer":{"kind":"expression","value":"(6, [0, 3, 4], [0, 4], [], 是)","explanation_zh":"擴展基礎核對=(6, [0, 3, 4], [0, 4], [], 是)；依完整明示資料逐欄精確重算；有限／合成資料核對不是一般形式證明；規格與decider分離；有限完整表不外推無限可判定性。"},"difficulty":{"band":"undergraduate_core","level":3,"skills":["有限決定問題"]},"variant":{"family_id":"qf-ext18-decision-domain-restriction","seed":202610186072,"parameters":{"n":6,"yes":[0,2,4],"decider":[true,false,true,false,true,true],"subset":[0,3,4],"domain":"Fin_decision_problem","operation":"decision-domain-restriction","semantic_template":"qf-ext18-decision-domain-restriction/{\"decider\":[true,false,true,false,true,true],\"n\":6,\"subset\":[0,3,4],\"yes\":[0,2,4]}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_arithmetic","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"僅為產生端候選及自檢；主端須另做驗收，不構成人工審定、普遍證明、Lean執行或形式Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-13","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261013-advance-20261018-r06-decision-problem-0073","batch_id":"batch-20261013-advance-20261018-r06-decision-problem-foundations","language":"zh-Hant","source_mko_ids":["mko-decision-problem"],"title_zh":"有限決定問題","stem_zh":"明示有限輸入域。操作=decision-domain-restriction；資料={\"n\":6,\"yes\":[1,2,4],\"decider\":[true,true,true,false,true,false],\"subset\":[1,4,5]}。請依 [n,subset,restricted_yes,restricted_mismatches,agrees] 的欄序回答。","answer":{"kind":"expression","value":"(6, [1, 4, 5], [1, 4], [], 是)","explanation_zh":"擴展基礎核對=(6, [1, 4, 5], [1, 4], [], 是)；依完整明示資料逐欄精確重算；有限／合成資料核對不是一般形式證明；規格與decider分離；有限完整表不外推無限可判定性。"},"difficulty":{"band":"undergraduate_core","level":3,"skills":["有限決定問題"]},"variant":{"family_id":"qf-ext18-decision-domain-restriction","seed":202610186073,"parameters":{"n":6,"yes":[1,2,4],"decider":[true,true,true,false,true,false],"subset":[1,4,5],"domain":"Fin_decision_problem","operation":"decision-domain-restriction","semantic_template":"qf-ext18-decision-domain-restriction/{\"decider\":[true,true,true,false,true,false],\"n\":6,\"subset\":[1,4,5],\"yes\":[1,2,4]}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_arithmetic","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"僅為產生端候選及自檢；主端須另做驗收，不構成人工審定、普遍證明、Lean執行或形式Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-13","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261013-advance-20261018-r06-decision-problem-0074","batch_id":"batch-20261013-advance-20261018-r06-decision-problem-foundations","language":"zh-Hant","source_mko_ids":["mko-decision-problem"],"title_zh":"有限決定問題","stem_zh":"明示有限輸入域。操作=decision-domain-restriction；資料={\"n\":6,\"yes\":[0,1,2,4],\"decider\":[true,false,true,false,true,false],\"subset\":[0,2,5]}。請依 [n,subset,restricted_yes,restricted_mismatches,agrees] 的欄序回答。","answer":{"kind":"expression","value":"(6, [0, 2, 5], [0, 2], [], 是)","explanation_zh":"擴展基礎核對=(6, [0, 2, 5], [0, 2], [], 是)；依完整明示資料逐欄精確重算；有限／合成資料核對不是一般形式證明；規格與decider分離；有限完整表不外推無限可判定性。"},"difficulty":{"band":"undergraduate_core","level":3,"skills":["有限決定問題"]},"variant":{"family_id":"qf-ext18-decision-domain-restriction","seed":202610186074,"parameters":{"n":6,"yes":[0,1,2,4],"decider":[true,false,true,false,true,false],"subset":[0,2,5],"domain":"Fin_decision_problem","operation":"decision-domain-restriction","semantic_template":"qf-ext18-decision-domain-restriction/{\"decider\":[true,false,true,false,true,false],\"n\":6,\"subset\":[0,2,5],\"yes\":[0,1,2,4]}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_arithmetic","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"僅為產生端候選及自檢；主端須另做驗收，不構成人工審定、普遍證明、Lean執行或形式Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-13","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261013-advance-20261018-r06-decision-problem-0075","batch_id":"batch-20261013-advance-20261018-r06-decision-problem-foundations","language":"zh-Hant","source_mko_ids":["mko-decision-problem"],"title_zh":"有限決定問題","stem_zh":"明示有限輸入域。操作=decision-domain-restriction；資料={\"n\":6,\"yes\":[3,4],\"decider\":[false,false,true,true,true,false],\"subset\":[0,1,3]}。請依 [n,subset,restricted_yes,restricted_mismatches,agrees] 的欄序回答。","answer":{"kind":"expression","value":"(6, [0, 1, 3], [3], [], 是)","explanation_zh":"擴展基礎核對=(6, [0, 1, 3], [3], [], 是)；依完整明示資料逐欄精確重算；有限／合成資料核對不是一般形式證明；規格與decider分離；有限完整表不外推無限可判定性。"},"difficulty":{"band":"undergraduate_core","level":3,"skills":["有限決定問題"]},"variant":{"family_id":"qf-ext18-decision-domain-restriction","seed":202610186075,"parameters":{"n":6,"yes":[3,4],"decider":[false,false,true,true,true,false],"subset":[0,1,3],"domain":"Fin_decision_problem","operation":"decision-domain-restriction","semantic_template":"qf-ext18-decision-domain-restriction/{\"decider\":[false,false,true,true,true,false],\"n\":6,\"subset\":[0,1,3],\"yes\":[3,4]}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_arithmetic","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"僅為產生端候選及自檢；主端須另做驗收，不構成人工審定、普遍證明、Lean執行或形式Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-13","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261013-advance-20261018-r06-decision-problem-0076","batch_id":"batch-20261013-advance-20261018-r06-decision-problem-foundations","language":"zh-Hant","source_mko_ids":["mko-decision-problem"],"title_zh":"有限決定問題","stem_zh":"明示有限輸入域。操作=decision-complete-vs-sample；資料={\"n\":6,\"yes\":[],\"decider\":[false,false,false,true,false,false],\"checked\":[0,1]}。請依 [n,checked,sample_mismatches,full_mismatches,sample_agrees,complete_agrees,classification] 的欄序回答。","answer":{"kind":"expression","value":"(6, [0, 1], [], [3], 是, 否, 樣本通過但完整失敗)","explanation_zh":"擴展基礎核對=(6, [0, 1], [], [3], 是, 否, 樣本通過但完整失敗)；依完整明示資料逐欄精確重算；有限／合成資料核對不是一般形式證明；規格與decider分離；有限完整表不外推無限可判定性。"},"difficulty":{"band":"undergraduate_core","level":1,"skills":["有限決定問題"]},"variant":{"family_id":"qf-ext18-decision-complete-vs-sample","seed":202610186076,"parameters":{"n":6,"yes":[],"decider":[false,false,false,true,false,false],"checked":[0,1],"domain":"Fin_decision_problem","operation":"decision-complete-vs-sample","semantic_template":"qf-ext18-decision-complete-vs-sample/{\"checked\":[0,1],\"decider\":[false,false,false,true,false,false],\"n\":6,\"yes\":[]}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_arithmetic","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"僅為產生端候選及自檢；主端須另做驗收，不構成人工審定、普遍證明、Lean執行或形式Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-13","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261013-advance-20261018-r06-decision-problem-0077","batch_id":"batch-20261013-advance-20261018-r06-decision-problem-foundations","language":"zh-Hant","source_mko_ids":["mko-decision-problem"],"title_zh":"有限決定問題","stem_zh":"明示有限輸入域。操作=decision-complete-vs-sample；資料={\"n\":6,\"yes\":[0],\"decider\":[true,false,false,false,true,false],\"checked\":[1,4]}。請依 [n,checked,sample_mismatches,full_mismatches,sample_agrees,complete_agrees,classification] 的欄序回答。","answer":{"kind":"expression","value":"(6, [1, 4], [4], [4], 否, 否, 樣本已失敗)","explanation_zh":"擴展基礎核對=(6, [1, 4], [4], [4], 否, 否, 樣本已失敗)；依完整明示資料逐欄精確重算；有限／合成資料核對不是一般形式證明；規格與decider分離；有限完整表不外推無限可判定性。"},"difficulty":{"band":"undergraduate_core","level":1,"skills":["有限決定問題"]},"variant":{"family_id":"qf-ext18-decision-complete-vs-sample","seed":202610186077,"parameters":{"n":6,"yes":[0],"decider":[true,false,false,false,true,false],"checked":[1,4],"domain":"Fin_decision_problem","operation":"decision-complete-vs-sample","semantic_template":"qf-ext18-decision-complete-vs-sample/{\"checked\":[1,4],\"decider\":[true,false,false,false,true,false],\"n\":6,\"yes\":[0]}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_arithmetic","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"僅為產生端候選及自檢；主端須另做驗收，不構成人工審定、普遍證明、Lean執行或形式Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-13","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261013-advance-20261018-r06-decision-problem-0078","batch_id":"batch-20261013-advance-20261018-r06-decision-problem-foundations","language":"zh-Hant","source_mko_ids":["mko-decision-problem"],"title_zh":"有限決定問題","stem_zh":"明示有限輸入域。操作=decision-complete-vs-sample；資料={\"n\":6,\"yes\":[1],\"decider\":[false,true,false,false,false,true],\"checked\":[0,2]}。請依 [n,checked,sample_mismatches,full_mismatches,sample_agrees,complete_agrees,classification] 的欄序回答。","answer":{"kind":"expression","value":"(6, [0, 2], [], [5], 是, 否, 樣本通過但完整失敗)","explanation_zh":"擴展基礎核對=(6, [0, 2], [], [5], 是, 否, 樣本通過但完整失敗)；依完整明示資料逐欄精確重算；有限／合成資料核對不是一般形式證明；規格與decider分離；有限完整表不外推無限可判定性。"},"difficulty":{"band":"undergraduate_core","level":1,"skills":["有限決定問題"]},"variant":{"family_id":"qf-ext18-decision-complete-vs-sample","seed":202610186078,"parameters":{"n":6,"yes":[1],"decider":[false,true,false,false,false,true],"checked":[0,2],"domain":"Fin_decision_problem","operation":"decision-complete-vs-sample","semantic_template":"qf-ext18-decision-complete-vs-sample/{\"checked\":[0,2],\"decider\":[false,true,false,false,false,true],\"n\":6,\"yes\":[1]}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_arithmetic","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"僅為產生端候選及自檢；主端須另做驗收，不構成人工審定、普遍證明、Lean執行或形式Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-13","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261013-advance-20261018-r06-decision-problem-0079","batch_id":"batch-20261013-advance-20261018-r06-decision-problem-foundations","language":"zh-Hant","source_mko_ids":["mko-decision-problem"],"title_zh":"有限決定問題","stem_zh":"明示有限輸入域。操作=decision-complete-vs-sample；資料={\"n\":6,\"yes\":[0,1],\"decider\":[false,true,false,false,false,false],\"checked\":[0,3]}。請依 [n,checked,sample_mismatches,full_mismatches,sample_agrees,complete_agrees,classification] 的欄序回答。","answer":{"kind":"expression","value":"(6, [0, 3], [0], [0], 否, 否, 樣本已失敗)","explanation_zh":"擴展基礎核對=(6, [0, 3], [0], [0], 否, 否, 樣本已失敗)；依完整明示資料逐欄精確重算；有限／合成資料核對不是一般形式證明；規格與decider分離；有限完整表不外推無限可判定性。"},"difficulty":{"band":"undergraduate_core","level":1,"skills":["有限決定問題"]},"variant":{"family_id":"qf-ext18-decision-complete-vs-sample","seed":202610186079,"parameters":{"n":6,"yes":[0,1],"decider":[false,true,false,false,false,false],"checked":[0,3],"domain":"Fin_decision_problem","operation":"decision-complete-vs-sample","semantic_template":"qf-ext18-decision-complete-vs-sample/{\"checked\":[0,3],\"decider\":[false,true,false,false,false,false],\"n\":6,\"yes\":[0,1]}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_arithmetic","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"僅為產生端候選及自檢；主端須另做驗收，不構成人工審定、普遍證明、Lean執行或形式Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-13","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261013-advance-20261018-r06-decision-problem-0080","batch_id":"batch-20261013-advance-20261018-r06-decision-problem-foundations","language":"zh-Hant","source_mko_ids":["mko-decision-problem"],"title_zh":"有限決定問題","stem_zh":"明示有限輸入域。操作=decision-complete-vs-sample；資料={\"n\":6,\"yes\":[2],\"decider\":[false,true,true,false,false,false],\"checked\":[1,2]}。請依 [n,checked,sample_mismatches,full_mismatches,sample_agrees,complete_agrees,classification] 的欄序回答。","answer":{"kind":"expression","value":"(6, [1, 2], [1], [1], 否, 否, 樣本已失敗)","explanation_zh":"擴展基礎核對=(6, [1, 2], [1], [1], 否, 否, 樣本已失敗)；依完整明示資料逐欄精確重算；有限／合成資料核對不是一般形式證明；規格與decider分離；有限完整表不外推無限可判定性。"},"difficulty":{"band":"undergraduate_core","level":1,"skills":["有限決定問題"]},"variant":{"family_id":"qf-ext18-decision-complete-vs-sample","seed":202610186080,"parameters":{"n":6,"yes":[2],"decider":[false,true,true,false,false,false],"checked":[1,2],"domain":"Fin_decision_problem","operation":"decision-complete-vs-sample","semantic_template":"qf-ext18-decision-complete-vs-sample/{\"checked\":[1,2],\"decider\":[false,true,true,false,false,false],\"n\":6,\"yes\":[2]}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_arithmetic","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"僅為產生端候選及自檢；主端須另做驗收，不構成人工審定、普遍證明、Lean執行或形式Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-13","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261013-advance-20261018-r06-decision-problem-0081","batch_id":"batch-20261013-advance-20261018-r06-decision-problem-foundations","language":"zh-Hant","source_mko_ids":["mko-decision-problem"],"title_zh":"有限決定問題","stem_zh":"明示有限輸入域。操作=decision-complete-vs-sample；資料={\"n\":6,\"yes\":[0,2],\"decider\":[true,false,false,false,false,false],\"checked\":[2,5]}。請依 [n,checked,sample_mismatches,full_mismatches,sample_agrees,complete_agrees,classification] 的欄序回答。","answer":{"kind":"expression","value":"(6, [2, 5], [2], [2], 否, 否, 樣本已失敗)","explanation_zh":"擴展基礎核對=(6, [2, 5], [2], [2], 否, 否, 樣本已失敗)；依完整明示資料逐欄精確重算；有限／合成資料核對不是一般形式證明；規格與decider分離；有限完整表不外推無限可判定性。"},"difficulty":{"band":"undergraduate_core","level":1,"skills":["有限決定問題"]},"variant":{"family_id":"qf-ext18-decision-complete-vs-sample","seed":202610186081,"parameters":{"n":6,"yes":[0,2],"decider":[true,false,false,false,false,false],"checked":[2,5],"domain":"Fin_decision_problem","operation":"decision-complete-vs-sample","semantic_template":"qf-ext18-decision-complete-vs-sample/{\"checked\":[2,5],\"decider\":[true,false,false,false,false,false],\"n\":6,\"yes\":[0,2]}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_arithmetic","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"僅為產生端候選及自檢；主端須另做驗收，不構成人工審定、普遍證明、Lean執行或形式Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-13","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261013-advance-20261018-r06-decision-problem-0082","batch_id":"batch-20261013-advance-20261018-r06-decision-problem-foundations","language":"zh-Hant","source_mko_ids":["mko-decision-problem"],"title_zh":"有限決定問題","stem_zh":"明示有限輸入域。操作=decision-complete-vs-sample；資料={\"n\":6,\"yes\":[1,2],\"decider\":[false,true,true,true,false,false],\"checked\":[0,1]}。請依 [n,checked,sample_mismatches,full_mismatches,sample_agrees,complete_agrees,classification] 的欄序回答。","answer":{"kind":"expression","value":"(6, [0, 1], [], [3], 是, 否, 樣本通過但完整失敗)","explanation_zh":"擴展基礎核對=(6, [0, 1], [], [3], 是, 否, 樣本通過但完整失敗)；依完整明示資料逐欄精確重算；有限／合成資料核對不是一般形式證明；規格與decider分離；有限完整表不外推無限可判定性。"},"difficulty":{"band":"undergraduate_core","level":1,"skills":["有限決定問題"]},"variant":{"family_id":"qf-ext18-decision-complete-vs-sample","seed":202610186082,"parameters":{"n":6,"yes":[1,2],"decider":[false,true,true,true,false,false],"checked":[0,1],"domain":"Fin_decision_problem","operation":"decision-complete-vs-sample","semantic_template":"qf-ext18-decision-complete-vs-sample/{\"checked\":[0,1],\"decider\":[false,true,true,true,false,false],\"n\":6,\"yes\":[1,2]}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_arithmetic","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"僅為產生端候選及自檢；主端須另做驗收，不構成人工審定、普遍證明、Lean執行或形式Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-13","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261013-advance-20261018-r06-decision-problem-0083","batch_id":"batch-20261013-advance-20261018-r06-decision-problem-foundations","language":"zh-Hant","source_mko_ids":["mko-decision-problem"],"title_zh":"有限決定問題","stem_zh":"明示有限輸入域。操作=decision-complete-vs-sample；資料={\"n\":6,\"yes\":[0,1,2],\"decider\":[true,true,true,false,true,false],\"checked\":[1,4]}。請依 [n,checked,sample_mismatches,full_mismatches,sample_agrees,complete_agrees,classification] 的欄序回答。","answer":{"kind":"expression","value":"(6, [1, 4], [4], [4], 否, 否, 樣本已失敗)","explanation_zh":"擴展基礎核對=(6, [1, 4], [4], [4], 否, 否, 樣本已失敗)；依完整明示資料逐欄精確重算；有限／合成資料核對不是一般形式證明；規格與decider分離；有限完整表不外推無限可判定性。"},"difficulty":{"band":"undergraduate_core","level":1,"skills":["有限決定問題"]},"variant":{"family_id":"qf-ext18-decision-complete-vs-sample","seed":202610186083,"parameters":{"n":6,"yes":[0,1,2],"decider":[true,true,true,false,true,false],"checked":[1,4],"domain":"Fin_decision_problem","operation":"decision-complete-vs-sample","semantic_template":"qf-ext18-decision-complete-vs-sample/{\"checked\":[1,4],\"decider\":[true,true,true,false,true,false],\"n\":6,\"yes\":[0,1,2]}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_arithmetic","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"僅為產生端候選及自檢；主端須另做驗收，不構成人工審定、普遍證明、Lean執行或形式Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-13","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261013-advance-20261018-r06-decision-problem-0084","batch_id":"batch-20261013-advance-20261018-r06-decision-problem-foundations","language":"zh-Hant","source_mko_ids":["mko-decision-problem"],"title_zh":"有限決定問題","stem_zh":"明示有限輸入域。操作=decision-complete-vs-sample；資料={\"n\":6,\"yes\":[3],\"decider\":[false,false,false,true,false,true],\"checked\":[0,2]}。請依 [n,checked,sample_mismatches,full_mismatches,sample_agrees,complete_agrees,classification] 的欄序回答。","answer":{"kind":"expression","value":"(6, [0, 2], [], [5], 是, 否, 樣本通過但完整失敗)","explanation_zh":"擴展基礎核對=(6, [0, 2], [], [5], 是, 否, 樣本通過但完整失敗)；依完整明示資料逐欄精確重算；有限／合成資料核對不是一般形式證明；規格與decider分離；有限完整表不外推無限可判定性。"},"difficulty":{"band":"undergraduate_core","level":2,"skills":["有限決定問題"]},"variant":{"family_id":"qf-ext18-decision-complete-vs-sample","seed":202610186084,"parameters":{"n":6,"yes":[3],"decider":[false,false,false,true,false,true],"checked":[0,2],"domain":"Fin_decision_problem","operation":"decision-complete-vs-sample","semantic_template":"qf-ext18-decision-complete-vs-sample/{\"checked\":[0,2],\"decider\":[false,false,false,true,false,true],\"n\":6,\"yes\":[3]}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_arithmetic","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"僅為產生端候選及自檢；主端須另做驗收，不構成人工審定、普遍證明、Lean執行或形式Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-13","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261013-advance-20261018-r06-decision-problem-0085","batch_id":"batch-20261013-advance-20261018-r06-decision-problem-foundations","language":"zh-Hant","source_mko_ids":["mko-decision-problem"],"title_zh":"有限決定問題","stem_zh":"明示有限輸入域。操作=decision-complete-vs-sample；資料={\"n\":6,\"yes\":[0,3],\"decider\":[false,false,false,true,false,false],\"checked\":[0,3]}。請依 [n,checked,sample_mismatches,full_mismatches,sample_agrees,complete_agrees,classification] 的欄序回答。","answer":{"kind":"expression","value":"(6, [0, 3], [0], [0], 否, 否, 樣本已失敗)","explanation_zh":"擴展基礎核對=(6, [0, 3], [0], [0], 否, 否, 樣本已失敗)；依完整明示資料逐欄精確重算；有限／合成資料核對不是一般形式證明；規格與decider分離；有限完整表不外推無限可判定性。"},"difficulty":{"band":"undergraduate_core","level":2,"skills":["有限決定問題"]},"variant":{"family_id":"qf-ext18-decision-complete-vs-sample","seed":202610186085,"parameters":{"n":6,"yes":[0,3],"decider":[false,false,false,true,false,false],"checked":[0,3],"domain":"Fin_decision_problem","operation":"decision-complete-vs-sample","semantic_template":"qf-ext18-decision-complete-vs-sample/{\"checked\":[0,3],\"decider\":[false,false,false,true,false,false],\"n\":6,\"yes\":[0,3]}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_arithmetic","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"僅為產生端候選及自檢；主端須另做驗收，不構成人工審定、普遍證明、Lean執行或形式Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-13","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261013-advance-20261018-r06-decision-problem-0086","batch_id":"batch-20261013-advance-20261018-r06-decision-problem-foundations","language":"zh-Hant","source_mko_ids":["mko-decision-problem"],"title_zh":"有限決定問題","stem_zh":"明示有限輸入域。操作=decision-complete-vs-sample；資料={\"n\":6,\"yes\":[1,3],\"decider\":[false,false,false,true,false,false],\"checked\":[1,2]}。請依 [n,checked,sample_mismatches,full_mismatches,sample_agrees,complete_agrees,classification] 的欄序回答。","answer":{"kind":"expression","value":"(6, [1, 2], [1], [1], 否, 否, 樣本已失敗)","explanation_zh":"擴展基礎核對=(6, [1, 2], [1], [1], 否, 否, 樣本已失敗)；依完整明示資料逐欄精確重算；有限／合成資料核對不是一般形式證明；規格與decider分離；有限完整表不外推無限可判定性。"},"difficulty":{"band":"undergraduate_core","level":2,"skills":["有限決定問題"]},"variant":{"family_id":"qf-ext18-decision-complete-vs-sample","seed":202610186086,"parameters":{"n":6,"yes":[1,3],"decider":[false,false,false,true,false,false],"checked":[1,2],"domain":"Fin_decision_problem","operation":"decision-complete-vs-sample","semantic_template":"qf-ext18-decision-complete-vs-sample/{\"checked\":[1,2],\"decider\":[false,false,false,true,false,false],\"n\":6,\"yes\":[1,3]}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_arithmetic","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"僅為產生端候選及自檢；主端須另做驗收，不構成人工審定、普遍證明、Lean執行或形式Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-13","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261013-advance-20261018-r06-decision-problem-0087","batch_id":"batch-20261013-advance-20261018-r06-decision-problem-foundations","language":"zh-Hant","source_mko_ids":["mko-decision-problem"],"title_zh":"有限決定問題","stem_zh":"明示有限輸入域。操作=decision-complete-vs-sample；資料={\"n\":6,\"yes\":[0,1,3],\"decider\":[true,true,true,true,false,false],\"checked\":[2,5]}。請依 [n,checked,sample_mismatches,full_mismatches,sample_agrees,complete_agrees,classification] 的欄序回答。","answer":{"kind":"expression","value":"(6, [2, 5], [2], [2], 否, 否, 樣本已失敗)","explanation_zh":"擴展基礎核對=(6, [2, 5], [2], [2], 否, 否, 樣本已失敗)；依完整明示資料逐欄精確重算；有限／合成資料核對不是一般形式證明；規格與decider分離；有限完整表不外推無限可判定性。"},"difficulty":{"band":"undergraduate_core","level":2,"skills":["有限決定問題"]},"variant":{"family_id":"qf-ext18-decision-complete-vs-sample","seed":202610186087,"parameters":{"n":6,"yes":[0,1,3],"decider":[true,true,true,true,false,false],"checked":[2,5],"domain":"Fin_decision_problem","operation":"decision-complete-vs-sample","semantic_template":"qf-ext18-decision-complete-vs-sample/{\"checked\":[2,5],\"decider\":[true,true,true,true,false,false],\"n\":6,\"yes\":[0,1,3]}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_arithmetic","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"僅為產生端候選及自檢；主端須另做驗收，不構成人工審定、普遍證明、Lean執行或形式Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-13","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261013-advance-20261018-r06-decision-problem-0088","batch_id":"batch-20261013-advance-20261018-r06-decision-problem-foundations","language":"zh-Hant","source_mko_ids":["mko-decision-problem"],"title_zh":"有限決定問題","stem_zh":"明示有限輸入域。操作=decision-complete-vs-sample；資料={\"n\":6,\"yes\":[2,3],\"decider\":[false,false,true,false,false,false],\"checked\":[0,1]}。請依 [n,checked,sample_mismatches,full_mismatches,sample_agrees,complete_agrees,classification] 的欄序回答。","answer":{"kind":"expression","value":"(6, [0, 1], [], [3], 是, 否, 樣本通過但完整失敗)","explanation_zh":"擴展基礎核對=(6, [0, 1], [], [3], 是, 否, 樣本通過但完整失敗)；依完整明示資料逐欄精確重算；有限／合成資料核對不是一般形式證明；規格與decider分離；有限完整表不外推無限可判定性。"},"difficulty":{"band":"undergraduate_core","level":2,"skills":["有限決定問題"]},"variant":{"family_id":"qf-ext18-decision-complete-vs-sample","seed":202610186088,"parameters":{"n":6,"yes":[2,3],"decider":[false,false,true,false,false,false],"checked":[0,1],"domain":"Fin_decision_problem","operation":"decision-complete-vs-sample","semantic_template":"qf-ext18-decision-complete-vs-sample/{\"checked\":[0,1],\"decider\":[false,false,true,false,false,false],\"n\":6,\"yes\":[2,3]}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_arithmetic","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"僅為產生端候選及自檢；主端須另做驗收，不構成人工審定、普遍證明、Lean執行或形式Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-13","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261013-advance-20261018-r06-decision-problem-0089","batch_id":"batch-20261013-advance-20261018-r06-decision-problem-foundations","language":"zh-Hant","source_mko_ids":["mko-decision-problem"],"title_zh":"有限決定問題","stem_zh":"明示有限輸入域。操作=decision-complete-vs-sample；資料={\"n\":6,\"yes\":[0,2,3],\"decider\":[true,false,true,true,true,false],\"checked\":[1,4]}。請依 [n,checked,sample_mismatches,full_mismatches,sample_agrees,complete_agrees,classification] 的欄序回答。","answer":{"kind":"expression","value":"(6, [1, 4], [4], [4], 否, 否, 樣本已失敗)","explanation_zh":"擴展基礎核對=(6, [1, 4], [4], [4], 否, 否, 樣本已失敗)；依完整明示資料逐欄精確重算；有限／合成資料核對不是一般形式證明；規格與decider分離；有限完整表不外推無限可判定性。"},"difficulty":{"band":"undergraduate_core","level":2,"skills":["有限決定問題"]},"variant":{"family_id":"qf-ext18-decision-complete-vs-sample","seed":202610186089,"parameters":{"n":6,"yes":[0,2,3],"decider":[true,false,true,true,true,false],"checked":[1,4],"domain":"Fin_decision_problem","operation":"decision-complete-vs-sample","semantic_template":"qf-ext18-decision-complete-vs-sample/{\"checked\":[1,4],\"decider\":[true,false,true,true,true,false],\"n\":6,\"yes\":[0,2,3]}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_arithmetic","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"僅為產生端候選及自檢；主端須另做驗收，不構成人工審定、普遍證明、Lean執行或形式Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-13","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261013-advance-20261018-r06-decision-problem-0090","batch_id":"batch-20261013-advance-20261018-r06-decision-problem-foundations","language":"zh-Hant","source_mko_ids":["mko-decision-problem"],"title_zh":"有限決定問題","stem_zh":"明示有限輸入域。操作=decision-complete-vs-sample；資料={\"n\":6,\"yes\":[1,2,3],\"decider\":[false,true,true,true,false,true],\"checked\":[0,2]}。請依 [n,checked,sample_mismatches,full_mismatches,sample_agrees,complete_agrees,classification] 的欄序回答。","answer":{"kind":"expression","value":"(6, [0, 2], [], [5], 是, 否, 樣本通過但完整失敗)","explanation_zh":"擴展基礎核對=(6, [0, 2], [], [5], 是, 否, 樣本通過但完整失敗)；依完整明示資料逐欄精確重算；有限／合成資料核對不是一般形式證明；規格與decider分離；有限完整表不外推無限可判定性。"},"difficulty":{"band":"undergraduate_core","level":2,"skills":["有限決定問題"]},"variant":{"family_id":"qf-ext18-decision-complete-vs-sample","seed":202610186090,"parameters":{"n":6,"yes":[1,2,3],"decider":[false,true,true,true,false,true],"checked":[0,2],"domain":"Fin_decision_problem","operation":"decision-complete-vs-sample","semantic_template":"qf-ext18-decision-complete-vs-sample/{\"checked\":[0,2],\"decider\":[false,true,true,true,false,true],\"n\":6,\"yes\":[1,2,3]}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_arithmetic","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"僅為產生端候選及自檢；主端須另做驗收，不構成人工審定、普遍證明、Lean執行或形式Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-13","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261013-advance-20261018-r06-decision-problem-0091","batch_id":"batch-20261013-advance-20261018-r06-decision-problem-foundations","language":"zh-Hant","source_mko_ids":["mko-decision-problem"],"title_zh":"有限決定問題","stem_zh":"明示有限輸入域。操作=decision-complete-vs-sample；資料={\"n\":6,\"yes\":[0,1,2,3],\"decider\":[false,true,true,true,false,false],\"checked\":[0,3]}。請依 [n,checked,sample_mismatches,full_mismatches,sample_agrees,complete_agrees,classification] 的欄序回答。","answer":{"kind":"expression","value":"(6, [0, 3], [0], [0], 否, 否, 樣本已失敗)","explanation_zh":"擴展基礎核對=(6, [0, 3], [0], [0], 否, 否, 樣本已失敗)；依完整明示資料逐欄精確重算；有限／合成資料核對不是一般形式證明；規格與decider分離；有限完整表不外推無限可判定性。"},"difficulty":{"band":"undergraduate_core","level":2,"skills":["有限決定問題"]},"variant":{"family_id":"qf-ext18-decision-complete-vs-sample","seed":202610186091,"parameters":{"n":6,"yes":[0,1,2,3],"decider":[false,true,true,true,false,false],"checked":[0,3],"domain":"Fin_decision_problem","operation":"decision-complete-vs-sample","semantic_template":"qf-ext18-decision-complete-vs-sample/{\"checked\":[0,3],\"decider\":[false,true,true,true,false,false],\"n\":6,\"yes\":[0,1,2,3]}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_arithmetic","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"僅為產生端候選及自檢；主端須另做驗收，不構成人工審定、普遍證明、Lean執行或形式Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-13","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261013-advance-20261018-r06-decision-problem-0092","batch_id":"batch-20261013-advance-20261018-r06-decision-problem-foundations","language":"zh-Hant","source_mko_ids":["mko-decision-problem"],"title_zh":"有限決定問題","stem_zh":"明示有限輸入域。操作=decision-complete-vs-sample；資料={\"n\":6,\"yes\":[4],\"decider\":[false,true,false,false,true,false],\"checked\":[1,2]}。請依 [n,checked,sample_mismatches,full_mismatches,sample_agrees,complete_agrees,classification] 的欄序回答。","answer":{"kind":"expression","value":"(6, [1, 2], [1], [1], 否, 否, 樣本已失敗)","explanation_zh":"擴展基礎核對=(6, [1, 2], [1], [1], 否, 否, 樣本已失敗)；依完整明示資料逐欄精確重算；有限／合成資料核對不是一般形式證明；規格與decider分離；有限完整表不外推無限可判定性。"},"difficulty":{"band":"undergraduate_core","level":2,"skills":["有限決定問題"]},"variant":{"family_id":"qf-ext18-decision-complete-vs-sample","seed":202610186092,"parameters":{"n":6,"yes":[4],"decider":[false,true,false,false,true,false],"checked":[1,2],"domain":"Fin_decision_problem","operation":"decision-complete-vs-sample","semantic_template":"qf-ext18-decision-complete-vs-sample/{\"checked\":[1,2],\"decider\":[false,true,false,false,true,false],\"n\":6,\"yes\":[4]}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_arithmetic","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"僅為產生端候選及自檢；主端須另做驗收，不構成人工審定、普遍證明、Lean執行或形式Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-13","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261013-advance-20261018-r06-decision-problem-0093","batch_id":"batch-20261013-advance-20261018-r06-decision-problem-foundations","language":"zh-Hant","source_mko_ids":["mko-decision-problem"],"title_zh":"有限決定問題","stem_zh":"明示有限輸入域。操作=decision-complete-vs-sample；資料={\"n\":6,\"yes\":[0,4],\"decider\":[true,false,true,false,true,false],\"checked\":[2,5]}。請依 [n,checked,sample_mismatches,full_mismatches,sample_agrees,complete_agrees,classification] 的欄序回答。","answer":{"kind":"expression","value":"(6, [2, 5], [2], [2], 否, 否, 樣本已失敗)","explanation_zh":"擴展基礎核對=(6, [2, 5], [2], [2], 否, 否, 樣本已失敗)；依完整明示資料逐欄精確重算；有限／合成資料核對不是一般形式證明；規格與decider分離；有限完整表不外推無限可判定性。"},"difficulty":{"band":"undergraduate_core","level":3,"skills":["有限決定問題"]},"variant":{"family_id":"qf-ext18-decision-complete-vs-sample","seed":202610186093,"parameters":{"n":6,"yes":[0,4],"decider":[true,false,true,false,true,false],"checked":[2,5],"domain":"Fin_decision_problem","operation":"decision-complete-vs-sample","semantic_template":"qf-ext18-decision-complete-vs-sample/{\"checked\":[2,5],\"decider\":[true,false,true,false,true,false],\"n\":6,\"yes\":[0,4]}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_arithmetic","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"僅為產生端候選及自檢；主端須另做驗收，不構成人工審定、普遍證明、Lean執行或形式Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-13","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261013-advance-20261018-r06-decision-problem-0094","batch_id":"batch-20261013-advance-20261018-r06-decision-problem-foundations","language":"zh-Hant","source_mko_ids":["mko-decision-problem"],"title_zh":"有限決定問題","stem_zh":"明示有限輸入域。操作=decision-complete-vs-sample；資料={\"n\":6,\"yes\":[1,4],\"decider\":[false,true,false,true,true,false],\"checked\":[0,1]}。請依 [n,checked,sample_mismatches,full_mismatches,sample_agrees,complete_agrees,classification] 的欄序回答。","answer":{"kind":"expression","value":"(6, [0, 1], [], [3], 是, 否, 樣本通過但完整失敗)","explanation_zh":"擴展基礎核對=(6, [0, 1], [], [3], 是, 否, 樣本通過但完整失敗)；依完整明示資料逐欄精確重算；有限／合成資料核對不是一般形式證明；規格與decider分離；有限完整表不外推無限可判定性。"},"difficulty":{"band":"undergraduate_core","level":3,"skills":["有限決定問題"]},"variant":{"family_id":"qf-ext18-decision-complete-vs-sample","seed":202610186094,"parameters":{"n":6,"yes":[1,4],"decider":[false,true,false,true,true,false],"checked":[0,1],"domain":"Fin_decision_problem","operation":"decision-complete-vs-sample","semantic_template":"qf-ext18-decision-complete-vs-sample/{\"checked\":[0,1],\"decider\":[false,true,false,true,true,false],\"n\":6,\"yes\":[1,4]}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_arithmetic","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"僅為產生端候選及自檢；主端須另做驗收，不構成人工審定、普遍證明、Lean執行或形式Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-13","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261013-advance-20261018-r06-decision-problem-0095","batch_id":"batch-20261013-advance-20261018-r06-decision-problem-foundations","language":"zh-Hant","source_mko_ids":["mko-decision-problem"],"title_zh":"有限決定問題","stem_zh":"明示有限輸入域。操作=decision-complete-vs-sample；資料={\"n\":6,\"yes\":[0,1,4],\"decider\":[true,true,false,false,false,false],\"checked\":[1,4]}。請依 [n,checked,sample_mismatches,full_mismatches,sample_agrees,complete_agrees,classification] 的欄序回答。","answer":{"kind":"expression","value":"(6, [1, 4], [4], [4], 否, 否, 樣本已失敗)","explanation_zh":"擴展基礎核對=(6, [1, 4], [4], [4], 否, 否, 樣本已失敗)；依完整明示資料逐欄精確重算；有限／合成資料核對不是一般形式證明；規格與decider分離；有限完整表不外推無限可判定性。"},"difficulty":{"band":"undergraduate_core","level":3,"skills":["有限決定問題"]},"variant":{"family_id":"qf-ext18-decision-complete-vs-sample","seed":202610186095,"parameters":{"n":6,"yes":[0,1,4],"decider":[true,true,false,false,false,false],"checked":[1,4],"domain":"Fin_decision_problem","operation":"decision-complete-vs-sample","semantic_template":"qf-ext18-decision-complete-vs-sample/{\"checked\":[1,4],\"decider\":[true,true,false,false,false,false],\"n\":6,\"yes\":[0,1,4]}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_arithmetic","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"僅為產生端候選及自檢；主端須另做驗收，不構成人工審定、普遍證明、Lean執行或形式Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-13","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261013-advance-20261018-r06-decision-problem-0096","batch_id":"batch-20261013-advance-20261018-r06-decision-problem-foundations","language":"zh-Hant","source_mko_ids":["mko-decision-problem"],"title_zh":"有限決定問題","stem_zh":"明示有限輸入域。操作=decision-complete-vs-sample；資料={\"n\":6,\"yes\":[2,4],\"decider\":[false,false,true,false,true,true],\"checked\":[0,2]}。請依 [n,checked,sample_mismatches,full_mismatches,sample_agrees,complete_agrees,classification] 的欄序回答。","answer":{"kind":"expression","value":"(6, [0, 2], [], [5], 是, 否, 樣本通過但完整失敗)","explanation_zh":"擴展基礎核對=(6, [0, 2], [], [5], 是, 否, 樣本通過但完整失敗)；依完整明示資料逐欄精確重算；有限／合成資料核對不是一般形式證明；規格與decider分離；有限完整表不外推無限可判定性。"},"difficulty":{"band":"undergraduate_core","level":3,"skills":["有限決定問題"]},"variant":{"family_id":"qf-ext18-decision-complete-vs-sample","seed":202610186096,"parameters":{"n":6,"yes":[2,4],"decider":[false,false,true,false,true,true],"checked":[0,2],"domain":"Fin_decision_problem","operation":"decision-complete-vs-sample","semantic_template":"qf-ext18-decision-complete-vs-sample/{\"checked\":[0,2],\"decider\":[false,false,true,false,true,true],\"n\":6,\"yes\":[2,4]}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_arithmetic","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"僅為產生端候選及自檢；主端須另做驗收，不構成人工審定、普遍證明、Lean執行或形式Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-13","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261013-advance-20261018-r06-decision-problem-0097","batch_id":"batch-20261013-advance-20261018-r06-decision-problem-foundations","language":"zh-Hant","source_mko_ids":["mko-decision-problem"],"title_zh":"有限決定問題","stem_zh":"明示有限輸入域。操作=decision-complete-vs-sample；資料={\"n\":6,\"yes\":[0,2,4],\"decider\":[false,false,true,false,true,false],\"checked\":[0,3]}。請依 [n,checked,sample_mismatches,full_mismatches,sample_agrees,complete_agrees,classification] 的欄序回答。","answer":{"kind":"expression","value":"(6, [0, 3], [0], [0], 否, 否, 樣本已失敗)","explanation_zh":"擴展基礎核對=(6, [0, 3], [0], [0], 否, 否, 樣本已失敗)；依完整明示資料逐欄精確重算；有限／合成資料核對不是一般形式證明；規格與decider分離；有限完整表不外推無限可判定性。"},"difficulty":{"band":"undergraduate_core","level":3,"skills":["有限決定問題"]},"variant":{"family_id":"qf-ext18-decision-complete-vs-sample","seed":202610186097,"parameters":{"n":6,"yes":[0,2,4],"decider":[false,false,true,false,true,false],"checked":[0,3],"domain":"Fin_decision_problem","operation":"decision-complete-vs-sample","semantic_template":"qf-ext18-decision-complete-vs-sample/{\"checked\":[0,3],\"decider\":[false,false,true,false,true,false],\"n\":6,\"yes\":[0,2,4]}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_arithmetic","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"僅為產生端候選及自檢；主端須另做驗收，不構成人工審定、普遍證明、Lean執行或形式Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-13","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261013-advance-20261018-r06-decision-problem-0098","batch_id":"batch-20261013-advance-20261018-r06-decision-problem-foundations","language":"zh-Hant","source_mko_ids":["mko-decision-problem"],"title_zh":"有限決定問題","stem_zh":"明示有限輸入域。操作=decision-complete-vs-sample；資料={\"n\":6,\"yes\":[1,2,4],\"decider\":[false,false,true,false,true,false],\"checked\":[1,2]}。請依 [n,checked,sample_mismatches,full_mismatches,sample_agrees,complete_agrees,classification] 的欄序回答。","answer":{"kind":"expression","value":"(6, [1, 2], [1], [1], 否, 否, 樣本已失敗)","explanation_zh":"擴展基礎核對=(6, [1, 2], [1], [1], 否, 否, 樣本已失敗)；依完整明示資料逐欄精確重算；有限／合成資料核對不是一般形式證明；規格與decider分離；有限完整表不外推無限可判定性。"},"difficulty":{"band":"undergraduate_core","level":3,"skills":["有限決定問題"]},"variant":{"family_id":"qf-ext18-decision-complete-vs-sample","seed":202610186098,"parameters":{"n":6,"yes":[1,2,4],"decider":[false,false,true,false,true,false],"checked":[1,2],"domain":"Fin_decision_problem","operation":"decision-complete-vs-sample","semantic_template":"qf-ext18-decision-complete-vs-sample/{\"checked\":[1,2],\"decider\":[false,false,true,false,true,false],\"n\":6,\"yes\":[1,2,4]}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_arithmetic","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"僅為產生端候選及自檢；主端須另做驗收，不構成人工審定、普遍證明、Lean執行或形式Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-13","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261013-advance-20261018-r06-decision-problem-0099","batch_id":"batch-20261013-advance-20261018-r06-decision-problem-foundations","language":"zh-Hant","source_mko_ids":["mko-decision-problem"],"title_zh":"有限決定問題","stem_zh":"明示有限輸入域。操作=decision-complete-vs-sample；資料={\"n\":6,\"yes\":[0,1,2,4],\"decider\":[true,true,false,false,true,false],\"checked\":[2,5]}。請依 [n,checked,sample_mismatches,full_mismatches,sample_agrees,complete_agrees,classification] 的欄序回答。","answer":{"kind":"expression","value":"(6, [2, 5], [2], [2], 否, 否, 樣本已失敗)","explanation_zh":"擴展基礎核對=(6, [2, 5], [2], [2], 否, 否, 樣本已失敗)；依完整明示資料逐欄精確重算；有限／合成資料核對不是一般形式證明；規格與decider分離；有限完整表不外推無限可判定性。"},"difficulty":{"band":"undergraduate_core","level":3,"skills":["有限決定問題"]},"variant":{"family_id":"qf-ext18-decision-complete-vs-sample","seed":202610186099,"parameters":{"n":6,"yes":[0,1,2,4],"decider":[true,true,false,false,true,false],"checked":[2,5],"domain":"Fin_decision_problem","operation":"decision-complete-vs-sample","semantic_template":"qf-ext18-decision-complete-vs-sample/{\"checked\":[2,5],\"decider\":[true,true,false,false,true,false],\"n\":6,\"yes\":[0,1,2,4]}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_arithmetic","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"僅為產生端候選及自檢；主端須另做驗收，不構成人工審定、普遍證明、Lean執行或形式Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-13","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261013-advance-20261018-r06-decision-problem-0100","batch_id":"batch-20261013-advance-20261018-r06-decision-problem-foundations","language":"zh-Hant","source_mko_ids":["mko-decision-problem"],"title_zh":"有限決定問題","stem_zh":"明示有限輸入域。操作=decision-complete-vs-sample；資料={\"n\":6,\"yes\":[3,4],\"decider\":[false,false,false,false,true,false],\"checked\":[0,1]}。請依 [n,checked,sample_mismatches,full_mismatches,sample_agrees,complete_agrees,classification] 的欄序回答。","answer":{"kind":"expression","value":"(6, [0, 1], [], [3], 是, 否, 樣本通過但完整失敗)","explanation_zh":"擴展基礎核對=(6, [0, 1], [], [3], 是, 否, 樣本通過但完整失敗)；依完整明示資料逐欄精確重算；有限／合成資料核對不是一般形式證明；規格與decider分離；有限完整表不外推無限可判定性。"},"difficulty":{"band":"undergraduate_core","level":3,"skills":["有限決定問題"]},"variant":{"family_id":"qf-ext18-decision-complete-vs-sample","seed":202610186100,"parameters":{"n":6,"yes":[3,4],"decider":[false,false,false,false,true,false],"checked":[0,1],"domain":"Fin_decision_problem","operation":"decision-complete-vs-sample","semantic_template":"qf-ext18-decision-complete-vs-sample/{\"checked\":[0,1],\"decider\":[false,false,false,false,true,false],\"n\":6,\"yes\":[3,4]}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_arithmetic","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"僅為產生端候選及自檢；主端須另做驗收，不構成人工審定、普遍證明、Lean執行或形式Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-13","contract_version":"ocme-question-factory-v0.1"}}