{"schema_version":"ocme-question-v0.1","id":"q-20261014-advance-20261029-r05-finite-filtration-0001","batch_id":"batch-20261014-advance-20261029-r05-finite-filtration-foundations","language":"zh-Hant","source_mko_ids":["mko-finite-filtration"],"title_zh":"有限filtration","stem_zh":"所有資訊partition位於同一有限樣本空間。操作=filtration-qualification；資料={\"n\":6,\"partitions\":[[0,0,0,0,0,0],[0,0,0,1,1,1],[0,0,0,0,10,10]]}。請依 [n,time_count,nesting_failures,filtration] 欄序回答。","answer":{"kind":"expression","value":"(6, 3, [[2, 0, 3], [2, 1, 3], [2, 2, 3]], 否)","explanation_zh":"Wave4第三層核對=(6, 3, [[2, 0, 3], [2, 1, 3], [2, 2, 3]], 否)；依完整明示資料重算；完整有限／symbolic certificate不自動升格為未聲明的一般定理；每個較晚partition須精確細化較早partition；filtration不自動推出adapted natural independent或Markov。"},"difficulty":{"band":"undergraduate_core","level":1,"skills":["有限filtration"]},"variant":{"family_id":"qf-mod29-filtration-qualification","seed":202610295001,"parameters":{"n":6,"partitions":[[0,0,0,0,0,0],[0,0,0,1,1,1],[0,0,0,0,10,10]],"domain":"Exact_finite_partition_filtration","operation":"filtration-qualification","semantic_template":"qf-mod29-filtration-qualification/{\"n\":6,\"partitions\":[[0,0,0,0,0,0],[0,0,0,1,1,1],[0,0,0,0,10,10]]}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_model","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"產生端候選須由主端重算；不構成人工審定、任意無限定理、一般域／UFD、Hilbert、一般條件期望、LLN／CLT、商集、Lean執行或形式Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-14","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261014-advance-20261029-r05-finite-filtration-0002","batch_id":"batch-20261014-advance-20261029-r05-finite-filtration-foundations","language":"zh-Hant","source_mko_ids":["mko-finite-filtration"],"title_zh":"有限filtration","stem_zh":"所有資訊partition位於同一有限樣本空間。操作=filtration-qualification；資料={\"n\":6,\"partitions\":[[0,0,0,0,0,0],[0,0,0,1,1,1],[1,0,0,10,10,10]]}。請依 [n,time_count,nesting_failures,filtration] 欄序回答。","answer":{"kind":"expression","value":"(6, 3, [], 是)","explanation_zh":"Wave4第三層核對=(6, 3, [], 是)；依完整明示資料重算；完整有限／symbolic certificate不自動升格為未聲明的一般定理；每個較晚partition須精確細化較早partition；filtration不自動推出adapted natural independent或Markov。"},"difficulty":{"band":"undergraduate_core","level":1,"skills":["有限filtration"]},"variant":{"family_id":"qf-mod29-filtration-qualification","seed":202610295002,"parameters":{"n":6,"partitions":[[0,0,0,0,0,0],[0,0,0,1,1,1],[1,0,0,10,10,10]],"domain":"Exact_finite_partition_filtration","operation":"filtration-qualification","semantic_template":"qf-mod29-filtration-qualification/{\"n\":6,\"partitions\":[[0,0,0,0,0,0],[0,0,0,1,1,1],[1,0,0,10,10,10]]}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_model","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"產生端候選須由主端重算；不構成人工審定、任意無限定理、一般域／UFD、Hilbert、一般條件期望、LLN／CLT、商集、Lean執行或形式Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-14","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261014-advance-20261029-r05-finite-filtration-0003","batch_id":"batch-20261014-advance-20261029-r05-finite-filtration-foundations","language":"zh-Hant","source_mko_ids":["mko-finite-filtration"],"title_zh":"有限filtration","stem_zh":"所有資訊partition位於同一有限樣本空間。操作=filtration-qualification；資料={\"n\":6,\"partitions\":[[0,0,0,0,0,0],[0,0,0,1,1,1],[0,1,0,10,10,10]]}。請依 [n,time_count,nesting_failures,filtration] 欄序回答。","answer":{"kind":"expression","value":"(6, 3, [], 是)","explanation_zh":"Wave4第三層核對=(6, 3, [], 是)；依完整明示資料重算；完整有限／symbolic certificate不自動升格為未聲明的一般定理；每個較晚partition須精確細化較早partition；filtration不自動推出adapted natural independent或Markov。"},"difficulty":{"band":"undergraduate_core","level":1,"skills":["有限filtration"]},"variant":{"family_id":"qf-mod29-filtration-qualification","seed":202610295003,"parameters":{"n":6,"partitions":[[0,0,0,0,0,0],[0,0,0,1,1,1],[0,1,0,10,10,10]],"domain":"Exact_finite_partition_filtration","operation":"filtration-qualification","semantic_template":"qf-mod29-filtration-qualification/{\"n\":6,\"partitions\":[[0,0,0,0,0,0],[0,0,0,1,1,1],[0,1,0,10,10,10]]}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_model","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"產生端候選須由主端重算；不構成人工審定、任意無限定理、一般域／UFD、Hilbert、一般條件期望、LLN／CLT、商集、Lean執行或形式Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-14","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261014-advance-20261029-r05-finite-filtration-0004","batch_id":"batch-20261014-advance-20261029-r05-finite-filtration-foundations","language":"zh-Hant","source_mko_ids":["mko-finite-filtration"],"title_zh":"有限filtration","stem_zh":"所有資訊partition位於同一有限樣本空間。操作=filtration-qualification；資料={\"n\":6,\"partitions\":[[0,0,0,0,0,0],[0,0,0,1,1,1],[1,1,0,10,10,10]]}。請依 [n,time_count,nesting_failures,filtration] 欄序回答。","answer":{"kind":"expression","value":"(6, 3, [], 是)","explanation_zh":"Wave4第三層核對=(6, 3, [], 是)；依完整明示資料重算；完整有限／symbolic certificate不自動升格為未聲明的一般定理；每個較晚partition須精確細化較早partition；filtration不自動推出adapted natural independent或Markov。"},"difficulty":{"band":"undergraduate_core","level":1,"skills":["有限filtration"]},"variant":{"family_id":"qf-mod29-filtration-qualification","seed":202610295004,"parameters":{"n":6,"partitions":[[0,0,0,0,0,0],[0,0,0,1,1,1],[1,1,0,10,10,10]],"domain":"Exact_finite_partition_filtration","operation":"filtration-qualification","semantic_template":"qf-mod29-filtration-qualification/{\"n\":6,\"partitions\":[[0,0,0,0,0,0],[0,0,0,1,1,1],[1,1,0,10,10,10]]}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_model","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"產生端候選須由主端重算；不構成人工審定、任意無限定理、一般域／UFD、Hilbert、一般條件期望、LLN／CLT、商集、Lean執行或形式Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-14","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261014-advance-20261029-r05-finite-filtration-0005","batch_id":"batch-20261014-advance-20261029-r05-finite-filtration-foundations","language":"zh-Hant","source_mko_ids":["mko-finite-filtration"],"title_zh":"有限filtration","stem_zh":"所有資訊partition位於同一有限樣本空間。操作=filtration-qualification；資料={\"n\":6,\"partitions\":[[0,0,0,0,0,0],[0,0,0,1,1,1],[0,0,1,10,10,10]]}。請依 [n,time_count,nesting_failures,filtration] 欄序回答。","answer":{"kind":"expression","value":"(6, 3, [], 是)","explanation_zh":"Wave4第三層核對=(6, 3, [], 是)；依完整明示資料重算；完整有限／symbolic certificate不自動升格為未聲明的一般定理；每個較晚partition須精確細化較早partition；filtration不自動推出adapted natural independent或Markov。"},"difficulty":{"band":"undergraduate_core","level":1,"skills":["有限filtration"]},"variant":{"family_id":"qf-mod29-filtration-qualification","seed":202610295005,"parameters":{"n":6,"partitions":[[0,0,0,0,0,0],[0,0,0,1,1,1],[0,0,1,10,10,10]],"domain":"Exact_finite_partition_filtration","operation":"filtration-qualification","semantic_template":"qf-mod29-filtration-qualification/{\"n\":6,\"partitions\":[[0,0,0,0,0,0],[0,0,0,1,1,1],[0,0,1,10,10,10]]}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_model","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"產生端候選須由主端重算；不構成人工審定、任意無限定理、一般域／UFD、Hilbert、一般條件期望、LLN／CLT、商集、Lean執行或形式Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-14","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261014-advance-20261029-r05-finite-filtration-0006","batch_id":"batch-20261014-advance-20261029-r05-finite-filtration-foundations","language":"zh-Hant","source_mko_ids":["mko-finite-filtration"],"title_zh":"有限filtration","stem_zh":"所有資訊partition位於同一有限樣本空間。操作=filtration-qualification；資料={\"n\":6,\"partitions\":[[0,0,0,0,0,0],[0,0,0,1,1,1],[1,0,1,1,10,10]]}。請依 [n,time_count,nesting_failures,filtration] 欄序回答。","answer":{"kind":"expression","value":"(6, 3, [[2, 0, 3], [2, 2, 3]], 否)","explanation_zh":"Wave4第三層核對=(6, 3, [[2, 0, 3], [2, 2, 3]], 否)；依完整明示資料重算；完整有限／symbolic certificate不自動升格為未聲明的一般定理；每個較晚partition須精確細化較早partition；filtration不自動推出adapted natural independent或Markov。"},"difficulty":{"band":"undergraduate_core","level":1,"skills":["有限filtration"]},"variant":{"family_id":"qf-mod29-filtration-qualification","seed":202610295006,"parameters":{"n":6,"partitions":[[0,0,0,0,0,0],[0,0,0,1,1,1],[1,0,1,1,10,10]],"domain":"Exact_finite_partition_filtration","operation":"filtration-qualification","semantic_template":"qf-mod29-filtration-qualification/{\"n\":6,\"partitions\":[[0,0,0,0,0,0],[0,0,0,1,1,1],[1,0,1,1,10,10]]}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_model","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"產生端候選須由主端重算；不構成人工審定、任意無限定理、一般域／UFD、Hilbert、一般條件期望、LLN／CLT、商集、Lean執行或形式Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-14","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261014-advance-20261029-r05-finite-filtration-0007","batch_id":"batch-20261014-advance-20261029-r05-finite-filtration-foundations","language":"zh-Hant","source_mko_ids":["mko-finite-filtration"],"title_zh":"有限filtration","stem_zh":"所有資訊partition位於同一有限樣本空間。操作=filtration-qualification；資料={\"n\":6,\"partitions\":[[0,0,0,0,0,0],[0,0,0,1,1,1],[0,1,1,10,10,10]]}。請依 [n,time_count,nesting_failures,filtration] 欄序回答。","answer":{"kind":"expression","value":"(6, 3, [], 是)","explanation_zh":"Wave4第三層核對=(6, 3, [], 是)；依完整明示資料重算；完整有限／symbolic certificate不自動升格為未聲明的一般定理；每個較晚partition須精確細化較早partition；filtration不自動推出adapted natural independent或Markov。"},"difficulty":{"band":"undergraduate_core","level":1,"skills":["有限filtration"]},"variant":{"family_id":"qf-mod29-filtration-qualification","seed":202610295007,"parameters":{"n":6,"partitions":[[0,0,0,0,0,0],[0,0,0,1,1,1],[0,1,1,10,10,10]],"domain":"Exact_finite_partition_filtration","operation":"filtration-qualification","semantic_template":"qf-mod29-filtration-qualification/{\"n\":6,\"partitions\":[[0,0,0,0,0,0],[0,0,0,1,1,1],[0,1,1,10,10,10]]}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_model","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"產生端候選須由主端重算；不構成人工審定、任意無限定理、一般域／UFD、Hilbert、一般條件期望、LLN／CLT、商集、Lean執行或形式Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-14","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261014-advance-20261029-r05-finite-filtration-0008","batch_id":"batch-20261014-advance-20261029-r05-finite-filtration-foundations","language":"zh-Hant","source_mko_ids":["mko-finite-filtration"],"title_zh":"有限filtration","stem_zh":"所有資訊partition位於同一有限樣本空間。操作=filtration-qualification；資料={\"n\":6,\"partitions\":[[0,0,0,0,0,0],[0,0,0,1,1,1],[1,1,1,10,10,10]]}。請依 [n,time_count,nesting_failures,filtration] 欄序回答。","answer":{"kind":"expression","value":"(6, 3, [], 是)","explanation_zh":"Wave4第三層核對=(6, 3, [], 是)；依完整明示資料重算；完整有限／symbolic certificate不自動升格為未聲明的一般定理；每個較晚partition須精確細化較早partition；filtration不自動推出adapted natural independent或Markov。"},"difficulty":{"band":"undergraduate_core","level":1,"skills":["有限filtration"]},"variant":{"family_id":"qf-mod29-filtration-qualification","seed":202610295008,"parameters":{"n":6,"partitions":[[0,0,0,0,0,0],[0,0,0,1,1,1],[1,1,1,10,10,10]],"domain":"Exact_finite_partition_filtration","operation":"filtration-qualification","semantic_template":"qf-mod29-filtration-qualification/{\"n\":6,\"partitions\":[[0,0,0,0,0,0],[0,0,0,1,1,1],[1,1,1,10,10,10]]}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_model","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"產生端候選須由主端重算；不構成人工審定、任意無限定理、一般域／UFD、Hilbert、一般條件期望、LLN／CLT、商集、Lean執行或形式Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-14","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261014-advance-20261029-r05-finite-filtration-0009","batch_id":"batch-20261014-advance-20261029-r05-finite-filtration-foundations","language":"zh-Hant","source_mko_ids":["mko-finite-filtration"],"title_zh":"有限filtration","stem_zh":"所有資訊partition位於同一有限樣本空間。操作=filtration-qualification；資料={\"n\":6,\"partitions\":[[0,0,0,0,0,0],[0,0,0,1,1,1],[0,0,0,11,10,10]]}。請依 [n,time_count,nesting_failures,filtration] 欄序回答。","answer":{"kind":"expression","value":"(6, 3, [], 是)","explanation_zh":"Wave4第三層核對=(6, 3, [], 是)；依完整明示資料重算；完整有限／symbolic certificate不自動升格為未聲明的一般定理；每個較晚partition須精確細化較早partition；filtration不自動推出adapted natural independent或Markov。"},"difficulty":{"band":"undergraduate_core","level":2,"skills":["有限filtration"]},"variant":{"family_id":"qf-mod29-filtration-qualification","seed":202610295009,"parameters":{"n":6,"partitions":[[0,0,0,0,0,0],[0,0,0,1,1,1],[0,0,0,11,10,10]],"domain":"Exact_finite_partition_filtration","operation":"filtration-qualification","semantic_template":"qf-mod29-filtration-qualification/{\"n\":6,\"partitions\":[[0,0,0,0,0,0],[0,0,0,1,1,1],[0,0,0,11,10,10]]}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_model","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"產生端候選須由主端重算；不構成人工審定、任意無限定理、一般域／UFD、Hilbert、一般條件期望、LLN／CLT、商集、Lean執行或形式Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-14","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261014-advance-20261029-r05-finite-filtration-0010","batch_id":"batch-20261014-advance-20261029-r05-finite-filtration-foundations","language":"zh-Hant","source_mko_ids":["mko-finite-filtration"],"title_zh":"有限filtration","stem_zh":"所有資訊partition位於同一有限樣本空間。操作=filtration-qualification；資料={\"n\":6,\"partitions\":[[0,0,0,0,0,0],[0,0,0,1,1,1],[1,0,0,11,10,10]]}。請依 [n,time_count,nesting_failures,filtration] 欄序回答。","answer":{"kind":"expression","value":"(6, 3, [], 是)","explanation_zh":"Wave4第三層核對=(6, 3, [], 是)；依完整明示資料重算；完整有限／symbolic certificate不自動升格為未聲明的一般定理；每個較晚partition須精確細化較早partition；filtration不自動推出adapted natural independent或Markov。"},"difficulty":{"band":"undergraduate_core","level":2,"skills":["有限filtration"]},"variant":{"family_id":"qf-mod29-filtration-qualification","seed":202610295010,"parameters":{"n":6,"partitions":[[0,0,0,0,0,0],[0,0,0,1,1,1],[1,0,0,11,10,10]],"domain":"Exact_finite_partition_filtration","operation":"filtration-qualification","semantic_template":"qf-mod29-filtration-qualification/{\"n\":6,\"partitions\":[[0,0,0,0,0,0],[0,0,0,1,1,1],[1,0,0,11,10,10]]}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_model","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"產生端候選須由主端重算；不構成人工審定、任意無限定理、一般域／UFD、Hilbert、一般條件期望、LLN／CLT、商集、Lean執行或形式Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-14","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261014-advance-20261029-r05-finite-filtration-0011","batch_id":"batch-20261014-advance-20261029-r05-finite-filtration-foundations","language":"zh-Hant","source_mko_ids":["mko-finite-filtration"],"title_zh":"有限filtration","stem_zh":"所有資訊partition位於同一有限樣本空間。操作=filtration-qualification；資料={\"n\":6,\"partitions\":[[0,0,0,0,0,0],[0,0,0,1,1,1],[0,1,0,0,10,10]]}。請依 [n,time_count,nesting_failures,filtration] 欄序回答。","answer":{"kind":"expression","value":"(6, 3, [[2, 0, 3], [2, 2, 3]], 否)","explanation_zh":"Wave4第三層核對=(6, 3, [[2, 0, 3], [2, 2, 3]], 否)；依完整明示資料重算；完整有限／symbolic certificate不自動升格為未聲明的一般定理；每個較晚partition須精確細化較早partition；filtration不自動推出adapted natural independent或Markov。"},"difficulty":{"band":"undergraduate_core","level":2,"skills":["有限filtration"]},"variant":{"family_id":"qf-mod29-filtration-qualification","seed":202610295011,"parameters":{"n":6,"partitions":[[0,0,0,0,0,0],[0,0,0,1,1,1],[0,1,0,0,10,10]],"domain":"Exact_finite_partition_filtration","operation":"filtration-qualification","semantic_template":"qf-mod29-filtration-qualification/{\"n\":6,\"partitions\":[[0,0,0,0,0,0],[0,0,0,1,1,1],[0,1,0,0,10,10]]}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_model","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"產生端候選須由主端重算；不構成人工審定、任意無限定理、一般域／UFD、Hilbert、一般條件期望、LLN／CLT、商集、Lean執行或形式Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-14","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261014-advance-20261029-r05-finite-filtration-0012","batch_id":"batch-20261014-advance-20261029-r05-finite-filtration-foundations","language":"zh-Hant","source_mko_ids":["mko-finite-filtration"],"title_zh":"有限filtration","stem_zh":"所有資訊partition位於同一有限樣本空間。操作=filtration-qualification；資料={\"n\":6,\"partitions\":[[0,0,0,0,0,0],[0,0,0,1,1,1],[1,1,0,11,10,10]]}。請依 [n,time_count,nesting_failures,filtration] 欄序回答。","answer":{"kind":"expression","value":"(6, 3, [], 是)","explanation_zh":"Wave4第三層核對=(6, 3, [], 是)；依完整明示資料重算；完整有限／symbolic certificate不自動升格為未聲明的一般定理；每個較晚partition須精確細化較早partition；filtration不自動推出adapted natural independent或Markov。"},"difficulty":{"band":"undergraduate_core","level":2,"skills":["有限filtration"]},"variant":{"family_id":"qf-mod29-filtration-qualification","seed":202610295012,"parameters":{"n":6,"partitions":[[0,0,0,0,0,0],[0,0,0,1,1,1],[1,1,0,11,10,10]],"domain":"Exact_finite_partition_filtration","operation":"filtration-qualification","semantic_template":"qf-mod29-filtration-qualification/{\"n\":6,\"partitions\":[[0,0,0,0,0,0],[0,0,0,1,1,1],[1,1,0,11,10,10]]}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_model","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"產生端候選須由主端重算；不構成人工審定、任意無限定理、一般域／UFD、Hilbert、一般條件期望、LLN／CLT、商集、Lean執行或形式Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-14","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261014-advance-20261029-r05-finite-filtration-0013","batch_id":"batch-20261014-advance-20261029-r05-finite-filtration-foundations","language":"zh-Hant","source_mko_ids":["mko-finite-filtration"],"title_zh":"有限filtration","stem_zh":"所有資訊partition位於同一有限樣本空間。操作=filtration-qualification；資料={\"n\":6,\"partitions\":[[0,0,0,0,0,0],[0,0,0,1,1,1],[0,0,1,11,10,10]]}。請依 [n,time_count,nesting_failures,filtration] 欄序回答。","answer":{"kind":"expression","value":"(6, 3, [], 是)","explanation_zh":"Wave4第三層核對=(6, 3, [], 是)；依完整明示資料重算；完整有限／symbolic certificate不自動升格為未聲明的一般定理；每個較晚partition須精確細化較早partition；filtration不自動推出adapted natural independent或Markov。"},"difficulty":{"band":"undergraduate_core","level":2,"skills":["有限filtration"]},"variant":{"family_id":"qf-mod29-filtration-qualification","seed":202610295013,"parameters":{"n":6,"partitions":[[0,0,0,0,0,0],[0,0,0,1,1,1],[0,0,1,11,10,10]],"domain":"Exact_finite_partition_filtration","operation":"filtration-qualification","semantic_template":"qf-mod29-filtration-qualification/{\"n\":6,\"partitions\":[[0,0,0,0,0,0],[0,0,0,1,1,1],[0,0,1,11,10,10]]}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_model","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"產生端候選須由主端重算；不構成人工審定、任意無限定理、一般域／UFD、Hilbert、一般條件期望、LLN／CLT、商集、Lean執行或形式Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-14","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261014-advance-20261029-r05-finite-filtration-0014","batch_id":"batch-20261014-advance-20261029-r05-finite-filtration-foundations","language":"zh-Hant","source_mko_ids":["mko-finite-filtration"],"title_zh":"有限filtration","stem_zh":"所有資訊partition位於同一有限樣本空間。操作=filtration-qualification；資料={\"n\":6,\"partitions\":[[0,0,0,0,0,0],[0,0,0,1,1,1],[1,0,1,11,10,10]]}。請依 [n,time_count,nesting_failures,filtration] 欄序回答。","answer":{"kind":"expression","value":"(6, 3, [], 是)","explanation_zh":"Wave4第三層核對=(6, 3, [], 是)；依完整明示資料重算；完整有限／symbolic certificate不自動升格為未聲明的一般定理；每個較晚partition須精確細化較早partition；filtration不自動推出adapted natural independent或Markov。"},"difficulty":{"band":"undergraduate_core","level":2,"skills":["有限filtration"]},"variant":{"family_id":"qf-mod29-filtration-qualification","seed":202610295014,"parameters":{"n":6,"partitions":[[0,0,0,0,0,0],[0,0,0,1,1,1],[1,0,1,11,10,10]],"domain":"Exact_finite_partition_filtration","operation":"filtration-qualification","semantic_template":"qf-mod29-filtration-qualification/{\"n\":6,\"partitions\":[[0,0,0,0,0,0],[0,0,0,1,1,1],[1,0,1,11,10,10]]}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_model","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"產生端候選須由主端重算；不構成人工審定、任意無限定理、一般域／UFD、Hilbert、一般條件期望、LLN／CLT、商集、Lean執行或形式Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-14","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261014-advance-20261029-r05-finite-filtration-0015","batch_id":"batch-20261014-advance-20261029-r05-finite-filtration-foundations","language":"zh-Hant","source_mko_ids":["mko-finite-filtration"],"title_zh":"有限filtration","stem_zh":"所有資訊partition位於同一有限樣本空間。操作=filtration-qualification；資料={\"n\":6,\"partitions\":[[0,0,0,0,0,0],[0,0,0,1,1,1],[0,1,1,11,10,10]]}。請依 [n,time_count,nesting_failures,filtration] 欄序回答。","answer":{"kind":"expression","value":"(6, 3, [], 是)","explanation_zh":"Wave4第三層核對=(6, 3, [], 是)；依完整明示資料重算；完整有限／symbolic certificate不自動升格為未聲明的一般定理；每個較晚partition須精確細化較早partition；filtration不自動推出adapted natural independent或Markov。"},"difficulty":{"band":"undergraduate_core","level":2,"skills":["有限filtration"]},"variant":{"family_id":"qf-mod29-filtration-qualification","seed":202610295015,"parameters":{"n":6,"partitions":[[0,0,0,0,0,0],[0,0,0,1,1,1],[0,1,1,11,10,10]],"domain":"Exact_finite_partition_filtration","operation":"filtration-qualification","semantic_template":"qf-mod29-filtration-qualification/{\"n\":6,\"partitions\":[[0,0,0,0,0,0],[0,0,0,1,1,1],[0,1,1,11,10,10]]}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_model","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"產生端候選須由主端重算；不構成人工審定、任意無限定理、一般域／UFD、Hilbert、一般條件期望、LLN／CLT、商集、Lean執行或形式Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-14","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261014-advance-20261029-r05-finite-filtration-0016","batch_id":"batch-20261014-advance-20261029-r05-finite-filtration-foundations","language":"zh-Hant","source_mko_ids":["mko-finite-filtration"],"title_zh":"有限filtration","stem_zh":"所有資訊partition位於同一有限樣本空間。操作=filtration-qualification；資料={\"n\":6,\"partitions\":[[0,0,0,0,0,0],[0,0,0,1,1,1],[1,1,1,1,10,10]]}。請依 [n,time_count,nesting_failures,filtration] 欄序回答。","answer":{"kind":"expression","value":"(6, 3, [[2, 0, 3], [2, 1, 3], [2, 2, 3]], 否)","explanation_zh":"Wave4第三層核對=(6, 3, [[2, 0, 3], [2, 1, 3], [2, 2, 3]], 否)；依完整明示資料重算；完整有限／symbolic certificate不自動升格為未聲明的一般定理；每個較晚partition須精確細化較早partition；filtration不自動推出adapted natural independent或Markov。"},"difficulty":{"band":"undergraduate_core","level":2,"skills":["有限filtration"]},"variant":{"family_id":"qf-mod29-filtration-qualification","seed":202610295016,"parameters":{"n":6,"partitions":[[0,0,0,0,0,0],[0,0,0,1,1,1],[1,1,1,1,10,10]],"domain":"Exact_finite_partition_filtration","operation":"filtration-qualification","semantic_template":"qf-mod29-filtration-qualification/{\"n\":6,\"partitions\":[[0,0,0,0,0,0],[0,0,0,1,1,1],[1,1,1,1,10,10]]}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_model","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"產生端候選須由主端重算；不構成人工審定、任意無限定理、一般域／UFD、Hilbert、一般條件期望、LLN／CLT、商集、Lean執行或形式Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-14","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261014-advance-20261029-r05-finite-filtration-0017","batch_id":"batch-20261014-advance-20261029-r05-finite-filtration-foundations","language":"zh-Hant","source_mko_ids":["mko-finite-filtration"],"title_zh":"有限filtration","stem_zh":"所有資訊partition位於同一有限樣本空間。操作=filtration-qualification；資料={\"n\":6,\"partitions\":[[0,0,0,0,0,0],[0,0,0,1,1,1],[0,0,0,10,11,10]]}。請依 [n,time_count,nesting_failures,filtration] 欄序回答。","answer":{"kind":"expression","value":"(6, 3, [], 是)","explanation_zh":"Wave4第三層核對=(6, 3, [], 是)；依完整明示資料重算；完整有限／symbolic certificate不自動升格為未聲明的一般定理；每個較晚partition須精確細化較早partition；filtration不自動推出adapted natural independent或Markov。"},"difficulty":{"band":"undergraduate_core","level":2,"skills":["有限filtration"]},"variant":{"family_id":"qf-mod29-filtration-qualification","seed":202610295017,"parameters":{"n":6,"partitions":[[0,0,0,0,0,0],[0,0,0,1,1,1],[0,0,0,10,11,10]],"domain":"Exact_finite_partition_filtration","operation":"filtration-qualification","semantic_template":"qf-mod29-filtration-qualification/{\"n\":6,\"partitions\":[[0,0,0,0,0,0],[0,0,0,1,1,1],[0,0,0,10,11,10]]}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_model","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"產生端候選須由主端重算；不構成人工審定、任意無限定理、一般域／UFD、Hilbert、一般條件期望、LLN／CLT、商集、Lean執行或形式Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-14","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261014-advance-20261029-r05-finite-filtration-0018","batch_id":"batch-20261014-advance-20261029-r05-finite-filtration-foundations","language":"zh-Hant","source_mko_ids":["mko-finite-filtration"],"title_zh":"有限filtration","stem_zh":"所有資訊partition位於同一有限樣本空間。操作=filtration-qualification；資料={\"n\":6,\"partitions\":[[0,0,0,0,0,0],[0,0,0,1,1,1],[1,0,0,10,11,10]]}。請依 [n,time_count,nesting_failures,filtration] 欄序回答。","answer":{"kind":"expression","value":"(6, 3, [], 是)","explanation_zh":"Wave4第三層核對=(6, 3, [], 是)；依完整明示資料重算；完整有限／symbolic certificate不自動升格為未聲明的一般定理；每個較晚partition須精確細化較早partition；filtration不自動推出adapted natural independent或Markov。"},"difficulty":{"band":"undergraduate_core","level":3,"skills":["有限filtration"]},"variant":{"family_id":"qf-mod29-filtration-qualification","seed":202610295018,"parameters":{"n":6,"partitions":[[0,0,0,0,0,0],[0,0,0,1,1,1],[1,0,0,10,11,10]],"domain":"Exact_finite_partition_filtration","operation":"filtration-qualification","semantic_template":"qf-mod29-filtration-qualification/{\"n\":6,\"partitions\":[[0,0,0,0,0,0],[0,0,0,1,1,1],[1,0,0,10,11,10]]}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_model","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"產生端候選須由主端重算；不構成人工審定、任意無限定理、一般域／UFD、Hilbert、一般條件期望、LLN／CLT、商集、Lean執行或形式Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-14","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261014-advance-20261029-r05-finite-filtration-0019","batch_id":"batch-20261014-advance-20261029-r05-finite-filtration-foundations","language":"zh-Hant","source_mko_ids":["mko-finite-filtration"],"title_zh":"有限filtration","stem_zh":"所有資訊partition位於同一有限樣本空間。操作=filtration-qualification；資料={\"n\":6,\"partitions\":[[0,0,0,0,0,0],[0,0,0,1,1,1],[0,1,0,10,11,10]]}。請依 [n,time_count,nesting_failures,filtration] 欄序回答。","answer":{"kind":"expression","value":"(6, 3, [], 是)","explanation_zh":"Wave4第三層核對=(6, 3, [], 是)；依完整明示資料重算；完整有限／symbolic certificate不自動升格為未聲明的一般定理；每個較晚partition須精確細化較早partition；filtration不自動推出adapted natural independent或Markov。"},"difficulty":{"band":"undergraduate_core","level":3,"skills":["有限filtration"]},"variant":{"family_id":"qf-mod29-filtration-qualification","seed":202610295019,"parameters":{"n":6,"partitions":[[0,0,0,0,0,0],[0,0,0,1,1,1],[0,1,0,10,11,10]],"domain":"Exact_finite_partition_filtration","operation":"filtration-qualification","semantic_template":"qf-mod29-filtration-qualification/{\"n\":6,\"partitions\":[[0,0,0,0,0,0],[0,0,0,1,1,1],[0,1,0,10,11,10]]}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_model","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"產生端候選須由主端重算；不構成人工審定、任意無限定理、一般域／UFD、Hilbert、一般條件期望、LLN／CLT、商集、Lean執行或形式Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-14","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261014-advance-20261029-r05-finite-filtration-0020","batch_id":"batch-20261014-advance-20261029-r05-finite-filtration-foundations","language":"zh-Hant","source_mko_ids":["mko-finite-filtration"],"title_zh":"有限filtration","stem_zh":"所有資訊partition位於同一有限樣本空間。操作=filtration-qualification；資料={\"n\":6,\"partitions\":[[0,0,0,0,0,0],[0,0,0,1,1,1],[1,1,0,10,11,10]]}。請依 [n,time_count,nesting_failures,filtration] 欄序回答。","answer":{"kind":"expression","value":"(6, 3, [], 是)","explanation_zh":"Wave4第三層核對=(6, 3, [], 是)；依完整明示資料重算；完整有限／symbolic certificate不自動升格為未聲明的一般定理；每個較晚partition須精確細化較早partition；filtration不自動推出adapted natural independent或Markov。"},"difficulty":{"band":"undergraduate_core","level":3,"skills":["有限filtration"]},"variant":{"family_id":"qf-mod29-filtration-qualification","seed":202610295020,"parameters":{"n":6,"partitions":[[0,0,0,0,0,0],[0,0,0,1,1,1],[1,1,0,10,11,10]],"domain":"Exact_finite_partition_filtration","operation":"filtration-qualification","semantic_template":"qf-mod29-filtration-qualification/{\"n\":6,\"partitions\":[[0,0,0,0,0,0],[0,0,0,1,1,1],[1,1,0,10,11,10]]}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_model","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"產生端候選須由主端重算；不構成人工審定、任意無限定理、一般域／UFD、Hilbert、一般條件期望、LLN／CLT、商集、Lean執行或形式Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-14","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261014-advance-20261029-r05-finite-filtration-0021","batch_id":"batch-20261014-advance-20261029-r05-finite-filtration-foundations","language":"zh-Hant","source_mko_ids":["mko-finite-filtration"],"title_zh":"有限filtration","stem_zh":"所有資訊partition位於同一有限樣本空間。操作=filtration-qualification；資料={\"n\":6,\"partitions\":[[0,0,0,0,0,0],[0,0,0,1,1,1],[0,0,1,0,11,10]]}。請依 [n,time_count,nesting_failures,filtration] 欄序回答。","answer":{"kind":"expression","value":"(6, 3, [[2, 0, 3], [2, 1, 3]], 否)","explanation_zh":"Wave4第三層核對=(6, 3, [[2, 0, 3], [2, 1, 3]], 否)；依完整明示資料重算；完整有限／symbolic certificate不自動升格為未聲明的一般定理；每個較晚partition須精確細化較早partition；filtration不自動推出adapted natural independent或Markov。"},"difficulty":{"band":"undergraduate_core","level":3,"skills":["有限filtration"]},"variant":{"family_id":"qf-mod29-filtration-qualification","seed":202610295021,"parameters":{"n":6,"partitions":[[0,0,0,0,0,0],[0,0,0,1,1,1],[0,0,1,0,11,10]],"domain":"Exact_finite_partition_filtration","operation":"filtration-qualification","semantic_template":"qf-mod29-filtration-qualification/{\"n\":6,\"partitions\":[[0,0,0,0,0,0],[0,0,0,1,1,1],[0,0,1,0,11,10]]}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_model","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"產生端候選須由主端重算；不構成人工審定、任意無限定理、一般域／UFD、Hilbert、一般條件期望、LLN／CLT、商集、Lean執行或形式Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-14","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261014-advance-20261029-r05-finite-filtration-0022","batch_id":"batch-20261014-advance-20261029-r05-finite-filtration-foundations","language":"zh-Hant","source_mko_ids":["mko-finite-filtration"],"title_zh":"有限filtration","stem_zh":"所有資訊partition位於同一有限樣本空間。操作=filtration-qualification；資料={\"n\":6,\"partitions\":[[0,0,0,0,0,0],[0,0,0,1,1,1],[1,0,1,10,11,10]]}。請依 [n,time_count,nesting_failures,filtration] 欄序回答。","answer":{"kind":"expression","value":"(6, 3, [], 是)","explanation_zh":"Wave4第三層核對=(6, 3, [], 是)；依完整明示資料重算；完整有限／symbolic certificate不自動升格為未聲明的一般定理；每個較晚partition須精確細化較早partition；filtration不自動推出adapted natural independent或Markov。"},"difficulty":{"band":"undergraduate_core","level":3,"skills":["有限filtration"]},"variant":{"family_id":"qf-mod29-filtration-qualification","seed":202610295022,"parameters":{"n":6,"partitions":[[0,0,0,0,0,0],[0,0,0,1,1,1],[1,0,1,10,11,10]],"domain":"Exact_finite_partition_filtration","operation":"filtration-qualification","semantic_template":"qf-mod29-filtration-qualification/{\"n\":6,\"partitions\":[[0,0,0,0,0,0],[0,0,0,1,1,1],[1,0,1,10,11,10]]}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_model","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"產生端候選須由主端重算；不構成人工審定、任意無限定理、一般域／UFD、Hilbert、一般條件期望、LLN／CLT、商集、Lean執行或形式Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-14","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261014-advance-20261029-r05-finite-filtration-0023","batch_id":"batch-20261014-advance-20261029-r05-finite-filtration-foundations","language":"zh-Hant","source_mko_ids":["mko-finite-filtration"],"title_zh":"有限filtration","stem_zh":"所有資訊partition位於同一有限樣本空間。操作=filtration-qualification；資料={\"n\":6,\"partitions\":[[0,0,0,0,0,0],[0,0,0,1,1,1],[0,1,1,10,11,10]]}。請依 [n,time_count,nesting_failures,filtration] 欄序回答。","answer":{"kind":"expression","value":"(6, 3, [], 是)","explanation_zh":"Wave4第三層核對=(6, 3, [], 是)；依完整明示資料重算；完整有限／symbolic certificate不自動升格為未聲明的一般定理；每個較晚partition須精確細化較早partition；filtration不自動推出adapted natural independent或Markov。"},"difficulty":{"band":"undergraduate_core","level":3,"skills":["有限filtration"]},"variant":{"family_id":"qf-mod29-filtration-qualification","seed":202610295023,"parameters":{"n":6,"partitions":[[0,0,0,0,0,0],[0,0,0,1,1,1],[0,1,1,10,11,10]],"domain":"Exact_finite_partition_filtration","operation":"filtration-qualification","semantic_template":"qf-mod29-filtration-qualification/{\"n\":6,\"partitions\":[[0,0,0,0,0,0],[0,0,0,1,1,1],[0,1,1,10,11,10]]}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_model","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"產生端候選須由主端重算；不構成人工審定、任意無限定理、一般域／UFD、Hilbert、一般條件期望、LLN／CLT、商集、Lean執行或形式Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-14","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261014-advance-20261029-r05-finite-filtration-0024","batch_id":"batch-20261014-advance-20261029-r05-finite-filtration-foundations","language":"zh-Hant","source_mko_ids":["mko-finite-filtration"],"title_zh":"有限filtration","stem_zh":"所有資訊partition位於同一有限樣本空間。操作=filtration-qualification；資料={\"n\":6,\"partitions\":[[0,0,0,0,0,0],[0,0,0,1,1,1],[1,1,1,10,11,10]]}。請依 [n,time_count,nesting_failures,filtration] 欄序回答。","answer":{"kind":"expression","value":"(6, 3, [], 是)","explanation_zh":"Wave4第三層核對=(6, 3, [], 是)；依完整明示資料重算；完整有限／symbolic certificate不自動升格為未聲明的一般定理；每個較晚partition須精確細化較早partition；filtration不自動推出adapted natural independent或Markov。"},"difficulty":{"band":"undergraduate_core","level":3,"skills":["有限filtration"]},"variant":{"family_id":"qf-mod29-filtration-qualification","seed":202610295024,"parameters":{"n":6,"partitions":[[0,0,0,0,0,0],[0,0,0,1,1,1],[1,1,1,10,11,10]],"domain":"Exact_finite_partition_filtration","operation":"filtration-qualification","semantic_template":"qf-mod29-filtration-qualification/{\"n\":6,\"partitions\":[[0,0,0,0,0,0],[0,0,0,1,1,1],[1,1,1,10,11,10]]}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_model","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"產生端候選須由主端重算；不構成人工審定、任意無限定理、一般域／UFD、Hilbert、一般條件期望、LLN／CLT、商集、Lean執行或形式Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-14","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261014-advance-20261029-r05-finite-filtration-0025","batch_id":"batch-20261014-advance-20261029-r05-finite-filtration-foundations","language":"zh-Hant","source_mko_ids":["mko-finite-filtration"],"title_zh":"有限filtration","stem_zh":"所有資訊partition位於同一有限樣本空間。操作=filtration-qualification；資料={\"n\":6,\"partitions\":[[0,0,0,0,0,0],[0,0,0,1,1,1],[0,0,0,11,11,10]]}。請依 [n,time_count,nesting_failures,filtration] 欄序回答。","answer":{"kind":"expression","value":"(6, 3, [], 是)","explanation_zh":"Wave4第三層核對=(6, 3, [], 是)；依完整明示資料重算；完整有限／symbolic certificate不自動升格為未聲明的一般定理；每個較晚partition須精確細化較早partition；filtration不自動推出adapted natural independent或Markov。"},"difficulty":{"band":"undergraduate_core","level":3,"skills":["有限filtration"]},"variant":{"family_id":"qf-mod29-filtration-qualification","seed":202610295025,"parameters":{"n":6,"partitions":[[0,0,0,0,0,0],[0,0,0,1,1,1],[0,0,0,11,11,10]],"domain":"Exact_finite_partition_filtration","operation":"filtration-qualification","semantic_template":"qf-mod29-filtration-qualification/{\"n\":6,\"partitions\":[[0,0,0,0,0,0],[0,0,0,1,1,1],[0,0,0,11,11,10]]}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_model","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"產生端候選須由主端重算；不構成人工審定、任意無限定理、一般域／UFD、Hilbert、一般條件期望、LLN／CLT、商集、Lean執行或形式Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-14","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261014-advance-20261029-r05-finite-filtration-0026","batch_id":"batch-20261014-advance-20261029-r05-finite-filtration-foundations","language":"zh-Hant","source_mko_ids":["mko-finite-filtration"],"title_zh":"有限filtration","stem_zh":"所有資訊partition位於同一有限樣本空間。操作=filtration-block-at-time；資料={\"n\":6,\"partitions\":[[0,0,0,0,0,0],[0,0,0,1,1,1],[0,0,0,10,10,10]],\"time\":0,\"outcome\":0}。請依 [time,outcome,information_block] 欄序回答。","answer":{"kind":"expression","value":"(0, 0, [0, 1, 2, 3, 4, 5])","explanation_zh":"Wave4第三層核對=(0, 0, [0, 1, 2, 3, 4, 5])；依完整明示資料重算；完整有限／symbolic certificate不自動升格為未聲明的一般定理；每個較晚partition須精確細化較早partition；filtration不自動推出adapted natural independent或Markov。"},"difficulty":{"band":"undergraduate_core","level":1,"skills":["有限filtration"]},"variant":{"family_id":"qf-mod29-filtration-block-at-time","seed":202610295026,"parameters":{"n":6,"partitions":[[0,0,0,0,0,0],[0,0,0,1,1,1],[0,0,0,10,10,10]],"time":0,"outcome":0,"domain":"Exact_finite_partition_filtration","operation":"filtration-block-at-time","semantic_template":"qf-mod29-filtration-block-at-time/{\"n\":6,\"outcome\":0,\"partitions\":[[0,0,0,0,0,0],[0,0,0,1,1,1],[0,0,0,10,10,10]],\"time\":0}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_model","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"產生端候選須由主端重算；不構成人工審定、任意無限定理、一般域／UFD、Hilbert、一般條件期望、LLN／CLT、商集、Lean執行或形式Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-14","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261014-advance-20261029-r05-finite-filtration-0027","batch_id":"batch-20261014-advance-20261029-r05-finite-filtration-foundations","language":"zh-Hant","source_mko_ids":["mko-finite-filtration"],"title_zh":"有限filtration","stem_zh":"所有資訊partition位於同一有限樣本空間。操作=filtration-block-at-time；資料={\"n\":6,\"partitions\":[[0,0,0,0,0,0],[0,0,0,1,1,1],[1,0,0,10,10,10]],\"time\":1,\"outcome\":1}。請依 [time,outcome,information_block] 欄序回答。","answer":{"kind":"expression","value":"(1, 1, [0, 1, 2])","explanation_zh":"Wave4第三層核對=(1, 1, [0, 1, 2])；依完整明示資料重算；完整有限／symbolic certificate不自動升格為未聲明的一般定理；每個較晚partition須精確細化較早partition；filtration不自動推出adapted natural independent或Markov。"},"difficulty":{"band":"undergraduate_core","level":1,"skills":["有限filtration"]},"variant":{"family_id":"qf-mod29-filtration-block-at-time","seed":202610295027,"parameters":{"n":6,"partitions":[[0,0,0,0,0,0],[0,0,0,1,1,1],[1,0,0,10,10,10]],"time":1,"outcome":1,"domain":"Exact_finite_partition_filtration","operation":"filtration-block-at-time","semantic_template":"qf-mod29-filtration-block-at-time/{\"n\":6,\"outcome\":1,\"partitions\":[[0,0,0,0,0,0],[0,0,0,1,1,1],[1,0,0,10,10,10]],\"time\":1}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_model","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"產生端候選須由主端重算；不構成人工審定、任意無限定理、一般域／UFD、Hilbert、一般條件期望、LLN／CLT、商集、Lean執行或形式Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-14","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261014-advance-20261029-r05-finite-filtration-0028","batch_id":"batch-20261014-advance-20261029-r05-finite-filtration-foundations","language":"zh-Hant","source_mko_ids":["mko-finite-filtration"],"title_zh":"有限filtration","stem_zh":"所有資訊partition位於同一有限樣本空間。操作=filtration-block-at-time；資料={\"n\":6,\"partitions\":[[0,0,0,0,0,0],[0,0,0,1,1,1],[0,1,0,10,10,10]],\"time\":2,\"outcome\":2}。請依 [time,outcome,information_block] 欄序回答。","answer":{"kind":"expression","value":"(2, 2, [0, 2])","explanation_zh":"Wave4第三層核對=(2, 2, [0, 2])；依完整明示資料重算；完整有限／symbolic certificate不自動升格為未聲明的一般定理；每個較晚partition須精確細化較早partition；filtration不自動推出adapted natural independent或Markov。"},"difficulty":{"band":"undergraduate_core","level":1,"skills":["有限filtration"]},"variant":{"family_id":"qf-mod29-filtration-block-at-time","seed":202610295028,"parameters":{"n":6,"partitions":[[0,0,0,0,0,0],[0,0,0,1,1,1],[0,1,0,10,10,10]],"time":2,"outcome":2,"domain":"Exact_finite_partition_filtration","operation":"filtration-block-at-time","semantic_template":"qf-mod29-filtration-block-at-time/{\"n\":6,\"outcome\":2,\"partitions\":[[0,0,0,0,0,0],[0,0,0,1,1,1],[0,1,0,10,10,10]],\"time\":2}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_model","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"產生端候選須由主端重算；不構成人工審定、任意無限定理、一般域／UFD、Hilbert、一般條件期望、LLN／CLT、商集、Lean執行或形式Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-14","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261014-advance-20261029-r05-finite-filtration-0029","batch_id":"batch-20261014-advance-20261029-r05-finite-filtration-foundations","language":"zh-Hant","source_mko_ids":["mko-finite-filtration"],"title_zh":"有限filtration","stem_zh":"所有資訊partition位於同一有限樣本空間。操作=filtration-block-at-time；資料={\"n\":6,\"partitions\":[[0,0,0,0,0,0],[0,0,0,1,1,1],[1,1,0,10,10,10]],\"time\":0,\"outcome\":3}。請依 [time,outcome,information_block] 欄序回答。","answer":{"kind":"expression","value":"(0, 3, [0, 1, 2, 3, 4, 5])","explanation_zh":"Wave4第三層核對=(0, 3, [0, 1, 2, 3, 4, 5])；依完整明示資料重算；完整有限／symbolic certificate不自動升格為未聲明的一般定理；每個較晚partition須精確細化較早partition；filtration不自動推出adapted natural independent或Markov。"},"difficulty":{"band":"undergraduate_core","level":1,"skills":["有限filtration"]},"variant":{"family_id":"qf-mod29-filtration-block-at-time","seed":202610295029,"parameters":{"n":6,"partitions":[[0,0,0,0,0,0],[0,0,0,1,1,1],[1,1,0,10,10,10]],"time":0,"outcome":3,"domain":"Exact_finite_partition_filtration","operation":"filtration-block-at-time","semantic_template":"qf-mod29-filtration-block-at-time/{\"n\":6,\"outcome\":3,\"partitions\":[[0,0,0,0,0,0],[0,0,0,1,1,1],[1,1,0,10,10,10]],\"time\":0}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_model","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"產生端候選須由主端重算；不構成人工審定、任意無限定理、一般域／UFD、Hilbert、一般條件期望、LLN／CLT、商集、Lean執行或形式Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-14","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261014-advance-20261029-r05-finite-filtration-0030","batch_id":"batch-20261014-advance-20261029-r05-finite-filtration-foundations","language":"zh-Hant","source_mko_ids":["mko-finite-filtration"],"title_zh":"有限filtration","stem_zh":"所有資訊partition位於同一有限樣本空間。操作=filtration-block-at-time；資料={\"n\":6,\"partitions\":[[0,0,0,0,0,0],[0,0,0,1,1,1],[0,0,1,10,10,10]],\"time\":1,\"outcome\":4}。請依 [time,outcome,information_block] 欄序回答。","answer":{"kind":"expression","value":"(1, 4, [3, 4, 5])","explanation_zh":"Wave4第三層核對=(1, 4, [3, 4, 5])；依完整明示資料重算；完整有限／symbolic certificate不自動升格為未聲明的一般定理；每個較晚partition須精確細化較早partition；filtration不自動推出adapted natural independent或Markov。"},"difficulty":{"band":"undergraduate_core","level":1,"skills":["有限filtration"]},"variant":{"family_id":"qf-mod29-filtration-block-at-time","seed":202610295030,"parameters":{"n":6,"partitions":[[0,0,0,0,0,0],[0,0,0,1,1,1],[0,0,1,10,10,10]],"time":1,"outcome":4,"domain":"Exact_finite_partition_filtration","operation":"filtration-block-at-time","semantic_template":"qf-mod29-filtration-block-at-time/{\"n\":6,\"outcome\":4,\"partitions\":[[0,0,0,0,0,0],[0,0,0,1,1,1],[0,0,1,10,10,10]],\"time\":1}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_model","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"產生端候選須由主端重算；不構成人工審定、任意無限定理、一般域／UFD、Hilbert、一般條件期望、LLN／CLT、商集、Lean執行或形式Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-14","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261014-advance-20261029-r05-finite-filtration-0031","batch_id":"batch-20261014-advance-20261029-r05-finite-filtration-foundations","language":"zh-Hant","source_mko_ids":["mko-finite-filtration"],"title_zh":"有限filtration","stem_zh":"所有資訊partition位於同一有限樣本空間。操作=filtration-block-at-time；資料={\"n\":6,\"partitions\":[[0,0,0,0,0,0],[0,0,0,1,1,1],[1,0,1,10,10,10]],\"time\":2,\"outcome\":5}。請依 [time,outcome,information_block] 欄序回答。","answer":{"kind":"expression","value":"(2, 5, [3, 4, 5])","explanation_zh":"Wave4第三層核對=(2, 5, [3, 4, 5])；依完整明示資料重算；完整有限／symbolic certificate不自動升格為未聲明的一般定理；每個較晚partition須精確細化較早partition；filtration不自動推出adapted natural independent或Markov。"},"difficulty":{"band":"undergraduate_core","level":1,"skills":["有限filtration"]},"variant":{"family_id":"qf-mod29-filtration-block-at-time","seed":202610295031,"parameters":{"n":6,"partitions":[[0,0,0,0,0,0],[0,0,0,1,1,1],[1,0,1,10,10,10]],"time":2,"outcome":5,"domain":"Exact_finite_partition_filtration","operation":"filtration-block-at-time","semantic_template":"qf-mod29-filtration-block-at-time/{\"n\":6,\"outcome\":5,\"partitions\":[[0,0,0,0,0,0],[0,0,0,1,1,1],[1,0,1,10,10,10]],\"time\":2}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_model","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"產生端候選須由主端重算；不構成人工審定、任意無限定理、一般域／UFD、Hilbert、一般條件期望、LLN／CLT、商集、Lean執行或形式Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-14","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261014-advance-20261029-r05-finite-filtration-0032","batch_id":"batch-20261014-advance-20261029-r05-finite-filtration-foundations","language":"zh-Hant","source_mko_ids":["mko-finite-filtration"],"title_zh":"有限filtration","stem_zh":"所有資訊partition位於同一有限樣本空間。操作=filtration-block-at-time；資料={\"n\":6,\"partitions\":[[0,0,0,0,0,0],[0,0,0,1,1,1],[0,1,1,10,10,10]],\"time\":0,\"outcome\":0}。請依 [time,outcome,information_block] 欄序回答。","answer":{"kind":"expression","value":"(0, 0, [0, 1, 2, 3, 4, 5])","explanation_zh":"Wave4第三層核對=(0, 0, [0, 1, 2, 3, 4, 5])；依完整明示資料重算；完整有限／symbolic certificate不自動升格為未聲明的一般定理；每個較晚partition須精確細化較早partition；filtration不自動推出adapted natural independent或Markov。"},"difficulty":{"band":"undergraduate_core","level":1,"skills":["有限filtration"]},"variant":{"family_id":"qf-mod29-filtration-block-at-time","seed":202610295032,"parameters":{"n":6,"partitions":[[0,0,0,0,0,0],[0,0,0,1,1,1],[0,1,1,10,10,10]],"time":0,"outcome":0,"domain":"Exact_finite_partition_filtration","operation":"filtration-block-at-time","semantic_template":"qf-mod29-filtration-block-at-time/{\"n\":6,\"outcome\":0,\"partitions\":[[0,0,0,0,0,0],[0,0,0,1,1,1],[0,1,1,10,10,10]],\"time\":0}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_model","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"產生端候選須由主端重算；不構成人工審定、任意無限定理、一般域／UFD、Hilbert、一般條件期望、LLN／CLT、商集、Lean執行或形式Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-14","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261014-advance-20261029-r05-finite-filtration-0033","batch_id":"batch-20261014-advance-20261029-r05-finite-filtration-foundations","language":"zh-Hant","source_mko_ids":["mko-finite-filtration"],"title_zh":"有限filtration","stem_zh":"所有資訊partition位於同一有限樣本空間。操作=filtration-block-at-time；資料={\"n\":6,\"partitions\":[[0,0,0,0,0,0],[0,0,0,1,1,1],[1,1,1,10,10,10]],\"time\":1,\"outcome\":1}。請依 [time,outcome,information_block] 欄序回答。","answer":{"kind":"expression","value":"(1, 1, [0, 1, 2])","explanation_zh":"Wave4第三層核對=(1, 1, [0, 1, 2])；依完整明示資料重算；完整有限／symbolic certificate不自動升格為未聲明的一般定理；每個較晚partition須精確細化較早partition；filtration不自動推出adapted natural independent或Markov。"},"difficulty":{"band":"undergraduate_core","level":1,"skills":["有限filtration"]},"variant":{"family_id":"qf-mod29-filtration-block-at-time","seed":202610295033,"parameters":{"n":6,"partitions":[[0,0,0,0,0,0],[0,0,0,1,1,1],[1,1,1,10,10,10]],"time":1,"outcome":1,"domain":"Exact_finite_partition_filtration","operation":"filtration-block-at-time","semantic_template":"qf-mod29-filtration-block-at-time/{\"n\":6,\"outcome\":1,\"partitions\":[[0,0,0,0,0,0],[0,0,0,1,1,1],[1,1,1,10,10,10]],\"time\":1}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_model","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"產生端候選須由主端重算；不構成人工審定、任意無限定理、一般域／UFD、Hilbert、一般條件期望、LLN／CLT、商集、Lean執行或形式Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-14","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261014-advance-20261029-r05-finite-filtration-0034","batch_id":"batch-20261014-advance-20261029-r05-finite-filtration-foundations","language":"zh-Hant","source_mko_ids":["mko-finite-filtration"],"title_zh":"有限filtration","stem_zh":"所有資訊partition位於同一有限樣本空間。操作=filtration-block-at-time；資料={\"n\":6,\"partitions\":[[0,0,0,0,0,0],[0,0,0,1,1,1],[0,0,0,11,10,10]],\"time\":2,\"outcome\":2}。請依 [time,outcome,information_block] 欄序回答。","answer":{"kind":"expression","value":"(2, 2, [0, 1, 2])","explanation_zh":"Wave4第三層核對=(2, 2, [0, 1, 2])；依完整明示資料重算；完整有限／symbolic certificate不自動升格為未聲明的一般定理；每個較晚partition須精確細化較早partition；filtration不自動推出adapted natural independent或Markov。"},"difficulty":{"band":"undergraduate_core","level":2,"skills":["有限filtration"]},"variant":{"family_id":"qf-mod29-filtration-block-at-time","seed":202610295034,"parameters":{"n":6,"partitions":[[0,0,0,0,0,0],[0,0,0,1,1,1],[0,0,0,11,10,10]],"time":2,"outcome":2,"domain":"Exact_finite_partition_filtration","operation":"filtration-block-at-time","semantic_template":"qf-mod29-filtration-block-at-time/{\"n\":6,\"outcome\":2,\"partitions\":[[0,0,0,0,0,0],[0,0,0,1,1,1],[0,0,0,11,10,10]],\"time\":2}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_model","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"產生端候選須由主端重算；不構成人工審定、任意無限定理、一般域／UFD、Hilbert、一般條件期望、LLN／CLT、商集、Lean執行或形式Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-14","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261014-advance-20261029-r05-finite-filtration-0035","batch_id":"batch-20261014-advance-20261029-r05-finite-filtration-foundations","language":"zh-Hant","source_mko_ids":["mko-finite-filtration"],"title_zh":"有限filtration","stem_zh":"所有資訊partition位於同一有限樣本空間。操作=filtration-block-at-time；資料={\"n\":6,\"partitions\":[[0,0,0,0,0,0],[0,0,0,1,1,1],[1,0,0,11,10,10]],\"time\":0,\"outcome\":3}。請依 [time,outcome,information_block] 欄序回答。","answer":{"kind":"expression","value":"(0, 3, [0, 1, 2, 3, 4, 5])","explanation_zh":"Wave4第三層核對=(0, 3, [0, 1, 2, 3, 4, 5])；依完整明示資料重算；完整有限／symbolic certificate不自動升格為未聲明的一般定理；每個較晚partition須精確細化較早partition；filtration不自動推出adapted natural independent或Markov。"},"difficulty":{"band":"undergraduate_core","level":2,"skills":["有限filtration"]},"variant":{"family_id":"qf-mod29-filtration-block-at-time","seed":202610295035,"parameters":{"n":6,"partitions":[[0,0,0,0,0,0],[0,0,0,1,1,1],[1,0,0,11,10,10]],"time":0,"outcome":3,"domain":"Exact_finite_partition_filtration","operation":"filtration-block-at-time","semantic_template":"qf-mod29-filtration-block-at-time/{\"n\":6,\"outcome\":3,\"partitions\":[[0,0,0,0,0,0],[0,0,0,1,1,1],[1,0,0,11,10,10]],\"time\":0}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_model","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"產生端候選須由主端重算；不構成人工審定、任意無限定理、一般域／UFD、Hilbert、一般條件期望、LLN／CLT、商集、Lean執行或形式Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-14","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261014-advance-20261029-r05-finite-filtration-0036","batch_id":"batch-20261014-advance-20261029-r05-finite-filtration-foundations","language":"zh-Hant","source_mko_ids":["mko-finite-filtration"],"title_zh":"有限filtration","stem_zh":"所有資訊partition位於同一有限樣本空間。操作=filtration-block-at-time；資料={\"n\":6,\"partitions\":[[0,0,0,0,0,0],[0,0,0,1,1,1],[0,1,0,11,10,10]],\"time\":1,\"outcome\":4}。請依 [time,outcome,information_block] 欄序回答。","answer":{"kind":"expression","value":"(1, 4, [3, 4, 5])","explanation_zh":"Wave4第三層核對=(1, 4, [3, 4, 5])；依完整明示資料重算；完整有限／symbolic certificate不自動升格為未聲明的一般定理；每個較晚partition須精確細化較早partition；filtration不自動推出adapted natural independent或Markov。"},"difficulty":{"band":"undergraduate_core","level":2,"skills":["有限filtration"]},"variant":{"family_id":"qf-mod29-filtration-block-at-time","seed":202610295036,"parameters":{"n":6,"partitions":[[0,0,0,0,0,0],[0,0,0,1,1,1],[0,1,0,11,10,10]],"time":1,"outcome":4,"domain":"Exact_finite_partition_filtration","operation":"filtration-block-at-time","semantic_template":"qf-mod29-filtration-block-at-time/{\"n\":6,\"outcome\":4,\"partitions\":[[0,0,0,0,0,0],[0,0,0,1,1,1],[0,1,0,11,10,10]],\"time\":1}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_model","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"產生端候選須由主端重算；不構成人工審定、任意無限定理、一般域／UFD、Hilbert、一般條件期望、LLN／CLT、商集、Lean執行或形式Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-14","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261014-advance-20261029-r05-finite-filtration-0037","batch_id":"batch-20261014-advance-20261029-r05-finite-filtration-foundations","language":"zh-Hant","source_mko_ids":["mko-finite-filtration"],"title_zh":"有限filtration","stem_zh":"所有資訊partition位於同一有限樣本空間。操作=filtration-block-at-time；資料={\"n\":6,\"partitions\":[[0,0,0,0,0,0],[0,0,0,1,1,1],[1,1,0,11,10,10]],\"time\":2,\"outcome\":5}。請依 [time,outcome,information_block] 欄序回答。","answer":{"kind":"expression","value":"(2, 5, [4, 5])","explanation_zh":"Wave4第三層核對=(2, 5, [4, 5])；依完整明示資料重算；完整有限／symbolic certificate不自動升格為未聲明的一般定理；每個較晚partition須精確細化較早partition；filtration不自動推出adapted natural independent或Markov。"},"difficulty":{"band":"undergraduate_core","level":2,"skills":["有限filtration"]},"variant":{"family_id":"qf-mod29-filtration-block-at-time","seed":202610295037,"parameters":{"n":6,"partitions":[[0,0,0,0,0,0],[0,0,0,1,1,1],[1,1,0,11,10,10]],"time":2,"outcome":5,"domain":"Exact_finite_partition_filtration","operation":"filtration-block-at-time","semantic_template":"qf-mod29-filtration-block-at-time/{\"n\":6,\"outcome\":5,\"partitions\":[[0,0,0,0,0,0],[0,0,0,1,1,1],[1,1,0,11,10,10]],\"time\":2}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_model","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"產生端候選須由主端重算；不構成人工審定、任意無限定理、一般域／UFD、Hilbert、一般條件期望、LLN／CLT、商集、Lean執行或形式Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-14","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261014-advance-20261029-r05-finite-filtration-0038","batch_id":"batch-20261014-advance-20261029-r05-finite-filtration-foundations","language":"zh-Hant","source_mko_ids":["mko-finite-filtration"],"title_zh":"有限filtration","stem_zh":"所有資訊partition位於同一有限樣本空間。操作=filtration-block-at-time；資料={\"n\":6,\"partitions\":[[0,0,0,0,0,0],[0,0,0,1,1,1],[0,0,1,11,10,10]],\"time\":0,\"outcome\":0}。請依 [time,outcome,information_block] 欄序回答。","answer":{"kind":"expression","value":"(0, 0, [0, 1, 2, 3, 4, 5])","explanation_zh":"Wave4第三層核對=(0, 0, [0, 1, 2, 3, 4, 5])；依完整明示資料重算；完整有限／symbolic certificate不自動升格為未聲明的一般定理；每個較晚partition須精確細化較早partition；filtration不自動推出adapted natural independent或Markov。"},"difficulty":{"band":"undergraduate_core","level":2,"skills":["有限filtration"]},"variant":{"family_id":"qf-mod29-filtration-block-at-time","seed":202610295038,"parameters":{"n":6,"partitions":[[0,0,0,0,0,0],[0,0,0,1,1,1],[0,0,1,11,10,10]],"time":0,"outcome":0,"domain":"Exact_finite_partition_filtration","operation":"filtration-block-at-time","semantic_template":"qf-mod29-filtration-block-at-time/{\"n\":6,\"outcome\":0,\"partitions\":[[0,0,0,0,0,0],[0,0,0,1,1,1],[0,0,1,11,10,10]],\"time\":0}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_model","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"產生端候選須由主端重算；不構成人工審定、任意無限定理、一般域／UFD、Hilbert、一般條件期望、LLN／CLT、商集、Lean執行或形式Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-14","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261014-advance-20261029-r05-finite-filtration-0039","batch_id":"batch-20261014-advance-20261029-r05-finite-filtration-foundations","language":"zh-Hant","source_mko_ids":["mko-finite-filtration"],"title_zh":"有限filtration","stem_zh":"所有資訊partition位於同一有限樣本空間。操作=filtration-block-at-time；資料={\"n\":6,\"partitions\":[[0,0,0,0,0,0],[0,0,0,1,1,1],[1,0,1,11,10,10]],\"time\":1,\"outcome\":1}。請依 [time,outcome,information_block] 欄序回答。","answer":{"kind":"expression","value":"(1, 1, [0, 1, 2])","explanation_zh":"Wave4第三層核對=(1, 1, [0, 1, 2])；依完整明示資料重算；完整有限／symbolic certificate不自動升格為未聲明的一般定理；每個較晚partition須精確細化較早partition；filtration不自動推出adapted natural independent或Markov。"},"difficulty":{"band":"undergraduate_core","level":2,"skills":["有限filtration"]},"variant":{"family_id":"qf-mod29-filtration-block-at-time","seed":202610295039,"parameters":{"n":6,"partitions":[[0,0,0,0,0,0],[0,0,0,1,1,1],[1,0,1,11,10,10]],"time":1,"outcome":1,"domain":"Exact_finite_partition_filtration","operation":"filtration-block-at-time","semantic_template":"qf-mod29-filtration-block-at-time/{\"n\":6,\"outcome\":1,\"partitions\":[[0,0,0,0,0,0],[0,0,0,1,1,1],[1,0,1,11,10,10]],\"time\":1}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_model","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"產生端候選須由主端重算；不構成人工審定、任意無限定理、一般域／UFD、Hilbert、一般條件期望、LLN／CLT、商集、Lean執行或形式Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-14","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261014-advance-20261029-r05-finite-filtration-0040","batch_id":"batch-20261014-advance-20261029-r05-finite-filtration-foundations","language":"zh-Hant","source_mko_ids":["mko-finite-filtration"],"title_zh":"有限filtration","stem_zh":"所有資訊partition位於同一有限樣本空間。操作=filtration-block-at-time；資料={\"n\":6,\"partitions\":[[0,0,0,0,0,0],[0,0,0,1,1,1],[0,1,1,11,10,10]],\"time\":2,\"outcome\":2}。請依 [time,outcome,information_block] 欄序回答。","answer":{"kind":"expression","value":"(2, 2, [1, 2])","explanation_zh":"Wave4第三層核對=(2, 2, [1, 2])；依完整明示資料重算；完整有限／symbolic certificate不自動升格為未聲明的一般定理；每個較晚partition須精確細化較早partition；filtration不自動推出adapted natural independent或Markov。"},"difficulty":{"band":"undergraduate_core","level":2,"skills":["有限filtration"]},"variant":{"family_id":"qf-mod29-filtration-block-at-time","seed":202610295040,"parameters":{"n":6,"partitions":[[0,0,0,0,0,0],[0,0,0,1,1,1],[0,1,1,11,10,10]],"time":2,"outcome":2,"domain":"Exact_finite_partition_filtration","operation":"filtration-block-at-time","semantic_template":"qf-mod29-filtration-block-at-time/{\"n\":6,\"outcome\":2,\"partitions\":[[0,0,0,0,0,0],[0,0,0,1,1,1],[0,1,1,11,10,10]],\"time\":2}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_model","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"產生端候選須由主端重算；不構成人工審定、任意無限定理、一般域／UFD、Hilbert、一般條件期望、LLN／CLT、商集、Lean執行或形式Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-14","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261014-advance-20261029-r05-finite-filtration-0041","batch_id":"batch-20261014-advance-20261029-r05-finite-filtration-foundations","language":"zh-Hant","source_mko_ids":["mko-finite-filtration"],"title_zh":"有限filtration","stem_zh":"所有資訊partition位於同一有限樣本空間。操作=filtration-block-at-time；資料={\"n\":6,\"partitions\":[[0,0,0,0,0,0],[0,0,0,1,1,1],[1,1,1,11,10,10]],\"time\":0,\"outcome\":3}。請依 [time,outcome,information_block] 欄序回答。","answer":{"kind":"expression","value":"(0, 3, [0, 1, 2, 3, 4, 5])","explanation_zh":"Wave4第三層核對=(0, 3, [0, 1, 2, 3, 4, 5])；依完整明示資料重算；完整有限／symbolic certificate不自動升格為未聲明的一般定理；每個較晚partition須精確細化較早partition；filtration不自動推出adapted natural independent或Markov。"},"difficulty":{"band":"undergraduate_core","level":2,"skills":["有限filtration"]},"variant":{"family_id":"qf-mod29-filtration-block-at-time","seed":202610295041,"parameters":{"n":6,"partitions":[[0,0,0,0,0,0],[0,0,0,1,1,1],[1,1,1,11,10,10]],"time":0,"outcome":3,"domain":"Exact_finite_partition_filtration","operation":"filtration-block-at-time","semantic_template":"qf-mod29-filtration-block-at-time/{\"n\":6,\"outcome\":3,\"partitions\":[[0,0,0,0,0,0],[0,0,0,1,1,1],[1,1,1,11,10,10]],\"time\":0}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_model","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"產生端候選須由主端重算；不構成人工審定、任意無限定理、一般域／UFD、Hilbert、一般條件期望、LLN／CLT、商集、Lean執行或形式Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-14","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261014-advance-20261029-r05-finite-filtration-0042","batch_id":"batch-20261014-advance-20261029-r05-finite-filtration-foundations","language":"zh-Hant","source_mko_ids":["mko-finite-filtration"],"title_zh":"有限filtration","stem_zh":"所有資訊partition位於同一有限樣本空間。操作=filtration-block-at-time；資料={\"n\":6,\"partitions\":[[0,0,0,0,0,0],[0,0,0,1,1,1],[0,0,0,10,11,10]],\"time\":1,\"outcome\":4}。請依 [time,outcome,information_block] 欄序回答。","answer":{"kind":"expression","value":"(1, 4, [3, 4, 5])","explanation_zh":"Wave4第三層核對=(1, 4, [3, 4, 5])；依完整明示資料重算；完整有限／symbolic certificate不自動升格為未聲明的一般定理；每個較晚partition須精確細化較早partition；filtration不自動推出adapted natural independent或Markov。"},"difficulty":{"band":"undergraduate_core","level":2,"skills":["有限filtration"]},"variant":{"family_id":"qf-mod29-filtration-block-at-time","seed":202610295042,"parameters":{"n":6,"partitions":[[0,0,0,0,0,0],[0,0,0,1,1,1],[0,0,0,10,11,10]],"time":1,"outcome":4,"domain":"Exact_finite_partition_filtration","operation":"filtration-block-at-time","semantic_template":"qf-mod29-filtration-block-at-time/{\"n\":6,\"outcome\":4,\"partitions\":[[0,0,0,0,0,0],[0,0,0,1,1,1],[0,0,0,10,11,10]],\"time\":1}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_model","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"產生端候選須由主端重算；不構成人工審定、任意無限定理、一般域／UFD、Hilbert、一般條件期望、LLN／CLT、商集、Lean執行或形式Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-14","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261014-advance-20261029-r05-finite-filtration-0043","batch_id":"batch-20261014-advance-20261029-r05-finite-filtration-foundations","language":"zh-Hant","source_mko_ids":["mko-finite-filtration"],"title_zh":"有限filtration","stem_zh":"所有資訊partition位於同一有限樣本空間。操作=filtration-block-at-time；資料={\"n\":6,\"partitions\":[[0,0,0,0,0,0],[0,0,0,1,1,1],[1,0,0,10,11,10]],\"time\":2,\"outcome\":5}。請依 [time,outcome,information_block] 欄序回答。","answer":{"kind":"expression","value":"(2, 5, [3, 5])","explanation_zh":"Wave4第三層核對=(2, 5, [3, 5])；依完整明示資料重算；完整有限／symbolic certificate不自動升格為未聲明的一般定理；每個較晚partition須精確細化較早partition；filtration不自動推出adapted natural independent或Markov。"},"difficulty":{"band":"undergraduate_core","level":3,"skills":["有限filtration"]},"variant":{"family_id":"qf-mod29-filtration-block-at-time","seed":202610295043,"parameters":{"n":6,"partitions":[[0,0,0,0,0,0],[0,0,0,1,1,1],[1,0,0,10,11,10]],"time":2,"outcome":5,"domain":"Exact_finite_partition_filtration","operation":"filtration-block-at-time","semantic_template":"qf-mod29-filtration-block-at-time/{\"n\":6,\"outcome\":5,\"partitions\":[[0,0,0,0,0,0],[0,0,0,1,1,1],[1,0,0,10,11,10]],\"time\":2}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_model","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"產生端候選須由主端重算；不構成人工審定、任意無限定理、一般域／UFD、Hilbert、一般條件期望、LLN／CLT、商集、Lean執行或形式Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-14","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261014-advance-20261029-r05-finite-filtration-0044","batch_id":"batch-20261014-advance-20261029-r05-finite-filtration-foundations","language":"zh-Hant","source_mko_ids":["mko-finite-filtration"],"title_zh":"有限filtration","stem_zh":"所有資訊partition位於同一有限樣本空間。操作=filtration-block-at-time；資料={\"n\":6,\"partitions\":[[0,0,0,0,0,0],[0,0,0,1,1,1],[0,1,0,10,11,10]],\"time\":0,\"outcome\":0}。請依 [time,outcome,information_block] 欄序回答。","answer":{"kind":"expression","value":"(0, 0, [0, 1, 2, 3, 4, 5])","explanation_zh":"Wave4第三層核對=(0, 0, [0, 1, 2, 3, 4, 5])；依完整明示資料重算；完整有限／symbolic certificate不自動升格為未聲明的一般定理；每個較晚partition須精確細化較早partition；filtration不自動推出adapted natural independent或Markov。"},"difficulty":{"band":"undergraduate_core","level":3,"skills":["有限filtration"]},"variant":{"family_id":"qf-mod29-filtration-block-at-time","seed":202610295044,"parameters":{"n":6,"partitions":[[0,0,0,0,0,0],[0,0,0,1,1,1],[0,1,0,10,11,10]],"time":0,"outcome":0,"domain":"Exact_finite_partition_filtration","operation":"filtration-block-at-time","semantic_template":"qf-mod29-filtration-block-at-time/{\"n\":6,\"outcome\":0,\"partitions\":[[0,0,0,0,0,0],[0,0,0,1,1,1],[0,1,0,10,11,10]],\"time\":0}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_model","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"產生端候選須由主端重算；不構成人工審定、任意無限定理、一般域／UFD、Hilbert、一般條件期望、LLN／CLT、商集、Lean執行或形式Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-14","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261014-advance-20261029-r05-finite-filtration-0045","batch_id":"batch-20261014-advance-20261029-r05-finite-filtration-foundations","language":"zh-Hant","source_mko_ids":["mko-finite-filtration"],"title_zh":"有限filtration","stem_zh":"所有資訊partition位於同一有限樣本空間。操作=filtration-block-at-time；資料={\"n\":6,\"partitions\":[[0,0,0,0,0,0],[0,0,0,1,1,1],[1,1,0,10,11,10]],\"time\":1,\"outcome\":1}。請依 [time,outcome,information_block] 欄序回答。","answer":{"kind":"expression","value":"(1, 1, [0, 1, 2])","explanation_zh":"Wave4第三層核對=(1, 1, [0, 1, 2])；依完整明示資料重算；完整有限／symbolic certificate不自動升格為未聲明的一般定理；每個較晚partition須精確細化較早partition；filtration不自動推出adapted natural independent或Markov。"},"difficulty":{"band":"undergraduate_core","level":3,"skills":["有限filtration"]},"variant":{"family_id":"qf-mod29-filtration-block-at-time","seed":202610295045,"parameters":{"n":6,"partitions":[[0,0,0,0,0,0],[0,0,0,1,1,1],[1,1,0,10,11,10]],"time":1,"outcome":1,"domain":"Exact_finite_partition_filtration","operation":"filtration-block-at-time","semantic_template":"qf-mod29-filtration-block-at-time/{\"n\":6,\"outcome\":1,\"partitions\":[[0,0,0,0,0,0],[0,0,0,1,1,1],[1,1,0,10,11,10]],\"time\":1}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_model","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"產生端候選須由主端重算；不構成人工審定、任意無限定理、一般域／UFD、Hilbert、一般條件期望、LLN／CLT、商集、Lean執行或形式Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-14","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261014-advance-20261029-r05-finite-filtration-0046","batch_id":"batch-20261014-advance-20261029-r05-finite-filtration-foundations","language":"zh-Hant","source_mko_ids":["mko-finite-filtration"],"title_zh":"有限filtration","stem_zh":"所有資訊partition位於同一有限樣本空間。操作=filtration-block-at-time；資料={\"n\":6,\"partitions\":[[0,0,0,0,0,0],[0,0,0,1,1,1],[0,0,1,10,11,10]],\"time\":2,\"outcome\":2}。請依 [time,outcome,information_block] 欄序回答。","answer":{"kind":"expression","value":"(2, 2, [2])","explanation_zh":"Wave4第三層核對=(2, 2, [2])；依完整明示資料重算；完整有限／symbolic certificate不自動升格為未聲明的一般定理；每個較晚partition須精確細化較早partition；filtration不自動推出adapted natural independent或Markov。"},"difficulty":{"band":"undergraduate_core","level":3,"skills":["有限filtration"]},"variant":{"family_id":"qf-mod29-filtration-block-at-time","seed":202610295046,"parameters":{"n":6,"partitions":[[0,0,0,0,0,0],[0,0,0,1,1,1],[0,0,1,10,11,10]],"time":2,"outcome":2,"domain":"Exact_finite_partition_filtration","operation":"filtration-block-at-time","semantic_template":"qf-mod29-filtration-block-at-time/{\"n\":6,\"outcome\":2,\"partitions\":[[0,0,0,0,0,0],[0,0,0,1,1,1],[0,0,1,10,11,10]],\"time\":2}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_model","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"產生端候選須由主端重算；不構成人工審定、任意無限定理、一般域／UFD、Hilbert、一般條件期望、LLN／CLT、商集、Lean執行或形式Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-14","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261014-advance-20261029-r05-finite-filtration-0047","batch_id":"batch-20261014-advance-20261029-r05-finite-filtration-foundations","language":"zh-Hant","source_mko_ids":["mko-finite-filtration"],"title_zh":"有限filtration","stem_zh":"所有資訊partition位於同一有限樣本空間。操作=filtration-block-at-time；資料={\"n\":6,\"partitions\":[[0,0,0,0,0,0],[0,0,0,1,1,1],[1,0,1,10,11,10]],\"time\":0,\"outcome\":3}。請依 [time,outcome,information_block] 欄序回答。","answer":{"kind":"expression","value":"(0, 3, [0, 1, 2, 3, 4, 5])","explanation_zh":"Wave4第三層核對=(0, 3, [0, 1, 2, 3, 4, 5])；依完整明示資料重算；完整有限／symbolic certificate不自動升格為未聲明的一般定理；每個較晚partition須精確細化較早partition；filtration不自動推出adapted natural independent或Markov。"},"difficulty":{"band":"undergraduate_core","level":3,"skills":["有限filtration"]},"variant":{"family_id":"qf-mod29-filtration-block-at-time","seed":202610295047,"parameters":{"n":6,"partitions":[[0,0,0,0,0,0],[0,0,0,1,1,1],[1,0,1,10,11,10]],"time":0,"outcome":3,"domain":"Exact_finite_partition_filtration","operation":"filtration-block-at-time","semantic_template":"qf-mod29-filtration-block-at-time/{\"n\":6,\"outcome\":3,\"partitions\":[[0,0,0,0,0,0],[0,0,0,1,1,1],[1,0,1,10,11,10]],\"time\":0}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_model","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"產生端候選須由主端重算；不構成人工審定、任意無限定理、一般域／UFD、Hilbert、一般條件期望、LLN／CLT、商集、Lean執行或形式Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-14","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261014-advance-20261029-r05-finite-filtration-0048","batch_id":"batch-20261014-advance-20261029-r05-finite-filtration-foundations","language":"zh-Hant","source_mko_ids":["mko-finite-filtration"],"title_zh":"有限filtration","stem_zh":"所有資訊partition位於同一有限樣本空間。操作=filtration-block-at-time；資料={\"n\":6,\"partitions\":[[0,0,0,0,0,0],[0,0,0,1,1,1],[0,1,1,10,11,10]],\"time\":1,\"outcome\":4}。請依 [time,outcome,information_block] 欄序回答。","answer":{"kind":"expression","value":"(1, 4, [3, 4, 5])","explanation_zh":"Wave4第三層核對=(1, 4, [3, 4, 5])；依完整明示資料重算；完整有限／symbolic certificate不自動升格為未聲明的一般定理；每個較晚partition須精確細化較早partition；filtration不自動推出adapted natural independent或Markov。"},"difficulty":{"band":"undergraduate_core","level":3,"skills":["有限filtration"]},"variant":{"family_id":"qf-mod29-filtration-block-at-time","seed":202610295048,"parameters":{"n":6,"partitions":[[0,0,0,0,0,0],[0,0,0,1,1,1],[0,1,1,10,11,10]],"time":1,"outcome":4,"domain":"Exact_finite_partition_filtration","operation":"filtration-block-at-time","semantic_template":"qf-mod29-filtration-block-at-time/{\"n\":6,\"outcome\":4,\"partitions\":[[0,0,0,0,0,0],[0,0,0,1,1,1],[0,1,1,10,11,10]],\"time\":1}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_model","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"產生端候選須由主端重算；不構成人工審定、任意無限定理、一般域／UFD、Hilbert、一般條件期望、LLN／CLT、商集、Lean執行或形式Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-14","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261014-advance-20261029-r05-finite-filtration-0049","batch_id":"batch-20261014-advance-20261029-r05-finite-filtration-foundations","language":"zh-Hant","source_mko_ids":["mko-finite-filtration"],"title_zh":"有限filtration","stem_zh":"所有資訊partition位於同一有限樣本空間。操作=filtration-block-at-time；資料={\"n\":6,\"partitions\":[[0,0,0,0,0,0],[0,0,0,1,1,1],[1,1,1,10,11,10]],\"time\":2,\"outcome\":5}。請依 [time,outcome,information_block] 欄序回答。","answer":{"kind":"expression","value":"(2, 5, [3, 5])","explanation_zh":"Wave4第三層核對=(2, 5, [3, 5])；依完整明示資料重算；完整有限／symbolic certificate不自動升格為未聲明的一般定理；每個較晚partition須精確細化較早partition；filtration不自動推出adapted natural independent或Markov。"},"difficulty":{"band":"undergraduate_core","level":3,"skills":["有限filtration"]},"variant":{"family_id":"qf-mod29-filtration-block-at-time","seed":202610295049,"parameters":{"n":6,"partitions":[[0,0,0,0,0,0],[0,0,0,1,1,1],[1,1,1,10,11,10]],"time":2,"outcome":5,"domain":"Exact_finite_partition_filtration","operation":"filtration-block-at-time","semantic_template":"qf-mod29-filtration-block-at-time/{\"n\":6,\"outcome\":5,\"partitions\":[[0,0,0,0,0,0],[0,0,0,1,1,1],[1,1,1,10,11,10]],\"time\":2}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_model","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"產生端候選須由主端重算；不構成人工審定、任意無限定理、一般域／UFD、Hilbert、一般條件期望、LLN／CLT、商集、Lean執行或形式Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-14","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261014-advance-20261029-r05-finite-filtration-0050","batch_id":"batch-20261014-advance-20261029-r05-finite-filtration-foundations","language":"zh-Hant","source_mko_ids":["mko-finite-filtration"],"title_zh":"有限filtration","stem_zh":"所有資訊partition位於同一有限樣本空間。操作=filtration-block-at-time；資料={\"n\":6,\"partitions\":[[0,0,0,0,0,0],[0,0,0,1,1,1],[0,0,0,11,11,10]],\"time\":0,\"outcome\":0}。請依 [time,outcome,information_block] 欄序回答。","answer":{"kind":"expression","value":"(0, 0, [0, 1, 2, 3, 4, 5])","explanation_zh":"Wave4第三層核對=(0, 0, [0, 1, 2, 3, 4, 5])；依完整明示資料重算；完整有限／symbolic certificate不自動升格為未聲明的一般定理；每個較晚partition須精確細化較早partition；filtration不自動推出adapted natural independent或Markov。"},"difficulty":{"band":"undergraduate_core","level":3,"skills":["有限filtration"]},"variant":{"family_id":"qf-mod29-filtration-block-at-time","seed":202610295050,"parameters":{"n":6,"partitions":[[0,0,0,0,0,0],[0,0,0,1,1,1],[0,0,0,11,11,10]],"time":0,"outcome":0,"domain":"Exact_finite_partition_filtration","operation":"filtration-block-at-time","semantic_template":"qf-mod29-filtration-block-at-time/{\"n\":6,\"outcome\":0,\"partitions\":[[0,0,0,0,0,0],[0,0,0,1,1,1],[0,0,0,11,11,10]],\"time\":0}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_model","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"產生端候選須由主端重算；不構成人工審定、任意無限定理、一般域／UFD、Hilbert、一般條件期望、LLN／CLT、商集、Lean執行或形式Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-14","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261014-advance-20261029-r05-finite-filtration-0051","batch_id":"batch-20261014-advance-20261029-r05-finite-filtration-foundations","language":"zh-Hant","source_mko_ids":["mko-finite-filtration"],"title_zh":"有限filtration","stem_zh":"所有資訊partition位於同一有限樣本空間。操作=filtration-adaptedness；資料={\"n\":6,\"partitions\":[[0,0,0,0,0,0],[0,0,0,1,1,1],[0,0,0,10,10,10]],\"process_values\":[[0,0,0,0,0,0],[1,2,1,2,2,2],[2,2,2,12,12,12]]}。請依 [filtration,measurability_failures,adapted,qualified_adapted_process] 欄序回答。","answer":{"kind":"expression","value":"(是, [[1, 0, [0, 1, 2], [1, 2]]], 否, 否)","explanation_zh":"Wave4第三層核對=(是, [[1, 0, [0, 1, 2], [1, 2]]], 否, 否)；依完整明示資料重算；完整有限／symbolic certificate不自動升格為未聲明的一般定理；每個較晚partition須精確細化較早partition；filtration不自動推出adapted natural independent或Markov。"},"difficulty":{"band":"undergraduate_core","level":1,"skills":["有限filtration"]},"variant":{"family_id":"qf-mod29-filtration-adaptedness","seed":202610295051,"parameters":{"n":6,"partitions":[[0,0,0,0,0,0],[0,0,0,1,1,1],[0,0,0,10,10,10]],"process_values":[[0,0,0,0,0,0],[1,2,1,2,2,2],[2,2,2,12,12,12]],"domain":"Exact_finite_partition_filtration","operation":"filtration-adaptedness","semantic_template":"qf-mod29-filtration-adaptedness/{\"n\":6,\"partitions\":[[0,0,0,0,0,0],[0,0,0,1,1,1],[0,0,0,10,10,10]],\"process_values\":[[0,0,0,0,0,0],[1,2,1,2,2,2],[2,2,2,12,12,12]]}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_model","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"產生端候選須由主端重算；不構成人工審定、任意無限定理、一般域／UFD、Hilbert、一般條件期望、LLN／CLT、商集、Lean執行或形式Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-14","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261014-advance-20261029-r05-finite-filtration-0052","batch_id":"batch-20261014-advance-20261029-r05-finite-filtration-foundations","language":"zh-Hant","source_mko_ids":["mko-finite-filtration"],"title_zh":"有限filtration","stem_zh":"所有資訊partition位於同一有限樣本空間。操作=filtration-adaptedness；資料={\"n\":6,\"partitions\":[[0,0,0,0,0,0],[0,0,0,1,1,1],[1,0,0,10,10,10]],\"process_values\":[[0,0,0,0,0,0],[1,1,1,2,2,2],[3,2,2,12,12,12]]}。請依 [filtration,measurability_failures,adapted,qualified_adapted_process] 欄序回答。","answer":{"kind":"expression","value":"(是, [], 是, 是)","explanation_zh":"Wave4第三層核對=(是, [], 是, 是)；依完整明示資料重算；完整有限／symbolic certificate不自動升格為未聲明的一般定理；每個較晚partition須精確細化較早partition；filtration不自動推出adapted natural independent或Markov。"},"difficulty":{"band":"undergraduate_core","level":1,"skills":["有限filtration"]},"variant":{"family_id":"qf-mod29-filtration-adaptedness","seed":202610295052,"parameters":{"n":6,"partitions":[[0,0,0,0,0,0],[0,0,0,1,1,1],[1,0,0,10,10,10]],"process_values":[[0,0,0,0,0,0],[1,1,1,2,2,2],[3,2,2,12,12,12]],"domain":"Exact_finite_partition_filtration","operation":"filtration-adaptedness","semantic_template":"qf-mod29-filtration-adaptedness/{\"n\":6,\"partitions\":[[0,0,0,0,0,0],[0,0,0,1,1,1],[1,0,0,10,10,10]],\"process_values\":[[0,0,0,0,0,0],[1,1,1,2,2,2],[3,2,2,12,12,12]]}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_model","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"產生端候選須由主端重算；不構成人工審定、任意無限定理、一般域／UFD、Hilbert、一般條件期望、LLN／CLT、商集、Lean執行或形式Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-14","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261014-advance-20261029-r05-finite-filtration-0053","batch_id":"batch-20261014-advance-20261029-r05-finite-filtration-foundations","language":"zh-Hant","source_mko_ids":["mko-finite-filtration"],"title_zh":"有限filtration","stem_zh":"所有資訊partition位於同一有限樣本空間。操作=filtration-adaptedness；資料={\"n\":6,\"partitions\":[[0,0,0,0,0,0],[0,0,0,1,1,1],[0,1,0,10,10,10]],\"process_values\":[[0,0,0,0,0,0],[1,1,1,2,2,2],[2,3,2,12,12,12]]}。請依 [filtration,measurability_failures,adapted,qualified_adapted_process] 欄序回答。","answer":{"kind":"expression","value":"(是, [], 是, 是)","explanation_zh":"Wave4第三層核對=(是, [], 是, 是)；依完整明示資料重算；完整有限／symbolic certificate不自動升格為未聲明的一般定理；每個較晚partition須精確細化較早partition；filtration不自動推出adapted natural independent或Markov。"},"difficulty":{"band":"undergraduate_core","level":1,"skills":["有限filtration"]},"variant":{"family_id":"qf-mod29-filtration-adaptedness","seed":202610295053,"parameters":{"n":6,"partitions":[[0,0,0,0,0,0],[0,0,0,1,1,1],[0,1,0,10,10,10]],"process_values":[[0,0,0,0,0,0],[1,1,1,2,2,2],[2,3,2,12,12,12]],"domain":"Exact_finite_partition_filtration","operation":"filtration-adaptedness","semantic_template":"qf-mod29-filtration-adaptedness/{\"n\":6,\"partitions\":[[0,0,0,0,0,0],[0,0,0,1,1,1],[0,1,0,10,10,10]],\"process_values\":[[0,0,0,0,0,0],[1,1,1,2,2,2],[2,3,2,12,12,12]]}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_model","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"產生端候選須由主端重算；不構成人工審定、任意無限定理、一般域／UFD、Hilbert、一般條件期望、LLN／CLT、商集、Lean執行或形式Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-14","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261014-advance-20261029-r05-finite-filtration-0054","batch_id":"batch-20261014-advance-20261029-r05-finite-filtration-foundations","language":"zh-Hant","source_mko_ids":["mko-finite-filtration"],"title_zh":"有限filtration","stem_zh":"所有資訊partition位於同一有限樣本空間。操作=filtration-adaptedness；資料={\"n\":6,\"partitions\":[[0,0,0,0,0,0],[0,0,0,1,1,1],[1,1,0,10,10,10]],\"process_values\":[[0,0,0,0,0,0],[1,1,1,2,2,2],[3,3,2,12,12,12]]}。請依 [filtration,measurability_failures,adapted,qualified_adapted_process] 欄序回答。","answer":{"kind":"expression","value":"(是, [], 是, 是)","explanation_zh":"Wave4第三層核對=(是, [], 是, 是)；依完整明示資料重算；完整有限／symbolic certificate不自動升格為未聲明的一般定理；每個較晚partition須精確細化較早partition；filtration不自動推出adapted natural independent或Markov。"},"difficulty":{"band":"undergraduate_core","level":1,"skills":["有限filtration"]},"variant":{"family_id":"qf-mod29-filtration-adaptedness","seed":202610295054,"parameters":{"n":6,"partitions":[[0,0,0,0,0,0],[0,0,0,1,1,1],[1,1,0,10,10,10]],"process_values":[[0,0,0,0,0,0],[1,1,1,2,2,2],[3,3,2,12,12,12]],"domain":"Exact_finite_partition_filtration","operation":"filtration-adaptedness","semantic_template":"qf-mod29-filtration-adaptedness/{\"n\":6,\"partitions\":[[0,0,0,0,0,0],[0,0,0,1,1,1],[1,1,0,10,10,10]],\"process_values\":[[0,0,0,0,0,0],[1,1,1,2,2,2],[3,3,2,12,12,12]]}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_model","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"產生端候選須由主端重算；不構成人工審定、任意無限定理、一般域／UFD、Hilbert、一般條件期望、LLN／CLT、商集、Lean執行或形式Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-14","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261014-advance-20261029-r05-finite-filtration-0055","batch_id":"batch-20261014-advance-20261029-r05-finite-filtration-foundations","language":"zh-Hant","source_mko_ids":["mko-finite-filtration"],"title_zh":"有限filtration","stem_zh":"所有資訊partition位於同一有限樣本空間。操作=filtration-adaptedness；資料={\"n\":6,\"partitions\":[[0,0,0,0,0,0],[0,0,0,1,1,1],[0,0,1,10,10,10]],\"process_values\":[[0,0,0,0,0,0],[1,1,1,2,2,2],[2,2,3,12,12,12]]}。請依 [filtration,measurability_failures,adapted,qualified_adapted_process] 欄序回答。","answer":{"kind":"expression","value":"(是, [], 是, 是)","explanation_zh":"Wave4第三層核對=(是, [], 是, 是)；依完整明示資料重算；完整有限／symbolic certificate不自動升格為未聲明的一般定理；每個較晚partition須精確細化較早partition；filtration不自動推出adapted natural independent或Markov。"},"difficulty":{"band":"undergraduate_core","level":1,"skills":["有限filtration"]},"variant":{"family_id":"qf-mod29-filtration-adaptedness","seed":202610295055,"parameters":{"n":6,"partitions":[[0,0,0,0,0,0],[0,0,0,1,1,1],[0,0,1,10,10,10]],"process_values":[[0,0,0,0,0,0],[1,1,1,2,2,2],[2,2,3,12,12,12]],"domain":"Exact_finite_partition_filtration","operation":"filtration-adaptedness","semantic_template":"qf-mod29-filtration-adaptedness/{\"n\":6,\"partitions\":[[0,0,0,0,0,0],[0,0,0,1,1,1],[0,0,1,10,10,10]],\"process_values\":[[0,0,0,0,0,0],[1,1,1,2,2,2],[2,2,3,12,12,12]]}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_model","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"產生端候選須由主端重算；不構成人工審定、任意無限定理、一般域／UFD、Hilbert、一般條件期望、LLN／CLT、商集、Lean執行或形式Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-14","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261014-advance-20261029-r05-finite-filtration-0056","batch_id":"batch-20261014-advance-20261029-r05-finite-filtration-foundations","language":"zh-Hant","source_mko_ids":["mko-finite-filtration"],"title_zh":"有限filtration","stem_zh":"所有資訊partition位於同一有限樣本空間。操作=filtration-adaptedness；資料={\"n\":6,\"partitions\":[[0,0,0,0,0,0],[0,0,0,1,1,1],[1,0,1,10,10,10]],\"process_values\":[[0,0,0,0,0,0],[1,2,1,2,2,2],[3,2,3,12,12,12]]}。請依 [filtration,measurability_failures,adapted,qualified_adapted_process] 欄序回答。","answer":{"kind":"expression","value":"(是, [[1, 0, [0, 1, 2], [1, 2]]], 否, 否)","explanation_zh":"Wave4第三層核對=(是, [[1, 0, [0, 1, 2], [1, 2]]], 否, 否)；依完整明示資料重算；完整有限／symbolic certificate不自動升格為未聲明的一般定理；每個較晚partition須精確細化較早partition；filtration不自動推出adapted natural independent或Markov。"},"difficulty":{"band":"undergraduate_core","level":1,"skills":["有限filtration"]},"variant":{"family_id":"qf-mod29-filtration-adaptedness","seed":202610295056,"parameters":{"n":6,"partitions":[[0,0,0,0,0,0],[0,0,0,1,1,1],[1,0,1,10,10,10]],"process_values":[[0,0,0,0,0,0],[1,2,1,2,2,2],[3,2,3,12,12,12]],"domain":"Exact_finite_partition_filtration","operation":"filtration-adaptedness","semantic_template":"qf-mod29-filtration-adaptedness/{\"n\":6,\"partitions\":[[0,0,0,0,0,0],[0,0,0,1,1,1],[1,0,1,10,10,10]],\"process_values\":[[0,0,0,0,0,0],[1,2,1,2,2,2],[3,2,3,12,12,12]]}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_model","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"產生端候選須由主端重算；不構成人工審定、任意無限定理、一般域／UFD、Hilbert、一般條件期望、LLN／CLT、商集、Lean執行或形式Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-14","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261014-advance-20261029-r05-finite-filtration-0057","batch_id":"batch-20261014-advance-20261029-r05-finite-filtration-foundations","language":"zh-Hant","source_mko_ids":["mko-finite-filtration"],"title_zh":"有限filtration","stem_zh":"所有資訊partition位於同一有限樣本空間。操作=filtration-adaptedness；資料={\"n\":6,\"partitions\":[[0,0,0,0,0,0],[0,0,0,1,1,1],[0,1,1,10,10,10]],\"process_values\":[[0,0,0,0,0,0],[1,1,1,2,2,2],[2,3,3,12,12,12]]}。請依 [filtration,measurability_failures,adapted,qualified_adapted_process] 欄序回答。","answer":{"kind":"expression","value":"(是, [], 是, 是)","explanation_zh":"Wave4第三層核對=(是, [], 是, 是)；依完整明示資料重算；完整有限／symbolic certificate不自動升格為未聲明的一般定理；每個較晚partition須精確細化較早partition；filtration不自動推出adapted natural independent或Markov。"},"difficulty":{"band":"undergraduate_core","level":1,"skills":["有限filtration"]},"variant":{"family_id":"qf-mod29-filtration-adaptedness","seed":202610295057,"parameters":{"n":6,"partitions":[[0,0,0,0,0,0],[0,0,0,1,1,1],[0,1,1,10,10,10]],"process_values":[[0,0,0,0,0,0],[1,1,1,2,2,2],[2,3,3,12,12,12]],"domain":"Exact_finite_partition_filtration","operation":"filtration-adaptedness","semantic_template":"qf-mod29-filtration-adaptedness/{\"n\":6,\"partitions\":[[0,0,0,0,0,0],[0,0,0,1,1,1],[0,1,1,10,10,10]],\"process_values\":[[0,0,0,0,0,0],[1,1,1,2,2,2],[2,3,3,12,12,12]]}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_model","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"產生端候選須由主端重算；不構成人工審定、任意無限定理、一般域／UFD、Hilbert、一般條件期望、LLN／CLT、商集、Lean執行或形式Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-14","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261014-advance-20261029-r05-finite-filtration-0058","batch_id":"batch-20261014-advance-20261029-r05-finite-filtration-foundations","language":"zh-Hant","source_mko_ids":["mko-finite-filtration"],"title_zh":"有限filtration","stem_zh":"所有資訊partition位於同一有限樣本空間。操作=filtration-adaptedness；資料={\"n\":6,\"partitions\":[[0,0,0,0,0,0],[0,0,0,1,1,1],[1,1,1,10,10,10]],\"process_values\":[[0,0,0,0,0,0],[1,1,1,2,2,2],[3,3,3,12,12,12]]}。請依 [filtration,measurability_failures,adapted,qualified_adapted_process] 欄序回答。","answer":{"kind":"expression","value":"(是, [], 是, 是)","explanation_zh":"Wave4第三層核對=(是, [], 是, 是)；依完整明示資料重算；完整有限／symbolic certificate不自動升格為未聲明的一般定理；每個較晚partition須精確細化較早partition；filtration不自動推出adapted natural independent或Markov。"},"difficulty":{"band":"undergraduate_core","level":1,"skills":["有限filtration"]},"variant":{"family_id":"qf-mod29-filtration-adaptedness","seed":202610295058,"parameters":{"n":6,"partitions":[[0,0,0,0,0,0],[0,0,0,1,1,1],[1,1,1,10,10,10]],"process_values":[[0,0,0,0,0,0],[1,1,1,2,2,2],[3,3,3,12,12,12]],"domain":"Exact_finite_partition_filtration","operation":"filtration-adaptedness","semantic_template":"qf-mod29-filtration-adaptedness/{\"n\":6,\"partitions\":[[0,0,0,0,0,0],[0,0,0,1,1,1],[1,1,1,10,10,10]],\"process_values\":[[0,0,0,0,0,0],[1,1,1,2,2,2],[3,3,3,12,12,12]]}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_model","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"產生端候選須由主端重算；不構成人工審定、任意無限定理、一般域／UFD、Hilbert、一般條件期望、LLN／CLT、商集、Lean執行或形式Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-14","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261014-advance-20261029-r05-finite-filtration-0059","batch_id":"batch-20261014-advance-20261029-r05-finite-filtration-foundations","language":"zh-Hant","source_mko_ids":["mko-finite-filtration"],"title_zh":"有限filtration","stem_zh":"所有資訊partition位於同一有限樣本空間。操作=filtration-adaptedness；資料={\"n\":6,\"partitions\":[[0,0,0,0,0,0],[0,0,0,1,1,1],[0,0,0,11,10,10]],\"process_values\":[[0,0,0,0,0,0],[1,1,1,2,2,2],[2,2,2,13,12,12]]}。請依 [filtration,measurability_failures,adapted,qualified_adapted_process] 欄序回答。","answer":{"kind":"expression","value":"(是, [], 是, 是)","explanation_zh":"Wave4第三層核對=(是, [], 是, 是)；依完整明示資料重算；完整有限／symbolic certificate不自動升格為未聲明的一般定理；每個較晚partition須精確細化較早partition；filtration不自動推出adapted natural independent或Markov。"},"difficulty":{"band":"undergraduate_core","level":2,"skills":["有限filtration"]},"variant":{"family_id":"qf-mod29-filtration-adaptedness","seed":202610295059,"parameters":{"n":6,"partitions":[[0,0,0,0,0,0],[0,0,0,1,1,1],[0,0,0,11,10,10]],"process_values":[[0,0,0,0,0,0],[1,1,1,2,2,2],[2,2,2,13,12,12]],"domain":"Exact_finite_partition_filtration","operation":"filtration-adaptedness","semantic_template":"qf-mod29-filtration-adaptedness/{\"n\":6,\"partitions\":[[0,0,0,0,0,0],[0,0,0,1,1,1],[0,0,0,11,10,10]],\"process_values\":[[0,0,0,0,0,0],[1,1,1,2,2,2],[2,2,2,13,12,12]]}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_model","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"產生端候選須由主端重算；不構成人工審定、任意無限定理、一般域／UFD、Hilbert、一般條件期望、LLN／CLT、商集、Lean執行或形式Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-14","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261014-advance-20261029-r05-finite-filtration-0060","batch_id":"batch-20261014-advance-20261029-r05-finite-filtration-foundations","language":"zh-Hant","source_mko_ids":["mko-finite-filtration"],"title_zh":"有限filtration","stem_zh":"所有資訊partition位於同一有限樣本空間。操作=filtration-adaptedness；資料={\"n\":6,\"partitions\":[[0,0,0,0,0,0],[0,0,0,1,1,1],[1,0,0,11,10,10]],\"process_values\":[[0,0,0,0,0,0],[1,1,1,2,2,2],[3,2,2,13,12,12]]}。請依 [filtration,measurability_failures,adapted,qualified_adapted_process] 欄序回答。","answer":{"kind":"expression","value":"(是, [], 是, 是)","explanation_zh":"Wave4第三層核對=(是, [], 是, 是)；依完整明示資料重算；完整有限／symbolic certificate不自動升格為未聲明的一般定理；每個較晚partition須精確細化較早partition；filtration不自動推出adapted natural independent或Markov。"},"difficulty":{"band":"undergraduate_core","level":2,"skills":["有限filtration"]},"variant":{"family_id":"qf-mod29-filtration-adaptedness","seed":202610295060,"parameters":{"n":6,"partitions":[[0,0,0,0,0,0],[0,0,0,1,1,1],[1,0,0,11,10,10]],"process_values":[[0,0,0,0,0,0],[1,1,1,2,2,2],[3,2,2,13,12,12]],"domain":"Exact_finite_partition_filtration","operation":"filtration-adaptedness","semantic_template":"qf-mod29-filtration-adaptedness/{\"n\":6,\"partitions\":[[0,0,0,0,0,0],[0,0,0,1,1,1],[1,0,0,11,10,10]],\"process_values\":[[0,0,0,0,0,0],[1,1,1,2,2,2],[3,2,2,13,12,12]]}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_model","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"產生端候選須由主端重算；不構成人工審定、任意無限定理、一般域／UFD、Hilbert、一般條件期望、LLN／CLT、商集、Lean執行或形式Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-14","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261014-advance-20261029-r05-finite-filtration-0061","batch_id":"batch-20261014-advance-20261029-r05-finite-filtration-foundations","language":"zh-Hant","source_mko_ids":["mko-finite-filtration"],"title_zh":"有限filtration","stem_zh":"所有資訊partition位於同一有限樣本空間。操作=filtration-adaptedness；資料={\"n\":6,\"partitions\":[[0,0,0,0,0,0],[0,0,0,1,1,1],[0,1,0,11,10,10]],\"process_values\":[[0,0,0,0,0,0],[1,2,1,2,2,2],[2,3,2,13,12,12]]}。請依 [filtration,measurability_failures,adapted,qualified_adapted_process] 欄序回答。","answer":{"kind":"expression","value":"(是, [[1, 0, [0, 1, 2], [1, 2]]], 否, 否)","explanation_zh":"Wave4第三層核對=(是, [[1, 0, [0, 1, 2], [1, 2]]], 否, 否)；依完整明示資料重算；完整有限／symbolic certificate不自動升格為未聲明的一般定理；每個較晚partition須精確細化較早partition；filtration不自動推出adapted natural independent或Markov。"},"difficulty":{"band":"undergraduate_core","level":2,"skills":["有限filtration"]},"variant":{"family_id":"qf-mod29-filtration-adaptedness","seed":202610295061,"parameters":{"n":6,"partitions":[[0,0,0,0,0,0],[0,0,0,1,1,1],[0,1,0,11,10,10]],"process_values":[[0,0,0,0,0,0],[1,2,1,2,2,2],[2,3,2,13,12,12]],"domain":"Exact_finite_partition_filtration","operation":"filtration-adaptedness","semantic_template":"qf-mod29-filtration-adaptedness/{\"n\":6,\"partitions\":[[0,0,0,0,0,0],[0,0,0,1,1,1],[0,1,0,11,10,10]],\"process_values\":[[0,0,0,0,0,0],[1,2,1,2,2,2],[2,3,2,13,12,12]]}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_model","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"產生端候選須由主端重算；不構成人工審定、任意無限定理、一般域／UFD、Hilbert、一般條件期望、LLN／CLT、商集、Lean執行或形式Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-14","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261014-advance-20261029-r05-finite-filtration-0062","batch_id":"batch-20261014-advance-20261029-r05-finite-filtration-foundations","language":"zh-Hant","source_mko_ids":["mko-finite-filtration"],"title_zh":"有限filtration","stem_zh":"所有資訊partition位於同一有限樣本空間。操作=filtration-adaptedness；資料={\"n\":6,\"partitions\":[[0,0,0,0,0,0],[0,0,0,1,1,1],[1,1,0,11,10,10]],\"process_values\":[[0,0,0,0,0,0],[1,1,1,2,2,2],[3,3,2,13,12,12]]}。請依 [filtration,measurability_failures,adapted,qualified_adapted_process] 欄序回答。","answer":{"kind":"expression","value":"(是, [], 是, 是)","explanation_zh":"Wave4第三層核對=(是, [], 是, 是)；依完整明示資料重算；完整有限／symbolic certificate不自動升格為未聲明的一般定理；每個較晚partition須精確細化較早partition；filtration不自動推出adapted natural independent或Markov。"},"difficulty":{"band":"undergraduate_core","level":2,"skills":["有限filtration"]},"variant":{"family_id":"qf-mod29-filtration-adaptedness","seed":202610295062,"parameters":{"n":6,"partitions":[[0,0,0,0,0,0],[0,0,0,1,1,1],[1,1,0,11,10,10]],"process_values":[[0,0,0,0,0,0],[1,1,1,2,2,2],[3,3,2,13,12,12]],"domain":"Exact_finite_partition_filtration","operation":"filtration-adaptedness","semantic_template":"qf-mod29-filtration-adaptedness/{\"n\":6,\"partitions\":[[0,0,0,0,0,0],[0,0,0,1,1,1],[1,1,0,11,10,10]],\"process_values\":[[0,0,0,0,0,0],[1,1,1,2,2,2],[3,3,2,13,12,12]]}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_model","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"產生端候選須由主端重算；不構成人工審定、任意無限定理、一般域／UFD、Hilbert、一般條件期望、LLN／CLT、商集、Lean執行或形式Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-14","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261014-advance-20261029-r05-finite-filtration-0063","batch_id":"batch-20261014-advance-20261029-r05-finite-filtration-foundations","language":"zh-Hant","source_mko_ids":["mko-finite-filtration"],"title_zh":"有限filtration","stem_zh":"所有資訊partition位於同一有限樣本空間。操作=filtration-adaptedness；資料={\"n\":6,\"partitions\":[[0,0,0,0,0,0],[0,0,0,1,1,1],[0,0,1,11,10,10]],\"process_values\":[[0,0,0,0,0,0],[1,1,1,2,2,2],[2,2,3,13,12,12]]}。請依 [filtration,measurability_failures,adapted,qualified_adapted_process] 欄序回答。","answer":{"kind":"expression","value":"(是, [], 是, 是)","explanation_zh":"Wave4第三層核對=(是, [], 是, 是)；依完整明示資料重算；完整有限／symbolic certificate不自動升格為未聲明的一般定理；每個較晚partition須精確細化較早partition；filtration不自動推出adapted natural independent或Markov。"},"difficulty":{"band":"undergraduate_core","level":2,"skills":["有限filtration"]},"variant":{"family_id":"qf-mod29-filtration-adaptedness","seed":202610295063,"parameters":{"n":6,"partitions":[[0,0,0,0,0,0],[0,0,0,1,1,1],[0,0,1,11,10,10]],"process_values":[[0,0,0,0,0,0],[1,1,1,2,2,2],[2,2,3,13,12,12]],"domain":"Exact_finite_partition_filtration","operation":"filtration-adaptedness","semantic_template":"qf-mod29-filtration-adaptedness/{\"n\":6,\"partitions\":[[0,0,0,0,0,0],[0,0,0,1,1,1],[0,0,1,11,10,10]],\"process_values\":[[0,0,0,0,0,0],[1,1,1,2,2,2],[2,2,3,13,12,12]]}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_model","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"產生端候選須由主端重算；不構成人工審定、任意無限定理、一般域／UFD、Hilbert、一般條件期望、LLN／CLT、商集、Lean執行或形式Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-14","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261014-advance-20261029-r05-finite-filtration-0064","batch_id":"batch-20261014-advance-20261029-r05-finite-filtration-foundations","language":"zh-Hant","source_mko_ids":["mko-finite-filtration"],"title_zh":"有限filtration","stem_zh":"所有資訊partition位於同一有限樣本空間。操作=filtration-adaptedness；資料={\"n\":6,\"partitions\":[[0,0,0,0,0,0],[0,0,0,1,1,1],[1,0,1,11,10,10]],\"process_values\":[[0,0,0,0,0,0],[1,1,1,2,2,2],[3,2,3,13,12,12]]}。請依 [filtration,measurability_failures,adapted,qualified_adapted_process] 欄序回答。","answer":{"kind":"expression","value":"(是, [], 是, 是)","explanation_zh":"Wave4第三層核對=(是, [], 是, 是)；依完整明示資料重算；完整有限／symbolic certificate不自動升格為未聲明的一般定理；每個較晚partition須精確細化較早partition；filtration不自動推出adapted natural independent或Markov。"},"difficulty":{"band":"undergraduate_core","level":2,"skills":["有限filtration"]},"variant":{"family_id":"qf-mod29-filtration-adaptedness","seed":202610295064,"parameters":{"n":6,"partitions":[[0,0,0,0,0,0],[0,0,0,1,1,1],[1,0,1,11,10,10]],"process_values":[[0,0,0,0,0,0],[1,1,1,2,2,2],[3,2,3,13,12,12]],"domain":"Exact_finite_partition_filtration","operation":"filtration-adaptedness","semantic_template":"qf-mod29-filtration-adaptedness/{\"n\":6,\"partitions\":[[0,0,0,0,0,0],[0,0,0,1,1,1],[1,0,1,11,10,10]],\"process_values\":[[0,0,0,0,0,0],[1,1,1,2,2,2],[3,2,3,13,12,12]]}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_model","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"產生端候選須由主端重算；不構成人工審定、任意無限定理、一般域／UFD、Hilbert、一般條件期望、LLN／CLT、商集、Lean執行或形式Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-14","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261014-advance-20261029-r05-finite-filtration-0065","batch_id":"batch-20261014-advance-20261029-r05-finite-filtration-foundations","language":"zh-Hant","source_mko_ids":["mko-finite-filtration"],"title_zh":"有限filtration","stem_zh":"所有資訊partition位於同一有限樣本空間。操作=filtration-adaptedness；資料={\"n\":6,\"partitions\":[[0,0,0,0,0,0],[0,0,0,1,1,1],[0,1,1,11,10,10]],\"process_values\":[[0,0,0,0,0,0],[1,1,1,2,2,2],[2,3,3,13,12,12]]}。請依 [filtration,measurability_failures,adapted,qualified_adapted_process] 欄序回答。","answer":{"kind":"expression","value":"(是, [], 是, 是)","explanation_zh":"Wave4第三層核對=(是, [], 是, 是)；依完整明示資料重算；完整有限／symbolic certificate不自動升格為未聲明的一般定理；每個較晚partition須精確細化較早partition；filtration不自動推出adapted natural independent或Markov。"},"difficulty":{"band":"undergraduate_core","level":2,"skills":["有限filtration"]},"variant":{"family_id":"qf-mod29-filtration-adaptedness","seed":202610295065,"parameters":{"n":6,"partitions":[[0,0,0,0,0,0],[0,0,0,1,1,1],[0,1,1,11,10,10]],"process_values":[[0,0,0,0,0,0],[1,1,1,2,2,2],[2,3,3,13,12,12]],"domain":"Exact_finite_partition_filtration","operation":"filtration-adaptedness","semantic_template":"qf-mod29-filtration-adaptedness/{\"n\":6,\"partitions\":[[0,0,0,0,0,0],[0,0,0,1,1,1],[0,1,1,11,10,10]],\"process_values\":[[0,0,0,0,0,0],[1,1,1,2,2,2],[2,3,3,13,12,12]]}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_model","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"產生端候選須由主端重算；不構成人工審定、任意無限定理、一般域／UFD、Hilbert、一般條件期望、LLN／CLT、商集、Lean執行或形式Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-14","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261014-advance-20261029-r05-finite-filtration-0066","batch_id":"batch-20261014-advance-20261029-r05-finite-filtration-foundations","language":"zh-Hant","source_mko_ids":["mko-finite-filtration"],"title_zh":"有限filtration","stem_zh":"所有資訊partition位於同一有限樣本空間。操作=filtration-adaptedness；資料={\"n\":6,\"partitions\":[[0,0,0,0,0,0],[0,0,0,1,1,1],[1,1,1,11,10,10]],\"process_values\":[[0,0,0,0,0,0],[1,2,1,2,2,2],[3,3,3,13,12,12]]}。請依 [filtration,measurability_failures,adapted,qualified_adapted_process] 欄序回答。","answer":{"kind":"expression","value":"(是, [[1, 0, [0, 1, 2], [1, 2]]], 否, 否)","explanation_zh":"Wave4第三層核對=(是, [[1, 0, [0, 1, 2], [1, 2]]], 否, 否)；依完整明示資料重算；完整有限／symbolic certificate不自動升格為未聲明的一般定理；每個較晚partition須精確細化較早partition；filtration不自動推出adapted natural independent或Markov。"},"difficulty":{"band":"undergraduate_core","level":2,"skills":["有限filtration"]},"variant":{"family_id":"qf-mod29-filtration-adaptedness","seed":202610295066,"parameters":{"n":6,"partitions":[[0,0,0,0,0,0],[0,0,0,1,1,1],[1,1,1,11,10,10]],"process_values":[[0,0,0,0,0,0],[1,2,1,2,2,2],[3,3,3,13,12,12]],"domain":"Exact_finite_partition_filtration","operation":"filtration-adaptedness","semantic_template":"qf-mod29-filtration-adaptedness/{\"n\":6,\"partitions\":[[0,0,0,0,0,0],[0,0,0,1,1,1],[1,1,1,11,10,10]],\"process_values\":[[0,0,0,0,0,0],[1,2,1,2,2,2],[3,3,3,13,12,12]]}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_model","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"產生端候選須由主端重算；不構成人工審定、任意無限定理、一般域／UFD、Hilbert、一般條件期望、LLN／CLT、商集、Lean執行或形式Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-14","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261014-advance-20261029-r05-finite-filtration-0067","batch_id":"batch-20261014-advance-20261029-r05-finite-filtration-foundations","language":"zh-Hant","source_mko_ids":["mko-finite-filtration"],"title_zh":"有限filtration","stem_zh":"所有資訊partition位於同一有限樣本空間。操作=filtration-adaptedness；資料={\"n\":6,\"partitions\":[[0,0,0,0,0,0],[0,0,0,1,1,1],[0,0,0,10,11,10]],\"process_values\":[[0,0,0,0,0,0],[1,1,1,2,2,2],[2,2,2,12,13,12]]}。請依 [filtration,measurability_failures,adapted,qualified_adapted_process] 欄序回答。","answer":{"kind":"expression","value":"(是, [], 是, 是)","explanation_zh":"Wave4第三層核對=(是, [], 是, 是)；依完整明示資料重算；完整有限／symbolic certificate不自動升格為未聲明的一般定理；每個較晚partition須精確細化較早partition；filtration不自動推出adapted natural independent或Markov。"},"difficulty":{"band":"undergraduate_core","level":2,"skills":["有限filtration"]},"variant":{"family_id":"qf-mod29-filtration-adaptedness","seed":202610295067,"parameters":{"n":6,"partitions":[[0,0,0,0,0,0],[0,0,0,1,1,1],[0,0,0,10,11,10]],"process_values":[[0,0,0,0,0,0],[1,1,1,2,2,2],[2,2,2,12,13,12]],"domain":"Exact_finite_partition_filtration","operation":"filtration-adaptedness","semantic_template":"qf-mod29-filtration-adaptedness/{\"n\":6,\"partitions\":[[0,0,0,0,0,0],[0,0,0,1,1,1],[0,0,0,10,11,10]],\"process_values\":[[0,0,0,0,0,0],[1,1,1,2,2,2],[2,2,2,12,13,12]]}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_model","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"產生端候選須由主端重算；不構成人工審定、任意無限定理、一般域／UFD、Hilbert、一般條件期望、LLN／CLT、商集、Lean執行或形式Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-14","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261014-advance-20261029-r05-finite-filtration-0068","batch_id":"batch-20261014-advance-20261029-r05-finite-filtration-foundations","language":"zh-Hant","source_mko_ids":["mko-finite-filtration"],"title_zh":"有限filtration","stem_zh":"所有資訊partition位於同一有限樣本空間。操作=filtration-adaptedness；資料={\"n\":6,\"partitions\":[[0,0,0,0,0,0],[0,0,0,1,1,1],[1,0,0,10,11,10]],\"process_values\":[[0,0,0,0,0,0],[1,1,1,2,2,2],[3,2,2,12,13,12]]}。請依 [filtration,measurability_failures,adapted,qualified_adapted_process] 欄序回答。","answer":{"kind":"expression","value":"(是, [], 是, 是)","explanation_zh":"Wave4第三層核對=(是, [], 是, 是)；依完整明示資料重算；完整有限／symbolic certificate不自動升格為未聲明的一般定理；每個較晚partition須精確細化較早partition；filtration不自動推出adapted natural independent或Markov。"},"difficulty":{"band":"undergraduate_core","level":3,"skills":["有限filtration"]},"variant":{"family_id":"qf-mod29-filtration-adaptedness","seed":202610295068,"parameters":{"n":6,"partitions":[[0,0,0,0,0,0],[0,0,0,1,1,1],[1,0,0,10,11,10]],"process_values":[[0,0,0,0,0,0],[1,1,1,2,2,2],[3,2,2,12,13,12]],"domain":"Exact_finite_partition_filtration","operation":"filtration-adaptedness","semantic_template":"qf-mod29-filtration-adaptedness/{\"n\":6,\"partitions\":[[0,0,0,0,0,0],[0,0,0,1,1,1],[1,0,0,10,11,10]],\"process_values\":[[0,0,0,0,0,0],[1,1,1,2,2,2],[3,2,2,12,13,12]]}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_model","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"產生端候選須由主端重算；不構成人工審定、任意無限定理、一般域／UFD、Hilbert、一般條件期望、LLN／CLT、商集、Lean執行或形式Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-14","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261014-advance-20261029-r05-finite-filtration-0069","batch_id":"batch-20261014-advance-20261029-r05-finite-filtration-foundations","language":"zh-Hant","source_mko_ids":["mko-finite-filtration"],"title_zh":"有限filtration","stem_zh":"所有資訊partition位於同一有限樣本空間。操作=filtration-adaptedness；資料={\"n\":6,\"partitions\":[[0,0,0,0,0,0],[0,0,0,1,1,1],[0,1,0,10,11,10]],\"process_values\":[[0,0,0,0,0,0],[1,1,1,2,2,2],[2,3,2,12,13,12]]}。請依 [filtration,measurability_failures,adapted,qualified_adapted_process] 欄序回答。","answer":{"kind":"expression","value":"(是, [], 是, 是)","explanation_zh":"Wave4第三層核對=(是, [], 是, 是)；依完整明示資料重算；完整有限／symbolic certificate不自動升格為未聲明的一般定理；每個較晚partition須精確細化較早partition；filtration不自動推出adapted natural independent或Markov。"},"difficulty":{"band":"undergraduate_core","level":3,"skills":["有限filtration"]},"variant":{"family_id":"qf-mod29-filtration-adaptedness","seed":202610295069,"parameters":{"n":6,"partitions":[[0,0,0,0,0,0],[0,0,0,1,1,1],[0,1,0,10,11,10]],"process_values":[[0,0,0,0,0,0],[1,1,1,2,2,2],[2,3,2,12,13,12]],"domain":"Exact_finite_partition_filtration","operation":"filtration-adaptedness","semantic_template":"qf-mod29-filtration-adaptedness/{\"n\":6,\"partitions\":[[0,0,0,0,0,0],[0,0,0,1,1,1],[0,1,0,10,11,10]],\"process_values\":[[0,0,0,0,0,0],[1,1,1,2,2,2],[2,3,2,12,13,12]]}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_model","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"產生端候選須由主端重算；不構成人工審定、任意無限定理、一般域／UFD、Hilbert、一般條件期望、LLN／CLT、商集、Lean執行或形式Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-14","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261014-advance-20261029-r05-finite-filtration-0070","batch_id":"batch-20261014-advance-20261029-r05-finite-filtration-foundations","language":"zh-Hant","source_mko_ids":["mko-finite-filtration"],"title_zh":"有限filtration","stem_zh":"所有資訊partition位於同一有限樣本空間。操作=filtration-adaptedness；資料={\"n\":6,\"partitions\":[[0,0,0,0,0,0],[0,0,0,1,1,1],[1,1,0,10,11,10]],\"process_values\":[[0,0,0,0,0,0],[1,1,1,2,2,2],[3,3,2,12,13,12]]}。請依 [filtration,measurability_failures,adapted,qualified_adapted_process] 欄序回答。","answer":{"kind":"expression","value":"(是, [], 是, 是)","explanation_zh":"Wave4第三層核對=(是, [], 是, 是)；依完整明示資料重算；完整有限／symbolic certificate不自動升格為未聲明的一般定理；每個較晚partition須精確細化較早partition；filtration不自動推出adapted natural independent或Markov。"},"difficulty":{"band":"undergraduate_core","level":3,"skills":["有限filtration"]},"variant":{"family_id":"qf-mod29-filtration-adaptedness","seed":202610295070,"parameters":{"n":6,"partitions":[[0,0,0,0,0,0],[0,0,0,1,1,1],[1,1,0,10,11,10]],"process_values":[[0,0,0,0,0,0],[1,1,1,2,2,2],[3,3,2,12,13,12]],"domain":"Exact_finite_partition_filtration","operation":"filtration-adaptedness","semantic_template":"qf-mod29-filtration-adaptedness/{\"n\":6,\"partitions\":[[0,0,0,0,0,0],[0,0,0,1,1,1],[1,1,0,10,11,10]],\"process_values\":[[0,0,0,0,0,0],[1,1,1,2,2,2],[3,3,2,12,13,12]]}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_model","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"產生端候選須由主端重算；不構成人工審定、任意無限定理、一般域／UFD、Hilbert、一般條件期望、LLN／CLT、商集、Lean執行或形式Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-14","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261014-advance-20261029-r05-finite-filtration-0071","batch_id":"batch-20261014-advance-20261029-r05-finite-filtration-foundations","language":"zh-Hant","source_mko_ids":["mko-finite-filtration"],"title_zh":"有限filtration","stem_zh":"所有資訊partition位於同一有限樣本空間。操作=filtration-adaptedness；資料={\"n\":6,\"partitions\":[[0,0,0,0,0,0],[0,0,0,1,1,1],[0,0,1,10,11,10]],\"process_values\":[[0,0,0,0,0,0],[1,2,1,2,2,2],[2,2,3,12,13,12]]}。請依 [filtration,measurability_failures,adapted,qualified_adapted_process] 欄序回答。","answer":{"kind":"expression","value":"(是, [[1, 0, [0, 1, 2], [1, 2]]], 否, 否)","explanation_zh":"Wave4第三層核對=(是, [[1, 0, [0, 1, 2], [1, 2]]], 否, 否)；依完整明示資料重算；完整有限／symbolic certificate不自動升格為未聲明的一般定理；每個較晚partition須精確細化較早partition；filtration不自動推出adapted natural independent或Markov。"},"difficulty":{"band":"undergraduate_core","level":3,"skills":["有限filtration"]},"variant":{"family_id":"qf-mod29-filtration-adaptedness","seed":202610295071,"parameters":{"n":6,"partitions":[[0,0,0,0,0,0],[0,0,0,1,1,1],[0,0,1,10,11,10]],"process_values":[[0,0,0,0,0,0],[1,2,1,2,2,2],[2,2,3,12,13,12]],"domain":"Exact_finite_partition_filtration","operation":"filtration-adaptedness","semantic_template":"qf-mod29-filtration-adaptedness/{\"n\":6,\"partitions\":[[0,0,0,0,0,0],[0,0,0,1,1,1],[0,0,1,10,11,10]],\"process_values\":[[0,0,0,0,0,0],[1,2,1,2,2,2],[2,2,3,12,13,12]]}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_model","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"產生端候選須由主端重算；不構成人工審定、任意無限定理、一般域／UFD、Hilbert、一般條件期望、LLN／CLT、商集、Lean執行或形式Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-14","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261014-advance-20261029-r05-finite-filtration-0072","batch_id":"batch-20261014-advance-20261029-r05-finite-filtration-foundations","language":"zh-Hant","source_mko_ids":["mko-finite-filtration"],"title_zh":"有限filtration","stem_zh":"所有資訊partition位於同一有限樣本空間。操作=filtration-adaptedness；資料={\"n\":6,\"partitions\":[[0,0,0,0,0,0],[0,0,0,1,1,1],[1,0,1,10,11,10]],\"process_values\":[[0,0,0,0,0,0],[1,1,1,2,2,2],[3,2,3,12,13,12]]}。請依 [filtration,measurability_failures,adapted,qualified_adapted_process] 欄序回答。","answer":{"kind":"expression","value":"(是, [], 是, 是)","explanation_zh":"Wave4第三層核對=(是, [], 是, 是)；依完整明示資料重算；完整有限／symbolic certificate不自動升格為未聲明的一般定理；每個較晚partition須精確細化較早partition；filtration不自動推出adapted natural independent或Markov。"},"difficulty":{"band":"undergraduate_core","level":3,"skills":["有限filtration"]},"variant":{"family_id":"qf-mod29-filtration-adaptedness","seed":202610295072,"parameters":{"n":6,"partitions":[[0,0,0,0,0,0],[0,0,0,1,1,1],[1,0,1,10,11,10]],"process_values":[[0,0,0,0,0,0],[1,1,1,2,2,2],[3,2,3,12,13,12]],"domain":"Exact_finite_partition_filtration","operation":"filtration-adaptedness","semantic_template":"qf-mod29-filtration-adaptedness/{\"n\":6,\"partitions\":[[0,0,0,0,0,0],[0,0,0,1,1,1],[1,0,1,10,11,10]],\"process_values\":[[0,0,0,0,0,0],[1,1,1,2,2,2],[3,2,3,12,13,12]]}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_model","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"產生端候選須由主端重算；不構成人工審定、任意無限定理、一般域／UFD、Hilbert、一般條件期望、LLN／CLT、商集、Lean執行或形式Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-14","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261014-advance-20261029-r05-finite-filtration-0073","batch_id":"batch-20261014-advance-20261029-r05-finite-filtration-foundations","language":"zh-Hant","source_mko_ids":["mko-finite-filtration"],"title_zh":"有限filtration","stem_zh":"所有資訊partition位於同一有限樣本空間。操作=filtration-adaptedness；資料={\"n\":6,\"partitions\":[[0,0,0,0,0,0],[0,0,0,1,1,1],[0,1,1,10,11,10]],\"process_values\":[[0,0,0,0,0,0],[1,1,1,2,2,2],[2,3,3,12,13,12]]}。請依 [filtration,measurability_failures,adapted,qualified_adapted_process] 欄序回答。","answer":{"kind":"expression","value":"(是, [], 是, 是)","explanation_zh":"Wave4第三層核對=(是, [], 是, 是)；依完整明示資料重算；完整有限／symbolic certificate不自動升格為未聲明的一般定理；每個較晚partition須精確細化較早partition；filtration不自動推出adapted natural independent或Markov。"},"difficulty":{"band":"undergraduate_core","level":3,"skills":["有限filtration"]},"variant":{"family_id":"qf-mod29-filtration-adaptedness","seed":202610295073,"parameters":{"n":6,"partitions":[[0,0,0,0,0,0],[0,0,0,1,1,1],[0,1,1,10,11,10]],"process_values":[[0,0,0,0,0,0],[1,1,1,2,2,2],[2,3,3,12,13,12]],"domain":"Exact_finite_partition_filtration","operation":"filtration-adaptedness","semantic_template":"qf-mod29-filtration-adaptedness/{\"n\":6,\"partitions\":[[0,0,0,0,0,0],[0,0,0,1,1,1],[0,1,1,10,11,10]],\"process_values\":[[0,0,0,0,0,0],[1,1,1,2,2,2],[2,3,3,12,13,12]]}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_model","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"產生端候選須由主端重算；不構成人工審定、任意無限定理、一般域／UFD、Hilbert、一般條件期望、LLN／CLT、商集、Lean執行或形式Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-14","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261014-advance-20261029-r05-finite-filtration-0074","batch_id":"batch-20261014-advance-20261029-r05-finite-filtration-foundations","language":"zh-Hant","source_mko_ids":["mko-finite-filtration"],"title_zh":"有限filtration","stem_zh":"所有資訊partition位於同一有限樣本空間。操作=filtration-adaptedness；資料={\"n\":6,\"partitions\":[[0,0,0,0,0,0],[0,0,0,1,1,1],[1,1,1,10,11,10]],\"process_values\":[[0,0,0,0,0,0],[1,1,1,2,2,2],[3,3,3,12,13,12]]}。請依 [filtration,measurability_failures,adapted,qualified_adapted_process] 欄序回答。","answer":{"kind":"expression","value":"(是, [], 是, 是)","explanation_zh":"Wave4第三層核對=(是, [], 是, 是)；依完整明示資料重算；完整有限／symbolic certificate不自動升格為未聲明的一般定理；每個較晚partition須精確細化較早partition；filtration不自動推出adapted natural independent或Markov。"},"difficulty":{"band":"undergraduate_core","level":3,"skills":["有限filtration"]},"variant":{"family_id":"qf-mod29-filtration-adaptedness","seed":202610295074,"parameters":{"n":6,"partitions":[[0,0,0,0,0,0],[0,0,0,1,1,1],[1,1,1,10,11,10]],"process_values":[[0,0,0,0,0,0],[1,1,1,2,2,2],[3,3,3,12,13,12]],"domain":"Exact_finite_partition_filtration","operation":"filtration-adaptedness","semantic_template":"qf-mod29-filtration-adaptedness/{\"n\":6,\"partitions\":[[0,0,0,0,0,0],[0,0,0,1,1,1],[1,1,1,10,11,10]],\"process_values\":[[0,0,0,0,0,0],[1,1,1,2,2,2],[3,3,3,12,13,12]]}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_model","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"產生端候選須由主端重算；不構成人工審定、任意無限定理、一般域／UFD、Hilbert、一般條件期望、LLN／CLT、商集、Lean執行或形式Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-14","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261014-advance-20261029-r05-finite-filtration-0075","batch_id":"batch-20261014-advance-20261029-r05-finite-filtration-foundations","language":"zh-Hant","source_mko_ids":["mko-finite-filtration"],"title_zh":"有限filtration","stem_zh":"所有資訊partition位於同一有限樣本空間。操作=filtration-adaptedness；資料={\"n\":6,\"partitions\":[[0,0,0,0,0,0],[0,0,0,1,1,1],[0,0,0,11,11,10]],\"process_values\":[[0,0,0,0,0,0],[1,1,1,2,2,2],[2,2,2,13,13,12]]}。請依 [filtration,measurability_failures,adapted,qualified_adapted_process] 欄序回答。","answer":{"kind":"expression","value":"(是, [], 是, 是)","explanation_zh":"Wave4第三層核對=(是, [], 是, 是)；依完整明示資料重算；完整有限／symbolic certificate不自動升格為未聲明的一般定理；每個較晚partition須精確細化較早partition；filtration不自動推出adapted natural independent或Markov。"},"difficulty":{"band":"undergraduate_core","level":3,"skills":["有限filtration"]},"variant":{"family_id":"qf-mod29-filtration-adaptedness","seed":202610295075,"parameters":{"n":6,"partitions":[[0,0,0,0,0,0],[0,0,0,1,1,1],[0,0,0,11,11,10]],"process_values":[[0,0,0,0,0,0],[1,1,1,2,2,2],[2,2,2,13,13,12]],"domain":"Exact_finite_partition_filtration","operation":"filtration-adaptedness","semantic_template":"qf-mod29-filtration-adaptedness/{\"n\":6,\"partitions\":[[0,0,0,0,0,0],[0,0,0,1,1,1],[0,0,0,11,11,10]],\"process_values\":[[0,0,0,0,0,0],[1,1,1,2,2,2],[2,2,2,13,13,12]]}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_model","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"產生端候選須由主端重算；不構成人工審定、任意無限定理、一般域／UFD、Hilbert、一般條件期望、LLN／CLT、商集、Lean執行或形式Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-14","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261014-advance-20261029-r05-finite-filtration-0076","batch_id":"batch-20261014-advance-20261029-r05-finite-filtration-foundations","language":"zh-Hant","source_mko_ids":["mko-finite-filtration"],"title_zh":"有限filtration","stem_zh":"所有資訊partition位於同一有限樣本空間。操作=filtration-event-measurability；資料={\"n\":6,\"partitions\":[[0,0,0,0,0,0],[0,0,0,1,1,1],[0,0,0,10,10,10]],\"time\":0,\"event\":[0]}。請依 [time,event,measurable,boundary] 欄序回答。","answer":{"kind":"expression","value":"(0, [0], 否, event_must_be_union_of_time_blocks)","explanation_zh":"Wave4第三層核對=(0, [0], 否, event_must_be_union_of_time_blocks)；依完整明示資料重算；完整有限／symbolic certificate不自動升格為未聲明的一般定理；每個較晚partition須精確細化較早partition；filtration不自動推出adapted natural independent或Markov。"},"difficulty":{"band":"undergraduate_core","level":1,"skills":["有限filtration"]},"variant":{"family_id":"qf-mod29-filtration-event-measurability","seed":202610295076,"parameters":{"n":6,"partitions":[[0,0,0,0,0,0],[0,0,0,1,1,1],[0,0,0,10,10,10]],"time":0,"event":[0],"domain":"Exact_finite_partition_filtration","operation":"filtration-event-measurability","semantic_template":"qf-mod29-filtration-event-measurability/{\"event\":[0],\"n\":6,\"partitions\":[[0,0,0,0,0,0],[0,0,0,1,1,1],[0,0,0,10,10,10]],\"time\":0}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_model","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"產生端候選須由主端重算；不構成人工審定、任意無限定理、一般域／UFD、Hilbert、一般條件期望、LLN／CLT、商集、Lean執行或形式Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-14","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261014-advance-20261029-r05-finite-filtration-0077","batch_id":"batch-20261014-advance-20261029-r05-finite-filtration-foundations","language":"zh-Hant","source_mko_ids":["mko-finite-filtration"],"title_zh":"有限filtration","stem_zh":"所有資訊partition位於同一有限樣本空間。操作=filtration-event-measurability；資料={\"n\":6,\"partitions\":[[0,0,0,0,0,0],[0,0,0,1,1,1],[1,0,0,10,10,10]],\"time\":1,\"event\":[0,1,2]}。請依 [time,event,measurable,boundary] 欄序回答。","answer":{"kind":"expression","value":"(1, [0, 1, 2], 是, event_must_be_union_of_time_blocks)","explanation_zh":"Wave4第三層核對=(1, [0, 1, 2], 是, event_must_be_union_of_time_blocks)；依完整明示資料重算；完整有限／symbolic certificate不自動升格為未聲明的一般定理；每個較晚partition須精確細化較早partition；filtration不自動推出adapted natural independent或Markov。"},"difficulty":{"band":"undergraduate_core","level":1,"skills":["有限filtration"]},"variant":{"family_id":"qf-mod29-filtration-event-measurability","seed":202610295077,"parameters":{"n":6,"partitions":[[0,0,0,0,0,0],[0,0,0,1,1,1],[1,0,0,10,10,10]],"time":1,"event":[0,1,2],"domain":"Exact_finite_partition_filtration","operation":"filtration-event-measurability","semantic_template":"qf-mod29-filtration-event-measurability/{\"event\":[0,1,2],\"n\":6,\"partitions\":[[0,0,0,0,0,0],[0,0,0,1,1,1],[1,0,0,10,10,10]],\"time\":1}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_model","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"產生端候選須由主端重算；不構成人工審定、任意無限定理、一般域／UFD、Hilbert、一般條件期望、LLN／CLT、商集、Lean執行或形式Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-14","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261014-advance-20261029-r05-finite-filtration-0078","batch_id":"batch-20261014-advance-20261029-r05-finite-filtration-foundations","language":"zh-Hant","source_mko_ids":["mko-finite-filtration"],"title_zh":"有限filtration","stem_zh":"所有資訊partition位於同一有限樣本空間。操作=filtration-event-measurability；資料={\"n\":6,\"partitions\":[[0,0,0,0,0,0],[0,0,0,1,1,1],[0,1,0,10,10,10]],\"time\":2,\"event\":[0,2]}。請依 [time,event,measurable,boundary] 欄序回答。","answer":{"kind":"expression","value":"(2, [0, 2], 是, event_must_be_union_of_time_blocks)","explanation_zh":"Wave4第三層核對=(2, [0, 2], 是, event_must_be_union_of_time_blocks)；依完整明示資料重算；完整有限／symbolic certificate不自動升格為未聲明的一般定理；每個較晚partition須精確細化較早partition；filtration不自動推出adapted natural independent或Markov。"},"difficulty":{"band":"undergraduate_core","level":1,"skills":["有限filtration"]},"variant":{"family_id":"qf-mod29-filtration-event-measurability","seed":202610295078,"parameters":{"n":6,"partitions":[[0,0,0,0,0,0],[0,0,0,1,1,1],[0,1,0,10,10,10]],"time":2,"event":[0,2],"domain":"Exact_finite_partition_filtration","operation":"filtration-event-measurability","semantic_template":"qf-mod29-filtration-event-measurability/{\"event\":[0,2],\"n\":6,\"partitions\":[[0,0,0,0,0,0],[0,0,0,1,1,1],[0,1,0,10,10,10]],\"time\":2}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_model","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"產生端候選須由主端重算；不構成人工審定、任意無限定理、一般域／UFD、Hilbert、一般條件期望、LLN／CLT、商集、Lean執行或形式Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-14","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261014-advance-20261029-r05-finite-filtration-0079","batch_id":"batch-20261014-advance-20261029-r05-finite-filtration-foundations","language":"zh-Hant","source_mko_ids":["mko-finite-filtration"],"title_zh":"有限filtration","stem_zh":"所有資訊partition位於同一有限樣本空間。操作=filtration-event-measurability；資料={\"n\":6,\"partitions\":[[0,0,0,0,0,0],[0,0,0,1,1,1],[1,1,0,10,10,10]],\"time\":0,\"event\":[0,1,2,3,4,5]}。請依 [time,event,measurable,boundary] 欄序回答。","answer":{"kind":"expression","value":"(0, [0, 1, 2, 3, 4, 5], 是, event_must_be_union_of_time_blocks)","explanation_zh":"Wave4第三層核對=(0, [0, 1, 2, 3, 4, 5], 是, event_must_be_union_of_time_blocks)；依完整明示資料重算；完整有限／symbolic certificate不自動升格為未聲明的一般定理；每個較晚partition須精確細化較早partition；filtration不自動推出adapted natural independent或Markov。"},"difficulty":{"band":"undergraduate_core","level":1,"skills":["有限filtration"]},"variant":{"family_id":"qf-mod29-filtration-event-measurability","seed":202610295079,"parameters":{"n":6,"partitions":[[0,0,0,0,0,0],[0,0,0,1,1,1],[1,1,0,10,10,10]],"time":0,"event":[0,1,2,3,4,5],"domain":"Exact_finite_partition_filtration","operation":"filtration-event-measurability","semantic_template":"qf-mod29-filtration-event-measurability/{\"event\":[0,1,2,3,4,5],\"n\":6,\"partitions\":[[0,0,0,0,0,0],[0,0,0,1,1,1],[1,1,0,10,10,10]],\"time\":0}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_model","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"產生端候選須由主端重算；不構成人工審定、任意無限定理、一般域／UFD、Hilbert、一般條件期望、LLN／CLT、商集、Lean執行或形式Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-14","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261014-advance-20261029-r05-finite-filtration-0080","batch_id":"batch-20261014-advance-20261029-r05-finite-filtration-foundations","language":"zh-Hant","source_mko_ids":["mko-finite-filtration"],"title_zh":"有限filtration","stem_zh":"所有資訊partition位於同一有限樣本空間。操作=filtration-event-measurability；資料={\"n\":6,\"partitions\":[[0,0,0,0,0,0],[0,0,0,1,1,1],[0,0,1,10,10,10]],\"time\":1,\"event\":[3]}。請依 [time,event,measurable,boundary] 欄序回答。","answer":{"kind":"expression","value":"(1, [3], 否, event_must_be_union_of_time_blocks)","explanation_zh":"Wave4第三層核對=(1, [3], 否, event_must_be_union_of_time_blocks)；依完整明示資料重算；完整有限／symbolic certificate不自動升格為未聲明的一般定理；每個較晚partition須精確細化較早partition；filtration不自動推出adapted natural independent或Markov。"},"difficulty":{"band":"undergraduate_core","level":1,"skills":["有限filtration"]},"variant":{"family_id":"qf-mod29-filtration-event-measurability","seed":202610295080,"parameters":{"n":6,"partitions":[[0,0,0,0,0,0],[0,0,0,1,1,1],[0,0,1,10,10,10]],"time":1,"event":[3],"domain":"Exact_finite_partition_filtration","operation":"filtration-event-measurability","semantic_template":"qf-mod29-filtration-event-measurability/{\"event\":[3],\"n\":6,\"partitions\":[[0,0,0,0,0,0],[0,0,0,1,1,1],[0,0,1,10,10,10]],\"time\":1}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_model","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"產生端候選須由主端重算；不構成人工審定、任意無限定理、一般域／UFD、Hilbert、一般條件期望、LLN／CLT、商集、Lean執行或形式Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-14","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261014-advance-20261029-r05-finite-filtration-0081","batch_id":"batch-20261014-advance-20261029-r05-finite-filtration-foundations","language":"zh-Hant","source_mko_ids":["mko-finite-filtration"],"title_zh":"有限filtration","stem_zh":"所有資訊partition位於同一有限樣本空間。操作=filtration-event-measurability；資料={\"n\":6,\"partitions\":[[0,0,0,0,0,0],[0,0,0,1,1,1],[1,0,1,10,10,10]],\"time\":2,\"event\":[3,4,5]}。請依 [time,event,measurable,boundary] 欄序回答。","answer":{"kind":"expression","value":"(2, [3, 4, 5], 是, event_must_be_union_of_time_blocks)","explanation_zh":"Wave4第三層核對=(2, [3, 4, 5], 是, event_must_be_union_of_time_blocks)；依完整明示資料重算；完整有限／symbolic certificate不自動升格為未聲明的一般定理；每個較晚partition須精確細化較早partition；filtration不自動推出adapted natural independent或Markov。"},"difficulty":{"band":"undergraduate_core","level":1,"skills":["有限filtration"]},"variant":{"family_id":"qf-mod29-filtration-event-measurability","seed":202610295081,"parameters":{"n":6,"partitions":[[0,0,0,0,0,0],[0,0,0,1,1,1],[1,0,1,10,10,10]],"time":2,"event":[3,4,5],"domain":"Exact_finite_partition_filtration","operation":"filtration-event-measurability","semantic_template":"qf-mod29-filtration-event-measurability/{\"event\":[3,4,5],\"n\":6,\"partitions\":[[0,0,0,0,0,0],[0,0,0,1,1,1],[1,0,1,10,10,10]],\"time\":2}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_model","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"產生端候選須由主端重算；不構成人工審定、任意無限定理、一般域／UFD、Hilbert、一般條件期望、LLN／CLT、商集、Lean執行或形式Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-14","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261014-advance-20261029-r05-finite-filtration-0082","batch_id":"batch-20261014-advance-20261029-r05-finite-filtration-foundations","language":"zh-Hant","source_mko_ids":["mko-finite-filtration"],"title_zh":"有限filtration","stem_zh":"所有資訊partition位於同一有限樣本空間。操作=filtration-event-measurability；資料={\"n\":6,\"partitions\":[[0,0,0,0,0,0],[0,0,0,1,1,1],[0,1,1,10,10,10]],\"time\":0,\"event\":[0,1,2,3,4,5]}。請依 [time,event,measurable,boundary] 欄序回答。","answer":{"kind":"expression","value":"(0, [0, 1, 2, 3, 4, 5], 是, event_must_be_union_of_time_blocks)","explanation_zh":"Wave4第三層核對=(0, [0, 1, 2, 3, 4, 5], 是, event_must_be_union_of_time_blocks)；依完整明示資料重算；完整有限／symbolic certificate不自動升格為未聲明的一般定理；每個較晚partition須精確細化較早partition；filtration不自動推出adapted natural independent或Markov。"},"difficulty":{"band":"undergraduate_core","level":1,"skills":["有限filtration"]},"variant":{"family_id":"qf-mod29-filtration-event-measurability","seed":202610295082,"parameters":{"n":6,"partitions":[[0,0,0,0,0,0],[0,0,0,1,1,1],[0,1,1,10,10,10]],"time":0,"event":[0,1,2,3,4,5],"domain":"Exact_finite_partition_filtration","operation":"filtration-event-measurability","semantic_template":"qf-mod29-filtration-event-measurability/{\"event\":[0,1,2,3,4,5],\"n\":6,\"partitions\":[[0,0,0,0,0,0],[0,0,0,1,1,1],[0,1,1,10,10,10]],\"time\":0}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_model","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"產生端候選須由主端重算；不構成人工審定、任意無限定理、一般域／UFD、Hilbert、一般條件期望、LLN／CLT、商集、Lean執行或形式Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-14","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261014-advance-20261029-r05-finite-filtration-0083","batch_id":"batch-20261014-advance-20261029-r05-finite-filtration-foundations","language":"zh-Hant","source_mko_ids":["mko-finite-filtration"],"title_zh":"有限filtration","stem_zh":"所有資訊partition位於同一有限樣本空間。操作=filtration-event-measurability；資料={\"n\":6,\"partitions\":[[0,0,0,0,0,0],[0,0,0,1,1,1],[1,1,1,10,10,10]],\"time\":1,\"event\":[0,1,2]}。請依 [time,event,measurable,boundary] 欄序回答。","answer":{"kind":"expression","value":"(1, [0, 1, 2], 是, event_must_be_union_of_time_blocks)","explanation_zh":"Wave4第三層核對=(1, [0, 1, 2], 是, event_must_be_union_of_time_blocks)；依完整明示資料重算；完整有限／symbolic certificate不自動升格為未聲明的一般定理；每個較晚partition須精確細化較早partition；filtration不自動推出adapted natural independent或Markov。"},"difficulty":{"band":"undergraduate_core","level":1,"skills":["有限filtration"]},"variant":{"family_id":"qf-mod29-filtration-event-measurability","seed":202610295083,"parameters":{"n":6,"partitions":[[0,0,0,0,0,0],[0,0,0,1,1,1],[1,1,1,10,10,10]],"time":1,"event":[0,1,2],"domain":"Exact_finite_partition_filtration","operation":"filtration-event-measurability","semantic_template":"qf-mod29-filtration-event-measurability/{\"event\":[0,1,2],\"n\":6,\"partitions\":[[0,0,0,0,0,0],[0,0,0,1,1,1],[1,1,1,10,10,10]],\"time\":1}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_model","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"產生端候選須由主端重算；不構成人工審定、任意無限定理、一般域／UFD、Hilbert、一般條件期望、LLN／CLT、商集、Lean執行或形式Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-14","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261014-advance-20261029-r05-finite-filtration-0084","batch_id":"batch-20261014-advance-20261029-r05-finite-filtration-foundations","language":"zh-Hant","source_mko_ids":["mko-finite-filtration"],"title_zh":"有限filtration","stem_zh":"所有資訊partition位於同一有限樣本空間。操作=filtration-event-measurability；資料={\"n\":6,\"partitions\":[[0,0,0,0,0,0],[0,0,0,1,1,1],[0,0,0,11,10,10]],\"time\":2,\"event\":[0]}。請依 [time,event,measurable,boundary] 欄序回答。","answer":{"kind":"expression","value":"(2, [0], 否, event_must_be_union_of_time_blocks)","explanation_zh":"Wave4第三層核對=(2, [0], 否, event_must_be_union_of_time_blocks)；依完整明示資料重算；完整有限／symbolic certificate不自動升格為未聲明的一般定理；每個較晚partition須精確細化較早partition；filtration不自動推出adapted natural independent或Markov。"},"difficulty":{"band":"undergraduate_core","level":2,"skills":["有限filtration"]},"variant":{"family_id":"qf-mod29-filtration-event-measurability","seed":202610295084,"parameters":{"n":6,"partitions":[[0,0,0,0,0,0],[0,0,0,1,1,1],[0,0,0,11,10,10]],"time":2,"event":[0],"domain":"Exact_finite_partition_filtration","operation":"filtration-event-measurability","semantic_template":"qf-mod29-filtration-event-measurability/{\"event\":[0],\"n\":6,\"partitions\":[[0,0,0,0,0,0],[0,0,0,1,1,1],[0,0,0,11,10,10]],\"time\":2}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_model","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"產生端候選須由主端重算；不構成人工審定、任意無限定理、一般域／UFD、Hilbert、一般條件期望、LLN／CLT、商集、Lean執行或形式Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-14","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261014-advance-20261029-r05-finite-filtration-0085","batch_id":"batch-20261014-advance-20261029-r05-finite-filtration-foundations","language":"zh-Hant","source_mko_ids":["mko-finite-filtration"],"title_zh":"有限filtration","stem_zh":"所有資訊partition位於同一有限樣本空間。操作=filtration-event-measurability；資料={\"n\":6,\"partitions\":[[0,0,0,0,0,0],[0,0,0,1,1,1],[1,0,0,11,10,10]],\"time\":0,\"event\":[0,1,2,3,4,5]}。請依 [time,event,measurable,boundary] 欄序回答。","answer":{"kind":"expression","value":"(0, [0, 1, 2, 3, 4, 5], 是, event_must_be_union_of_time_blocks)","explanation_zh":"Wave4第三層核對=(0, [0, 1, 2, 3, 4, 5], 是, event_must_be_union_of_time_blocks)；依完整明示資料重算；完整有限／symbolic certificate不自動升格為未聲明的一般定理；每個較晚partition須精確細化較早partition；filtration不自動推出adapted natural independent或Markov。"},"difficulty":{"band":"undergraduate_core","level":2,"skills":["有限filtration"]},"variant":{"family_id":"qf-mod29-filtration-event-measurability","seed":202610295085,"parameters":{"n":6,"partitions":[[0,0,0,0,0,0],[0,0,0,1,1,1],[1,0,0,11,10,10]],"time":0,"event":[0,1,2,3,4,5],"domain":"Exact_finite_partition_filtration","operation":"filtration-event-measurability","semantic_template":"qf-mod29-filtration-event-measurability/{\"event\":[0,1,2,3,4,5],\"n\":6,\"partitions\":[[0,0,0,0,0,0],[0,0,0,1,1,1],[1,0,0,11,10,10]],\"time\":0}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_model","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"產生端候選須由主端重算；不構成人工審定、任意無限定理、一般域／UFD、Hilbert、一般條件期望、LLN／CLT、商集、Lean執行或形式Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-14","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261014-advance-20261029-r05-finite-filtration-0086","batch_id":"batch-20261014-advance-20261029-r05-finite-filtration-foundations","language":"zh-Hant","source_mko_ids":["mko-finite-filtration"],"title_zh":"有限filtration","stem_zh":"所有資訊partition位於同一有限樣本空間。操作=filtration-event-measurability；資料={\"n\":6,\"partitions\":[[0,0,0,0,0,0],[0,0,0,1,1,1],[0,1,0,11,10,10]],\"time\":1,\"event\":[3,4,5]}。請依 [time,event,measurable,boundary] 欄序回答。","answer":{"kind":"expression","value":"(1, [3, 4, 5], 是, event_must_be_union_of_time_blocks)","explanation_zh":"Wave4第三層核對=(1, [3, 4, 5], 是, event_must_be_union_of_time_blocks)；依完整明示資料重算；完整有限／symbolic certificate不自動升格為未聲明的一般定理；每個較晚partition須精確細化較早partition；filtration不自動推出adapted natural independent或Markov。"},"difficulty":{"band":"undergraduate_core","level":2,"skills":["有限filtration"]},"variant":{"family_id":"qf-mod29-filtration-event-measurability","seed":202610295086,"parameters":{"n":6,"partitions":[[0,0,0,0,0,0],[0,0,0,1,1,1],[0,1,0,11,10,10]],"time":1,"event":[3,4,5],"domain":"Exact_finite_partition_filtration","operation":"filtration-event-measurability","semantic_template":"qf-mod29-filtration-event-measurability/{\"event\":[3,4,5],\"n\":6,\"partitions\":[[0,0,0,0,0,0],[0,0,0,1,1,1],[0,1,0,11,10,10]],\"time\":1}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_model","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"產生端候選須由主端重算；不構成人工審定、任意無限定理、一般域／UFD、Hilbert、一般條件期望、LLN／CLT、商集、Lean執行或形式Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-14","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261014-advance-20261029-r05-finite-filtration-0087","batch_id":"batch-20261014-advance-20261029-r05-finite-filtration-foundations","language":"zh-Hant","source_mko_ids":["mko-finite-filtration"],"title_zh":"有限filtration","stem_zh":"所有資訊partition位於同一有限樣本空間。操作=filtration-event-measurability；資料={\"n\":6,\"partitions\":[[0,0,0,0,0,0],[0,0,0,1,1,1],[1,1,0,11,10,10]],\"time\":2,\"event\":[4,5]}。請依 [time,event,measurable,boundary] 欄序回答。","answer":{"kind":"expression","value":"(2, [4, 5], 是, event_must_be_union_of_time_blocks)","explanation_zh":"Wave4第三層核對=(2, [4, 5], 是, event_must_be_union_of_time_blocks)；依完整明示資料重算；完整有限／symbolic certificate不自動升格為未聲明的一般定理；每個較晚partition須精確細化較早partition；filtration不自動推出adapted natural independent或Markov。"},"difficulty":{"band":"undergraduate_core","level":2,"skills":["有限filtration"]},"variant":{"family_id":"qf-mod29-filtration-event-measurability","seed":202610295087,"parameters":{"n":6,"partitions":[[0,0,0,0,0,0],[0,0,0,1,1,1],[1,1,0,11,10,10]],"time":2,"event":[4,5],"domain":"Exact_finite_partition_filtration","operation":"filtration-event-measurability","semantic_template":"qf-mod29-filtration-event-measurability/{\"event\":[4,5],\"n\":6,\"partitions\":[[0,0,0,0,0,0],[0,0,0,1,1,1],[1,1,0,11,10,10]],\"time\":2}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_model","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"產生端候選須由主端重算；不構成人工審定、任意無限定理、一般域／UFD、Hilbert、一般條件期望、LLN／CLT、商集、Lean執行或形式Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-14","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261014-advance-20261029-r05-finite-filtration-0088","batch_id":"batch-20261014-advance-20261029-r05-finite-filtration-foundations","language":"zh-Hant","source_mko_ids":["mko-finite-filtration"],"title_zh":"有限filtration","stem_zh":"所有資訊partition位於同一有限樣本空間。操作=filtration-event-measurability；資料={\"n\":6,\"partitions\":[[0,0,0,0,0,0],[0,0,0,1,1,1],[0,0,1,11,10,10]],\"time\":0,\"event\":[0]}。請依 [time,event,measurable,boundary] 欄序回答。","answer":{"kind":"expression","value":"(0, [0], 否, event_must_be_union_of_time_blocks)","explanation_zh":"Wave4第三層核對=(0, [0], 否, event_must_be_union_of_time_blocks)；依完整明示資料重算；完整有限／symbolic certificate不自動升格為未聲明的一般定理；每個較晚partition須精確細化較早partition；filtration不自動推出adapted natural independent或Markov。"},"difficulty":{"band":"undergraduate_core","level":2,"skills":["有限filtration"]},"variant":{"family_id":"qf-mod29-filtration-event-measurability","seed":202610295088,"parameters":{"n":6,"partitions":[[0,0,0,0,0,0],[0,0,0,1,1,1],[0,0,1,11,10,10]],"time":0,"event":[0],"domain":"Exact_finite_partition_filtration","operation":"filtration-event-measurability","semantic_template":"qf-mod29-filtration-event-measurability/{\"event\":[0],\"n\":6,\"partitions\":[[0,0,0,0,0,0],[0,0,0,1,1,1],[0,0,1,11,10,10]],\"time\":0}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_model","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"產生端候選須由主端重算；不構成人工審定、任意無限定理、一般域／UFD、Hilbert、一般條件期望、LLN／CLT、商集、Lean執行或形式Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-14","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261014-advance-20261029-r05-finite-filtration-0089","batch_id":"batch-20261014-advance-20261029-r05-finite-filtration-foundations","language":"zh-Hant","source_mko_ids":["mko-finite-filtration"],"title_zh":"有限filtration","stem_zh":"所有資訊partition位於同一有限樣本空間。操作=filtration-event-measurability；資料={\"n\":6,\"partitions\":[[0,0,0,0,0,0],[0,0,0,1,1,1],[1,0,1,11,10,10]],\"time\":1,\"event\":[0,1,2]}。請依 [time,event,measurable,boundary] 欄序回答。","answer":{"kind":"expression","value":"(1, [0, 1, 2], 是, event_must_be_union_of_time_blocks)","explanation_zh":"Wave4第三層核對=(1, [0, 1, 2], 是, event_must_be_union_of_time_blocks)；依完整明示資料重算；完整有限／symbolic certificate不自動升格為未聲明的一般定理；每個較晚partition須精確細化較早partition；filtration不自動推出adapted natural independent或Markov。"},"difficulty":{"band":"undergraduate_core","level":2,"skills":["有限filtration"]},"variant":{"family_id":"qf-mod29-filtration-event-measurability","seed":202610295089,"parameters":{"n":6,"partitions":[[0,0,0,0,0,0],[0,0,0,1,1,1],[1,0,1,11,10,10]],"time":1,"event":[0,1,2],"domain":"Exact_finite_partition_filtration","operation":"filtration-event-measurability","semantic_template":"qf-mod29-filtration-event-measurability/{\"event\":[0,1,2],\"n\":6,\"partitions\":[[0,0,0,0,0,0],[0,0,0,1,1,1],[1,0,1,11,10,10]],\"time\":1}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_model","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"產生端候選須由主端重算；不構成人工審定、任意無限定理、一般域／UFD、Hilbert、一般條件期望、LLN／CLT、商集、Lean執行或形式Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-14","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261014-advance-20261029-r05-finite-filtration-0090","batch_id":"batch-20261014-advance-20261029-r05-finite-filtration-foundations","language":"zh-Hant","source_mko_ids":["mko-finite-filtration"],"title_zh":"有限filtration","stem_zh":"所有資訊partition位於同一有限樣本空間。操作=filtration-event-measurability；資料={\"n\":6,\"partitions\":[[0,0,0,0,0,0],[0,0,0,1,1,1],[0,1,1,11,10,10]],\"time\":2,\"event\":[1,2]}。請依 [time,event,measurable,boundary] 欄序回答。","answer":{"kind":"expression","value":"(2, [1, 2], 是, event_must_be_union_of_time_blocks)","explanation_zh":"Wave4第三層核對=(2, [1, 2], 是, event_must_be_union_of_time_blocks)；依完整明示資料重算；完整有限／symbolic certificate不自動升格為未聲明的一般定理；每個較晚partition須精確細化較早partition；filtration不自動推出adapted natural independent或Markov。"},"difficulty":{"band":"undergraduate_core","level":2,"skills":["有限filtration"]},"variant":{"family_id":"qf-mod29-filtration-event-measurability","seed":202610295090,"parameters":{"n":6,"partitions":[[0,0,0,0,0,0],[0,0,0,1,1,1],[0,1,1,11,10,10]],"time":2,"event":[1,2],"domain":"Exact_finite_partition_filtration","operation":"filtration-event-measurability","semantic_template":"qf-mod29-filtration-event-measurability/{\"event\":[1,2],\"n\":6,\"partitions\":[[0,0,0,0,0,0],[0,0,0,1,1,1],[0,1,1,11,10,10]],\"time\":2}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_model","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"產生端候選須由主端重算；不構成人工審定、任意無限定理、一般域／UFD、Hilbert、一般條件期望、LLN／CLT、商集、Lean執行或形式Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-14","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261014-advance-20261029-r05-finite-filtration-0091","batch_id":"batch-20261014-advance-20261029-r05-finite-filtration-foundations","language":"zh-Hant","source_mko_ids":["mko-finite-filtration"],"title_zh":"有限filtration","stem_zh":"所有資訊partition位於同一有限樣本空間。操作=filtration-event-measurability；資料={\"n\":6,\"partitions\":[[0,0,0,0,0,0],[0,0,0,1,1,1],[1,1,1,11,10,10]],\"time\":0,\"event\":[0,1,2,3,4,5]}。請依 [time,event,measurable,boundary] 欄序回答。","answer":{"kind":"expression","value":"(0, [0, 1, 2, 3, 4, 5], 是, event_must_be_union_of_time_blocks)","explanation_zh":"Wave4第三層核對=(0, [0, 1, 2, 3, 4, 5], 是, event_must_be_union_of_time_blocks)；依完整明示資料重算；完整有限／symbolic certificate不自動升格為未聲明的一般定理；每個較晚partition須精確細化較早partition；filtration不自動推出adapted natural independent或Markov。"},"difficulty":{"band":"undergraduate_core","level":2,"skills":["有限filtration"]},"variant":{"family_id":"qf-mod29-filtration-event-measurability","seed":202610295091,"parameters":{"n":6,"partitions":[[0,0,0,0,0,0],[0,0,0,1,1,1],[1,1,1,11,10,10]],"time":0,"event":[0,1,2,3,4,5],"domain":"Exact_finite_partition_filtration","operation":"filtration-event-measurability","semantic_template":"qf-mod29-filtration-event-measurability/{\"event\":[0,1,2,3,4,5],\"n\":6,\"partitions\":[[0,0,0,0,0,0],[0,0,0,1,1,1],[1,1,1,11,10,10]],\"time\":0}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_model","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"產生端候選須由主端重算；不構成人工審定、任意無限定理、一般域／UFD、Hilbert、一般條件期望、LLN／CLT、商集、Lean執行或形式Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-14","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261014-advance-20261029-r05-finite-filtration-0092","batch_id":"batch-20261014-advance-20261029-r05-finite-filtration-foundations","language":"zh-Hant","source_mko_ids":["mko-finite-filtration"],"title_zh":"有限filtration","stem_zh":"所有資訊partition位於同一有限樣本空間。操作=filtration-event-measurability；資料={\"n\":6,\"partitions\":[[0,0,0,0,0,0],[0,0,0,1,1,1],[0,0,0,10,11,10]],\"time\":1,\"event\":[3]}。請依 [time,event,measurable,boundary] 欄序回答。","answer":{"kind":"expression","value":"(1, [3], 否, event_must_be_union_of_time_blocks)","explanation_zh":"Wave4第三層核對=(1, [3], 否, event_must_be_union_of_time_blocks)；依完整明示資料重算；完整有限／symbolic certificate不自動升格為未聲明的一般定理；每個較晚partition須精確細化較早partition；filtration不自動推出adapted natural independent或Markov。"},"difficulty":{"band":"undergraduate_core","level":2,"skills":["有限filtration"]},"variant":{"family_id":"qf-mod29-filtration-event-measurability","seed":202610295092,"parameters":{"n":6,"partitions":[[0,0,0,0,0,0],[0,0,0,1,1,1],[0,0,0,10,11,10]],"time":1,"event":[3],"domain":"Exact_finite_partition_filtration","operation":"filtration-event-measurability","semantic_template":"qf-mod29-filtration-event-measurability/{\"event\":[3],\"n\":6,\"partitions\":[[0,0,0,0,0,0],[0,0,0,1,1,1],[0,0,0,10,11,10]],\"time\":1}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_model","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"產生端候選須由主端重算；不構成人工審定、任意無限定理、一般域／UFD、Hilbert、一般條件期望、LLN／CLT、商集、Lean執行或形式Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-14","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261014-advance-20261029-r05-finite-filtration-0093","batch_id":"batch-20261014-advance-20261029-r05-finite-filtration-foundations","language":"zh-Hant","source_mko_ids":["mko-finite-filtration"],"title_zh":"有限filtration","stem_zh":"所有資訊partition位於同一有限樣本空間。操作=filtration-event-measurability；資料={\"n\":6,\"partitions\":[[0,0,0,0,0,0],[0,0,0,1,1,1],[1,0,0,10,11,10]],\"time\":2,\"event\":[3,5]}。請依 [time,event,measurable,boundary] 欄序回答。","answer":{"kind":"expression","value":"(2, [3, 5], 是, event_must_be_union_of_time_blocks)","explanation_zh":"Wave4第三層核對=(2, [3, 5], 是, event_must_be_union_of_time_blocks)；依完整明示資料重算；完整有限／symbolic certificate不自動升格為未聲明的一般定理；每個較晚partition須精確細化較早partition；filtration不自動推出adapted natural independent或Markov。"},"difficulty":{"band":"undergraduate_core","level":3,"skills":["有限filtration"]},"variant":{"family_id":"qf-mod29-filtration-event-measurability","seed":202610295093,"parameters":{"n":6,"partitions":[[0,0,0,0,0,0],[0,0,0,1,1,1],[1,0,0,10,11,10]],"time":2,"event":[3,5],"domain":"Exact_finite_partition_filtration","operation":"filtration-event-measurability","semantic_template":"qf-mod29-filtration-event-measurability/{\"event\":[3,5],\"n\":6,\"partitions\":[[0,0,0,0,0,0],[0,0,0,1,1,1],[1,0,0,10,11,10]],\"time\":2}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_model","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"產生端候選須由主端重算；不構成人工審定、任意無限定理、一般域／UFD、Hilbert、一般條件期望、LLN／CLT、商集、Lean執行或形式Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-14","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261014-advance-20261029-r05-finite-filtration-0094","batch_id":"batch-20261014-advance-20261029-r05-finite-filtration-foundations","language":"zh-Hant","source_mko_ids":["mko-finite-filtration"],"title_zh":"有限filtration","stem_zh":"所有資訊partition位於同一有限樣本空間。操作=filtration-event-measurability；資料={\"n\":6,\"partitions\":[[0,0,0,0,0,0],[0,0,0,1,1,1],[0,1,0,10,11,10]],\"time\":0,\"event\":[0,1,2,3,4,5]}。請依 [time,event,measurable,boundary] 欄序回答。","answer":{"kind":"expression","value":"(0, [0, 1, 2, 3, 4, 5], 是, event_must_be_union_of_time_blocks)","explanation_zh":"Wave4第三層核對=(0, [0, 1, 2, 3, 4, 5], 是, event_must_be_union_of_time_blocks)；依完整明示資料重算；完整有限／symbolic certificate不自動升格為未聲明的一般定理；每個較晚partition須精確細化較早partition；filtration不自動推出adapted natural independent或Markov。"},"difficulty":{"band":"undergraduate_core","level":3,"skills":["有限filtration"]},"variant":{"family_id":"qf-mod29-filtration-event-measurability","seed":202610295094,"parameters":{"n":6,"partitions":[[0,0,0,0,0,0],[0,0,0,1,1,1],[0,1,0,10,11,10]],"time":0,"event":[0,1,2,3,4,5],"domain":"Exact_finite_partition_filtration","operation":"filtration-event-measurability","semantic_template":"qf-mod29-filtration-event-measurability/{\"event\":[0,1,2,3,4,5],\"n\":6,\"partitions\":[[0,0,0,0,0,0],[0,0,0,1,1,1],[0,1,0,10,11,10]],\"time\":0}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_model","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"產生端候選須由主端重算；不構成人工審定、任意無限定理、一般域／UFD、Hilbert、一般條件期望、LLN／CLT、商集、Lean執行或形式Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-14","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261014-advance-20261029-r05-finite-filtration-0095","batch_id":"batch-20261014-advance-20261029-r05-finite-filtration-foundations","language":"zh-Hant","source_mko_ids":["mko-finite-filtration"],"title_zh":"有限filtration","stem_zh":"所有資訊partition位於同一有限樣本空間。操作=filtration-event-measurability；資料={\"n\":6,\"partitions\":[[0,0,0,0,0,0],[0,0,0,1,1,1],[1,1,0,10,11,10]],\"time\":1,\"event\":[0,1,2]}。請依 [time,event,measurable,boundary] 欄序回答。","answer":{"kind":"expression","value":"(1, [0, 1, 2], 是, event_must_be_union_of_time_blocks)","explanation_zh":"Wave4第三層核對=(1, [0, 1, 2], 是, event_must_be_union_of_time_blocks)；依完整明示資料重算；完整有限／symbolic certificate不自動升格為未聲明的一般定理；每個較晚partition須精確細化較早partition；filtration不自動推出adapted natural independent或Markov。"},"difficulty":{"band":"undergraduate_core","level":3,"skills":["有限filtration"]},"variant":{"family_id":"qf-mod29-filtration-event-measurability","seed":202610295095,"parameters":{"n":6,"partitions":[[0,0,0,0,0,0],[0,0,0,1,1,1],[1,1,0,10,11,10]],"time":1,"event":[0,1,2],"domain":"Exact_finite_partition_filtration","operation":"filtration-event-measurability","semantic_template":"qf-mod29-filtration-event-measurability/{\"event\":[0,1,2],\"n\":6,\"partitions\":[[0,0,0,0,0,0],[0,0,0,1,1,1],[1,1,0,10,11,10]],\"time\":1}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_model","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"產生端候選須由主端重算；不構成人工審定、任意無限定理、一般域／UFD、Hilbert、一般條件期望、LLN／CLT、商集、Lean執行或形式Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-14","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261014-advance-20261029-r05-finite-filtration-0096","batch_id":"batch-20261014-advance-20261029-r05-finite-filtration-foundations","language":"zh-Hant","source_mko_ids":["mko-finite-filtration"],"title_zh":"有限filtration","stem_zh":"所有資訊partition位於同一有限樣本空間。操作=filtration-event-measurability；資料={\"n\":6,\"partitions\":[[0,0,0,0,0,0],[0,0,0,1,1,1],[0,0,1,10,11,10]],\"time\":2,\"event\":[2]}。請依 [time,event,measurable,boundary] 欄序回答。","answer":{"kind":"expression","value":"(2, [2], 是, event_must_be_union_of_time_blocks)","explanation_zh":"Wave4第三層核對=(2, [2], 是, event_must_be_union_of_time_blocks)；依完整明示資料重算；完整有限／symbolic certificate不自動升格為未聲明的一般定理；每個較晚partition須精確細化較早partition；filtration不自動推出adapted natural independent或Markov。"},"difficulty":{"band":"undergraduate_core","level":3,"skills":["有限filtration"]},"variant":{"family_id":"qf-mod29-filtration-event-measurability","seed":202610295096,"parameters":{"n":6,"partitions":[[0,0,0,0,0,0],[0,0,0,1,1,1],[0,0,1,10,11,10]],"time":2,"event":[2],"domain":"Exact_finite_partition_filtration","operation":"filtration-event-measurability","semantic_template":"qf-mod29-filtration-event-measurability/{\"event\":[2],\"n\":6,\"partitions\":[[0,0,0,0,0,0],[0,0,0,1,1,1],[0,0,1,10,11,10]],\"time\":2}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_model","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"產生端候選須由主端重算；不構成人工審定、任意無限定理、一般域／UFD、Hilbert、一般條件期望、LLN／CLT、商集、Lean執行或形式Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-14","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261014-advance-20261029-r05-finite-filtration-0097","batch_id":"batch-20261014-advance-20261029-r05-finite-filtration-foundations","language":"zh-Hant","source_mko_ids":["mko-finite-filtration"],"title_zh":"有限filtration","stem_zh":"所有資訊partition位於同一有限樣本空間。操作=filtration-event-measurability；資料={\"n\":6,\"partitions\":[[0,0,0,0,0,0],[0,0,0,1,1,1],[1,0,1,10,11,10]],\"time\":0,\"event\":[0,1,2,3,4,5]}。請依 [time,event,measurable,boundary] 欄序回答。","answer":{"kind":"expression","value":"(0, [0, 1, 2, 3, 4, 5], 是, event_must_be_union_of_time_blocks)","explanation_zh":"Wave4第三層核對=(0, [0, 1, 2, 3, 4, 5], 是, event_must_be_union_of_time_blocks)；依完整明示資料重算；完整有限／symbolic certificate不自動升格為未聲明的一般定理；每個較晚partition須精確細化較早partition；filtration不自動推出adapted natural independent或Markov。"},"difficulty":{"band":"undergraduate_core","level":3,"skills":["有限filtration"]},"variant":{"family_id":"qf-mod29-filtration-event-measurability","seed":202610295097,"parameters":{"n":6,"partitions":[[0,0,0,0,0,0],[0,0,0,1,1,1],[1,0,1,10,11,10]],"time":0,"event":[0,1,2,3,4,5],"domain":"Exact_finite_partition_filtration","operation":"filtration-event-measurability","semantic_template":"qf-mod29-filtration-event-measurability/{\"event\":[0,1,2,3,4,5],\"n\":6,\"partitions\":[[0,0,0,0,0,0],[0,0,0,1,1,1],[1,0,1,10,11,10]],\"time\":0}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_model","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"產生端候選須由主端重算；不構成人工審定、任意無限定理、一般域／UFD、Hilbert、一般條件期望、LLN／CLT、商集、Lean執行或形式Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-14","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261014-advance-20261029-r05-finite-filtration-0098","batch_id":"batch-20261014-advance-20261029-r05-finite-filtration-foundations","language":"zh-Hant","source_mko_ids":["mko-finite-filtration"],"title_zh":"有限filtration","stem_zh":"所有資訊partition位於同一有限樣本空間。操作=filtration-event-measurability；資料={\"n\":6,\"partitions\":[[0,0,0,0,0,0],[0,0,0,1,1,1],[0,1,1,10,11,10]],\"time\":1,\"event\":[3,4,5]}。請依 [time,event,measurable,boundary] 欄序回答。","answer":{"kind":"expression","value":"(1, [3, 4, 5], 是, event_must_be_union_of_time_blocks)","explanation_zh":"Wave4第三層核對=(1, [3, 4, 5], 是, event_must_be_union_of_time_blocks)；依完整明示資料重算；完整有限／symbolic certificate不自動升格為未聲明的一般定理；每個較晚partition須精確細化較早partition；filtration不自動推出adapted natural independent或Markov。"},"difficulty":{"band":"undergraduate_core","level":3,"skills":["有限filtration"]},"variant":{"family_id":"qf-mod29-filtration-event-measurability","seed":202610295098,"parameters":{"n":6,"partitions":[[0,0,0,0,0,0],[0,0,0,1,1,1],[0,1,1,10,11,10]],"time":1,"event":[3,4,5],"domain":"Exact_finite_partition_filtration","operation":"filtration-event-measurability","semantic_template":"qf-mod29-filtration-event-measurability/{\"event\":[3,4,5],\"n\":6,\"partitions\":[[0,0,0,0,0,0],[0,0,0,1,1,1],[0,1,1,10,11,10]],\"time\":1}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_model","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"產生端候選須由主端重算；不構成人工審定、任意無限定理、一般域／UFD、Hilbert、一般條件期望、LLN／CLT、商集、Lean執行或形式Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-14","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261014-advance-20261029-r05-finite-filtration-0099","batch_id":"batch-20261014-advance-20261029-r05-finite-filtration-foundations","language":"zh-Hant","source_mko_ids":["mko-finite-filtration"],"title_zh":"有限filtration","stem_zh":"所有資訊partition位於同一有限樣本空間。操作=filtration-event-measurability；資料={\"n\":6,\"partitions\":[[0,0,0,0,0,0],[0,0,0,1,1,1],[1,1,1,10,11,10]],\"time\":2,\"event\":[3,5]}。請依 [time,event,measurable,boundary] 欄序回答。","answer":{"kind":"expression","value":"(2, [3, 5], 是, event_must_be_union_of_time_blocks)","explanation_zh":"Wave4第三層核對=(2, [3, 5], 是, event_must_be_union_of_time_blocks)；依完整明示資料重算；完整有限／symbolic certificate不自動升格為未聲明的一般定理；每個較晚partition須精確細化較早partition；filtration不自動推出adapted natural independent或Markov。"},"difficulty":{"band":"undergraduate_core","level":3,"skills":["有限filtration"]},"variant":{"family_id":"qf-mod29-filtration-event-measurability","seed":202610295099,"parameters":{"n":6,"partitions":[[0,0,0,0,0,0],[0,0,0,1,1,1],[1,1,1,10,11,10]],"time":2,"event":[3,5],"domain":"Exact_finite_partition_filtration","operation":"filtration-event-measurability","semantic_template":"qf-mod29-filtration-event-measurability/{\"event\":[3,5],\"n\":6,\"partitions\":[[0,0,0,0,0,0],[0,0,0,1,1,1],[1,1,1,10,11,10]],\"time\":2}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_model","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"產生端候選須由主端重算；不構成人工審定、任意無限定理、一般域／UFD、Hilbert、一般條件期望、LLN／CLT、商集、Lean執行或形式Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-14","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261014-advance-20261029-r05-finite-filtration-0100","batch_id":"batch-20261014-advance-20261029-r05-finite-filtration-foundations","language":"zh-Hant","source_mko_ids":["mko-finite-filtration"],"title_zh":"有限filtration","stem_zh":"所有資訊partition位於同一有限樣本空間。操作=filtration-event-measurability；資料={\"n\":6,\"partitions\":[[0,0,0,0,0,0],[0,0,0,1,1,1],[0,0,0,11,11,10]],\"time\":0,\"event\":[0]}。請依 [time,event,measurable,boundary] 欄序回答。","answer":{"kind":"expression","value":"(0, [0], 否, event_must_be_union_of_time_blocks)","explanation_zh":"Wave4第三層核對=(0, [0], 否, event_must_be_union_of_time_blocks)；依完整明示資料重算；完整有限／symbolic certificate不自動升格為未聲明的一般定理；每個較晚partition須精確細化較早partition；filtration不自動推出adapted natural independent或Markov。"},"difficulty":{"band":"undergraduate_core","level":3,"skills":["有限filtration"]},"variant":{"family_id":"qf-mod29-filtration-event-measurability","seed":202610295100,"parameters":{"n":6,"partitions":[[0,0,0,0,0,0],[0,0,0,1,1,1],[0,0,0,11,11,10]],"time":0,"event":[0],"domain":"Exact_finite_partition_filtration","operation":"filtration-event-measurability","semantic_template":"qf-mod29-filtration-event-measurability/{\"event\":[0],\"n\":6,\"partitions\":[[0,0,0,0,0,0],[0,0,0,1,1,1],[0,0,0,11,11,10]],\"time\":0}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_model","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"產生端候選須由主端重算；不構成人工審定、任意無限定理、一般域／UFD、Hilbert、一般條件期望、LLN／CLT、商集、Lean執行或形式Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-14","contract_version":"ocme-question-factory-v0.1"}}