{"schema_version":"ocme-question-v0.1","id":"q-20261014-advance-20261110-r04-law-of-total-variance-0001","batch_id":"batch-20261014-advance-20261110-r04-law-of-total-variance-foundations","language":"zh-Hant","source_mko_ids":["mko-law-of-total-variance"],"title_zh":"全變異數公式","stem_zh":"同一有限law與完整disjoint partition生成的G。操作=totalvar-partition-qualification；資料={\"masses\":[[1,10],[2,10],[7,10],[0,1]],\"values\":[0,1,3,99],\"partition\":[[0,1],[2,3]]}。請依 exact_ordered_tuple_declared_by_interface 欄序回答。","answer":{"kind":"expression","value":"([[0, 1], [2, 3]], [[0, [0, 1], 3/10], [1, [2, 3], 7/10]], 是, 23/10, 121/100)","explanation_zh":"Wave6第四層核對=([[0, 1], [2, 3]], [[0, [0, 1], 3/10], [1, [2, 3], 7/10]], 是, 23/10, 121/100)；依完整明示資料獨立重算；within與between terms使用同一law及同一cells且兩項皆不可省略；zero-mass cell禁止conditional division且外層加權貢獻為0；不要求partition events independent。"},"difficulty":{"band":"undergraduate_core","level":1,"skills":["全變異數公式"]},"variant":{"family_id":"qf-mod41-totalvar-partition-qualification","seed":202611104001,"parameters":{"masses":[[1,10],[2,10],[7,10],[0,1]],"values":[0,1,3,99],"partition":[[0,1],[2,3]],"domain":"Finite_partition_total_variance","operation":"totalvar-partition-qualification","semantic_template":"qf-mod41-totalvar-partition-qualification/{\"masses\":[[1,10],[2,10],[7,10],[0,1]],\"partition\":[[0,1],[2,3]],\"values\":[0,1,3,99]}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_or_symbolic_model","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"候選須主端重算；不構成人工審定、sampled orbit-stabilizer、sampled MVT、reverse compactness、zero-mass division、underspecified recurrence、incomplete divisor inversion、bounded-search PDA rejection、Lean或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-20261110-r04-law-of-total-variance-0002","batch_id":"batch-20261014-advance-20261110-r04-law-of-total-variance-foundations","language":"zh-Hant","source_mko_ids":["mko-law-of-total-variance"],"title_zh":"全變異數公式","stem_zh":"同一有限law與完整disjoint partition生成的G。操作=totalvar-partition-qualification；資料={\"masses\":[[1,11],[2,11],[8,11],[0,1]],\"values\":[1,2,4,100],\"partition\":[[0,1],[2,3]]}。請依 exact_ordered_tuple_declared_by_interface 欄序回答。","answer":{"kind":"expression","value":"([[0, 1], [2, 3]], [[0, [0, 1], 3/11], [1, [2, 3], 8/11]], 是, 37/11, 138/121)","explanation_zh":"Wave6第四層核對=([[0, 1], [2, 3]], [[0, [0, 1], 3/11], [1, [2, 3], 8/11]], 是, 37/11, 138/121)；依完整明示資料獨立重算；within與between terms使用同一law及同一cells且兩項皆不可省略；zero-mass cell禁止conditional division且外層加權貢獻為0；不要求partition events independent。"},"difficulty":{"band":"undergraduate_core","level":1,"skills":["全變異數公式"]},"variant":{"family_id":"qf-mod41-totalvar-partition-qualification","seed":202611104002,"parameters":{"masses":[[1,11],[2,11],[8,11],[0,1]],"values":[1,2,4,100],"partition":[[0,1],[2,3]],"domain":"Finite_partition_total_variance","operation":"totalvar-partition-qualification","semantic_template":"qf-mod41-totalvar-partition-qualification/{\"masses\":[[1,11],[2,11],[8,11],[0,1]],\"partition\":[[0,1],[2,3]],\"values\":[1,2,4,100]}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_or_symbolic_model","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"候選須主端重算；不構成人工審定、sampled orbit-stabilizer、sampled MVT、reverse compactness、zero-mass division、underspecified recurrence、incomplete divisor inversion、bounded-search PDA rejection、Lean或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-20261110-r04-law-of-total-variance-0003","batch_id":"batch-20261014-advance-20261110-r04-law-of-total-variance-foundations","language":"zh-Hant","source_mko_ids":["mko-law-of-total-variance"],"title_zh":"全變異數公式","stem_zh":"同一有限law與完整disjoint partition生成的G。操作=totalvar-partition-qualification；資料={\"masses\":[[1,12],[2,12],[9,12],[0,1]],\"values\":[2,3,5,101],\"partition\":[[0,1],[2,3]]}。請依 exact_ordered_tuple_declared_by_interface 欄序回答。","answer":{"kind":"expression","value":"([[0, 1], [2, 3]], [[0, [0, 1], 1/4], [1, [2, 3], 3/4]], 是, 53/12, 155/144)","explanation_zh":"Wave6第四層核對=([[0, 1], [2, 3]], [[0, [0, 1], 1/4], [1, [2, 3], 3/4]], 是, 53/12, 155/144)；依完整明示資料獨立重算；within與between terms使用同一law及同一cells且兩項皆不可省略；zero-mass cell禁止conditional division且外層加權貢獻為0；不要求partition events independent。"},"difficulty":{"band":"undergraduate_core","level":1,"skills":["全變異數公式"]},"variant":{"family_id":"qf-mod41-totalvar-partition-qualification","seed":202611104003,"parameters":{"masses":[[1,12],[2,12],[9,12],[0,1]],"values":[2,3,5,101],"partition":[[0,1],[2,3]],"domain":"Finite_partition_total_variance","operation":"totalvar-partition-qualification","semantic_template":"qf-mod41-totalvar-partition-qualification/{\"masses\":[[1,12],[2,12],[9,12],[0,1]],\"partition\":[[0,1],[2,3]],\"values\":[2,3,5,101]}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_or_symbolic_model","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"候選須主端重算；不構成人工審定、sampled orbit-stabilizer、sampled MVT、reverse compactness、zero-mass division、underspecified recurrence、incomplete divisor inversion、bounded-search PDA rejection、Lean或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-20261110-r04-law-of-total-variance-0004","batch_id":"batch-20261014-advance-20261110-r04-law-of-total-variance-foundations","language":"zh-Hant","source_mko_ids":["mko-law-of-total-variance"],"title_zh":"全變異數公式","stem_zh":"同一有限law與完整disjoint partition生成的G。操作=totalvar-partition-qualification；資料={\"masses\":[[1,13],[2,13],[10,13],[0,1]],\"values\":[3,4,6,102],\"partition\":[[0,1],[2,3]]}。請依 exact_ordered_tuple_declared_by_interface 欄序回答。","answer":{"kind":"expression","value":"([[0, 1], [2, 3]], [[0, [0, 1], 3/13], [1, [2, 3], 10/13]], 是, 71/13, 172/169)","explanation_zh":"Wave6第四層核對=([[0, 1], [2, 3]], [[0, [0, 1], 3/13], [1, [2, 3], 10/13]], 是, 71/13, 172/169)；依完整明示資料獨立重算；within與between terms使用同一law及同一cells且兩項皆不可省略；zero-mass cell禁止conditional division且外層加權貢獻為0；不要求partition events independent。"},"difficulty":{"band":"undergraduate_core","level":1,"skills":["全變異數公式"]},"variant":{"family_id":"qf-mod41-totalvar-partition-qualification","seed":202611104004,"parameters":{"masses":[[1,13],[2,13],[10,13],[0,1]],"values":[3,4,6,102],"partition":[[0,1],[2,3]],"domain":"Finite_partition_total_variance","operation":"totalvar-partition-qualification","semantic_template":"qf-mod41-totalvar-partition-qualification/{\"masses\":[[1,13],[2,13],[10,13],[0,1]],\"partition\":[[0,1],[2,3]],\"values\":[3,4,6,102]}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_or_symbolic_model","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"候選須主端重算；不構成人工審定、sampled orbit-stabilizer、sampled MVT、reverse compactness、zero-mass division、underspecified recurrence、incomplete divisor inversion、bounded-search PDA rejection、Lean或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-20261110-r04-law-of-total-variance-0005","batch_id":"batch-20261014-advance-20261110-r04-law-of-total-variance-foundations","language":"zh-Hant","source_mko_ids":["mko-law-of-total-variance"],"title_zh":"全變異數公式","stem_zh":"同一有限law與完整disjoint partition生成的G。操作=totalvar-partition-qualification；資料={\"masses\":[[1,14],[2,14],[11,14],[0,1]],\"values\":[4,5,7,103],\"partition\":[[0,1],[2,3]]}。請依 exact_ordered_tuple_declared_by_interface 欄序回答。","answer":{"kind":"expression","value":"([[0, 1], [2, 3]], [[0, [0, 1], 3/14], [1, [2, 3], 11/14]], 是, 13/2, 27/28)","explanation_zh":"Wave6第四層核對=([[0, 1], [2, 3]], [[0, [0, 1], 3/14], [1, [2, 3], 11/14]], 是, 13/2, 27/28)；依完整明示資料獨立重算；within與between terms使用同一law及同一cells且兩項皆不可省略；zero-mass cell禁止conditional division且外層加權貢獻為0；不要求partition events independent。"},"difficulty":{"band":"undergraduate_core","level":1,"skills":["全變異數公式"]},"variant":{"family_id":"qf-mod41-totalvar-partition-qualification","seed":202611104005,"parameters":{"masses":[[1,14],[2,14],[11,14],[0,1]],"values":[4,5,7,103],"partition":[[0,1],[2,3]],"domain":"Finite_partition_total_variance","operation":"totalvar-partition-qualification","semantic_template":"qf-mod41-totalvar-partition-qualification/{\"masses\":[[1,14],[2,14],[11,14],[0,1]],\"partition\":[[0,1],[2,3]],\"values\":[4,5,7,103]}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_or_symbolic_model","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"候選須主端重算；不構成人工審定、sampled orbit-stabilizer、sampled MVT、reverse compactness、zero-mass division、underspecified recurrence、incomplete divisor inversion、bounded-search PDA rejection、Lean或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-20261110-r04-law-of-total-variance-0006","batch_id":"batch-20261014-advance-20261110-r04-law-of-total-variance-foundations","language":"zh-Hant","source_mko_ids":["mko-law-of-total-variance"],"title_zh":"全變異數公式","stem_zh":"同一有限law與完整disjoint partition生成的G。操作=totalvar-partition-qualification；資料={\"masses\":[[1,15],[2,15],[12,15],[0,1]],\"values\":[5,6,8,104],\"partition\":[[0,1],[2,3]]}。請依 exact_ordered_tuple_declared_by_interface 欄序回答。","answer":{"kind":"expression","value":"([[0, 1], [2, 3]], [[0, [0, 1], 1/5], [1, [2, 3], 4/5]], 是, 113/15, 206/225)","explanation_zh":"Wave6第四層核對=([[0, 1], [2, 3]], [[0, [0, 1], 1/5], [1, [2, 3], 4/5]], 是, 113/15, 206/225)；依完整明示資料獨立重算；within與between terms使用同一law及同一cells且兩項皆不可省略；zero-mass cell禁止conditional division且外層加權貢獻為0；不要求partition events independent。"},"difficulty":{"band":"undergraduate_core","level":1,"skills":["全變異數公式"]},"variant":{"family_id":"qf-mod41-totalvar-partition-qualification","seed":202611104006,"parameters":{"masses":[[1,15],[2,15],[12,15],[0,1]],"values":[5,6,8,104],"partition":[[0,1],[2,3]],"domain":"Finite_partition_total_variance","operation":"totalvar-partition-qualification","semantic_template":"qf-mod41-totalvar-partition-qualification/{\"masses\":[[1,15],[2,15],[12,15],[0,1]],\"partition\":[[0,1],[2,3]],\"values\":[5,6,8,104]}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_or_symbolic_model","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"候選須主端重算；不構成人工審定、sampled orbit-stabilizer、sampled MVT、reverse compactness、zero-mass division、underspecified recurrence、incomplete divisor inversion、bounded-search PDA rejection、Lean或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-20261110-r04-law-of-total-variance-0007","batch_id":"batch-20261014-advance-20261110-r04-law-of-total-variance-foundations","language":"zh-Hant","source_mko_ids":["mko-law-of-total-variance"],"title_zh":"全變異數公式","stem_zh":"同一有限law與完整disjoint partition生成的G。操作=totalvar-partition-qualification；資料={\"masses\":[[1,16],[2,16],[13,16],[0,1]],\"values\":[6,7,9,105],\"partition\":[[0,1],[2,3]]}。請依 exact_ordered_tuple_declared_by_interface 欄序回答。","answer":{"kind":"expression","value":"([[0, 1], [2, 3]], [[0, [0, 1], 3/16], [1, [2, 3], 13/16]], 是, 137/16, 223/256)","explanation_zh":"Wave6第四層核對=([[0, 1], [2, 3]], [[0, [0, 1], 3/16], [1, [2, 3], 13/16]], 是, 137/16, 223/256)；依完整明示資料獨立重算；within與between terms使用同一law及同一cells且兩項皆不可省略；zero-mass cell禁止conditional division且外層加權貢獻為0；不要求partition events independent。"},"difficulty":{"band":"undergraduate_core","level":1,"skills":["全變異數公式"]},"variant":{"family_id":"qf-mod41-totalvar-partition-qualification","seed":202611104007,"parameters":{"masses":[[1,16],[2,16],[13,16],[0,1]],"values":[6,7,9,105],"partition":[[0,1],[2,3]],"domain":"Finite_partition_total_variance","operation":"totalvar-partition-qualification","semantic_template":"qf-mod41-totalvar-partition-qualification/{\"masses\":[[1,16],[2,16],[13,16],[0,1]],\"partition\":[[0,1],[2,3]],\"values\":[6,7,9,105]}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_or_symbolic_model","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"候選須主端重算；不構成人工審定、sampled orbit-stabilizer、sampled MVT、reverse compactness、zero-mass division、underspecified recurrence、incomplete divisor inversion、bounded-search PDA rejection、Lean或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-20261110-r04-law-of-total-variance-0008","batch_id":"batch-20261014-advance-20261110-r04-law-of-total-variance-foundations","language":"zh-Hant","source_mko_ids":["mko-law-of-total-variance"],"title_zh":"全變異數公式","stem_zh":"同一有限law與完整disjoint partition生成的G。操作=totalvar-partition-qualification；資料={\"masses\":[[1,17],[2,17],[14,17],[0,1]],\"values\":[7,8,10,106],\"partition\":[[0,1],[2,3]]}。請依 exact_ordered_tuple_declared_by_interface 欄序回答。","answer":{"kind":"expression","value":"([[0, 1], [2, 3]], [[0, [0, 1], 3/17], [1, [2, 3], 14/17]], 是, 163/17, 240/289)","explanation_zh":"Wave6第四層核對=([[0, 1], [2, 3]], [[0, [0, 1], 3/17], [1, [2, 3], 14/17]], 是, 163/17, 240/289)；依完整明示資料獨立重算；within與between terms使用同一law及同一cells且兩項皆不可省略；zero-mass cell禁止conditional division且外層加權貢獻為0；不要求partition events independent。"},"difficulty":{"band":"undergraduate_core","level":1,"skills":["全變異數公式"]},"variant":{"family_id":"qf-mod41-totalvar-partition-qualification","seed":202611104008,"parameters":{"masses":[[1,17],[2,17],[14,17],[0,1]],"values":[7,8,10,106],"partition":[[0,1],[2,3]],"domain":"Finite_partition_total_variance","operation":"totalvar-partition-qualification","semantic_template":"qf-mod41-totalvar-partition-qualification/{\"masses\":[[1,17],[2,17],[14,17],[0,1]],\"partition\":[[0,1],[2,3]],\"values\":[7,8,10,106]}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_or_symbolic_model","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"候選須主端重算；不構成人工審定、sampled orbit-stabilizer、sampled MVT、reverse compactness、zero-mass division、underspecified recurrence、incomplete divisor inversion、bounded-search PDA rejection、Lean或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-20261110-r04-law-of-total-variance-0009","batch_id":"batch-20261014-advance-20261110-r04-law-of-total-variance-foundations","language":"zh-Hant","source_mko_ids":["mko-law-of-total-variance"],"title_zh":"全變異數公式","stem_zh":"同一有限law與完整disjoint partition生成的G。操作=totalvar-partition-qualification；資料={\"masses\":[[1,18],[2,18],[15,18],[0,1]],\"values\":[8,9,11,107],\"partition\":[[0,1],[2,3]]}。請依 exact_ordered_tuple_declared_by_interface 欄序回答。","answer":{"kind":"expression","value":"([[0, 1], [2, 3]], [[0, [0, 1], 1/6], [1, [2, 3], 5/6]], 是, 191/18, 257/324)","explanation_zh":"Wave6第四層核對=([[0, 1], [2, 3]], [[0, [0, 1], 1/6], [1, [2, 3], 5/6]], 是, 191/18, 257/324)；依完整明示資料獨立重算；within與between terms使用同一law及同一cells且兩項皆不可省略；zero-mass cell禁止conditional division且外層加權貢獻為0；不要求partition events independent。"},"difficulty":{"band":"undergraduate_core","level":2,"skills":["全變異數公式"]},"variant":{"family_id":"qf-mod41-totalvar-partition-qualification","seed":202611104009,"parameters":{"masses":[[1,18],[2,18],[15,18],[0,1]],"values":[8,9,11,107],"partition":[[0,1],[2,3]],"domain":"Finite_partition_total_variance","operation":"totalvar-partition-qualification","semantic_template":"qf-mod41-totalvar-partition-qualification/{\"masses\":[[1,18],[2,18],[15,18],[0,1]],\"partition\":[[0,1],[2,3]],\"values\":[8,9,11,107]}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_or_symbolic_model","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"候選須主端重算；不構成人工審定、sampled orbit-stabilizer、sampled MVT、reverse compactness、zero-mass division、underspecified recurrence、incomplete divisor inversion、bounded-search PDA rejection、Lean或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-20261110-r04-law-of-total-variance-0010","batch_id":"batch-20261014-advance-20261110-r04-law-of-total-variance-foundations","language":"zh-Hant","source_mko_ids":["mko-law-of-total-variance"],"title_zh":"全變異數公式","stem_zh":"同一有限law與完整disjoint partition生成的G。操作=totalvar-partition-qualification；資料={\"masses\":[[1,19],[2,19],[16,19],[0,1]],\"values\":[9,10,12,108],\"partition\":[[0,1],[2,3]]}。請依 exact_ordered_tuple_declared_by_interface 欄序回答。","answer":{"kind":"expression","value":"([[0, 1], [2, 3]], [[0, [0, 1], 3/19], [1, [2, 3], 16/19]], 是, 221/19, 274/361)","explanation_zh":"Wave6第四層核對=([[0, 1], [2, 3]], [[0, [0, 1], 3/19], [1, [2, 3], 16/19]], 是, 221/19, 274/361)；依完整明示資料獨立重算；within與between terms使用同一law及同一cells且兩項皆不可省略；zero-mass cell禁止conditional division且外層加權貢獻為0；不要求partition events independent。"},"difficulty":{"band":"undergraduate_core","level":2,"skills":["全變異數公式"]},"variant":{"family_id":"qf-mod41-totalvar-partition-qualification","seed":202611104010,"parameters":{"masses":[[1,19],[2,19],[16,19],[0,1]],"values":[9,10,12,108],"partition":[[0,1],[2,3]],"domain":"Finite_partition_total_variance","operation":"totalvar-partition-qualification","semantic_template":"qf-mod41-totalvar-partition-qualification/{\"masses\":[[1,19],[2,19],[16,19],[0,1]],\"partition\":[[0,1],[2,3]],\"values\":[9,10,12,108]}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_or_symbolic_model","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"候選須主端重算；不構成人工審定、sampled orbit-stabilizer、sampled MVT、reverse compactness、zero-mass division、underspecified recurrence、incomplete divisor inversion、bounded-search PDA rejection、Lean或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-20261110-r04-law-of-total-variance-0011","batch_id":"batch-20261014-advance-20261110-r04-law-of-total-variance-foundations","language":"zh-Hant","source_mko_ids":["mko-law-of-total-variance"],"title_zh":"全變異數公式","stem_zh":"同一有限law與完整disjoint partition生成的G。操作=totalvar-partition-qualification；資料={\"masses\":[[1,20],[2,20],[17,20],[0,1]],\"values\":[10,11,13,109],\"partition\":[[0,1],[2,3]]}。請依 exact_ordered_tuple_declared_by_interface 欄序回答。","answer":{"kind":"expression","value":"([[0, 1], [2, 3]], [[0, [0, 1], 3/20], [1, [2, 3], 17/20]], 是, 253/20, 291/400)","explanation_zh":"Wave6第四層核對=([[0, 1], [2, 3]], [[0, [0, 1], 3/20], [1, [2, 3], 17/20]], 是, 253/20, 291/400)；依完整明示資料獨立重算；within與between terms使用同一law及同一cells且兩項皆不可省略；zero-mass cell禁止conditional division且外層加權貢獻為0；不要求partition events independent。"},"difficulty":{"band":"undergraduate_core","level":2,"skills":["全變異數公式"]},"variant":{"family_id":"qf-mod41-totalvar-partition-qualification","seed":202611104011,"parameters":{"masses":[[1,20],[2,20],[17,20],[0,1]],"values":[10,11,13,109],"partition":[[0,1],[2,3]],"domain":"Finite_partition_total_variance","operation":"totalvar-partition-qualification","semantic_template":"qf-mod41-totalvar-partition-qualification/{\"masses\":[[1,20],[2,20],[17,20],[0,1]],\"partition\":[[0,1],[2,3]],\"values\":[10,11,13,109]}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_or_symbolic_model","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"候選須主端重算；不構成人工審定、sampled orbit-stabilizer、sampled MVT、reverse compactness、zero-mass division、underspecified recurrence、incomplete divisor inversion、bounded-search PDA rejection、Lean或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-20261110-r04-law-of-total-variance-0012","batch_id":"batch-20261014-advance-20261110-r04-law-of-total-variance-foundations","language":"zh-Hant","source_mko_ids":["mko-law-of-total-variance"],"title_zh":"全變異數公式","stem_zh":"同一有限law與完整disjoint partition生成的G。操作=totalvar-partition-qualification；資料={\"masses\":[[1,21],[2,21],[18,21],[0,1]],\"values\":[11,12,14,110],\"partition\":[[0,1],[2,3]]}。請依 exact_ordered_tuple_declared_by_interface 欄序回答。","answer":{"kind":"expression","value":"([[0, 1], [2, 3]], [[0, [0, 1], 1/7], [1, [2, 3], 6/7]], 是, 41/3, 44/63)","explanation_zh":"Wave6第四層核對=([[0, 1], [2, 3]], [[0, [0, 1], 1/7], [1, [2, 3], 6/7]], 是, 41/3, 44/63)；依完整明示資料獨立重算；within與between terms使用同一law及同一cells且兩項皆不可省略；zero-mass cell禁止conditional division且外層加權貢獻為0；不要求partition events independent。"},"difficulty":{"band":"undergraduate_core","level":2,"skills":["全變異數公式"]},"variant":{"family_id":"qf-mod41-totalvar-partition-qualification","seed":202611104012,"parameters":{"masses":[[1,21],[2,21],[18,21],[0,1]],"values":[11,12,14,110],"partition":[[0,1],[2,3]],"domain":"Finite_partition_total_variance","operation":"totalvar-partition-qualification","semantic_template":"qf-mod41-totalvar-partition-qualification/{\"masses\":[[1,21],[2,21],[18,21],[0,1]],\"partition\":[[0,1],[2,3]],\"values\":[11,12,14,110]}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_or_symbolic_model","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"候選須主端重算；不構成人工審定、sampled orbit-stabilizer、sampled MVT、reverse compactness、zero-mass division、underspecified recurrence、incomplete divisor inversion、bounded-search PDA rejection、Lean或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-20261110-r04-law-of-total-variance-0013","batch_id":"batch-20261014-advance-20261110-r04-law-of-total-variance-foundations","language":"zh-Hant","source_mko_ids":["mko-law-of-total-variance"],"title_zh":"全變異數公式","stem_zh":"同一有限law與完整disjoint partition生成的G。操作=totalvar-partition-qualification；資料={\"masses\":[[1,22],[2,22],[19,22],[0,1]],\"values\":[12,13,15,111],\"partition\":[[0,1],[2,3]]}。請依 exact_ordered_tuple_declared_by_interface 欄序回答。","answer":{"kind":"expression","value":"([[0, 1], [2, 3]], [[0, [0, 1], 3/22], [1, [2, 3], 19/22]], 是, 323/22, 325/484)","explanation_zh":"Wave6第四層核對=([[0, 1], [2, 3]], [[0, [0, 1], 3/22], [1, [2, 3], 19/22]], 是, 323/22, 325/484)；依完整明示資料獨立重算；within與between terms使用同一law及同一cells且兩項皆不可省略；zero-mass cell禁止conditional division且外層加權貢獻為0；不要求partition events independent。"},"difficulty":{"band":"undergraduate_core","level":2,"skills":["全變異數公式"]},"variant":{"family_id":"qf-mod41-totalvar-partition-qualification","seed":202611104013,"parameters":{"masses":[[1,22],[2,22],[19,22],[0,1]],"values":[12,13,15,111],"partition":[[0,1],[2,3]],"domain":"Finite_partition_total_variance","operation":"totalvar-partition-qualification","semantic_template":"qf-mod41-totalvar-partition-qualification/{\"masses\":[[1,22],[2,22],[19,22],[0,1]],\"partition\":[[0,1],[2,3]],\"values\":[12,13,15,111]}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_or_symbolic_model","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"候選須主端重算；不構成人工審定、sampled orbit-stabilizer、sampled MVT、reverse compactness、zero-mass division、underspecified recurrence、incomplete divisor inversion、bounded-search PDA rejection、Lean或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-20261110-r04-law-of-total-variance-0014","batch_id":"batch-20261014-advance-20261110-r04-law-of-total-variance-foundations","language":"zh-Hant","source_mko_ids":["mko-law-of-total-variance"],"title_zh":"全變異數公式","stem_zh":"同一有限law與完整disjoint partition生成的G。操作=totalvar-partition-qualification；資料={\"masses\":[[1,23],[2,23],[20,23],[0,1]],\"values\":[13,14,16,112],\"partition\":[[0,1],[2,3]]}。請依 exact_ordered_tuple_declared_by_interface 欄序回答。","answer":{"kind":"expression","value":"([[0, 1], [2, 3]], [[0, [0, 1], 3/23], [1, [2, 3], 20/23]], 是, 361/23, 342/529)","explanation_zh":"Wave6第四層核對=([[0, 1], [2, 3]], [[0, [0, 1], 3/23], [1, [2, 3], 20/23]], 是, 361/23, 342/529)；依完整明示資料獨立重算；within與between terms使用同一law及同一cells且兩項皆不可省略；zero-mass cell禁止conditional division且外層加權貢獻為0；不要求partition events independent。"},"difficulty":{"band":"undergraduate_core","level":2,"skills":["全變異數公式"]},"variant":{"family_id":"qf-mod41-totalvar-partition-qualification","seed":202611104014,"parameters":{"masses":[[1,23],[2,23],[20,23],[0,1]],"values":[13,14,16,112],"partition":[[0,1],[2,3]],"domain":"Finite_partition_total_variance","operation":"totalvar-partition-qualification","semantic_template":"qf-mod41-totalvar-partition-qualification/{\"masses\":[[1,23],[2,23],[20,23],[0,1]],\"partition\":[[0,1],[2,3]],\"values\":[13,14,16,112]}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_or_symbolic_model","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"候選須主端重算；不構成人工審定、sampled orbit-stabilizer、sampled MVT、reverse compactness、zero-mass division、underspecified recurrence、incomplete divisor inversion、bounded-search PDA rejection、Lean或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-20261110-r04-law-of-total-variance-0015","batch_id":"batch-20261014-advance-20261110-r04-law-of-total-variance-foundations","language":"zh-Hant","source_mko_ids":["mko-law-of-total-variance"],"title_zh":"全變異數公式","stem_zh":"同一有限law與完整disjoint partition生成的G。操作=totalvar-partition-qualification；資料={\"masses\":[[1,24],[2,24],[21,24],[0,1]],\"values\":[14,15,17,113],\"partition\":[[0,1],[2,3]]}。請依 exact_ordered_tuple_declared_by_interface 欄序回答。","answer":{"kind":"expression","value":"([[0, 1], [2, 3]], [[0, [0, 1], 1/8], [1, [2, 3], 7/8]], 是, 401/24, 359/576)","explanation_zh":"Wave6第四層核對=([[0, 1], [2, 3]], [[0, [0, 1], 1/8], [1, [2, 3], 7/8]], 是, 401/24, 359/576)；依完整明示資料獨立重算；within與between terms使用同一law及同一cells且兩項皆不可省略；zero-mass cell禁止conditional division且外層加權貢獻為0；不要求partition events independent。"},"difficulty":{"band":"undergraduate_core","level":2,"skills":["全變異數公式"]},"variant":{"family_id":"qf-mod41-totalvar-partition-qualification","seed":202611104015,"parameters":{"masses":[[1,24],[2,24],[21,24],[0,1]],"values":[14,15,17,113],"partition":[[0,1],[2,3]],"domain":"Finite_partition_total_variance","operation":"totalvar-partition-qualification","semantic_template":"qf-mod41-totalvar-partition-qualification/{\"masses\":[[1,24],[2,24],[21,24],[0,1]],\"partition\":[[0,1],[2,3]],\"values\":[14,15,17,113]}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_or_symbolic_model","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"候選須主端重算；不構成人工審定、sampled orbit-stabilizer、sampled MVT、reverse compactness、zero-mass division、underspecified recurrence、incomplete divisor inversion、bounded-search PDA rejection、Lean或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-20261110-r04-law-of-total-variance-0016","batch_id":"batch-20261014-advance-20261110-r04-law-of-total-variance-foundations","language":"zh-Hant","source_mko_ids":["mko-law-of-total-variance"],"title_zh":"全變異數公式","stem_zh":"同一有限law與完整disjoint partition生成的G。操作=totalvar-partition-qualification；資料={\"masses\":[[1,25],[2,25],[22,25],[0,1]],\"values\":[15,16,18,114],\"partition\":[[0,1],[2,3]]}。請依 exact_ordered_tuple_declared_by_interface 欄序回答。","answer":{"kind":"expression","value":"([[0, 1], [2, 3]], [[0, [0, 1], 3/25], [1, [2, 3], 22/25]], 是, 443/25, 376/625)","explanation_zh":"Wave6第四層核對=([[0, 1], [2, 3]], [[0, [0, 1], 3/25], [1, [2, 3], 22/25]], 是, 443/25, 376/625)；依完整明示資料獨立重算；within與between terms使用同一law及同一cells且兩項皆不可省略；zero-mass cell禁止conditional division且外層加權貢獻為0；不要求partition events independent。"},"difficulty":{"band":"undergraduate_core","level":2,"skills":["全變異數公式"]},"variant":{"family_id":"qf-mod41-totalvar-partition-qualification","seed":202611104016,"parameters":{"masses":[[1,25],[2,25],[22,25],[0,1]],"values":[15,16,18,114],"partition":[[0,1],[2,3]],"domain":"Finite_partition_total_variance","operation":"totalvar-partition-qualification","semantic_template":"qf-mod41-totalvar-partition-qualification/{\"masses\":[[1,25],[2,25],[22,25],[0,1]],\"partition\":[[0,1],[2,3]],\"values\":[15,16,18,114]}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_or_symbolic_model","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"候選須主端重算；不構成人工審定、sampled orbit-stabilizer、sampled MVT、reverse compactness、zero-mass division、underspecified recurrence、incomplete divisor inversion、bounded-search PDA rejection、Lean或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-20261110-r04-law-of-total-variance-0017","batch_id":"batch-20261014-advance-20261110-r04-law-of-total-variance-foundations","language":"zh-Hant","source_mko_ids":["mko-law-of-total-variance"],"title_zh":"全變異數公式","stem_zh":"同一有限law與完整disjoint partition生成的G。操作=totalvar-partition-qualification；資料={\"masses\":[[1,26],[2,26],[23,26],[0,1]],\"values\":[16,17,19,115],\"partition\":[[0,1],[2,3]]}。請依 exact_ordered_tuple_declared_by_interface 欄序回答。","answer":{"kind":"expression","value":"([[0, 1], [2, 3]], [[0, [0, 1], 3/26], [1, [2, 3], 23/26]], 是, 487/26, 393/676)","explanation_zh":"Wave6第四層核對=([[0, 1], [2, 3]], [[0, [0, 1], 3/26], [1, [2, 3], 23/26]], 是, 487/26, 393/676)；依完整明示資料獨立重算；within與between terms使用同一law及同一cells且兩項皆不可省略；zero-mass cell禁止conditional division且外層加權貢獻為0；不要求partition events independent。"},"difficulty":{"band":"undergraduate_core","level":2,"skills":["全變異數公式"]},"variant":{"family_id":"qf-mod41-totalvar-partition-qualification","seed":202611104017,"parameters":{"masses":[[1,26],[2,26],[23,26],[0,1]],"values":[16,17,19,115],"partition":[[0,1],[2,3]],"domain":"Finite_partition_total_variance","operation":"totalvar-partition-qualification","semantic_template":"qf-mod41-totalvar-partition-qualification/{\"masses\":[[1,26],[2,26],[23,26],[0,1]],\"partition\":[[0,1],[2,3]],\"values\":[16,17,19,115]}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_or_symbolic_model","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"候選須主端重算；不構成人工審定、sampled orbit-stabilizer、sampled MVT、reverse compactness、zero-mass division、underspecified recurrence、incomplete divisor inversion、bounded-search PDA rejection、Lean或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-20261110-r04-law-of-total-variance-0018","batch_id":"batch-20261014-advance-20261110-r04-law-of-total-variance-foundations","language":"zh-Hant","source_mko_ids":["mko-law-of-total-variance"],"title_zh":"全變異數公式","stem_zh":"同一有限law與完整disjoint partition生成的G。操作=totalvar-partition-qualification；資料={\"masses\":[[1,27],[2,27],[24,27],[0,1]],\"values\":[17,18,20,116],\"partition\":[[0,1],[2,3]]}。請依 exact_ordered_tuple_declared_by_interface 欄序回答。","answer":{"kind":"expression","value":"([[0, 1], [2, 3]], [[0, [0, 1], 1/9], [1, [2, 3], 8/9]], 是, 533/27, 410/729)","explanation_zh":"Wave6第四層核對=([[0, 1], [2, 3]], [[0, [0, 1], 1/9], [1, [2, 3], 8/9]], 是, 533/27, 410/729)；依完整明示資料獨立重算；within與between terms使用同一law及同一cells且兩項皆不可省略；zero-mass cell禁止conditional division且外層加權貢獻為0；不要求partition events independent。"},"difficulty":{"band":"undergraduate_core","level":3,"skills":["全變異數公式"]},"variant":{"family_id":"qf-mod41-totalvar-partition-qualification","seed":202611104018,"parameters":{"masses":[[1,27],[2,27],[24,27],[0,1]],"values":[17,18,20,116],"partition":[[0,1],[2,3]],"domain":"Finite_partition_total_variance","operation":"totalvar-partition-qualification","semantic_template":"qf-mod41-totalvar-partition-qualification/{\"masses\":[[1,27],[2,27],[24,27],[0,1]],\"partition\":[[0,1],[2,3]],\"values\":[17,18,20,116]}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_or_symbolic_model","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"候選須主端重算；不構成人工審定、sampled orbit-stabilizer、sampled MVT、reverse compactness、zero-mass division、underspecified recurrence、incomplete divisor inversion、bounded-search PDA rejection、Lean或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-20261110-r04-law-of-total-variance-0019","batch_id":"batch-20261014-advance-20261110-r04-law-of-total-variance-foundations","language":"zh-Hant","source_mko_ids":["mko-law-of-total-variance"],"title_zh":"全變異數公式","stem_zh":"同一有限law與完整disjoint partition生成的G。操作=totalvar-partition-qualification；資料={\"masses\":[[1,28],[2,28],[25,28],[0,1]],\"values\":[18,19,21,117],\"partition\":[[0,1],[2,3]]}。請依 exact_ordered_tuple_declared_by_interface 欄序回答。","answer":{"kind":"expression","value":"([[0, 1], [2, 3]], [[0, [0, 1], 3/28], [1, [2, 3], 25/28]], 是, 83/4, 61/112)","explanation_zh":"Wave6第四層核對=([[0, 1], [2, 3]], [[0, [0, 1], 3/28], [1, [2, 3], 25/28]], 是, 83/4, 61/112)；依完整明示資料獨立重算；within與between terms使用同一law及同一cells且兩項皆不可省略；zero-mass cell禁止conditional division且外層加權貢獻為0；不要求partition events independent。"},"difficulty":{"band":"undergraduate_core","level":3,"skills":["全變異數公式"]},"variant":{"family_id":"qf-mod41-totalvar-partition-qualification","seed":202611104019,"parameters":{"masses":[[1,28],[2,28],[25,28],[0,1]],"values":[18,19,21,117],"partition":[[0,1],[2,3]],"domain":"Finite_partition_total_variance","operation":"totalvar-partition-qualification","semantic_template":"qf-mod41-totalvar-partition-qualification/{\"masses\":[[1,28],[2,28],[25,28],[0,1]],\"partition\":[[0,1],[2,3]],\"values\":[18,19,21,117]}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_or_symbolic_model","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"候選須主端重算；不構成人工審定、sampled orbit-stabilizer、sampled MVT、reverse compactness、zero-mass division、underspecified recurrence、incomplete divisor inversion、bounded-search PDA rejection、Lean或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-20261110-r04-law-of-total-variance-0020","batch_id":"batch-20261014-advance-20261110-r04-law-of-total-variance-foundations","language":"zh-Hant","source_mko_ids":["mko-law-of-total-variance"],"title_zh":"全變異數公式","stem_zh":"同一有限law與完整disjoint partition生成的G。操作=totalvar-partition-qualification；資料={\"masses\":[[1,29],[2,29],[26,29],[0,1]],\"values\":[19,20,22,118],\"partition\":[[0,1],[2,3]]}。請依 exact_ordered_tuple_declared_by_interface 欄序回答。","answer":{"kind":"expression","value":"([[0, 1], [2, 3]], [[0, [0, 1], 3/29], [1, [2, 3], 26/29]], 是, 631/29, 444/841)","explanation_zh":"Wave6第四層核對=([[0, 1], [2, 3]], [[0, [0, 1], 3/29], [1, [2, 3], 26/29]], 是, 631/29, 444/841)；依完整明示資料獨立重算；within與between terms使用同一law及同一cells且兩項皆不可省略；zero-mass cell禁止conditional division且外層加權貢獻為0；不要求partition events independent。"},"difficulty":{"band":"undergraduate_core","level":3,"skills":["全變異數公式"]},"variant":{"family_id":"qf-mod41-totalvar-partition-qualification","seed":202611104020,"parameters":{"masses":[[1,29],[2,29],[26,29],[0,1]],"values":[19,20,22,118],"partition":[[0,1],[2,3]],"domain":"Finite_partition_total_variance","operation":"totalvar-partition-qualification","semantic_template":"qf-mod41-totalvar-partition-qualification/{\"masses\":[[1,29],[2,29],[26,29],[0,1]],\"partition\":[[0,1],[2,3]],\"values\":[19,20,22,118]}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_or_symbolic_model","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"候選須主端重算；不構成人工審定、sampled orbit-stabilizer、sampled MVT、reverse compactness、zero-mass division、underspecified recurrence、incomplete divisor inversion、bounded-search PDA rejection、Lean或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-20261110-r04-law-of-total-variance-0021","batch_id":"batch-20261014-advance-20261110-r04-law-of-total-variance-foundations","language":"zh-Hant","source_mko_ids":["mko-law-of-total-variance"],"title_zh":"全變異數公式","stem_zh":"同一有限law與完整disjoint partition生成的G。操作=totalvar-partition-qualification；資料={\"masses\":[[1,30],[2,30],[27,30],[0,1]],\"values\":[20,21,23,119],\"partition\":[[0,1],[2,3]]}。請依 exact_ordered_tuple_declared_by_interface 欄序回答。","answer":{"kind":"expression","value":"([[0, 1], [2, 3]], [[0, [0, 1], 1/10], [1, [2, 3], 9/10]], 是, 683/30, 461/900)","explanation_zh":"Wave6第四層核對=([[0, 1], [2, 3]], [[0, [0, 1], 1/10], [1, [2, 3], 9/10]], 是, 683/30, 461/900)；依完整明示資料獨立重算；within與between terms使用同一law及同一cells且兩項皆不可省略；zero-mass cell禁止conditional division且外層加權貢獻為0；不要求partition events independent。"},"difficulty":{"band":"undergraduate_core","level":3,"skills":["全變異數公式"]},"variant":{"family_id":"qf-mod41-totalvar-partition-qualification","seed":202611104021,"parameters":{"masses":[[1,30],[2,30],[27,30],[0,1]],"values":[20,21,23,119],"partition":[[0,1],[2,3]],"domain":"Finite_partition_total_variance","operation":"totalvar-partition-qualification","semantic_template":"qf-mod41-totalvar-partition-qualification/{\"masses\":[[1,30],[2,30],[27,30],[0,1]],\"partition\":[[0,1],[2,3]],\"values\":[20,21,23,119]}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_or_symbolic_model","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"候選須主端重算；不構成人工審定、sampled orbit-stabilizer、sampled MVT、reverse compactness、zero-mass division、underspecified recurrence、incomplete divisor inversion、bounded-search PDA rejection、Lean或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-20261110-r04-law-of-total-variance-0022","batch_id":"batch-20261014-advance-20261110-r04-law-of-total-variance-foundations","language":"zh-Hant","source_mko_ids":["mko-law-of-total-variance"],"title_zh":"全變異數公式","stem_zh":"同一有限law與完整disjoint partition生成的G。操作=totalvar-partition-qualification；資料={\"masses\":[[1,31],[2,31],[28,31],[0,1]],\"values\":[21,22,24,120],\"partition\":[[0,1],[2,3]]}。請依 exact_ordered_tuple_declared_by_interface 欄序回答。","answer":{"kind":"expression","value":"([[0, 1], [2, 3]], [[0, [0, 1], 3/31], [1, [2, 3], 28/31]], 是, 737/31, 478/961)","explanation_zh":"Wave6第四層核對=([[0, 1], [2, 3]], [[0, [0, 1], 3/31], [1, [2, 3], 28/31]], 是, 737/31, 478/961)；依完整明示資料獨立重算；within與between terms使用同一law及同一cells且兩項皆不可省略；zero-mass cell禁止conditional division且外層加權貢獻為0；不要求partition events independent。"},"difficulty":{"band":"undergraduate_core","level":3,"skills":["全變異數公式"]},"variant":{"family_id":"qf-mod41-totalvar-partition-qualification","seed":202611104022,"parameters":{"masses":[[1,31],[2,31],[28,31],[0,1]],"values":[21,22,24,120],"partition":[[0,1],[2,3]],"domain":"Finite_partition_total_variance","operation":"totalvar-partition-qualification","semantic_template":"qf-mod41-totalvar-partition-qualification/{\"masses\":[[1,31],[2,31],[28,31],[0,1]],\"partition\":[[0,1],[2,3]],\"values\":[21,22,24,120]}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_or_symbolic_model","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"候選須主端重算；不構成人工審定、sampled orbit-stabilizer、sampled MVT、reverse compactness、zero-mass division、underspecified recurrence、incomplete divisor inversion、bounded-search PDA rejection、Lean或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-20261110-r04-law-of-total-variance-0023","batch_id":"batch-20261014-advance-20261110-r04-law-of-total-variance-foundations","language":"zh-Hant","source_mko_ids":["mko-law-of-total-variance"],"title_zh":"全變異數公式","stem_zh":"同一有限law與完整disjoint partition生成的G。操作=totalvar-partition-qualification；資料={\"masses\":[[1,32],[2,32],[29,32],[0,1]],\"values\":[22,23,25,121],\"partition\":[[0,1],[2,3]]}。請依 exact_ordered_tuple_declared_by_interface 欄序回答。","answer":{"kind":"expression","value":"([[0, 1], [2, 3]], [[0, [0, 1], 3/32], [1, [2, 3], 29/32]], 是, 793/32, 495/1024)","explanation_zh":"Wave6第四層核對=([[0, 1], [2, 3]], [[0, [0, 1], 3/32], [1, [2, 3], 29/32]], 是, 793/32, 495/1024)；依完整明示資料獨立重算；within與between terms使用同一law及同一cells且兩項皆不可省略；zero-mass cell禁止conditional division且外層加權貢獻為0；不要求partition events independent。"},"difficulty":{"band":"undergraduate_core","level":3,"skills":["全變異數公式"]},"variant":{"family_id":"qf-mod41-totalvar-partition-qualification","seed":202611104023,"parameters":{"masses":[[1,32],[2,32],[29,32],[0,1]],"values":[22,23,25,121],"partition":[[0,1],[2,3]],"domain":"Finite_partition_total_variance","operation":"totalvar-partition-qualification","semantic_template":"qf-mod41-totalvar-partition-qualification/{\"masses\":[[1,32],[2,32],[29,32],[0,1]],\"partition\":[[0,1],[2,3]],\"values\":[22,23,25,121]}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_or_symbolic_model","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"候選須主端重算；不構成人工審定、sampled orbit-stabilizer、sampled MVT、reverse compactness、zero-mass division、underspecified recurrence、incomplete divisor inversion、bounded-search PDA rejection、Lean或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-20261110-r04-law-of-total-variance-0024","batch_id":"batch-20261014-advance-20261110-r04-law-of-total-variance-foundations","language":"zh-Hant","source_mko_ids":["mko-law-of-total-variance"],"title_zh":"全變異數公式","stem_zh":"同一有限law與完整disjoint partition生成的G。操作=totalvar-partition-qualification；資料={\"masses\":[[1,33],[2,33],[30,33],[0,1]],\"values\":[23,24,26,122],\"partition\":[[0,1],[2,3]]}。請依 exact_ordered_tuple_declared_by_interface 欄序回答。","answer":{"kind":"expression","value":"([[0, 1], [2, 3]], [[0, [0, 1], 1/11], [1, [2, 3], 10/11]], 是, 851/33, 512/1089)","explanation_zh":"Wave6第四層核對=([[0, 1], [2, 3]], [[0, [0, 1], 1/11], [1, [2, 3], 10/11]], 是, 851/33, 512/1089)；依完整明示資料獨立重算；within與between terms使用同一law及同一cells且兩項皆不可省略；zero-mass cell禁止conditional division且外層加權貢獻為0；不要求partition events independent。"},"difficulty":{"band":"undergraduate_core","level":3,"skills":["全變異數公式"]},"variant":{"family_id":"qf-mod41-totalvar-partition-qualification","seed":202611104024,"parameters":{"masses":[[1,33],[2,33],[30,33],[0,1]],"values":[23,24,26,122],"partition":[[0,1],[2,3]],"domain":"Finite_partition_total_variance","operation":"totalvar-partition-qualification","semantic_template":"qf-mod41-totalvar-partition-qualification/{\"masses\":[[1,33],[2,33],[30,33],[0,1]],\"partition\":[[0,1],[2,3]],\"values\":[23,24,26,122]}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_or_symbolic_model","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"候選須主端重算；不構成人工審定、sampled orbit-stabilizer、sampled MVT、reverse compactness、zero-mass division、underspecified recurrence、incomplete divisor inversion、bounded-search PDA rejection、Lean或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-20261110-r04-law-of-total-variance-0025","batch_id":"batch-20261014-advance-20261110-r04-law-of-total-variance-foundations","language":"zh-Hant","source_mko_ids":["mko-law-of-total-variance"],"title_zh":"全變異數公式","stem_zh":"同一有限law與完整disjoint partition生成的G。操作=totalvar-partition-qualification；資料={\"masses\":[[1,34],[2,34],[31,34],[0,1]],\"values\":[24,25,27,123],\"partition\":[[0,1],[2,3]]}。請依 exact_ordered_tuple_declared_by_interface 欄序回答。","answer":{"kind":"expression","value":"([[0, 1], [2, 3]], [[0, [0, 1], 3/34], [1, [2, 3], 31/34]], 是, 911/34, 529/1156)","explanation_zh":"Wave6第四層核對=([[0, 1], [2, 3]], [[0, [0, 1], 3/34], [1, [2, 3], 31/34]], 是, 911/34, 529/1156)；依完整明示資料獨立重算；within與between terms使用同一law及同一cells且兩項皆不可省略；zero-mass cell禁止conditional division且外層加權貢獻為0；不要求partition events independent。"},"difficulty":{"band":"undergraduate_core","level":3,"skills":["全變異數公式"]},"variant":{"family_id":"qf-mod41-totalvar-partition-qualification","seed":202611104025,"parameters":{"masses":[[1,34],[2,34],[31,34],[0,1]],"values":[24,25,27,123],"partition":[[0,1],[2,3]],"domain":"Finite_partition_total_variance","operation":"totalvar-partition-qualification","semantic_template":"qf-mod41-totalvar-partition-qualification/{\"masses\":[[1,34],[2,34],[31,34],[0,1]],\"partition\":[[0,1],[2,3]],\"values\":[24,25,27,123]}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_or_symbolic_model","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"候選須主端重算；不構成人工審定、sampled orbit-stabilizer、sampled MVT、reverse compactness、zero-mass division、underspecified recurrence、incomplete divisor inversion、bounded-search PDA rejection、Lean或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-20261110-r04-law-of-total-variance-0026","batch_id":"batch-20261014-advance-20261110-r04-law-of-total-variance-foundations","language":"zh-Hant","source_mko_ids":["mko-law-of-total-variance"],"title_zh":"全變異數公式","stem_zh":"同一有限law與完整disjoint partition生成的G。操作=totalvar-within-between-components；資料={\"masses\":[[1,10],[2,10],[7,10],[0,1]],\"values\":[0,1,3,99],\"partition\":[[0,1],[2,3]]}。請依 exact_ordered_tuple_declared_by_interface 欄序回答。","answer":{"kind":"expression","value":"([[0, [0, 1], 3/10, 2/3, 2/9], [1, [2, 3], 7/10, 3, 0]], 1/15, 343/300, same_law_same_partition_within_and_between_terms)","explanation_zh":"Wave6第四層核對=([[0, [0, 1], 3/10, 2/3, 2/9], [1, [2, 3], 7/10, 3, 0]], 1/15, 343/300, same_law_same_partition_within_and_between_terms)；依完整明示資料獨立重算；within與between terms使用同一law及同一cells且兩項皆不可省略；zero-mass cell禁止conditional division且外層加權貢獻為0；不要求partition events independent。"},"difficulty":{"band":"undergraduate_core","level":1,"skills":["全變異數公式"]},"variant":{"family_id":"qf-mod41-totalvar-within-between-components","seed":202611104026,"parameters":{"masses":[[1,10],[2,10],[7,10],[0,1]],"values":[0,1,3,99],"partition":[[0,1],[2,3]],"domain":"Finite_partition_total_variance","operation":"totalvar-within-between-components","semantic_template":"qf-mod41-totalvar-within-between-components/{\"masses\":[[1,10],[2,10],[7,10],[0,1]],\"partition\":[[0,1],[2,3]],\"values\":[0,1,3,99]}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_or_symbolic_model","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"候選須主端重算；不構成人工審定、sampled orbit-stabilizer、sampled MVT、reverse compactness、zero-mass division、underspecified recurrence、incomplete divisor inversion、bounded-search PDA rejection、Lean或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-20261110-r04-law-of-total-variance-0027","batch_id":"batch-20261014-advance-20261110-r04-law-of-total-variance-foundations","language":"zh-Hant","source_mko_ids":["mko-law-of-total-variance"],"title_zh":"全變異數公式","stem_zh":"同一有限law與完整disjoint partition生成的G。操作=totalvar-within-between-components；資料={\"masses\":[[1,11],[2,11],[8,11],[0,1]],\"values\":[1,2,4,100],\"partition\":[[0,1],[2,3]]}。請依 exact_ordered_tuple_declared_by_interface 欄序回答。","answer":{"kind":"expression","value":"([[0, [0, 1], 3/11, 5/3, 2/9], [1, [2, 3], 8/11, 4, 0]], 2/33, 392/363, same_law_same_partition_within_and_between_terms)","explanation_zh":"Wave6第四層核對=([[0, [0, 1], 3/11, 5/3, 2/9], [1, [2, 3], 8/11, 4, 0]], 2/33, 392/363, same_law_same_partition_within_and_between_terms)；依完整明示資料獨立重算；within與between terms使用同一law及同一cells且兩項皆不可省略；zero-mass cell禁止conditional division且外層加權貢獻為0；不要求partition events independent。"},"difficulty":{"band":"undergraduate_core","level":1,"skills":["全變異數公式"]},"variant":{"family_id":"qf-mod41-totalvar-within-between-components","seed":202611104027,"parameters":{"masses":[[1,11],[2,11],[8,11],[0,1]],"values":[1,2,4,100],"partition":[[0,1],[2,3]],"domain":"Finite_partition_total_variance","operation":"totalvar-within-between-components","semantic_template":"qf-mod41-totalvar-within-between-components/{\"masses\":[[1,11],[2,11],[8,11],[0,1]],\"partition\":[[0,1],[2,3]],\"values\":[1,2,4,100]}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_or_symbolic_model","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"候選須主端重算；不構成人工審定、sampled orbit-stabilizer、sampled MVT、reverse compactness、zero-mass division、underspecified recurrence、incomplete divisor inversion、bounded-search PDA rejection、Lean或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-20261110-r04-law-of-total-variance-0028","batch_id":"batch-20261014-advance-20261110-r04-law-of-total-variance-foundations","language":"zh-Hant","source_mko_ids":["mko-law-of-total-variance"],"title_zh":"全變異數公式","stem_zh":"同一有限law與完整disjoint partition生成的G。操作=totalvar-within-between-components；資料={\"masses\":[[1,12],[2,12],[9,12],[0,1]],\"values\":[2,3,5,101],\"partition\":[[0,1],[2,3]]}。請依 exact_ordered_tuple_declared_by_interface 欄序回答。","answer":{"kind":"expression","value":"([[0, [0, 1], 1/4, 8/3, 2/9], [1, [2, 3], 3/4, 5, 0]], 1/18, 49/48, same_law_same_partition_within_and_between_terms)","explanation_zh":"Wave6第四層核對=([[0, [0, 1], 1/4, 8/3, 2/9], [1, [2, 3], 3/4, 5, 0]], 1/18, 49/48, same_law_same_partition_within_and_between_terms)；依完整明示資料獨立重算；within與between terms使用同一law及同一cells且兩項皆不可省略；zero-mass cell禁止conditional division且外層加權貢獻為0；不要求partition events independent。"},"difficulty":{"band":"undergraduate_core","level":1,"skills":["全變異數公式"]},"variant":{"family_id":"qf-mod41-totalvar-within-between-components","seed":202611104028,"parameters":{"masses":[[1,12],[2,12],[9,12],[0,1]],"values":[2,3,5,101],"partition":[[0,1],[2,3]],"domain":"Finite_partition_total_variance","operation":"totalvar-within-between-components","semantic_template":"qf-mod41-totalvar-within-between-components/{\"masses\":[[1,12],[2,12],[9,12],[0,1]],\"partition\":[[0,1],[2,3]],\"values\":[2,3,5,101]}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_or_symbolic_model","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"候選須主端重算；不構成人工審定、sampled orbit-stabilizer、sampled MVT、reverse compactness、zero-mass division、underspecified recurrence、incomplete divisor inversion、bounded-search PDA rejection、Lean或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-20261110-r04-law-of-total-variance-0029","batch_id":"batch-20261014-advance-20261110-r04-law-of-total-variance-foundations","language":"zh-Hant","source_mko_ids":["mko-law-of-total-variance"],"title_zh":"全變異數公式","stem_zh":"同一有限law與完整disjoint partition生成的G。操作=totalvar-within-between-components；資料={\"masses\":[[1,13],[2,13],[10,13],[0,1]],\"values\":[3,4,6,102],\"partition\":[[0,1],[2,3]]}。請依 exact_ordered_tuple_declared_by_interface 欄序回答。","answer":{"kind":"expression","value":"([[0, [0, 1], 3/13, 11/3, 2/9], [1, [2, 3], 10/13, 6, 0]], 2/39, 490/507, same_law_same_partition_within_and_between_terms)","explanation_zh":"Wave6第四層核對=([[0, [0, 1], 3/13, 11/3, 2/9], [1, [2, 3], 10/13, 6, 0]], 2/39, 490/507, same_law_same_partition_within_and_between_terms)；依完整明示資料獨立重算；within與between terms使用同一law及同一cells且兩項皆不可省略；zero-mass cell禁止conditional division且外層加權貢獻為0；不要求partition events independent。"},"difficulty":{"band":"undergraduate_core","level":1,"skills":["全變異數公式"]},"variant":{"family_id":"qf-mod41-totalvar-within-between-components","seed":202611104029,"parameters":{"masses":[[1,13],[2,13],[10,13],[0,1]],"values":[3,4,6,102],"partition":[[0,1],[2,3]],"domain":"Finite_partition_total_variance","operation":"totalvar-within-between-components","semantic_template":"qf-mod41-totalvar-within-between-components/{\"masses\":[[1,13],[2,13],[10,13],[0,1]],\"partition\":[[0,1],[2,3]],\"values\":[3,4,6,102]}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_or_symbolic_model","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"候選須主端重算；不構成人工審定、sampled orbit-stabilizer、sampled MVT、reverse compactness、zero-mass division、underspecified recurrence、incomplete divisor inversion、bounded-search PDA rejection、Lean或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-20261110-r04-law-of-total-variance-0030","batch_id":"batch-20261014-advance-20261110-r04-law-of-total-variance-foundations","language":"zh-Hant","source_mko_ids":["mko-law-of-total-variance"],"title_zh":"全變異數公式","stem_zh":"同一有限law與完整disjoint partition生成的G。操作=totalvar-within-between-components；資料={\"masses\":[[1,14],[2,14],[11,14],[0,1]],\"values\":[4,5,7,103],\"partition\":[[0,1],[2,3]]}。請依 exact_ordered_tuple_declared_by_interface 欄序回答。","answer":{"kind":"expression","value":"([[0, [0, 1], 3/14, 14/3, 2/9], [1, [2, 3], 11/14, 7, 0]], 1/21, 11/12, same_law_same_partition_within_and_between_terms)","explanation_zh":"Wave6第四層核對=([[0, [0, 1], 3/14, 14/3, 2/9], [1, [2, 3], 11/14, 7, 0]], 1/21, 11/12, same_law_same_partition_within_and_between_terms)；依完整明示資料獨立重算；within與between terms使用同一law及同一cells且兩項皆不可省略；zero-mass cell禁止conditional division且外層加權貢獻為0；不要求partition events independent。"},"difficulty":{"band":"undergraduate_core","level":1,"skills":["全變異數公式"]},"variant":{"family_id":"qf-mod41-totalvar-within-between-components","seed":202611104030,"parameters":{"masses":[[1,14],[2,14],[11,14],[0,1]],"values":[4,5,7,103],"partition":[[0,1],[2,3]],"domain":"Finite_partition_total_variance","operation":"totalvar-within-between-components","semantic_template":"qf-mod41-totalvar-within-between-components/{\"masses\":[[1,14],[2,14],[11,14],[0,1]],\"partition\":[[0,1],[2,3]],\"values\":[4,5,7,103]}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_or_symbolic_model","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"候選須主端重算；不構成人工審定、sampled orbit-stabilizer、sampled MVT、reverse compactness、zero-mass division、underspecified recurrence、incomplete divisor inversion、bounded-search PDA rejection、Lean或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-20261110-r04-law-of-total-variance-0031","batch_id":"batch-20261014-advance-20261110-r04-law-of-total-variance-foundations","language":"zh-Hant","source_mko_ids":["mko-law-of-total-variance"],"title_zh":"全變異數公式","stem_zh":"同一有限law與完整disjoint partition生成的G。操作=totalvar-within-between-components；資料={\"masses\":[[1,15],[2,15],[12,15],[0,1]],\"values\":[5,6,8,104],\"partition\":[[0,1],[2,3]]}。請依 exact_ordered_tuple_declared_by_interface 欄序回答。","answer":{"kind":"expression","value":"([[0, [0, 1], 1/5, 17/3, 2/9], [1, [2, 3], 4/5, 8, 0]], 2/45, 196/225, same_law_same_partition_within_and_between_terms)","explanation_zh":"Wave6第四層核對=([[0, [0, 1], 1/5, 17/3, 2/9], [1, [2, 3], 4/5, 8, 0]], 2/45, 196/225, same_law_same_partition_within_and_between_terms)；依完整明示資料獨立重算；within與between terms使用同一law及同一cells且兩項皆不可省略；zero-mass cell禁止conditional division且外層加權貢獻為0；不要求partition events independent。"},"difficulty":{"band":"undergraduate_core","level":1,"skills":["全變異數公式"]},"variant":{"family_id":"qf-mod41-totalvar-within-between-components","seed":202611104031,"parameters":{"masses":[[1,15],[2,15],[12,15],[0,1]],"values":[5,6,8,104],"partition":[[0,1],[2,3]],"domain":"Finite_partition_total_variance","operation":"totalvar-within-between-components","semantic_template":"qf-mod41-totalvar-within-between-components/{\"masses\":[[1,15],[2,15],[12,15],[0,1]],\"partition\":[[0,1],[2,3]],\"values\":[5,6,8,104]}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_or_symbolic_model","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"候選須主端重算；不構成人工審定、sampled orbit-stabilizer、sampled MVT、reverse compactness、zero-mass division、underspecified recurrence、incomplete divisor inversion、bounded-search PDA rejection、Lean或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-20261110-r04-law-of-total-variance-0032","batch_id":"batch-20261014-advance-20261110-r04-law-of-total-variance-foundations","language":"zh-Hant","source_mko_ids":["mko-law-of-total-variance"],"title_zh":"全變異數公式","stem_zh":"同一有限law與完整disjoint partition生成的G。操作=totalvar-within-between-components；資料={\"masses\":[[1,16],[2,16],[13,16],[0,1]],\"values\":[6,7,9,105],\"partition\":[[0,1],[2,3]]}。請依 exact_ordered_tuple_declared_by_interface 欄序回答。","answer":{"kind":"expression","value":"([[0, [0, 1], 3/16, 20/3, 2/9], [1, [2, 3], 13/16, 9, 0]], 1/24, 637/768, same_law_same_partition_within_and_between_terms)","explanation_zh":"Wave6第四層核對=([[0, [0, 1], 3/16, 20/3, 2/9], [1, [2, 3], 13/16, 9, 0]], 1/24, 637/768, same_law_same_partition_within_and_between_terms)；依完整明示資料獨立重算；within與between terms使用同一law及同一cells且兩項皆不可省略；zero-mass cell禁止conditional division且外層加權貢獻為0；不要求partition events independent。"},"difficulty":{"band":"undergraduate_core","level":1,"skills":["全變異數公式"]},"variant":{"family_id":"qf-mod41-totalvar-within-between-components","seed":202611104032,"parameters":{"masses":[[1,16],[2,16],[13,16],[0,1]],"values":[6,7,9,105],"partition":[[0,1],[2,3]],"domain":"Finite_partition_total_variance","operation":"totalvar-within-between-components","semantic_template":"qf-mod41-totalvar-within-between-components/{\"masses\":[[1,16],[2,16],[13,16],[0,1]],\"partition\":[[0,1],[2,3]],\"values\":[6,7,9,105]}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_or_symbolic_model","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"候選須主端重算；不構成人工審定、sampled orbit-stabilizer、sampled MVT、reverse compactness、zero-mass division、underspecified recurrence、incomplete divisor inversion、bounded-search PDA rejection、Lean或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-20261110-r04-law-of-total-variance-0033","batch_id":"batch-20261014-advance-20261110-r04-law-of-total-variance-foundations","language":"zh-Hant","source_mko_ids":["mko-law-of-total-variance"],"title_zh":"全變異數公式","stem_zh":"同一有限law與完整disjoint partition生成的G。操作=totalvar-within-between-components；資料={\"masses\":[[1,17],[2,17],[14,17],[0,1]],\"values\":[7,8,10,106],\"partition\":[[0,1],[2,3]]}。請依 exact_ordered_tuple_declared_by_interface 欄序回答。","answer":{"kind":"expression","value":"([[0, [0, 1], 3/17, 23/3, 2/9], [1, [2, 3], 14/17, 10, 0]], 2/51, 686/867, same_law_same_partition_within_and_between_terms)","explanation_zh":"Wave6第四層核對=([[0, [0, 1], 3/17, 23/3, 2/9], [1, [2, 3], 14/17, 10, 0]], 2/51, 686/867, same_law_same_partition_within_and_between_terms)；依完整明示資料獨立重算；within與between terms使用同一law及同一cells且兩項皆不可省略；zero-mass cell禁止conditional division且外層加權貢獻為0；不要求partition events independent。"},"difficulty":{"band":"undergraduate_core","level":1,"skills":["全變異數公式"]},"variant":{"family_id":"qf-mod41-totalvar-within-between-components","seed":202611104033,"parameters":{"masses":[[1,17],[2,17],[14,17],[0,1]],"values":[7,8,10,106],"partition":[[0,1],[2,3]],"domain":"Finite_partition_total_variance","operation":"totalvar-within-between-components","semantic_template":"qf-mod41-totalvar-within-between-components/{\"masses\":[[1,17],[2,17],[14,17],[0,1]],\"partition\":[[0,1],[2,3]],\"values\":[7,8,10,106]}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_or_symbolic_model","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"候選須主端重算；不構成人工審定、sampled orbit-stabilizer、sampled MVT、reverse compactness、zero-mass division、underspecified recurrence、incomplete divisor inversion、bounded-search PDA rejection、Lean或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-20261110-r04-law-of-total-variance-0034","batch_id":"batch-20261014-advance-20261110-r04-law-of-total-variance-foundations","language":"zh-Hant","source_mko_ids":["mko-law-of-total-variance"],"title_zh":"全變異數公式","stem_zh":"同一有限law與完整disjoint partition生成的G。操作=totalvar-within-between-components；資料={\"masses\":[[1,18],[2,18],[15,18],[0,1]],\"values\":[8,9,11,107],\"partition\":[[0,1],[2,3]]}。請依 exact_ordered_tuple_declared_by_interface 欄序回答。","answer":{"kind":"expression","value":"([[0, [0, 1], 1/6, 26/3, 2/9], [1, [2, 3], 5/6, 11, 0]], 1/27, 245/324, same_law_same_partition_within_and_between_terms)","explanation_zh":"Wave6第四層核對=([[0, [0, 1], 1/6, 26/3, 2/9], [1, [2, 3], 5/6, 11, 0]], 1/27, 245/324, same_law_same_partition_within_and_between_terms)；依完整明示資料獨立重算；within與between terms使用同一law及同一cells且兩項皆不可省略；zero-mass cell禁止conditional division且外層加權貢獻為0；不要求partition events independent。"},"difficulty":{"band":"undergraduate_core","level":2,"skills":["全變異數公式"]},"variant":{"family_id":"qf-mod41-totalvar-within-between-components","seed":202611104034,"parameters":{"masses":[[1,18],[2,18],[15,18],[0,1]],"values":[8,9,11,107],"partition":[[0,1],[2,3]],"domain":"Finite_partition_total_variance","operation":"totalvar-within-between-components","semantic_template":"qf-mod41-totalvar-within-between-components/{\"masses\":[[1,18],[2,18],[15,18],[0,1]],\"partition\":[[0,1],[2,3]],\"values\":[8,9,11,107]}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_or_symbolic_model","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"候選須主端重算；不構成人工審定、sampled orbit-stabilizer、sampled MVT、reverse compactness、zero-mass division、underspecified recurrence、incomplete divisor inversion、bounded-search PDA rejection、Lean或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-20261110-r04-law-of-total-variance-0035","batch_id":"batch-20261014-advance-20261110-r04-law-of-total-variance-foundations","language":"zh-Hant","source_mko_ids":["mko-law-of-total-variance"],"title_zh":"全變異數公式","stem_zh":"同一有限law與完整disjoint partition生成的G。操作=totalvar-within-between-components；資料={\"masses\":[[1,19],[2,19],[16,19],[0,1]],\"values\":[9,10,12,108],\"partition\":[[0,1],[2,3]]}。請依 exact_ordered_tuple_declared_by_interface 欄序回答。","answer":{"kind":"expression","value":"([[0, [0, 1], 3/19, 29/3, 2/9], [1, [2, 3], 16/19, 12, 0]], 2/57, 784/1083, same_law_same_partition_within_and_between_terms)","explanation_zh":"Wave6第四層核對=([[0, [0, 1], 3/19, 29/3, 2/9], [1, [2, 3], 16/19, 12, 0]], 2/57, 784/1083, same_law_same_partition_within_and_between_terms)；依完整明示資料獨立重算；within與between terms使用同一law及同一cells且兩項皆不可省略；zero-mass cell禁止conditional division且外層加權貢獻為0；不要求partition events independent。"},"difficulty":{"band":"undergraduate_core","level":2,"skills":["全變異數公式"]},"variant":{"family_id":"qf-mod41-totalvar-within-between-components","seed":202611104035,"parameters":{"masses":[[1,19],[2,19],[16,19],[0,1]],"values":[9,10,12,108],"partition":[[0,1],[2,3]],"domain":"Finite_partition_total_variance","operation":"totalvar-within-between-components","semantic_template":"qf-mod41-totalvar-within-between-components/{\"masses\":[[1,19],[2,19],[16,19],[0,1]],\"partition\":[[0,1],[2,3]],\"values\":[9,10,12,108]}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_or_symbolic_model","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"候選須主端重算；不構成人工審定、sampled orbit-stabilizer、sampled MVT、reverse compactness、zero-mass division、underspecified recurrence、incomplete divisor inversion、bounded-search PDA rejection、Lean或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-20261110-r04-law-of-total-variance-0036","batch_id":"batch-20261014-advance-20261110-r04-law-of-total-variance-foundations","language":"zh-Hant","source_mko_ids":["mko-law-of-total-variance"],"title_zh":"全變異數公式","stem_zh":"同一有限law與完整disjoint partition生成的G。操作=totalvar-within-between-components；資料={\"masses\":[[1,20],[2,20],[17,20],[0,1]],\"values\":[10,11,13,109],\"partition\":[[0,1],[2,3]]}。請依 exact_ordered_tuple_declared_by_interface 欄序回答。","answer":{"kind":"expression","value":"([[0, [0, 1], 3/20, 32/3, 2/9], [1, [2, 3], 17/20, 13, 0]], 1/30, 833/1200, same_law_same_partition_within_and_between_terms)","explanation_zh":"Wave6第四層核對=([[0, [0, 1], 3/20, 32/3, 2/9], [1, [2, 3], 17/20, 13, 0]], 1/30, 833/1200, same_law_same_partition_within_and_between_terms)；依完整明示資料獨立重算；within與between terms使用同一law及同一cells且兩項皆不可省略；zero-mass cell禁止conditional division且外層加權貢獻為0；不要求partition events independent。"},"difficulty":{"band":"undergraduate_core","level":2,"skills":["全變異數公式"]},"variant":{"family_id":"qf-mod41-totalvar-within-between-components","seed":202611104036,"parameters":{"masses":[[1,20],[2,20],[17,20],[0,1]],"values":[10,11,13,109],"partition":[[0,1],[2,3]],"domain":"Finite_partition_total_variance","operation":"totalvar-within-between-components","semantic_template":"qf-mod41-totalvar-within-between-components/{\"masses\":[[1,20],[2,20],[17,20],[0,1]],\"partition\":[[0,1],[2,3]],\"values\":[10,11,13,109]}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_or_symbolic_model","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"候選須主端重算；不構成人工審定、sampled orbit-stabilizer、sampled MVT、reverse compactness、zero-mass division、underspecified recurrence、incomplete divisor inversion、bounded-search PDA rejection、Lean或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-20261110-r04-law-of-total-variance-0037","batch_id":"batch-20261014-advance-20261110-r04-law-of-total-variance-foundations","language":"zh-Hant","source_mko_ids":["mko-law-of-total-variance"],"title_zh":"全變異數公式","stem_zh":"同一有限law與完整disjoint partition生成的G。操作=totalvar-within-between-components；資料={\"masses\":[[1,21],[2,21],[18,21],[0,1]],\"values\":[11,12,14,110],\"partition\":[[0,1],[2,3]]}。請依 exact_ordered_tuple_declared_by_interface 欄序回答。","answer":{"kind":"expression","value":"([[0, [0, 1], 1/7, 35/3, 2/9], [1, [2, 3], 6/7, 14, 0]], 2/63, 2/3, same_law_same_partition_within_and_between_terms)","explanation_zh":"Wave6第四層核對=([[0, [0, 1], 1/7, 35/3, 2/9], [1, [2, 3], 6/7, 14, 0]], 2/63, 2/3, same_law_same_partition_within_and_between_terms)；依完整明示資料獨立重算；within與between terms使用同一law及同一cells且兩項皆不可省略；zero-mass cell禁止conditional division且外層加權貢獻為0；不要求partition events independent。"},"difficulty":{"band":"undergraduate_core","level":2,"skills":["全變異數公式"]},"variant":{"family_id":"qf-mod41-totalvar-within-between-components","seed":202611104037,"parameters":{"masses":[[1,21],[2,21],[18,21],[0,1]],"values":[11,12,14,110],"partition":[[0,1],[2,3]],"domain":"Finite_partition_total_variance","operation":"totalvar-within-between-components","semantic_template":"qf-mod41-totalvar-within-between-components/{\"masses\":[[1,21],[2,21],[18,21],[0,1]],\"partition\":[[0,1],[2,3]],\"values\":[11,12,14,110]}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_or_symbolic_model","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"候選須主端重算；不構成人工審定、sampled orbit-stabilizer、sampled MVT、reverse compactness、zero-mass division、underspecified recurrence、incomplete divisor inversion、bounded-search PDA rejection、Lean或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-20261110-r04-law-of-total-variance-0038","batch_id":"batch-20261014-advance-20261110-r04-law-of-total-variance-foundations","language":"zh-Hant","source_mko_ids":["mko-law-of-total-variance"],"title_zh":"全變異數公式","stem_zh":"同一有限law與完整disjoint partition生成的G。操作=totalvar-within-between-components；資料={\"masses\":[[1,22],[2,22],[19,22],[0,1]],\"values\":[12,13,15,111],\"partition\":[[0,1],[2,3]]}。請依 exact_ordered_tuple_declared_by_interface 欄序回答。","answer":{"kind":"expression","value":"([[0, [0, 1], 3/22, 38/3, 2/9], [1, [2, 3], 19/22, 15, 0]], 1/33, 931/1452, same_law_same_partition_within_and_between_terms)","explanation_zh":"Wave6第四層核對=([[0, [0, 1], 3/22, 38/3, 2/9], [1, [2, 3], 19/22, 15, 0]], 1/33, 931/1452, same_law_same_partition_within_and_between_terms)；依完整明示資料獨立重算；within與between terms使用同一law及同一cells且兩項皆不可省略；zero-mass cell禁止conditional division且外層加權貢獻為0；不要求partition events independent。"},"difficulty":{"band":"undergraduate_core","level":2,"skills":["全變異數公式"]},"variant":{"family_id":"qf-mod41-totalvar-within-between-components","seed":202611104038,"parameters":{"masses":[[1,22],[2,22],[19,22],[0,1]],"values":[12,13,15,111],"partition":[[0,1],[2,3]],"domain":"Finite_partition_total_variance","operation":"totalvar-within-between-components","semantic_template":"qf-mod41-totalvar-within-between-components/{\"masses\":[[1,22],[2,22],[19,22],[0,1]],\"partition\":[[0,1],[2,3]],\"values\":[12,13,15,111]}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_or_symbolic_model","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"候選須主端重算；不構成人工審定、sampled orbit-stabilizer、sampled MVT、reverse compactness、zero-mass division、underspecified recurrence、incomplete divisor inversion、bounded-search PDA rejection、Lean或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-20261110-r04-law-of-total-variance-0039","batch_id":"batch-20261014-advance-20261110-r04-law-of-total-variance-foundations","language":"zh-Hant","source_mko_ids":["mko-law-of-total-variance"],"title_zh":"全變異數公式","stem_zh":"同一有限law與完整disjoint partition生成的G。操作=totalvar-within-between-components；資料={\"masses\":[[1,23],[2,23],[20,23],[0,1]],\"values\":[13,14,16,112],\"partition\":[[0,1],[2,3]]}。請依 exact_ordered_tuple_declared_by_interface 欄序回答。","answer":{"kind":"expression","value":"([[0, [0, 1], 3/23, 41/3, 2/9], [1, [2, 3], 20/23, 16, 0]], 2/69, 980/1587, same_law_same_partition_within_and_between_terms)","explanation_zh":"Wave6第四層核對=([[0, [0, 1], 3/23, 41/3, 2/9], [1, [2, 3], 20/23, 16, 0]], 2/69, 980/1587, same_law_same_partition_within_and_between_terms)；依完整明示資料獨立重算；within與between terms使用同一law及同一cells且兩項皆不可省略；zero-mass cell禁止conditional division且外層加權貢獻為0；不要求partition events independent。"},"difficulty":{"band":"undergraduate_core","level":2,"skills":["全變異數公式"]},"variant":{"family_id":"qf-mod41-totalvar-within-between-components","seed":202611104039,"parameters":{"masses":[[1,23],[2,23],[20,23],[0,1]],"values":[13,14,16,112],"partition":[[0,1],[2,3]],"domain":"Finite_partition_total_variance","operation":"totalvar-within-between-components","semantic_template":"qf-mod41-totalvar-within-between-components/{\"masses\":[[1,23],[2,23],[20,23],[0,1]],\"partition\":[[0,1],[2,3]],\"values\":[13,14,16,112]}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_or_symbolic_model","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"候選須主端重算；不構成人工審定、sampled orbit-stabilizer、sampled MVT、reverse compactness、zero-mass division、underspecified recurrence、incomplete divisor inversion、bounded-search PDA rejection、Lean或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-20261110-r04-law-of-total-variance-0040","batch_id":"batch-20261014-advance-20261110-r04-law-of-total-variance-foundations","language":"zh-Hant","source_mko_ids":["mko-law-of-total-variance"],"title_zh":"全變異數公式","stem_zh":"同一有限law與完整disjoint partition生成的G。操作=totalvar-within-between-components；資料={\"masses\":[[1,24],[2,24],[21,24],[0,1]],\"values\":[14,15,17,113],\"partition\":[[0,1],[2,3]]}。請依 exact_ordered_tuple_declared_by_interface 欄序回答。","answer":{"kind":"expression","value":"([[0, [0, 1], 1/8, 44/3, 2/9], [1, [2, 3], 7/8, 17, 0]], 1/36, 343/576, same_law_same_partition_within_and_between_terms)","explanation_zh":"Wave6第四層核對=([[0, [0, 1], 1/8, 44/3, 2/9], [1, [2, 3], 7/8, 17, 0]], 1/36, 343/576, same_law_same_partition_within_and_between_terms)；依完整明示資料獨立重算；within與between terms使用同一law及同一cells且兩項皆不可省略；zero-mass cell禁止conditional division且外層加權貢獻為0；不要求partition events independent。"},"difficulty":{"band":"undergraduate_core","level":2,"skills":["全變異數公式"]},"variant":{"family_id":"qf-mod41-totalvar-within-between-components","seed":202611104040,"parameters":{"masses":[[1,24],[2,24],[21,24],[0,1]],"values":[14,15,17,113],"partition":[[0,1],[2,3]],"domain":"Finite_partition_total_variance","operation":"totalvar-within-between-components","semantic_template":"qf-mod41-totalvar-within-between-components/{\"masses\":[[1,24],[2,24],[21,24],[0,1]],\"partition\":[[0,1],[2,3]],\"values\":[14,15,17,113]}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_or_symbolic_model","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"候選須主端重算；不構成人工審定、sampled orbit-stabilizer、sampled MVT、reverse compactness、zero-mass division、underspecified recurrence、incomplete divisor inversion、bounded-search PDA rejection、Lean或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-20261110-r04-law-of-total-variance-0041","batch_id":"batch-20261014-advance-20261110-r04-law-of-total-variance-foundations","language":"zh-Hant","source_mko_ids":["mko-law-of-total-variance"],"title_zh":"全變異數公式","stem_zh":"同一有限law與完整disjoint partition生成的G。操作=totalvar-within-between-components；資料={\"masses\":[[1,25],[2,25],[22,25],[0,1]],\"values\":[15,16,18,114],\"partition\":[[0,1],[2,3]]}。請依 exact_ordered_tuple_declared_by_interface 欄序回答。","answer":{"kind":"expression","value":"([[0, [0, 1], 3/25, 47/3, 2/9], [1, [2, 3], 22/25, 18, 0]], 2/75, 1078/1875, same_law_same_partition_within_and_between_terms)","explanation_zh":"Wave6第四層核對=([[0, [0, 1], 3/25, 47/3, 2/9], [1, [2, 3], 22/25, 18, 0]], 2/75, 1078/1875, same_law_same_partition_within_and_between_terms)；依完整明示資料獨立重算；within與between terms使用同一law及同一cells且兩項皆不可省略；zero-mass cell禁止conditional division且外層加權貢獻為0；不要求partition events independent。"},"difficulty":{"band":"undergraduate_core","level":2,"skills":["全變異數公式"]},"variant":{"family_id":"qf-mod41-totalvar-within-between-components","seed":202611104041,"parameters":{"masses":[[1,25],[2,25],[22,25],[0,1]],"values":[15,16,18,114],"partition":[[0,1],[2,3]],"domain":"Finite_partition_total_variance","operation":"totalvar-within-between-components","semantic_template":"qf-mod41-totalvar-within-between-components/{\"masses\":[[1,25],[2,25],[22,25],[0,1]],\"partition\":[[0,1],[2,3]],\"values\":[15,16,18,114]}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_or_symbolic_model","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"候選須主端重算；不構成人工審定、sampled orbit-stabilizer、sampled MVT、reverse compactness、zero-mass division、underspecified recurrence、incomplete divisor inversion、bounded-search PDA rejection、Lean或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-20261110-r04-law-of-total-variance-0042","batch_id":"batch-20261014-advance-20261110-r04-law-of-total-variance-foundations","language":"zh-Hant","source_mko_ids":["mko-law-of-total-variance"],"title_zh":"全變異數公式","stem_zh":"同一有限law與完整disjoint partition生成的G。操作=totalvar-within-between-components；資料={\"masses\":[[1,26],[2,26],[23,26],[0,1]],\"values\":[16,17,19,115],\"partition\":[[0,1],[2,3]]}。請依 exact_ordered_tuple_declared_by_interface 欄序回答。","answer":{"kind":"expression","value":"([[0, [0, 1], 3/26, 50/3, 2/9], [1, [2, 3], 23/26, 19, 0]], 1/39, 1127/2028, same_law_same_partition_within_and_between_terms)","explanation_zh":"Wave6第四層核對=([[0, [0, 1], 3/26, 50/3, 2/9], [1, [2, 3], 23/26, 19, 0]], 1/39, 1127/2028, same_law_same_partition_within_and_between_terms)；依完整明示資料獨立重算；within與between terms使用同一law及同一cells且兩項皆不可省略；zero-mass cell禁止conditional division且外層加權貢獻為0；不要求partition events independent。"},"difficulty":{"band":"undergraduate_core","level":2,"skills":["全變異數公式"]},"variant":{"family_id":"qf-mod41-totalvar-within-between-components","seed":202611104042,"parameters":{"masses":[[1,26],[2,26],[23,26],[0,1]],"values":[16,17,19,115],"partition":[[0,1],[2,3]],"domain":"Finite_partition_total_variance","operation":"totalvar-within-between-components","semantic_template":"qf-mod41-totalvar-within-between-components/{\"masses\":[[1,26],[2,26],[23,26],[0,1]],\"partition\":[[0,1],[2,3]],\"values\":[16,17,19,115]}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_or_symbolic_model","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"候選須主端重算；不構成人工審定、sampled orbit-stabilizer、sampled MVT、reverse compactness、zero-mass division、underspecified recurrence、incomplete divisor inversion、bounded-search PDA rejection、Lean或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-20261110-r04-law-of-total-variance-0043","batch_id":"batch-20261014-advance-20261110-r04-law-of-total-variance-foundations","language":"zh-Hant","source_mko_ids":["mko-law-of-total-variance"],"title_zh":"全變異數公式","stem_zh":"同一有限law與完整disjoint partition生成的G。操作=totalvar-within-between-components；資料={\"masses\":[[1,27],[2,27],[24,27],[0,1]],\"values\":[17,18,20,116],\"partition\":[[0,1],[2,3]]}。請依 exact_ordered_tuple_declared_by_interface 欄序回答。","answer":{"kind":"expression","value":"([[0, [0, 1], 1/9, 53/3, 2/9], [1, [2, 3], 8/9, 20, 0]], 2/81, 392/729, same_law_same_partition_within_and_between_terms)","explanation_zh":"Wave6第四層核對=([[0, [0, 1], 1/9, 53/3, 2/9], [1, [2, 3], 8/9, 20, 0]], 2/81, 392/729, same_law_same_partition_within_and_between_terms)；依完整明示資料獨立重算；within與between terms使用同一law及同一cells且兩項皆不可省略；zero-mass cell禁止conditional division且外層加權貢獻為0；不要求partition events independent。"},"difficulty":{"band":"undergraduate_core","level":3,"skills":["全變異數公式"]},"variant":{"family_id":"qf-mod41-totalvar-within-between-components","seed":202611104043,"parameters":{"masses":[[1,27],[2,27],[24,27],[0,1]],"values":[17,18,20,116],"partition":[[0,1],[2,3]],"domain":"Finite_partition_total_variance","operation":"totalvar-within-between-components","semantic_template":"qf-mod41-totalvar-within-between-components/{\"masses\":[[1,27],[2,27],[24,27],[0,1]],\"partition\":[[0,1],[2,3]],\"values\":[17,18,20,116]}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_or_symbolic_model","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"候選須主端重算；不構成人工審定、sampled orbit-stabilizer、sampled MVT、reverse compactness、zero-mass division、underspecified recurrence、incomplete divisor inversion、bounded-search PDA rejection、Lean或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-20261110-r04-law-of-total-variance-0044","batch_id":"batch-20261014-advance-20261110-r04-law-of-total-variance-foundations","language":"zh-Hant","source_mko_ids":["mko-law-of-total-variance"],"title_zh":"全變異數公式","stem_zh":"同一有限law與完整disjoint partition生成的G。操作=totalvar-within-between-components；資料={\"masses\":[[1,28],[2,28],[25,28],[0,1]],\"values\":[18,19,21,117],\"partition\":[[0,1],[2,3]]}。請依 exact_ordered_tuple_declared_by_interface 欄序回答。","answer":{"kind":"expression","value":"([[0, [0, 1], 3/28, 56/3, 2/9], [1, [2, 3], 25/28, 21, 0]], 1/42, 25/48, same_law_same_partition_within_and_between_terms)","explanation_zh":"Wave6第四層核對=([[0, [0, 1], 3/28, 56/3, 2/9], [1, [2, 3], 25/28, 21, 0]], 1/42, 25/48, same_law_same_partition_within_and_between_terms)；依完整明示資料獨立重算；within與between terms使用同一law及同一cells且兩項皆不可省略；zero-mass cell禁止conditional division且外層加權貢獻為0；不要求partition events independent。"},"difficulty":{"band":"undergraduate_core","level":3,"skills":["全變異數公式"]},"variant":{"family_id":"qf-mod41-totalvar-within-between-components","seed":202611104044,"parameters":{"masses":[[1,28],[2,28],[25,28],[0,1]],"values":[18,19,21,117],"partition":[[0,1],[2,3]],"domain":"Finite_partition_total_variance","operation":"totalvar-within-between-components","semantic_template":"qf-mod41-totalvar-within-between-components/{\"masses\":[[1,28],[2,28],[25,28],[0,1]],\"partition\":[[0,1],[2,3]],\"values\":[18,19,21,117]}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_or_symbolic_model","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"候選須主端重算；不構成人工審定、sampled orbit-stabilizer、sampled MVT、reverse compactness、zero-mass division、underspecified recurrence、incomplete divisor inversion、bounded-search PDA rejection、Lean或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-20261110-r04-law-of-total-variance-0045","batch_id":"batch-20261014-advance-20261110-r04-law-of-total-variance-foundations","language":"zh-Hant","source_mko_ids":["mko-law-of-total-variance"],"title_zh":"全變異數公式","stem_zh":"同一有限law與完整disjoint partition生成的G。操作=totalvar-within-between-components；資料={\"masses\":[[1,29],[2,29],[26,29],[0,1]],\"values\":[19,20,22,118],\"partition\":[[0,1],[2,3]]}。請依 exact_ordered_tuple_declared_by_interface 欄序回答。","answer":{"kind":"expression","value":"([[0, [0, 1], 3/29, 59/3, 2/9], [1, [2, 3], 26/29, 22, 0]], 2/87, 1274/2523, same_law_same_partition_within_and_between_terms)","explanation_zh":"Wave6第四層核對=([[0, [0, 1], 3/29, 59/3, 2/9], [1, [2, 3], 26/29, 22, 0]], 2/87, 1274/2523, same_law_same_partition_within_and_between_terms)；依完整明示資料獨立重算；within與between terms使用同一law及同一cells且兩項皆不可省略；zero-mass cell禁止conditional division且外層加權貢獻為0；不要求partition events independent。"},"difficulty":{"band":"undergraduate_core","level":3,"skills":["全變異數公式"]},"variant":{"family_id":"qf-mod41-totalvar-within-between-components","seed":202611104045,"parameters":{"masses":[[1,29],[2,29],[26,29],[0,1]],"values":[19,20,22,118],"partition":[[0,1],[2,3]],"domain":"Finite_partition_total_variance","operation":"totalvar-within-between-components","semantic_template":"qf-mod41-totalvar-within-between-components/{\"masses\":[[1,29],[2,29],[26,29],[0,1]],\"partition\":[[0,1],[2,3]],\"values\":[19,20,22,118]}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_or_symbolic_model","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"候選須主端重算；不構成人工審定、sampled orbit-stabilizer、sampled MVT、reverse compactness、zero-mass division、underspecified recurrence、incomplete divisor inversion、bounded-search PDA rejection、Lean或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-20261110-r04-law-of-total-variance-0046","batch_id":"batch-20261014-advance-20261110-r04-law-of-total-variance-foundations","language":"zh-Hant","source_mko_ids":["mko-law-of-total-variance"],"title_zh":"全變異數公式","stem_zh":"同一有限law與完整disjoint partition生成的G。操作=totalvar-within-between-components；資料={\"masses\":[[1,30],[2,30],[27,30],[0,1]],\"values\":[20,21,23,119],\"partition\":[[0,1],[2,3]]}。請依 exact_ordered_tuple_declared_by_interface 欄序回答。","answer":{"kind":"expression","value":"([[0, [0, 1], 1/10, 62/3, 2/9], [1, [2, 3], 9/10, 23, 0]], 1/45, 49/100, same_law_same_partition_within_and_between_terms)","explanation_zh":"Wave6第四層核對=([[0, [0, 1], 1/10, 62/3, 2/9], [1, [2, 3], 9/10, 23, 0]], 1/45, 49/100, same_law_same_partition_within_and_between_terms)；依完整明示資料獨立重算；within與between terms使用同一law及同一cells且兩項皆不可省略；zero-mass cell禁止conditional division且外層加權貢獻為0；不要求partition events independent。"},"difficulty":{"band":"undergraduate_core","level":3,"skills":["全變異數公式"]},"variant":{"family_id":"qf-mod41-totalvar-within-between-components","seed":202611104046,"parameters":{"masses":[[1,30],[2,30],[27,30],[0,1]],"values":[20,21,23,119],"partition":[[0,1],[2,3]],"domain":"Finite_partition_total_variance","operation":"totalvar-within-between-components","semantic_template":"qf-mod41-totalvar-within-between-components/{\"masses\":[[1,30],[2,30],[27,30],[0,1]],\"partition\":[[0,1],[2,3]],\"values\":[20,21,23,119]}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_or_symbolic_model","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"候選須主端重算；不構成人工審定、sampled orbit-stabilizer、sampled MVT、reverse compactness、zero-mass division、underspecified recurrence、incomplete divisor inversion、bounded-search PDA rejection、Lean或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-20261110-r04-law-of-total-variance-0047","batch_id":"batch-20261014-advance-20261110-r04-law-of-total-variance-foundations","language":"zh-Hant","source_mko_ids":["mko-law-of-total-variance"],"title_zh":"全變異數公式","stem_zh":"同一有限law與完整disjoint partition生成的G。操作=totalvar-within-between-components；資料={\"masses\":[[1,31],[2,31],[28,31],[0,1]],\"values\":[21,22,24,120],\"partition\":[[0,1],[2,3]]}。請依 exact_ordered_tuple_declared_by_interface 欄序回答。","answer":{"kind":"expression","value":"([[0, [0, 1], 3/31, 65/3, 2/9], [1, [2, 3], 28/31, 24, 0]], 2/93, 1372/2883, same_law_same_partition_within_and_between_terms)","explanation_zh":"Wave6第四層核對=([[0, [0, 1], 3/31, 65/3, 2/9], [1, [2, 3], 28/31, 24, 0]], 2/93, 1372/2883, same_law_same_partition_within_and_between_terms)；依完整明示資料獨立重算；within與between terms使用同一law及同一cells且兩項皆不可省略；zero-mass cell禁止conditional division且外層加權貢獻為0；不要求partition events independent。"},"difficulty":{"band":"undergraduate_core","level":3,"skills":["全變異數公式"]},"variant":{"family_id":"qf-mod41-totalvar-within-between-components","seed":202611104047,"parameters":{"masses":[[1,31],[2,31],[28,31],[0,1]],"values":[21,22,24,120],"partition":[[0,1],[2,3]],"domain":"Finite_partition_total_variance","operation":"totalvar-within-between-components","semantic_template":"qf-mod41-totalvar-within-between-components/{\"masses\":[[1,31],[2,31],[28,31],[0,1]],\"partition\":[[0,1],[2,3]],\"values\":[21,22,24,120]}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_or_symbolic_model","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"候選須主端重算；不構成人工審定、sampled orbit-stabilizer、sampled MVT、reverse compactness、zero-mass division、underspecified recurrence、incomplete divisor inversion、bounded-search PDA rejection、Lean或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-20261110-r04-law-of-total-variance-0048","batch_id":"batch-20261014-advance-20261110-r04-law-of-total-variance-foundations","language":"zh-Hant","source_mko_ids":["mko-law-of-total-variance"],"title_zh":"全變異數公式","stem_zh":"同一有限law與完整disjoint partition生成的G。操作=totalvar-within-between-components；資料={\"masses\":[[1,32],[2,32],[29,32],[0,1]],\"values\":[22,23,25,121],\"partition\":[[0,1],[2,3]]}。請依 exact_ordered_tuple_declared_by_interface 欄序回答。","answer":{"kind":"expression","value":"([[0, [0, 1], 3/32, 68/3, 2/9], [1, [2, 3], 29/32, 25, 0]], 1/48, 1421/3072, same_law_same_partition_within_and_between_terms)","explanation_zh":"Wave6第四層核對=([[0, [0, 1], 3/32, 68/3, 2/9], [1, [2, 3], 29/32, 25, 0]], 1/48, 1421/3072, same_law_same_partition_within_and_between_terms)；依完整明示資料獨立重算；within與between terms使用同一law及同一cells且兩項皆不可省略；zero-mass cell禁止conditional division且外層加權貢獻為0；不要求partition events independent。"},"difficulty":{"band":"undergraduate_core","level":3,"skills":["全變異數公式"]},"variant":{"family_id":"qf-mod41-totalvar-within-between-components","seed":202611104048,"parameters":{"masses":[[1,32],[2,32],[29,32],[0,1]],"values":[22,23,25,121],"partition":[[0,1],[2,3]],"domain":"Finite_partition_total_variance","operation":"totalvar-within-between-components","semantic_template":"qf-mod41-totalvar-within-between-components/{\"masses\":[[1,32],[2,32],[29,32],[0,1]],\"partition\":[[0,1],[2,3]],\"values\":[22,23,25,121]}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_or_symbolic_model","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"候選須主端重算；不構成人工審定、sampled orbit-stabilizer、sampled MVT、reverse compactness、zero-mass division、underspecified recurrence、incomplete divisor inversion、bounded-search PDA rejection、Lean或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-20261110-r04-law-of-total-variance-0049","batch_id":"batch-20261014-advance-20261110-r04-law-of-total-variance-foundations","language":"zh-Hant","source_mko_ids":["mko-law-of-total-variance"],"title_zh":"全變異數公式","stem_zh":"同一有限law與完整disjoint partition生成的G。操作=totalvar-within-between-components；資料={\"masses\":[[1,33],[2,33],[30,33],[0,1]],\"values\":[23,24,26,122],\"partition\":[[0,1],[2,3]]}。請依 exact_ordered_tuple_declared_by_interface 欄序回答。","answer":{"kind":"expression","value":"([[0, [0, 1], 1/11, 71/3, 2/9], [1, [2, 3], 10/11, 26, 0]], 2/99, 490/1089, same_law_same_partition_within_and_between_terms)","explanation_zh":"Wave6第四層核對=([[0, [0, 1], 1/11, 71/3, 2/9], [1, [2, 3], 10/11, 26, 0]], 2/99, 490/1089, same_law_same_partition_within_and_between_terms)；依完整明示資料獨立重算；within與between terms使用同一law及同一cells且兩項皆不可省略；zero-mass cell禁止conditional division且外層加權貢獻為0；不要求partition events independent。"},"difficulty":{"band":"undergraduate_core","level":3,"skills":["全變異數公式"]},"variant":{"family_id":"qf-mod41-totalvar-within-between-components","seed":202611104049,"parameters":{"masses":[[1,33],[2,33],[30,33],[0,1]],"values":[23,24,26,122],"partition":[[0,1],[2,3]],"domain":"Finite_partition_total_variance","operation":"totalvar-within-between-components","semantic_template":"qf-mod41-totalvar-within-between-components/{\"masses\":[[1,33],[2,33],[30,33],[0,1]],\"partition\":[[0,1],[2,3]],\"values\":[23,24,26,122]}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_or_symbolic_model","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"候選須主端重算；不構成人工審定、sampled orbit-stabilizer、sampled MVT、reverse compactness、zero-mass division、underspecified recurrence、incomplete divisor inversion、bounded-search PDA rejection、Lean或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-20261110-r04-law-of-total-variance-0050","batch_id":"batch-20261014-advance-20261110-r04-law-of-total-variance-foundations","language":"zh-Hant","source_mko_ids":["mko-law-of-total-variance"],"title_zh":"全變異數公式","stem_zh":"同一有限law與完整disjoint partition生成的G。操作=totalvar-within-between-components；資料={\"masses\":[[1,34],[2,34],[31,34],[0,1]],\"values\":[24,25,27,123],\"partition\":[[0,1],[2,3]]}。請依 exact_ordered_tuple_declared_by_interface 欄序回答。","answer":{"kind":"expression","value":"([[0, [0, 1], 3/34, 74/3, 2/9], [1, [2, 3], 31/34, 27, 0]], 1/51, 1519/3468, same_law_same_partition_within_and_between_terms)","explanation_zh":"Wave6第四層核對=([[0, [0, 1], 3/34, 74/3, 2/9], [1, [2, 3], 31/34, 27, 0]], 1/51, 1519/3468, same_law_same_partition_within_and_between_terms)；依完整明示資料獨立重算；within與between terms使用同一law及同一cells且兩項皆不可省略；zero-mass cell禁止conditional division且外層加權貢獻為0；不要求partition events independent。"},"difficulty":{"band":"undergraduate_core","level":3,"skills":["全變異數公式"]},"variant":{"family_id":"qf-mod41-totalvar-within-between-components","seed":202611104050,"parameters":{"masses":[[1,34],[2,34],[31,34],[0,1]],"values":[24,25,27,123],"partition":[[0,1],[2,3]],"domain":"Finite_partition_total_variance","operation":"totalvar-within-between-components","semantic_template":"qf-mod41-totalvar-within-between-components/{\"masses\":[[1,34],[2,34],[31,34],[0,1]],\"partition\":[[0,1],[2,3]],\"values\":[24,25,27,123]}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_or_symbolic_model","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"候選須主端重算；不構成人工審定、sampled orbit-stabilizer、sampled MVT、reverse compactness、zero-mass division、underspecified recurrence、incomplete divisor inversion、bounded-search PDA rejection、Lean或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-20261110-r04-law-of-total-variance-0051","batch_id":"batch-20261014-advance-20261110-r04-law-of-total-variance-foundations","language":"zh-Hant","source_mko_ids":["mko-law-of-total-variance"],"title_zh":"全變異數公式","stem_zh":"同一有限law與完整disjoint partition生成的G。操作=totalvar-full-identity；資料={\"masses\":[[1,10],[2,10],[7,10],[0,1]],\"values\":[0,1,3,99],\"partition\":[[0,1],[2,3]]}。請依 exact_ordered_tuple_declared_by_interface 欄序回答。","answer":{"kind":"expression","value":"(121/100, 1/15, 343/300, 121/100, 是)","explanation_zh":"Wave6第四層核對=(121/100, 1/15, 343/300, 121/100, 是)；依完整明示資料獨立重算；within與between terms使用同一law及同一cells且兩項皆不可省略；zero-mass cell禁止conditional division且外層加權貢獻為0；不要求partition events independent。"},"difficulty":{"band":"undergraduate_core","level":1,"skills":["全變異數公式"]},"variant":{"family_id":"qf-mod41-totalvar-full-identity","seed":202611104051,"parameters":{"masses":[[1,10],[2,10],[7,10],[0,1]],"values":[0,1,3,99],"partition":[[0,1],[2,3]],"domain":"Finite_partition_total_variance","operation":"totalvar-full-identity","semantic_template":"qf-mod41-totalvar-full-identity/{\"masses\":[[1,10],[2,10],[7,10],[0,1]],\"partition\":[[0,1],[2,3]],\"values\":[0,1,3,99]}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_or_symbolic_model","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"候選須主端重算；不構成人工審定、sampled orbit-stabilizer、sampled MVT、reverse compactness、zero-mass division、underspecified recurrence、incomplete divisor inversion、bounded-search PDA rejection、Lean或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-20261110-r04-law-of-total-variance-0052","batch_id":"batch-20261014-advance-20261110-r04-law-of-total-variance-foundations","language":"zh-Hant","source_mko_ids":["mko-law-of-total-variance"],"title_zh":"全變異數公式","stem_zh":"同一有限law與完整disjoint partition生成的G。操作=totalvar-full-identity；資料={\"masses\":[[1,11],[2,11],[8,11],[0,1]],\"values\":[1,2,4,100],\"partition\":[[0,1],[2,3]]}。請依 exact_ordered_tuple_declared_by_interface 欄序回答。","answer":{"kind":"expression","value":"(138/121, 2/33, 392/363, 138/121, 是)","explanation_zh":"Wave6第四層核對=(138/121, 2/33, 392/363, 138/121, 是)；依完整明示資料獨立重算；within與between terms使用同一law及同一cells且兩項皆不可省略；zero-mass cell禁止conditional division且外層加權貢獻為0；不要求partition events independent。"},"difficulty":{"band":"undergraduate_core","level":1,"skills":["全變異數公式"]},"variant":{"family_id":"qf-mod41-totalvar-full-identity","seed":202611104052,"parameters":{"masses":[[1,11],[2,11],[8,11],[0,1]],"values":[1,2,4,100],"partition":[[0,1],[2,3]],"domain":"Finite_partition_total_variance","operation":"totalvar-full-identity","semantic_template":"qf-mod41-totalvar-full-identity/{\"masses\":[[1,11],[2,11],[8,11],[0,1]],\"partition\":[[0,1],[2,3]],\"values\":[1,2,4,100]}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_or_symbolic_model","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"候選須主端重算；不構成人工審定、sampled orbit-stabilizer、sampled MVT、reverse compactness、zero-mass division、underspecified recurrence、incomplete divisor inversion、bounded-search PDA rejection、Lean或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-20261110-r04-law-of-total-variance-0053","batch_id":"batch-20261014-advance-20261110-r04-law-of-total-variance-foundations","language":"zh-Hant","source_mko_ids":["mko-law-of-total-variance"],"title_zh":"全變異數公式","stem_zh":"同一有限law與完整disjoint partition生成的G。操作=totalvar-full-identity；資料={\"masses\":[[1,12],[2,12],[9,12],[0,1]],\"values\":[2,3,5,101],\"partition\":[[0,1],[2,3]]}。請依 exact_ordered_tuple_declared_by_interface 欄序回答。","answer":{"kind":"expression","value":"(155/144, 1/18, 49/48, 155/144, 是)","explanation_zh":"Wave6第四層核對=(155/144, 1/18, 49/48, 155/144, 是)；依完整明示資料獨立重算；within與between terms使用同一law及同一cells且兩項皆不可省略；zero-mass cell禁止conditional division且外層加權貢獻為0；不要求partition events independent。"},"difficulty":{"band":"undergraduate_core","level":1,"skills":["全變異數公式"]},"variant":{"family_id":"qf-mod41-totalvar-full-identity","seed":202611104053,"parameters":{"masses":[[1,12],[2,12],[9,12],[0,1]],"values":[2,3,5,101],"partition":[[0,1],[2,3]],"domain":"Finite_partition_total_variance","operation":"totalvar-full-identity","semantic_template":"qf-mod41-totalvar-full-identity/{\"masses\":[[1,12],[2,12],[9,12],[0,1]],\"partition\":[[0,1],[2,3]],\"values\":[2,3,5,101]}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_or_symbolic_model","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"候選須主端重算；不構成人工審定、sampled orbit-stabilizer、sampled MVT、reverse compactness、zero-mass division、underspecified recurrence、incomplete divisor inversion、bounded-search PDA rejection、Lean或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-20261110-r04-law-of-total-variance-0054","batch_id":"batch-20261014-advance-20261110-r04-law-of-total-variance-foundations","language":"zh-Hant","source_mko_ids":["mko-law-of-total-variance"],"title_zh":"全變異數公式","stem_zh":"同一有限law與完整disjoint partition生成的G。操作=totalvar-full-identity；資料={\"masses\":[[1,13],[2,13],[10,13],[0,1]],\"values\":[3,4,6,102],\"partition\":[[0,1],[2,3]]}。請依 exact_ordered_tuple_declared_by_interface 欄序回答。","answer":{"kind":"expression","value":"(172/169, 2/39, 490/507, 172/169, 是)","explanation_zh":"Wave6第四層核對=(172/169, 2/39, 490/507, 172/169, 是)；依完整明示資料獨立重算；within與between terms使用同一law及同一cells且兩項皆不可省略；zero-mass cell禁止conditional division且外層加權貢獻為0；不要求partition events independent。"},"difficulty":{"band":"undergraduate_core","level":1,"skills":["全變異數公式"]},"variant":{"family_id":"qf-mod41-totalvar-full-identity","seed":202611104054,"parameters":{"masses":[[1,13],[2,13],[10,13],[0,1]],"values":[3,4,6,102],"partition":[[0,1],[2,3]],"domain":"Finite_partition_total_variance","operation":"totalvar-full-identity","semantic_template":"qf-mod41-totalvar-full-identity/{\"masses\":[[1,13],[2,13],[10,13],[0,1]],\"partition\":[[0,1],[2,3]],\"values\":[3,4,6,102]}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_or_symbolic_model","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"候選須主端重算；不構成人工審定、sampled orbit-stabilizer、sampled MVT、reverse compactness、zero-mass division、underspecified recurrence、incomplete divisor inversion、bounded-search PDA rejection、Lean或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-20261110-r04-law-of-total-variance-0055","batch_id":"batch-20261014-advance-20261110-r04-law-of-total-variance-foundations","language":"zh-Hant","source_mko_ids":["mko-law-of-total-variance"],"title_zh":"全變異數公式","stem_zh":"同一有限law與完整disjoint partition生成的G。操作=totalvar-full-identity；資料={\"masses\":[[1,14],[2,14],[11,14],[0,1]],\"values\":[4,5,7,103],\"partition\":[[0,1],[2,3]]}。請依 exact_ordered_tuple_declared_by_interface 欄序回答。","answer":{"kind":"expression","value":"(27/28, 1/21, 11/12, 27/28, 是)","explanation_zh":"Wave6第四層核對=(27/28, 1/21, 11/12, 27/28, 是)；依完整明示資料獨立重算；within與between terms使用同一law及同一cells且兩項皆不可省略；zero-mass cell禁止conditional division且外層加權貢獻為0；不要求partition events independent。"},"difficulty":{"band":"undergraduate_core","level":1,"skills":["全變異數公式"]},"variant":{"family_id":"qf-mod41-totalvar-full-identity","seed":202611104055,"parameters":{"masses":[[1,14],[2,14],[11,14],[0,1]],"values":[4,5,7,103],"partition":[[0,1],[2,3]],"domain":"Finite_partition_total_variance","operation":"totalvar-full-identity","semantic_template":"qf-mod41-totalvar-full-identity/{\"masses\":[[1,14],[2,14],[11,14],[0,1]],\"partition\":[[0,1],[2,3]],\"values\":[4,5,7,103]}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_or_symbolic_model","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"候選須主端重算；不構成人工審定、sampled orbit-stabilizer、sampled MVT、reverse compactness、zero-mass division、underspecified recurrence、incomplete divisor inversion、bounded-search PDA rejection、Lean或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-20261110-r04-law-of-total-variance-0056","batch_id":"batch-20261014-advance-20261110-r04-law-of-total-variance-foundations","language":"zh-Hant","source_mko_ids":["mko-law-of-total-variance"],"title_zh":"全變異數公式","stem_zh":"同一有限law與完整disjoint partition生成的G。操作=totalvar-full-identity；資料={\"masses\":[[1,15],[2,15],[12,15],[0,1]],\"values\":[5,6,8,104],\"partition\":[[0,1],[2,3]]}。請依 exact_ordered_tuple_declared_by_interface 欄序回答。","answer":{"kind":"expression","value":"(206/225, 2/45, 196/225, 206/225, 是)","explanation_zh":"Wave6第四層核對=(206/225, 2/45, 196/225, 206/225, 是)；依完整明示資料獨立重算；within與between terms使用同一law及同一cells且兩項皆不可省略；zero-mass cell禁止conditional division且外層加權貢獻為0；不要求partition events independent。"},"difficulty":{"band":"undergraduate_core","level":1,"skills":["全變異數公式"]},"variant":{"family_id":"qf-mod41-totalvar-full-identity","seed":202611104056,"parameters":{"masses":[[1,15],[2,15],[12,15],[0,1]],"values":[5,6,8,104],"partition":[[0,1],[2,3]],"domain":"Finite_partition_total_variance","operation":"totalvar-full-identity","semantic_template":"qf-mod41-totalvar-full-identity/{\"masses\":[[1,15],[2,15],[12,15],[0,1]],\"partition\":[[0,1],[2,3]],\"values\":[5,6,8,104]}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_or_symbolic_model","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"候選須主端重算；不構成人工審定、sampled orbit-stabilizer、sampled MVT、reverse compactness、zero-mass division、underspecified recurrence、incomplete divisor inversion、bounded-search PDA rejection、Lean或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-20261110-r04-law-of-total-variance-0057","batch_id":"batch-20261014-advance-20261110-r04-law-of-total-variance-foundations","language":"zh-Hant","source_mko_ids":["mko-law-of-total-variance"],"title_zh":"全變異數公式","stem_zh":"同一有限law與完整disjoint partition生成的G。操作=totalvar-full-identity；資料={\"masses\":[[1,16],[2,16],[13,16],[0,1]],\"values\":[6,7,9,105],\"partition\":[[0,1],[2,3]]}。請依 exact_ordered_tuple_declared_by_interface 欄序回答。","answer":{"kind":"expression","value":"(223/256, 1/24, 637/768, 223/256, 是)","explanation_zh":"Wave6第四層核對=(223/256, 1/24, 637/768, 223/256, 是)；依完整明示資料獨立重算；within與between terms使用同一law及同一cells且兩項皆不可省略；zero-mass cell禁止conditional division且外層加權貢獻為0；不要求partition events independent。"},"difficulty":{"band":"undergraduate_core","level":1,"skills":["全變異數公式"]},"variant":{"family_id":"qf-mod41-totalvar-full-identity","seed":202611104057,"parameters":{"masses":[[1,16],[2,16],[13,16],[0,1]],"values":[6,7,9,105],"partition":[[0,1],[2,3]],"domain":"Finite_partition_total_variance","operation":"totalvar-full-identity","semantic_template":"qf-mod41-totalvar-full-identity/{\"masses\":[[1,16],[2,16],[13,16],[0,1]],\"partition\":[[0,1],[2,3]],\"values\":[6,7,9,105]}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_or_symbolic_model","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"候選須主端重算；不構成人工審定、sampled orbit-stabilizer、sampled MVT、reverse compactness、zero-mass division、underspecified recurrence、incomplete divisor inversion、bounded-search PDA rejection、Lean或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-20261110-r04-law-of-total-variance-0058","batch_id":"batch-20261014-advance-20261110-r04-law-of-total-variance-foundations","language":"zh-Hant","source_mko_ids":["mko-law-of-total-variance"],"title_zh":"全變異數公式","stem_zh":"同一有限law與完整disjoint partition生成的G。操作=totalvar-full-identity；資料={\"masses\":[[1,17],[2,17],[14,17],[0,1]],\"values\":[7,8,10,106],\"partition\":[[0,1],[2,3]]}。請依 exact_ordered_tuple_declared_by_interface 欄序回答。","answer":{"kind":"expression","value":"(240/289, 2/51, 686/867, 240/289, 是)","explanation_zh":"Wave6第四層核對=(240/289, 2/51, 686/867, 240/289, 是)；依完整明示資料獨立重算；within與between terms使用同一law及同一cells且兩項皆不可省略；zero-mass cell禁止conditional division且外層加權貢獻為0；不要求partition events independent。"},"difficulty":{"band":"undergraduate_core","level":1,"skills":["全變異數公式"]},"variant":{"family_id":"qf-mod41-totalvar-full-identity","seed":202611104058,"parameters":{"masses":[[1,17],[2,17],[14,17],[0,1]],"values":[7,8,10,106],"partition":[[0,1],[2,3]],"domain":"Finite_partition_total_variance","operation":"totalvar-full-identity","semantic_template":"qf-mod41-totalvar-full-identity/{\"masses\":[[1,17],[2,17],[14,17],[0,1]],\"partition\":[[0,1],[2,3]],\"values\":[7,8,10,106]}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_or_symbolic_model","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"候選須主端重算；不構成人工審定、sampled orbit-stabilizer、sampled MVT、reverse compactness、zero-mass division、underspecified recurrence、incomplete divisor inversion、bounded-search PDA rejection、Lean或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-20261110-r04-law-of-total-variance-0059","batch_id":"batch-20261014-advance-20261110-r04-law-of-total-variance-foundations","language":"zh-Hant","source_mko_ids":["mko-law-of-total-variance"],"title_zh":"全變異數公式","stem_zh":"同一有限law與完整disjoint partition生成的G。操作=totalvar-full-identity；資料={\"masses\":[[1,18],[2,18],[15,18],[0,1]],\"values\":[8,9,11,107],\"partition\":[[0,1],[2,3]]}。請依 exact_ordered_tuple_declared_by_interface 欄序回答。","answer":{"kind":"expression","value":"(257/324, 1/27, 245/324, 257/324, 是)","explanation_zh":"Wave6第四層核對=(257/324, 1/27, 245/324, 257/324, 是)；依完整明示資料獨立重算；within與between terms使用同一law及同一cells且兩項皆不可省略；zero-mass cell禁止conditional division且外層加權貢獻為0；不要求partition events independent。"},"difficulty":{"band":"undergraduate_core","level":2,"skills":["全變異數公式"]},"variant":{"family_id":"qf-mod41-totalvar-full-identity","seed":202611104059,"parameters":{"masses":[[1,18],[2,18],[15,18],[0,1]],"values":[8,9,11,107],"partition":[[0,1],[2,3]],"domain":"Finite_partition_total_variance","operation":"totalvar-full-identity","semantic_template":"qf-mod41-totalvar-full-identity/{\"masses\":[[1,18],[2,18],[15,18],[0,1]],\"partition\":[[0,1],[2,3]],\"values\":[8,9,11,107]}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_or_symbolic_model","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"候選須主端重算；不構成人工審定、sampled orbit-stabilizer、sampled MVT、reverse compactness、zero-mass division、underspecified recurrence、incomplete divisor inversion、bounded-search PDA rejection、Lean或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-20261110-r04-law-of-total-variance-0060","batch_id":"batch-20261014-advance-20261110-r04-law-of-total-variance-foundations","language":"zh-Hant","source_mko_ids":["mko-law-of-total-variance"],"title_zh":"全變異數公式","stem_zh":"同一有限law與完整disjoint partition生成的G。操作=totalvar-full-identity；資料={\"masses\":[[1,19],[2,19],[16,19],[0,1]],\"values\":[9,10,12,108],\"partition\":[[0,1],[2,3]]}。請依 exact_ordered_tuple_declared_by_interface 欄序回答。","answer":{"kind":"expression","value":"(274/361, 2/57, 784/1083, 274/361, 是)","explanation_zh":"Wave6第四層核對=(274/361, 2/57, 784/1083, 274/361, 是)；依完整明示資料獨立重算；within與between terms使用同一law及同一cells且兩項皆不可省略；zero-mass cell禁止conditional division且外層加權貢獻為0；不要求partition events independent。"},"difficulty":{"band":"undergraduate_core","level":2,"skills":["全變異數公式"]},"variant":{"family_id":"qf-mod41-totalvar-full-identity","seed":202611104060,"parameters":{"masses":[[1,19],[2,19],[16,19],[0,1]],"values":[9,10,12,108],"partition":[[0,1],[2,3]],"domain":"Finite_partition_total_variance","operation":"totalvar-full-identity","semantic_template":"qf-mod41-totalvar-full-identity/{\"masses\":[[1,19],[2,19],[16,19],[0,1]],\"partition\":[[0,1],[2,3]],\"values\":[9,10,12,108]}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_or_symbolic_model","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"候選須主端重算；不構成人工審定、sampled orbit-stabilizer、sampled MVT、reverse compactness、zero-mass division、underspecified recurrence、incomplete divisor inversion、bounded-search PDA rejection、Lean或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-20261110-r04-law-of-total-variance-0061","batch_id":"batch-20261014-advance-20261110-r04-law-of-total-variance-foundations","language":"zh-Hant","source_mko_ids":["mko-law-of-total-variance"],"title_zh":"全變異數公式","stem_zh":"同一有限law與完整disjoint partition生成的G。操作=totalvar-full-identity；資料={\"masses\":[[1,20],[2,20],[17,20],[0,1]],\"values\":[10,11,13,109],\"partition\":[[0,1],[2,3]]}。請依 exact_ordered_tuple_declared_by_interface 欄序回答。","answer":{"kind":"expression","value":"(291/400, 1/30, 833/1200, 291/400, 是)","explanation_zh":"Wave6第四層核對=(291/400, 1/30, 833/1200, 291/400, 是)；依完整明示資料獨立重算；within與between terms使用同一law及同一cells且兩項皆不可省略；zero-mass cell禁止conditional division且外層加權貢獻為0；不要求partition events independent。"},"difficulty":{"band":"undergraduate_core","level":2,"skills":["全變異數公式"]},"variant":{"family_id":"qf-mod41-totalvar-full-identity","seed":202611104061,"parameters":{"masses":[[1,20],[2,20],[17,20],[0,1]],"values":[10,11,13,109],"partition":[[0,1],[2,3]],"domain":"Finite_partition_total_variance","operation":"totalvar-full-identity","semantic_template":"qf-mod41-totalvar-full-identity/{\"masses\":[[1,20],[2,20],[17,20],[0,1]],\"partition\":[[0,1],[2,3]],\"values\":[10,11,13,109]}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_or_symbolic_model","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"候選須主端重算；不構成人工審定、sampled orbit-stabilizer、sampled MVT、reverse compactness、zero-mass division、underspecified recurrence、incomplete divisor inversion、bounded-search PDA rejection、Lean或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-20261110-r04-law-of-total-variance-0062","batch_id":"batch-20261014-advance-20261110-r04-law-of-total-variance-foundations","language":"zh-Hant","source_mko_ids":["mko-law-of-total-variance"],"title_zh":"全變異數公式","stem_zh":"同一有限law與完整disjoint partition生成的G。操作=totalvar-full-identity；資料={\"masses\":[[1,21],[2,21],[18,21],[0,1]],\"values\":[11,12,14,110],\"partition\":[[0,1],[2,3]]}。請依 exact_ordered_tuple_declared_by_interface 欄序回答。","answer":{"kind":"expression","value":"(44/63, 2/63, 2/3, 44/63, 是)","explanation_zh":"Wave6第四層核對=(44/63, 2/63, 2/3, 44/63, 是)；依完整明示資料獨立重算；within與between terms使用同一law及同一cells且兩項皆不可省略；zero-mass cell禁止conditional division且外層加權貢獻為0；不要求partition events independent。"},"difficulty":{"band":"undergraduate_core","level":2,"skills":["全變異數公式"]},"variant":{"family_id":"qf-mod41-totalvar-full-identity","seed":202611104062,"parameters":{"masses":[[1,21],[2,21],[18,21],[0,1]],"values":[11,12,14,110],"partition":[[0,1],[2,3]],"domain":"Finite_partition_total_variance","operation":"totalvar-full-identity","semantic_template":"qf-mod41-totalvar-full-identity/{\"masses\":[[1,21],[2,21],[18,21],[0,1]],\"partition\":[[0,1],[2,3]],\"values\":[11,12,14,110]}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_or_symbolic_model","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"候選須主端重算；不構成人工審定、sampled orbit-stabilizer、sampled MVT、reverse compactness、zero-mass division、underspecified recurrence、incomplete divisor inversion、bounded-search PDA rejection、Lean或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-20261110-r04-law-of-total-variance-0063","batch_id":"batch-20261014-advance-20261110-r04-law-of-total-variance-foundations","language":"zh-Hant","source_mko_ids":["mko-law-of-total-variance"],"title_zh":"全變異數公式","stem_zh":"同一有限law與完整disjoint partition生成的G。操作=totalvar-full-identity；資料={\"masses\":[[1,22],[2,22],[19,22],[0,1]],\"values\":[12,13,15,111],\"partition\":[[0,1],[2,3]]}。請依 exact_ordered_tuple_declared_by_interface 欄序回答。","answer":{"kind":"expression","value":"(325/484, 1/33, 931/1452, 325/484, 是)","explanation_zh":"Wave6第四層核對=(325/484, 1/33, 931/1452, 325/484, 是)；依完整明示資料獨立重算；within與between terms使用同一law及同一cells且兩項皆不可省略；zero-mass cell禁止conditional division且外層加權貢獻為0；不要求partition events independent。"},"difficulty":{"band":"undergraduate_core","level":2,"skills":["全變異數公式"]},"variant":{"family_id":"qf-mod41-totalvar-full-identity","seed":202611104063,"parameters":{"masses":[[1,22],[2,22],[19,22],[0,1]],"values":[12,13,15,111],"partition":[[0,1],[2,3]],"domain":"Finite_partition_total_variance","operation":"totalvar-full-identity","semantic_template":"qf-mod41-totalvar-full-identity/{\"masses\":[[1,22],[2,22],[19,22],[0,1]],\"partition\":[[0,1],[2,3]],\"values\":[12,13,15,111]}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_or_symbolic_model","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"候選須主端重算；不構成人工審定、sampled orbit-stabilizer、sampled MVT、reverse compactness、zero-mass division、underspecified recurrence、incomplete divisor inversion、bounded-search PDA rejection、Lean或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-20261110-r04-law-of-total-variance-0064","batch_id":"batch-20261014-advance-20261110-r04-law-of-total-variance-foundations","language":"zh-Hant","source_mko_ids":["mko-law-of-total-variance"],"title_zh":"全變異數公式","stem_zh":"同一有限law與完整disjoint partition生成的G。操作=totalvar-full-identity；資料={\"masses\":[[1,23],[2,23],[20,23],[0,1]],\"values\":[13,14,16,112],\"partition\":[[0,1],[2,3]]}。請依 exact_ordered_tuple_declared_by_interface 欄序回答。","answer":{"kind":"expression","value":"(342/529, 2/69, 980/1587, 342/529, 是)","explanation_zh":"Wave6第四層核對=(342/529, 2/69, 980/1587, 342/529, 是)；依完整明示資料獨立重算；within與between terms使用同一law及同一cells且兩項皆不可省略；zero-mass cell禁止conditional division且外層加權貢獻為0；不要求partition events independent。"},"difficulty":{"band":"undergraduate_core","level":2,"skills":["全變異數公式"]},"variant":{"family_id":"qf-mod41-totalvar-full-identity","seed":202611104064,"parameters":{"masses":[[1,23],[2,23],[20,23],[0,1]],"values":[13,14,16,112],"partition":[[0,1],[2,3]],"domain":"Finite_partition_total_variance","operation":"totalvar-full-identity","semantic_template":"qf-mod41-totalvar-full-identity/{\"masses\":[[1,23],[2,23],[20,23],[0,1]],\"partition\":[[0,1],[2,3]],\"values\":[13,14,16,112]}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_or_symbolic_model","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"候選須主端重算；不構成人工審定、sampled orbit-stabilizer、sampled MVT、reverse compactness、zero-mass division、underspecified recurrence、incomplete divisor inversion、bounded-search PDA rejection、Lean或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-20261110-r04-law-of-total-variance-0065","batch_id":"batch-20261014-advance-20261110-r04-law-of-total-variance-foundations","language":"zh-Hant","source_mko_ids":["mko-law-of-total-variance"],"title_zh":"全變異數公式","stem_zh":"同一有限law與完整disjoint partition生成的G。操作=totalvar-full-identity；資料={\"masses\":[[1,24],[2,24],[21,24],[0,1]],\"values\":[14,15,17,113],\"partition\":[[0,1],[2,3]]}。請依 exact_ordered_tuple_declared_by_interface 欄序回答。","answer":{"kind":"expression","value":"(359/576, 1/36, 343/576, 359/576, 是)","explanation_zh":"Wave6第四層核對=(359/576, 1/36, 343/576, 359/576, 是)；依完整明示資料獨立重算；within與between terms使用同一law及同一cells且兩項皆不可省略；zero-mass cell禁止conditional division且外層加權貢獻為0；不要求partition events independent。"},"difficulty":{"band":"undergraduate_core","level":2,"skills":["全變異數公式"]},"variant":{"family_id":"qf-mod41-totalvar-full-identity","seed":202611104065,"parameters":{"masses":[[1,24],[2,24],[21,24],[0,1]],"values":[14,15,17,113],"partition":[[0,1],[2,3]],"domain":"Finite_partition_total_variance","operation":"totalvar-full-identity","semantic_template":"qf-mod41-totalvar-full-identity/{\"masses\":[[1,24],[2,24],[21,24],[0,1]],\"partition\":[[0,1],[2,3]],\"values\":[14,15,17,113]}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_or_symbolic_model","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"候選須主端重算；不構成人工審定、sampled orbit-stabilizer、sampled MVT、reverse compactness、zero-mass division、underspecified recurrence、incomplete divisor inversion、bounded-search PDA rejection、Lean或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-20261110-r04-law-of-total-variance-0066","batch_id":"batch-20261014-advance-20261110-r04-law-of-total-variance-foundations","language":"zh-Hant","source_mko_ids":["mko-law-of-total-variance"],"title_zh":"全變異數公式","stem_zh":"同一有限law與完整disjoint partition生成的G。操作=totalvar-full-identity；資料={\"masses\":[[1,25],[2,25],[22,25],[0,1]],\"values\":[15,16,18,114],\"partition\":[[0,1],[2,3]]}。請依 exact_ordered_tuple_declared_by_interface 欄序回答。","answer":{"kind":"expression","value":"(376/625, 2/75, 1078/1875, 376/625, 是)","explanation_zh":"Wave6第四層核對=(376/625, 2/75, 1078/1875, 376/625, 是)；依完整明示資料獨立重算；within與between terms使用同一law及同一cells且兩項皆不可省略；zero-mass cell禁止conditional division且外層加權貢獻為0；不要求partition events independent。"},"difficulty":{"band":"undergraduate_core","level":2,"skills":["全變異數公式"]},"variant":{"family_id":"qf-mod41-totalvar-full-identity","seed":202611104066,"parameters":{"masses":[[1,25],[2,25],[22,25],[0,1]],"values":[15,16,18,114],"partition":[[0,1],[2,3]],"domain":"Finite_partition_total_variance","operation":"totalvar-full-identity","semantic_template":"qf-mod41-totalvar-full-identity/{\"masses\":[[1,25],[2,25],[22,25],[0,1]],\"partition\":[[0,1],[2,3]],\"values\":[15,16,18,114]}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_or_symbolic_model","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"候選須主端重算；不構成人工審定、sampled orbit-stabilizer、sampled MVT、reverse compactness、zero-mass division、underspecified recurrence、incomplete divisor inversion、bounded-search PDA rejection、Lean或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-20261110-r04-law-of-total-variance-0067","batch_id":"batch-20261014-advance-20261110-r04-law-of-total-variance-foundations","language":"zh-Hant","source_mko_ids":["mko-law-of-total-variance"],"title_zh":"全變異數公式","stem_zh":"同一有限law與完整disjoint partition生成的G。操作=totalvar-full-identity；資料={\"masses\":[[1,26],[2,26],[23,26],[0,1]],\"values\":[16,17,19,115],\"partition\":[[0,1],[2,3]]}。請依 exact_ordered_tuple_declared_by_interface 欄序回答。","answer":{"kind":"expression","value":"(393/676, 1/39, 1127/2028, 393/676, 是)","explanation_zh":"Wave6第四層核對=(393/676, 1/39, 1127/2028, 393/676, 是)；依完整明示資料獨立重算；within與between terms使用同一law及同一cells且兩項皆不可省略；zero-mass cell禁止conditional division且外層加權貢獻為0；不要求partition events independent。"},"difficulty":{"band":"undergraduate_core","level":2,"skills":["全變異數公式"]},"variant":{"family_id":"qf-mod41-totalvar-full-identity","seed":202611104067,"parameters":{"masses":[[1,26],[2,26],[23,26],[0,1]],"values":[16,17,19,115],"partition":[[0,1],[2,3]],"domain":"Finite_partition_total_variance","operation":"totalvar-full-identity","semantic_template":"qf-mod41-totalvar-full-identity/{\"masses\":[[1,26],[2,26],[23,26],[0,1]],\"partition\":[[0,1],[2,3]],\"values\":[16,17,19,115]}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_or_symbolic_model","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"候選須主端重算；不構成人工審定、sampled orbit-stabilizer、sampled MVT、reverse compactness、zero-mass division、underspecified recurrence、incomplete divisor inversion、bounded-search PDA rejection、Lean或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-20261110-r04-law-of-total-variance-0068","batch_id":"batch-20261014-advance-20261110-r04-law-of-total-variance-foundations","language":"zh-Hant","source_mko_ids":["mko-law-of-total-variance"],"title_zh":"全變異數公式","stem_zh":"同一有限law與完整disjoint partition生成的G。操作=totalvar-full-identity；資料={\"masses\":[[1,27],[2,27],[24,27],[0,1]],\"values\":[17,18,20,116],\"partition\":[[0,1],[2,3]]}。請依 exact_ordered_tuple_declared_by_interface 欄序回答。","answer":{"kind":"expression","value":"(410/729, 2/81, 392/729, 410/729, 是)","explanation_zh":"Wave6第四層核對=(410/729, 2/81, 392/729, 410/729, 是)；依完整明示資料獨立重算；within與between terms使用同一law及同一cells且兩項皆不可省略；zero-mass cell禁止conditional division且外層加權貢獻為0；不要求partition events independent。"},"difficulty":{"band":"undergraduate_core","level":3,"skills":["全變異數公式"]},"variant":{"family_id":"qf-mod41-totalvar-full-identity","seed":202611104068,"parameters":{"masses":[[1,27],[2,27],[24,27],[0,1]],"values":[17,18,20,116],"partition":[[0,1],[2,3]],"domain":"Finite_partition_total_variance","operation":"totalvar-full-identity","semantic_template":"qf-mod41-totalvar-full-identity/{\"masses\":[[1,27],[2,27],[24,27],[0,1]],\"partition\":[[0,1],[2,3]],\"values\":[17,18,20,116]}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_or_symbolic_model","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"候選須主端重算；不構成人工審定、sampled orbit-stabilizer、sampled MVT、reverse compactness、zero-mass division、underspecified recurrence、incomplete divisor inversion、bounded-search PDA rejection、Lean或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-20261110-r04-law-of-total-variance-0069","batch_id":"batch-20261014-advance-20261110-r04-law-of-total-variance-foundations","language":"zh-Hant","source_mko_ids":["mko-law-of-total-variance"],"title_zh":"全變異數公式","stem_zh":"同一有限law與完整disjoint partition生成的G。操作=totalvar-full-identity；資料={\"masses\":[[1,28],[2,28],[25,28],[0,1]],\"values\":[18,19,21,117],\"partition\":[[0,1],[2,3]]}。請依 exact_ordered_tuple_declared_by_interface 欄序回答。","answer":{"kind":"expression","value":"(61/112, 1/42, 25/48, 61/112, 是)","explanation_zh":"Wave6第四層核對=(61/112, 1/42, 25/48, 61/112, 是)；依完整明示資料獨立重算；within與between terms使用同一law及同一cells且兩項皆不可省略；zero-mass cell禁止conditional division且外層加權貢獻為0；不要求partition events independent。"},"difficulty":{"band":"undergraduate_core","level":3,"skills":["全變異數公式"]},"variant":{"family_id":"qf-mod41-totalvar-full-identity","seed":202611104069,"parameters":{"masses":[[1,28],[2,28],[25,28],[0,1]],"values":[18,19,21,117],"partition":[[0,1],[2,3]],"domain":"Finite_partition_total_variance","operation":"totalvar-full-identity","semantic_template":"qf-mod41-totalvar-full-identity/{\"masses\":[[1,28],[2,28],[25,28],[0,1]],\"partition\":[[0,1],[2,3]],\"values\":[18,19,21,117]}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_or_symbolic_model","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"候選須主端重算；不構成人工審定、sampled orbit-stabilizer、sampled MVT、reverse compactness、zero-mass division、underspecified recurrence、incomplete divisor inversion、bounded-search PDA rejection、Lean或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-20261110-r04-law-of-total-variance-0070","batch_id":"batch-20261014-advance-20261110-r04-law-of-total-variance-foundations","language":"zh-Hant","source_mko_ids":["mko-law-of-total-variance"],"title_zh":"全變異數公式","stem_zh":"同一有限law與完整disjoint partition生成的G。操作=totalvar-full-identity；資料={\"masses\":[[1,29],[2,29],[26,29],[0,1]],\"values\":[19,20,22,118],\"partition\":[[0,1],[2,3]]}。請依 exact_ordered_tuple_declared_by_interface 欄序回答。","answer":{"kind":"expression","value":"(444/841, 2/87, 1274/2523, 444/841, 是)","explanation_zh":"Wave6第四層核對=(444/841, 2/87, 1274/2523, 444/841, 是)；依完整明示資料獨立重算；within與between terms使用同一law及同一cells且兩項皆不可省略；zero-mass cell禁止conditional division且外層加權貢獻為0；不要求partition events independent。"},"difficulty":{"band":"undergraduate_core","level":3,"skills":["全變異數公式"]},"variant":{"family_id":"qf-mod41-totalvar-full-identity","seed":202611104070,"parameters":{"masses":[[1,29],[2,29],[26,29],[0,1]],"values":[19,20,22,118],"partition":[[0,1],[2,3]],"domain":"Finite_partition_total_variance","operation":"totalvar-full-identity","semantic_template":"qf-mod41-totalvar-full-identity/{\"masses\":[[1,29],[2,29],[26,29],[0,1]],\"partition\":[[0,1],[2,3]],\"values\":[19,20,22,118]}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_or_symbolic_model","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"候選須主端重算；不構成人工審定、sampled orbit-stabilizer、sampled MVT、reverse compactness、zero-mass division、underspecified recurrence、incomplete divisor inversion、bounded-search PDA rejection、Lean或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-20261110-r04-law-of-total-variance-0071","batch_id":"batch-20261014-advance-20261110-r04-law-of-total-variance-foundations","language":"zh-Hant","source_mko_ids":["mko-law-of-total-variance"],"title_zh":"全變異數公式","stem_zh":"同一有限law與完整disjoint partition生成的G。操作=totalvar-full-identity；資料={\"masses\":[[1,30],[2,30],[27,30],[0,1]],\"values\":[20,21,23,119],\"partition\":[[0,1],[2,3]]}。請依 exact_ordered_tuple_declared_by_interface 欄序回答。","answer":{"kind":"expression","value":"(461/900, 1/45, 49/100, 461/900, 是)","explanation_zh":"Wave6第四層核對=(461/900, 1/45, 49/100, 461/900, 是)；依完整明示資料獨立重算；within與between terms使用同一law及同一cells且兩項皆不可省略；zero-mass cell禁止conditional division且外層加權貢獻為0；不要求partition events independent。"},"difficulty":{"band":"undergraduate_core","level":3,"skills":["全變異數公式"]},"variant":{"family_id":"qf-mod41-totalvar-full-identity","seed":202611104071,"parameters":{"masses":[[1,30],[2,30],[27,30],[0,1]],"values":[20,21,23,119],"partition":[[0,1],[2,3]],"domain":"Finite_partition_total_variance","operation":"totalvar-full-identity","semantic_template":"qf-mod41-totalvar-full-identity/{\"masses\":[[1,30],[2,30],[27,30],[0,1]],\"partition\":[[0,1],[2,3]],\"values\":[20,21,23,119]}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_or_symbolic_model","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"候選須主端重算；不構成人工審定、sampled orbit-stabilizer、sampled MVT、reverse compactness、zero-mass division、underspecified recurrence、incomplete divisor inversion、bounded-search PDA rejection、Lean或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-20261110-r04-law-of-total-variance-0072","batch_id":"batch-20261014-advance-20261110-r04-law-of-total-variance-foundations","language":"zh-Hant","source_mko_ids":["mko-law-of-total-variance"],"title_zh":"全變異數公式","stem_zh":"同一有限law與完整disjoint partition生成的G。操作=totalvar-full-identity；資料={\"masses\":[[1,31],[2,31],[28,31],[0,1]],\"values\":[21,22,24,120],\"partition\":[[0,1],[2,3]]}。請依 exact_ordered_tuple_declared_by_interface 欄序回答。","answer":{"kind":"expression","value":"(478/961, 2/93, 1372/2883, 478/961, 是)","explanation_zh":"Wave6第四層核對=(478/961, 2/93, 1372/2883, 478/961, 是)；依完整明示資料獨立重算；within與between terms使用同一law及同一cells且兩項皆不可省略；zero-mass cell禁止conditional division且外層加權貢獻為0；不要求partition events independent。"},"difficulty":{"band":"undergraduate_core","level":3,"skills":["全變異數公式"]},"variant":{"family_id":"qf-mod41-totalvar-full-identity","seed":202611104072,"parameters":{"masses":[[1,31],[2,31],[28,31],[0,1]],"values":[21,22,24,120],"partition":[[0,1],[2,3]],"domain":"Finite_partition_total_variance","operation":"totalvar-full-identity","semantic_template":"qf-mod41-totalvar-full-identity/{\"masses\":[[1,31],[2,31],[28,31],[0,1]],\"partition\":[[0,1],[2,3]],\"values\":[21,22,24,120]}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_or_symbolic_model","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"候選須主端重算；不構成人工審定、sampled orbit-stabilizer、sampled MVT、reverse compactness、zero-mass division、underspecified recurrence、incomplete divisor inversion、bounded-search PDA rejection、Lean或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-20261110-r04-law-of-total-variance-0073","batch_id":"batch-20261014-advance-20261110-r04-law-of-total-variance-foundations","language":"zh-Hant","source_mko_ids":["mko-law-of-total-variance"],"title_zh":"全變異數公式","stem_zh":"同一有限law與完整disjoint partition生成的G。操作=totalvar-full-identity；資料={\"masses\":[[1,32],[2,32],[29,32],[0,1]],\"values\":[22,23,25,121],\"partition\":[[0,1],[2,3]]}。請依 exact_ordered_tuple_declared_by_interface 欄序回答。","answer":{"kind":"expression","value":"(495/1024, 1/48, 1421/3072, 495/1024, 是)","explanation_zh":"Wave6第四層核對=(495/1024, 1/48, 1421/3072, 495/1024, 是)；依完整明示資料獨立重算；within與between terms使用同一law及同一cells且兩項皆不可省略；zero-mass cell禁止conditional division且外層加權貢獻為0；不要求partition events independent。"},"difficulty":{"band":"undergraduate_core","level":3,"skills":["全變異數公式"]},"variant":{"family_id":"qf-mod41-totalvar-full-identity","seed":202611104073,"parameters":{"masses":[[1,32],[2,32],[29,32],[0,1]],"values":[22,23,25,121],"partition":[[0,1],[2,3]],"domain":"Finite_partition_total_variance","operation":"totalvar-full-identity","semantic_template":"qf-mod41-totalvar-full-identity/{\"masses\":[[1,32],[2,32],[29,32],[0,1]],\"partition\":[[0,1],[2,3]],\"values\":[22,23,25,121]}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_or_symbolic_model","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"候選須主端重算；不構成人工審定、sampled orbit-stabilizer、sampled MVT、reverse compactness、zero-mass division、underspecified recurrence、incomplete divisor inversion、bounded-search PDA rejection、Lean或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-20261110-r04-law-of-total-variance-0074","batch_id":"batch-20261014-advance-20261110-r04-law-of-total-variance-foundations","language":"zh-Hant","source_mko_ids":["mko-law-of-total-variance"],"title_zh":"全變異數公式","stem_zh":"同一有限law與完整disjoint partition生成的G。操作=totalvar-full-identity；資料={\"masses\":[[1,33],[2,33],[30,33],[0,1]],\"values\":[23,24,26,122],\"partition\":[[0,1],[2,3]]}。請依 exact_ordered_tuple_declared_by_interface 欄序回答。","answer":{"kind":"expression","value":"(512/1089, 2/99, 490/1089, 512/1089, 是)","explanation_zh":"Wave6第四層核對=(512/1089, 2/99, 490/1089, 512/1089, 是)；依完整明示資料獨立重算；within與between terms使用同一law及同一cells且兩項皆不可省略；zero-mass cell禁止conditional division且外層加權貢獻為0；不要求partition events independent。"},"difficulty":{"band":"undergraduate_core","level":3,"skills":["全變異數公式"]},"variant":{"family_id":"qf-mod41-totalvar-full-identity","seed":202611104074,"parameters":{"masses":[[1,33],[2,33],[30,33],[0,1]],"values":[23,24,26,122],"partition":[[0,1],[2,3]],"domain":"Finite_partition_total_variance","operation":"totalvar-full-identity","semantic_template":"qf-mod41-totalvar-full-identity/{\"masses\":[[1,33],[2,33],[30,33],[0,1]],\"partition\":[[0,1],[2,3]],\"values\":[23,24,26,122]}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_or_symbolic_model","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"候選須主端重算；不構成人工審定、sampled orbit-stabilizer、sampled MVT、reverse compactness、zero-mass division、underspecified recurrence、incomplete divisor inversion、bounded-search PDA rejection、Lean或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-20261110-r04-law-of-total-variance-0075","batch_id":"batch-20261014-advance-20261110-r04-law-of-total-variance-foundations","language":"zh-Hant","source_mko_ids":["mko-law-of-total-variance"],"title_zh":"全變異數公式","stem_zh":"同一有限law與完整disjoint partition生成的G。操作=totalvar-full-identity；資料={\"masses\":[[1,34],[2,34],[31,34],[0,1]],\"values\":[24,25,27,123],\"partition\":[[0,1],[2,3]]}。請依 exact_ordered_tuple_declared_by_interface 欄序回答。","answer":{"kind":"expression","value":"(529/1156, 1/51, 1519/3468, 529/1156, 是)","explanation_zh":"Wave6第四層核對=(529/1156, 1/51, 1519/3468, 529/1156, 是)；依完整明示資料獨立重算；within與between terms使用同一law及同一cells且兩項皆不可省略；zero-mass cell禁止conditional division且外層加權貢獻為0；不要求partition events independent。"},"difficulty":{"band":"undergraduate_core","level":3,"skills":["全變異數公式"]},"variant":{"family_id":"qf-mod41-totalvar-full-identity","seed":202611104075,"parameters":{"masses":[[1,34],[2,34],[31,34],[0,1]],"values":[24,25,27,123],"partition":[[0,1],[2,3]],"domain":"Finite_partition_total_variance","operation":"totalvar-full-identity","semantic_template":"qf-mod41-totalvar-full-identity/{\"masses\":[[1,34],[2,34],[31,34],[0,1]],\"partition\":[[0,1],[2,3]],\"values\":[24,25,27,123]}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_or_symbolic_model","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"候選須主端重算；不構成人工審定、sampled orbit-stabilizer、sampled MVT、reverse compactness、zero-mass division、underspecified recurrence、incomplete divisor inversion、bounded-search PDA rejection、Lean或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-20261110-r04-law-of-total-variance-0076","batch_id":"batch-20261014-advance-20261110-r04-law-of-total-variance-foundations","language":"zh-Hant","source_mko_ids":["mko-law-of-total-variance"],"title_zh":"全變異數公式","stem_zh":"同一有限law與完整disjoint partition生成的G。操作=totalvar-zero-mass-boundary；資料={\"masses\":[[1,10],[2,10],[7,10],[0,1]],\"values\":[0,1,3,99],\"partition\":[[0,1,2],[3]]}。請依 exact_ordered_tuple_declared_by_interface 欄序回答。","answer":{"kind":"expression","value":"([[0, [0, 1, 2], 1, 23/10, 121/100], [1, [3], 0, null, null]], 121/100, 0, 121/100, 是, 否, zero_mass_cell_not_divided_and_outer_weighted_contribution_zero)","explanation_zh":"Wave6第四層核對=([[0, [0, 1, 2], 1, 23/10, 121/100], [1, [3], 0, null, null]], 121/100, 0, 121/100, 是, 否, zero_mass_cell_not_divided_and_outer_weighted_contribution_zero)；依完整明示資料獨立重算；within與between terms使用同一law及同一cells且兩項皆不可省略；zero-mass cell禁止conditional division且外層加權貢獻為0；不要求partition events independent。"},"difficulty":{"band":"undergraduate_core","level":1,"skills":["全變異數公式"]},"variant":{"family_id":"qf-mod41-totalvar-zero-mass-boundary","seed":202611104076,"parameters":{"masses":[[1,10],[2,10],[7,10],[0,1]],"values":[0,1,3,99],"partition":[[0,1,2],[3]],"domain":"Finite_partition_total_variance","operation":"totalvar-zero-mass-boundary","semantic_template":"qf-mod41-totalvar-zero-mass-boundary/{\"masses\":[[1,10],[2,10],[7,10],[0,1]],\"partition\":[[0,1,2],[3]],\"values\":[0,1,3,99]}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_or_symbolic_model","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"候選須主端重算；不構成人工審定、sampled orbit-stabilizer、sampled MVT、reverse compactness、zero-mass division、underspecified recurrence、incomplete divisor inversion、bounded-search PDA rejection、Lean或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-20261110-r04-law-of-total-variance-0077","batch_id":"batch-20261014-advance-20261110-r04-law-of-total-variance-foundations","language":"zh-Hant","source_mko_ids":["mko-law-of-total-variance"],"title_zh":"全變異數公式","stem_zh":"同一有限law與完整disjoint partition生成的G。操作=totalvar-zero-mass-boundary；資料={\"masses\":[[1,11],[2,11],[8,11],[0,1]],\"values\":[1,2,4,100],\"partition\":[[0,1,2],[3]]}。請依 exact_ordered_tuple_declared_by_interface 欄序回答。","answer":{"kind":"expression","value":"([[0, [0, 1, 2], 1, 37/11, 138/121], [1, [3], 0, null, null]], 138/121, 0, 138/121, 是, 否, zero_mass_cell_not_divided_and_outer_weighted_contribution_zero)","explanation_zh":"Wave6第四層核對=([[0, [0, 1, 2], 1, 37/11, 138/121], [1, [3], 0, null, null]], 138/121, 0, 138/121, 是, 否, zero_mass_cell_not_divided_and_outer_weighted_contribution_zero)；依完整明示資料獨立重算；within與between terms使用同一law及同一cells且兩項皆不可省略；zero-mass cell禁止conditional division且外層加權貢獻為0；不要求partition events independent。"},"difficulty":{"band":"undergraduate_core","level":1,"skills":["全變異數公式"]},"variant":{"family_id":"qf-mod41-totalvar-zero-mass-boundary","seed":202611104077,"parameters":{"masses":[[1,11],[2,11],[8,11],[0,1]],"values":[1,2,4,100],"partition":[[0,1,2],[3]],"domain":"Finite_partition_total_variance","operation":"totalvar-zero-mass-boundary","semantic_template":"qf-mod41-totalvar-zero-mass-boundary/{\"masses\":[[1,11],[2,11],[8,11],[0,1]],\"partition\":[[0,1,2],[3]],\"values\":[1,2,4,100]}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_or_symbolic_model","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"候選須主端重算；不構成人工審定、sampled orbit-stabilizer、sampled MVT、reverse compactness、zero-mass division、underspecified recurrence、incomplete divisor inversion、bounded-search PDA rejection、Lean或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-20261110-r04-law-of-total-variance-0078","batch_id":"batch-20261014-advance-20261110-r04-law-of-total-variance-foundations","language":"zh-Hant","source_mko_ids":["mko-law-of-total-variance"],"title_zh":"全變異數公式","stem_zh":"同一有限law與完整disjoint partition生成的G。操作=totalvar-zero-mass-boundary；資料={\"masses\":[[1,12],[2,12],[9,12],[0,1]],\"values\":[2,3,5,101],\"partition\":[[0,1,2],[3]]}。請依 exact_ordered_tuple_declared_by_interface 欄序回答。","answer":{"kind":"expression","value":"([[0, [0, 1, 2], 1, 53/12, 155/144], [1, [3], 0, null, null]], 155/144, 0, 155/144, 是, 否, zero_mass_cell_not_divided_and_outer_weighted_contribution_zero)","explanation_zh":"Wave6第四層核對=([[0, [0, 1, 2], 1, 53/12, 155/144], [1, [3], 0, null, null]], 155/144, 0, 155/144, 是, 否, zero_mass_cell_not_divided_and_outer_weighted_contribution_zero)；依完整明示資料獨立重算；within與between terms使用同一law及同一cells且兩項皆不可省略；zero-mass cell禁止conditional division且外層加權貢獻為0；不要求partition events independent。"},"difficulty":{"band":"undergraduate_core","level":1,"skills":["全變異數公式"]},"variant":{"family_id":"qf-mod41-totalvar-zero-mass-boundary","seed":202611104078,"parameters":{"masses":[[1,12],[2,12],[9,12],[0,1]],"values":[2,3,5,101],"partition":[[0,1,2],[3]],"domain":"Finite_partition_total_variance","operation":"totalvar-zero-mass-boundary","semantic_template":"qf-mod41-totalvar-zero-mass-boundary/{\"masses\":[[1,12],[2,12],[9,12],[0,1]],\"partition\":[[0,1,2],[3]],\"values\":[2,3,5,101]}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_or_symbolic_model","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"候選須主端重算；不構成人工審定、sampled orbit-stabilizer、sampled MVT、reverse compactness、zero-mass division、underspecified recurrence、incomplete divisor inversion、bounded-search PDA rejection、Lean或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-20261110-r04-law-of-total-variance-0079","batch_id":"batch-20261014-advance-20261110-r04-law-of-total-variance-foundations","language":"zh-Hant","source_mko_ids":["mko-law-of-total-variance"],"title_zh":"全變異數公式","stem_zh":"同一有限law與完整disjoint partition生成的G。操作=totalvar-zero-mass-boundary；資料={\"masses\":[[1,13],[2,13],[10,13],[0,1]],\"values\":[3,4,6,102],\"partition\":[[0,1,2],[3]]}。請依 exact_ordered_tuple_declared_by_interface 欄序回答。","answer":{"kind":"expression","value":"([[0, [0, 1, 2], 1, 71/13, 172/169], [1, [3], 0, null, null]], 172/169, 0, 172/169, 是, 否, zero_mass_cell_not_divided_and_outer_weighted_contribution_zero)","explanation_zh":"Wave6第四層核對=([[0, [0, 1, 2], 1, 71/13, 172/169], [1, [3], 0, null, null]], 172/169, 0, 172/169, 是, 否, zero_mass_cell_not_divided_and_outer_weighted_contribution_zero)；依完整明示資料獨立重算；within與between terms使用同一law及同一cells且兩項皆不可省略；zero-mass cell禁止conditional division且外層加權貢獻為0；不要求partition events independent。"},"difficulty":{"band":"undergraduate_core","level":1,"skills":["全變異數公式"]},"variant":{"family_id":"qf-mod41-totalvar-zero-mass-boundary","seed":202611104079,"parameters":{"masses":[[1,13],[2,13],[10,13],[0,1]],"values":[3,4,6,102],"partition":[[0,1,2],[3]],"domain":"Finite_partition_total_variance","operation":"totalvar-zero-mass-boundary","semantic_template":"qf-mod41-totalvar-zero-mass-boundary/{\"masses\":[[1,13],[2,13],[10,13],[0,1]],\"partition\":[[0,1,2],[3]],\"values\":[3,4,6,102]}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_or_symbolic_model","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"候選須主端重算；不構成人工審定、sampled orbit-stabilizer、sampled MVT、reverse compactness、zero-mass division、underspecified recurrence、incomplete divisor inversion、bounded-search PDA rejection、Lean或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-20261110-r04-law-of-total-variance-0080","batch_id":"batch-20261014-advance-20261110-r04-law-of-total-variance-foundations","language":"zh-Hant","source_mko_ids":["mko-law-of-total-variance"],"title_zh":"全變異數公式","stem_zh":"同一有限law與完整disjoint partition生成的G。操作=totalvar-zero-mass-boundary；資料={\"masses\":[[1,14],[2,14],[11,14],[0,1]],\"values\":[4,5,7,103],\"partition\":[[0,1,2],[3]]}。請依 exact_ordered_tuple_declared_by_interface 欄序回答。","answer":{"kind":"expression","value":"([[0, [0, 1, 2], 1, 13/2, 27/28], [1, [3], 0, null, null]], 27/28, 0, 27/28, 是, 否, zero_mass_cell_not_divided_and_outer_weighted_contribution_zero)","explanation_zh":"Wave6第四層核對=([[0, [0, 1, 2], 1, 13/2, 27/28], [1, [3], 0, null, null]], 27/28, 0, 27/28, 是, 否, zero_mass_cell_not_divided_and_outer_weighted_contribution_zero)；依完整明示資料獨立重算；within與between terms使用同一law及同一cells且兩項皆不可省略；zero-mass cell禁止conditional division且外層加權貢獻為0；不要求partition events independent。"},"difficulty":{"band":"undergraduate_core","level":1,"skills":["全變異數公式"]},"variant":{"family_id":"qf-mod41-totalvar-zero-mass-boundary","seed":202611104080,"parameters":{"masses":[[1,14],[2,14],[11,14],[0,1]],"values":[4,5,7,103],"partition":[[0,1,2],[3]],"domain":"Finite_partition_total_variance","operation":"totalvar-zero-mass-boundary","semantic_template":"qf-mod41-totalvar-zero-mass-boundary/{\"masses\":[[1,14],[2,14],[11,14],[0,1]],\"partition\":[[0,1,2],[3]],\"values\":[4,5,7,103]}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_or_symbolic_model","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"候選須主端重算；不構成人工審定、sampled orbit-stabilizer、sampled MVT、reverse compactness、zero-mass division、underspecified recurrence、incomplete divisor inversion、bounded-search PDA rejection、Lean或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-20261110-r04-law-of-total-variance-0081","batch_id":"batch-20261014-advance-20261110-r04-law-of-total-variance-foundations","language":"zh-Hant","source_mko_ids":["mko-law-of-total-variance"],"title_zh":"全變異數公式","stem_zh":"同一有限law與完整disjoint partition生成的G。操作=totalvar-zero-mass-boundary；資料={\"masses\":[[1,15],[2,15],[12,15],[0,1]],\"values\":[5,6,8,104],\"partition\":[[0,1,2],[3]]}。請依 exact_ordered_tuple_declared_by_interface 欄序回答。","answer":{"kind":"expression","value":"([[0, [0, 1, 2], 1, 113/15, 206/225], [1, [3], 0, null, null]], 206/225, 0, 206/225, 是, 否, zero_mass_cell_not_divided_and_outer_weighted_contribution_zero)","explanation_zh":"Wave6第四層核對=([[0, [0, 1, 2], 1, 113/15, 206/225], [1, [3], 0, null, null]], 206/225, 0, 206/225, 是, 否, zero_mass_cell_not_divided_and_outer_weighted_contribution_zero)；依完整明示資料獨立重算；within與between terms使用同一law及同一cells且兩項皆不可省略；zero-mass cell禁止conditional division且外層加權貢獻為0；不要求partition events independent。"},"difficulty":{"band":"undergraduate_core","level":1,"skills":["全變異數公式"]},"variant":{"family_id":"qf-mod41-totalvar-zero-mass-boundary","seed":202611104081,"parameters":{"masses":[[1,15],[2,15],[12,15],[0,1]],"values":[5,6,8,104],"partition":[[0,1,2],[3]],"domain":"Finite_partition_total_variance","operation":"totalvar-zero-mass-boundary","semantic_template":"qf-mod41-totalvar-zero-mass-boundary/{\"masses\":[[1,15],[2,15],[12,15],[0,1]],\"partition\":[[0,1,2],[3]],\"values\":[5,6,8,104]}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_or_symbolic_model","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"候選須主端重算；不構成人工審定、sampled orbit-stabilizer、sampled MVT、reverse compactness、zero-mass division、underspecified recurrence、incomplete divisor inversion、bounded-search PDA rejection、Lean或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-20261110-r04-law-of-total-variance-0082","batch_id":"batch-20261014-advance-20261110-r04-law-of-total-variance-foundations","language":"zh-Hant","source_mko_ids":["mko-law-of-total-variance"],"title_zh":"全變異數公式","stem_zh":"同一有限law與完整disjoint partition生成的G。操作=totalvar-zero-mass-boundary；資料={\"masses\":[[1,16],[2,16],[13,16],[0,1]],\"values\":[6,7,9,105],\"partition\":[[0,1,2],[3]]}。請依 exact_ordered_tuple_declared_by_interface 欄序回答。","answer":{"kind":"expression","value":"([[0, [0, 1, 2], 1, 137/16, 223/256], [1, [3], 0, null, null]], 223/256, 0, 223/256, 是, 否, zero_mass_cell_not_divided_and_outer_weighted_contribution_zero)","explanation_zh":"Wave6第四層核對=([[0, [0, 1, 2], 1, 137/16, 223/256], [1, [3], 0, null, null]], 223/256, 0, 223/256, 是, 否, zero_mass_cell_not_divided_and_outer_weighted_contribution_zero)；依完整明示資料獨立重算；within與between terms使用同一law及同一cells且兩項皆不可省略；zero-mass cell禁止conditional division且外層加權貢獻為0；不要求partition events independent。"},"difficulty":{"band":"undergraduate_core","level":1,"skills":["全變異數公式"]},"variant":{"family_id":"qf-mod41-totalvar-zero-mass-boundary","seed":202611104082,"parameters":{"masses":[[1,16],[2,16],[13,16],[0,1]],"values":[6,7,9,105],"partition":[[0,1,2],[3]],"domain":"Finite_partition_total_variance","operation":"totalvar-zero-mass-boundary","semantic_template":"qf-mod41-totalvar-zero-mass-boundary/{\"masses\":[[1,16],[2,16],[13,16],[0,1]],\"partition\":[[0,1,2],[3]],\"values\":[6,7,9,105]}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_or_symbolic_model","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"候選須主端重算；不構成人工審定、sampled orbit-stabilizer、sampled MVT、reverse compactness、zero-mass division、underspecified recurrence、incomplete divisor inversion、bounded-search PDA rejection、Lean或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-20261110-r04-law-of-total-variance-0083","batch_id":"batch-20261014-advance-20261110-r04-law-of-total-variance-foundations","language":"zh-Hant","source_mko_ids":["mko-law-of-total-variance"],"title_zh":"全變異數公式","stem_zh":"同一有限law與完整disjoint partition生成的G。操作=totalvar-zero-mass-boundary；資料={\"masses\":[[1,17],[2,17],[14,17],[0,1]],\"values\":[7,8,10,106],\"partition\":[[0,1,2],[3]]}。請依 exact_ordered_tuple_declared_by_interface 欄序回答。","answer":{"kind":"expression","value":"([[0, [0, 1, 2], 1, 163/17, 240/289], [1, [3], 0, null, null]], 240/289, 0, 240/289, 是, 否, zero_mass_cell_not_divided_and_outer_weighted_contribution_zero)","explanation_zh":"Wave6第四層核對=([[0, [0, 1, 2], 1, 163/17, 240/289], [1, [3], 0, null, null]], 240/289, 0, 240/289, 是, 否, zero_mass_cell_not_divided_and_outer_weighted_contribution_zero)；依完整明示資料獨立重算；within與between terms使用同一law及同一cells且兩項皆不可省略；zero-mass cell禁止conditional division且外層加權貢獻為0；不要求partition events independent。"},"difficulty":{"band":"undergraduate_core","level":1,"skills":["全變異數公式"]},"variant":{"family_id":"qf-mod41-totalvar-zero-mass-boundary","seed":202611104083,"parameters":{"masses":[[1,17],[2,17],[14,17],[0,1]],"values":[7,8,10,106],"partition":[[0,1,2],[3]],"domain":"Finite_partition_total_variance","operation":"totalvar-zero-mass-boundary","semantic_template":"qf-mod41-totalvar-zero-mass-boundary/{\"masses\":[[1,17],[2,17],[14,17],[0,1]],\"partition\":[[0,1,2],[3]],\"values\":[7,8,10,106]}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_or_symbolic_model","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"候選須主端重算；不構成人工審定、sampled orbit-stabilizer、sampled MVT、reverse compactness、zero-mass division、underspecified recurrence、incomplete divisor inversion、bounded-search PDA rejection、Lean或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-20261110-r04-law-of-total-variance-0084","batch_id":"batch-20261014-advance-20261110-r04-law-of-total-variance-foundations","language":"zh-Hant","source_mko_ids":["mko-law-of-total-variance"],"title_zh":"全變異數公式","stem_zh":"同一有限law與完整disjoint partition生成的G。操作=totalvar-zero-mass-boundary；資料={\"masses\":[[1,18],[2,18],[15,18],[0,1]],\"values\":[8,9,11,107],\"partition\":[[0,1,2],[3]]}。請依 exact_ordered_tuple_declared_by_interface 欄序回答。","answer":{"kind":"expression","value":"([[0, [0, 1, 2], 1, 191/18, 257/324], [1, [3], 0, null, null]], 257/324, 0, 257/324, 是, 否, zero_mass_cell_not_divided_and_outer_weighted_contribution_zero)","explanation_zh":"Wave6第四層核對=([[0, [0, 1, 2], 1, 191/18, 257/324], [1, [3], 0, null, null]], 257/324, 0, 257/324, 是, 否, zero_mass_cell_not_divided_and_outer_weighted_contribution_zero)；依完整明示資料獨立重算；within與between terms使用同一law及同一cells且兩項皆不可省略；zero-mass cell禁止conditional division且外層加權貢獻為0；不要求partition events independent。"},"difficulty":{"band":"undergraduate_core","level":2,"skills":["全變異數公式"]},"variant":{"family_id":"qf-mod41-totalvar-zero-mass-boundary","seed":202611104084,"parameters":{"masses":[[1,18],[2,18],[15,18],[0,1]],"values":[8,9,11,107],"partition":[[0,1,2],[3]],"domain":"Finite_partition_total_variance","operation":"totalvar-zero-mass-boundary","semantic_template":"qf-mod41-totalvar-zero-mass-boundary/{\"masses\":[[1,18],[2,18],[15,18],[0,1]],\"partition\":[[0,1,2],[3]],\"values\":[8,9,11,107]}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_or_symbolic_model","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"候選須主端重算；不構成人工審定、sampled orbit-stabilizer、sampled MVT、reverse compactness、zero-mass division、underspecified recurrence、incomplete divisor inversion、bounded-search PDA rejection、Lean或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-20261110-r04-law-of-total-variance-0085","batch_id":"batch-20261014-advance-20261110-r04-law-of-total-variance-foundations","language":"zh-Hant","source_mko_ids":["mko-law-of-total-variance"],"title_zh":"全變異數公式","stem_zh":"同一有限law與完整disjoint partition生成的G。操作=totalvar-zero-mass-boundary；資料={\"masses\":[[1,19],[2,19],[16,19],[0,1]],\"values\":[9,10,12,108],\"partition\":[[0,1,2],[3]]}。請依 exact_ordered_tuple_declared_by_interface 欄序回答。","answer":{"kind":"expression","value":"([[0, [0, 1, 2], 1, 221/19, 274/361], [1, [3], 0, null, null]], 274/361, 0, 274/361, 是, 否, zero_mass_cell_not_divided_and_outer_weighted_contribution_zero)","explanation_zh":"Wave6第四層核對=([[0, [0, 1, 2], 1, 221/19, 274/361], [1, [3], 0, null, null]], 274/361, 0, 274/361, 是, 否, zero_mass_cell_not_divided_and_outer_weighted_contribution_zero)；依完整明示資料獨立重算；within與between terms使用同一law及同一cells且兩項皆不可省略；zero-mass cell禁止conditional division且外層加權貢獻為0；不要求partition events independent。"},"difficulty":{"band":"undergraduate_core","level":2,"skills":["全變異數公式"]},"variant":{"family_id":"qf-mod41-totalvar-zero-mass-boundary","seed":202611104085,"parameters":{"masses":[[1,19],[2,19],[16,19],[0,1]],"values":[9,10,12,108],"partition":[[0,1,2],[3]],"domain":"Finite_partition_total_variance","operation":"totalvar-zero-mass-boundary","semantic_template":"qf-mod41-totalvar-zero-mass-boundary/{\"masses\":[[1,19],[2,19],[16,19],[0,1]],\"partition\":[[0,1,2],[3]],\"values\":[9,10,12,108]}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_or_symbolic_model","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"候選須主端重算；不構成人工審定、sampled orbit-stabilizer、sampled MVT、reverse compactness、zero-mass division、underspecified recurrence、incomplete divisor inversion、bounded-search PDA rejection、Lean或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-20261110-r04-law-of-total-variance-0086","batch_id":"batch-20261014-advance-20261110-r04-law-of-total-variance-foundations","language":"zh-Hant","source_mko_ids":["mko-law-of-total-variance"],"title_zh":"全變異數公式","stem_zh":"同一有限law與完整disjoint partition生成的G。操作=totalvar-zero-mass-boundary；資料={\"masses\":[[1,20],[2,20],[17,20],[0,1]],\"values\":[10,11,13,109],\"partition\":[[0,1,2],[3]]}。請依 exact_ordered_tuple_declared_by_interface 欄序回答。","answer":{"kind":"expression","value":"([[0, [0, 1, 2], 1, 253/20, 291/400], [1, [3], 0, null, null]], 291/400, 0, 291/400, 是, 否, zero_mass_cell_not_divided_and_outer_weighted_contribution_zero)","explanation_zh":"Wave6第四層核對=([[0, [0, 1, 2], 1, 253/20, 291/400], [1, [3], 0, null, null]], 291/400, 0, 291/400, 是, 否, zero_mass_cell_not_divided_and_outer_weighted_contribution_zero)；依完整明示資料獨立重算；within與between terms使用同一law及同一cells且兩項皆不可省略；zero-mass cell禁止conditional division且外層加權貢獻為0；不要求partition events independent。"},"difficulty":{"band":"undergraduate_core","level":2,"skills":["全變異數公式"]},"variant":{"family_id":"qf-mod41-totalvar-zero-mass-boundary","seed":202611104086,"parameters":{"masses":[[1,20],[2,20],[17,20],[0,1]],"values":[10,11,13,109],"partition":[[0,1,2],[3]],"domain":"Finite_partition_total_variance","operation":"totalvar-zero-mass-boundary","semantic_template":"qf-mod41-totalvar-zero-mass-boundary/{\"masses\":[[1,20],[2,20],[17,20],[0,1]],\"partition\":[[0,1,2],[3]],\"values\":[10,11,13,109]}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_or_symbolic_model","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"候選須主端重算；不構成人工審定、sampled orbit-stabilizer、sampled MVT、reverse compactness、zero-mass division、underspecified recurrence、incomplete divisor inversion、bounded-search PDA rejection、Lean或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-20261110-r04-law-of-total-variance-0087","batch_id":"batch-20261014-advance-20261110-r04-law-of-total-variance-foundations","language":"zh-Hant","source_mko_ids":["mko-law-of-total-variance"],"title_zh":"全變異數公式","stem_zh":"同一有限law與完整disjoint partition生成的G。操作=totalvar-zero-mass-boundary；資料={\"masses\":[[1,21],[2,21],[18,21],[0,1]],\"values\":[11,12,14,110],\"partition\":[[0,1,2],[3]]}。請依 exact_ordered_tuple_declared_by_interface 欄序回答。","answer":{"kind":"expression","value":"([[0, [0, 1, 2], 1, 41/3, 44/63], [1, [3], 0, null, null]], 44/63, 0, 44/63, 是, 否, zero_mass_cell_not_divided_and_outer_weighted_contribution_zero)","explanation_zh":"Wave6第四層核對=([[0, [0, 1, 2], 1, 41/3, 44/63], [1, [3], 0, null, null]], 44/63, 0, 44/63, 是, 否, zero_mass_cell_not_divided_and_outer_weighted_contribution_zero)；依完整明示資料獨立重算；within與between terms使用同一law及同一cells且兩項皆不可省略；zero-mass cell禁止conditional division且外層加權貢獻為0；不要求partition events independent。"},"difficulty":{"band":"undergraduate_core","level":2,"skills":["全變異數公式"]},"variant":{"family_id":"qf-mod41-totalvar-zero-mass-boundary","seed":202611104087,"parameters":{"masses":[[1,21],[2,21],[18,21],[0,1]],"values":[11,12,14,110],"partition":[[0,1,2],[3]],"domain":"Finite_partition_total_variance","operation":"totalvar-zero-mass-boundary","semantic_template":"qf-mod41-totalvar-zero-mass-boundary/{\"masses\":[[1,21],[2,21],[18,21],[0,1]],\"partition\":[[0,1,2],[3]],\"values\":[11,12,14,110]}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_or_symbolic_model","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"候選須主端重算；不構成人工審定、sampled orbit-stabilizer、sampled MVT、reverse compactness、zero-mass division、underspecified recurrence、incomplete divisor inversion、bounded-search PDA rejection、Lean或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-20261110-r04-law-of-total-variance-0088","batch_id":"batch-20261014-advance-20261110-r04-law-of-total-variance-foundations","language":"zh-Hant","source_mko_ids":["mko-law-of-total-variance"],"title_zh":"全變異數公式","stem_zh":"同一有限law與完整disjoint partition生成的G。操作=totalvar-zero-mass-boundary；資料={\"masses\":[[1,22],[2,22],[19,22],[0,1]],\"values\":[12,13,15,111],\"partition\":[[0,1,2],[3]]}。請依 exact_ordered_tuple_declared_by_interface 欄序回答。","answer":{"kind":"expression","value":"([[0, [0, 1, 2], 1, 323/22, 325/484], [1, [3], 0, null, null]], 325/484, 0, 325/484, 是, 否, zero_mass_cell_not_divided_and_outer_weighted_contribution_zero)","explanation_zh":"Wave6第四層核對=([[0, [0, 1, 2], 1, 323/22, 325/484], [1, [3], 0, null, null]], 325/484, 0, 325/484, 是, 否, zero_mass_cell_not_divided_and_outer_weighted_contribution_zero)；依完整明示資料獨立重算；within與between terms使用同一law及同一cells且兩項皆不可省略；zero-mass cell禁止conditional division且外層加權貢獻為0；不要求partition events independent。"},"difficulty":{"band":"undergraduate_core","level":2,"skills":["全變異數公式"]},"variant":{"family_id":"qf-mod41-totalvar-zero-mass-boundary","seed":202611104088,"parameters":{"masses":[[1,22],[2,22],[19,22],[0,1]],"values":[12,13,15,111],"partition":[[0,1,2],[3]],"domain":"Finite_partition_total_variance","operation":"totalvar-zero-mass-boundary","semantic_template":"qf-mod41-totalvar-zero-mass-boundary/{\"masses\":[[1,22],[2,22],[19,22],[0,1]],\"partition\":[[0,1,2],[3]],\"values\":[12,13,15,111]}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_or_symbolic_model","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"候選須主端重算；不構成人工審定、sampled orbit-stabilizer、sampled MVT、reverse compactness、zero-mass division、underspecified recurrence、incomplete divisor inversion、bounded-search PDA rejection、Lean或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-20261110-r04-law-of-total-variance-0089","batch_id":"batch-20261014-advance-20261110-r04-law-of-total-variance-foundations","language":"zh-Hant","source_mko_ids":["mko-law-of-total-variance"],"title_zh":"全變異數公式","stem_zh":"同一有限law與完整disjoint partition生成的G。操作=totalvar-zero-mass-boundary；資料={\"masses\":[[1,23],[2,23],[20,23],[0,1]],\"values\":[13,14,16,112],\"partition\":[[0,1,2],[3]]}。請依 exact_ordered_tuple_declared_by_interface 欄序回答。","answer":{"kind":"expression","value":"([[0, [0, 1, 2], 1, 361/23, 342/529], [1, [3], 0, null, null]], 342/529, 0, 342/529, 是, 否, zero_mass_cell_not_divided_and_outer_weighted_contribution_zero)","explanation_zh":"Wave6第四層核對=([[0, [0, 1, 2], 1, 361/23, 342/529], [1, [3], 0, null, null]], 342/529, 0, 342/529, 是, 否, zero_mass_cell_not_divided_and_outer_weighted_contribution_zero)；依完整明示資料獨立重算；within與between terms使用同一law及同一cells且兩項皆不可省略；zero-mass cell禁止conditional division且外層加權貢獻為0；不要求partition events independent。"},"difficulty":{"band":"undergraduate_core","level":2,"skills":["全變異數公式"]},"variant":{"family_id":"qf-mod41-totalvar-zero-mass-boundary","seed":202611104089,"parameters":{"masses":[[1,23],[2,23],[20,23],[0,1]],"values":[13,14,16,112],"partition":[[0,1,2],[3]],"domain":"Finite_partition_total_variance","operation":"totalvar-zero-mass-boundary","semantic_template":"qf-mod41-totalvar-zero-mass-boundary/{\"masses\":[[1,23],[2,23],[20,23],[0,1]],\"partition\":[[0,1,2],[3]],\"values\":[13,14,16,112]}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_or_symbolic_model","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"候選須主端重算；不構成人工審定、sampled orbit-stabilizer、sampled MVT、reverse compactness、zero-mass division、underspecified recurrence、incomplete divisor inversion、bounded-search PDA rejection、Lean或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-20261110-r04-law-of-total-variance-0090","batch_id":"batch-20261014-advance-20261110-r04-law-of-total-variance-foundations","language":"zh-Hant","source_mko_ids":["mko-law-of-total-variance"],"title_zh":"全變異數公式","stem_zh":"同一有限law與完整disjoint partition生成的G。操作=totalvar-zero-mass-boundary；資料={\"masses\":[[1,24],[2,24],[21,24],[0,1]],\"values\":[14,15,17,113],\"partition\":[[0,1,2],[3]]}。請依 exact_ordered_tuple_declared_by_interface 欄序回答。","answer":{"kind":"expression","value":"([[0, [0, 1, 2], 1, 401/24, 359/576], [1, [3], 0, null, null]], 359/576, 0, 359/576, 是, 否, zero_mass_cell_not_divided_and_outer_weighted_contribution_zero)","explanation_zh":"Wave6第四層核對=([[0, [0, 1, 2], 1, 401/24, 359/576], [1, [3], 0, null, null]], 359/576, 0, 359/576, 是, 否, zero_mass_cell_not_divided_and_outer_weighted_contribution_zero)；依完整明示資料獨立重算；within與between terms使用同一law及同一cells且兩項皆不可省略；zero-mass cell禁止conditional division且外層加權貢獻為0；不要求partition events independent。"},"difficulty":{"band":"undergraduate_core","level":2,"skills":["全變異數公式"]},"variant":{"family_id":"qf-mod41-totalvar-zero-mass-boundary","seed":202611104090,"parameters":{"masses":[[1,24],[2,24],[21,24],[0,1]],"values":[14,15,17,113],"partition":[[0,1,2],[3]],"domain":"Finite_partition_total_variance","operation":"totalvar-zero-mass-boundary","semantic_template":"qf-mod41-totalvar-zero-mass-boundary/{\"masses\":[[1,24],[2,24],[21,24],[0,1]],\"partition\":[[0,1,2],[3]],\"values\":[14,15,17,113]}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_or_symbolic_model","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"候選須主端重算；不構成人工審定、sampled orbit-stabilizer、sampled MVT、reverse compactness、zero-mass division、underspecified recurrence、incomplete divisor inversion、bounded-search PDA rejection、Lean或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-20261110-r04-law-of-total-variance-0091","batch_id":"batch-20261014-advance-20261110-r04-law-of-total-variance-foundations","language":"zh-Hant","source_mko_ids":["mko-law-of-total-variance"],"title_zh":"全變異數公式","stem_zh":"同一有限law與完整disjoint partition生成的G。操作=totalvar-zero-mass-boundary；資料={\"masses\":[[1,25],[2,25],[22,25],[0,1]],\"values\":[15,16,18,114],\"partition\":[[0,1,2],[3]]}。請依 exact_ordered_tuple_declared_by_interface 欄序回答。","answer":{"kind":"expression","value":"([[0, [0, 1, 2], 1, 443/25, 376/625], [1, [3], 0, null, null]], 376/625, 0, 376/625, 是, 否, zero_mass_cell_not_divided_and_outer_weighted_contribution_zero)","explanation_zh":"Wave6第四層核對=([[0, [0, 1, 2], 1, 443/25, 376/625], [1, [3], 0, null, null]], 376/625, 0, 376/625, 是, 否, zero_mass_cell_not_divided_and_outer_weighted_contribution_zero)；依完整明示資料獨立重算；within與between terms使用同一law及同一cells且兩項皆不可省略；zero-mass cell禁止conditional division且外層加權貢獻為0；不要求partition events independent。"},"difficulty":{"band":"undergraduate_core","level":2,"skills":["全變異數公式"]},"variant":{"family_id":"qf-mod41-totalvar-zero-mass-boundary","seed":202611104091,"parameters":{"masses":[[1,25],[2,25],[22,25],[0,1]],"values":[15,16,18,114],"partition":[[0,1,2],[3]],"domain":"Finite_partition_total_variance","operation":"totalvar-zero-mass-boundary","semantic_template":"qf-mod41-totalvar-zero-mass-boundary/{\"masses\":[[1,25],[2,25],[22,25],[0,1]],\"partition\":[[0,1,2],[3]],\"values\":[15,16,18,114]}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_or_symbolic_model","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"候選須主端重算；不構成人工審定、sampled orbit-stabilizer、sampled MVT、reverse compactness、zero-mass division、underspecified recurrence、incomplete divisor inversion、bounded-search PDA rejection、Lean或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-20261110-r04-law-of-total-variance-0092","batch_id":"batch-20261014-advance-20261110-r04-law-of-total-variance-foundations","language":"zh-Hant","source_mko_ids":["mko-law-of-total-variance"],"title_zh":"全變異數公式","stem_zh":"同一有限law與完整disjoint partition生成的G。操作=totalvar-zero-mass-boundary；資料={\"masses\":[[1,26],[2,26],[23,26],[0,1]],\"values\":[16,17,19,115],\"partition\":[[0,1,2],[3]]}。請依 exact_ordered_tuple_declared_by_interface 欄序回答。","answer":{"kind":"expression","value":"([[0, [0, 1, 2], 1, 487/26, 393/676], [1, [3], 0, null, null]], 393/676, 0, 393/676, 是, 否, zero_mass_cell_not_divided_and_outer_weighted_contribution_zero)","explanation_zh":"Wave6第四層核對=([[0, [0, 1, 2], 1, 487/26, 393/676], [1, [3], 0, null, null]], 393/676, 0, 393/676, 是, 否, zero_mass_cell_not_divided_and_outer_weighted_contribution_zero)；依完整明示資料獨立重算；within與between terms使用同一law及同一cells且兩項皆不可省略；zero-mass cell禁止conditional division且外層加權貢獻為0；不要求partition events independent。"},"difficulty":{"band":"undergraduate_core","level":2,"skills":["全變異數公式"]},"variant":{"family_id":"qf-mod41-totalvar-zero-mass-boundary","seed":202611104092,"parameters":{"masses":[[1,26],[2,26],[23,26],[0,1]],"values":[16,17,19,115],"partition":[[0,1,2],[3]],"domain":"Finite_partition_total_variance","operation":"totalvar-zero-mass-boundary","semantic_template":"qf-mod41-totalvar-zero-mass-boundary/{\"masses\":[[1,26],[2,26],[23,26],[0,1]],\"partition\":[[0,1,2],[3]],\"values\":[16,17,19,115]}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_or_symbolic_model","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"候選須主端重算；不構成人工審定、sampled orbit-stabilizer、sampled MVT、reverse compactness、zero-mass division、underspecified recurrence、incomplete divisor inversion、bounded-search PDA rejection、Lean或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-20261110-r04-law-of-total-variance-0093","batch_id":"batch-20261014-advance-20261110-r04-law-of-total-variance-foundations","language":"zh-Hant","source_mko_ids":["mko-law-of-total-variance"],"title_zh":"全變異數公式","stem_zh":"同一有限law與完整disjoint partition生成的G。操作=totalvar-zero-mass-boundary；資料={\"masses\":[[1,27],[2,27],[24,27],[0,1]],\"values\":[17,18,20,116],\"partition\":[[0,1,2],[3]]}。請依 exact_ordered_tuple_declared_by_interface 欄序回答。","answer":{"kind":"expression","value":"([[0, [0, 1, 2], 1, 533/27, 410/729], [1, [3], 0, null, null]], 410/729, 0, 410/729, 是, 否, zero_mass_cell_not_divided_and_outer_weighted_contribution_zero)","explanation_zh":"Wave6第四層核對=([[0, [0, 1, 2], 1, 533/27, 410/729], [1, [3], 0, null, null]], 410/729, 0, 410/729, 是, 否, zero_mass_cell_not_divided_and_outer_weighted_contribution_zero)；依完整明示資料獨立重算；within與between terms使用同一law及同一cells且兩項皆不可省略；zero-mass cell禁止conditional division且外層加權貢獻為0；不要求partition events independent。"},"difficulty":{"band":"undergraduate_core","level":3,"skills":["全變異數公式"]},"variant":{"family_id":"qf-mod41-totalvar-zero-mass-boundary","seed":202611104093,"parameters":{"masses":[[1,27],[2,27],[24,27],[0,1]],"values":[17,18,20,116],"partition":[[0,1,2],[3]],"domain":"Finite_partition_total_variance","operation":"totalvar-zero-mass-boundary","semantic_template":"qf-mod41-totalvar-zero-mass-boundary/{\"masses\":[[1,27],[2,27],[24,27],[0,1]],\"partition\":[[0,1,2],[3]],\"values\":[17,18,20,116]}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_or_symbolic_model","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"候選須主端重算；不構成人工審定、sampled orbit-stabilizer、sampled MVT、reverse compactness、zero-mass division、underspecified recurrence、incomplete divisor inversion、bounded-search PDA rejection、Lean或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-20261110-r04-law-of-total-variance-0094","batch_id":"batch-20261014-advance-20261110-r04-law-of-total-variance-foundations","language":"zh-Hant","source_mko_ids":["mko-law-of-total-variance"],"title_zh":"全變異數公式","stem_zh":"同一有限law與完整disjoint partition生成的G。操作=totalvar-zero-mass-boundary；資料={\"masses\":[[1,28],[2,28],[25,28],[0,1]],\"values\":[18,19,21,117],\"partition\":[[0,1,2],[3]]}。請依 exact_ordered_tuple_declared_by_interface 欄序回答。","answer":{"kind":"expression","value":"([[0, [0, 1, 2], 1, 83/4, 61/112], [1, [3], 0, null, null]], 61/112, 0, 61/112, 是, 否, zero_mass_cell_not_divided_and_outer_weighted_contribution_zero)","explanation_zh":"Wave6第四層核對=([[0, [0, 1, 2], 1, 83/4, 61/112], [1, [3], 0, null, null]], 61/112, 0, 61/112, 是, 否, zero_mass_cell_not_divided_and_outer_weighted_contribution_zero)；依完整明示資料獨立重算；within與between terms使用同一law及同一cells且兩項皆不可省略；zero-mass cell禁止conditional division且外層加權貢獻為0；不要求partition events independent。"},"difficulty":{"band":"undergraduate_core","level":3,"skills":["全變異數公式"]},"variant":{"family_id":"qf-mod41-totalvar-zero-mass-boundary","seed":202611104094,"parameters":{"masses":[[1,28],[2,28],[25,28],[0,1]],"values":[18,19,21,117],"partition":[[0,1,2],[3]],"domain":"Finite_partition_total_variance","operation":"totalvar-zero-mass-boundary","semantic_template":"qf-mod41-totalvar-zero-mass-boundary/{\"masses\":[[1,28],[2,28],[25,28],[0,1]],\"partition\":[[0,1,2],[3]],\"values\":[18,19,21,117]}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_or_symbolic_model","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"候選須主端重算；不構成人工審定、sampled orbit-stabilizer、sampled MVT、reverse compactness、zero-mass division、underspecified recurrence、incomplete divisor inversion、bounded-search PDA rejection、Lean或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-20261110-r04-law-of-total-variance-0095","batch_id":"batch-20261014-advance-20261110-r04-law-of-total-variance-foundations","language":"zh-Hant","source_mko_ids":["mko-law-of-total-variance"],"title_zh":"全變異數公式","stem_zh":"同一有限law與完整disjoint partition生成的G。操作=totalvar-zero-mass-boundary；資料={\"masses\":[[1,29],[2,29],[26,29],[0,1]],\"values\":[19,20,22,118],\"partition\":[[0,1,2],[3]]}。請依 exact_ordered_tuple_declared_by_interface 欄序回答。","answer":{"kind":"expression","value":"([[0, [0, 1, 2], 1, 631/29, 444/841], [1, [3], 0, null, null]], 444/841, 0, 444/841, 是, 否, zero_mass_cell_not_divided_and_outer_weighted_contribution_zero)","explanation_zh":"Wave6第四層核對=([[0, [0, 1, 2], 1, 631/29, 444/841], [1, [3], 0, null, null]], 444/841, 0, 444/841, 是, 否, zero_mass_cell_not_divided_and_outer_weighted_contribution_zero)；依完整明示資料獨立重算；within與between terms使用同一law及同一cells且兩項皆不可省略；zero-mass cell禁止conditional division且外層加權貢獻為0；不要求partition events independent。"},"difficulty":{"band":"undergraduate_core","level":3,"skills":["全變異數公式"]},"variant":{"family_id":"qf-mod41-totalvar-zero-mass-boundary","seed":202611104095,"parameters":{"masses":[[1,29],[2,29],[26,29],[0,1]],"values":[19,20,22,118],"partition":[[0,1,2],[3]],"domain":"Finite_partition_total_variance","operation":"totalvar-zero-mass-boundary","semantic_template":"qf-mod41-totalvar-zero-mass-boundary/{\"masses\":[[1,29],[2,29],[26,29],[0,1]],\"partition\":[[0,1,2],[3]],\"values\":[19,20,22,118]}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_or_symbolic_model","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"候選須主端重算；不構成人工審定、sampled orbit-stabilizer、sampled MVT、reverse compactness、zero-mass division、underspecified recurrence、incomplete divisor inversion、bounded-search PDA rejection、Lean或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-20261110-r04-law-of-total-variance-0096","batch_id":"batch-20261014-advance-20261110-r04-law-of-total-variance-foundations","language":"zh-Hant","source_mko_ids":["mko-law-of-total-variance"],"title_zh":"全變異數公式","stem_zh":"同一有限law與完整disjoint partition生成的G。操作=totalvar-zero-mass-boundary；資料={\"masses\":[[1,30],[2,30],[27,30],[0,1]],\"values\":[20,21,23,119],\"partition\":[[0,1,2],[3]]}。請依 exact_ordered_tuple_declared_by_interface 欄序回答。","answer":{"kind":"expression","value":"([[0, [0, 1, 2], 1, 683/30, 461/900], [1, [3], 0, null, null]], 461/900, 0, 461/900, 是, 否, zero_mass_cell_not_divided_and_outer_weighted_contribution_zero)","explanation_zh":"Wave6第四層核對=([[0, [0, 1, 2], 1, 683/30, 461/900], [1, [3], 0, null, null]], 461/900, 0, 461/900, 是, 否, zero_mass_cell_not_divided_and_outer_weighted_contribution_zero)；依完整明示資料獨立重算；within與between terms使用同一law及同一cells且兩項皆不可省略；zero-mass cell禁止conditional division且外層加權貢獻為0；不要求partition events independent。"},"difficulty":{"band":"undergraduate_core","level":3,"skills":["全變異數公式"]},"variant":{"family_id":"qf-mod41-totalvar-zero-mass-boundary","seed":202611104096,"parameters":{"masses":[[1,30],[2,30],[27,30],[0,1]],"values":[20,21,23,119],"partition":[[0,1,2],[3]],"domain":"Finite_partition_total_variance","operation":"totalvar-zero-mass-boundary","semantic_template":"qf-mod41-totalvar-zero-mass-boundary/{\"masses\":[[1,30],[2,30],[27,30],[0,1]],\"partition\":[[0,1,2],[3]],\"values\":[20,21,23,119]}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_or_symbolic_model","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"候選須主端重算；不構成人工審定、sampled orbit-stabilizer、sampled MVT、reverse compactness、zero-mass division、underspecified recurrence、incomplete divisor inversion、bounded-search PDA rejection、Lean或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-20261110-r04-law-of-total-variance-0097","batch_id":"batch-20261014-advance-20261110-r04-law-of-total-variance-foundations","language":"zh-Hant","source_mko_ids":["mko-law-of-total-variance"],"title_zh":"全變異數公式","stem_zh":"同一有限law與完整disjoint partition生成的G。操作=totalvar-zero-mass-boundary；資料={\"masses\":[[1,31],[2,31],[28,31],[0,1]],\"values\":[21,22,24,120],\"partition\":[[0,1,2],[3]]}。請依 exact_ordered_tuple_declared_by_interface 欄序回答。","answer":{"kind":"expression","value":"([[0, [0, 1, 2], 1, 737/31, 478/961], [1, [3], 0, null, null]], 478/961, 0, 478/961, 是, 否, zero_mass_cell_not_divided_and_outer_weighted_contribution_zero)","explanation_zh":"Wave6第四層核對=([[0, [0, 1, 2], 1, 737/31, 478/961], [1, [3], 0, null, null]], 478/961, 0, 478/961, 是, 否, zero_mass_cell_not_divided_and_outer_weighted_contribution_zero)；依完整明示資料獨立重算；within與between terms使用同一law及同一cells且兩項皆不可省略；zero-mass cell禁止conditional division且外層加權貢獻為0；不要求partition events independent。"},"difficulty":{"band":"undergraduate_core","level":3,"skills":["全變異數公式"]},"variant":{"family_id":"qf-mod41-totalvar-zero-mass-boundary","seed":202611104097,"parameters":{"masses":[[1,31],[2,31],[28,31],[0,1]],"values":[21,22,24,120],"partition":[[0,1,2],[3]],"domain":"Finite_partition_total_variance","operation":"totalvar-zero-mass-boundary","semantic_template":"qf-mod41-totalvar-zero-mass-boundary/{\"masses\":[[1,31],[2,31],[28,31],[0,1]],\"partition\":[[0,1,2],[3]],\"values\":[21,22,24,120]}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_or_symbolic_model","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"候選須主端重算；不構成人工審定、sampled orbit-stabilizer、sampled MVT、reverse compactness、zero-mass division、underspecified recurrence、incomplete divisor inversion、bounded-search PDA rejection、Lean或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-20261110-r04-law-of-total-variance-0098","batch_id":"batch-20261014-advance-20261110-r04-law-of-total-variance-foundations","language":"zh-Hant","source_mko_ids":["mko-law-of-total-variance"],"title_zh":"全變異數公式","stem_zh":"同一有限law與完整disjoint partition生成的G。操作=totalvar-zero-mass-boundary；資料={\"masses\":[[1,32],[2,32],[29,32],[0,1]],\"values\":[22,23,25,121],\"partition\":[[0,1,2],[3]]}。請依 exact_ordered_tuple_declared_by_interface 欄序回答。","answer":{"kind":"expression","value":"([[0, [0, 1, 2], 1, 793/32, 495/1024], [1, [3], 0, null, null]], 495/1024, 0, 495/1024, 是, 否, zero_mass_cell_not_divided_and_outer_weighted_contribution_zero)","explanation_zh":"Wave6第四層核對=([[0, [0, 1, 2], 1, 793/32, 495/1024], [1, [3], 0, null, null]], 495/1024, 0, 495/1024, 是, 否, zero_mass_cell_not_divided_and_outer_weighted_contribution_zero)；依完整明示資料獨立重算；within與between terms使用同一law及同一cells且兩項皆不可省略；zero-mass cell禁止conditional division且外層加權貢獻為0；不要求partition events independent。"},"difficulty":{"band":"undergraduate_core","level":3,"skills":["全變異數公式"]},"variant":{"family_id":"qf-mod41-totalvar-zero-mass-boundary","seed":202611104098,"parameters":{"masses":[[1,32],[2,32],[29,32],[0,1]],"values":[22,23,25,121],"partition":[[0,1,2],[3]],"domain":"Finite_partition_total_variance","operation":"totalvar-zero-mass-boundary","semantic_template":"qf-mod41-totalvar-zero-mass-boundary/{\"masses\":[[1,32],[2,32],[29,32],[0,1]],\"partition\":[[0,1,2],[3]],\"values\":[22,23,25,121]}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_or_symbolic_model","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"候選須主端重算；不構成人工審定、sampled orbit-stabilizer、sampled MVT、reverse compactness、zero-mass division、underspecified recurrence、incomplete divisor inversion、bounded-search PDA rejection、Lean或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-20261110-r04-law-of-total-variance-0099","batch_id":"batch-20261014-advance-20261110-r04-law-of-total-variance-foundations","language":"zh-Hant","source_mko_ids":["mko-law-of-total-variance"],"title_zh":"全變異數公式","stem_zh":"同一有限law與完整disjoint partition生成的G。操作=totalvar-zero-mass-boundary；資料={\"masses\":[[1,33],[2,33],[30,33],[0,1]],\"values\":[23,24,26,122],\"partition\":[[0,1,2],[3]]}。請依 exact_ordered_tuple_declared_by_interface 欄序回答。","answer":{"kind":"expression","value":"([[0, [0, 1, 2], 1, 851/33, 512/1089], [1, [3], 0, null, null]], 512/1089, 0, 512/1089, 是, 否, zero_mass_cell_not_divided_and_outer_weighted_contribution_zero)","explanation_zh":"Wave6第四層核對=([[0, [0, 1, 2], 1, 851/33, 512/1089], [1, [3], 0, null, null]], 512/1089, 0, 512/1089, 是, 否, zero_mass_cell_not_divided_and_outer_weighted_contribution_zero)；依完整明示資料獨立重算；within與between terms使用同一law及同一cells且兩項皆不可省略；zero-mass cell禁止conditional division且外層加權貢獻為0；不要求partition events independent。"},"difficulty":{"band":"undergraduate_core","level":3,"skills":["全變異數公式"]},"variant":{"family_id":"qf-mod41-totalvar-zero-mass-boundary","seed":202611104099,"parameters":{"masses":[[1,33],[2,33],[30,33],[0,1]],"values":[23,24,26,122],"partition":[[0,1,2],[3]],"domain":"Finite_partition_total_variance","operation":"totalvar-zero-mass-boundary","semantic_template":"qf-mod41-totalvar-zero-mass-boundary/{\"masses\":[[1,33],[2,33],[30,33],[0,1]],\"partition\":[[0,1,2],[3]],\"values\":[23,24,26,122]}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_or_symbolic_model","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"候選須主端重算；不構成人工審定、sampled orbit-stabilizer、sampled MVT、reverse compactness、zero-mass division、underspecified recurrence、incomplete divisor inversion、bounded-search PDA rejection、Lean或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-20261110-r04-law-of-total-variance-0100","batch_id":"batch-20261014-advance-20261110-r04-law-of-total-variance-foundations","language":"zh-Hant","source_mko_ids":["mko-law-of-total-variance"],"title_zh":"全變異數公式","stem_zh":"同一有限law與完整disjoint partition生成的G。操作=totalvar-zero-mass-boundary；資料={\"masses\":[[1,34],[2,34],[31,34],[0,1]],\"values\":[24,25,27,123],\"partition\":[[0,1,2],[3]]}。請依 exact_ordered_tuple_declared_by_interface 欄序回答。","answer":{"kind":"expression","value":"([[0, [0, 1, 2], 1, 911/34, 529/1156], [1, [3], 0, null, null]], 529/1156, 0, 529/1156, 是, 否, zero_mass_cell_not_divided_and_outer_weighted_contribution_zero)","explanation_zh":"Wave6第四層核對=([[0, [0, 1, 2], 1, 911/34, 529/1156], [1, [3], 0, null, null]], 529/1156, 0, 529/1156, 是, 否, zero_mass_cell_not_divided_and_outer_weighted_contribution_zero)；依完整明示資料獨立重算；within與between terms使用同一law及同一cells且兩項皆不可省略；zero-mass cell禁止conditional division且外層加權貢獻為0；不要求partition events independent。"},"difficulty":{"band":"undergraduate_core","level":3,"skills":["全變異數公式"]},"variant":{"family_id":"qf-mod41-totalvar-zero-mass-boundary","seed":202611104100,"parameters":{"masses":[[1,34],[2,34],[31,34],[0,1]],"values":[24,25,27,123],"partition":[[0,1,2],[3]],"domain":"Finite_partition_total_variance","operation":"totalvar-zero-mass-boundary","semantic_template":"qf-mod41-totalvar-zero-mass-boundary/{\"masses\":[[1,34],[2,34],[31,34],[0,1]],\"partition\":[[0,1,2],[3]],\"values\":[24,25,27,123]}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_or_symbolic_model","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"候選須主端重算；不構成人工審定、sampled orbit-stabilizer、sampled MVT、reverse compactness、zero-mass division、underspecified recurrence、incomplete divisor inversion、bounded-search PDA rejection、Lean或Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-14","contract_version":"ocme-question-factory-v0.1"}}