{"schema_version":"ocme-question-v0.1","id":"q-20261013-advance-20261019-r04-computational-model-0001","batch_id":"batch-20261013-advance-20261019-r04-computational-model-foundations","language":"zh-Hant","source_mko_ids":["mko-computational-model"],"title_zh":"有限轉移計算模型","stem_zh":"完整有限轉移模型。操作=model-reachable-states；資料={\"n\":6,\"init\":[0],\"halt\":[5],\"steps\":[[0,1],[1,2],[2,5]]}。請依 [n,init,halt,steps,reachable] 欄序回答。","answer":{"kind":"expression","value":"(6, [0], [5], [[0, 1], [1, 2], [2, 5]], [0, 1, 2, 5])","explanation_zh":"第二批擴展核對=(6, [0], [5], [[0, 1], [1, 2], [2, 5]], [0, 1, 2, 5])；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；halt與stuck分離；有限prefix不證一般終止。"},"difficulty":{"band":"undergraduate_core","level":1,"skills":["有限轉移計算模型"]},"variant":{"family_id":"qf-ext19-model-reachable-states","seed":202610194001,"parameters":{"n":6,"init":[0],"halt":[5],"steps":[[0,1],[1,2],[2,5]],"domain":"Fin_transition_model","operation":"model-reachable-states","semantic_template":"qf-ext19-model-reachable-states/{\"halt\":[5],\"init\":[0],\"n\":6,\"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-r04-computational-model-0003","batch_id":"batch-20261013-advance-20261019-r04-computational-model-foundations","language":"zh-Hant","source_mko_ids":["mko-computational-model"],"title_zh":"有限轉移計算模型","stem_zh":"完整有限轉移模型。操作=model-reachable-states；資料={\"n\":6,\"init\":[0],\"halt\":[5],\"steps\":[[0,1],[1,2],[2,5],[3,4]]}。請依 [n,init,halt,steps,reachable] 欄序回答。","answer":{"kind":"expression","value":"(6, [0], [5], [[0, 1], [1, 2], [2, 5], [3, 4]], [0, 1, 2, 5])","explanation_zh":"第二批擴展核對=(6, [0], [5], [[0, 1], [1, 2], [2, 5], [3, 4]], [0, 1, 2, 5])；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；halt與stuck分離；有限prefix不證一般終止。"},"difficulty":{"band":"undergraduate_core","level":1,"skills":["有限轉移計算模型"]},"variant":{"family_id":"qf-ext19-model-reachable-states","seed":202610194003,"parameters":{"n":6,"init":[0],"halt":[5],"steps":[[0,1],[1,2],[2,5],[3,4]],"domain":"Fin_transition_model","operation":"model-reachable-states","semantic_template":"qf-ext19-model-reachable-states/{\"halt\":[5],\"init\":[0],\"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-r04-computational-model-0004","batch_id":"batch-20261013-advance-20261019-r04-computational-model-foundations","language":"zh-Hant","source_mko_ids":["mko-computational-model"],"title_zh":"有限轉移計算模型","stem_zh":"完整有限轉移模型。操作=model-reachable-states；資料={\"n\":6,\"init\":[0],\"halt\":[5],\"steps\":[[0,1],[1,2],[2,5],[0,3],[3,4]]}。請依 [n,init,halt,steps,reachable] 欄序回答。","answer":{"kind":"expression","value":"(6, [0], [5], [[0, 1], [0, 3], [1, 2], [2, 5], [3, 4]], [0, 1, 2, 3, 4, 5])","explanation_zh":"第二批擴展核對=(6, [0], [5], [[0, 1], [0, 3], [1, 2], [2, 5], [3, 4]], [0, 1, 2, 3, 4, 5])；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；halt與stuck分離；有限prefix不證一般終止。"},"difficulty":{"band":"undergraduate_core","level":1,"skills":["有限轉移計算模型"]},"variant":{"family_id":"qf-ext19-model-reachable-states","seed":202610194004,"parameters":{"n":6,"init":[0],"halt":[5],"steps":[[0,1],[1,2],[2,5],[0,3],[3,4]],"domain":"Fin_transition_model","operation":"model-reachable-states","semantic_template":"qf-ext19-model-reachable-states/{\"halt\":[5],\"init\":[0],\"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-r04-computational-model-0005","batch_id":"batch-20261013-advance-20261019-r04-computational-model-foundations","language":"zh-Hant","source_mko_ids":["mko-computational-model"],"title_zh":"有限轉移計算模型","stem_zh":"完整有限轉移模型。操作=model-reachable-states；資料={\"n\":6,\"init\":[0],\"halt\":[5],\"steps\":[[0,1],[1,2],[2,5],[4,5]]}。請依 [n,init,halt,steps,reachable] 欄序回答。","answer":{"kind":"expression","value":"(6, [0], [5], [[0, 1], [1, 2], [2, 5], [4, 5]], [0, 1, 2, 5])","explanation_zh":"第二批擴展核對=(6, [0], [5], [[0, 1], [1, 2], [2, 5], [4, 5]], [0, 1, 2, 5])；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；halt與stuck分離；有限prefix不證一般終止。"},"difficulty":{"band":"undergraduate_core","level":1,"skills":["有限轉移計算模型"]},"variant":{"family_id":"qf-ext19-model-reachable-states","seed":202610194005,"parameters":{"n":6,"init":[0],"halt":[5],"steps":[[0,1],[1,2],[2,5],[4,5]],"domain":"Fin_transition_model","operation":"model-reachable-states","semantic_template":"qf-ext19-model-reachable-states/{\"halt\":[5],\"init\":[0],\"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-r04-computational-model-0006","batch_id":"batch-20261013-advance-20261019-r04-computational-model-foundations","language":"zh-Hant","source_mko_ids":["mko-computational-model"],"title_zh":"有限轉移計算模型","stem_zh":"完整有限轉移模型。操作=model-reachable-states；資料={\"n\":6,\"init\":[0],\"halt\":[5],\"steps\":[[0,1],[1,2],[2,5],[0,3],[4,5]]}。請依 [n,init,halt,steps,reachable] 欄序回答。","answer":{"kind":"expression","value":"(6, [0], [5], [[0, 1], [0, 3], [1, 2], [2, 5], [4, 5]], [0, 1, 2, 3, 5])","explanation_zh":"第二批擴展核對=(6, [0], [5], [[0, 1], [0, 3], [1, 2], [2, 5], [4, 5]], [0, 1, 2, 3, 5])；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；halt與stuck分離；有限prefix不證一般終止。"},"difficulty":{"band":"undergraduate_core","level":1,"skills":["有限轉移計算模型"]},"variant":{"family_id":"qf-ext19-model-reachable-states","seed":202610194006,"parameters":{"n":6,"init":[0],"halt":[5],"steps":[[0,1],[1,2],[2,5],[0,3],[4,5]],"domain":"Fin_transition_model","operation":"model-reachable-states","semantic_template":"qf-ext19-model-reachable-states/{\"halt\":[5],\"init\":[0],\"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-r04-computational-model-0007","batch_id":"batch-20261013-advance-20261019-r04-computational-model-foundations","language":"zh-Hant","source_mko_ids":["mko-computational-model"],"title_zh":"有限轉移計算模型","stem_zh":"完整有限轉移模型。操作=model-reachable-states；資料={\"n\":6,\"init\":[0],\"halt\":[5],\"steps\":[[0,1],[1,2],[2,5],[3,4],[4,5]]}。請依 [n,init,halt,steps,reachable] 欄序回答。","answer":{"kind":"expression","value":"(6, [0], [5], [[0, 1], [1, 2], [2, 5], [3, 4], [4, 5]], [0, 1, 2, 5])","explanation_zh":"第二批擴展核對=(6, [0], [5], [[0, 1], [1, 2], [2, 5], [3, 4], [4, 5]], [0, 1, 2, 5])；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；halt與stuck分離；有限prefix不證一般終止。"},"difficulty":{"band":"undergraduate_core","level":1,"skills":["有限轉移計算模型"]},"variant":{"family_id":"qf-ext19-model-reachable-states","seed":202610194007,"parameters":{"n":6,"init":[0],"halt":[5],"steps":[[0,1],[1,2],[2,5],[3,4],[4,5]],"domain":"Fin_transition_model","operation":"model-reachable-states","semantic_template":"qf-ext19-model-reachable-states/{\"halt\":[5],\"init\":[0],\"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-r04-computational-model-0008","batch_id":"batch-20261013-advance-20261019-r04-computational-model-foundations","language":"zh-Hant","source_mko_ids":["mko-computational-model"],"title_zh":"有限轉移計算模型","stem_zh":"完整有限轉移模型。操作=model-reachable-states；資料={\"n\":6,\"init\":[0],\"halt\":[5],\"steps\":[[0,1],[1,2],[2,5],[0,3],[3,4],[4,5]]}。請依 [n,init,halt,steps,reachable] 欄序回答。","answer":{"kind":"expression","value":"(6, [0], [5], [[0, 1], [0, 3], [1, 2], [2, 5], [3, 4], [4, 5]], [0, 1, 2, 3, 4, 5])","explanation_zh":"第二批擴展核對=(6, [0], [5], [[0, 1], [0, 3], [1, 2], [2, 5], [3, 4], [4, 5]], [0, 1, 2, 3, 4, 5])；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；halt與stuck分離；有限prefix不證一般終止。"},"difficulty":{"band":"undergraduate_core","level":1,"skills":["有限轉移計算模型"]},"variant":{"family_id":"qf-ext19-model-reachable-states","seed":202610194008,"parameters":{"n":6,"init":[0],"halt":[5],"steps":[[0,1],[1,2],[2,5],[0,3],[3,4],[4,5]],"domain":"Fin_transition_model","operation":"model-reachable-states","semantic_template":"qf-ext19-model-reachable-states/{\"halt\":[5],\"init\":[0],\"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"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261013-advance-20261019-r04-computational-model-0009","batch_id":"batch-20261013-advance-20261019-r04-computational-model-foundations","language":"zh-Hant","source_mko_ids":["mko-computational-model"],"title_zh":"有限轉移計算模型","stem_zh":"完整有限轉移模型。操作=model-reachable-states；資料={\"n\":6,\"init\":[0],\"halt\":[5],\"steps\":[[0,1],[1,2],[2,5],[2,1]]}。請依 [n,init,halt,steps,reachable] 欄序回答。","answer":{"kind":"expression","value":"(6, [0], [5], [[0, 1], [1, 2], [2, 1], [2, 5]], [0, 1, 2, 5])","explanation_zh":"第二批擴展核對=(6, [0], [5], [[0, 1], [1, 2], [2, 1], [2, 5]], [0, 1, 2, 5])；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；halt與stuck分離；有限prefix不證一般終止。"},"difficulty":{"band":"undergraduate_core","level":2,"skills":["有限轉移計算模型"]},"variant":{"family_id":"qf-ext19-model-reachable-states","seed":202610194009,"parameters":{"n":6,"init":[0],"halt":[5],"steps":[[0,1],[1,2],[2,5],[2,1]],"domain":"Fin_transition_model","operation":"model-reachable-states","semantic_template":"qf-ext19-model-reachable-states/{\"halt\":[5],\"init\":[0],\"n\":6,\"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-r04-computational-model-0010","batch_id":"batch-20261013-advance-20261019-r04-computational-model-foundations","language":"zh-Hant","source_mko_ids":["mko-computational-model"],"title_zh":"有限轉移計算模型","stem_zh":"完整有限轉移模型。操作=model-reachable-states；資料={\"n\":6,\"init\":[0],\"halt\":[5],\"steps\":[[0,1],[1,2],[2,5],[0,3],[2,1]]}。請依 [n,init,halt,steps,reachable] 欄序回答。","answer":{"kind":"expression","value":"(6, [0], [5], [[0, 1], [0, 3], [1, 2], [2, 1], [2, 5]], [0, 1, 2, 3, 5])","explanation_zh":"第二批擴展核對=(6, [0], [5], [[0, 1], [0, 3], [1, 2], [2, 1], [2, 5]], [0, 1, 2, 3, 5])；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；halt與stuck分離；有限prefix不證一般終止。"},"difficulty":{"band":"undergraduate_core","level":2,"skills":["有限轉移計算模型"]},"variant":{"family_id":"qf-ext19-model-reachable-states","seed":202610194010,"parameters":{"n":6,"init":[0],"halt":[5],"steps":[[0,1],[1,2],[2,5],[0,3],[2,1]],"domain":"Fin_transition_model","operation":"model-reachable-states","semantic_template":"qf-ext19-model-reachable-states/{\"halt\":[5],\"init\":[0],\"n\":6,\"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-r04-computational-model-0011","batch_id":"batch-20261013-advance-20261019-r04-computational-model-foundations","language":"zh-Hant","source_mko_ids":["mko-computational-model"],"title_zh":"有限轉移計算模型","stem_zh":"完整有限轉移模型。操作=model-reachable-states；資料={\"n\":6,\"init\":[0],\"halt\":[5],\"steps\":[[0,1],[1,2],[2,5],[3,4],[2,1]]}。請依 [n,init,halt,steps,reachable] 欄序回答。","answer":{"kind":"expression","value":"(6, [0], [5], [[0, 1], [1, 2], [2, 1], [2, 5], [3, 4]], [0, 1, 2, 5])","explanation_zh":"第二批擴展核對=(6, [0], [5], [[0, 1], [1, 2], [2, 1], [2, 5], [3, 4]], [0, 1, 2, 5])；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；halt與stuck分離；有限prefix不證一般終止。"},"difficulty":{"band":"undergraduate_core","level":2,"skills":["有限轉移計算模型"]},"variant":{"family_id":"qf-ext19-model-reachable-states","seed":202610194011,"parameters":{"n":6,"init":[0],"halt":[5],"steps":[[0,1],[1,2],[2,5],[3,4],[2,1]],"domain":"Fin_transition_model","operation":"model-reachable-states","semantic_template":"qf-ext19-model-reachable-states/{\"halt\":[5],\"init\":[0],\"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-r04-computational-model-0012","batch_id":"batch-20261013-advance-20261019-r04-computational-model-foundations","language":"zh-Hant","source_mko_ids":["mko-computational-model"],"title_zh":"有限轉移計算模型","stem_zh":"完整有限轉移模型。操作=model-reachable-states；資料={\"n\":6,\"init\":[0],\"halt\":[5],\"steps\":[[0,1],[1,2],[2,5],[0,3],[3,4],[2,1]]}。請依 [n,init,halt,steps,reachable] 欄序回答。","answer":{"kind":"expression","value":"(6, [0], [5], [[0, 1], [0, 3], [1, 2], [2, 1], [2, 5], [3, 4]], [0, 1, 2, 3, 4, 5])","explanation_zh":"第二批擴展核對=(6, [0], [5], [[0, 1], [0, 3], [1, 2], [2, 1], [2, 5], [3, 4]], [0, 1, 2, 3, 4, 5])；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；halt與stuck分離；有限prefix不證一般終止。"},"difficulty":{"band":"undergraduate_core","level":2,"skills":["有限轉移計算模型"]},"variant":{"family_id":"qf-ext19-model-reachable-states","seed":202610194012,"parameters":{"n":6,"init":[0],"halt":[5],"steps":[[0,1],[1,2],[2,5],[0,3],[3,4],[2,1]],"domain":"Fin_transition_model","operation":"model-reachable-states","semantic_template":"qf-ext19-model-reachable-states/{\"halt\":[5],\"init\":[0],\"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-r04-computational-model-0013","batch_id":"batch-20261013-advance-20261019-r04-computational-model-foundations","language":"zh-Hant","source_mko_ids":["mko-computational-model"],"title_zh":"有限轉移計算模型","stem_zh":"完整有限轉移模型。操作=model-reachable-states；資料={\"n\":6,\"init\":[0],\"halt\":[5],\"steps\":[[0,1],[1,2],[2,5],[4,5],[2,1]]}。請依 [n,init,halt,steps,reachable] 欄序回答。","answer":{"kind":"expression","value":"(6, [0], [5], [[0, 1], [1, 2], [2, 1], [2, 5], [4, 5]], [0, 1, 2, 5])","explanation_zh":"第二批擴展核對=(6, [0], [5], [[0, 1], [1, 2], [2, 1], [2, 5], [4, 5]], [0, 1, 2, 5])；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；halt與stuck分離；有限prefix不證一般終止。"},"difficulty":{"band":"undergraduate_core","level":2,"skills":["有限轉移計算模型"]},"variant":{"family_id":"qf-ext19-model-reachable-states","seed":202610194013,"parameters":{"n":6,"init":[0],"halt":[5],"steps":[[0,1],[1,2],[2,5],[4,5],[2,1]],"domain":"Fin_transition_model","operation":"model-reachable-states","semantic_template":"qf-ext19-model-reachable-states/{\"halt\":[5],\"init\":[0],\"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-r04-computational-model-0014","batch_id":"batch-20261013-advance-20261019-r04-computational-model-foundations","language":"zh-Hant","source_mko_ids":["mko-computational-model"],"title_zh":"有限轉移計算模型","stem_zh":"完整有限轉移模型。操作=model-reachable-states；資料={\"n\":6,\"init\":[0],\"halt\":[5],\"steps\":[[0,1],[1,2],[2,5],[0,3],[4,5],[2,1]]}。請依 [n,init,halt,steps,reachable] 欄序回答。","answer":{"kind":"expression","value":"(6, [0], [5], [[0, 1], [0, 3], [1, 2], [2, 1], [2, 5], [4, 5]], [0, 1, 2, 3, 5])","explanation_zh":"第二批擴展核對=(6, [0], [5], [[0, 1], [0, 3], [1, 2], [2, 1], [2, 5], [4, 5]], [0, 1, 2, 3, 5])；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；halt與stuck分離；有限prefix不證一般終止。"},"difficulty":{"band":"undergraduate_core","level":2,"skills":["有限轉移計算模型"]},"variant":{"family_id":"qf-ext19-model-reachable-states","seed":202610194014,"parameters":{"n":6,"init":[0],"halt":[5],"steps":[[0,1],[1,2],[2,5],[0,3],[4,5],[2,1]],"domain":"Fin_transition_model","operation":"model-reachable-states","semantic_template":"qf-ext19-model-reachable-states/{\"halt\":[5],\"init\":[0],\"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-r04-computational-model-0015","batch_id":"batch-20261013-advance-20261019-r04-computational-model-foundations","language":"zh-Hant","source_mko_ids":["mko-computational-model"],"title_zh":"有限轉移計算模型","stem_zh":"完整有限轉移模型。操作=model-reachable-states；資料={\"n\":6,\"init\":[0],\"halt\":[5],\"steps\":[[0,1],[1,2],[2,5],[3,4],[4,5],[2,1]]}。請依 [n,init,halt,steps,reachable] 欄序回答。","answer":{"kind":"expression","value":"(6, [0], [5], [[0, 1], [1, 2], [2, 1], [2, 5], [3, 4], [4, 5]], [0, 1, 2, 5])","explanation_zh":"第二批擴展核對=(6, [0], [5], [[0, 1], [1, 2], [2, 1], [2, 5], [3, 4], [4, 5]], [0, 1, 2, 5])；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；halt與stuck分離；有限prefix不證一般終止。"},"difficulty":{"band":"undergraduate_core","level":2,"skills":["有限轉移計算模型"]},"variant":{"family_id":"qf-ext19-model-reachable-states","seed":202610194015,"parameters":{"n":6,"init":[0],"halt":[5],"steps":[[0,1],[1,2],[2,5],[3,4],[4,5],[2,1]],"domain":"Fin_transition_model","operation":"model-reachable-states","semantic_template":"qf-ext19-model-reachable-states/{\"halt\":[5],\"init\":[0],\"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-r04-computational-model-0016","batch_id":"batch-20261013-advance-20261019-r04-computational-model-foundations","language":"zh-Hant","source_mko_ids":["mko-computational-model"],"title_zh":"有限轉移計算模型","stem_zh":"完整有限轉移模型。操作=model-reachable-states；資料={\"n\":6,\"init\":[0],\"halt\":[5],\"steps\":[[0,1],[1,2],[2,5],[0,3],[3,4],[4,5],[2,1]]}。請依 [n,init,halt,steps,reachable] 欄序回答。","answer":{"kind":"expression","value":"(6, [0], [5], [[0, 1], [0, 3], [1, 2], [2, 1], [2, 5], [3, 4], [4, 5]], [0, 1, 2, 3, 4, 5])","explanation_zh":"第二批擴展核對=(6, [0], [5], [[0, 1], [0, 3], [1, 2], [2, 1], [2, 5], [3, 4], [4, 5]], [0, 1, 2, 3, 4, 5])；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；halt與stuck分離；有限prefix不證一般終止。"},"difficulty":{"band":"undergraduate_core","level":2,"skills":["有限轉移計算模型"]},"variant":{"family_id":"qf-ext19-model-reachable-states","seed":202610194016,"parameters":{"n":6,"init":[0],"halt":[5],"steps":[[0,1],[1,2],[2,5],[0,3],[3,4],[4,5],[2,1]],"domain":"Fin_transition_model","operation":"model-reachable-states","semantic_template":"qf-ext19-model-reachable-states/{\"halt\":[5],\"init\":[0],\"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-r04-computational-model-0017","batch_id":"batch-20261013-advance-20261019-r04-computational-model-foundations","language":"zh-Hant","source_mko_ids":["mko-computational-model"],"title_zh":"有限轉移計算模型","stem_zh":"完整有限轉移模型。操作=model-reachable-states；資料={\"n\":6,\"init\":[0],\"halt\":[5],\"steps\":[[0,1],[1,2],[2,5],[1,1]]}。請依 [n,init,halt,steps,reachable] 欄序回答。","answer":{"kind":"expression","value":"(6, [0], [5], [[0, 1], [1, 1], [1, 2], [2, 5]], [0, 1, 2, 5])","explanation_zh":"第二批擴展核對=(6, [0], [5], [[0, 1], [1, 1], [1, 2], [2, 5]], [0, 1, 2, 5])；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；halt與stuck分離；有限prefix不證一般終止。"},"difficulty":{"band":"undergraduate_core","level":2,"skills":["有限轉移計算模型"]},"variant":{"family_id":"qf-ext19-model-reachable-states","seed":202610194017,"parameters":{"n":6,"init":[0],"halt":[5],"steps":[[0,1],[1,2],[2,5],[1,1]],"domain":"Fin_transition_model","operation":"model-reachable-states","semantic_template":"qf-ext19-model-reachable-states/{\"halt\":[5],\"init\":[0],\"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-r04-computational-model-0018","batch_id":"batch-20261013-advance-20261019-r04-computational-model-foundations","language":"zh-Hant","source_mko_ids":["mko-computational-model"],"title_zh":"有限轉移計算模型","stem_zh":"完整有限轉移模型。操作=model-reachable-states；資料={\"n\":6,\"init\":[0],\"halt\":[5],\"steps\":[[0,1],[1,2],[2,5],[0,3],[1,1]]}。請依 [n,init,halt,steps,reachable] 欄序回答。","answer":{"kind":"expression","value":"(6, [0], [5], [[0, 1], [0, 3], [1, 1], [1, 2], [2, 5]], [0, 1, 2, 3, 5])","explanation_zh":"第二批擴展核對=(6, [0], [5], [[0, 1], [0, 3], [1, 1], [1, 2], [2, 5]], [0, 1, 2, 3, 5])；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；halt與stuck分離；有限prefix不證一般終止。"},"difficulty":{"band":"undergraduate_core","level":3,"skills":["有限轉移計算模型"]},"variant":{"family_id":"qf-ext19-model-reachable-states","seed":202610194018,"parameters":{"n":6,"init":[0],"halt":[5],"steps":[[0,1],[1,2],[2,5],[0,3],[1,1]],"domain":"Fin_transition_model","operation":"model-reachable-states","semantic_template":"qf-ext19-model-reachable-states/{\"halt\":[5],\"init\":[0],\"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-r04-computational-model-0019","batch_id":"batch-20261013-advance-20261019-r04-computational-model-foundations","language":"zh-Hant","source_mko_ids":["mko-computational-model"],"title_zh":"有限轉移計算模型","stem_zh":"完整有限轉移模型。操作=model-reachable-states；資料={\"n\":6,\"init\":[0],\"halt\":[5],\"steps\":[[0,1],[1,2],[2,5],[3,4],[1,1]]}。請依 [n,init,halt,steps,reachable] 欄序回答。","answer":{"kind":"expression","value":"(6, [0], [5], [[0, 1], [1, 1], [1, 2], [2, 5], [3, 4]], [0, 1, 2, 5])","explanation_zh":"第二批擴展核對=(6, [0], [5], [[0, 1], [1, 1], [1, 2], [2, 5], [3, 4]], [0, 1, 2, 5])；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；halt與stuck分離；有限prefix不證一般終止。"},"difficulty":{"band":"undergraduate_core","level":3,"skills":["有限轉移計算模型"]},"variant":{"family_id":"qf-ext19-model-reachable-states","seed":202610194019,"parameters":{"n":6,"init":[0],"halt":[5],"steps":[[0,1],[1,2],[2,5],[3,4],[1,1]],"domain":"Fin_transition_model","operation":"model-reachable-states","semantic_template":"qf-ext19-model-reachable-states/{\"halt\":[5],\"init\":[0],\"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-r04-computational-model-0020","batch_id":"batch-20261013-advance-20261019-r04-computational-model-foundations","language":"zh-Hant","source_mko_ids":["mko-computational-model"],"title_zh":"有限轉移計算模型","stem_zh":"完整有限轉移模型。操作=model-reachable-states；資料={\"n\":6,\"init\":[0],\"halt\":[5],\"steps\":[[0,1],[1,2],[2,5],[0,3],[3,4],[1,1]]}。請依 [n,init,halt,steps,reachable] 欄序回答。","answer":{"kind":"expression","value":"(6, [0], [5], [[0, 1], [0, 3], [1, 1], [1, 2], [2, 5], [3, 4]], [0, 1, 2, 3, 4, 5])","explanation_zh":"第二批擴展核對=(6, [0], [5], [[0, 1], [0, 3], [1, 1], [1, 2], [2, 5], [3, 4]], [0, 1, 2, 3, 4, 5])；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；halt與stuck分離；有限prefix不證一般終止。"},"difficulty":{"band":"undergraduate_core","level":3,"skills":["有限轉移計算模型"]},"variant":{"family_id":"qf-ext19-model-reachable-states","seed":202610194020,"parameters":{"n":6,"init":[0],"halt":[5],"steps":[[0,1],[1,2],[2,5],[0,3],[3,4],[1,1]],"domain":"Fin_transition_model","operation":"model-reachable-states","semantic_template":"qf-ext19-model-reachable-states/{\"halt\":[5],\"init\":[0],\"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-r04-computational-model-0021","batch_id":"batch-20261013-advance-20261019-r04-computational-model-foundations","language":"zh-Hant","source_mko_ids":["mko-computational-model"],"title_zh":"有限轉移計算模型","stem_zh":"完整有限轉移模型。操作=model-reachable-states；資料={\"n\":6,\"init\":[0],\"halt\":[5],\"steps\":[[0,1],[1,2],[2,5],[4,5],[1,1]]}。請依 [n,init,halt,steps,reachable] 欄序回答。","answer":{"kind":"expression","value":"(6, [0], [5], [[0, 1], [1, 1], [1, 2], [2, 5], [4, 5]], [0, 1, 2, 5])","explanation_zh":"第二批擴展核對=(6, [0], [5], [[0, 1], [1, 1], [1, 2], [2, 5], [4, 5]], [0, 1, 2, 5])；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；halt與stuck分離；有限prefix不證一般終止。"},"difficulty":{"band":"undergraduate_core","level":3,"skills":["有限轉移計算模型"]},"variant":{"family_id":"qf-ext19-model-reachable-states","seed":202610194021,"parameters":{"n":6,"init":[0],"halt":[5],"steps":[[0,1],[1,2],[2,5],[4,5],[1,1]],"domain":"Fin_transition_model","operation":"model-reachable-states","semantic_template":"qf-ext19-model-reachable-states/{\"halt\":[5],\"init\":[0],\"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-r04-computational-model-0022","batch_id":"batch-20261013-advance-20261019-r04-computational-model-foundations","language":"zh-Hant","source_mko_ids":["mko-computational-model"],"title_zh":"有限轉移計算模型","stem_zh":"完整有限轉移模型。操作=model-reachable-states；資料={\"n\":6,\"init\":[0],\"halt\":[5],\"steps\":[[0,1],[1,2],[2,5],[0,3],[4,5],[1,1]]}。請依 [n,init,halt,steps,reachable] 欄序回答。","answer":{"kind":"expression","value":"(6, [0], [5], [[0, 1], [0, 3], [1, 1], [1, 2], [2, 5], [4, 5]], [0, 1, 2, 3, 5])","explanation_zh":"第二批擴展核對=(6, [0], [5], [[0, 1], [0, 3], [1, 1], [1, 2], [2, 5], [4, 5]], [0, 1, 2, 3, 5])；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；halt與stuck分離；有限prefix不證一般終止。"},"difficulty":{"band":"undergraduate_core","level":3,"skills":["有限轉移計算模型"]},"variant":{"family_id":"qf-ext19-model-reachable-states","seed":202610194022,"parameters":{"n":6,"init":[0],"halt":[5],"steps":[[0,1],[1,2],[2,5],[0,3],[4,5],[1,1]],"domain":"Fin_transition_model","operation":"model-reachable-states","semantic_template":"qf-ext19-model-reachable-states/{\"halt\":[5],\"init\":[0],\"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-r04-computational-model-0023","batch_id":"batch-20261013-advance-20261019-r04-computational-model-foundations","language":"zh-Hant","source_mko_ids":["mko-computational-model"],"title_zh":"有限轉移計算模型","stem_zh":"完整有限轉移模型。操作=model-reachable-states；資料={\"n\":6,\"init\":[0],\"halt\":[5],\"steps\":[[0,1],[1,2],[2,5],[3,4],[4,5],[1,1]]}。請依 [n,init,halt,steps,reachable] 欄序回答。","answer":{"kind":"expression","value":"(6, [0], [5], [[0, 1], [1, 1], [1, 2], [2, 5], [3, 4], [4, 5]], [0, 1, 2, 5])","explanation_zh":"第二批擴展核對=(6, [0], [5], [[0, 1], [1, 1], [1, 2], [2, 5], [3, 4], [4, 5]], [0, 1, 2, 5])；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；halt與stuck分離；有限prefix不證一般終止。"},"difficulty":{"band":"undergraduate_core","level":3,"skills":["有限轉移計算模型"]},"variant":{"family_id":"qf-ext19-model-reachable-states","seed":202610194023,"parameters":{"n":6,"init":[0],"halt":[5],"steps":[[0,1],[1,2],[2,5],[3,4],[4,5],[1,1]],"domain":"Fin_transition_model","operation":"model-reachable-states","semantic_template":"qf-ext19-model-reachable-states/{\"halt\":[5],\"init\":[0],\"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-r04-computational-model-0024","batch_id":"batch-20261013-advance-20261019-r04-computational-model-foundations","language":"zh-Hant","source_mko_ids":["mko-computational-model"],"title_zh":"有限轉移計算模型","stem_zh":"完整有限轉移模型。操作=model-reachable-states；資料={\"n\":6,\"init\":[0],\"halt\":[5],\"steps\":[[0,1],[1,2],[2,5],[0,3],[3,4],[4,5],[1,1]]}。請依 [n,init,halt,steps,reachable] 欄序回答。","answer":{"kind":"expression","value":"(6, [0], [5], [[0, 1], [0, 3], [1, 1], [1, 2], [2, 5], [3, 4], [4, 5]], [0, 1, 2, 3, 4, 5])","explanation_zh":"第二批擴展核對=(6, [0], [5], [[0, 1], [0, 3], [1, 1], [1, 2], [2, 5], [3, 4], [4, 5]], [0, 1, 2, 3, 4, 5])；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；halt與stuck分離；有限prefix不證一般終止。"},"difficulty":{"band":"undergraduate_core","level":3,"skills":["有限轉移計算模型"]},"variant":{"family_id":"qf-ext19-model-reachable-states","seed":202610194024,"parameters":{"n":6,"init":[0],"halt":[5],"steps":[[0,1],[1,2],[2,5],[0,3],[3,4],[4,5],[1,1]],"domain":"Fin_transition_model","operation":"model-reachable-states","semantic_template":"qf-ext19-model-reachable-states/{\"halt\":[5],\"init\":[0],\"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-r04-computational-model-0025","batch_id":"batch-20261013-advance-20261019-r04-computational-model-foundations","language":"zh-Hant","source_mko_ids":["mko-computational-model"],"title_zh":"有限轉移計算模型","stem_zh":"完整有限轉移模型。操作=model-reachable-states；資料={\"n\":6,\"init\":[0],\"halt\":[5],\"steps\":[[0,1],[1,2],[2,5],[2,1],[1,1]]}。請依 [n,init,halt,steps,reachable] 欄序回答。","answer":{"kind":"expression","value":"(6, [0], [5], [[0, 1], [1, 1], [1, 2], [2, 1], [2, 5]], [0, 1, 2, 5])","explanation_zh":"第二批擴展核對=(6, [0], [5], [[0, 1], [1, 1], [1, 2], [2, 1], [2, 5]], [0, 1, 2, 5])；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；halt與stuck分離；有限prefix不證一般終止。"},"difficulty":{"band":"undergraduate_core","level":3,"skills":["有限轉移計算模型"]},"variant":{"family_id":"qf-ext19-model-reachable-states","seed":202610194025,"parameters":{"n":6,"init":[0],"halt":[5],"steps":[[0,1],[1,2],[2,5],[2,1],[1,1]],"domain":"Fin_transition_model","operation":"model-reachable-states","semantic_template":"qf-ext19-model-reachable-states/{\"halt\":[5],\"init\":[0],\"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-r04-computational-model-0026","batch_id":"batch-20261013-advance-20261019-r04-computational-model-foundations","language":"zh-Hant","source_mko_ids":["mko-computational-model"],"title_zh":"有限轉移計算模型","stem_zh":"完整有限轉移模型。操作=model-trace-qualification；資料={\"n\":6,\"init\":[0],\"halt\":[5],\"steps\":[[0,1],[1,2],[2,5]],\"trace\":[0,1,2,5]}。請依 [trace,typed_mask,nonempty,initial,step_flags,continued_after_halt,valid] 欄序回答。","answer":{"kind":"expression","value":"([0, 1, 2, 5], [是, 是, 是, 是], 是, 是, [是, 是, 是], 否, 是)","explanation_zh":"第二批擴展核對=([0, 1, 2, 5], [是, 是, 是, 是], 是, 是, [是, 是, 是], 否, 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；halt與stuck分離；有限prefix不證一般終止。"},"difficulty":{"band":"undergraduate_core","level":1,"skills":["有限轉移計算模型"]},"variant":{"family_id":"qf-ext19-model-trace-qualification","seed":202610194026,"parameters":{"n":6,"init":[0],"halt":[5],"steps":[[0,1],[1,2],[2,5]],"trace":[0,1,2,5],"domain":"Fin_transition_model","operation":"model-trace-qualification","semantic_template":"qf-ext19-model-trace-qualification/{\"halt\":[5],\"init\":[0],\"n\":6,\"steps\":[[0,1],[1,2],[2,5]],\"trace\":[0,1,2,5]}"}},"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-r04-computational-model-0027","batch_id":"batch-20261013-advance-20261019-r04-computational-model-foundations","language":"zh-Hant","source_mko_ids":["mko-computational-model"],"title_zh":"有限轉移計算模型","stem_zh":"完整有限轉移模型。操作=model-trace-qualification；資料={\"n\":6,\"init\":[0],\"halt\":[5],\"steps\":[[0,1],[1,2],[2,5],[0,3]],\"trace\":[0,4]}。請依 [trace,typed_mask,nonempty,initial,step_flags,continued_after_halt,valid] 欄序回答。","answer":{"kind":"expression","value":"([0, 4], [是, 是], 是, 是, [否], 否, 否)","explanation_zh":"第二批擴展核對=([0, 4], [是, 是], 是, 是, [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；halt與stuck分離；有限prefix不證一般終止。"},"difficulty":{"band":"undergraduate_core","level":1,"skills":["有限轉移計算模型"]},"variant":{"family_id":"qf-ext19-model-trace-qualification","seed":202610194027,"parameters":{"n":6,"init":[0],"halt":[5],"steps":[[0,1],[1,2],[2,5],[0,3]],"trace":[0,4],"domain":"Fin_transition_model","operation":"model-trace-qualification","semantic_template":"qf-ext19-model-trace-qualification/{\"halt\":[5],\"init\":[0],\"n\":6,\"steps\":[[0,1],[0,3],[1,2],[2,5]],\"trace\":[0,4]}"}},"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-r04-computational-model-0028","batch_id":"batch-20261013-advance-20261019-r04-computational-model-foundations","language":"zh-Hant","source_mko_ids":["mko-computational-model"],"title_zh":"有限轉移計算模型","stem_zh":"完整有限轉移模型。操作=model-trace-qualification；資料={\"n\":6,\"init\":[0],\"halt\":[5],\"steps\":[[0,1],[1,2],[2,5],[3,4]],\"trace\":[0,1,2,5,5]}。請依 [trace,typed_mask,nonempty,initial,step_flags,continued_after_halt,valid] 欄序回答。","answer":{"kind":"expression","value":"([0, 1, 2, 5, 5], [是, 是, 是, 是, 是], 是, 是, [是, 是, 是, 否], 是, 否)","explanation_zh":"第二批擴展核對=([0, 1, 2, 5, 5], [是, 是, 是, 是, 是], 是, 是, [是, 是, 是, 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；halt與stuck分離；有限prefix不證一般終止。"},"difficulty":{"band":"undergraduate_core","level":1,"skills":["有限轉移計算模型"]},"variant":{"family_id":"qf-ext19-model-trace-qualification","seed":202610194028,"parameters":{"n":6,"init":[0],"halt":[5],"steps":[[0,1],[1,2],[2,5],[3,4]],"trace":[0,1,2,5,5],"domain":"Fin_transition_model","operation":"model-trace-qualification","semantic_template":"qf-ext19-model-trace-qualification/{\"halt\":[5],\"init\":[0],\"n\":6,\"steps\":[[0,1],[1,2],[2,5],[3,4]],\"trace\":[0,1,2,5,5]}"}},"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-r04-computational-model-0029","batch_id":"batch-20261013-advance-20261019-r04-computational-model-foundations","language":"zh-Hant","source_mko_ids":["mko-computational-model"],"title_zh":"有限轉移計算模型","stem_zh":"完整有限轉移模型。操作=model-trace-qualification；資料={\"n\":6,\"init\":[0],\"halt\":[5],\"steps\":[[0,1],[1,2],[2,5],[0,3],[3,4]],\"trace\":[0,6]}。請依 [trace,typed_mask,nonempty,initial,step_flags,continued_after_halt,valid] 欄序回答。","answer":{"kind":"expression","value":"([0, 6], [是, 否], 是, 是, [否], 否, 否)","explanation_zh":"第二批擴展核對=([0, 6], [是, 否], 是, 是, [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；halt與stuck分離；有限prefix不證一般終止。"},"difficulty":{"band":"undergraduate_core","level":1,"skills":["有限轉移計算模型"]},"variant":{"family_id":"qf-ext19-model-trace-qualification","seed":202610194029,"parameters":{"n":6,"init":[0],"halt":[5],"steps":[[0,1],[1,2],[2,5],[0,3],[3,4]],"trace":[0,6],"domain":"Fin_transition_model","operation":"model-trace-qualification","semantic_template":"qf-ext19-model-trace-qualification/{\"halt\":[5],\"init\":[0],\"n\":6,\"steps\":[[0,1],[0,3],[1,2],[2,5],[3,4]],\"trace\":[0,6]}"}},"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-r04-computational-model-0030","batch_id":"batch-20261013-advance-20261019-r04-computational-model-foundations","language":"zh-Hant","source_mko_ids":["mko-computational-model"],"title_zh":"有限轉移計算模型","stem_zh":"完整有限轉移模型。操作=model-trace-qualification；資料={\"n\":6,\"init\":[0],\"halt\":[5],\"steps\":[[0,1],[1,2],[2,5],[4,5]],\"trace\":[0,1,2,5]}。請依 [trace,typed_mask,nonempty,initial,step_flags,continued_after_halt,valid] 欄序回答。","answer":{"kind":"expression","value":"([0, 1, 2, 5], [是, 是, 是, 是], 是, 是, [是, 是, 是], 否, 是)","explanation_zh":"第二批擴展核對=([0, 1, 2, 5], [是, 是, 是, 是], 是, 是, [是, 是, 是], 否, 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；halt與stuck分離；有限prefix不證一般終止。"},"difficulty":{"band":"undergraduate_core","level":1,"skills":["有限轉移計算模型"]},"variant":{"family_id":"qf-ext19-model-trace-qualification","seed":202610194030,"parameters":{"n":6,"init":[0],"halt":[5],"steps":[[0,1],[1,2],[2,5],[4,5]],"trace":[0,1,2,5],"domain":"Fin_transition_model","operation":"model-trace-qualification","semantic_template":"qf-ext19-model-trace-qualification/{\"halt\":[5],\"init\":[0],\"n\":6,\"steps\":[[0,1],[1,2],[2,5],[4,5]],\"trace\":[0,1,2,5]}"}},"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-r04-computational-model-0031","batch_id":"batch-20261013-advance-20261019-r04-computational-model-foundations","language":"zh-Hant","source_mko_ids":["mko-computational-model"],"title_zh":"有限轉移計算模型","stem_zh":"完整有限轉移模型。操作=model-trace-qualification；資料={\"n\":6,\"init\":[0],\"halt\":[5],\"steps\":[[0,1],[1,2],[2,5],[0,3],[4,5]],\"trace\":[0,4]}。請依 [trace,typed_mask,nonempty,initial,step_flags,continued_after_halt,valid] 欄序回答。","answer":{"kind":"expression","value":"([0, 4], [是, 是], 是, 是, [否], 否, 否)","explanation_zh":"第二批擴展核對=([0, 4], [是, 是], 是, 是, [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；halt與stuck分離；有限prefix不證一般終止。"},"difficulty":{"band":"undergraduate_core","level":1,"skills":["有限轉移計算模型"]},"variant":{"family_id":"qf-ext19-model-trace-qualification","seed":202610194031,"parameters":{"n":6,"init":[0],"halt":[5],"steps":[[0,1],[1,2],[2,5],[0,3],[4,5]],"trace":[0,4],"domain":"Fin_transition_model","operation":"model-trace-qualification","semantic_template":"qf-ext19-model-trace-qualification/{\"halt\":[5],\"init\":[0],\"n\":6,\"steps\":[[0,1],[0,3],[1,2],[2,5],[4,5]],\"trace\":[0,4]}"}},"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-r04-computational-model-0032","batch_id":"batch-20261013-advance-20261019-r04-computational-model-foundations","language":"zh-Hant","source_mko_ids":["mko-computational-model"],"title_zh":"有限轉移計算模型","stem_zh":"完整有限轉移模型。操作=model-trace-qualification；資料={\"n\":6,\"init\":[0],\"halt\":[5],\"steps\":[[0,1],[1,2],[2,5],[3,4],[4,5]],\"trace\":[0,1,2,5,5]}。請依 [trace,typed_mask,nonempty,initial,step_flags,continued_after_halt,valid] 欄序回答。","answer":{"kind":"expression","value":"([0, 1, 2, 5, 5], [是, 是, 是, 是, 是], 是, 是, [是, 是, 是, 否], 是, 否)","explanation_zh":"第二批擴展核對=([0, 1, 2, 5, 5], [是, 是, 是, 是, 是], 是, 是, [是, 是, 是, 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；halt與stuck分離；有限prefix不證一般終止。"},"difficulty":{"band":"undergraduate_core","level":1,"skills":["有限轉移計算模型"]},"variant":{"family_id":"qf-ext19-model-trace-qualification","seed":202610194032,"parameters":{"n":6,"init":[0],"halt":[5],"steps":[[0,1],[1,2],[2,5],[3,4],[4,5]],"trace":[0,1,2,5,5],"domain":"Fin_transition_model","operation":"model-trace-qualification","semantic_template":"qf-ext19-model-trace-qualification/{\"halt\":[5],\"init\":[0],\"n\":6,\"steps\":[[0,1],[1,2],[2,5],[3,4],[4,5]],\"trace\":[0,1,2,5,5]}"}},"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-r04-computational-model-0033","batch_id":"batch-20261013-advance-20261019-r04-computational-model-foundations","language":"zh-Hant","source_mko_ids":["mko-computational-model"],"title_zh":"有限轉移計算模型","stem_zh":"完整有限轉移模型。操作=model-trace-qualification；資料={\"n\":6,\"init\":[0],\"halt\":[5],\"steps\":[[0,1],[1,2],[2,5],[0,3],[3,4],[4,5]],\"trace\":[0,6]}。請依 [trace,typed_mask,nonempty,initial,step_flags,continued_after_halt,valid] 欄序回答。","answer":{"kind":"expression","value":"([0, 6], [是, 否], 是, 是, [否], 否, 否)","explanation_zh":"第二批擴展核對=([0, 6], [是, 否], 是, 是, [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；halt與stuck分離；有限prefix不證一般終止。"},"difficulty":{"band":"undergraduate_core","level":1,"skills":["有限轉移計算模型"]},"variant":{"family_id":"qf-ext19-model-trace-qualification","seed":202610194033,"parameters":{"n":6,"init":[0],"halt":[5],"steps":[[0,1],[1,2],[2,5],[0,3],[3,4],[4,5]],"trace":[0,6],"domain":"Fin_transition_model","operation":"model-trace-qualification","semantic_template":"qf-ext19-model-trace-qualification/{\"halt\":[5],\"init\":[0],\"n\":6,\"steps\":[[0,1],[0,3],[1,2],[2,5],[3,4],[4,5]],\"trace\":[0,6]}"}},"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-r04-computational-model-0034","batch_id":"batch-20261013-advance-20261019-r04-computational-model-foundations","language":"zh-Hant","source_mko_ids":["mko-computational-model"],"title_zh":"有限轉移計算模型","stem_zh":"完整有限轉移模型。操作=model-trace-qualification；資料={\"n\":6,\"init\":[0],\"halt\":[5],\"steps\":[[0,1],[1,2],[2,5],[2,1]],\"trace\":[0,1,2,5]}。請依 [trace,typed_mask,nonempty,initial,step_flags,continued_after_halt,valid] 欄序回答。","answer":{"kind":"expression","value":"([0, 1, 2, 5], [是, 是, 是, 是], 是, 是, [是, 是, 是], 否, 是)","explanation_zh":"第二批擴展核對=([0, 1, 2, 5], [是, 是, 是, 是], 是, 是, [是, 是, 是], 否, 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；halt與stuck分離；有限prefix不證一般終止。"},"difficulty":{"band":"undergraduate_core","level":2,"skills":["有限轉移計算模型"]},"variant":{"family_id":"qf-ext19-model-trace-qualification","seed":202610194034,"parameters":{"n":6,"init":[0],"halt":[5],"steps":[[0,1],[1,2],[2,5],[2,1]],"trace":[0,1,2,5],"domain":"Fin_transition_model","operation":"model-trace-qualification","semantic_template":"qf-ext19-model-trace-qualification/{\"halt\":[5],\"init\":[0],\"n\":6,\"steps\":[[0,1],[1,2],[2,1],[2,5]],\"trace\":[0,1,2,5]}"}},"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-r04-computational-model-0035","batch_id":"batch-20261013-advance-20261019-r04-computational-model-foundations","language":"zh-Hant","source_mko_ids":["mko-computational-model"],"title_zh":"有限轉移計算模型","stem_zh":"完整有限轉移模型。操作=model-trace-qualification；資料={\"n\":6,\"init\":[0],\"halt\":[5],\"steps\":[[0,1],[1,2],[2,5],[0,3],[2,1]],\"trace\":[0,4]}。請依 [trace,typed_mask,nonempty,initial,step_flags,continued_after_halt,valid] 欄序回答。","answer":{"kind":"expression","value":"([0, 4], [是, 是], 是, 是, [否], 否, 否)","explanation_zh":"第二批擴展核對=([0, 4], [是, 是], 是, 是, [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；halt與stuck分離；有限prefix不證一般終止。"},"difficulty":{"band":"undergraduate_core","level":2,"skills":["有限轉移計算模型"]},"variant":{"family_id":"qf-ext19-model-trace-qualification","seed":202610194035,"parameters":{"n":6,"init":[0],"halt":[5],"steps":[[0,1],[1,2],[2,5],[0,3],[2,1]],"trace":[0,4],"domain":"Fin_transition_model","operation":"model-trace-qualification","semantic_template":"qf-ext19-model-trace-qualification/{\"halt\":[5],\"init\":[0],\"n\":6,\"steps\":[[0,1],[0,3],[1,2],[2,1],[2,5]],\"trace\":[0,4]}"}},"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-r04-computational-model-0036","batch_id":"batch-20261013-advance-20261019-r04-computational-model-foundations","language":"zh-Hant","source_mko_ids":["mko-computational-model"],"title_zh":"有限轉移計算模型","stem_zh":"完整有限轉移模型。操作=model-trace-qualification；資料={\"n\":6,\"init\":[0],\"halt\":[5],\"steps\":[[0,1],[1,2],[2,5],[3,4],[2,1]],\"trace\":[0,1,2,5,5]}。請依 [trace,typed_mask,nonempty,initial,step_flags,continued_after_halt,valid] 欄序回答。","answer":{"kind":"expression","value":"([0, 1, 2, 5, 5], [是, 是, 是, 是, 是], 是, 是, [是, 是, 是, 否], 是, 否)","explanation_zh":"第二批擴展核對=([0, 1, 2, 5, 5], [是, 是, 是, 是, 是], 是, 是, [是, 是, 是, 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；halt與stuck分離；有限prefix不證一般終止。"},"difficulty":{"band":"undergraduate_core","level":2,"skills":["有限轉移計算模型"]},"variant":{"family_id":"qf-ext19-model-trace-qualification","seed":202610194036,"parameters":{"n":6,"init":[0],"halt":[5],"steps":[[0,1],[1,2],[2,5],[3,4],[2,1]],"trace":[0,1,2,5,5],"domain":"Fin_transition_model","operation":"model-trace-qualification","semantic_template":"qf-ext19-model-trace-qualification/{\"halt\":[5],\"init\":[0],\"n\":6,\"steps\":[[0,1],[1,2],[2,1],[2,5],[3,4]],\"trace\":[0,1,2,5,5]}"}},"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-r04-computational-model-0037","batch_id":"batch-20261013-advance-20261019-r04-computational-model-foundations","language":"zh-Hant","source_mko_ids":["mko-computational-model"],"title_zh":"有限轉移計算模型","stem_zh":"完整有限轉移模型。操作=model-trace-qualification；資料={\"n\":6,\"init\":[0],\"halt\":[5],\"steps\":[[0,1],[1,2],[2,5],[0,3],[3,4],[2,1]],\"trace\":[0,6]}。請依 [trace,typed_mask,nonempty,initial,step_flags,continued_after_halt,valid] 欄序回答。","answer":{"kind":"expression","value":"([0, 6], [是, 否], 是, 是, [否], 否, 否)","explanation_zh":"第二批擴展核對=([0, 6], [是, 否], 是, 是, [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；halt與stuck分離；有限prefix不證一般終止。"},"difficulty":{"band":"undergraduate_core","level":2,"skills":["有限轉移計算模型"]},"variant":{"family_id":"qf-ext19-model-trace-qualification","seed":202610194037,"parameters":{"n":6,"init":[0],"halt":[5],"steps":[[0,1],[1,2],[2,5],[0,3],[3,4],[2,1]],"trace":[0,6],"domain":"Fin_transition_model","operation":"model-trace-qualification","semantic_template":"qf-ext19-model-trace-qualification/{\"halt\":[5],\"init\":[0],\"n\":6,\"steps\":[[0,1],[0,3],[1,2],[2,1],[2,5],[3,4]],\"trace\":[0,6]}"}},"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-r04-computational-model-0038","batch_id":"batch-20261013-advance-20261019-r04-computational-model-foundations","language":"zh-Hant","source_mko_ids":["mko-computational-model"],"title_zh":"有限轉移計算模型","stem_zh":"完整有限轉移模型。操作=model-trace-qualification；資料={\"n\":6,\"init\":[0],\"halt\":[5],\"steps\":[[0,1],[1,2],[2,5],[4,5],[2,1]],\"trace\":[0,1,2,5]}。請依 [trace,typed_mask,nonempty,initial,step_flags,continued_after_halt,valid] 欄序回答。","answer":{"kind":"expression","value":"([0, 1, 2, 5], [是, 是, 是, 是], 是, 是, [是, 是, 是], 否, 是)","explanation_zh":"第二批擴展核對=([0, 1, 2, 5], [是, 是, 是, 是], 是, 是, [是, 是, 是], 否, 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；halt與stuck分離；有限prefix不證一般終止。"},"difficulty":{"band":"undergraduate_core","level":2,"skills":["有限轉移計算模型"]},"variant":{"family_id":"qf-ext19-model-trace-qualification","seed":202610194038,"parameters":{"n":6,"init":[0],"halt":[5],"steps":[[0,1],[1,2],[2,5],[4,5],[2,1]],"trace":[0,1,2,5],"domain":"Fin_transition_model","operation":"model-trace-qualification","semantic_template":"qf-ext19-model-trace-qualification/{\"halt\":[5],\"init\":[0],\"n\":6,\"steps\":[[0,1],[1,2],[2,1],[2,5],[4,5]],\"trace\":[0,1,2,5]}"}},"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-r04-computational-model-0039","batch_id":"batch-20261013-advance-20261019-r04-computational-model-foundations","language":"zh-Hant","source_mko_ids":["mko-computational-model"],"title_zh":"有限轉移計算模型","stem_zh":"完整有限轉移模型。操作=model-trace-qualification；資料={\"n\":6,\"init\":[0],\"halt\":[5],\"steps\":[[0,1],[1,2],[2,5],[0,3],[4,5],[2,1]],\"trace\":[0,4]}。請依 [trace,typed_mask,nonempty,initial,step_flags,continued_after_halt,valid] 欄序回答。","answer":{"kind":"expression","value":"([0, 4], [是, 是], 是, 是, [否], 否, 否)","explanation_zh":"第二批擴展核對=([0, 4], [是, 是], 是, 是, [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；halt與stuck分離；有限prefix不證一般終止。"},"difficulty":{"band":"undergraduate_core","level":2,"skills":["有限轉移計算模型"]},"variant":{"family_id":"qf-ext19-model-trace-qualification","seed":202610194039,"parameters":{"n":6,"init":[0],"halt":[5],"steps":[[0,1],[1,2],[2,5],[0,3],[4,5],[2,1]],"trace":[0,4],"domain":"Fin_transition_model","operation":"model-trace-qualification","semantic_template":"qf-ext19-model-trace-qualification/{\"halt\":[5],\"init\":[0],\"n\":6,\"steps\":[[0,1],[0,3],[1,2],[2,1],[2,5],[4,5]],\"trace\":[0,4]}"}},"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-r04-computational-model-0040","batch_id":"batch-20261013-advance-20261019-r04-computational-model-foundations","language":"zh-Hant","source_mko_ids":["mko-computational-model"],"title_zh":"有限轉移計算模型","stem_zh":"完整有限轉移模型。操作=model-trace-qualification；資料={\"n\":6,\"init\":[0],\"halt\":[5],\"steps\":[[0,1],[1,2],[2,5],[3,4],[4,5],[2,1]],\"trace\":[0,1,2,5,5]}。請依 [trace,typed_mask,nonempty,initial,step_flags,continued_after_halt,valid] 欄序回答。","answer":{"kind":"expression","value":"([0, 1, 2, 5, 5], [是, 是, 是, 是, 是], 是, 是, [是, 是, 是, 否], 是, 否)","explanation_zh":"第二批擴展核對=([0, 1, 2, 5, 5], [是, 是, 是, 是, 是], 是, 是, [是, 是, 是, 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；halt與stuck分離；有限prefix不證一般終止。"},"difficulty":{"band":"undergraduate_core","level":2,"skills":["有限轉移計算模型"]},"variant":{"family_id":"qf-ext19-model-trace-qualification","seed":202610194040,"parameters":{"n":6,"init":[0],"halt":[5],"steps":[[0,1],[1,2],[2,5],[3,4],[4,5],[2,1]],"trace":[0,1,2,5,5],"domain":"Fin_transition_model","operation":"model-trace-qualification","semantic_template":"qf-ext19-model-trace-qualification/{\"halt\":[5],\"init\":[0],\"n\":6,\"steps\":[[0,1],[1,2],[2,1],[2,5],[3,4],[4,5]],\"trace\":[0,1,2,5,5]}"}},"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-r04-computational-model-0041","batch_id":"batch-20261013-advance-20261019-r04-computational-model-foundations","language":"zh-Hant","source_mko_ids":["mko-computational-model"],"title_zh":"有限轉移計算模型","stem_zh":"完整有限轉移模型。操作=model-trace-qualification；資料={\"n\":6,\"init\":[0],\"halt\":[5],\"steps\":[[0,1],[1,2],[2,5],[0,3],[3,4],[4,5],[2,1]],\"trace\":[0,6]}。請依 [trace,typed_mask,nonempty,initial,step_flags,continued_after_halt,valid] 欄序回答。","answer":{"kind":"expression","value":"([0, 6], [是, 否], 是, 是, [否], 否, 否)","explanation_zh":"第二批擴展核對=([0, 6], [是, 否], 是, 是, [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；halt與stuck分離；有限prefix不證一般終止。"},"difficulty":{"band":"undergraduate_core","level":2,"skills":["有限轉移計算模型"]},"variant":{"family_id":"qf-ext19-model-trace-qualification","seed":202610194041,"parameters":{"n":6,"init":[0],"halt":[5],"steps":[[0,1],[1,2],[2,5],[0,3],[3,4],[4,5],[2,1]],"trace":[0,6],"domain":"Fin_transition_model","operation":"model-trace-qualification","semantic_template":"qf-ext19-model-trace-qualification/{\"halt\":[5],\"init\":[0],\"n\":6,\"steps\":[[0,1],[0,3],[1,2],[2,1],[2,5],[3,4],[4,5]],\"trace\":[0,6]}"}},"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-r04-computational-model-0042","batch_id":"batch-20261013-advance-20261019-r04-computational-model-foundations","language":"zh-Hant","source_mko_ids":["mko-computational-model"],"title_zh":"有限轉移計算模型","stem_zh":"完整有限轉移模型。操作=model-trace-qualification；資料={\"n\":6,\"init\":[0],\"halt\":[5],\"steps\":[[0,1],[1,2],[2,5],[1,1]],\"trace\":[0,1,2,5]}。請依 [trace,typed_mask,nonempty,initial,step_flags,continued_after_halt,valid] 欄序回答。","answer":{"kind":"expression","value":"([0, 1, 2, 5], [是, 是, 是, 是], 是, 是, [是, 是, 是], 否, 是)","explanation_zh":"第二批擴展核對=([0, 1, 2, 5], [是, 是, 是, 是], 是, 是, [是, 是, 是], 否, 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；halt與stuck分離；有限prefix不證一般終止。"},"difficulty":{"band":"undergraduate_core","level":2,"skills":["有限轉移計算模型"]},"variant":{"family_id":"qf-ext19-model-trace-qualification","seed":202610194042,"parameters":{"n":6,"init":[0],"halt":[5],"steps":[[0,1],[1,2],[2,5],[1,1]],"trace":[0,1,2,5],"domain":"Fin_transition_model","operation":"model-trace-qualification","semantic_template":"qf-ext19-model-trace-qualification/{\"halt\":[5],\"init\":[0],\"n\":6,\"steps\":[[0,1],[1,1],[1,2],[2,5]],\"trace\":[0,1,2,5]}"}},"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-r04-computational-model-0043","batch_id":"batch-20261013-advance-20261019-r04-computational-model-foundations","language":"zh-Hant","source_mko_ids":["mko-computational-model"],"title_zh":"有限轉移計算模型","stem_zh":"完整有限轉移模型。操作=model-trace-qualification；資料={\"n\":6,\"init\":[0],\"halt\":[5],\"steps\":[[0,1],[1,2],[2,5],[0,3],[1,1]],\"trace\":[0,4]}。請依 [trace,typed_mask,nonempty,initial,step_flags,continued_after_halt,valid] 欄序回答。","answer":{"kind":"expression","value":"([0, 4], [是, 是], 是, 是, [否], 否, 否)","explanation_zh":"第二批擴展核對=([0, 4], [是, 是], 是, 是, [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；halt與stuck分離；有限prefix不證一般終止。"},"difficulty":{"band":"undergraduate_core","level":3,"skills":["有限轉移計算模型"]},"variant":{"family_id":"qf-ext19-model-trace-qualification","seed":202610194043,"parameters":{"n":6,"init":[0],"halt":[5],"steps":[[0,1],[1,2],[2,5],[0,3],[1,1]],"trace":[0,4],"domain":"Fin_transition_model","operation":"model-trace-qualification","semantic_template":"qf-ext19-model-trace-qualification/{\"halt\":[5],\"init\":[0],\"n\":6,\"steps\":[[0,1],[0,3],[1,1],[1,2],[2,5]],\"trace\":[0,4]}"}},"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-r04-computational-model-0044","batch_id":"batch-20261013-advance-20261019-r04-computational-model-foundations","language":"zh-Hant","source_mko_ids":["mko-computational-model"],"title_zh":"有限轉移計算模型","stem_zh":"完整有限轉移模型。操作=model-trace-qualification；資料={\"n\":6,\"init\":[0],\"halt\":[5],\"steps\":[[0,1],[1,2],[2,5],[3,4],[1,1]],\"trace\":[0,1,2,5,5]}。請依 [trace,typed_mask,nonempty,initial,step_flags,continued_after_halt,valid] 欄序回答。","answer":{"kind":"expression","value":"([0, 1, 2, 5, 5], [是, 是, 是, 是, 是], 是, 是, [是, 是, 是, 否], 是, 否)","explanation_zh":"第二批擴展核對=([0, 1, 2, 5, 5], [是, 是, 是, 是, 是], 是, 是, [是, 是, 是, 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；halt與stuck分離；有限prefix不證一般終止。"},"difficulty":{"band":"undergraduate_core","level":3,"skills":["有限轉移計算模型"]},"variant":{"family_id":"qf-ext19-model-trace-qualification","seed":202610194044,"parameters":{"n":6,"init":[0],"halt":[5],"steps":[[0,1],[1,2],[2,5],[3,4],[1,1]],"trace":[0,1,2,5,5],"domain":"Fin_transition_model","operation":"model-trace-qualification","semantic_template":"qf-ext19-model-trace-qualification/{\"halt\":[5],\"init\":[0],\"n\":6,\"steps\":[[0,1],[1,1],[1,2],[2,5],[3,4]],\"trace\":[0,1,2,5,5]}"}},"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-r04-computational-model-0045","batch_id":"batch-20261013-advance-20261019-r04-computational-model-foundations","language":"zh-Hant","source_mko_ids":["mko-computational-model"],"title_zh":"有限轉移計算模型","stem_zh":"完整有限轉移模型。操作=model-trace-qualification；資料={\"n\":6,\"init\":[0],\"halt\":[5],\"steps\":[[0,1],[1,2],[2,5],[0,3],[3,4],[1,1]],\"trace\":[0,6]}。請依 [trace,typed_mask,nonempty,initial,step_flags,continued_after_halt,valid] 欄序回答。","answer":{"kind":"expression","value":"([0, 6], [是, 否], 是, 是, [否], 否, 否)","explanation_zh":"第二批擴展核對=([0, 6], [是, 否], 是, 是, [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；halt與stuck分離；有限prefix不證一般終止。"},"difficulty":{"band":"undergraduate_core","level":3,"skills":["有限轉移計算模型"]},"variant":{"family_id":"qf-ext19-model-trace-qualification","seed":202610194045,"parameters":{"n":6,"init":[0],"halt":[5],"steps":[[0,1],[1,2],[2,5],[0,3],[3,4],[1,1]],"trace":[0,6],"domain":"Fin_transition_model","operation":"model-trace-qualification","semantic_template":"qf-ext19-model-trace-qualification/{\"halt\":[5],\"init\":[0],\"n\":6,\"steps\":[[0,1],[0,3],[1,1],[1,2],[2,5],[3,4]],\"trace\":[0,6]}"}},"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-r04-computational-model-0046","batch_id":"batch-20261013-advance-20261019-r04-computational-model-foundations","language":"zh-Hant","source_mko_ids":["mko-computational-model"],"title_zh":"有限轉移計算模型","stem_zh":"完整有限轉移模型。操作=model-trace-qualification；資料={\"n\":6,\"init\":[0],\"halt\":[5],\"steps\":[[0,1],[1,2],[2,5],[4,5],[1,1]],\"trace\":[0,1,2,5]}。請依 [trace,typed_mask,nonempty,initial,step_flags,continued_after_halt,valid] 欄序回答。","answer":{"kind":"expression","value":"([0, 1, 2, 5], [是, 是, 是, 是], 是, 是, [是, 是, 是], 否, 是)","explanation_zh":"第二批擴展核對=([0, 1, 2, 5], [是, 是, 是, 是], 是, 是, [是, 是, 是], 否, 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；halt與stuck分離；有限prefix不證一般終止。"},"difficulty":{"band":"undergraduate_core","level":3,"skills":["有限轉移計算模型"]},"variant":{"family_id":"qf-ext19-model-trace-qualification","seed":202610194046,"parameters":{"n":6,"init":[0],"halt":[5],"steps":[[0,1],[1,2],[2,5],[4,5],[1,1]],"trace":[0,1,2,5],"domain":"Fin_transition_model","operation":"model-trace-qualification","semantic_template":"qf-ext19-model-trace-qualification/{\"halt\":[5],\"init\":[0],\"n\":6,\"steps\":[[0,1],[1,1],[1,2],[2,5],[4,5]],\"trace\":[0,1,2,5]}"}},"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-r04-computational-model-0047","batch_id":"batch-20261013-advance-20261019-r04-computational-model-foundations","language":"zh-Hant","source_mko_ids":["mko-computational-model"],"title_zh":"有限轉移計算模型","stem_zh":"完整有限轉移模型。操作=model-trace-qualification；資料={\"n\":6,\"init\":[0],\"halt\":[5],\"steps\":[[0,1],[1,2],[2,5],[0,3],[4,5],[1,1]],\"trace\":[0,4]}。請依 [trace,typed_mask,nonempty,initial,step_flags,continued_after_halt,valid] 欄序回答。","answer":{"kind":"expression","value":"([0, 4], [是, 是], 是, 是, [否], 否, 否)","explanation_zh":"第二批擴展核對=([0, 4], [是, 是], 是, 是, [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；halt與stuck分離；有限prefix不證一般終止。"},"difficulty":{"band":"undergraduate_core","level":3,"skills":["有限轉移計算模型"]},"variant":{"family_id":"qf-ext19-model-trace-qualification","seed":202610194047,"parameters":{"n":6,"init":[0],"halt":[5],"steps":[[0,1],[1,2],[2,5],[0,3],[4,5],[1,1]],"trace":[0,4],"domain":"Fin_transition_model","operation":"model-trace-qualification","semantic_template":"qf-ext19-model-trace-qualification/{\"halt\":[5],\"init\":[0],\"n\":6,\"steps\":[[0,1],[0,3],[1,1],[1,2],[2,5],[4,5]],\"trace\":[0,4]}"}},"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-r04-computational-model-0048","batch_id":"batch-20261013-advance-20261019-r04-computational-model-foundations","language":"zh-Hant","source_mko_ids":["mko-computational-model"],"title_zh":"有限轉移計算模型","stem_zh":"完整有限轉移模型。操作=model-trace-qualification；資料={\"n\":6,\"init\":[0],\"halt\":[5],\"steps\":[[0,1],[1,2],[2,5],[3,4],[4,5],[1,1]],\"trace\":[0,1,2,5,5]}。請依 [trace,typed_mask,nonempty,initial,step_flags,continued_after_halt,valid] 欄序回答。","answer":{"kind":"expression","value":"([0, 1, 2, 5, 5], [是, 是, 是, 是, 是], 是, 是, [是, 是, 是, 否], 是, 否)","explanation_zh":"第二批擴展核對=([0, 1, 2, 5, 5], [是, 是, 是, 是, 是], 是, 是, [是, 是, 是, 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；halt與stuck分離；有限prefix不證一般終止。"},"difficulty":{"band":"undergraduate_core","level":3,"skills":["有限轉移計算模型"]},"variant":{"family_id":"qf-ext19-model-trace-qualification","seed":202610194048,"parameters":{"n":6,"init":[0],"halt":[5],"steps":[[0,1],[1,2],[2,5],[3,4],[4,5],[1,1]],"trace":[0,1,2,5,5],"domain":"Fin_transition_model","operation":"model-trace-qualification","semantic_template":"qf-ext19-model-trace-qualification/{\"halt\":[5],\"init\":[0],\"n\":6,\"steps\":[[0,1],[1,1],[1,2],[2,5],[3,4],[4,5]],\"trace\":[0,1,2,5,5]}"}},"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-r04-computational-model-0049","batch_id":"batch-20261013-advance-20261019-r04-computational-model-foundations","language":"zh-Hant","source_mko_ids":["mko-computational-model"],"title_zh":"有限轉移計算模型","stem_zh":"完整有限轉移模型。操作=model-trace-qualification；資料={\"n\":6,\"init\":[0],\"halt\":[5],\"steps\":[[0,1],[1,2],[2,5],[0,3],[3,4],[4,5],[1,1]],\"trace\":[0,6]}。請依 [trace,typed_mask,nonempty,initial,step_flags,continued_after_halt,valid] 欄序回答。","answer":{"kind":"expression","value":"([0, 6], [是, 否], 是, 是, [否], 否, 否)","explanation_zh":"第二批擴展核對=([0, 6], [是, 否], 是, 是, [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；halt與stuck分離；有限prefix不證一般終止。"},"difficulty":{"band":"undergraduate_core","level":3,"skills":["有限轉移計算模型"]},"variant":{"family_id":"qf-ext19-model-trace-qualification","seed":202610194049,"parameters":{"n":6,"init":[0],"halt":[5],"steps":[[0,1],[1,2],[2,5],[0,3],[3,4],[4,5],[1,1]],"trace":[0,6],"domain":"Fin_transition_model","operation":"model-trace-qualification","semantic_template":"qf-ext19-model-trace-qualification/{\"halt\":[5],\"init\":[0],\"n\":6,\"steps\":[[0,1],[0,3],[1,1],[1,2],[2,5],[3,4],[4,5]],\"trace\":[0,6]}"}},"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-r04-computational-model-0050","batch_id":"batch-20261013-advance-20261019-r04-computational-model-foundations","language":"zh-Hant","source_mko_ids":["mko-computational-model"],"title_zh":"有限轉移計算模型","stem_zh":"完整有限轉移模型。操作=model-trace-qualification；資料={\"n\":6,\"init\":[0],\"halt\":[5],\"steps\":[[0,1],[1,2],[2,5],[2,1],[1,1]],\"trace\":[0,1,2,5]}。請依 [trace,typed_mask,nonempty,initial,step_flags,continued_after_halt,valid] 欄序回答。","answer":{"kind":"expression","value":"([0, 1, 2, 5], [是, 是, 是, 是], 是, 是, [是, 是, 是], 否, 是)","explanation_zh":"第二批擴展核對=([0, 1, 2, 5], [是, 是, 是, 是], 是, 是, [是, 是, 是], 否, 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；halt與stuck分離；有限prefix不證一般終止。"},"difficulty":{"band":"undergraduate_core","level":3,"skills":["有限轉移計算模型"]},"variant":{"family_id":"qf-ext19-model-trace-qualification","seed":202610194050,"parameters":{"n":6,"init":[0],"halt":[5],"steps":[[0,1],[1,2],[2,5],[2,1],[1,1]],"trace":[0,1,2,5],"domain":"Fin_transition_model","operation":"model-trace-qualification","semantic_template":"qf-ext19-model-trace-qualification/{\"halt\":[5],\"init\":[0],\"n\":6,\"steps\":[[0,1],[1,1],[1,2],[2,1],[2,5]],\"trace\":[0,1,2,5]}"}},"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-r04-computational-model-0051","batch_id":"batch-20261013-advance-20261019-r04-computational-model-foundations","language":"zh-Hant","source_mko_ids":["mko-computational-model"],"title_zh":"有限轉移計算模型","stem_zh":"完整有限轉移模型。操作=model-halt-stuck-classification；資料={\"n\":6,\"init\":[0],\"halt\":[5],\"steps\":[[0,1],[1,2],[2,5]]}。請依 [reachable,reachable_halt,reachable_stuck,reachable_active] 欄序回答。","answer":{"kind":"expression","value":"([0, 1, 2, 5], [5], [], [0, 1, 2])","explanation_zh":"第二批擴展核對=([0, 1, 2, 5], [5], [], [0, 1, 2])；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；halt與stuck分離；有限prefix不證一般終止。"},"difficulty":{"band":"undergraduate_core","level":1,"skills":["有限轉移計算模型"]},"variant":{"family_id":"qf-ext19-model-halt-stuck-classification","seed":202610194051,"parameters":{"n":6,"init":[0],"halt":[5],"steps":[[0,1],[1,2],[2,5]],"domain":"Fin_transition_model","operation":"model-halt-stuck-classification","semantic_template":"qf-ext19-model-halt-stuck-classification/{\"halt\":[5],\"init\":[0],\"n\":6,\"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-r04-computational-model-0052","batch_id":"batch-20261013-advance-20261019-r04-computational-model-foundations","language":"zh-Hant","source_mko_ids":["mko-computational-model"],"title_zh":"有限轉移計算模型","stem_zh":"完整有限轉移模型。操作=model-halt-stuck-classification；資料={\"n\":6,\"init\":[0],\"halt\":[5],\"steps\":[[0,1],[1,2],[2,5],[0,3]]}。請依 [reachable,reachable_halt,reachable_stuck,reachable_active] 欄序回答。","answer":{"kind":"expression","value":"([0, 1, 2, 3, 5], [5], [3], [0, 1, 2])","explanation_zh":"第二批擴展核對=([0, 1, 2, 3, 5], [5], [3], [0, 1, 2])；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；halt與stuck分離；有限prefix不證一般終止。"},"difficulty":{"band":"undergraduate_core","level":1,"skills":["有限轉移計算模型"]},"variant":{"family_id":"qf-ext19-model-halt-stuck-classification","seed":202610194052,"parameters":{"n":6,"init":[0],"halt":[5],"steps":[[0,1],[1,2],[2,5],[0,3]],"domain":"Fin_transition_model","operation":"model-halt-stuck-classification","semantic_template":"qf-ext19-model-halt-stuck-classification/{\"halt\":[5],\"init\":[0],\"n\":6,\"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-r04-computational-model-0053","batch_id":"batch-20261013-advance-20261019-r04-computational-model-foundations","language":"zh-Hant","source_mko_ids":["mko-computational-model"],"title_zh":"有限轉移計算模型","stem_zh":"完整有限轉移模型。操作=model-halt-stuck-classification；資料={\"n\":6,\"init\":[0],\"halt\":[5],\"steps\":[[0,1],[1,2],[2,5],[3,4]]}。請依 [reachable,reachable_halt,reachable_stuck,reachable_active] 欄序回答。","answer":{"kind":"expression","value":"([0, 1, 2, 5], [5], [], [0, 1, 2])","explanation_zh":"第二批擴展核對=([0, 1, 2, 5], [5], [], [0, 1, 2])；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；halt與stuck分離；有限prefix不證一般終止。"},"difficulty":{"band":"undergraduate_core","level":1,"skills":["有限轉移計算模型"]},"variant":{"family_id":"qf-ext19-model-halt-stuck-classification","seed":202610194053,"parameters":{"n":6,"init":[0],"halt":[5],"steps":[[0,1],[1,2],[2,5],[3,4]],"domain":"Fin_transition_model","operation":"model-halt-stuck-classification","semantic_template":"qf-ext19-model-halt-stuck-classification/{\"halt\":[5],\"init\":[0],\"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-r04-computational-model-0054","batch_id":"batch-20261013-advance-20261019-r04-computational-model-foundations","language":"zh-Hant","source_mko_ids":["mko-computational-model"],"title_zh":"有限轉移計算模型","stem_zh":"完整有限轉移模型。操作=model-halt-stuck-classification；資料={\"n\":6,\"init\":[0],\"halt\":[5],\"steps\":[[0,1],[1,2],[2,5],[0,3],[3,4]]}。請依 [reachable,reachable_halt,reachable_stuck,reachable_active] 欄序回答。","answer":{"kind":"expression","value":"([0, 1, 2, 3, 4, 5], [5], [4], [0, 1, 2, 3])","explanation_zh":"第二批擴展核對=([0, 1, 2, 3, 4, 5], [5], [4], [0, 1, 2, 3])；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；halt與stuck分離；有限prefix不證一般終止。"},"difficulty":{"band":"undergraduate_core","level":1,"skills":["有限轉移計算模型"]},"variant":{"family_id":"qf-ext19-model-halt-stuck-classification","seed":202610194054,"parameters":{"n":6,"init":[0],"halt":[5],"steps":[[0,1],[1,2],[2,5],[0,3],[3,4]],"domain":"Fin_transition_model","operation":"model-halt-stuck-classification","semantic_template":"qf-ext19-model-halt-stuck-classification/{\"halt\":[5],\"init\":[0],\"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-r04-computational-model-0055","batch_id":"batch-20261013-advance-20261019-r04-computational-model-foundations","language":"zh-Hant","source_mko_ids":["mko-computational-model"],"title_zh":"有限轉移計算模型","stem_zh":"完整有限轉移模型。操作=model-halt-stuck-classification；資料={\"n\":6,\"init\":[0],\"halt\":[5],\"steps\":[[0,1],[1,2],[2,5],[4,5]]}。請依 [reachable,reachable_halt,reachable_stuck,reachable_active] 欄序回答。","answer":{"kind":"expression","value":"([0, 1, 2, 5], [5], [], [0, 1, 2])","explanation_zh":"第二批擴展核對=([0, 1, 2, 5], [5], [], [0, 1, 2])；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；halt與stuck分離；有限prefix不證一般終止。"},"difficulty":{"band":"undergraduate_core","level":1,"skills":["有限轉移計算模型"]},"variant":{"family_id":"qf-ext19-model-halt-stuck-classification","seed":202610194055,"parameters":{"n":6,"init":[0],"halt":[5],"steps":[[0,1],[1,2],[2,5],[4,5]],"domain":"Fin_transition_model","operation":"model-halt-stuck-classification","semantic_template":"qf-ext19-model-halt-stuck-classification/{\"halt\":[5],\"init\":[0],\"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-r04-computational-model-0056","batch_id":"batch-20261013-advance-20261019-r04-computational-model-foundations","language":"zh-Hant","source_mko_ids":["mko-computational-model"],"title_zh":"有限轉移計算模型","stem_zh":"完整有限轉移模型。操作=model-halt-stuck-classification；資料={\"n\":6,\"init\":[0],\"halt\":[5],\"steps\":[[0,1],[1,2],[2,5],[0,3],[4,5]]}。請依 [reachable,reachable_halt,reachable_stuck,reachable_active] 欄序回答。","answer":{"kind":"expression","value":"([0, 1, 2, 3, 5], [5], [3], [0, 1, 2])","explanation_zh":"第二批擴展核對=([0, 1, 2, 3, 5], [5], [3], [0, 1, 2])；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；halt與stuck分離；有限prefix不證一般終止。"},"difficulty":{"band":"undergraduate_core","level":1,"skills":["有限轉移計算模型"]},"variant":{"family_id":"qf-ext19-model-halt-stuck-classification","seed":202610194056,"parameters":{"n":6,"init":[0],"halt":[5],"steps":[[0,1],[1,2],[2,5],[0,3],[4,5]],"domain":"Fin_transition_model","operation":"model-halt-stuck-classification","semantic_template":"qf-ext19-model-halt-stuck-classification/{\"halt\":[5],\"init\":[0],\"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-r04-computational-model-0057","batch_id":"batch-20261013-advance-20261019-r04-computational-model-foundations","language":"zh-Hant","source_mko_ids":["mko-computational-model"],"title_zh":"有限轉移計算模型","stem_zh":"完整有限轉移模型。操作=model-halt-stuck-classification；資料={\"n\":6,\"init\":[0],\"halt\":[5],\"steps\":[[0,1],[1,2],[2,5],[3,4],[4,5]]}。請依 [reachable,reachable_halt,reachable_stuck,reachable_active] 欄序回答。","answer":{"kind":"expression","value":"([0, 1, 2, 5], [5], [], [0, 1, 2])","explanation_zh":"第二批擴展核對=([0, 1, 2, 5], [5], [], [0, 1, 2])；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；halt與stuck分離；有限prefix不證一般終止。"},"difficulty":{"band":"undergraduate_core","level":1,"skills":["有限轉移計算模型"]},"variant":{"family_id":"qf-ext19-model-halt-stuck-classification","seed":202610194057,"parameters":{"n":6,"init":[0],"halt":[5],"steps":[[0,1],[1,2],[2,5],[3,4],[4,5]],"domain":"Fin_transition_model","operation":"model-halt-stuck-classification","semantic_template":"qf-ext19-model-halt-stuck-classification/{\"halt\":[5],\"init\":[0],\"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-r04-computational-model-0058","batch_id":"batch-20261013-advance-20261019-r04-computational-model-foundations","language":"zh-Hant","source_mko_ids":["mko-computational-model"],"title_zh":"有限轉移計算模型","stem_zh":"完整有限轉移模型。操作=model-halt-stuck-classification；資料={\"n\":6,\"init\":[0],\"halt\":[5],\"steps\":[[0,1],[1,2],[2,5],[0,3],[3,4],[4,5]]}。請依 [reachable,reachable_halt,reachable_stuck,reachable_active] 欄序回答。","answer":{"kind":"expression","value":"([0, 1, 2, 3, 4, 5], [5], [], [0, 1, 2, 3, 4])","explanation_zh":"第二批擴展核對=([0, 1, 2, 3, 4, 5], [5], [], [0, 1, 2, 3, 4])；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；halt與stuck分離；有限prefix不證一般終止。"},"difficulty":{"band":"undergraduate_core","level":1,"skills":["有限轉移計算模型"]},"variant":{"family_id":"qf-ext19-model-halt-stuck-classification","seed":202610194058,"parameters":{"n":6,"init":[0],"halt":[5],"steps":[[0,1],[1,2],[2,5],[0,3],[3,4],[4,5]],"domain":"Fin_transition_model","operation":"model-halt-stuck-classification","semantic_template":"qf-ext19-model-halt-stuck-classification/{\"halt\":[5],\"init\":[0],\"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"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261013-advance-20261019-r04-computational-model-0059","batch_id":"batch-20261013-advance-20261019-r04-computational-model-foundations","language":"zh-Hant","source_mko_ids":["mko-computational-model"],"title_zh":"有限轉移計算模型","stem_zh":"完整有限轉移模型。操作=model-halt-stuck-classification；資料={\"n\":6,\"init\":[0],\"halt\":[5],\"steps\":[[0,1],[1,2],[2,5],[2,1]]}。請依 [reachable,reachable_halt,reachable_stuck,reachable_active] 欄序回答。","answer":{"kind":"expression","value":"([0, 1, 2, 5], [5], [], [0, 1, 2])","explanation_zh":"第二批擴展核對=([0, 1, 2, 5], [5], [], [0, 1, 2])；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；halt與stuck分離；有限prefix不證一般終止。"},"difficulty":{"band":"undergraduate_core","level":2,"skills":["有限轉移計算模型"]},"variant":{"family_id":"qf-ext19-model-halt-stuck-classification","seed":202610194059,"parameters":{"n":6,"init":[0],"halt":[5],"steps":[[0,1],[1,2],[2,5],[2,1]],"domain":"Fin_transition_model","operation":"model-halt-stuck-classification","semantic_template":"qf-ext19-model-halt-stuck-classification/{\"halt\":[5],\"init\":[0],\"n\":6,\"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-r04-computational-model-0060","batch_id":"batch-20261013-advance-20261019-r04-computational-model-foundations","language":"zh-Hant","source_mko_ids":["mko-computational-model"],"title_zh":"有限轉移計算模型","stem_zh":"完整有限轉移模型。操作=model-halt-stuck-classification；資料={\"n\":6,\"init\":[0],\"halt\":[5],\"steps\":[[0,1],[1,2],[2,5],[0,3],[2,1]]}。請依 [reachable,reachable_halt,reachable_stuck,reachable_active] 欄序回答。","answer":{"kind":"expression","value":"([0, 1, 2, 3, 5], [5], [3], [0, 1, 2])","explanation_zh":"第二批擴展核對=([0, 1, 2, 3, 5], [5], [3], [0, 1, 2])；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；halt與stuck分離；有限prefix不證一般終止。"},"difficulty":{"band":"undergraduate_core","level":2,"skills":["有限轉移計算模型"]},"variant":{"family_id":"qf-ext19-model-halt-stuck-classification","seed":202610194060,"parameters":{"n":6,"init":[0],"halt":[5],"steps":[[0,1],[1,2],[2,5],[0,3],[2,1]],"domain":"Fin_transition_model","operation":"model-halt-stuck-classification","semantic_template":"qf-ext19-model-halt-stuck-classification/{\"halt\":[5],\"init\":[0],\"n\":6,\"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-r04-computational-model-0061","batch_id":"batch-20261013-advance-20261019-r04-computational-model-foundations","language":"zh-Hant","source_mko_ids":["mko-computational-model"],"title_zh":"有限轉移計算模型","stem_zh":"完整有限轉移模型。操作=model-halt-stuck-classification；資料={\"n\":6,\"init\":[0],\"halt\":[5],\"steps\":[[0,1],[1,2],[2,5],[3,4],[2,1]]}。請依 [reachable,reachable_halt,reachable_stuck,reachable_active] 欄序回答。","answer":{"kind":"expression","value":"([0, 1, 2, 5], [5], [], [0, 1, 2])","explanation_zh":"第二批擴展核對=([0, 1, 2, 5], [5], [], [0, 1, 2])；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；halt與stuck分離；有限prefix不證一般終止。"},"difficulty":{"band":"undergraduate_core","level":2,"skills":["有限轉移計算模型"]},"variant":{"family_id":"qf-ext19-model-halt-stuck-classification","seed":202610194061,"parameters":{"n":6,"init":[0],"halt":[5],"steps":[[0,1],[1,2],[2,5],[3,4],[2,1]],"domain":"Fin_transition_model","operation":"model-halt-stuck-classification","semantic_template":"qf-ext19-model-halt-stuck-classification/{\"halt\":[5],\"init\":[0],\"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-r04-computational-model-0062","batch_id":"batch-20261013-advance-20261019-r04-computational-model-foundations","language":"zh-Hant","source_mko_ids":["mko-computational-model"],"title_zh":"有限轉移計算模型","stem_zh":"完整有限轉移模型。操作=model-halt-stuck-classification；資料={\"n\":6,\"init\":[0],\"halt\":[5],\"steps\":[[0,1],[1,2],[2,5],[0,3],[3,4],[2,1]]}。請依 [reachable,reachable_halt,reachable_stuck,reachable_active] 欄序回答。","answer":{"kind":"expression","value":"([0, 1, 2, 3, 4, 5], [5], [4], [0, 1, 2, 3])","explanation_zh":"第二批擴展核對=([0, 1, 2, 3, 4, 5], [5], [4], [0, 1, 2, 3])；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；halt與stuck分離；有限prefix不證一般終止。"},"difficulty":{"band":"undergraduate_core","level":2,"skills":["有限轉移計算模型"]},"variant":{"family_id":"qf-ext19-model-halt-stuck-classification","seed":202610194062,"parameters":{"n":6,"init":[0],"halt":[5],"steps":[[0,1],[1,2],[2,5],[0,3],[3,4],[2,1]],"domain":"Fin_transition_model","operation":"model-halt-stuck-classification","semantic_template":"qf-ext19-model-halt-stuck-classification/{\"halt\":[5],\"init\":[0],\"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-r04-computational-model-0063","batch_id":"batch-20261013-advance-20261019-r04-computational-model-foundations","language":"zh-Hant","source_mko_ids":["mko-computational-model"],"title_zh":"有限轉移計算模型","stem_zh":"完整有限轉移模型。操作=model-halt-stuck-classification；資料={\"n\":6,\"init\":[0],\"halt\":[5],\"steps\":[[0,1],[1,2],[2,5],[4,5],[2,1]]}。請依 [reachable,reachable_halt,reachable_stuck,reachable_active] 欄序回答。","answer":{"kind":"expression","value":"([0, 1, 2, 5], [5], [], [0, 1, 2])","explanation_zh":"第二批擴展核對=([0, 1, 2, 5], [5], [], [0, 1, 2])；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；halt與stuck分離；有限prefix不證一般終止。"},"difficulty":{"band":"undergraduate_core","level":2,"skills":["有限轉移計算模型"]},"variant":{"family_id":"qf-ext19-model-halt-stuck-classification","seed":202610194063,"parameters":{"n":6,"init":[0],"halt":[5],"steps":[[0,1],[1,2],[2,5],[4,5],[2,1]],"domain":"Fin_transition_model","operation":"model-halt-stuck-classification","semantic_template":"qf-ext19-model-halt-stuck-classification/{\"halt\":[5],\"init\":[0],\"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-r04-computational-model-0064","batch_id":"batch-20261013-advance-20261019-r04-computational-model-foundations","language":"zh-Hant","source_mko_ids":["mko-computational-model"],"title_zh":"有限轉移計算模型","stem_zh":"完整有限轉移模型。操作=model-halt-stuck-classification；資料={\"n\":6,\"init\":[0],\"halt\":[5],\"steps\":[[0,1],[1,2],[2,5],[0,3],[4,5],[2,1]]}。請依 [reachable,reachable_halt,reachable_stuck,reachable_active] 欄序回答。","answer":{"kind":"expression","value":"([0, 1, 2, 3, 5], [5], [3], [0, 1, 2])","explanation_zh":"第二批擴展核對=([0, 1, 2, 3, 5], [5], [3], [0, 1, 2])；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；halt與stuck分離；有限prefix不證一般終止。"},"difficulty":{"band":"undergraduate_core","level":2,"skills":["有限轉移計算模型"]},"variant":{"family_id":"qf-ext19-model-halt-stuck-classification","seed":202610194064,"parameters":{"n":6,"init":[0],"halt":[5],"steps":[[0,1],[1,2],[2,5],[0,3],[4,5],[2,1]],"domain":"Fin_transition_model","operation":"model-halt-stuck-classification","semantic_template":"qf-ext19-model-halt-stuck-classification/{\"halt\":[5],\"init\":[0],\"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-r04-computational-model-0065","batch_id":"batch-20261013-advance-20261019-r04-computational-model-foundations","language":"zh-Hant","source_mko_ids":["mko-computational-model"],"title_zh":"有限轉移計算模型","stem_zh":"完整有限轉移模型。操作=model-halt-stuck-classification；資料={\"n\":6,\"init\":[0],\"halt\":[5],\"steps\":[[0,1],[1,2],[2,5],[3,4],[4,5],[2,1]]}。請依 [reachable,reachable_halt,reachable_stuck,reachable_active] 欄序回答。","answer":{"kind":"expression","value":"([0, 1, 2, 5], [5], [], [0, 1, 2])","explanation_zh":"第二批擴展核對=([0, 1, 2, 5], [5], [], [0, 1, 2])；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；halt與stuck分離；有限prefix不證一般終止。"},"difficulty":{"band":"undergraduate_core","level":2,"skills":["有限轉移計算模型"]},"variant":{"family_id":"qf-ext19-model-halt-stuck-classification","seed":202610194065,"parameters":{"n":6,"init":[0],"halt":[5],"steps":[[0,1],[1,2],[2,5],[3,4],[4,5],[2,1]],"domain":"Fin_transition_model","operation":"model-halt-stuck-classification","semantic_template":"qf-ext19-model-halt-stuck-classification/{\"halt\":[5],\"init\":[0],\"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-r04-computational-model-0066","batch_id":"batch-20261013-advance-20261019-r04-computational-model-foundations","language":"zh-Hant","source_mko_ids":["mko-computational-model"],"title_zh":"有限轉移計算模型","stem_zh":"完整有限轉移模型。操作=model-halt-stuck-classification；資料={\"n\":6,\"init\":[0],\"halt\":[5],\"steps\":[[0,1],[1,2],[2,5],[0,3],[3,4],[4,5],[2,1]]}。請依 [reachable,reachable_halt,reachable_stuck,reachable_active] 欄序回答。","answer":{"kind":"expression","value":"([0, 1, 2, 3, 4, 5], [5], [], [0, 1, 2, 3, 4])","explanation_zh":"第二批擴展核對=([0, 1, 2, 3, 4, 5], [5], [], [0, 1, 2, 3, 4])；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；halt與stuck分離；有限prefix不證一般終止。"},"difficulty":{"band":"undergraduate_core","level":2,"skills":["有限轉移計算模型"]},"variant":{"family_id":"qf-ext19-model-halt-stuck-classification","seed":202610194066,"parameters":{"n":6,"init":[0],"halt":[5],"steps":[[0,1],[1,2],[2,5],[0,3],[3,4],[4,5],[2,1]],"domain":"Fin_transition_model","operation":"model-halt-stuck-classification","semantic_template":"qf-ext19-model-halt-stuck-classification/{\"halt\":[5],\"init\":[0],\"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-r04-computational-model-0067","batch_id":"batch-20261013-advance-20261019-r04-computational-model-foundations","language":"zh-Hant","source_mko_ids":["mko-computational-model"],"title_zh":"有限轉移計算模型","stem_zh":"完整有限轉移模型。操作=model-halt-stuck-classification；資料={\"n\":6,\"init\":[0],\"halt\":[5],\"steps\":[[0,1],[1,2],[2,5],[1,1]]}。請依 [reachable,reachable_halt,reachable_stuck,reachable_active] 欄序回答。","answer":{"kind":"expression","value":"([0, 1, 2, 5], [5], [], [0, 1, 2])","explanation_zh":"第二批擴展核對=([0, 1, 2, 5], [5], [], [0, 1, 2])；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；halt與stuck分離；有限prefix不證一般終止。"},"difficulty":{"band":"undergraduate_core","level":2,"skills":["有限轉移計算模型"]},"variant":{"family_id":"qf-ext19-model-halt-stuck-classification","seed":202610194067,"parameters":{"n":6,"init":[0],"halt":[5],"steps":[[0,1],[1,2],[2,5],[1,1]],"domain":"Fin_transition_model","operation":"model-halt-stuck-classification","semantic_template":"qf-ext19-model-halt-stuck-classification/{\"halt\":[5],\"init\":[0],\"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-r04-computational-model-0068","batch_id":"batch-20261013-advance-20261019-r04-computational-model-foundations","language":"zh-Hant","source_mko_ids":["mko-computational-model"],"title_zh":"有限轉移計算模型","stem_zh":"完整有限轉移模型。操作=model-halt-stuck-classification；資料={\"n\":6,\"init\":[0],\"halt\":[5],\"steps\":[[0,1],[1,2],[2,5],[0,3],[1,1]]}。請依 [reachable,reachable_halt,reachable_stuck,reachable_active] 欄序回答。","answer":{"kind":"expression","value":"([0, 1, 2, 3, 5], [5], [3], [0, 1, 2])","explanation_zh":"第二批擴展核對=([0, 1, 2, 3, 5], [5], [3], [0, 1, 2])；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；halt與stuck分離；有限prefix不證一般終止。"},"difficulty":{"band":"undergraduate_core","level":3,"skills":["有限轉移計算模型"]},"variant":{"family_id":"qf-ext19-model-halt-stuck-classification","seed":202610194068,"parameters":{"n":6,"init":[0],"halt":[5],"steps":[[0,1],[1,2],[2,5],[0,3],[1,1]],"domain":"Fin_transition_model","operation":"model-halt-stuck-classification","semantic_template":"qf-ext19-model-halt-stuck-classification/{\"halt\":[5],\"init\":[0],\"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-r04-computational-model-0069","batch_id":"batch-20261013-advance-20261019-r04-computational-model-foundations","language":"zh-Hant","source_mko_ids":["mko-computational-model"],"title_zh":"有限轉移計算模型","stem_zh":"完整有限轉移模型。操作=model-halt-stuck-classification；資料={\"n\":6,\"init\":[0],\"halt\":[5],\"steps\":[[0,1],[1,2],[2,5],[3,4],[1,1]]}。請依 [reachable,reachable_halt,reachable_stuck,reachable_active] 欄序回答。","answer":{"kind":"expression","value":"([0, 1, 2, 5], [5], [], [0, 1, 2])","explanation_zh":"第二批擴展核對=([0, 1, 2, 5], [5], [], [0, 1, 2])；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；halt與stuck分離；有限prefix不證一般終止。"},"difficulty":{"band":"undergraduate_core","level":3,"skills":["有限轉移計算模型"]},"variant":{"family_id":"qf-ext19-model-halt-stuck-classification","seed":202610194069,"parameters":{"n":6,"init":[0],"halt":[5],"steps":[[0,1],[1,2],[2,5],[3,4],[1,1]],"domain":"Fin_transition_model","operation":"model-halt-stuck-classification","semantic_template":"qf-ext19-model-halt-stuck-classification/{\"halt\":[5],\"init\":[0],\"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-r04-computational-model-0070","batch_id":"batch-20261013-advance-20261019-r04-computational-model-foundations","language":"zh-Hant","source_mko_ids":["mko-computational-model"],"title_zh":"有限轉移計算模型","stem_zh":"完整有限轉移模型。操作=model-halt-stuck-classification；資料={\"n\":6,\"init\":[0],\"halt\":[5],\"steps\":[[0,1],[1,2],[2,5],[0,3],[3,4],[1,1]]}。請依 [reachable,reachable_halt,reachable_stuck,reachable_active] 欄序回答。","answer":{"kind":"expression","value":"([0, 1, 2, 3, 4, 5], [5], [4], [0, 1, 2, 3])","explanation_zh":"第二批擴展核對=([0, 1, 2, 3, 4, 5], [5], [4], [0, 1, 2, 3])；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；halt與stuck分離；有限prefix不證一般終止。"},"difficulty":{"band":"undergraduate_core","level":3,"skills":["有限轉移計算模型"]},"variant":{"family_id":"qf-ext19-model-halt-stuck-classification","seed":202610194070,"parameters":{"n":6,"init":[0],"halt":[5],"steps":[[0,1],[1,2],[2,5],[0,3],[3,4],[1,1]],"domain":"Fin_transition_model","operation":"model-halt-stuck-classification","semantic_template":"qf-ext19-model-halt-stuck-classification/{\"halt\":[5],\"init\":[0],\"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-r04-computational-model-0071","batch_id":"batch-20261013-advance-20261019-r04-computational-model-foundations","language":"zh-Hant","source_mko_ids":["mko-computational-model"],"title_zh":"有限轉移計算模型","stem_zh":"完整有限轉移模型。操作=model-halt-stuck-classification；資料={\"n\":6,\"init\":[0],\"halt\":[5],\"steps\":[[0,1],[1,2],[2,5],[4,5],[1,1]]}。請依 [reachable,reachable_halt,reachable_stuck,reachable_active] 欄序回答。","answer":{"kind":"expression","value":"([0, 1, 2, 5], [5], [], [0, 1, 2])","explanation_zh":"第二批擴展核對=([0, 1, 2, 5], [5], [], [0, 1, 2])；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；halt與stuck分離；有限prefix不證一般終止。"},"difficulty":{"band":"undergraduate_core","level":3,"skills":["有限轉移計算模型"]},"variant":{"family_id":"qf-ext19-model-halt-stuck-classification","seed":202610194071,"parameters":{"n":6,"init":[0],"halt":[5],"steps":[[0,1],[1,2],[2,5],[4,5],[1,1]],"domain":"Fin_transition_model","operation":"model-halt-stuck-classification","semantic_template":"qf-ext19-model-halt-stuck-classification/{\"halt\":[5],\"init\":[0],\"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-r04-computational-model-0072","batch_id":"batch-20261013-advance-20261019-r04-computational-model-foundations","language":"zh-Hant","source_mko_ids":["mko-computational-model"],"title_zh":"有限轉移計算模型","stem_zh":"完整有限轉移模型。操作=model-halt-stuck-classification；資料={\"n\":6,\"init\":[0],\"halt\":[5],\"steps\":[[0,1],[1,2],[2,5],[0,3],[4,5],[1,1]]}。請依 [reachable,reachable_halt,reachable_stuck,reachable_active] 欄序回答。","answer":{"kind":"expression","value":"([0, 1, 2, 3, 5], [5], [3], [0, 1, 2])","explanation_zh":"第二批擴展核對=([0, 1, 2, 3, 5], [5], [3], [0, 1, 2])；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；halt與stuck分離；有限prefix不證一般終止。"},"difficulty":{"band":"undergraduate_core","level":3,"skills":["有限轉移計算模型"]},"variant":{"family_id":"qf-ext19-model-halt-stuck-classification","seed":202610194072,"parameters":{"n":6,"init":[0],"halt":[5],"steps":[[0,1],[1,2],[2,5],[0,3],[4,5],[1,1]],"domain":"Fin_transition_model","operation":"model-halt-stuck-classification","semantic_template":"qf-ext19-model-halt-stuck-classification/{\"halt\":[5],\"init\":[0],\"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-r04-computational-model-0073","batch_id":"batch-20261013-advance-20261019-r04-computational-model-foundations","language":"zh-Hant","source_mko_ids":["mko-computational-model"],"title_zh":"有限轉移計算模型","stem_zh":"完整有限轉移模型。操作=model-halt-stuck-classification；資料={\"n\":6,\"init\":[0],\"halt\":[5],\"steps\":[[0,1],[1,2],[2,5],[3,4],[4,5],[1,1]]}。請依 [reachable,reachable_halt,reachable_stuck,reachable_active] 欄序回答。","answer":{"kind":"expression","value":"([0, 1, 2, 5], [5], [], [0, 1, 2])","explanation_zh":"第二批擴展核對=([0, 1, 2, 5], [5], [], [0, 1, 2])；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；halt與stuck分離；有限prefix不證一般終止。"},"difficulty":{"band":"undergraduate_core","level":3,"skills":["有限轉移計算模型"]},"variant":{"family_id":"qf-ext19-model-halt-stuck-classification","seed":202610194073,"parameters":{"n":6,"init":[0],"halt":[5],"steps":[[0,1],[1,2],[2,5],[3,4],[4,5],[1,1]],"domain":"Fin_transition_model","operation":"model-halt-stuck-classification","semantic_template":"qf-ext19-model-halt-stuck-classification/{\"halt\":[5],\"init\":[0],\"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-r04-computational-model-0074","batch_id":"batch-20261013-advance-20261019-r04-computational-model-foundations","language":"zh-Hant","source_mko_ids":["mko-computational-model"],"title_zh":"有限轉移計算模型","stem_zh":"完整有限轉移模型。操作=model-halt-stuck-classification；資料={\"n\":6,\"init\":[0],\"halt\":[5],\"steps\":[[0,1],[1,2],[2,5],[0,3],[3,4],[4,5],[1,1]]}。請依 [reachable,reachable_halt,reachable_stuck,reachable_active] 欄序回答。","answer":{"kind":"expression","value":"([0, 1, 2, 3, 4, 5], [5], [], [0, 1, 2, 3, 4])","explanation_zh":"第二批擴展核對=([0, 1, 2, 3, 4, 5], [5], [], [0, 1, 2, 3, 4])；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；halt與stuck分離；有限prefix不證一般終止。"},"difficulty":{"band":"undergraduate_core","level":3,"skills":["有限轉移計算模型"]},"variant":{"family_id":"qf-ext19-model-halt-stuck-classification","seed":202610194074,"parameters":{"n":6,"init":[0],"halt":[5],"steps":[[0,1],[1,2],[2,5],[0,3],[3,4],[4,5],[1,1]],"domain":"Fin_transition_model","operation":"model-halt-stuck-classification","semantic_template":"qf-ext19-model-halt-stuck-classification/{\"halt\":[5],\"init\":[0],\"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-r04-computational-model-0075","batch_id":"batch-20261013-advance-20261019-r04-computational-model-foundations","language":"zh-Hant","source_mko_ids":["mko-computational-model"],"title_zh":"有限轉移計算模型","stem_zh":"完整有限轉移模型。操作=model-halt-stuck-classification；資料={\"n\":6,\"init\":[0],\"halt\":[5],\"steps\":[[0,1],[1,2],[2,5],[2,1],[1,1]]}。請依 [reachable,reachable_halt,reachable_stuck,reachable_active] 欄序回答。","answer":{"kind":"expression","value":"([0, 1, 2, 5], [5], [], [0, 1, 2])","explanation_zh":"第二批擴展核對=([0, 1, 2, 5], [5], [], [0, 1, 2])；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；halt與stuck分離；有限prefix不證一般終止。"},"difficulty":{"band":"undergraduate_core","level":3,"skills":["有限轉移計算模型"]},"variant":{"family_id":"qf-ext19-model-halt-stuck-classification","seed":202610194075,"parameters":{"n":6,"init":[0],"halt":[5],"steps":[[0,1],[1,2],[2,5],[2,1],[1,1]],"domain":"Fin_transition_model","operation":"model-halt-stuck-classification","semantic_template":"qf-ext19-model-halt-stuck-classification/{\"halt\":[5],\"init\":[0],\"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-r04-computational-model-0076","batch_id":"batch-20261013-advance-20261019-r04-computational-model-foundations","language":"zh-Hant","source_mko_ids":["mko-computational-model"],"title_zh":"有限轉移計算模型","stem_zh":"完整有限轉移模型。操作=model-cycle-termination-risk；資料={\"n\":6,\"init\":[0],\"halt\":[5],\"steps\":[[0,1],[1,2],[2,5]]}。請依 [reachable,stuck,cycle,all_paths_halt,classification] 欄序回答。","answer":{"kind":"expression","value":"([0, 1, 2, 5], [], 否, 是, 有限模型全部路徑到達halt)","explanation_zh":"第二批擴展核對=([0, 1, 2, 5], [], 否, 是, 有限模型全部路徑到達halt)；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；halt與stuck分離；有限prefix不證一般終止。"},"difficulty":{"band":"undergraduate_core","level":1,"skills":["有限轉移計算模型"]},"variant":{"family_id":"qf-ext19-model-cycle-termination-risk","seed":202610194076,"parameters":{"n":6,"init":[0],"halt":[5],"steps":[[0,1],[1,2],[2,5]],"domain":"Fin_transition_model","operation":"model-cycle-termination-risk","semantic_template":"qf-ext19-model-cycle-termination-risk/{\"halt\":[5],\"init\":[0],\"n\":6,\"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-r04-computational-model-0077","batch_id":"batch-20261013-advance-20261019-r04-computational-model-foundations","language":"zh-Hant","source_mko_ids":["mko-computational-model"],"title_zh":"有限轉移計算模型","stem_zh":"完整有限轉移模型。操作=model-cycle-termination-risk；資料={\"n\":6,\"init\":[0],\"halt\":[5],\"steps\":[[0,1],[1,2],[2,5],[0,3]]}。請依 [reachable,stuck,cycle,all_paths_halt,classification] 欄序回答。","answer":{"kind":"expression","value":"([0, 1, 2, 3, 5], [3], 否, 否, reachable stuck非停止狀態)","explanation_zh":"第二批擴展核對=([0, 1, 2, 3, 5], [3], 否, 否, reachable stuck非停止狀態)；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；halt與stuck分離；有限prefix不證一般終止。"},"difficulty":{"band":"undergraduate_core","level":1,"skills":["有限轉移計算模型"]},"variant":{"family_id":"qf-ext19-model-cycle-termination-risk","seed":202610194077,"parameters":{"n":6,"init":[0],"halt":[5],"steps":[[0,1],[1,2],[2,5],[0,3]],"domain":"Fin_transition_model","operation":"model-cycle-termination-risk","semantic_template":"qf-ext19-model-cycle-termination-risk/{\"halt\":[5],\"init\":[0],\"n\":6,\"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-r04-computational-model-0078","batch_id":"batch-20261013-advance-20261019-r04-computational-model-foundations","language":"zh-Hant","source_mko_ids":["mko-computational-model"],"title_zh":"有限轉移計算模型","stem_zh":"完整有限轉移模型。操作=model-cycle-termination-risk；資料={\"n\":6,\"init\":[0],\"halt\":[5],\"steps\":[[0,1],[1,2],[2,5],[3,4]]}。請依 [reachable,stuck,cycle,all_paths_halt,classification] 欄序回答。","answer":{"kind":"expression","value":"([0, 1, 2, 5], [], 否, 是, 有限模型全部路徑到達halt)","explanation_zh":"第二批擴展核對=([0, 1, 2, 5], [], 否, 是, 有限模型全部路徑到達halt)；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；halt與stuck分離；有限prefix不證一般終止。"},"difficulty":{"band":"undergraduate_core","level":1,"skills":["有限轉移計算模型"]},"variant":{"family_id":"qf-ext19-model-cycle-termination-risk","seed":202610194078,"parameters":{"n":6,"init":[0],"halt":[5],"steps":[[0,1],[1,2],[2,5],[3,4]],"domain":"Fin_transition_model","operation":"model-cycle-termination-risk","semantic_template":"qf-ext19-model-cycle-termination-risk/{\"halt\":[5],\"init\":[0],\"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-r04-computational-model-0079","batch_id":"batch-20261013-advance-20261019-r04-computational-model-foundations","language":"zh-Hant","source_mko_ids":["mko-computational-model"],"title_zh":"有限轉移計算模型","stem_zh":"完整有限轉移模型。操作=model-cycle-termination-risk；資料={\"n\":6,\"init\":[0],\"halt\":[5],\"steps\":[[0,1],[1,2],[2,5],[0,3],[3,4]]}。請依 [reachable,stuck,cycle,all_paths_halt,classification] 欄序回答。","answer":{"kind":"expression","value":"([0, 1, 2, 3, 4, 5], [4], 否, 否, reachable stuck非停止狀態)","explanation_zh":"第二批擴展核對=([0, 1, 2, 3, 4, 5], [4], 否, 否, reachable stuck非停止狀態)；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；halt與stuck分離；有限prefix不證一般終止。"},"difficulty":{"band":"undergraduate_core","level":1,"skills":["有限轉移計算模型"]},"variant":{"family_id":"qf-ext19-model-cycle-termination-risk","seed":202610194079,"parameters":{"n":6,"init":[0],"halt":[5],"steps":[[0,1],[1,2],[2,5],[0,3],[3,4]],"domain":"Fin_transition_model","operation":"model-cycle-termination-risk","semantic_template":"qf-ext19-model-cycle-termination-risk/{\"halt\":[5],\"init\":[0],\"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-r04-computational-model-0080","batch_id":"batch-20261013-advance-20261019-r04-computational-model-foundations","language":"zh-Hant","source_mko_ids":["mko-computational-model"],"title_zh":"有限轉移計算模型","stem_zh":"完整有限轉移模型。操作=model-cycle-termination-risk；資料={\"n\":6,\"init\":[0],\"halt\":[5],\"steps\":[[0,1],[1,2],[2,5],[4,5]]}。請依 [reachable,stuck,cycle,all_paths_halt,classification] 欄序回答。","answer":{"kind":"expression","value":"([0, 1, 2, 5], [], 否, 是, 有限模型全部路徑到達halt)","explanation_zh":"第二批擴展核對=([0, 1, 2, 5], [], 否, 是, 有限模型全部路徑到達halt)；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；halt與stuck分離；有限prefix不證一般終止。"},"difficulty":{"band":"undergraduate_core","level":1,"skills":["有限轉移計算模型"]},"variant":{"family_id":"qf-ext19-model-cycle-termination-risk","seed":202610194080,"parameters":{"n":6,"init":[0],"halt":[5],"steps":[[0,1],[1,2],[2,5],[4,5]],"domain":"Fin_transition_model","operation":"model-cycle-termination-risk","semantic_template":"qf-ext19-model-cycle-termination-risk/{\"halt\":[5],\"init\":[0],\"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-r04-computational-model-0081","batch_id":"batch-20261013-advance-20261019-r04-computational-model-foundations","language":"zh-Hant","source_mko_ids":["mko-computational-model"],"title_zh":"有限轉移計算模型","stem_zh":"完整有限轉移模型。操作=model-cycle-termination-risk；資料={\"n\":6,\"init\":[0],\"halt\":[5],\"steps\":[[0,1],[1,2],[2,5],[0,3],[4,5]]}。請依 [reachable,stuck,cycle,all_paths_halt,classification] 欄序回答。","answer":{"kind":"expression","value":"([0, 1, 2, 3, 5], [3], 否, 否, reachable stuck非停止狀態)","explanation_zh":"第二批擴展核對=([0, 1, 2, 3, 5], [3], 否, 否, reachable stuck非停止狀態)；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；halt與stuck分離；有限prefix不證一般終止。"},"difficulty":{"band":"undergraduate_core","level":1,"skills":["有限轉移計算模型"]},"variant":{"family_id":"qf-ext19-model-cycle-termination-risk","seed":202610194081,"parameters":{"n":6,"init":[0],"halt":[5],"steps":[[0,1],[1,2],[2,5],[0,3],[4,5]],"domain":"Fin_transition_model","operation":"model-cycle-termination-risk","semantic_template":"qf-ext19-model-cycle-termination-risk/{\"halt\":[5],\"init\":[0],\"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-r04-computational-model-0082","batch_id":"batch-20261013-advance-20261019-r04-computational-model-foundations","language":"zh-Hant","source_mko_ids":["mko-computational-model"],"title_zh":"有限轉移計算模型","stem_zh":"完整有限轉移模型。操作=model-cycle-termination-risk；資料={\"n\":6,\"init\":[0],\"halt\":[5],\"steps\":[[0,1],[1,2],[2,5],[3,4],[4,5]]}。請依 [reachable,stuck,cycle,all_paths_halt,classification] 欄序回答。","answer":{"kind":"expression","value":"([0, 1, 2, 5], [], 否, 是, 有限模型全部路徑到達halt)","explanation_zh":"第二批擴展核對=([0, 1, 2, 5], [], 否, 是, 有限模型全部路徑到達halt)；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；halt與stuck分離；有限prefix不證一般終止。"},"difficulty":{"band":"undergraduate_core","level":1,"skills":["有限轉移計算模型"]},"variant":{"family_id":"qf-ext19-model-cycle-termination-risk","seed":202610194082,"parameters":{"n":6,"init":[0],"halt":[5],"steps":[[0,1],[1,2],[2,5],[3,4],[4,5]],"domain":"Fin_transition_model","operation":"model-cycle-termination-risk","semantic_template":"qf-ext19-model-cycle-termination-risk/{\"halt\":[5],\"init\":[0],\"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-r04-computational-model-0083","batch_id":"batch-20261013-advance-20261019-r04-computational-model-foundations","language":"zh-Hant","source_mko_ids":["mko-computational-model"],"title_zh":"有限轉移計算模型","stem_zh":"完整有限轉移模型。操作=model-cycle-termination-risk；資料={\"n\":6,\"init\":[0],\"halt\":[5],\"steps\":[[0,1],[1,2],[2,5],[0,3],[3,4],[4,5]]}。請依 [reachable,stuck,cycle,all_paths_halt,classification] 欄序回答。","answer":{"kind":"expression","value":"([0, 1, 2, 3, 4, 5], [], 否, 是, 有限模型全部路徑到達halt)","explanation_zh":"第二批擴展核對=([0, 1, 2, 3, 4, 5], [], 否, 是, 有限模型全部路徑到達halt)；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；halt與stuck分離；有限prefix不證一般終止。"},"difficulty":{"band":"undergraduate_core","level":1,"skills":["有限轉移計算模型"]},"variant":{"family_id":"qf-ext19-model-cycle-termination-risk","seed":202610194083,"parameters":{"n":6,"init":[0],"halt":[5],"steps":[[0,1],[1,2],[2,5],[0,3],[3,4],[4,5]],"domain":"Fin_transition_model","operation":"model-cycle-termination-risk","semantic_template":"qf-ext19-model-cycle-termination-risk/{\"halt\":[5],\"init\":[0],\"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"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261013-advance-20261019-r04-computational-model-0084","batch_id":"batch-20261013-advance-20261019-r04-computational-model-foundations","language":"zh-Hant","source_mko_ids":["mko-computational-model"],"title_zh":"有限轉移計算模型","stem_zh":"完整有限轉移模型。操作=model-cycle-termination-risk；資料={\"n\":6,\"init\":[0],\"halt\":[5],\"steps\":[[0,1],[1,2],[2,5],[2,1]]}。請依 [reachable,stuck,cycle,all_paths_halt,classification] 欄序回答。","answer":{"kind":"expression","value":"([0, 1, 2, 5], [], 是, 否, reachable非停止cycle)","explanation_zh":"第二批擴展核對=([0, 1, 2, 5], [], 是, 否, reachable非停止cycle)；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；halt與stuck分離；有限prefix不證一般終止。"},"difficulty":{"band":"undergraduate_core","level":2,"skills":["有限轉移計算模型"]},"variant":{"family_id":"qf-ext19-model-cycle-termination-risk","seed":202610194084,"parameters":{"n":6,"init":[0],"halt":[5],"steps":[[0,1],[1,2],[2,5],[2,1]],"domain":"Fin_transition_model","operation":"model-cycle-termination-risk","semantic_template":"qf-ext19-model-cycle-termination-risk/{\"halt\":[5],\"init\":[0],\"n\":6,\"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-r04-computational-model-0085","batch_id":"batch-20261013-advance-20261019-r04-computational-model-foundations","language":"zh-Hant","source_mko_ids":["mko-computational-model"],"title_zh":"有限轉移計算模型","stem_zh":"完整有限轉移模型。操作=model-cycle-termination-risk；資料={\"n\":6,\"init\":[0],\"halt\":[5],\"steps\":[[0,1],[1,2],[2,5],[0,3],[2,1]]}。請依 [reachable,stuck,cycle,all_paths_halt,classification] 欄序回答。","answer":{"kind":"expression","value":"([0, 1, 2, 3, 5], [3], 是, 否, reachable非停止cycle)","explanation_zh":"第二批擴展核對=([0, 1, 2, 3, 5], [3], 是, 否, reachable非停止cycle)；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；halt與stuck分離；有限prefix不證一般終止。"},"difficulty":{"band":"undergraduate_core","level":2,"skills":["有限轉移計算模型"]},"variant":{"family_id":"qf-ext19-model-cycle-termination-risk","seed":202610194085,"parameters":{"n":6,"init":[0],"halt":[5],"steps":[[0,1],[1,2],[2,5],[0,3],[2,1]],"domain":"Fin_transition_model","operation":"model-cycle-termination-risk","semantic_template":"qf-ext19-model-cycle-termination-risk/{\"halt\":[5],\"init\":[0],\"n\":6,\"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-r04-computational-model-0086","batch_id":"batch-20261013-advance-20261019-r04-computational-model-foundations","language":"zh-Hant","source_mko_ids":["mko-computational-model"],"title_zh":"有限轉移計算模型","stem_zh":"完整有限轉移模型。操作=model-cycle-termination-risk；資料={\"n\":6,\"init\":[0],\"halt\":[5],\"steps\":[[0,1],[1,2],[2,5],[3,4],[2,1]]}。請依 [reachable,stuck,cycle,all_paths_halt,classification] 欄序回答。","answer":{"kind":"expression","value":"([0, 1, 2, 5], [], 是, 否, reachable非停止cycle)","explanation_zh":"第二批擴展核對=([0, 1, 2, 5], [], 是, 否, reachable非停止cycle)；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；halt與stuck分離；有限prefix不證一般終止。"},"difficulty":{"band":"undergraduate_core","level":2,"skills":["有限轉移計算模型"]},"variant":{"family_id":"qf-ext19-model-cycle-termination-risk","seed":202610194086,"parameters":{"n":6,"init":[0],"halt":[5],"steps":[[0,1],[1,2],[2,5],[3,4],[2,1]],"domain":"Fin_transition_model","operation":"model-cycle-termination-risk","semantic_template":"qf-ext19-model-cycle-termination-risk/{\"halt\":[5],\"init\":[0],\"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-r04-computational-model-0087","batch_id":"batch-20261013-advance-20261019-r04-computational-model-foundations","language":"zh-Hant","source_mko_ids":["mko-computational-model"],"title_zh":"有限轉移計算模型","stem_zh":"完整有限轉移模型。操作=model-cycle-termination-risk；資料={\"n\":6,\"init\":[0],\"halt\":[5],\"steps\":[[0,1],[1,2],[2,5],[0,3],[3,4],[2,1]]}。請依 [reachable,stuck,cycle,all_paths_halt,classification] 欄序回答。","answer":{"kind":"expression","value":"([0, 1, 2, 3, 4, 5], [4], 是, 否, reachable非停止cycle)","explanation_zh":"第二批擴展核對=([0, 1, 2, 3, 4, 5], [4], 是, 否, reachable非停止cycle)；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；halt與stuck分離；有限prefix不證一般終止。"},"difficulty":{"band":"undergraduate_core","level":2,"skills":["有限轉移計算模型"]},"variant":{"family_id":"qf-ext19-model-cycle-termination-risk","seed":202610194087,"parameters":{"n":6,"init":[0],"halt":[5],"steps":[[0,1],[1,2],[2,5],[0,3],[3,4],[2,1]],"domain":"Fin_transition_model","operation":"model-cycle-termination-risk","semantic_template":"qf-ext19-model-cycle-termination-risk/{\"halt\":[5],\"init\":[0],\"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-r04-computational-model-0088","batch_id":"batch-20261013-advance-20261019-r04-computational-model-foundations","language":"zh-Hant","source_mko_ids":["mko-computational-model"],"title_zh":"有限轉移計算模型","stem_zh":"完整有限轉移模型。操作=model-cycle-termination-risk；資料={\"n\":6,\"init\":[0],\"halt\":[5],\"steps\":[[0,1],[1,2],[2,5],[4,5],[2,1]]}。請依 [reachable,stuck,cycle,all_paths_halt,classification] 欄序回答。","answer":{"kind":"expression","value":"([0, 1, 2, 5], [], 是, 否, reachable非停止cycle)","explanation_zh":"第二批擴展核對=([0, 1, 2, 5], [], 是, 否, reachable非停止cycle)；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；halt與stuck分離；有限prefix不證一般終止。"},"difficulty":{"band":"undergraduate_core","level":2,"skills":["有限轉移計算模型"]},"variant":{"family_id":"qf-ext19-model-cycle-termination-risk","seed":202610194088,"parameters":{"n":6,"init":[0],"halt":[5],"steps":[[0,1],[1,2],[2,5],[4,5],[2,1]],"domain":"Fin_transition_model","operation":"model-cycle-termination-risk","semantic_template":"qf-ext19-model-cycle-termination-risk/{\"halt\":[5],\"init\":[0],\"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-r04-computational-model-0089","batch_id":"batch-20261013-advance-20261019-r04-computational-model-foundations","language":"zh-Hant","source_mko_ids":["mko-computational-model"],"title_zh":"有限轉移計算模型","stem_zh":"完整有限轉移模型。操作=model-cycle-termination-risk；資料={\"n\":6,\"init\":[0],\"halt\":[5],\"steps\":[[0,1],[1,2],[2,5],[0,3],[4,5],[2,1]]}。請依 [reachable,stuck,cycle,all_paths_halt,classification] 欄序回答。","answer":{"kind":"expression","value":"([0, 1, 2, 3, 5], [3], 是, 否, reachable非停止cycle)","explanation_zh":"第二批擴展核對=([0, 1, 2, 3, 5], [3], 是, 否, reachable非停止cycle)；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；halt與stuck分離；有限prefix不證一般終止。"},"difficulty":{"band":"undergraduate_core","level":2,"skills":["有限轉移計算模型"]},"variant":{"family_id":"qf-ext19-model-cycle-termination-risk","seed":202610194089,"parameters":{"n":6,"init":[0],"halt":[5],"steps":[[0,1],[1,2],[2,5],[0,3],[4,5],[2,1]],"domain":"Fin_transition_model","operation":"model-cycle-termination-risk","semantic_template":"qf-ext19-model-cycle-termination-risk/{\"halt\":[5],\"init\":[0],\"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-r04-computational-model-0090","batch_id":"batch-20261013-advance-20261019-r04-computational-model-foundations","language":"zh-Hant","source_mko_ids":["mko-computational-model"],"title_zh":"有限轉移計算模型","stem_zh":"完整有限轉移模型。操作=model-cycle-termination-risk；資料={\"n\":6,\"init\":[0],\"halt\":[5],\"steps\":[[0,1],[1,2],[2,5],[3,4],[4,5],[2,1]]}。請依 [reachable,stuck,cycle,all_paths_halt,classification] 欄序回答。","answer":{"kind":"expression","value":"([0, 1, 2, 5], [], 是, 否, reachable非停止cycle)","explanation_zh":"第二批擴展核對=([0, 1, 2, 5], [], 是, 否, reachable非停止cycle)；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；halt與stuck分離；有限prefix不證一般終止。"},"difficulty":{"band":"undergraduate_core","level":2,"skills":["有限轉移計算模型"]},"variant":{"family_id":"qf-ext19-model-cycle-termination-risk","seed":202610194090,"parameters":{"n":6,"init":[0],"halt":[5],"steps":[[0,1],[1,2],[2,5],[3,4],[4,5],[2,1]],"domain":"Fin_transition_model","operation":"model-cycle-termination-risk","semantic_template":"qf-ext19-model-cycle-termination-risk/{\"halt\":[5],\"init\":[0],\"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-r04-computational-model-0091","batch_id":"batch-20261013-advance-20261019-r04-computational-model-foundations","language":"zh-Hant","source_mko_ids":["mko-computational-model"],"title_zh":"有限轉移計算模型","stem_zh":"完整有限轉移模型。操作=model-cycle-termination-risk；資料={\"n\":6,\"init\":[0],\"halt\":[5],\"steps\":[[0,1],[1,2],[2,5],[0,3],[3,4],[4,5],[2,1]]}。請依 [reachable,stuck,cycle,all_paths_halt,classification] 欄序回答。","answer":{"kind":"expression","value":"([0, 1, 2, 3, 4, 5], [], 是, 否, reachable非停止cycle)","explanation_zh":"第二批擴展核對=([0, 1, 2, 3, 4, 5], [], 是, 否, reachable非停止cycle)；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；halt與stuck分離；有限prefix不證一般終止。"},"difficulty":{"band":"undergraduate_core","level":2,"skills":["有限轉移計算模型"]},"variant":{"family_id":"qf-ext19-model-cycle-termination-risk","seed":202610194091,"parameters":{"n":6,"init":[0],"halt":[5],"steps":[[0,1],[1,2],[2,5],[0,3],[3,4],[4,5],[2,1]],"domain":"Fin_transition_model","operation":"model-cycle-termination-risk","semantic_template":"qf-ext19-model-cycle-termination-risk/{\"halt\":[5],\"init\":[0],\"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-r04-computational-model-0092","batch_id":"batch-20261013-advance-20261019-r04-computational-model-foundations","language":"zh-Hant","source_mko_ids":["mko-computational-model"],"title_zh":"有限轉移計算模型","stem_zh":"完整有限轉移模型。操作=model-cycle-termination-risk；資料={\"n\":6,\"init\":[0],\"halt\":[5],\"steps\":[[0,1],[1,2],[2,5],[1,1]]}。請依 [reachable,stuck,cycle,all_paths_halt,classification] 欄序回答。","answer":{"kind":"expression","value":"([0, 1, 2, 5], [], 是, 否, reachable非停止cycle)","explanation_zh":"第二批擴展核對=([0, 1, 2, 5], [], 是, 否, reachable非停止cycle)；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；halt與stuck分離；有限prefix不證一般終止。"},"difficulty":{"band":"undergraduate_core","level":2,"skills":["有限轉移計算模型"]},"variant":{"family_id":"qf-ext19-model-cycle-termination-risk","seed":202610194092,"parameters":{"n":6,"init":[0],"halt":[5],"steps":[[0,1],[1,2],[2,5],[1,1]],"domain":"Fin_transition_model","operation":"model-cycle-termination-risk","semantic_template":"qf-ext19-model-cycle-termination-risk/{\"halt\":[5],\"init\":[0],\"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-r04-computational-model-0093","batch_id":"batch-20261013-advance-20261019-r04-computational-model-foundations","language":"zh-Hant","source_mko_ids":["mko-computational-model"],"title_zh":"有限轉移計算模型","stem_zh":"完整有限轉移模型。操作=model-cycle-termination-risk；資料={\"n\":6,\"init\":[0],\"halt\":[5],\"steps\":[[0,1],[1,2],[2,5],[0,3],[1,1]]}。請依 [reachable,stuck,cycle,all_paths_halt,classification] 欄序回答。","answer":{"kind":"expression","value":"([0, 1, 2, 3, 5], [3], 是, 否, reachable非停止cycle)","explanation_zh":"第二批擴展核對=([0, 1, 2, 3, 5], [3], 是, 否, reachable非停止cycle)；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；halt與stuck分離；有限prefix不證一般終止。"},"difficulty":{"band":"undergraduate_core","level":3,"skills":["有限轉移計算模型"]},"variant":{"family_id":"qf-ext19-model-cycle-termination-risk","seed":202610194093,"parameters":{"n":6,"init":[0],"halt":[5],"steps":[[0,1],[1,2],[2,5],[0,3],[1,1]],"domain":"Fin_transition_model","operation":"model-cycle-termination-risk","semantic_template":"qf-ext19-model-cycle-termination-risk/{\"halt\":[5],\"init\":[0],\"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-r04-computational-model-0094","batch_id":"batch-20261013-advance-20261019-r04-computational-model-foundations","language":"zh-Hant","source_mko_ids":["mko-computational-model"],"title_zh":"有限轉移計算模型","stem_zh":"完整有限轉移模型。操作=model-cycle-termination-risk；資料={\"n\":6,\"init\":[0],\"halt\":[5],\"steps\":[[0,1],[1,2],[2,5],[3,4],[1,1]]}。請依 [reachable,stuck,cycle,all_paths_halt,classification] 欄序回答。","answer":{"kind":"expression","value":"([0, 1, 2, 5], [], 是, 否, reachable非停止cycle)","explanation_zh":"第二批擴展核對=([0, 1, 2, 5], [], 是, 否, reachable非停止cycle)；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；halt與stuck分離；有限prefix不證一般終止。"},"difficulty":{"band":"undergraduate_core","level":3,"skills":["有限轉移計算模型"]},"variant":{"family_id":"qf-ext19-model-cycle-termination-risk","seed":202610194094,"parameters":{"n":6,"init":[0],"halt":[5],"steps":[[0,1],[1,2],[2,5],[3,4],[1,1]],"domain":"Fin_transition_model","operation":"model-cycle-termination-risk","semantic_template":"qf-ext19-model-cycle-termination-risk/{\"halt\":[5],\"init\":[0],\"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-r04-computational-model-0095","batch_id":"batch-20261013-advance-20261019-r04-computational-model-foundations","language":"zh-Hant","source_mko_ids":["mko-computational-model"],"title_zh":"有限轉移計算模型","stem_zh":"完整有限轉移模型。操作=model-cycle-termination-risk；資料={\"n\":6,\"init\":[0],\"halt\":[5],\"steps\":[[0,1],[1,2],[2,5],[0,3],[3,4],[1,1]]}。請依 [reachable,stuck,cycle,all_paths_halt,classification] 欄序回答。","answer":{"kind":"expression","value":"([0, 1, 2, 3, 4, 5], [4], 是, 否, reachable非停止cycle)","explanation_zh":"第二批擴展核對=([0, 1, 2, 3, 4, 5], [4], 是, 否, reachable非停止cycle)；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；halt與stuck分離；有限prefix不證一般終止。"},"difficulty":{"band":"undergraduate_core","level":3,"skills":["有限轉移計算模型"]},"variant":{"family_id":"qf-ext19-model-cycle-termination-risk","seed":202610194095,"parameters":{"n":6,"init":[0],"halt":[5],"steps":[[0,1],[1,2],[2,5],[0,3],[3,4],[1,1]],"domain":"Fin_transition_model","operation":"model-cycle-termination-risk","semantic_template":"qf-ext19-model-cycle-termination-risk/{\"halt\":[5],\"init\":[0],\"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-r04-computational-model-0096","batch_id":"batch-20261013-advance-20261019-r04-computational-model-foundations","language":"zh-Hant","source_mko_ids":["mko-computational-model"],"title_zh":"有限轉移計算模型","stem_zh":"完整有限轉移模型。操作=model-cycle-termination-risk；資料={\"n\":6,\"init\":[0],\"halt\":[5],\"steps\":[[0,1],[1,2],[2,5],[4,5],[1,1]]}。請依 [reachable,stuck,cycle,all_paths_halt,classification] 欄序回答。","answer":{"kind":"expression","value":"([0, 1, 2, 5], [], 是, 否, reachable非停止cycle)","explanation_zh":"第二批擴展核對=([0, 1, 2, 5], [], 是, 否, reachable非停止cycle)；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；halt與stuck分離；有限prefix不證一般終止。"},"difficulty":{"band":"undergraduate_core","level":3,"skills":["有限轉移計算模型"]},"variant":{"family_id":"qf-ext19-model-cycle-termination-risk","seed":202610194096,"parameters":{"n":6,"init":[0],"halt":[5],"steps":[[0,1],[1,2],[2,5],[4,5],[1,1]],"domain":"Fin_transition_model","operation":"model-cycle-termination-risk","semantic_template":"qf-ext19-model-cycle-termination-risk/{\"halt\":[5],\"init\":[0],\"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-r04-computational-model-0097","batch_id":"batch-20261013-advance-20261019-r04-computational-model-foundations","language":"zh-Hant","source_mko_ids":["mko-computational-model"],"title_zh":"有限轉移計算模型","stem_zh":"完整有限轉移模型。操作=model-cycle-termination-risk；資料={\"n\":6,\"init\":[0],\"halt\":[5],\"steps\":[[0,1],[1,2],[2,5],[0,3],[4,5],[1,1]]}。請依 [reachable,stuck,cycle,all_paths_halt,classification] 欄序回答。","answer":{"kind":"expression","value":"([0, 1, 2, 3, 5], [3], 是, 否, reachable非停止cycle)","explanation_zh":"第二批擴展核對=([0, 1, 2, 3, 5], [3], 是, 否, reachable非停止cycle)；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；halt與stuck分離；有限prefix不證一般終止。"},"difficulty":{"band":"undergraduate_core","level":3,"skills":["有限轉移計算模型"]},"variant":{"family_id":"qf-ext19-model-cycle-termination-risk","seed":202610194097,"parameters":{"n":6,"init":[0],"halt":[5],"steps":[[0,1],[1,2],[2,5],[0,3],[4,5],[1,1]],"domain":"Fin_transition_model","operation":"model-cycle-termination-risk","semantic_template":"qf-ext19-model-cycle-termination-risk/{\"halt\":[5],\"init\":[0],\"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-r04-computational-model-0098","batch_id":"batch-20261013-advance-20261019-r04-computational-model-foundations","language":"zh-Hant","source_mko_ids":["mko-computational-model"],"title_zh":"有限轉移計算模型","stem_zh":"完整有限轉移模型。操作=model-cycle-termination-risk；資料={\"n\":6,\"init\":[0],\"halt\":[5],\"steps\":[[0,1],[1,2],[2,5],[3,4],[4,5],[1,1]]}。請依 [reachable,stuck,cycle,all_paths_halt,classification] 欄序回答。","answer":{"kind":"expression","value":"([0, 1, 2, 5], [], 是, 否, reachable非停止cycle)","explanation_zh":"第二批擴展核對=([0, 1, 2, 5], [], 是, 否, reachable非停止cycle)；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；halt與stuck分離；有限prefix不證一般終止。"},"difficulty":{"band":"undergraduate_core","level":3,"skills":["有限轉移計算模型"]},"variant":{"family_id":"qf-ext19-model-cycle-termination-risk","seed":202610194098,"parameters":{"n":6,"init":[0],"halt":[5],"steps":[[0,1],[1,2],[2,5],[3,4],[4,5],[1,1]],"domain":"Fin_transition_model","operation":"model-cycle-termination-risk","semantic_template":"qf-ext19-model-cycle-termination-risk/{\"halt\":[5],\"init\":[0],\"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-r04-computational-model-0099","batch_id":"batch-20261013-advance-20261019-r04-computational-model-foundations","language":"zh-Hant","source_mko_ids":["mko-computational-model"],"title_zh":"有限轉移計算模型","stem_zh":"完整有限轉移模型。操作=model-cycle-termination-risk；資料={\"n\":6,\"init\":[0],\"halt\":[5],\"steps\":[[0,1],[1,2],[2,5],[0,3],[3,4],[4,5],[1,1]]}。請依 [reachable,stuck,cycle,all_paths_halt,classification] 欄序回答。","answer":{"kind":"expression","value":"([0, 1, 2, 3, 4, 5], [], 是, 否, reachable非停止cycle)","explanation_zh":"第二批擴展核對=([0, 1, 2, 3, 4, 5], [], 是, 否, reachable非停止cycle)；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；halt與stuck分離；有限prefix不證一般終止。"},"difficulty":{"band":"undergraduate_core","level":3,"skills":["有限轉移計算模型"]},"variant":{"family_id":"qf-ext19-model-cycle-termination-risk","seed":202610194099,"parameters":{"n":6,"init":[0],"halt":[5],"steps":[[0,1],[1,2],[2,5],[0,3],[3,4],[4,5],[1,1]],"domain":"Fin_transition_model","operation":"model-cycle-termination-risk","semantic_template":"qf-ext19-model-cycle-termination-risk/{\"halt\":[5],\"init\":[0],\"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-r04-computational-model-0100","batch_id":"batch-20261013-advance-20261019-r04-computational-model-foundations","language":"zh-Hant","source_mko_ids":["mko-computational-model"],"title_zh":"有限轉移計算模型","stem_zh":"完整有限轉移模型。操作=model-cycle-termination-risk；資料={\"n\":6,\"init\":[0],\"halt\":[5],\"steps\":[[0,1],[1,2],[2,5],[2,1],[1,1]]}。請依 [reachable,stuck,cycle,all_paths_halt,classification] 欄序回答。","answer":{"kind":"expression","value":"([0, 1, 2, 5], [], 是, 否, reachable非停止cycle)","explanation_zh":"第二批擴展核對=([0, 1, 2, 5], [], 是, 否, reachable非停止cycle)；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；halt與stuck分離；有限prefix不證一般終止。"},"difficulty":{"band":"undergraduate_core","level":3,"skills":["有限轉移計算模型"]},"variant":{"family_id":"qf-ext19-model-cycle-termination-risk","seed":202610194100,"parameters":{"n":6,"init":[0],"halt":[5],"steps":[[0,1],[1,2],[2,5],[2,1],[1,1]],"domain":"Fin_transition_model","operation":"model-cycle-termination-risk","semantic_template":"qf-ext19-model-cycle-termination-risk/{\"halt\":[5],\"init\":[0],\"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"}}