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{"schema_version":"ocme-question-v0.1","id":"q-20261013-advance-20261019-r05-algorithm-correctness-0003","batch_id":"batch-20261013-advance-20261019-r05-algorithm-correctness-foundations","language":"zh-Hant","source_mko_ids":["mko-algorithm-correctness"],"title_zh":"算法正確性責任","stem_zh":"完整有限正確性模型。操作=correctness-invariant-audit；資料={\"n\":6,\"init\":[0],\"halt\":[5],\"steps\":[[0,1],[1,2],[2,5],[3,4]],\"invariant\":[0,1,2,5]}。請依 [invariant,init_in_invariant,bad_steps,step_preserved,inductive,covers_reachable] 欄序回答。","answer":{"kind":"expression","value":"([0, 1, 2, 5], 是, [], 是, 是, 是)","explanation_zh":"第二批擴展核對=([0, 1, 2, 5], 是, [], 是, 是, 是)；依完整明示資料重算；有限／合成資料核對不是一般形式證明；部分正確性與終止性分離；一條成功路徑不證總正確。"},"difficulty":{"band":"undergraduate_core","level":1,"skills":["算法正確性責任"]},"variant":{"family_id":"qf-ext19-correctness-invariant-audit","seed":202610195003,"parameters":{"n":6,"init":[0],"halt":[5],"steps":[[0,1],[1,2],[2,5],[3,4]],"invariant":[0,1,2,5],"domain":"Fin_correctness_model","operation":"correctness-invariant-audit","semantic_template":"qf-ext19-correctness-invariant-audit/{\"halt\":[5],\"init\":[0],\"invariant\":[0,1,2,5],\"n\":6,\"steps\":[[0,1],[1,2],[2,5],[3,4]]}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_model","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"僅為產生端候選及自檢；主端須另驗，不構成人工審定、一般程式證明、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-20261019-r05-algorithm-correctness-0004","batch_id":"batch-20261013-advance-20261019-r05-algorithm-correctness-foundations","language":"zh-Hant","source_mko_ids":["mko-algorithm-correctness"],"title_zh":"算法正確性責任","stem_zh":"完整有限正確性模型。操作=correctness-invariant-audit；資料={\"n\":6,\"init\":[0],\"halt\":[5],\"steps\":[[0,1],[1,2],[2,5],[0,3],[3,4]],\"invariant\":[0,1,2,3,4,5]}。請依 [invariant,init_in_invariant,bad_steps,step_preserved,inductive,covers_reachable] 欄序回答。","answer":{"kind":"expression","value":"([0, 1, 2, 3, 4, 5], 是, [], 是, 是, 是)","explanation_zh":"第二批擴展核對=([0, 1, 2, 3, 4, 5], 是, [], 是, 是, 是)；依完整明示資料重算；有限／合成資料核對不是一般形式證明；部分正確性與終止性分離；一條成功路徑不證總正確。"},"difficulty":{"band":"undergraduate_core","level":1,"skills":["算法正確性責任"]},"variant":{"family_id":"qf-ext19-correctness-invariant-audit","seed":202610195004,"parameters":{"n":6,"init":[0],"halt":[5],"steps":[[0,1],[1,2],[2,5],[0,3],[3,4]],"invariant":[0,1,2,3,4,5],"domain":"Fin_correctness_model","operation":"correctness-invariant-audit","semantic_template":"qf-ext19-correctness-invariant-audit/{\"halt\":[5],\"init\":[0],\"invariant\":[0,1,2,3,4,5],\"n\":6,\"steps\":[[0,1],[0,3],[1,2],[2,5],[3,4]]}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_model","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"僅為產生端候選及自檢；主端須另驗，不構成人工審定、一般程式證明、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-20261019-r05-algorithm-correctness-0005","batch_id":"batch-20261013-advance-20261019-r05-algorithm-correctness-foundations","language":"zh-Hant","source_mko_ids":["mko-algorithm-correctness"],"title_zh":"算法正確性責任","stem_zh":"完整有限正確性模型。操作=correctness-invariant-audit；資料={\"n\":6,\"init\":[0],\"halt\":[5],\"steps\":[[0,1],[1,2],[2,5],[4,5]],\"invariant\":[0,1,2,5]}。請依 [invariant,init_in_invariant,bad_steps,step_preserved,inductive,covers_reachable] 欄序回答。","answer":{"kind":"expression","value":"([0, 1, 2, 5], 是, [], 是, 是, 是)","explanation_zh":"第二批擴展核對=([0, 1, 2, 5], 是, [], 是, 是, 是)；依完整明示資料重算；有限／合成資料核對不是一般形式證明；部分正確性與終止性分離；一條成功路徑不證總正確。"},"difficulty":{"band":"undergraduate_core","level":1,"skills":["算法正確性責任"]},"variant":{"family_id":"qf-ext19-correctness-invariant-audit","seed":202610195005,"parameters":{"n":6,"init":[0],"halt":[5],"steps":[[0,1],[1,2],[2,5],[4,5]],"invariant":[0,1,2,5],"domain":"Fin_correctness_model","operation":"correctness-invariant-audit","semantic_template":"qf-ext19-correctness-invariant-audit/{\"halt\":[5],\"init\":[0],\"invariant\":[0,1,2,5],\"n\":6,\"steps\":[[0,1],[1,2],[2,5],[4,5]]}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_model","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"僅為產生端候選及自檢；主端須另驗，不構成人工審定、一般程式證明、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-20261019-r05-algorithm-correctness-0006","batch_id":"batch-20261013-advance-20261019-r05-algorithm-correctness-foundations","language":"zh-Hant","source_mko_ids":["mko-algorithm-correctness"],"title_zh":"算法正確性責任","stem_zh":"完整有限正確性模型。操作=correctness-invariant-audit；資料={\"n\":6,\"init\":[0],\"halt\":[5],\"steps\":[[0,1],[1,2],[2,5],[0,3],[4,5]],\"invariant\":[0,1,2,5]}。請依 [invariant,init_in_invariant,bad_steps,step_preserved,inductive,covers_reachable] 欄序回答。","answer":{"kind":"expression","value":"([0, 1, 2, 5], 是, [[0, 3]], 否, 否, 否)","explanation_zh":"第二批擴展核對=([0, 1, 2, 5], 是, [[0, 3]], 否, 否, 否)；依完整明示資料重算；有限／合成資料核對不是一般形式證明；部分正確性與終止性分離；一條成功路徑不證總正確。"},"difficulty":{"band":"undergraduate_core","level":1,"skills":["算法正確性責任"]},"variant":{"family_id":"qf-ext19-correctness-invariant-audit","seed":202610195006,"parameters":{"n":6,"init":[0],"halt":[5],"steps":[[0,1],[1,2],[2,5],[0,3],[4,5]],"invariant":[0,1,2,5],"domain":"Fin_correctness_model","operation":"correctness-invariant-audit","semantic_template":"qf-ext19-correctness-invariant-audit/{\"halt\":[5],\"init\":[0],\"invariant\":[0,1,2,5],\"n\":6,\"steps\":[[0,1],[0,3],[1,2],[2,5],[4,5]]}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_model","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"僅為產生端候選及自檢；主端須另驗，不構成人工審定、一般程式證明、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-20261019-r05-algorithm-correctness-0007","batch_id":"batch-20261013-advance-20261019-r05-algorithm-correctness-foundations","language":"zh-Hant","source_mko_ids":["mko-algorithm-correctness"],"title_zh":"算法正確性責任","stem_zh":"完整有限正確性模型。操作=correctness-invariant-audit；資料={\"n\":6,\"init\":[0],\"halt\":[5],\"steps\":[[0,1],[1,2],[2,5],[3,4],[4,5]],\"invariant\":[0,1,2,3,4,5]}。請依 [invariant,init_in_invariant,bad_steps,step_preserved,inductive,covers_reachable] 欄序回答。","answer":{"kind":"expression","value":"([0, 1, 2, 3, 4, 5], 是, [], 是, 是, 是)","explanation_zh":"第二批擴展核對=([0, 1, 2, 3, 4, 5], 是, [], 是, 是, 是)；依完整明示資料重算；有限／合成資料核對不是一般形式證明；部分正確性與終止性分離；一條成功路徑不證總正確。"},"difficulty":{"band":"undergraduate_core","level":1,"skills":["算法正確性責任"]},"variant":{"family_id":"qf-ext19-correctness-invariant-audit","seed":202610195007,"parameters":{"n":6,"init":[0],"halt":[5],"steps":[[0,1],[1,2],[2,5],[3,4],[4,5]],"invariant":[0,1,2,3,4,5],"domain":"Fin_correctness_model","operation":"correctness-invariant-audit","semantic_template":"qf-ext19-correctness-invariant-audit/{\"halt\":[5],\"init\":[0],\"invariant\":[0,1,2,3,4,5],\"n\":6,\"steps\":[[0,1],[1,2],[2,5],[3,4],[4,5]]}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_model","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"僅為產生端候選及自檢；主端須另驗，不構成人工審定、一般程式證明、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-20261019-r05-algorithm-correctness-0008","batch_id":"batch-20261013-advance-20261019-r05-algorithm-correctness-foundations","language":"zh-Hant","source_mko_ids":["mko-algorithm-correctness"],"title_zh":"算法正確性責任","stem_zh":"完整有限正確性模型。操作=correctness-invariant-audit；資料={\"n\":6,\"init\":[0],\"halt\":[5],\"steps\":[[0,1],[1,2],[2,5],[0,3],[3,4],[4,5]],\"invariant\":[0,1,2,5]}。請依 [invariant,init_in_invariant,bad_steps,step_preserved,inductive,covers_reachable] 欄序回答。","answer":{"kind":"expression","value":"([0, 1, 2, 5], 是, [[0, 3]], 否, 否, 否)","explanation_zh":"第二批擴展核對=([0, 1, 2, 5], 是, [[0, 3]], 否, 否, 否)；依完整明示資料重算；有限／合成資料核對不是一般形式證明；部分正確性與終止性分離；一條成功路徑不證總正確。"},"difficulty":{"band":"undergraduate_core","level":1,"skills":["算法正確性責任"]},"variant":{"family_id":"qf-ext19-correctness-invariant-audit","seed":202610195008,"parameters":{"n":6,"init":[0],"halt":[5],"steps":[[0,1],[1,2],[2,5],[0,3],[3,4],[4,5]],"invariant":[0,1,2,5],"domain":"Fin_correctness_model","operation":"correctness-invariant-audit","semantic_template":"qf-ext19-correctness-invariant-audit/{\"halt\":[5],\"init\":[0],\"invariant\":[0,1,2,5],\"n\":6,\"steps\":[[0,1],[0,3],[1,2],[2,5],[3,4],[4,5]]}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_model","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"僅為產生端候選及自檢；主端須另驗，不構成人工審定、一般程式證明、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"}}
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{"schema_version":"ocme-question-v0.1","id":"q-20261013-advance-20261019-r05-algorithm-correctness-0011","batch_id":"batch-20261013-advance-20261019-r05-algorithm-correctness-foundations","language":"zh-Hant","source_mko_ids":["mko-algorithm-correctness"],"title_zh":"算法正確性責任","stem_zh":"完整有限正確性模型。操作=correctness-invariant-audit；資料={\"n\":6,\"init\":[0],\"halt\":[5],\"steps\":[[0,1],[1,2],[2,5],[3,4],[2,1]],\"invariant\":[0,1,2,5]}。請依 [invariant,init_in_invariant,bad_steps,step_preserved,inductive,covers_reachable] 欄序回答。","answer":{"kind":"expression","value":"([0, 1, 2, 5], 是, [], 是, 是, 是)","explanation_zh":"第二批擴展核對=([0, 1, 2, 5], 是, [], 是, 是, 是)；依完整明示資料重算；有限／合成資料核對不是一般形式證明；部分正確性與終止性分離；一條成功路徑不證總正確。"},"difficulty":{"band":"undergraduate_core","level":2,"skills":["算法正確性責任"]},"variant":{"family_id":"qf-ext19-correctness-invariant-audit","seed":202610195011,"parameters":{"n":6,"init":[0],"halt":[5],"steps":[[0,1],[1,2],[2,5],[3,4],[2,1]],"invariant":[0,1,2,5],"domain":"Fin_correctness_model","operation":"correctness-invariant-audit","semantic_template":"qf-ext19-correctness-invariant-audit/{\"halt\":[5],\"init\":[0],\"invariant\":[0,1,2,5],\"n\":6,\"steps\":[[0,1],[1,2],[2,1],[2,5],[3,4]]}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_model","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"僅為產生端候選及自檢；主端須另驗，不構成人工審定、一般程式證明、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-20261019-r05-algorithm-correctness-0012","batch_id":"batch-20261013-advance-20261019-r05-algorithm-correctness-foundations","language":"zh-Hant","source_mko_ids":["mko-algorithm-correctness"],"title_zh":"算法正確性責任","stem_zh":"完整有限正確性模型。操作=correctness-invariant-audit；資料={\"n\":6,\"init\":[0],\"halt\":[5],\"steps\":[[0,1],[1,2],[2,5],[0,3],[3,4],[2,1]],\"invariant\":[0,1,2,5]}。請依 [invariant,init_in_invariant,bad_steps,step_preserved,inductive,covers_reachable] 欄序回答。","answer":{"kind":"expression","value":"([0, 1, 2, 5], 是, [[0, 3]], 否, 否, 否)","explanation_zh":"第二批擴展核對=([0, 1, 2, 5], 是, [[0, 3]], 否, 否, 否)；依完整明示資料重算；有限／合成資料核對不是一般形式證明；部分正確性與終止性分離；一條成功路徑不證總正確。"},"difficulty":{"band":"undergraduate_core","level":2,"skills":["算法正確性責任"]},"variant":{"family_id":"qf-ext19-correctness-invariant-audit","seed":202610195012,"parameters":{"n":6,"init":[0],"halt":[5],"steps":[[0,1],[1,2],[2,5],[0,3],[3,4],[2,1]],"invariant":[0,1,2,5],"domain":"Fin_correctness_model","operation":"correctness-invariant-audit","semantic_template":"qf-ext19-correctness-invariant-audit/{\"halt\":[5],\"init\":[0],\"invariant\":[0,1,2,5],\"n\":6,\"steps\":[[0,1],[0,3],[1,2],[2,1],[2,5],[3,4]]}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_model","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"僅為產生端候選及自檢；主端須另驗，不構成人工審定、一般程式證明、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-20261019-r05-algorithm-correctness-0013","batch_id":"batch-20261013-advance-20261019-r05-algorithm-correctness-foundations","language":"zh-Hant","source_mko_ids":["mko-algorithm-correctness"],"title_zh":"算法正確性責任","stem_zh":"完整有限正確性模型。操作=correctness-invariant-audit；資料={\"n\":6,\"init\":[0],\"halt\":[5],\"steps\":[[0,1],[1,2],[2,5],[4,5],[2,1]],\"invariant\":[0,1,2,3,4,5]}。請依 [invariant,init_in_invariant,bad_steps,step_preserved,inductive,covers_reachable] 欄序回答。","answer":{"kind":"expression","value":"([0, 1, 2, 3, 4, 5], 是, [], 是, 是, 是)","explanation_zh":"第二批擴展核對=([0, 1, 2, 3, 4, 5], 是, [], 是, 是, 是)；依完整明示資料重算；有限／合成資料核對不是一般形式證明；部分正確性與終止性分離；一條成功路徑不證總正確。"},"difficulty":{"band":"undergraduate_core","level":2,"skills":["算法正確性責任"]},"variant":{"family_id":"qf-ext19-correctness-invariant-audit","seed":202610195013,"parameters":{"n":6,"init":[0],"halt":[5],"steps":[[0,1],[1,2],[2,5],[4,5],[2,1]],"invariant":[0,1,2,3,4,5],"domain":"Fin_correctness_model","operation":"correctness-invariant-audit","semantic_template":"qf-ext19-correctness-invariant-audit/{\"halt\":[5],\"init\":[0],\"invariant\":[0,1,2,3,4,5],\"n\":6,\"steps\":[[0,1],[1,2],[2,1],[2,5],[4,5]]}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_model","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"僅為產生端候選及自檢；主端須另驗，不構成人工審定、一般程式證明、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-20261019-r05-algorithm-correctness-0014","batch_id":"batch-20261013-advance-20261019-r05-algorithm-correctness-foundations","language":"zh-Hant","source_mko_ids":["mko-algorithm-correctness"],"title_zh":"算法正確性責任","stem_zh":"完整有限正確性模型。操作=correctness-invariant-audit；資料={\"n\":6,\"init\":[0],\"halt\":[5],\"steps\":[[0,1],[1,2],[2,5],[0,3],[4,5],[2,1]],\"invariant\":[0,1,2,5]}。請依 [invariant,init_in_invariant,bad_steps,step_preserved,inductive,covers_reachable] 欄序回答。","answer":{"kind":"expression","value":"([0, 1, 2, 5], 是, [[0, 3]], 否, 否, 否)","explanation_zh":"第二批擴展核對=([0, 1, 2, 5], 是, [[0, 3]], 否, 否, 否)；依完整明示資料重算；有限／合成資料核對不是一般形式證明；部分正確性與終止性分離；一條成功路徑不證總正確。"},"difficulty":{"band":"undergraduate_core","level":2,"skills":["算法正確性責任"]},"variant":{"family_id":"qf-ext19-correctness-invariant-audit","seed":202610195014,"parameters":{"n":6,"init":[0],"halt":[5],"steps":[[0,1],[1,2],[2,5],[0,3],[4,5],[2,1]],"invariant":[0,1,2,5],"domain":"Fin_correctness_model","operation":"correctness-invariant-audit","semantic_template":"qf-ext19-correctness-invariant-audit/{\"halt\":[5],\"init\":[0],\"invariant\":[0,1,2,5],\"n\":6,\"steps\":[[0,1],[0,3],[1,2],[2,1],[2,5],[4,5]]}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_model","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"僅為產生端候選及自檢；主端須另驗，不構成人工審定、一般程式證明、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-20261019-r05-algorithm-correctness-0015","batch_id":"batch-20261013-advance-20261019-r05-algorithm-correctness-foundations","language":"zh-Hant","source_mko_ids":["mko-algorithm-correctness"],"title_zh":"算法正確性責任","stem_zh":"完整有限正確性模型。操作=correctness-invariant-audit；資料={\"n\":6,\"init\":[0],\"halt\":[5],\"steps\":[[0,1],[1,2],[2,5],[3,4],[4,5],[2,1]],\"invariant\":[0,1,2,5]}。請依 [invariant,init_in_invariant,bad_steps,step_preserved,inductive,covers_reachable] 欄序回答。","answer":{"kind":"expression","value":"([0, 1, 2, 5], 是, [], 是, 是, 是)","explanation_zh":"第二批擴展核對=([0, 1, 2, 5], 是, [], 是, 是, 是)；依完整明示資料重算；有限／合成資料核對不是一般形式證明；部分正確性與終止性分離；一條成功路徑不證總正確。"},"difficulty":{"band":"undergraduate_core","level":2,"skills":["算法正確性責任"]},"variant":{"family_id":"qf-ext19-correctness-invariant-audit","seed":202610195015,"parameters":{"n":6,"init":[0],"halt":[5],"steps":[[0,1],[1,2],[2,5],[3,4],[4,5],[2,1]],"invariant":[0,1,2,5],"domain":"Fin_correctness_model","operation":"correctness-invariant-audit","semantic_template":"qf-ext19-correctness-invariant-audit/{\"halt\":[5],\"init\":[0],\"invariant\":[0,1,2,5],\"n\":6,\"steps\":[[0,1],[1,2],[2,1],[2,5],[3,4],[4,5]]}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_model","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"僅為產生端候選及自檢；主端須另驗，不構成人工審定、一般程式證明、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-20261019-r05-algorithm-correctness-0016","batch_id":"batch-20261013-advance-20261019-r05-algorithm-correctness-foundations","language":"zh-Hant","source_mko_ids":["mko-algorithm-correctness"],"title_zh":"算法正確性責任","stem_zh":"完整有限正確性模型。操作=correctness-invariant-audit；資料={\"n\":6,\"init\":[0],\"halt\":[5],\"steps\":[[0,1],[1,2],[2,5],[0,3],[3,4],[4,5],[2,1]],\"invariant\":[0,1,2,3,4,5]}。請依 [invariant,init_in_invariant,bad_steps,step_preserved,inductive,covers_reachable] 欄序回答。","answer":{"kind":"expression","value":"([0, 1, 2, 3, 4, 5], 是, [], 是, 是, 是)","explanation_zh":"第二批擴展核對=([0, 1, 2, 3, 4, 5], 是, [], 是, 是, 是)；依完整明示資料重算；有限／合成資料核對不是一般形式證明；部分正確性與終止性分離；一條成功路徑不證總正確。"},"difficulty":{"band":"undergraduate_core","level":2,"skills":["算法正確性責任"]},"variant":{"family_id":"qf-ext19-correctness-invariant-audit","seed":202610195016,"parameters":{"n":6,"init":[0],"halt":[5],"steps":[[0,1],[1,2],[2,5],[0,3],[3,4],[4,5],[2,1]],"invariant":[0,1,2,3,4,5],"domain":"Fin_correctness_model","operation":"correctness-invariant-audit","semantic_template":"qf-ext19-correctness-invariant-audit/{\"halt\":[5],\"init\":[0],\"invariant\":[0,1,2,3,4,5],\"n\":6,\"steps\":[[0,1],[0,3],[1,2],[2,1],[2,5],[3,4],[4,5]]}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_model","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"僅為產生端候選及自檢；主端須另驗，不構成人工審定、一般程式證明、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-20261019-r05-algorithm-correctness-0017","batch_id":"batch-20261013-advance-20261019-r05-algorithm-correctness-foundations","language":"zh-Hant","source_mko_ids":["mko-algorithm-correctness"],"title_zh":"算法正確性責任","stem_zh":"完整有限正確性模型。操作=correctness-invariant-audit；資料={\"n\":6,\"init\":[0],\"halt\":[5],\"steps\":[[0,1],[1,2],[2,5],[1,1]],\"invariant\":[0,1,2,5]}。請依 [invariant,init_in_invariant,bad_steps,step_preserved,inductive,covers_reachable] 欄序回答。","answer":{"kind":"expression","value":"([0, 1, 2, 5], 是, [], 是, 是, 是)","explanation_zh":"第二批擴展核對=([0, 1, 2, 5], 是, [], 是, 是, 是)；依完整明示資料重算；有限／合成資料核對不是一般形式證明；部分正確性與終止性分離；一條成功路徑不證總正確。"},"difficulty":{"band":"undergraduate_core","level":2,"skills":["算法正確性責任"]},"variant":{"family_id":"qf-ext19-correctness-invariant-audit","seed":202610195017,"parameters":{"n":6,"init":[0],"halt":[5],"steps":[[0,1],[1,2],[2,5],[1,1]],"invariant":[0,1,2,5],"domain":"Fin_correctness_model","operation":"correctness-invariant-audit","semantic_template":"qf-ext19-correctness-invariant-audit/{\"halt\":[5],\"init\":[0],\"invariant\":[0,1,2,5],\"n\":6,\"steps\":[[0,1],[1,1],[1,2],[2,5]]}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_model","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"僅為產生端候選及自檢；主端須另驗，不構成人工審定、一般程式證明、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-20261019-r05-algorithm-correctness-0018","batch_id":"batch-20261013-advance-20261019-r05-algorithm-correctness-foundations","language":"zh-Hant","source_mko_ids":["mko-algorithm-correctness"],"title_zh":"算法正確性責任","stem_zh":"完整有限正確性模型。操作=correctness-invariant-audit；資料={\"n\":6,\"init\":[0],\"halt\":[5],\"steps\":[[0,1],[1,2],[2,5],[0,3],[1,1]],\"invariant\":[0,1,2,5]}。請依 [invariant,init_in_invariant,bad_steps,step_preserved,inductive,covers_reachable] 欄序回答。","answer":{"kind":"expression","value":"([0, 1, 2, 5], 是, [[0, 3]], 否, 否, 否)","explanation_zh":"第二批擴展核對=([0, 1, 2, 5], 是, [[0, 3]], 否, 否, 否)；依完整明示資料重算；有限／合成資料核對不是一般形式證明；部分正確性與終止性分離；一條成功路徑不證總正確。"},"difficulty":{"band":"undergraduate_core","level":3,"skills":["算法正確性責任"]},"variant":{"family_id":"qf-ext19-correctness-invariant-audit","seed":202610195018,"parameters":{"n":6,"init":[0],"halt":[5],"steps":[[0,1],[1,2],[2,5],[0,3],[1,1]],"invariant":[0,1,2,5],"domain":"Fin_correctness_model","operation":"correctness-invariant-audit","semantic_template":"qf-ext19-correctness-invariant-audit/{\"halt\":[5],\"init\":[0],\"invariant\":[0,1,2,5],\"n\":6,\"steps\":[[0,1],[0,3],[1,1],[1,2],[2,5]]}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_model","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"僅為產生端候選及自檢；主端須另驗，不構成人工審定、一般程式證明、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-20261019-r05-algorithm-correctness-0019","batch_id":"batch-20261013-advance-20261019-r05-algorithm-correctness-foundations","language":"zh-Hant","source_mko_ids":["mko-algorithm-correctness"],"title_zh":"算法正確性責任","stem_zh":"完整有限正確性模型。操作=correctness-invariant-audit；資料={\"n\":6,\"init\":[0],\"halt\":[5],\"steps\":[[0,1],[1,2],[2,5],[3,4],[1,1]],\"invariant\":[0,1,2,3,4,5]}。請依 [invariant,init_in_invariant,bad_steps,step_preserved,inductive,covers_reachable] 欄序回答。","answer":{"kind":"expression","value":"([0, 1, 2, 3, 4, 5], 是, [], 是, 是, 是)","explanation_zh":"第二批擴展核對=([0, 1, 2, 3, 4, 5], 是, [], 是, 是, 是)；依完整明示資料重算；有限／合成資料核對不是一般形式證明；部分正確性與終止性分離；一條成功路徑不證總正確。"},"difficulty":{"band":"undergraduate_core","level":3,"skills":["算法正確性責任"]},"variant":{"family_id":"qf-ext19-correctness-invariant-audit","seed":202610195019,"parameters":{"n":6,"init":[0],"halt":[5],"steps":[[0,1],[1,2],[2,5],[3,4],[1,1]],"invariant":[0,1,2,3,4,5],"domain":"Fin_correctness_model","operation":"correctness-invariant-audit","semantic_template":"qf-ext19-correctness-invariant-audit/{\"halt\":[5],\"init\":[0],\"invariant\":[0,1,2,3,4,5],\"n\":6,\"steps\":[[0,1],[1,1],[1,2],[2,5],[3,4]]}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_model","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"僅為產生端候選及自檢；主端須另驗，不構成人工審定、一般程式證明、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-20261019-r05-algorithm-correctness-0020","batch_id":"batch-20261013-advance-20261019-r05-algorithm-correctness-foundations","language":"zh-Hant","source_mko_ids":["mko-algorithm-correctness"],"title_zh":"算法正確性責任","stem_zh":"完整有限正確性模型。操作=correctness-invariant-audit；資料={\"n\":6,\"init\":[0],\"halt\":[5],\"steps\":[[0,1],[1,2],[2,5],[0,3],[3,4],[1,1]],\"invariant\":[0,1,2,5]}。請依 [invariant,init_in_invariant,bad_steps,step_preserved,inductive,covers_reachable] 欄序回答。","answer":{"kind":"expression","value":"([0, 1, 2, 5], 是, [[0, 3]], 否, 否, 否)","explanation_zh":"第二批擴展核對=([0, 1, 2, 5], 是, [[0, 3]], 否, 否, 否)；依完整明示資料重算；有限／合成資料核對不是一般形式證明；部分正確性與終止性分離；一條成功路徑不證總正確。"},"difficulty":{"band":"undergraduate_core","level":3,"skills":["算法正確性責任"]},"variant":{"family_id":"qf-ext19-correctness-invariant-audit","seed":202610195020,"parameters":{"n":6,"init":[0],"halt":[5],"steps":[[0,1],[1,2],[2,5],[0,3],[3,4],[1,1]],"invariant":[0,1,2,5],"domain":"Fin_correctness_model","operation":"correctness-invariant-audit","semantic_template":"qf-ext19-correctness-invariant-audit/{\"halt\":[5],\"init\":[0],\"invariant\":[0,1,2,5],\"n\":6,\"steps\":[[0,1],[0,3],[1,1],[1,2],[2,5],[3,4]]}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_model","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"僅為產生端候選及自檢；主端須另驗，不構成人工審定、一般程式證明、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-20261019-r05-algorithm-correctness-0021","batch_id":"batch-20261013-advance-20261019-r05-algorithm-correctness-foundations","language":"zh-Hant","source_mko_ids":["mko-algorithm-correctness"],"title_zh":"算法正確性責任","stem_zh":"完整有限正確性模型。操作=correctness-invariant-audit；資料={\"n\":6,\"init\":[0],\"halt\":[5],\"steps\":[[0,1],[1,2],[2,5],[4,5],[1,1]],\"invariant\":[0,1,2,5]}。請依 [invariant,init_in_invariant,bad_steps,step_preserved,inductive,covers_reachable] 欄序回答。","answer":{"kind":"expression","value":"([0, 1, 2, 5], 是, [], 是, 是, 是)","explanation_zh":"第二批擴展核對=([0, 1, 2, 5], 是, [], 是, 是, 是)；依完整明示資料重算；有限／合成資料核對不是一般形式證明；部分正確性與終止性分離；一條成功路徑不證總正確。"},"difficulty":{"band":"undergraduate_core","level":3,"skills":["算法正確性責任"]},"variant":{"family_id":"qf-ext19-correctness-invariant-audit","seed":202610195021,"parameters":{"n":6,"init":[0],"halt":[5],"steps":[[0,1],[1,2],[2,5],[4,5],[1,1]],"invariant":[0,1,2,5],"domain":"Fin_correctness_model","operation":"correctness-invariant-audit","semantic_template":"qf-ext19-correctness-invariant-audit/{\"halt\":[5],\"init\":[0],\"invariant\":[0,1,2,5],\"n\":6,\"steps\":[[0,1],[1,1],[1,2],[2,5],[4,5]]}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_model","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"僅為產生端候選及自檢；主端須另驗，不構成人工審定、一般程式證明、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-20261019-r05-algorithm-correctness-0022","batch_id":"batch-20261013-advance-20261019-r05-algorithm-correctness-foundations","language":"zh-Hant","source_mko_ids":["mko-algorithm-correctness"],"title_zh":"算法正確性責任","stem_zh":"完整有限正確性模型。操作=correctness-invariant-audit；資料={\"n\":6,\"init\":[0],\"halt\":[5],\"steps\":[[0,1],[1,2],[2,5],[0,3],[4,5],[1,1]],\"invariant\":[0,1,2,3,4,5]}。請依 [invariant,init_in_invariant,bad_steps,step_preserved,inductive,covers_reachable] 欄序回答。","answer":{"kind":"expression","value":"([0, 1, 2, 3, 4, 5], 是, [], 是, 是, 是)","explanation_zh":"第二批擴展核對=([0, 1, 2, 3, 4, 5], 是, [], 是, 是, 是)；依完整明示資料重算；有限／合成資料核對不是一般形式證明；部分正確性與終止性分離；一條成功路徑不證總正確。"},"difficulty":{"band":"undergraduate_core","level":3,"skills":["算法正確性責任"]},"variant":{"family_id":"qf-ext19-correctness-invariant-audit","seed":202610195022,"parameters":{"n":6,"init":[0],"halt":[5],"steps":[[0,1],[1,2],[2,5],[0,3],[4,5],[1,1]],"invariant":[0,1,2,3,4,5],"domain":"Fin_correctness_model","operation":"correctness-invariant-audit","semantic_template":"qf-ext19-correctness-invariant-audit/{\"halt\":[5],\"init\":[0],\"invariant\":[0,1,2,3,4,5],\"n\":6,\"steps\":[[0,1],[0,3],[1,1],[1,2],[2,5],[4,5]]}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_model","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"僅為產生端候選及自檢；主端須另驗，不構成人工審定、一般程式證明、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-20261019-r05-algorithm-correctness-0023","batch_id":"batch-20261013-advance-20261019-r05-algorithm-correctness-foundations","language":"zh-Hant","source_mko_ids":["mko-algorithm-correctness"],"title_zh":"算法正確性責任","stem_zh":"完整有限正確性模型。操作=correctness-invariant-audit；資料={\"n\":6,\"init\":[0],\"halt\":[5],\"steps\":[[0,1],[1,2],[2,5],[3,4],[4,5],[1,1]],\"invariant\":[0,1,2,5]}。請依 [invariant,init_in_invariant,bad_steps,step_preserved,inductive,covers_reachable] 欄序回答。","answer":{"kind":"expression","value":"([0, 1, 2, 5], 是, [], 是, 是, 是)","explanation_zh":"第二批擴展核對=([0, 1, 2, 5], 是, [], 是, 是, 是)；依完整明示資料重算；有限／合成資料核對不是一般形式證明；部分正確性與終止性分離；一條成功路徑不證總正確。"},"difficulty":{"band":"undergraduate_core","level":3,"skills":["算法正確性責任"]},"variant":{"family_id":"qf-ext19-correctness-invariant-audit","seed":202610195023,"parameters":{"n":6,"init":[0],"halt":[5],"steps":[[0,1],[1,2],[2,5],[3,4],[4,5],[1,1]],"invariant":[0,1,2,5],"domain":"Fin_correctness_model","operation":"correctness-invariant-audit","semantic_template":"qf-ext19-correctness-invariant-audit/{\"halt\":[5],\"init\":[0],\"invariant\":[0,1,2,5],\"n\":6,\"steps\":[[0,1],[1,1],[1,2],[2,5],[3,4],[4,5]]}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_model","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"僅為產生端候選及自檢；主端須另驗，不構成人工審定、一般程式證明、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-20261019-r05-algorithm-correctness-0024","batch_id":"batch-20261013-advance-20261019-r05-algorithm-correctness-foundations","language":"zh-Hant","source_mko_ids":["mko-algorithm-correctness"],"title_zh":"算法正確性責任","stem_zh":"完整有限正確性模型。操作=correctness-invariant-audit；資料={\"n\":6,\"init\":[0],\"halt\":[5],\"steps\":[[0,1],[1,2],[2,5],[0,3],[3,4],[4,5],[1,1]],\"invariant\":[0,1,2,5]}。請依 [invariant,init_in_invariant,bad_steps,step_preserved,inductive,covers_reachable] 欄序回答。","answer":{"kind":"expression","value":"([0, 1, 2, 5], 是, [[0, 3]], 否, 否, 否)","explanation_zh":"第二批擴展核對=([0, 1, 2, 5], 是, [[0, 3]], 否, 否, 否)；依完整明示資料重算；有限／合成資料核對不是一般形式證明；部分正確性與終止性分離；一條成功路徑不證總正確。"},"difficulty":{"band":"undergraduate_core","level":3,"skills":["算法正確性責任"]},"variant":{"family_id":"qf-ext19-correctness-invariant-audit","seed":202610195024,"parameters":{"n":6,"init":[0],"halt":[5],"steps":[[0,1],[1,2],[2,5],[0,3],[3,4],[4,5],[1,1]],"invariant":[0,1,2,5],"domain":"Fin_correctness_model","operation":"correctness-invariant-audit","semantic_template":"qf-ext19-correctness-invariant-audit/{\"halt\":[5],\"init\":[0],\"invariant\":[0,1,2,5],\"n\":6,\"steps\":[[0,1],[0,3],[1,1],[1,2],[2,5],[3,4],[4,5]]}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_model","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"僅為產生端候選及自檢；主端須另驗，不構成人工審定、一般程式證明、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-20261019-r05-algorithm-correctness-0025","batch_id":"batch-20261013-advance-20261019-r05-algorithm-correctness-foundations","language":"zh-Hant","source_mko_ids":["mko-algorithm-correctness"],"title_zh":"算法正確性責任","stem_zh":"完整有限正確性模型。操作=correctness-invariant-audit；資料={\"n\":6,\"init\":[0],\"halt\":[5],\"steps\":[[0,1],[1,2],[2,5],[2,1],[1,1]],\"invariant\":[0,1,2,3,4,5]}。請依 [invariant,init_in_invariant,bad_steps,step_preserved,inductive,covers_reachable] 欄序回答。","answer":{"kind":"expression","value":"([0, 1, 2, 3, 4, 5], 是, [], 是, 是, 是)","explanation_zh":"第二批擴展核對=([0, 1, 2, 3, 4, 5], 是, [], 是, 是, 是)；依完整明示資料重算；有限／合成資料核對不是一般形式證明；部分正確性與終止性分離；一條成功路徑不證總正確。"},"difficulty":{"band":"undergraduate_core","level":3,"skills":["算法正確性責任"]},"variant":{"family_id":"qf-ext19-correctness-invariant-audit","seed":202610195025,"parameters":{"n":6,"init":[0],"halt":[5],"steps":[[0,1],[1,2],[2,5],[2,1],[1,1]],"invariant":[0,1,2,3,4,5],"domain":"Fin_correctness_model","operation":"correctness-invariant-audit","semantic_template":"qf-ext19-correctness-invariant-audit/{\"halt\":[5],\"init\":[0],\"invariant\":[0,1,2,3,4,5],\"n\":6,\"steps\":[[0,1],[1,1],[1,2],[2,1],[2,5]]}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_model","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"僅為產生端候選及自檢；主端須另驗，不構成人工審定、一般程式證明、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-20261019-r05-algorithm-correctness-0026","batch_id":"batch-20261013-advance-20261019-r05-algorithm-correctness-foundations","language":"zh-Hant","source_mko_ids":["mko-algorithm-correctness"],"title_zh":"算法正確性責任","stem_zh":"完整有限正確性模型。操作=correctness-partial-audit；資料={\"n\":6,\"init\":[0],\"halt\":[5],\"steps\":[[0,1],[1,2],[2,5]],\"post\":[]}。請依 [reachable_halts,post,bad_halts,partial_correct,vacuous] 欄序回答。","answer":{"kind":"expression","value":"([5], [], [5], 否, 否)","explanation_zh":"第二批擴展核對=([5], [], [5], 否, 否)；依完整明示資料重算；有限／合成資料核對不是一般形式證明；部分正確性與終止性分離；一條成功路徑不證總正確。"},"difficulty":{"band":"undergraduate_core","level":1,"skills":["算法正確性責任"]},"variant":{"family_id":"qf-ext19-correctness-partial-audit","seed":202610195026,"parameters":{"n":6,"init":[0],"halt":[5],"steps":[[0,1],[1,2],[2,5]],"post":[],"domain":"Fin_correctness_model","operation":"correctness-partial-audit","semantic_template":"qf-ext19-correctness-partial-audit/{\"halt\":[5],\"init\":[0],\"n\":6,\"post\":[],\"steps\":[[0,1],[1,2],[2,5]]}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_model","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"僅為產生端候選及自檢；主端須另驗，不構成人工審定、一般程式證明、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-20261019-r05-algorithm-correctness-0027","batch_id":"batch-20261013-advance-20261019-r05-algorithm-correctness-foundations","language":"zh-Hant","source_mko_ids":["mko-algorithm-correctness"],"title_zh":"算法正確性責任","stem_zh":"完整有限正確性模型。操作=correctness-partial-audit；資料={\"n\":6,\"init\":[0],\"halt\":[5],\"steps\":[[0,1],[1,2],[2,5],[0,3]],\"post\":[5]}。請依 [reachable_halts,post,bad_halts,partial_correct,vacuous] 欄序回答。","answer":{"kind":"expression","value":"([5], [5], [], 是, 否)","explanation_zh":"第二批擴展核對=([5], [5], [], 是, 否)；依完整明示資料重算；有限／合成資料核對不是一般形式證明；部分正確性與終止性分離；一條成功路徑不證總正確。"},"difficulty":{"band":"undergraduate_core","level":1,"skills":["算法正確性責任"]},"variant":{"family_id":"qf-ext19-correctness-partial-audit","seed":202610195027,"parameters":{"n":6,"init":[0],"halt":[5],"steps":[[0,1],[1,2],[2,5],[0,3]],"post":[5],"domain":"Fin_correctness_model","operation":"correctness-partial-audit","semantic_template":"qf-ext19-correctness-partial-audit/{\"halt\":[5],\"init\":[0],\"n\":6,\"post\":[5],\"steps\":[[0,1],[0,3],[1,2],[2,5]]}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_model","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"僅為產生端候選及自檢；主端須另驗，不構成人工審定、一般程式證明、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-20261019-r05-algorithm-correctness-0028","batch_id":"batch-20261013-advance-20261019-r05-algorithm-correctness-foundations","language":"zh-Hant","source_mko_ids":["mko-algorithm-correctness"],"title_zh":"算法正確性責任","stem_zh":"完整有限正確性模型。操作=correctness-partial-audit；資料={\"n\":6,\"init\":[0],\"halt\":[5],\"steps\":[[0,1],[1,2],[2,5],[3,4]],\"post\":[]}。請依 [reachable_halts,post,bad_halts,partial_correct,vacuous] 欄序回答。","answer":{"kind":"expression","value":"([5], [], [5], 否, 否)","explanation_zh":"第二批擴展核對=([5], [], [5], 否, 否)；依完整明示資料重算；有限／合成資料核對不是一般形式證明；部分正確性與終止性分離；一條成功路徑不證總正確。"},"difficulty":{"band":"undergraduate_core","level":1,"skills":["算法正確性責任"]},"variant":{"family_id":"qf-ext19-correctness-partial-audit","seed":202610195028,"parameters":{"n":6,"init":[0],"halt":[5],"steps":[[0,1],[1,2],[2,5],[3,4]],"post":[],"domain":"Fin_correctness_model","operation":"correctness-partial-audit","semantic_template":"qf-ext19-correctness-partial-audit/{\"halt\":[5],\"init\":[0],\"n\":6,\"post\":[],\"steps\":[[0,1],[1,2],[2,5],[3,4]]}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_model","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"僅為產生端候選及自檢；主端須另驗，不構成人工審定、一般程式證明、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-20261019-r05-algorithm-correctness-0029","batch_id":"batch-20261013-advance-20261019-r05-algorithm-correctness-foundations","language":"zh-Hant","source_mko_ids":["mko-algorithm-correctness"],"title_zh":"算法正確性責任","stem_zh":"完整有限正確性模型。操作=correctness-partial-audit；資料={\"n\":6,\"init\":[0],\"halt\":[5],\"steps\":[[0,1],[1,2],[2,5],[0,3],[3,4]],\"post\":[5]}。請依 [reachable_halts,post,bad_halts,partial_correct,vacuous] 欄序回答。","answer":{"kind":"expression","value":"([5], [5], [], 是, 否)","explanation_zh":"第二批擴展核對=([5], [5], [], 是, 否)；依完整明示資料重算；有限／合成資料核對不是一般形式證明；部分正確性與終止性分離；一條成功路徑不證總正確。"},"difficulty":{"band":"undergraduate_core","level":1,"skills":["算法正確性責任"]},"variant":{"family_id":"qf-ext19-correctness-partial-audit","seed":202610195029,"parameters":{"n":6,"init":[0],"halt":[5],"steps":[[0,1],[1,2],[2,5],[0,3],[3,4]],"post":[5],"domain":"Fin_correctness_model","operation":"correctness-partial-audit","semantic_template":"qf-ext19-correctness-partial-audit/{\"halt\":[5],\"init\":[0],\"n\":6,\"post\":[5],\"steps\":[[0,1],[0,3],[1,2],[2,5],[3,4]]}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_model","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"僅為產生端候選及自檢；主端須另驗，不構成人工審定、一般程式證明、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-20261019-r05-algorithm-correctness-0030","batch_id":"batch-20261013-advance-20261019-r05-algorithm-correctness-foundations","language":"zh-Hant","source_mko_ids":["mko-algorithm-correctness"],"title_zh":"算法正確性責任","stem_zh":"完整有限正確性模型。操作=correctness-partial-audit；資料={\"n\":6,\"init\":[0],\"halt\":[5],\"steps\":[[0,1],[1,2],[2,5],[4,5]],\"post\":[]}。請依 [reachable_halts,post,bad_halts,partial_correct,vacuous] 欄序回答。","answer":{"kind":"expression","value":"([5], [], [5], 否, 否)","explanation_zh":"第二批擴展核對=([5], [], [5], 否, 否)；依完整明示資料重算；有限／合成資料核對不是一般形式證明；部分正確性與終止性分離；一條成功路徑不證總正確。"},"difficulty":{"band":"undergraduate_core","level":1,"skills":["算法正確性責任"]},"variant":{"family_id":"qf-ext19-correctness-partial-audit","seed":202610195030,"parameters":{"n":6,"init":[0],"halt":[5],"steps":[[0,1],[1,2],[2,5],[4,5]],"post":[],"domain":"Fin_correctness_model","operation":"correctness-partial-audit","semantic_template":"qf-ext19-correctness-partial-audit/{\"halt\":[5],\"init\":[0],\"n\":6,\"post\":[],\"steps\":[[0,1],[1,2],[2,5],[4,5]]}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_model","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"僅為產生端候選及自檢；主端須另驗，不構成人工審定、一般程式證明、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-20261019-r05-algorithm-correctness-0031","batch_id":"batch-20261013-advance-20261019-r05-algorithm-correctness-foundations","language":"zh-Hant","source_mko_ids":["mko-algorithm-correctness"],"title_zh":"算法正確性責任","stem_zh":"完整有限正確性模型。操作=correctness-partial-audit；資料={\"n\":6,\"init\":[0],\"halt\":[5],\"steps\":[[0,1],[1,2],[2,5],[0,3],[4,5]],\"post\":[5]}。請依 [reachable_halts,post,bad_halts,partial_correct,vacuous] 欄序回答。","answer":{"kind":"expression","value":"([5], [5], [], 是, 否)","explanation_zh":"第二批擴展核對=([5], [5], [], 是, 否)；依完整明示資料重算；有限／合成資料核對不是一般形式證明；部分正確性與終止性分離；一條成功路徑不證總正確。"},"difficulty":{"band":"undergraduate_core","level":1,"skills":["算法正確性責任"]},"variant":{"family_id":"qf-ext19-correctness-partial-audit","seed":202610195031,"parameters":{"n":6,"init":[0],"halt":[5],"steps":[[0,1],[1,2],[2,5],[0,3],[4,5]],"post":[5],"domain":"Fin_correctness_model","operation":"correctness-partial-audit","semantic_template":"qf-ext19-correctness-partial-audit/{\"halt\":[5],\"init\":[0],\"n\":6,\"post\":[5],\"steps\":[[0,1],[0,3],[1,2],[2,5],[4,5]]}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_model","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"僅為產生端候選及自檢；主端須另驗，不構成人工審定、一般程式證明、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-20261019-r05-algorithm-correctness-0032","batch_id":"batch-20261013-advance-20261019-r05-algorithm-correctness-foundations","language":"zh-Hant","source_mko_ids":["mko-algorithm-correctness"],"title_zh":"算法正確性責任","stem_zh":"完整有限正確性模型。操作=correctness-partial-audit；資料={\"n\":6,\"init\":[0],\"halt\":[5],\"steps\":[[0,1],[1,2],[2,5],[3,4],[4,5]],\"post\":[]}。請依 [reachable_halts,post,bad_halts,partial_correct,vacuous] 欄序回答。","answer":{"kind":"expression","value":"([5], [], [5], 否, 否)","explanation_zh":"第二批擴展核對=([5], [], [5], 否, 否)；依完整明示資料重算；有限／合成資料核對不是一般形式證明；部分正確性與終止性分離；一條成功路徑不證總正確。"},"difficulty":{"band":"undergraduate_core","level":1,"skills":["算法正確性責任"]},"variant":{"family_id":"qf-ext19-correctness-partial-audit","seed":202610195032,"parameters":{"n":6,"init":[0],"halt":[5],"steps":[[0,1],[1,2],[2,5],[3,4],[4,5]],"post":[],"domain":"Fin_correctness_model","operation":"correctness-partial-audit","semantic_template":"qf-ext19-correctness-partial-audit/{\"halt\":[5],\"init\":[0],\"n\":6,\"post\":[],\"steps\":[[0,1],[1,2],[2,5],[3,4],[4,5]]}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_model","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"僅為產生端候選及自檢；主端須另驗，不構成人工審定、一般程式證明、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-20261019-r05-algorithm-correctness-0033","batch_id":"batch-20261013-advance-20261019-r05-algorithm-correctness-foundations","language":"zh-Hant","source_mko_ids":["mko-algorithm-correctness"],"title_zh":"算法正確性責任","stem_zh":"完整有限正確性模型。操作=correctness-partial-audit；資料={\"n\":6,\"init\":[0],\"halt\":[5],\"steps\":[[0,1],[1,2],[2,5],[0,3],[3,4],[4,5]],\"post\":[5]}。請依 [reachable_halts,post,bad_halts,partial_correct,vacuous] 欄序回答。","answer":{"kind":"expression","value":"([5], [5], [], 是, 否)","explanation_zh":"第二批擴展核對=([5], [5], [], 是, 否)；依完整明示資料重算；有限／合成資料核對不是一般形式證明；部分正確性與終止性分離；一條成功路徑不證總正確。"},"difficulty":{"band":"undergraduate_core","level":1,"skills":["算法正確性責任"]},"variant":{"family_id":"qf-ext19-correctness-partial-audit","seed":202610195033,"parameters":{"n":6,"init":[0],"halt":[5],"steps":[[0,1],[1,2],[2,5],[0,3],[3,4],[4,5]],"post":[5],"domain":"Fin_correctness_model","operation":"correctness-partial-audit","semantic_template":"qf-ext19-correctness-partial-audit/{\"halt\":[5],\"init\":[0],\"n\":6,\"post\":[5],\"steps\":[[0,1],[0,3],[1,2],[2,5],[3,4],[4,5]]}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_model","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"僅為產生端候選及自檢；主端須另驗，不構成人工審定、一般程式證明、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-20261019-r05-algorithm-correctness-0034","batch_id":"batch-20261013-advance-20261019-r05-algorithm-correctness-foundations","language":"zh-Hant","source_mko_ids":["mko-algorithm-correctness"],"title_zh":"算法正確性責任","stem_zh":"完整有限正確性模型。操作=correctness-partial-audit；資料={\"n\":6,\"init\":[0],\"halt\":[5],\"steps\":[[0,1],[1,2],[2,5],[2,1]],\"post\":[]}。請依 [reachable_halts,post,bad_halts,partial_correct,vacuous] 欄序回答。","answer":{"kind":"expression","value":"([5], [], [5], 否, 否)","explanation_zh":"第二批擴展核對=([5], [], [5], 否, 否)；依完整明示資料重算；有限／合成資料核對不是一般形式證明；部分正確性與終止性分離；一條成功路徑不證總正確。"},"difficulty":{"band":"undergraduate_core","level":2,"skills":["算法正確性責任"]},"variant":{"family_id":"qf-ext19-correctness-partial-audit","seed":202610195034,"parameters":{"n":6,"init":[0],"halt":[5],"steps":[[0,1],[1,2],[2,5],[2,1]],"post":[],"domain":"Fin_correctness_model","operation":"correctness-partial-audit","semantic_template":"qf-ext19-correctness-partial-audit/{\"halt\":[5],\"init\":[0],\"n\":6,\"post\":[],\"steps\":[[0,1],[1,2],[2,1],[2,5]]}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_model","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"僅為產生端候選及自檢；主端須另驗，不構成人工審定、一般程式證明、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-20261019-r05-algorithm-correctness-0035","batch_id":"batch-20261013-advance-20261019-r05-algorithm-correctness-foundations","language":"zh-Hant","source_mko_ids":["mko-algorithm-correctness"],"title_zh":"算法正確性責任","stem_zh":"完整有限正確性模型。操作=correctness-partial-audit；資料={\"n\":6,\"init\":[0],\"halt\":[5],\"steps\":[[0,1],[1,2],[2,5],[0,3],[2,1]],\"post\":[5]}。請依 [reachable_halts,post,bad_halts,partial_correct,vacuous] 欄序回答。","answer":{"kind":"expression","value":"([5], [5], [], 是, 否)","explanation_zh":"第二批擴展核對=([5], [5], [], 是, 否)；依完整明示資料重算；有限／合成資料核對不是一般形式證明；部分正確性與終止性分離；一條成功路徑不證總正確。"},"difficulty":{"band":"undergraduate_core","level":2,"skills":["算法正確性責任"]},"variant":{"family_id":"qf-ext19-correctness-partial-audit","seed":202610195035,"parameters":{"n":6,"init":[0],"halt":[5],"steps":[[0,1],[1,2],[2,5],[0,3],[2,1]],"post":[5],"domain":"Fin_correctness_model","operation":"correctness-partial-audit","semantic_template":"qf-ext19-correctness-partial-audit/{\"halt\":[5],\"init\":[0],\"n\":6,\"post\":[5],\"steps\":[[0,1],[0,3],[1,2],[2,1],[2,5]]}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_model","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"僅為產生端候選及自檢；主端須另驗，不構成人工審定、一般程式證明、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-20261019-r05-algorithm-correctness-0036","batch_id":"batch-20261013-advance-20261019-r05-algorithm-correctness-foundations","language":"zh-Hant","source_mko_ids":["mko-algorithm-correctness"],"title_zh":"算法正確性責任","stem_zh":"完整有限正確性模型。操作=correctness-partial-audit；資料={\"n\":6,\"init\":[0],\"halt\":[5],\"steps\":[[0,1],[1,2],[2,5],[3,4],[2,1]],\"post\":[]}。請依 [reachable_halts,post,bad_halts,partial_correct,vacuous] 欄序回答。","answer":{"kind":"expression","value":"([5], [], [5], 否, 否)","explanation_zh":"第二批擴展核對=([5], [], [5], 否, 否)；依完整明示資料重算；有限／合成資料核對不是一般形式證明；部分正確性與終止性分離；一條成功路徑不證總正確。"},"difficulty":{"band":"undergraduate_core","level":2,"skills":["算法正確性責任"]},"variant":{"family_id":"qf-ext19-correctness-partial-audit","seed":202610195036,"parameters":{"n":6,"init":[0],"halt":[5],"steps":[[0,1],[1,2],[2,5],[3,4],[2,1]],"post":[],"domain":"Fin_correctness_model","operation":"correctness-partial-audit","semantic_template":"qf-ext19-correctness-partial-audit/{\"halt\":[5],\"init\":[0],\"n\":6,\"post\":[],\"steps\":[[0,1],[1,2],[2,1],[2,5],[3,4]]}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_model","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"僅為產生端候選及自檢；主端須另驗，不構成人工審定、一般程式證明、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-20261019-r05-algorithm-correctness-0037","batch_id":"batch-20261013-advance-20261019-r05-algorithm-correctness-foundations","language":"zh-Hant","source_mko_ids":["mko-algorithm-correctness"],"title_zh":"算法正確性責任","stem_zh":"完整有限正確性模型。操作=correctness-partial-audit；資料={\"n\":6,\"init\":[0],\"halt\":[5],\"steps\":[[0,1],[1,2],[2,5],[0,3],[3,4],[2,1]],\"post\":[5]}。請依 [reachable_halts,post,bad_halts,partial_correct,vacuous] 欄序回答。","answer":{"kind":"expression","value":"([5], [5], [], 是, 否)","explanation_zh":"第二批擴展核對=([5], [5], [], 是, 否)；依完整明示資料重算；有限／合成資料核對不是一般形式證明；部分正確性與終止性分離；一條成功路徑不證總正確。"},"difficulty":{"band":"undergraduate_core","level":2,"skills":["算法正確性責任"]},"variant":{"family_id":"qf-ext19-correctness-partial-audit","seed":202610195037,"parameters":{"n":6,"init":[0],"halt":[5],"steps":[[0,1],[1,2],[2,5],[0,3],[3,4],[2,1]],"post":[5],"domain":"Fin_correctness_model","operation":"correctness-partial-audit","semantic_template":"qf-ext19-correctness-partial-audit/{\"halt\":[5],\"init\":[0],\"n\":6,\"post\":[5],\"steps\":[[0,1],[0,3],[1,2],[2,1],[2,5],[3,4]]}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_model","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"僅為產生端候選及自檢；主端須另驗，不構成人工審定、一般程式證明、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-20261019-r05-algorithm-correctness-0038","batch_id":"batch-20261013-advance-20261019-r05-algorithm-correctness-foundations","language":"zh-Hant","source_mko_ids":["mko-algorithm-correctness"],"title_zh":"算法正確性責任","stem_zh":"完整有限正確性模型。操作=correctness-partial-audit；資料={\"n\":6,\"init\":[0],\"halt\":[5],\"steps\":[[0,1],[1,2],[2,5],[4,5],[2,1]],\"post\":[]}。請依 [reachable_halts,post,bad_halts,partial_correct,vacuous] 欄序回答。","answer":{"kind":"expression","value":"([5], [], [5], 否, 否)","explanation_zh":"第二批擴展核對=([5], [], [5], 否, 否)；依完整明示資料重算；有限／合成資料核對不是一般形式證明；部分正確性與終止性分離；一條成功路徑不證總正確。"},"difficulty":{"band":"undergraduate_core","level":2,"skills":["算法正確性責任"]},"variant":{"family_id":"qf-ext19-correctness-partial-audit","seed":202610195038,"parameters":{"n":6,"init":[0],"halt":[5],"steps":[[0,1],[1,2],[2,5],[4,5],[2,1]],"post":[],"domain":"Fin_correctness_model","operation":"correctness-partial-audit","semantic_template":"qf-ext19-correctness-partial-audit/{\"halt\":[5],\"init\":[0],\"n\":6,\"post\":[],\"steps\":[[0,1],[1,2],[2,1],[2,5],[4,5]]}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_model","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"僅為產生端候選及自檢；主端須另驗，不構成人工審定、一般程式證明、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-20261019-r05-algorithm-correctness-0039","batch_id":"batch-20261013-advance-20261019-r05-algorithm-correctness-foundations","language":"zh-Hant","source_mko_ids":["mko-algorithm-correctness"],"title_zh":"算法正確性責任","stem_zh":"完整有限正確性模型。操作=correctness-partial-audit；資料={\"n\":6,\"init\":[0],\"halt\":[5],\"steps\":[[0,1],[1,2],[2,5],[0,3],[4,5],[2,1]],\"post\":[5]}。請依 [reachable_halts,post,bad_halts,partial_correct,vacuous] 欄序回答。","answer":{"kind":"expression","value":"([5], [5], [], 是, 否)","explanation_zh":"第二批擴展核對=([5], [5], [], 是, 否)；依完整明示資料重算；有限／合成資料核對不是一般形式證明；部分正確性與終止性分離；一條成功路徑不證總正確。"},"difficulty":{"band":"undergraduate_core","level":2,"skills":["算法正確性責任"]},"variant":{"family_id":"qf-ext19-correctness-partial-audit","seed":202610195039,"parameters":{"n":6,"init":[0],"halt":[5],"steps":[[0,1],[1,2],[2,5],[0,3],[4,5],[2,1]],"post":[5],"domain":"Fin_correctness_model","operation":"correctness-partial-audit","semantic_template":"qf-ext19-correctness-partial-audit/{\"halt\":[5],\"init\":[0],\"n\":6,\"post\":[5],\"steps\":[[0,1],[0,3],[1,2],[2,1],[2,5],[4,5]]}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_model","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"僅為產生端候選及自檢；主端須另驗，不構成人工審定、一般程式證明、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-20261019-r05-algorithm-correctness-0040","batch_id":"batch-20261013-advance-20261019-r05-algorithm-correctness-foundations","language":"zh-Hant","source_mko_ids":["mko-algorithm-correctness"],"title_zh":"算法正確性責任","stem_zh":"完整有限正確性模型。操作=correctness-partial-audit；資料={\"n\":6,\"init\":[0],\"halt\":[5],\"steps\":[[0,1],[1,2],[2,5],[3,4],[4,5],[2,1]],\"post\":[]}。請依 [reachable_halts,post,bad_halts,partial_correct,vacuous] 欄序回答。","answer":{"kind":"expression","value":"([5], [], [5], 否, 否)","explanation_zh":"第二批擴展核對=([5], [], [5], 否, 否)；依完整明示資料重算；有限／合成資料核對不是一般形式證明；部分正確性與終止性分離；一條成功路徑不證總正確。"},"difficulty":{"band":"undergraduate_core","level":2,"skills":["算法正確性責任"]},"variant":{"family_id":"qf-ext19-correctness-partial-audit","seed":202610195040,"parameters":{"n":6,"init":[0],"halt":[5],"steps":[[0,1],[1,2],[2,5],[3,4],[4,5],[2,1]],"post":[],"domain":"Fin_correctness_model","operation":"correctness-partial-audit","semantic_template":"qf-ext19-correctness-partial-audit/{\"halt\":[5],\"init\":[0],\"n\":6,\"post\":[],\"steps\":[[0,1],[1,2],[2,1],[2,5],[3,4],[4,5]]}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_model","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"僅為產生端候選及自檢；主端須另驗，不構成人工審定、一般程式證明、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-20261019-r05-algorithm-correctness-0041","batch_id":"batch-20261013-advance-20261019-r05-algorithm-correctness-foundations","language":"zh-Hant","source_mko_ids":["mko-algorithm-correctness"],"title_zh":"算法正確性責任","stem_zh":"完整有限正確性模型。操作=correctness-partial-audit；資料={\"n\":6,\"init\":[0],\"halt\":[5],\"steps\":[[0,1],[1,2],[2,5],[0,3],[3,4],[4,5],[2,1]],\"post\":[5]}。請依 [reachable_halts,post,bad_halts,partial_correct,vacuous] 欄序回答。","answer":{"kind":"expression","value":"([5], [5], [], 是, 否)","explanation_zh":"第二批擴展核對=([5], [5], [], 是, 否)；依完整明示資料重算；有限／合成資料核對不是一般形式證明；部分正確性與終止性分離；一條成功路徑不證總正確。"},"difficulty":{"band":"undergraduate_core","level":2,"skills":["算法正確性責任"]},"variant":{"family_id":"qf-ext19-correctness-partial-audit","seed":202610195041,"parameters":{"n":6,"init":[0],"halt":[5],"steps":[[0,1],[1,2],[2,5],[0,3],[3,4],[4,5],[2,1]],"post":[5],"domain":"Fin_correctness_model","operation":"correctness-partial-audit","semantic_template":"qf-ext19-correctness-partial-audit/{\"halt\":[5],\"init\":[0],\"n\":6,\"post\":[5],\"steps\":[[0,1],[0,3],[1,2],[2,1],[2,5],[3,4],[4,5]]}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_model","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"僅為產生端候選及自檢；主端須另驗，不構成人工審定、一般程式證明、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-20261019-r05-algorithm-correctness-0042","batch_id":"batch-20261013-advance-20261019-r05-algorithm-correctness-foundations","language":"zh-Hant","source_mko_ids":["mko-algorithm-correctness"],"title_zh":"算法正確性責任","stem_zh":"完整有限正確性模型。操作=correctness-partial-audit；資料={\"n\":6,\"init\":[0],\"halt\":[5],\"steps\":[[0,1],[1,2],[2,5],[1,1]],\"post\":[]}。請依 [reachable_halts,post,bad_halts,partial_correct,vacuous] 欄序回答。","answer":{"kind":"expression","value":"([5], [], [5], 否, 否)","explanation_zh":"第二批擴展核對=([5], [], [5], 否, 否)；依完整明示資料重算；有限／合成資料核對不是一般形式證明；部分正確性與終止性分離；一條成功路徑不證總正確。"},"difficulty":{"band":"undergraduate_core","level":2,"skills":["算法正確性責任"]},"variant":{"family_id":"qf-ext19-correctness-partial-audit","seed":202610195042,"parameters":{"n":6,"init":[0],"halt":[5],"steps":[[0,1],[1,2],[2,5],[1,1]],"post":[],"domain":"Fin_correctness_model","operation":"correctness-partial-audit","semantic_template":"qf-ext19-correctness-partial-audit/{\"halt\":[5],\"init\":[0],\"n\":6,\"post\":[],\"steps\":[[0,1],[1,1],[1,2],[2,5]]}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_model","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"僅為產生端候選及自檢；主端須另驗，不構成人工審定、一般程式證明、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-20261019-r05-algorithm-correctness-0043","batch_id":"batch-20261013-advance-20261019-r05-algorithm-correctness-foundations","language":"zh-Hant","source_mko_ids":["mko-algorithm-correctness"],"title_zh":"算法正確性責任","stem_zh":"完整有限正確性模型。操作=correctness-partial-audit；資料={\"n\":6,\"init\":[0],\"halt\":[5],\"steps\":[[0,1],[1,2],[2,5],[0,3],[1,1]],\"post\":[5]}。請依 [reachable_halts,post,bad_halts,partial_correct,vacuous] 欄序回答。","answer":{"kind":"expression","value":"([5], [5], [], 是, 否)","explanation_zh":"第二批擴展核對=([5], [5], [], 是, 否)；依完整明示資料重算；有限／合成資料核對不是一般形式證明；部分正確性與終止性分離；一條成功路徑不證總正確。"},"difficulty":{"band":"undergraduate_core","level":3,"skills":["算法正確性責任"]},"variant":{"family_id":"qf-ext19-correctness-partial-audit","seed":202610195043,"parameters":{"n":6,"init":[0],"halt":[5],"steps":[[0,1],[1,2],[2,5],[0,3],[1,1]],"post":[5],"domain":"Fin_correctness_model","operation":"correctness-partial-audit","semantic_template":"qf-ext19-correctness-partial-audit/{\"halt\":[5],\"init\":[0],\"n\":6,\"post\":[5],\"steps\":[[0,1],[0,3],[1,1],[1,2],[2,5]]}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_model","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"僅為產生端候選及自檢；主端須另驗，不構成人工審定、一般程式證明、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-20261019-r05-algorithm-correctness-0044","batch_id":"batch-20261013-advance-20261019-r05-algorithm-correctness-foundations","language":"zh-Hant","source_mko_ids":["mko-algorithm-correctness"],"title_zh":"算法正確性責任","stem_zh":"完整有限正確性模型。操作=correctness-partial-audit；資料={\"n\":6,\"init\":[0],\"halt\":[5],\"steps\":[[0,1],[1,2],[2,5],[3,4],[1,1]],\"post\":[]}。請依 [reachable_halts,post,bad_halts,partial_correct,vacuous] 欄序回答。","answer":{"kind":"expression","value":"([5], [], [5], 否, 否)","explanation_zh":"第二批擴展核對=([5], [], [5], 否, 否)；依完整明示資料重算；有限／合成資料核對不是一般形式證明；部分正確性與終止性分離；一條成功路徑不證總正確。"},"difficulty":{"band":"undergraduate_core","level":3,"skills":["算法正確性責任"]},"variant":{"family_id":"qf-ext19-correctness-partial-audit","seed":202610195044,"parameters":{"n":6,"init":[0],"halt":[5],"steps":[[0,1],[1,2],[2,5],[3,4],[1,1]],"post":[],"domain":"Fin_correctness_model","operation":"correctness-partial-audit","semantic_template":"qf-ext19-correctness-partial-audit/{\"halt\":[5],\"init\":[0],\"n\":6,\"post\":[],\"steps\":[[0,1],[1,1],[1,2],[2,5],[3,4]]}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_model","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"僅為產生端候選及自檢；主端須另驗，不構成人工審定、一般程式證明、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-20261019-r05-algorithm-correctness-0045","batch_id":"batch-20261013-advance-20261019-r05-algorithm-correctness-foundations","language":"zh-Hant","source_mko_ids":["mko-algorithm-correctness"],"title_zh":"算法正確性責任","stem_zh":"完整有限正確性模型。操作=correctness-partial-audit；資料={\"n\":6,\"init\":[0],\"halt\":[5],\"steps\":[[0,1],[1,2],[2,5],[0,3],[3,4],[1,1]],\"post\":[5]}。請依 [reachable_halts,post,bad_halts,partial_correct,vacuous] 欄序回答。","answer":{"kind":"expression","value":"([5], [5], [], 是, 否)","explanation_zh":"第二批擴展核對=([5], [5], [], 是, 否)；依完整明示資料重算；有限／合成資料核對不是一般形式證明；部分正確性與終止性分離；一條成功路徑不證總正確。"},"difficulty":{"band":"undergraduate_core","level":3,"skills":["算法正確性責任"]},"variant":{"family_id":"qf-ext19-correctness-partial-audit","seed":202610195045,"parameters":{"n":6,"init":[0],"halt":[5],"steps":[[0,1],[1,2],[2,5],[0,3],[3,4],[1,1]],"post":[5],"domain":"Fin_correctness_model","operation":"correctness-partial-audit","semantic_template":"qf-ext19-correctness-partial-audit/{\"halt\":[5],\"init\":[0],\"n\":6,\"post\":[5],\"steps\":[[0,1],[0,3],[1,1],[1,2],[2,5],[3,4]]}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_model","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"僅為產生端候選及自檢；主端須另驗，不構成人工審定、一般程式證明、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-20261019-r05-algorithm-correctness-0046","batch_id":"batch-20261013-advance-20261019-r05-algorithm-correctness-foundations","language":"zh-Hant","source_mko_ids":["mko-algorithm-correctness"],"title_zh":"算法正確性責任","stem_zh":"完整有限正確性模型。操作=correctness-partial-audit；資料={\"n\":6,\"init\":[0],\"halt\":[5],\"steps\":[[0,1],[1,2],[2,5],[4,5],[1,1]],\"post\":[]}。請依 [reachable_halts,post,bad_halts,partial_correct,vacuous] 欄序回答。","answer":{"kind":"expression","value":"([5], [], [5], 否, 否)","explanation_zh":"第二批擴展核對=([5], [], [5], 否, 否)；依完整明示資料重算；有限／合成資料核對不是一般形式證明；部分正確性與終止性分離；一條成功路徑不證總正確。"},"difficulty":{"band":"undergraduate_core","level":3,"skills":["算法正確性責任"]},"variant":{"family_id":"qf-ext19-correctness-partial-audit","seed":202610195046,"parameters":{"n":6,"init":[0],"halt":[5],"steps":[[0,1],[1,2],[2,5],[4,5],[1,1]],"post":[],"domain":"Fin_correctness_model","operation":"correctness-partial-audit","semantic_template":"qf-ext19-correctness-partial-audit/{\"halt\":[5],\"init\":[0],\"n\":6,\"post\":[],\"steps\":[[0,1],[1,1],[1,2],[2,5],[4,5]]}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_model","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"僅為產生端候選及自檢；主端須另驗，不構成人工審定、一般程式證明、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-20261019-r05-algorithm-correctness-0047","batch_id":"batch-20261013-advance-20261019-r05-algorithm-correctness-foundations","language":"zh-Hant","source_mko_ids":["mko-algorithm-correctness"],"title_zh":"算法正確性責任","stem_zh":"完整有限正確性模型。操作=correctness-partial-audit；資料={\"n\":6,\"init\":[0],\"halt\":[5],\"steps\":[[0,1],[1,2],[2,5],[0,3],[4,5],[1,1]],\"post\":[5]}。請依 [reachable_halts,post,bad_halts,partial_correct,vacuous] 欄序回答。","answer":{"kind":"expression","value":"([5], [5], [], 是, 否)","explanation_zh":"第二批擴展核對=([5], [5], [], 是, 否)；依完整明示資料重算；有限／合成資料核對不是一般形式證明；部分正確性與終止性分離；一條成功路徑不證總正確。"},"difficulty":{"band":"undergraduate_core","level":3,"skills":["算法正確性責任"]},"variant":{"family_id":"qf-ext19-correctness-partial-audit","seed":202610195047,"parameters":{"n":6,"init":[0],"halt":[5],"steps":[[0,1],[1,2],[2,5],[0,3],[4,5],[1,1]],"post":[5],"domain":"Fin_correctness_model","operation":"correctness-partial-audit","semantic_template":"qf-ext19-correctness-partial-audit/{\"halt\":[5],\"init\":[0],\"n\":6,\"post\":[5],\"steps\":[[0,1],[0,3],[1,1],[1,2],[2,5],[4,5]]}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_model","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"僅為產生端候選及自檢；主端須另驗，不構成人工審定、一般程式證明、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-20261019-r05-algorithm-correctness-0048","batch_id":"batch-20261013-advance-20261019-r05-algorithm-correctness-foundations","language":"zh-Hant","source_mko_ids":["mko-algorithm-correctness"],"title_zh":"算法正確性責任","stem_zh":"完整有限正確性模型。操作=correctness-partial-audit；資料={\"n\":6,\"init\":[0],\"halt\":[5],\"steps\":[[0,1],[1,2],[2,5],[3,4],[4,5],[1,1]],\"post\":[]}。請依 [reachable_halts,post,bad_halts,partial_correct,vacuous] 欄序回答。","answer":{"kind":"expression","value":"([5], [], [5], 否, 否)","explanation_zh":"第二批擴展核對=([5], [], [5], 否, 否)；依完整明示資料重算；有限／合成資料核對不是一般形式證明；部分正確性與終止性分離；一條成功路徑不證總正確。"},"difficulty":{"band":"undergraduate_core","level":3,"skills":["算法正確性責任"]},"variant":{"family_id":"qf-ext19-correctness-partial-audit","seed":202610195048,"parameters":{"n":6,"init":[0],"halt":[5],"steps":[[0,1],[1,2],[2,5],[3,4],[4,5],[1,1]],"post":[],"domain":"Fin_correctness_model","operation":"correctness-partial-audit","semantic_template":"qf-ext19-correctness-partial-audit/{\"halt\":[5],\"init\":[0],\"n\":6,\"post\":[],\"steps\":[[0,1],[1,1],[1,2],[2,5],[3,4],[4,5]]}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_model","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"僅為產生端候選及自檢；主端須另驗，不構成人工審定、一般程式證明、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-20261019-r05-algorithm-correctness-0049","batch_id":"batch-20261013-advance-20261019-r05-algorithm-correctness-foundations","language":"zh-Hant","source_mko_ids":["mko-algorithm-correctness"],"title_zh":"算法正確性責任","stem_zh":"完整有限正確性模型。操作=correctness-partial-audit；資料={\"n\":6,\"init\":[0],\"halt\":[5],\"steps\":[[0,1],[1,2],[2,5],[0,3],[3,4],[4,5],[1,1]],\"post\":[5]}。請依 [reachable_halts,post,bad_halts,partial_correct,vacuous] 欄序回答。","answer":{"kind":"expression","value":"([5], [5], [], 是, 否)","explanation_zh":"第二批擴展核對=([5], [5], [], 是, 否)；依完整明示資料重算；有限／合成資料核對不是一般形式證明；部分正確性與終止性分離；一條成功路徑不證總正確。"},"difficulty":{"band":"undergraduate_core","level":3,"skills":["算法正確性責任"]},"variant":{"family_id":"qf-ext19-correctness-partial-audit","seed":202610195049,"parameters":{"n":6,"init":[0],"halt":[5],"steps":[[0,1],[1,2],[2,5],[0,3],[3,4],[4,5],[1,1]],"post":[5],"domain":"Fin_correctness_model","operation":"correctness-partial-audit","semantic_template":"qf-ext19-correctness-partial-audit/{\"halt\":[5],\"init\":[0],\"n\":6,\"post\":[5],\"steps\":[[0,1],[0,3],[1,1],[1,2],[2,5],[3,4],[4,5]]}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_model","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"僅為產生端候選及自檢；主端須另驗，不構成人工審定、一般程式證明、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-20261019-r05-algorithm-correctness-0050","batch_id":"batch-20261013-advance-20261019-r05-algorithm-correctness-foundations","language":"zh-Hant","source_mko_ids":["mko-algorithm-correctness"],"title_zh":"算法正確性責任","stem_zh":"完整有限正確性模型。操作=correctness-partial-audit；資料={\"n\":6,\"init\":[0],\"halt\":[5],\"steps\":[[0,1],[1,2],[2,5],[2,1],[1,1]],\"post\":[]}。請依 [reachable_halts,post,bad_halts,partial_correct,vacuous] 欄序回答。","answer":{"kind":"expression","value":"([5], [], [5], 否, 否)","explanation_zh":"第二批擴展核對=([5], [], [5], 否, 否)；依完整明示資料重算；有限／合成資料核對不是一般形式證明；部分正確性與終止性分離；一條成功路徑不證總正確。"},"difficulty":{"band":"undergraduate_core","level":3,"skills":["算法正確性責任"]},"variant":{"family_id":"qf-ext19-correctness-partial-audit","seed":202610195050,"parameters":{"n":6,"init":[0],"halt":[5],"steps":[[0,1],[1,2],[2,5],[2,1],[1,1]],"post":[],"domain":"Fin_correctness_model","operation":"correctness-partial-audit","semantic_template":"qf-ext19-correctness-partial-audit/{\"halt\":[5],\"init\":[0],\"n\":6,\"post\":[],\"steps\":[[0,1],[1,1],[1,2],[2,1],[2,5]]}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_model","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"僅為產生端候選及自檢；主端須另驗，不構成人工審定、一般程式證明、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-20261019-r05-algorithm-correctness-0051","batch_id":"batch-20261013-advance-20261019-r05-algorithm-correctness-foundations","language":"zh-Hant","source_mko_ids":["mko-algorithm-correctness"],"title_zh":"算法正確性責任","stem_zh":"完整有限正確性模型。操作=correctness-ranking-audit；資料={\"n\":6,\"init\":[0],\"halt\":[5],\"steps\":[[0,1],[1,2],[2,5]],\"rank\":[6,5,4,3,2,0]}。請依 [rank,bad_decrease_edges,ranking_valid,stuck,ranking_plus_no_stuck,actual_termination] 欄序回答。","answer":{"kind":"expression","value":"([6, 5, 4, 3, 2, 0], [], 是, [], 是, 是)","explanation_zh":"第二批擴展核對=([6, 5, 4, 3, 2, 0], [], 是, [], 是, 是)；依完整明示資料重算；有限／合成資料核對不是一般形式證明；部分正確性與終止性分離；一條成功路徑不證總正確。"},"difficulty":{"band":"undergraduate_core","level":1,"skills":["算法正確性責任"]},"variant":{"family_id":"qf-ext19-correctness-ranking-audit","seed":202610195051,"parameters":{"n":6,"init":[0],"halt":[5],"steps":[[0,1],[1,2],[2,5]],"rank":[6,5,4,3,2,0],"domain":"Fin_correctness_model","operation":"correctness-ranking-audit","semantic_template":"qf-ext19-correctness-ranking-audit/{\"halt\":[5],\"init\":[0],\"n\":6,\"rank\":[6,5,4,3,2,0],\"steps\":[[0,1],[1,2],[2,5]]}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_model","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"僅為產生端候選及自檢；主端須另驗，不構成人工審定、一般程式證明、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"}}
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{"schema_version":"ocme-question-v0.1","id":"q-20261013-advance-20261019-r05-algorithm-correctness-0053","batch_id":"batch-20261013-advance-20261019-r05-algorithm-correctness-foundations","language":"zh-Hant","source_mko_ids":["mko-algorithm-correctness"],"title_zh":"算法正確性責任","stem_zh":"完整有限正確性模型。操作=correctness-ranking-audit；資料={\"n\":6,\"init\":[0],\"halt\":[5],\"steps\":[[0,1],[1,2],[2,5],[3,4]],\"rank\":[8,5,4,3,2,0]}。請依 [rank,bad_decrease_edges,ranking_valid,stuck,ranking_plus_no_stuck,actual_termination] 欄序回答。","answer":{"kind":"expression","value":"([8, 5, 4, 3, 2, 0], [], 是, [], 是, 是)","explanation_zh":"第二批擴展核對=([8, 5, 4, 3, 2, 0], [], 是, [], 是, 是)；依完整明示資料重算；有限／合成資料核對不是一般形式證明；部分正確性與終止性分離；一條成功路徑不證總正確。"},"difficulty":{"band":"undergraduate_core","level":1,"skills":["算法正確性責任"]},"variant":{"family_id":"qf-ext19-correctness-ranking-audit","seed":202610195053,"parameters":{"n":6,"init":[0],"halt":[5],"steps":[[0,1],[1,2],[2,5],[3,4]],"rank":[8,5,4,3,2,0],"domain":"Fin_correctness_model","operation":"correctness-ranking-audit","semantic_template":"qf-ext19-correctness-ranking-audit/{\"halt\":[5],\"init\":[0],\"n\":6,\"rank\":[8,5,4,3,2,0],\"steps\":[[0,1],[1,2],[2,5],[3,4]]}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_model","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"僅為產生端候選及自檢；主端須另驗，不構成人工審定、一般程式證明、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"}}
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{"schema_version":"ocme-question-v0.1","id":"q-20261013-advance-20261019-r05-algorithm-correctness-0062","batch_id":"batch-20261013-advance-20261019-r05-algorithm-correctness-foundations","language":"zh-Hant","source_mko_ids":["mko-algorithm-correctness"],"title_zh":"算法正確性責任","stem_zh":"完整有限正確性模型。操作=correctness-ranking-audit；資料={\"n\":6,\"init\":[0],\"halt\":[5],\"steps\":[[0,1],[1,2],[2,5],[0,3],[3,4],[2,1]],\"rank\":[17,5,4,3,2,0]}。請依 [rank,bad_decrease_edges,ranking_valid,stuck,ranking_plus_no_stuck,actual_termination] 欄序回答。","answer":{"kind":"expression","value":"([17, 5, 4, 3, 2, 0], [[2, 1]], 否, [4], 否, 否)","explanation_zh":"第二批擴展核對=([17, 5, 4, 3, 2, 0], [[2, 1]], 否, [4], 否, 否)；依完整明示資料重算；有限／合成資料核對不是一般形式證明；部分正確性與終止性分離；一條成功路徑不證總正確。"},"difficulty":{"band":"undergraduate_core","level":2,"skills":["算法正確性責任"]},"variant":{"family_id":"qf-ext19-correctness-ranking-audit","seed":202610195062,"parameters":{"n":6,"init":[0],"halt":[5],"steps":[[0,1],[1,2],[2,5],[0,3],[3,4],[2,1]],"rank":[17,5,4,3,2,0],"domain":"Fin_correctness_model","operation":"correctness-ranking-audit","semantic_template":"qf-ext19-correctness-ranking-audit/{\"halt\":[5],\"init\":[0],\"n\":6,\"rank\":[17,5,4,3,2,0],\"steps\":[[0,1],[0,3],[1,2],[2,1],[2,5],[3,4]]}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_model","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"僅為產生端候選及自檢；主端須另驗，不構成人工審定、一般程式證明、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-20261019-r05-algorithm-correctness-0063","batch_id":"batch-20261013-advance-20261019-r05-algorithm-correctness-foundations","language":"zh-Hant","source_mko_ids":["mko-algorithm-correctness"],"title_zh":"算法正確性責任","stem_zh":"完整有限正確性模型。操作=correctness-ranking-audit；資料={\"n\":6,\"init\":[0],\"halt\":[5],\"steps\":[[0,1],[1,2],[2,5],[4,5],[2,1]],\"rank\":[18,5,4,3,2,0]}。請依 [rank,bad_decrease_edges,ranking_valid,stuck,ranking_plus_no_stuck,actual_termination] 欄序回答。","answer":{"kind":"expression","value":"([18, 5, 4, 3, 2, 0], [[2, 1]], 否, [], 否, 否)","explanation_zh":"第二批擴展核對=([18, 5, 4, 3, 2, 0], [[2, 1]], 否, [], 否, 否)；依完整明示資料重算；有限／合成資料核對不是一般形式證明；部分正確性與終止性分離；一條成功路徑不證總正確。"},"difficulty":{"band":"undergraduate_core","level":2,"skills":["算法正確性責任"]},"variant":{"family_id":"qf-ext19-correctness-ranking-audit","seed":202610195063,"parameters":{"n":6,"init":[0],"halt":[5],"steps":[[0,1],[1,2],[2,5],[4,5],[2,1]],"rank":[18,5,4,3,2,0],"domain":"Fin_correctness_model","operation":"correctness-ranking-audit","semantic_template":"qf-ext19-correctness-ranking-audit/{\"halt\":[5],\"init\":[0],\"n\":6,\"rank\":[18,5,4,3,2,0],\"steps\":[[0,1],[1,2],[2,1],[2,5],[4,5]]}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_model","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"僅為產生端候選及自檢；主端須另驗，不構成人工審定、一般程式證明、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-20261019-r05-algorithm-correctness-0064","batch_id":"batch-20261013-advance-20261019-r05-algorithm-correctness-foundations","language":"zh-Hant","source_mko_ids":["mko-algorithm-correctness"],"title_zh":"算法正確性責任","stem_zh":"完整有限正確性模型。操作=correctness-ranking-audit；資料={\"n\":6,\"init\":[0],\"halt\":[5],\"steps\":[[0,1],[1,2],[2,5],[0,3],[4,5],[2,1]],\"rank\":[19,5,4,3,2,0]}。請依 [rank,bad_decrease_edges,ranking_valid,stuck,ranking_plus_no_stuck,actual_termination] 欄序回答。","answer":{"kind":"expression","value":"([19, 5, 4, 3, 2, 0], [[2, 1]], 否, [3], 否, 否)","explanation_zh":"第二批擴展核對=([19, 5, 4, 3, 2, 0], [[2, 1]], 否, [3], 否, 否)；依完整明示資料重算；有限／合成資料核對不是一般形式證明；部分正確性與終止性分離；一條成功路徑不證總正確。"},"difficulty":{"band":"undergraduate_core","level":2,"skills":["算法正確性責任"]},"variant":{"family_id":"qf-ext19-correctness-ranking-audit","seed":202610195064,"parameters":{"n":6,"init":[0],"halt":[5],"steps":[[0,1],[1,2],[2,5],[0,3],[4,5],[2,1]],"rank":[19,5,4,3,2,0],"domain":"Fin_correctness_model","operation":"correctness-ranking-audit","semantic_template":"qf-ext19-correctness-ranking-audit/{\"halt\":[5],\"init\":[0],\"n\":6,\"rank\":[19,5,4,3,2,0],\"steps\":[[0,1],[0,3],[1,2],[2,1],[2,5],[4,5]]}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_model","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"僅為產生端候選及自檢；主端須另驗，不構成人工審定、一般程式證明、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-20261019-r05-algorithm-correctness-0065","batch_id":"batch-20261013-advance-20261019-r05-algorithm-correctness-foundations","language":"zh-Hant","source_mko_ids":["mko-algorithm-correctness"],"title_zh":"算法正確性責任","stem_zh":"完整有限正確性模型。操作=correctness-ranking-audit；資料={\"n\":6,\"init\":[0],\"halt\":[5],\"steps\":[[0,1],[1,2],[2,5],[3,4],[4,5],[2,1]],\"rank\":[20,5,4,3,2,0]}。請依 [rank,bad_decrease_edges,ranking_valid,stuck,ranking_plus_no_stuck,actual_termination] 欄序回答。","answer":{"kind":"expression","value":"([20, 5, 4, 3, 2, 0], [[2, 1]], 否, [], 否, 否)","explanation_zh":"第二批擴展核對=([20, 5, 4, 3, 2, 0], [[2, 1]], 否, [], 否, 否)；依完整明示資料重算；有限／合成資料核對不是一般形式證明；部分正確性與終止性分離；一條成功路徑不證總正確。"},"difficulty":{"band":"undergraduate_core","level":2,"skills":["算法正確性責任"]},"variant":{"family_id":"qf-ext19-correctness-ranking-audit","seed":202610195065,"parameters":{"n":6,"init":[0],"halt":[5],"steps":[[0,1],[1,2],[2,5],[3,4],[4,5],[2,1]],"rank":[20,5,4,3,2,0],"domain":"Fin_correctness_model","operation":"correctness-ranking-audit","semantic_template":"qf-ext19-correctness-ranking-audit/{\"halt\":[5],\"init\":[0],\"n\":6,\"rank\":[20,5,4,3,2,0],\"steps\":[[0,1],[1,2],[2,1],[2,5],[3,4],[4,5]]}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_model","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"僅為產生端候選及自檢；主端須另驗，不構成人工審定、一般程式證明、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-20261019-r05-algorithm-correctness-0066","batch_id":"batch-20261013-advance-20261019-r05-algorithm-correctness-foundations","language":"zh-Hant","source_mko_ids":["mko-algorithm-correctness"],"title_zh":"算法正確性責任","stem_zh":"完整有限正確性模型。操作=correctness-ranking-audit；資料={\"n\":6,\"init\":[0],\"halt\":[5],\"steps\":[[0,1],[1,2],[2,5],[0,3],[3,4],[4,5],[2,1]],\"rank\":[21,5,4,3,2,0]}。請依 [rank,bad_decrease_edges,ranking_valid,stuck,ranking_plus_no_stuck,actual_termination] 欄序回答。","answer":{"kind":"expression","value":"([21, 5, 4, 3, 2, 0], [[2, 1]], 否, [], 否, 否)","explanation_zh":"第二批擴展核對=([21, 5, 4, 3, 2, 0], [[2, 1]], 否, [], 否, 否)；依完整明示資料重算；有限／合成資料核對不是一般形式證明；部分正確性與終止性分離；一條成功路徑不證總正確。"},"difficulty":{"band":"undergraduate_core","level":2,"skills":["算法正確性責任"]},"variant":{"family_id":"qf-ext19-correctness-ranking-audit","seed":202610195066,"parameters":{"n":6,"init":[0],"halt":[5],"steps":[[0,1],[1,2],[2,5],[0,3],[3,4],[4,5],[2,1]],"rank":[21,5,4,3,2,0],"domain":"Fin_correctness_model","operation":"correctness-ranking-audit","semantic_template":"qf-ext19-correctness-ranking-audit/{\"halt\":[5],\"init\":[0],\"n\":6,\"rank\":[21,5,4,3,2,0],\"steps\":[[0,1],[0,3],[1,2],[2,1],[2,5],[3,4],[4,5]]}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_model","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"僅為產生端候選及自檢；主端須另驗，不構成人工審定、一般程式證明、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-20261019-r05-algorithm-correctness-0067","batch_id":"batch-20261013-advance-20261019-r05-algorithm-correctness-foundations","language":"zh-Hant","source_mko_ids":["mko-algorithm-correctness"],"title_zh":"算法正確性責任","stem_zh":"完整有限正確性模型。操作=correctness-ranking-audit；資料={\"n\":6,\"init\":[0],\"halt\":[5],\"steps\":[[0,1],[1,2],[2,5],[1,1]],\"rank\":[22,5,4,3,2,0]}。請依 [rank,bad_decrease_edges,ranking_valid,stuck,ranking_plus_no_stuck,actual_termination] 欄序回答。","answer":{"kind":"expression","value":"([22, 5, 4, 3, 2, 0], [[1, 1]], 否, [], 否, 否)","explanation_zh":"第二批擴展核對=([22, 5, 4, 3, 2, 0], [[1, 1]], 否, [], 否, 否)；依完整明示資料重算；有限／合成資料核對不是一般形式證明；部分正確性與終止性分離；一條成功路徑不證總正確。"},"difficulty":{"band":"undergraduate_core","level":2,"skills":["算法正確性責任"]},"variant":{"family_id":"qf-ext19-correctness-ranking-audit","seed":202610195067,"parameters":{"n":6,"init":[0],"halt":[5],"steps":[[0,1],[1,2],[2,5],[1,1]],"rank":[22,5,4,3,2,0],"domain":"Fin_correctness_model","operation":"correctness-ranking-audit","semantic_template":"qf-ext19-correctness-ranking-audit/{\"halt\":[5],\"init\":[0],\"n\":6,\"rank\":[22,5,4,3,2,0],\"steps\":[[0,1],[1,1],[1,2],[2,5]]}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_model","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"僅為產生端候選及自檢；主端須另驗，不構成人工審定、一般程式證明、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-20261019-r05-algorithm-correctness-0068","batch_id":"batch-20261013-advance-20261019-r05-algorithm-correctness-foundations","language":"zh-Hant","source_mko_ids":["mko-algorithm-correctness"],"title_zh":"算法正確性責任","stem_zh":"完整有限正確性模型。操作=correctness-ranking-audit；資料={\"n\":6,\"init\":[0],\"halt\":[5],\"steps\":[[0,1],[1,2],[2,5],[0,3],[1,1]],\"rank\":[23,5,4,3,2,0]}。請依 [rank,bad_decrease_edges,ranking_valid,stuck,ranking_plus_no_stuck,actual_termination] 欄序回答。","answer":{"kind":"expression","value":"([23, 5, 4, 3, 2, 0], [[1, 1]], 否, [3], 否, 否)","explanation_zh":"第二批擴展核對=([23, 5, 4, 3, 2, 0], [[1, 1]], 否, [3], 否, 否)；依完整明示資料重算；有限／合成資料核對不是一般形式證明；部分正確性與終止性分離；一條成功路徑不證總正確。"},"difficulty":{"band":"undergraduate_core","level":3,"skills":["算法正確性責任"]},"variant":{"family_id":"qf-ext19-correctness-ranking-audit","seed":202610195068,"parameters":{"n":6,"init":[0],"halt":[5],"steps":[[0,1],[1,2],[2,5],[0,3],[1,1]],"rank":[23,5,4,3,2,0],"domain":"Fin_correctness_model","operation":"correctness-ranking-audit","semantic_template":"qf-ext19-correctness-ranking-audit/{\"halt\":[5],\"init\":[0],\"n\":6,\"rank\":[23,5,4,3,2,0],\"steps\":[[0,1],[0,3],[1,1],[1,2],[2,5]]}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_model","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"僅為產生端候選及自檢；主端須另驗，不構成人工審定、一般程式證明、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-20261019-r05-algorithm-correctness-0069","batch_id":"batch-20261013-advance-20261019-r05-algorithm-correctness-foundations","language":"zh-Hant","source_mko_ids":["mko-algorithm-correctness"],"title_zh":"算法正確性責任","stem_zh":"完整有限正確性模型。操作=correctness-ranking-audit；資料={\"n\":6,\"init\":[0],\"halt\":[5],\"steps\":[[0,1],[1,2],[2,5],[3,4],[1,1]],\"rank\":[24,5,4,3,2,0]}。請依 [rank,bad_decrease_edges,ranking_valid,stuck,ranking_plus_no_stuck,actual_termination] 欄序回答。","answer":{"kind":"expression","value":"([24, 5, 4, 3, 2, 0], [[1, 1]], 否, [], 否, 否)","explanation_zh":"第二批擴展核對=([24, 5, 4, 3, 2, 0], [[1, 1]], 否, [], 否, 否)；依完整明示資料重算；有限／合成資料核對不是一般形式證明；部分正確性與終止性分離；一條成功路徑不證總正確。"},"difficulty":{"band":"undergraduate_core","level":3,"skills":["算法正確性責任"]},"variant":{"family_id":"qf-ext19-correctness-ranking-audit","seed":202610195069,"parameters":{"n":6,"init":[0],"halt":[5],"steps":[[0,1],[1,2],[2,5],[3,4],[1,1]],"rank":[24,5,4,3,2,0],"domain":"Fin_correctness_model","operation":"correctness-ranking-audit","semantic_template":"qf-ext19-correctness-ranking-audit/{\"halt\":[5],\"init\":[0],\"n\":6,\"rank\":[24,5,4,3,2,0],\"steps\":[[0,1],[1,1],[1,2],[2,5],[3,4]]}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_model","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"僅為產生端候選及自檢；主端須另驗，不構成人工審定、一般程式證明、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-20261019-r05-algorithm-correctness-0070","batch_id":"batch-20261013-advance-20261019-r05-algorithm-correctness-foundations","language":"zh-Hant","source_mko_ids":["mko-algorithm-correctness"],"title_zh":"算法正確性責任","stem_zh":"完整有限正確性模型。操作=correctness-ranking-audit；資料={\"n\":6,\"init\":[0],\"halt\":[5],\"steps\":[[0,1],[1,2],[2,5],[0,3],[3,4],[1,1]],\"rank\":[25,5,4,3,2,0]}。請依 [rank,bad_decrease_edges,ranking_valid,stuck,ranking_plus_no_stuck,actual_termination] 欄序回答。","answer":{"kind":"expression","value":"([25, 5, 4, 3, 2, 0], [[1, 1]], 否, [4], 否, 否)","explanation_zh":"第二批擴展核對=([25, 5, 4, 3, 2, 0], [[1, 1]], 否, [4], 否, 否)；依完整明示資料重算；有限／合成資料核對不是一般形式證明；部分正確性與終止性分離；一條成功路徑不證總正確。"},"difficulty":{"band":"undergraduate_core","level":3,"skills":["算法正確性責任"]},"variant":{"family_id":"qf-ext19-correctness-ranking-audit","seed":202610195070,"parameters":{"n":6,"init":[0],"halt":[5],"steps":[[0,1],[1,2],[2,5],[0,3],[3,4],[1,1]],"rank":[25,5,4,3,2,0],"domain":"Fin_correctness_model","operation":"correctness-ranking-audit","semantic_template":"qf-ext19-correctness-ranking-audit/{\"halt\":[5],\"init\":[0],\"n\":6,\"rank\":[25,5,4,3,2,0],\"steps\":[[0,1],[0,3],[1,1],[1,2],[2,5],[3,4]]}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_model","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"僅為產生端候選及自檢；主端須另驗，不構成人工審定、一般程式證明、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-20261019-r05-algorithm-correctness-0071","batch_id":"batch-20261013-advance-20261019-r05-algorithm-correctness-foundations","language":"zh-Hant","source_mko_ids":["mko-algorithm-correctness"],"title_zh":"算法正確性責任","stem_zh":"完整有限正確性模型。操作=correctness-ranking-audit；資料={\"n\":6,\"init\":[0],\"halt\":[5],\"steps\":[[0,1],[1,2],[2,5],[4,5],[1,1]],\"rank\":[26,5,4,3,2,0]}。請依 [rank,bad_decrease_edges,ranking_valid,stuck,ranking_plus_no_stuck,actual_termination] 欄序回答。","answer":{"kind":"expression","value":"([26, 5, 4, 3, 2, 0], [[1, 1]], 否, [], 否, 否)","explanation_zh":"第二批擴展核對=([26, 5, 4, 3, 2, 0], [[1, 1]], 否, [], 否, 否)；依完整明示資料重算；有限／合成資料核對不是一般形式證明；部分正確性與終止性分離；一條成功路徑不證總正確。"},"difficulty":{"band":"undergraduate_core","level":3,"skills":["算法正確性責任"]},"variant":{"family_id":"qf-ext19-correctness-ranking-audit","seed":202610195071,"parameters":{"n":6,"init":[0],"halt":[5],"steps":[[0,1],[1,2],[2,5],[4,5],[1,1]],"rank":[26,5,4,3,2,0],"domain":"Fin_correctness_model","operation":"correctness-ranking-audit","semantic_template":"qf-ext19-correctness-ranking-audit/{\"halt\":[5],\"init\":[0],\"n\":6,\"rank\":[26,5,4,3,2,0],\"steps\":[[0,1],[1,1],[1,2],[2,5],[4,5]]}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_model","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"僅為產生端候選及自檢；主端須另驗，不構成人工審定、一般程式證明、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-20261019-r05-algorithm-correctness-0072","batch_id":"batch-20261013-advance-20261019-r05-algorithm-correctness-foundations","language":"zh-Hant","source_mko_ids":["mko-algorithm-correctness"],"title_zh":"算法正確性責任","stem_zh":"完整有限正確性模型。操作=correctness-ranking-audit；資料={\"n\":6,\"init\":[0],\"halt\":[5],\"steps\":[[0,1],[1,2],[2,5],[0,3],[4,5],[1,1]],\"rank\":[27,5,4,3,2,0]}。請依 [rank,bad_decrease_edges,ranking_valid,stuck,ranking_plus_no_stuck,actual_termination] 欄序回答。","answer":{"kind":"expression","value":"([27, 5, 4, 3, 2, 0], [[1, 1]], 否, [3], 否, 否)","explanation_zh":"第二批擴展核對=([27, 5, 4, 3, 2, 0], [[1, 1]], 否, [3], 否, 否)；依完整明示資料重算；有限／合成資料核對不是一般形式證明；部分正確性與終止性分離；一條成功路徑不證總正確。"},"difficulty":{"band":"undergraduate_core","level":3,"skills":["算法正確性責任"]},"variant":{"family_id":"qf-ext19-correctness-ranking-audit","seed":202610195072,"parameters":{"n":6,"init":[0],"halt":[5],"steps":[[0,1],[1,2],[2,5],[0,3],[4,5],[1,1]],"rank":[27,5,4,3,2,0],"domain":"Fin_correctness_model","operation":"correctness-ranking-audit","semantic_template":"qf-ext19-correctness-ranking-audit/{\"halt\":[5],\"init\":[0],\"n\":6,\"rank\":[27,5,4,3,2,0],\"steps\":[[0,1],[0,3],[1,1],[1,2],[2,5],[4,5]]}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_model","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"僅為產生端候選及自檢；主端須另驗，不構成人工審定、一般程式證明、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-20261019-r05-algorithm-correctness-0073","batch_id":"batch-20261013-advance-20261019-r05-algorithm-correctness-foundations","language":"zh-Hant","source_mko_ids":["mko-algorithm-correctness"],"title_zh":"算法正確性責任","stem_zh":"完整有限正確性模型。操作=correctness-ranking-audit；資料={\"n\":6,\"init\":[0],\"halt\":[5],\"steps\":[[0,1],[1,2],[2,5],[3,4],[4,5],[1,1]],\"rank\":[28,5,4,3,2,0]}。請依 [rank,bad_decrease_edges,ranking_valid,stuck,ranking_plus_no_stuck,actual_termination] 欄序回答。","answer":{"kind":"expression","value":"([28, 5, 4, 3, 2, 0], [[1, 1]], 否, [], 否, 否)","explanation_zh":"第二批擴展核對=([28, 5, 4, 3, 2, 0], [[1, 1]], 否, [], 否, 否)；依完整明示資料重算；有限／合成資料核對不是一般形式證明；部分正確性與終止性分離；一條成功路徑不證總正確。"},"difficulty":{"band":"undergraduate_core","level":3,"skills":["算法正確性責任"]},"variant":{"family_id":"qf-ext19-correctness-ranking-audit","seed":202610195073,"parameters":{"n":6,"init":[0],"halt":[5],"steps":[[0,1],[1,2],[2,5],[3,4],[4,5],[1,1]],"rank":[28,5,4,3,2,0],"domain":"Fin_correctness_model","operation":"correctness-ranking-audit","semantic_template":"qf-ext19-correctness-ranking-audit/{\"halt\":[5],\"init\":[0],\"n\":6,\"rank\":[28,5,4,3,2,0],\"steps\":[[0,1],[1,1],[1,2],[2,5],[3,4],[4,5]]}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_model","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"僅為產生端候選及自檢；主端須另驗，不構成人工審定、一般程式證明、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-20261019-r05-algorithm-correctness-0074","batch_id":"batch-20261013-advance-20261019-r05-algorithm-correctness-foundations","language":"zh-Hant","source_mko_ids":["mko-algorithm-correctness"],"title_zh":"算法正確性責任","stem_zh":"完整有限正確性模型。操作=correctness-ranking-audit；資料={\"n\":6,\"init\":[0],\"halt\":[5],\"steps\":[[0,1],[1,2],[2,5],[0,3],[3,4],[4,5],[1,1]],\"rank\":[29,5,4,3,2,0]}。請依 [rank,bad_decrease_edges,ranking_valid,stuck,ranking_plus_no_stuck,actual_termination] 欄序回答。","answer":{"kind":"expression","value":"([29, 5, 4, 3, 2, 0], [[1, 1]], 否, [], 否, 否)","explanation_zh":"第二批擴展核對=([29, 5, 4, 3, 2, 0], [[1, 1]], 否, [], 否, 否)；依完整明示資料重算；有限／合成資料核對不是一般形式證明；部分正確性與終止性分離；一條成功路徑不證總正確。"},"difficulty":{"band":"undergraduate_core","level":3,"skills":["算法正確性責任"]},"variant":{"family_id":"qf-ext19-correctness-ranking-audit","seed":202610195074,"parameters":{"n":6,"init":[0],"halt":[5],"steps":[[0,1],[1,2],[2,5],[0,3],[3,4],[4,5],[1,1]],"rank":[29,5,4,3,2,0],"domain":"Fin_correctness_model","operation":"correctness-ranking-audit","semantic_template":"qf-ext19-correctness-ranking-audit/{\"halt\":[5],\"init\":[0],\"n\":6,\"rank\":[29,5,4,3,2,0],\"steps\":[[0,1],[0,3],[1,1],[1,2],[2,5],[3,4],[4,5]]}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_model","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"僅為產生端候選及自檢；主端須另驗，不構成人工審定、一般程式證明、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-20261019-r05-algorithm-correctness-0075","batch_id":"batch-20261013-advance-20261019-r05-algorithm-correctness-foundations","language":"zh-Hant","source_mko_ids":["mko-algorithm-correctness"],"title_zh":"算法正確性責任","stem_zh":"完整有限正確性模型。操作=correctness-ranking-audit；資料={\"n\":6,\"init\":[0],\"halt\":[5],\"steps\":[[0,1],[1,2],[2,5],[2,1],[1,1]],\"rank\":[30,5,4,3,2,0]}。請依 [rank,bad_decrease_edges,ranking_valid,stuck,ranking_plus_no_stuck,actual_termination] 欄序回答。","answer":{"kind":"expression","value":"([30, 5, 4, 3, 2, 0], [[1, 1], [2, 1]], 否, [], 否, 否)","explanation_zh":"第二批擴展核對=([30, 5, 4, 3, 2, 0], [[1, 1], [2, 1]], 否, [], 否, 否)；依完整明示資料重算；有限／合成資料核對不是一般形式證明；部分正確性與終止性分離；一條成功路徑不證總正確。"},"difficulty":{"band":"undergraduate_core","level":3,"skills":["算法正確性責任"]},"variant":{"family_id":"qf-ext19-correctness-ranking-audit","seed":202610195075,"parameters":{"n":6,"init":[0],"halt":[5],"steps":[[0,1],[1,2],[2,5],[2,1],[1,1]],"rank":[30,5,4,3,2,0],"domain":"Fin_correctness_model","operation":"correctness-ranking-audit","semantic_template":"qf-ext19-correctness-ranking-audit/{\"halt\":[5],\"init\":[0],\"n\":6,\"rank\":[30,5,4,3,2,0],\"steps\":[[0,1],[1,1],[1,2],[2,1],[2,5]]}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_model","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"僅為產生端候選及自檢；主端須另驗，不構成人工審定、一般程式證明、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-20261019-r05-algorithm-correctness-0076","batch_id":"batch-20261013-advance-20261019-r05-algorithm-correctness-foundations","language":"zh-Hant","source_mko_ids":["mko-algorithm-correctness"],"title_zh":"算法正確性責任","stem_zh":"完整有限正確性模型。操作=correctness-total-separation；資料={\"n\":6,\"init\":[0],\"halt\":[5],\"steps\":[[0,1],[1,2],[2,5]],\"post\":[]}。請依 [reachable_halts,post,bad_halts,partial,vacuous,stuck,cycle,termination,total] 欄序回答。","answer":{"kind":"expression","value":"([5], [], [5], 否, 否, [], 否, 是, 否)","explanation_zh":"第二批擴展核對=([5], [], [5], 否, 否, [], 否, 是, 否)；依完整明示資料重算；有限／合成資料核對不是一般形式證明；部分正確性與終止性分離；一條成功路徑不證總正確。"},"difficulty":{"band":"undergraduate_core","level":1,"skills":["算法正確性責任"]},"variant":{"family_id":"qf-ext19-correctness-total-separation","seed":202610195076,"parameters":{"n":6,"init":[0],"halt":[5],"steps":[[0,1],[1,2],[2,5]],"post":[],"domain":"Fin_correctness_model","operation":"correctness-total-separation","semantic_template":"qf-ext19-correctness-total-separation/{\"halt\":[5],\"init\":[0],\"n\":6,\"post\":[],\"steps\":[[0,1],[1,2],[2,5]]}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_model","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"僅為產生端候選及自檢；主端須另驗，不構成人工審定、一般程式證明、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-20261019-r05-algorithm-correctness-0077","batch_id":"batch-20261013-advance-20261019-r05-algorithm-correctness-foundations","language":"zh-Hant","source_mko_ids":["mko-algorithm-correctness"],"title_zh":"算法正確性責任","stem_zh":"完整有限正確性模型。操作=correctness-total-separation；資料={\"n\":6,\"init\":[0],\"halt\":[5],\"steps\":[[0,1],[1,2],[2,5],[0,3]],\"post\":[5]}。請依 [reachable_halts,post,bad_halts,partial,vacuous,stuck,cycle,termination,total] 欄序回答。","answer":{"kind":"expression","value":"([5], [5], [], 是, 否, [3], 否, 否, 否)","explanation_zh":"第二批擴展核對=([5], [5], [], 是, 否, [3], 否, 否, 否)；依完整明示資料重算；有限／合成資料核對不是一般形式證明；部分正確性與終止性分離；一條成功路徑不證總正確。"},"difficulty":{"band":"undergraduate_core","level":1,"skills":["算法正確性責任"]},"variant":{"family_id":"qf-ext19-correctness-total-separation","seed":202610195077,"parameters":{"n":6,"init":[0],"halt":[5],"steps":[[0,1],[1,2],[2,5],[0,3]],"post":[5],"domain":"Fin_correctness_model","operation":"correctness-total-separation","semantic_template":"qf-ext19-correctness-total-separation/{\"halt\":[5],\"init\":[0],\"n\":6,\"post\":[5],\"steps\":[[0,1],[0,3],[1,2],[2,5]]}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_model","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"僅為產生端候選及自檢；主端須另驗，不構成人工審定、一般程式證明、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-20261019-r05-algorithm-correctness-0078","batch_id":"batch-20261013-advance-20261019-r05-algorithm-correctness-foundations","language":"zh-Hant","source_mko_ids":["mko-algorithm-correctness"],"title_zh":"算法正確性責任","stem_zh":"完整有限正確性模型。操作=correctness-total-separation；資料={\"n\":6,\"init\":[0],\"halt\":[5],\"steps\":[[0,1],[1,2],[2,5],[3,4]],\"post\":[]}。請依 [reachable_halts,post,bad_halts,partial,vacuous,stuck,cycle,termination,total] 欄序回答。","answer":{"kind":"expression","value":"([5], [], [5], 否, 否, [], 否, 是, 否)","explanation_zh":"第二批擴展核對=([5], [], [5], 否, 否, [], 否, 是, 否)；依完整明示資料重算；有限／合成資料核對不是一般形式證明；部分正確性與終止性分離；一條成功路徑不證總正確。"},"difficulty":{"band":"undergraduate_core","level":1,"skills":["算法正確性責任"]},"variant":{"family_id":"qf-ext19-correctness-total-separation","seed":202610195078,"parameters":{"n":6,"init":[0],"halt":[5],"steps":[[0,1],[1,2],[2,5],[3,4]],"post":[],"domain":"Fin_correctness_model","operation":"correctness-total-separation","semantic_template":"qf-ext19-correctness-total-separation/{\"halt\":[5],\"init\":[0],\"n\":6,\"post\":[],\"steps\":[[0,1],[1,2],[2,5],[3,4]]}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_model","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"僅為產生端候選及自檢；主端須另驗，不構成人工審定、一般程式證明、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-20261019-r05-algorithm-correctness-0079","batch_id":"batch-20261013-advance-20261019-r05-algorithm-correctness-foundations","language":"zh-Hant","source_mko_ids":["mko-algorithm-correctness"],"title_zh":"算法正確性責任","stem_zh":"完整有限正確性模型。操作=correctness-total-separation；資料={\"n\":6,\"init\":[0],\"halt\":[5],\"steps\":[[0,1],[1,2],[2,5],[0,3],[3,4]],\"post\":[5]}。請依 [reachable_halts,post,bad_halts,partial,vacuous,stuck,cycle,termination,total] 欄序回答。","answer":{"kind":"expression","value":"([5], [5], [], 是, 否, [4], 否, 否, 否)","explanation_zh":"第二批擴展核對=([5], [5], [], 是, 否, [4], 否, 否, 否)；依完整明示資料重算；有限／合成資料核對不是一般形式證明；部分正確性與終止性分離；一條成功路徑不證總正確。"},"difficulty":{"band":"undergraduate_core","level":1,"skills":["算法正確性責任"]},"variant":{"family_id":"qf-ext19-correctness-total-separation","seed":202610195079,"parameters":{"n":6,"init":[0],"halt":[5],"steps":[[0,1],[1,2],[2,5],[0,3],[3,4]],"post":[5],"domain":"Fin_correctness_model","operation":"correctness-total-separation","semantic_template":"qf-ext19-correctness-total-separation/{\"halt\":[5],\"init\":[0],\"n\":6,\"post\":[5],\"steps\":[[0,1],[0,3],[1,2],[2,5],[3,4]]}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_model","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"僅為產生端候選及自檢；主端須另驗，不構成人工審定、一般程式證明、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-20261019-r05-algorithm-correctness-0080","batch_id":"batch-20261013-advance-20261019-r05-algorithm-correctness-foundations","language":"zh-Hant","source_mko_ids":["mko-algorithm-correctness"],"title_zh":"算法正確性責任","stem_zh":"完整有限正確性模型。操作=correctness-total-separation；資料={\"n\":6,\"init\":[0],\"halt\":[5],\"steps\":[[0,1],[1,2],[2,5],[4,5]],\"post\":[]}。請依 [reachable_halts,post,bad_halts,partial,vacuous,stuck,cycle,termination,total] 欄序回答。","answer":{"kind":"expression","value":"([5], [], [5], 否, 否, [], 否, 是, 否)","explanation_zh":"第二批擴展核對=([5], [], [5], 否, 否, [], 否, 是, 否)；依完整明示資料重算；有限／合成資料核對不是一般形式證明；部分正確性與終止性分離；一條成功路徑不證總正確。"},"difficulty":{"band":"undergraduate_core","level":1,"skills":["算法正確性責任"]},"variant":{"family_id":"qf-ext19-correctness-total-separation","seed":202610195080,"parameters":{"n":6,"init":[0],"halt":[5],"steps":[[0,1],[1,2],[2,5],[4,5]],"post":[],"domain":"Fin_correctness_model","operation":"correctness-total-separation","semantic_template":"qf-ext19-correctness-total-separation/{\"halt\":[5],\"init\":[0],\"n\":6,\"post\":[],\"steps\":[[0,1],[1,2],[2,5],[4,5]]}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_model","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"僅為產生端候選及自檢；主端須另驗，不構成人工審定、一般程式證明、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-20261019-r05-algorithm-correctness-0081","batch_id":"batch-20261013-advance-20261019-r05-algorithm-correctness-foundations","language":"zh-Hant","source_mko_ids":["mko-algorithm-correctness"],"title_zh":"算法正確性責任","stem_zh":"完整有限正確性模型。操作=correctness-total-separation；資料={\"n\":6,\"init\":[0],\"halt\":[5],\"steps\":[[0,1],[1,2],[2,5],[0,3],[4,5]],\"post\":[5]}。請依 [reachable_halts,post,bad_halts,partial,vacuous,stuck,cycle,termination,total] 欄序回答。","answer":{"kind":"expression","value":"([5], [5], [], 是, 否, [3], 否, 否, 否)","explanation_zh":"第二批擴展核對=([5], [5], [], 是, 否, [3], 否, 否, 否)；依完整明示資料重算；有限／合成資料核對不是一般形式證明；部分正確性與終止性分離；一條成功路徑不證總正確。"},"difficulty":{"band":"undergraduate_core","level":1,"skills":["算法正確性責任"]},"variant":{"family_id":"qf-ext19-correctness-total-separation","seed":202610195081,"parameters":{"n":6,"init":[0],"halt":[5],"steps":[[0,1],[1,2],[2,5],[0,3],[4,5]],"post":[5],"domain":"Fin_correctness_model","operation":"correctness-total-separation","semantic_template":"qf-ext19-correctness-total-separation/{\"halt\":[5],\"init\":[0],\"n\":6,\"post\":[5],\"steps\":[[0,1],[0,3],[1,2],[2,5],[4,5]]}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_model","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"僅為產生端候選及自檢；主端須另驗，不構成人工審定、一般程式證明、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-20261019-r05-algorithm-correctness-0082","batch_id":"batch-20261013-advance-20261019-r05-algorithm-correctness-foundations","language":"zh-Hant","source_mko_ids":["mko-algorithm-correctness"],"title_zh":"算法正確性責任","stem_zh":"完整有限正確性模型。操作=correctness-total-separation；資料={\"n\":6,\"init\":[0],\"halt\":[5],\"steps\":[[0,1],[1,2],[2,5],[3,4],[4,5]],\"post\":[]}。請依 [reachable_halts,post,bad_halts,partial,vacuous,stuck,cycle,termination,total] 欄序回答。","answer":{"kind":"expression","value":"([5], [], [5], 否, 否, [], 否, 是, 否)","explanation_zh":"第二批擴展核對=([5], [], [5], 否, 否, [], 否, 是, 否)；依完整明示資料重算；有限／合成資料核對不是一般形式證明；部分正確性與終止性分離；一條成功路徑不證總正確。"},"difficulty":{"band":"undergraduate_core","level":1,"skills":["算法正確性責任"]},"variant":{"family_id":"qf-ext19-correctness-total-separation","seed":202610195082,"parameters":{"n":6,"init":[0],"halt":[5],"steps":[[0,1],[1,2],[2,5],[3,4],[4,5]],"post":[],"domain":"Fin_correctness_model","operation":"correctness-total-separation","semantic_template":"qf-ext19-correctness-total-separation/{\"halt\":[5],\"init\":[0],\"n\":6,\"post\":[],\"steps\":[[0,1],[1,2],[2,5],[3,4],[4,5]]}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_model","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"僅為產生端候選及自檢；主端須另驗，不構成人工審定、一般程式證明、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-20261019-r05-algorithm-correctness-0083","batch_id":"batch-20261013-advance-20261019-r05-algorithm-correctness-foundations","language":"zh-Hant","source_mko_ids":["mko-algorithm-correctness"],"title_zh":"算法正確性責任","stem_zh":"完整有限正確性模型。操作=correctness-total-separation；資料={\"n\":6,\"init\":[0],\"halt\":[5],\"steps\":[[0,1],[1,2],[2,5],[0,3],[3,4],[4,5]],\"post\":[5]}。請依 [reachable_halts,post,bad_halts,partial,vacuous,stuck,cycle,termination,total] 欄序回答。","answer":{"kind":"expression","value":"([5], [5], [], 是, 否, [], 否, 是, 是)","explanation_zh":"第二批擴展核對=([5], [5], [], 是, 否, [], 否, 是, 是)；依完整明示資料重算；有限／合成資料核對不是一般形式證明；部分正確性與終止性分離；一條成功路徑不證總正確。"},"difficulty":{"band":"undergraduate_core","level":1,"skills":["算法正確性責任"]},"variant":{"family_id":"qf-ext19-correctness-total-separation","seed":202610195083,"parameters":{"n":6,"init":[0],"halt":[5],"steps":[[0,1],[1,2],[2,5],[0,3],[3,4],[4,5]],"post":[5],"domain":"Fin_correctness_model","operation":"correctness-total-separation","semantic_template":"qf-ext19-correctness-total-separation/{\"halt\":[5],\"init\":[0],\"n\":6,\"post\":[5],\"steps\":[[0,1],[0,3],[1,2],[2,5],[3,4],[4,5]]}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_model","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"僅為產生端候選及自檢；主端須另驗，不構成人工審定、一般程式證明、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-20261019-r05-algorithm-correctness-0084","batch_id":"batch-20261013-advance-20261019-r05-algorithm-correctness-foundations","language":"zh-Hant","source_mko_ids":["mko-algorithm-correctness"],"title_zh":"算法正確性責任","stem_zh":"完整有限正確性模型。操作=correctness-total-separation；資料={\"n\":6,\"init\":[0],\"halt\":[5],\"steps\":[[0,1],[1,2],[2,5],[2,1]],\"post\":[]}。請依 [reachable_halts,post,bad_halts,partial,vacuous,stuck,cycle,termination,total] 欄序回答。","answer":{"kind":"expression","value":"([5], [], [5], 否, 否, [], 是, 否, 否)","explanation_zh":"第二批擴展核對=([5], [], [5], 否, 否, [], 是, 否, 否)；依完整明示資料重算；有限／合成資料核對不是一般形式證明；部分正確性與終止性分離；一條成功路徑不證總正確。"},"difficulty":{"band":"undergraduate_core","level":2,"skills":["算法正確性責任"]},"variant":{"family_id":"qf-ext19-correctness-total-separation","seed":202610195084,"parameters":{"n":6,"init":[0],"halt":[5],"steps":[[0,1],[1,2],[2,5],[2,1]],"post":[],"domain":"Fin_correctness_model","operation":"correctness-total-separation","semantic_template":"qf-ext19-correctness-total-separation/{\"halt\":[5],\"init\":[0],\"n\":6,\"post\":[],\"steps\":[[0,1],[1,2],[2,1],[2,5]]}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_model","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"僅為產生端候選及自檢；主端須另驗，不構成人工審定、一般程式證明、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-20261019-r05-algorithm-correctness-0085","batch_id":"batch-20261013-advance-20261019-r05-algorithm-correctness-foundations","language":"zh-Hant","source_mko_ids":["mko-algorithm-correctness"],"title_zh":"算法正確性責任","stem_zh":"完整有限正確性模型。操作=correctness-total-separation；資料={\"n\":6,\"init\":[0],\"halt\":[5],\"steps\":[[0,1],[1,2],[2,5],[0,3],[2,1]],\"post\":[5]}。請依 [reachable_halts,post,bad_halts,partial,vacuous,stuck,cycle,termination,total] 欄序回答。","answer":{"kind":"expression","value":"([5], [5], [], 是, 否, [3], 是, 否, 否)","explanation_zh":"第二批擴展核對=([5], [5], [], 是, 否, [3], 是, 否, 否)；依完整明示資料重算；有限／合成資料核對不是一般形式證明；部分正確性與終止性分離；一條成功路徑不證總正確。"},"difficulty":{"band":"undergraduate_core","level":2,"skills":["算法正確性責任"]},"variant":{"family_id":"qf-ext19-correctness-total-separation","seed":202610195085,"parameters":{"n":6,"init":[0],"halt":[5],"steps":[[0,1],[1,2],[2,5],[0,3],[2,1]],"post":[5],"domain":"Fin_correctness_model","operation":"correctness-total-separation","semantic_template":"qf-ext19-correctness-total-separation/{\"halt\":[5],\"init\":[0],\"n\":6,\"post\":[5],\"steps\":[[0,1],[0,3],[1,2],[2,1],[2,5]]}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_model","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"僅為產生端候選及自檢；主端須另驗，不構成人工審定、一般程式證明、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-20261019-r05-algorithm-correctness-0086","batch_id":"batch-20261013-advance-20261019-r05-algorithm-correctness-foundations","language":"zh-Hant","source_mko_ids":["mko-algorithm-correctness"],"title_zh":"算法正確性責任","stem_zh":"完整有限正確性模型。操作=correctness-total-separation；資料={\"n\":6,\"init\":[0],\"halt\":[5],\"steps\":[[0,1],[1,2],[2,5],[3,4],[2,1]],\"post\":[]}。請依 [reachable_halts,post,bad_halts,partial,vacuous,stuck,cycle,termination,total] 欄序回答。","answer":{"kind":"expression","value":"([5], [], [5], 否, 否, [], 是, 否, 否)","explanation_zh":"第二批擴展核對=([5], [], [5], 否, 否, [], 是, 否, 否)；依完整明示資料重算；有限／合成資料核對不是一般形式證明；部分正確性與終止性分離；一條成功路徑不證總正確。"},"difficulty":{"band":"undergraduate_core","level":2,"skills":["算法正確性責任"]},"variant":{"family_id":"qf-ext19-correctness-total-separation","seed":202610195086,"parameters":{"n":6,"init":[0],"halt":[5],"steps":[[0,1],[1,2],[2,5],[3,4],[2,1]],"post":[],"domain":"Fin_correctness_model","operation":"correctness-total-separation","semantic_template":"qf-ext19-correctness-total-separation/{\"halt\":[5],\"init\":[0],\"n\":6,\"post\":[],\"steps\":[[0,1],[1,2],[2,1],[2,5],[3,4]]}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_model","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"僅為產生端候選及自檢；主端須另驗，不構成人工審定、一般程式證明、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-20261019-r05-algorithm-correctness-0087","batch_id":"batch-20261013-advance-20261019-r05-algorithm-correctness-foundations","language":"zh-Hant","source_mko_ids":["mko-algorithm-correctness"],"title_zh":"算法正確性責任","stem_zh":"完整有限正確性模型。操作=correctness-total-separation；資料={\"n\":6,\"init\":[0],\"halt\":[5],\"steps\":[[0,1],[1,2],[2,5],[0,3],[3,4],[2,1]],\"post\":[5]}。請依 [reachable_halts,post,bad_halts,partial,vacuous,stuck,cycle,termination,total] 欄序回答。","answer":{"kind":"expression","value":"([5], [5], [], 是, 否, [4], 是, 否, 否)","explanation_zh":"第二批擴展核對=([5], [5], [], 是, 否, [4], 是, 否, 否)；依完整明示資料重算；有限／合成資料核對不是一般形式證明；部分正確性與終止性分離；一條成功路徑不證總正確。"},"difficulty":{"band":"undergraduate_core","level":2,"skills":["算法正確性責任"]},"variant":{"family_id":"qf-ext19-correctness-total-separation","seed":202610195087,"parameters":{"n":6,"init":[0],"halt":[5],"steps":[[0,1],[1,2],[2,5],[0,3],[3,4],[2,1]],"post":[5],"domain":"Fin_correctness_model","operation":"correctness-total-separation","semantic_template":"qf-ext19-correctness-total-separation/{\"halt\":[5],\"init\":[0],\"n\":6,\"post\":[5],\"steps\":[[0,1],[0,3],[1,2],[2,1],[2,5],[3,4]]}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_model","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"僅為產生端候選及自檢；主端須另驗，不構成人工審定、一般程式證明、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-20261019-r05-algorithm-correctness-0088","batch_id":"batch-20261013-advance-20261019-r05-algorithm-correctness-foundations","language":"zh-Hant","source_mko_ids":["mko-algorithm-correctness"],"title_zh":"算法正確性責任","stem_zh":"完整有限正確性模型。操作=correctness-total-separation；資料={\"n\":6,\"init\":[0],\"halt\":[5],\"steps\":[[0,1],[1,2],[2,5],[4,5],[2,1]],\"post\":[]}。請依 [reachable_halts,post,bad_halts,partial,vacuous,stuck,cycle,termination,total] 欄序回答。","answer":{"kind":"expression","value":"([5], [], [5], 否, 否, [], 是, 否, 否)","explanation_zh":"第二批擴展核對=([5], [], [5], 否, 否, [], 是, 否, 否)；依完整明示資料重算；有限／合成資料核對不是一般形式證明；部分正確性與終止性分離；一條成功路徑不證總正確。"},"difficulty":{"band":"undergraduate_core","level":2,"skills":["算法正確性責任"]},"variant":{"family_id":"qf-ext19-correctness-total-separation","seed":202610195088,"parameters":{"n":6,"init":[0],"halt":[5],"steps":[[0,1],[1,2],[2,5],[4,5],[2,1]],"post":[],"domain":"Fin_correctness_model","operation":"correctness-total-separation","semantic_template":"qf-ext19-correctness-total-separation/{\"halt\":[5],\"init\":[0],\"n\":6,\"post\":[],\"steps\":[[0,1],[1,2],[2,1],[2,5],[4,5]]}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_model","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"僅為產生端候選及自檢；主端須另驗，不構成人工審定、一般程式證明、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-20261019-r05-algorithm-correctness-0089","batch_id":"batch-20261013-advance-20261019-r05-algorithm-correctness-foundations","language":"zh-Hant","source_mko_ids":["mko-algorithm-correctness"],"title_zh":"算法正確性責任","stem_zh":"完整有限正確性模型。操作=correctness-total-separation；資料={\"n\":6,\"init\":[0],\"halt\":[5],\"steps\":[[0,1],[1,2],[2,5],[0,3],[4,5],[2,1]],\"post\":[5]}。請依 [reachable_halts,post,bad_halts,partial,vacuous,stuck,cycle,termination,total] 欄序回答。","answer":{"kind":"expression","value":"([5], [5], [], 是, 否, [3], 是, 否, 否)","explanation_zh":"第二批擴展核對=([5], [5], [], 是, 否, [3], 是, 否, 否)；依完整明示資料重算；有限／合成資料核對不是一般形式證明；部分正確性與終止性分離；一條成功路徑不證總正確。"},"difficulty":{"band":"undergraduate_core","level":2,"skills":["算法正確性責任"]},"variant":{"family_id":"qf-ext19-correctness-total-separation","seed":202610195089,"parameters":{"n":6,"init":[0],"halt":[5],"steps":[[0,1],[1,2],[2,5],[0,3],[4,5],[2,1]],"post":[5],"domain":"Fin_correctness_model","operation":"correctness-total-separation","semantic_template":"qf-ext19-correctness-total-separation/{\"halt\":[5],\"init\":[0],\"n\":6,\"post\":[5],\"steps\":[[0,1],[0,3],[1,2],[2,1],[2,5],[4,5]]}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_model","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"僅為產生端候選及自檢；主端須另驗，不構成人工審定、一般程式證明、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-20261019-r05-algorithm-correctness-0090","batch_id":"batch-20261013-advance-20261019-r05-algorithm-correctness-foundations","language":"zh-Hant","source_mko_ids":["mko-algorithm-correctness"],"title_zh":"算法正確性責任","stem_zh":"完整有限正確性模型。操作=correctness-total-separation；資料={\"n\":6,\"init\":[0],\"halt\":[5],\"steps\":[[0,1],[1,2],[2,5],[3,4],[4,5],[2,1]],\"post\":[]}。請依 [reachable_halts,post,bad_halts,partial,vacuous,stuck,cycle,termination,total] 欄序回答。","answer":{"kind":"expression","value":"([5], [], [5], 否, 否, [], 是, 否, 否)","explanation_zh":"第二批擴展核對=([5], [], [5], 否, 否, [], 是, 否, 否)；依完整明示資料重算；有限／合成資料核對不是一般形式證明；部分正確性與終止性分離；一條成功路徑不證總正確。"},"difficulty":{"band":"undergraduate_core","level":2,"skills":["算法正確性責任"]},"variant":{"family_id":"qf-ext19-correctness-total-separation","seed":202610195090,"parameters":{"n":6,"init":[0],"halt":[5],"steps":[[0,1],[1,2],[2,5],[3,4],[4,5],[2,1]],"post":[],"domain":"Fin_correctness_model","operation":"correctness-total-separation","semantic_template":"qf-ext19-correctness-total-separation/{\"halt\":[5],\"init\":[0],\"n\":6,\"post\":[],\"steps\":[[0,1],[1,2],[2,1],[2,5],[3,4],[4,5]]}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_model","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"僅為產生端候選及自檢；主端須另驗，不構成人工審定、一般程式證明、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-20261019-r05-algorithm-correctness-0091","batch_id":"batch-20261013-advance-20261019-r05-algorithm-correctness-foundations","language":"zh-Hant","source_mko_ids":["mko-algorithm-correctness"],"title_zh":"算法正確性責任","stem_zh":"完整有限正確性模型。操作=correctness-total-separation；資料={\"n\":6,\"init\":[0],\"halt\":[5],\"steps\":[[0,1],[1,2],[2,5],[0,3],[3,4],[4,5],[2,1]],\"post\":[5]}。請依 [reachable_halts,post,bad_halts,partial,vacuous,stuck,cycle,termination,total] 欄序回答。","answer":{"kind":"expression","value":"([5], [5], [], 是, 否, [], 是, 否, 否)","explanation_zh":"第二批擴展核對=([5], [5], [], 是, 否, [], 是, 否, 否)；依完整明示資料重算；有限／合成資料核對不是一般形式證明；部分正確性與終止性分離；一條成功路徑不證總正確。"},"difficulty":{"band":"undergraduate_core","level":2,"skills":["算法正確性責任"]},"variant":{"family_id":"qf-ext19-correctness-total-separation","seed":202610195091,"parameters":{"n":6,"init":[0],"halt":[5],"steps":[[0,1],[1,2],[2,5],[0,3],[3,4],[4,5],[2,1]],"post":[5],"domain":"Fin_correctness_model","operation":"correctness-total-separation","semantic_template":"qf-ext19-correctness-total-separation/{\"halt\":[5],\"init\":[0],\"n\":6,\"post\":[5],\"steps\":[[0,1],[0,3],[1,2],[2,1],[2,5],[3,4],[4,5]]}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_model","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"僅為產生端候選及自檢；主端須另驗，不構成人工審定、一般程式證明、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-20261019-r05-algorithm-correctness-0092","batch_id":"batch-20261013-advance-20261019-r05-algorithm-correctness-foundations","language":"zh-Hant","source_mko_ids":["mko-algorithm-correctness"],"title_zh":"算法正確性責任","stem_zh":"完整有限正確性模型。操作=correctness-total-separation；資料={\"n\":6,\"init\":[0],\"halt\":[5],\"steps\":[[0,1],[1,2],[2,5],[1,1]],\"post\":[]}。請依 [reachable_halts,post,bad_halts,partial,vacuous,stuck,cycle,termination,total] 欄序回答。","answer":{"kind":"expression","value":"([5], [], [5], 否, 否, [], 是, 否, 否)","explanation_zh":"第二批擴展核對=([5], [], [5], 否, 否, [], 是, 否, 否)；依完整明示資料重算；有限／合成資料核對不是一般形式證明；部分正確性與終止性分離；一條成功路徑不證總正確。"},"difficulty":{"band":"undergraduate_core","level":2,"skills":["算法正確性責任"]},"variant":{"family_id":"qf-ext19-correctness-total-separation","seed":202610195092,"parameters":{"n":6,"init":[0],"halt":[5],"steps":[[0,1],[1,2],[2,5],[1,1]],"post":[],"domain":"Fin_correctness_model","operation":"correctness-total-separation","semantic_template":"qf-ext19-correctness-total-separation/{\"halt\":[5],\"init\":[0],\"n\":6,\"post\":[],\"steps\":[[0,1],[1,1],[1,2],[2,5]]}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_model","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"僅為產生端候選及自檢；主端須另驗，不構成人工審定、一般程式證明、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-20261019-r05-algorithm-correctness-0093","batch_id":"batch-20261013-advance-20261019-r05-algorithm-correctness-foundations","language":"zh-Hant","source_mko_ids":["mko-algorithm-correctness"],"title_zh":"算法正確性責任","stem_zh":"完整有限正確性模型。操作=correctness-total-separation；資料={\"n\":6,\"init\":[0],\"halt\":[5],\"steps\":[[0,1],[1,2],[2,5],[0,3],[1,1]],\"post\":[5]}。請依 [reachable_halts,post,bad_halts,partial,vacuous,stuck,cycle,termination,total] 欄序回答。","answer":{"kind":"expression","value":"([5], [5], [], 是, 否, [3], 是, 否, 否)","explanation_zh":"第二批擴展核對=([5], [5], [], 是, 否, [3], 是, 否, 否)；依完整明示資料重算；有限／合成資料核對不是一般形式證明；部分正確性與終止性分離；一條成功路徑不證總正確。"},"difficulty":{"band":"undergraduate_core","level":3,"skills":["算法正確性責任"]},"variant":{"family_id":"qf-ext19-correctness-total-separation","seed":202610195093,"parameters":{"n":6,"init":[0],"halt":[5],"steps":[[0,1],[1,2],[2,5],[0,3],[1,1]],"post":[5],"domain":"Fin_correctness_model","operation":"correctness-total-separation","semantic_template":"qf-ext19-correctness-total-separation/{\"halt\":[5],\"init\":[0],\"n\":6,\"post\":[5],\"steps\":[[0,1],[0,3],[1,1],[1,2],[2,5]]}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_model","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"僅為產生端候選及自檢；主端須另驗，不構成人工審定、一般程式證明、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-20261019-r05-algorithm-correctness-0094","batch_id":"batch-20261013-advance-20261019-r05-algorithm-correctness-foundations","language":"zh-Hant","source_mko_ids":["mko-algorithm-correctness"],"title_zh":"算法正確性責任","stem_zh":"完整有限正確性模型。操作=correctness-total-separation；資料={\"n\":6,\"init\":[0],\"halt\":[5],\"steps\":[[0,1],[1,2],[2,5],[3,4],[1,1]],\"post\":[]}。請依 [reachable_halts,post,bad_halts,partial,vacuous,stuck,cycle,termination,total] 欄序回答。","answer":{"kind":"expression","value":"([5], [], [5], 否, 否, [], 是, 否, 否)","explanation_zh":"第二批擴展核對=([5], [], [5], 否, 否, [], 是, 否, 否)；依完整明示資料重算；有限／合成資料核對不是一般形式證明；部分正確性與終止性分離；一條成功路徑不證總正確。"},"difficulty":{"band":"undergraduate_core","level":3,"skills":["算法正確性責任"]},"variant":{"family_id":"qf-ext19-correctness-total-separation","seed":202610195094,"parameters":{"n":6,"init":[0],"halt":[5],"steps":[[0,1],[1,2],[2,5],[3,4],[1,1]],"post":[],"domain":"Fin_correctness_model","operation":"correctness-total-separation","semantic_template":"qf-ext19-correctness-total-separation/{\"halt\":[5],\"init\":[0],\"n\":6,\"post\":[],\"steps\":[[0,1],[1,1],[1,2],[2,5],[3,4]]}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_model","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"僅為產生端候選及自檢；主端須另驗，不構成人工審定、一般程式證明、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-20261019-r05-algorithm-correctness-0095","batch_id":"batch-20261013-advance-20261019-r05-algorithm-correctness-foundations","language":"zh-Hant","source_mko_ids":["mko-algorithm-correctness"],"title_zh":"算法正確性責任","stem_zh":"完整有限正確性模型。操作=correctness-total-separation；資料={\"n\":6,\"init\":[0],\"halt\":[5],\"steps\":[[0,1],[1,2],[2,5],[0,3],[3,4],[1,1]],\"post\":[5]}。請依 [reachable_halts,post,bad_halts,partial,vacuous,stuck,cycle,termination,total] 欄序回答。","answer":{"kind":"expression","value":"([5], [5], [], 是, 否, [4], 是, 否, 否)","explanation_zh":"第二批擴展核對=([5], [5], [], 是, 否, [4], 是, 否, 否)；依完整明示資料重算；有限／合成資料核對不是一般形式證明；部分正確性與終止性分離；一條成功路徑不證總正確。"},"difficulty":{"band":"undergraduate_core","level":3,"skills":["算法正確性責任"]},"variant":{"family_id":"qf-ext19-correctness-total-separation","seed":202610195095,"parameters":{"n":6,"init":[0],"halt":[5],"steps":[[0,1],[1,2],[2,5],[0,3],[3,4],[1,1]],"post":[5],"domain":"Fin_correctness_model","operation":"correctness-total-separation","semantic_template":"qf-ext19-correctness-total-separation/{\"halt\":[5],\"init\":[0],\"n\":6,\"post\":[5],\"steps\":[[0,1],[0,3],[1,1],[1,2],[2,5],[3,4]]}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_model","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"僅為產生端候選及自檢；主端須另驗，不構成人工審定、一般程式證明、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-20261019-r05-algorithm-correctness-0096","batch_id":"batch-20261013-advance-20261019-r05-algorithm-correctness-foundations","language":"zh-Hant","source_mko_ids":["mko-algorithm-correctness"],"title_zh":"算法正確性責任","stem_zh":"完整有限正確性模型。操作=correctness-total-separation；資料={\"n\":6,\"init\":[0],\"halt\":[5],\"steps\":[[0,1],[1,2],[2,5],[4,5],[1,1]],\"post\":[]}。請依 [reachable_halts,post,bad_halts,partial,vacuous,stuck,cycle,termination,total] 欄序回答。","answer":{"kind":"expression","value":"([5], [], [5], 否, 否, [], 是, 否, 否)","explanation_zh":"第二批擴展核對=([5], [], [5], 否, 否, [], 是, 否, 否)；依完整明示資料重算；有限／合成資料核對不是一般形式證明；部分正確性與終止性分離；一條成功路徑不證總正確。"},"difficulty":{"band":"undergraduate_core","level":3,"skills":["算法正確性責任"]},"variant":{"family_id":"qf-ext19-correctness-total-separation","seed":202610195096,"parameters":{"n":6,"init":[0],"halt":[5],"steps":[[0,1],[1,2],[2,5],[4,5],[1,1]],"post":[],"domain":"Fin_correctness_model","operation":"correctness-total-separation","semantic_template":"qf-ext19-correctness-total-separation/{\"halt\":[5],\"init\":[0],\"n\":6,\"post\":[],\"steps\":[[0,1],[1,1],[1,2],[2,5],[4,5]]}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_model","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"僅為產生端候選及自檢；主端須另驗，不構成人工審定、一般程式證明、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-20261019-r05-algorithm-correctness-0097","batch_id":"batch-20261013-advance-20261019-r05-algorithm-correctness-foundations","language":"zh-Hant","source_mko_ids":["mko-algorithm-correctness"],"title_zh":"算法正確性責任","stem_zh":"完整有限正確性模型。操作=correctness-total-separation；資料={\"n\":6,\"init\":[0],\"halt\":[5],\"steps\":[[0,1],[1,2],[2,5],[0,3],[4,5],[1,1]],\"post\":[5]}。請依 [reachable_halts,post,bad_halts,partial,vacuous,stuck,cycle,termination,total] 欄序回答。","answer":{"kind":"expression","value":"([5], [5], [], 是, 否, [3], 是, 否, 否)","explanation_zh":"第二批擴展核對=([5], [5], [], 是, 否, [3], 是, 否, 否)；依完整明示資料重算；有限／合成資料核對不是一般形式證明；部分正確性與終止性分離；一條成功路徑不證總正確。"},"difficulty":{"band":"undergraduate_core","level":3,"skills":["算法正確性責任"]},"variant":{"family_id":"qf-ext19-correctness-total-separation","seed":202610195097,"parameters":{"n":6,"init":[0],"halt":[5],"steps":[[0,1],[1,2],[2,5],[0,3],[4,5],[1,1]],"post":[5],"domain":"Fin_correctness_model","operation":"correctness-total-separation","semantic_template":"qf-ext19-correctness-total-separation/{\"halt\":[5],\"init\":[0],\"n\":6,\"post\":[5],\"steps\":[[0,1],[0,3],[1,1],[1,2],[2,5],[4,5]]}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_model","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"僅為產生端候選及自檢；主端須另驗，不構成人工審定、一般程式證明、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-20261019-r05-algorithm-correctness-0098","batch_id":"batch-20261013-advance-20261019-r05-algorithm-correctness-foundations","language":"zh-Hant","source_mko_ids":["mko-algorithm-correctness"],"title_zh":"算法正確性責任","stem_zh":"完整有限正確性模型。操作=correctness-total-separation；資料={\"n\":6,\"init\":[0],\"halt\":[5],\"steps\":[[0,1],[1,2],[2,5],[3,4],[4,5],[1,1]],\"post\":[]}。請依 [reachable_halts,post,bad_halts,partial,vacuous,stuck,cycle,termination,total] 欄序回答。","answer":{"kind":"expression","value":"([5], [], [5], 否, 否, [], 是, 否, 否)","explanation_zh":"第二批擴展核對=([5], [], [5], 否, 否, [], 是, 否, 否)；依完整明示資料重算；有限／合成資料核對不是一般形式證明；部分正確性與終止性分離；一條成功路徑不證總正確。"},"difficulty":{"band":"undergraduate_core","level":3,"skills":["算法正確性責任"]},"variant":{"family_id":"qf-ext19-correctness-total-separation","seed":202610195098,"parameters":{"n":6,"init":[0],"halt":[5],"steps":[[0,1],[1,2],[2,5],[3,4],[4,5],[1,1]],"post":[],"domain":"Fin_correctness_model","operation":"correctness-total-separation","semantic_template":"qf-ext19-correctness-total-separation/{\"halt\":[5],\"init\":[0],\"n\":6,\"post\":[],\"steps\":[[0,1],[1,1],[1,2],[2,5],[3,4],[4,5]]}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_model","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"僅為產生端候選及自檢；主端須另驗，不構成人工審定、一般程式證明、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-20261019-r05-algorithm-correctness-0099","batch_id":"batch-20261013-advance-20261019-r05-algorithm-correctness-foundations","language":"zh-Hant","source_mko_ids":["mko-algorithm-correctness"],"title_zh":"算法正確性責任","stem_zh":"完整有限正確性模型。操作=correctness-total-separation；資料={\"n\":6,\"init\":[0],\"halt\":[5],\"steps\":[[0,1],[1,2],[2,5],[0,3],[3,4],[4,5],[1,1]],\"post\":[5]}。請依 [reachable_halts,post,bad_halts,partial,vacuous,stuck,cycle,termination,total] 欄序回答。","answer":{"kind":"expression","value":"([5], [5], [], 是, 否, [], 是, 否, 否)","explanation_zh":"第二批擴展核對=([5], [5], [], 是, 否, [], 是, 否, 否)；依完整明示資料重算；有限／合成資料核對不是一般形式證明；部分正確性與終止性分離；一條成功路徑不證總正確。"},"difficulty":{"band":"undergraduate_core","level":3,"skills":["算法正確性責任"]},"variant":{"family_id":"qf-ext19-correctness-total-separation","seed":202610195099,"parameters":{"n":6,"init":[0],"halt":[5],"steps":[[0,1],[1,2],[2,5],[0,3],[3,4],[4,5],[1,1]],"post":[5],"domain":"Fin_correctness_model","operation":"correctness-total-separation","semantic_template":"qf-ext19-correctness-total-separation/{\"halt\":[5],\"init\":[0],\"n\":6,\"post\":[5],\"steps\":[[0,1],[0,3],[1,1],[1,2],[2,5],[3,4],[4,5]]}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_model","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"僅為產生端候選及自檢；主端須另驗，不構成人工審定、一般程式證明、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-20261019-r05-algorithm-correctness-0100","batch_id":"batch-20261013-advance-20261019-r05-algorithm-correctness-foundations","language":"zh-Hant","source_mko_ids":["mko-algorithm-correctness"],"title_zh":"算法正確性責任","stem_zh":"完整有限正確性模型。操作=correctness-total-separation；資料={\"n\":6,\"init\":[0],\"halt\":[5],\"steps\":[[0,1],[1,2],[2,5],[2,1],[1,1]],\"post\":[]}。請依 [reachable_halts,post,bad_halts,partial,vacuous,stuck,cycle,termination,total] 欄序回答。","answer":{"kind":"expression","value":"([5], [], [5], 否, 否, [], 是, 否, 否)","explanation_zh":"第二批擴展核對=([5], [], [5], 否, 否, [], 是, 否, 否)；依完整明示資料重算；有限／合成資料核對不是一般形式證明；部分正確性與終止性分離；一條成功路徑不證總正確。"},"difficulty":{"band":"undergraduate_core","level":3,"skills":["算法正確性責任"]},"variant":{"family_id":"qf-ext19-correctness-total-separation","seed":202610195100,"parameters":{"n":6,"init":[0],"halt":[5],"steps":[[0,1],[1,2],[2,5],[2,1],[1,1]],"post":[],"domain":"Fin_correctness_model","operation":"correctness-total-separation","semantic_template":"qf-ext19-correctness-total-separation/{\"halt\":[5],\"init\":[0],\"n\":6,\"post\":[],\"steps\":[[0,1],[1,1],[1,2],[2,1],[2,5]]}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_model","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"僅為產生端候選及自檢；主端須另驗，不構成人工審定、一般程式證明、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"}}