{"schema_version":"ocme-question-v0.1","id":"q-20261015-advance-20261116-r05-finite-sufficient-statistic-0001","batch_id":"batch-20261015-advance-20261116-r05-finite-sufficient-statistic-foundations","language":"zh-Hant","source_mko_ids":["mko-finite-sufficient-statistic"],"title_zh":"有限模型充分統計量","stem_zh":"total statistic fibers與正質量conditional laws的完整theta-invariance責任。操作=suff-fibers；資料={\"theta_values\":[\"a0\",\"b0\"],\"samples\":[0,1,2,3],\"probability_rows\":[[[2,5],[1,10],[2,5],[1,10]],[[1,10],[2,5],[1,10],[2,5]]],\"statistic\":[0,1,0,1]}。請依 exact_ordered_tuple_declared_by_interface 欄序回答。","answer":{"kind":"expression","value":"([0, 1, 2, 3], [0, 1, 0, 1], [[0, [0, 2]], [1, [1, 3]]], 是, total_statistic_fibers_partition_sample_space)","explanation_zh":"Wave6第十層核對=([0, 1, 2, 3], [0, 1, 0, 1], [[0, [0, 2]], [1, [1, 3]]], 是, total_statistic_fibers_partition_sample_space)；依完整明示資料獨立重算；zero-mass conditional保持undefined，nonsufficient需明示witness；identity/constant boundaries分開且不使用factorization theorem或宣稱估計品質。"},"difficulty":{"band":"undergraduate_core","level":1,"skills":["有限模型充分統計量"]},"variant":{"family_id":"qf-mod47-suff-fibers","seed":202611165001,"parameters":{"theta_values":["a0","b0"],"samples":[0,1,2,3],"probability_rows":[[[2,5],[1,10],[2,5],[1,10]],[[1,10],[2,5],[1,10],[2,5]]],"statistic":[0,1,0,1],"domain":"Exact_finite_sufficient_statistic","operation":"suff-fibers","semantic_template":"qf-mod47-suff-fibers/{\"probability_rows\":[[[2,5],[1,10],[2,5],[1,10]],[[1,10],[2,5],[1,10],[2,5]]],\"samples\":[0,1,2,3],\"statistic\":[0,1,0,1],\"theta_values\":[\"a0\",\"b0\"]}"}},"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、一般Banach／IVT／Taylor證明、MLE漸近性、factorization theorem、一般DAG iff或primitive-root主張、Lean或Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-15","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261015-advance-20261116-r05-finite-sufficient-statistic-0002","batch_id":"batch-20261015-advance-20261116-r05-finite-sufficient-statistic-foundations","language":"zh-Hant","source_mko_ids":["mko-finite-sufficient-statistic"],"title_zh":"有限模型充分統計量","stem_zh":"total statistic fibers與正質量conditional laws的完整theta-invariance責任。操作=suff-fibers；資料={\"theta_values\":[\"a1\",\"b1\"],\"samples\":[10,11,12,13],\"probability_rows\":[[[2,5],[1,10],[2,5],[1,10]],[[1,10],[2,5],[1,10],[2,5]]],\"statistic\":[0,1,0,1]}。請依 exact_ordered_tuple_declared_by_interface 欄序回答。","answer":{"kind":"expression","value":"([10, 11, 12, 13], [0, 1, 0, 1], [[0, [10, 12]], [1, [11, 13]]], 是, total_statistic_fibers_partition_sample_space)","explanation_zh":"Wave6第十層核對=([10, 11, 12, 13], [0, 1, 0, 1], [[0, [10, 12]], [1, [11, 13]]], 是, total_statistic_fibers_partition_sample_space)；依完整明示資料獨立重算；zero-mass conditional保持undefined，nonsufficient需明示witness；identity/constant boundaries分開且不使用factorization theorem或宣稱估計品質。"},"difficulty":{"band":"undergraduate_core","level":1,"skills":["有限模型充分統計量"]},"variant":{"family_id":"qf-mod47-suff-fibers","seed":202611165002,"parameters":{"theta_values":["a1","b1"],"samples":[10,11,12,13],"probability_rows":[[[2,5],[1,10],[2,5],[1,10]],[[1,10],[2,5],[1,10],[2,5]]],"statistic":[0,1,0,1],"domain":"Exact_finite_sufficient_statistic","operation":"suff-fibers","semantic_template":"qf-mod47-suff-fibers/{\"probability_rows\":[[[2,5],[1,10],[2,5],[1,10]],[[1,10],[2,5],[1,10],[2,5]]],\"samples\":[10,11,12,13],\"statistic\":[0,1,0,1],\"theta_values\":[\"a1\",\"b1\"]}"}},"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、一般Banach／IVT／Taylor證明、MLE漸近性、factorization theorem、一般DAG iff或primitive-root主張、Lean或Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-15","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261015-advance-20261116-r05-finite-sufficient-statistic-0003","batch_id":"batch-20261015-advance-20261116-r05-finite-sufficient-statistic-foundations","language":"zh-Hant","source_mko_ids":["mko-finite-sufficient-statistic"],"title_zh":"有限模型充分統計量","stem_zh":"total statistic fibers與正質量conditional laws的完整theta-invariance責任。操作=suff-fibers；資料={\"theta_values\":[\"a2\",\"b2\"],\"samples\":[20,21,22,23],\"probability_rows\":[[[2,5],[1,10],[2,5],[1,10]],[[1,10],[2,5],[1,10],[2,5]]],\"statistic\":[0,1,0,1]}。請依 exact_ordered_tuple_declared_by_interface 欄序回答。","answer":{"kind":"expression","value":"([20, 21, 22, 23], [0, 1, 0, 1], [[0, [20, 22]], [1, [21, 23]]], 是, total_statistic_fibers_partition_sample_space)","explanation_zh":"Wave6第十層核對=([20, 21, 22, 23], [0, 1, 0, 1], [[0, [20, 22]], [1, [21, 23]]], 是, total_statistic_fibers_partition_sample_space)；依完整明示資料獨立重算；zero-mass conditional保持undefined，nonsufficient需明示witness；identity/constant boundaries分開且不使用factorization theorem或宣稱估計品質。"},"difficulty":{"band":"undergraduate_core","level":1,"skills":["有限模型充分統計量"]},"variant":{"family_id":"qf-mod47-suff-fibers","seed":202611165003,"parameters":{"theta_values":["a2","b2"],"samples":[20,21,22,23],"probability_rows":[[[2,5],[1,10],[2,5],[1,10]],[[1,10],[2,5],[1,10],[2,5]]],"statistic":[0,1,0,1],"domain":"Exact_finite_sufficient_statistic","operation":"suff-fibers","semantic_template":"qf-mod47-suff-fibers/{\"probability_rows\":[[[2,5],[1,10],[2,5],[1,10]],[[1,10],[2,5],[1,10],[2,5]]],\"samples\":[20,21,22,23],\"statistic\":[0,1,0,1],\"theta_values\":[\"a2\",\"b2\"]}"}},"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、一般Banach／IVT／Taylor證明、MLE漸近性、factorization theorem、一般DAG iff或primitive-root主張、Lean或Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-15","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261015-advance-20261116-r05-finite-sufficient-statistic-0004","batch_id":"batch-20261015-advance-20261116-r05-finite-sufficient-statistic-foundations","language":"zh-Hant","source_mko_ids":["mko-finite-sufficient-statistic"],"title_zh":"有限模型充分統計量","stem_zh":"total statistic fibers與正質量conditional laws的完整theta-invariance責任。操作=suff-fibers；資料={\"theta_values\":[\"a3\",\"b3\"],\"samples\":[30,31,32,33],\"probability_rows\":[[[2,5],[1,10],[2,5],[1,10]],[[1,10],[2,5],[1,10],[2,5]]],\"statistic\":[0,1,0,1]}。請依 exact_ordered_tuple_declared_by_interface 欄序回答。","answer":{"kind":"expression","value":"([30, 31, 32, 33], [0, 1, 0, 1], [[0, [30, 32]], [1, [31, 33]]], 是, total_statistic_fibers_partition_sample_space)","explanation_zh":"Wave6第十層核對=([30, 31, 32, 33], [0, 1, 0, 1], [[0, [30, 32]], [1, [31, 33]]], 是, total_statistic_fibers_partition_sample_space)；依完整明示資料獨立重算；zero-mass conditional保持undefined，nonsufficient需明示witness；identity/constant boundaries分開且不使用factorization theorem或宣稱估計品質。"},"difficulty":{"band":"undergraduate_core","level":1,"skills":["有限模型充分統計量"]},"variant":{"family_id":"qf-mod47-suff-fibers","seed":202611165004,"parameters":{"theta_values":["a3","b3"],"samples":[30,31,32,33],"probability_rows":[[[2,5],[1,10],[2,5],[1,10]],[[1,10],[2,5],[1,10],[2,5]]],"statistic":[0,1,0,1],"domain":"Exact_finite_sufficient_statistic","operation":"suff-fibers","semantic_template":"qf-mod47-suff-fibers/{\"probability_rows\":[[[2,5],[1,10],[2,5],[1,10]],[[1,10],[2,5],[1,10],[2,5]]],\"samples\":[30,31,32,33],\"statistic\":[0,1,0,1],\"theta_values\":[\"a3\",\"b3\"]}"}},"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、一般Banach／IVT／Taylor證明、MLE漸近性、factorization theorem、一般DAG iff或primitive-root主張、Lean或Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-15","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261015-advance-20261116-r05-finite-sufficient-statistic-0005","batch_id":"batch-20261015-advance-20261116-r05-finite-sufficient-statistic-foundations","language":"zh-Hant","source_mko_ids":["mko-finite-sufficient-statistic"],"title_zh":"有限模型充分統計量","stem_zh":"total statistic fibers與正質量conditional laws的完整theta-invariance責任。操作=suff-fibers；資料={\"theta_values\":[\"a4\",\"b4\"],\"samples\":[40,41,42,43],\"probability_rows\":[[[2,5],[1,10],[2,5],[1,10]],[[1,10],[2,5],[1,10],[2,5]]],\"statistic\":[0,1,0,1]}。請依 exact_ordered_tuple_declared_by_interface 欄序回答。","answer":{"kind":"expression","value":"([40, 41, 42, 43], [0, 1, 0, 1], [[0, [40, 42]], [1, [41, 43]]], 是, total_statistic_fibers_partition_sample_space)","explanation_zh":"Wave6第十層核對=([40, 41, 42, 43], [0, 1, 0, 1], [[0, [40, 42]], [1, [41, 43]]], 是, total_statistic_fibers_partition_sample_space)；依完整明示資料獨立重算；zero-mass conditional保持undefined，nonsufficient需明示witness；identity/constant boundaries分開且不使用factorization theorem或宣稱估計品質。"},"difficulty":{"band":"undergraduate_core","level":1,"skills":["有限模型充分統計量"]},"variant":{"family_id":"qf-mod47-suff-fibers","seed":202611165005,"parameters":{"theta_values":["a4","b4"],"samples":[40,41,42,43],"probability_rows":[[[2,5],[1,10],[2,5],[1,10]],[[1,10],[2,5],[1,10],[2,5]]],"statistic":[0,1,0,1],"domain":"Exact_finite_sufficient_statistic","operation":"suff-fibers","semantic_template":"qf-mod47-suff-fibers/{\"probability_rows\":[[[2,5],[1,10],[2,5],[1,10]],[[1,10],[2,5],[1,10],[2,5]]],\"samples\":[40,41,42,43],\"statistic\":[0,1,0,1],\"theta_values\":[\"a4\",\"b4\"]}"}},"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、一般Banach／IVT／Taylor證明、MLE漸近性、factorization theorem、一般DAG iff或primitive-root主張、Lean或Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-15","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261015-advance-20261116-r05-finite-sufficient-statistic-0006","batch_id":"batch-20261015-advance-20261116-r05-finite-sufficient-statistic-foundations","language":"zh-Hant","source_mko_ids":["mko-finite-sufficient-statistic"],"title_zh":"有限模型充分統計量","stem_zh":"total statistic fibers與正質量conditional laws的完整theta-invariance責任。操作=suff-fibers；資料={\"theta_values\":[\"a5\",\"b5\"],\"samples\":[50,51,52,53],\"probability_rows\":[[[2,5],[1,10],[2,5],[1,10]],[[1,10],[2,5],[1,10],[2,5]]],\"statistic\":[0,1,0,1]}。請依 exact_ordered_tuple_declared_by_interface 欄序回答。","answer":{"kind":"expression","value":"([50, 51, 52, 53], [0, 1, 0, 1], [[0, [50, 52]], [1, [51, 53]]], 是, total_statistic_fibers_partition_sample_space)","explanation_zh":"Wave6第十層核對=([50, 51, 52, 53], [0, 1, 0, 1], [[0, [50, 52]], [1, [51, 53]]], 是, total_statistic_fibers_partition_sample_space)；依完整明示資料獨立重算；zero-mass conditional保持undefined，nonsufficient需明示witness；identity/constant boundaries分開且不使用factorization theorem或宣稱估計品質。"},"difficulty":{"band":"undergraduate_core","level":1,"skills":["有限模型充分統計量"]},"variant":{"family_id":"qf-mod47-suff-fibers","seed":202611165006,"parameters":{"theta_values":["a5","b5"],"samples":[50,51,52,53],"probability_rows":[[[2,5],[1,10],[2,5],[1,10]],[[1,10],[2,5],[1,10],[2,5]]],"statistic":[0,1,0,1],"domain":"Exact_finite_sufficient_statistic","operation":"suff-fibers","semantic_template":"qf-mod47-suff-fibers/{\"probability_rows\":[[[2,5],[1,10],[2,5],[1,10]],[[1,10],[2,5],[1,10],[2,5]]],\"samples\":[50,51,52,53],\"statistic\":[0,1,0,1],\"theta_values\":[\"a5\",\"b5\"]}"}},"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、一般Banach／IVT／Taylor證明、MLE漸近性、factorization theorem、一般DAG iff或primitive-root主張、Lean或Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-15","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261015-advance-20261116-r05-finite-sufficient-statistic-0007","batch_id":"batch-20261015-advance-20261116-r05-finite-sufficient-statistic-foundations","language":"zh-Hant","source_mko_ids":["mko-finite-sufficient-statistic"],"title_zh":"有限模型充分統計量","stem_zh":"total statistic fibers與正質量conditional laws的完整theta-invariance責任。操作=suff-fibers；資料={\"theta_values\":[\"a6\",\"b6\"],\"samples\":[60,61,62,63],\"probability_rows\":[[[2,5],[1,10],[2,5],[1,10]],[[1,10],[2,5],[1,10],[2,5]]],\"statistic\":[0,1,0,1]}。請依 exact_ordered_tuple_declared_by_interface 欄序回答。","answer":{"kind":"expression","value":"([60, 61, 62, 63], [0, 1, 0, 1], [[0, [60, 62]], [1, [61, 63]]], 是, total_statistic_fibers_partition_sample_space)","explanation_zh":"Wave6第十層核對=([60, 61, 62, 63], [0, 1, 0, 1], [[0, [60, 62]], [1, [61, 63]]], 是, total_statistic_fibers_partition_sample_space)；依完整明示資料獨立重算；zero-mass conditional保持undefined，nonsufficient需明示witness；identity/constant boundaries分開且不使用factorization theorem或宣稱估計品質。"},"difficulty":{"band":"undergraduate_core","level":1,"skills":["有限模型充分統計量"]},"variant":{"family_id":"qf-mod47-suff-fibers","seed":202611165007,"parameters":{"theta_values":["a6","b6"],"samples":[60,61,62,63],"probability_rows":[[[2,5],[1,10],[2,5],[1,10]],[[1,10],[2,5],[1,10],[2,5]]],"statistic":[0,1,0,1],"domain":"Exact_finite_sufficient_statistic","operation":"suff-fibers","semantic_template":"qf-mod47-suff-fibers/{\"probability_rows\":[[[2,5],[1,10],[2,5],[1,10]],[[1,10],[2,5],[1,10],[2,5]]],\"samples\":[60,61,62,63],\"statistic\":[0,1,0,1],\"theta_values\":[\"a6\",\"b6\"]}"}},"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、一般Banach／IVT／Taylor證明、MLE漸近性、factorization theorem、一般DAG iff或primitive-root主張、Lean或Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-15","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261015-advance-20261116-r05-finite-sufficient-statistic-0008","batch_id":"batch-20261015-advance-20261116-r05-finite-sufficient-statistic-foundations","language":"zh-Hant","source_mko_ids":["mko-finite-sufficient-statistic"],"title_zh":"有限模型充分統計量","stem_zh":"total statistic fibers與正質量conditional laws的完整theta-invariance責任。操作=suff-fibers；資料={\"theta_values\":[\"a7\",\"b7\"],\"samples\":[70,71,72,73],\"probability_rows\":[[[2,5],[1,10],[2,5],[1,10]],[[1,10],[2,5],[1,10],[2,5]]],\"statistic\":[0,1,0,1]}。請依 exact_ordered_tuple_declared_by_interface 欄序回答。","answer":{"kind":"expression","value":"([70, 71, 72, 73], [0, 1, 0, 1], [[0, [70, 72]], [1, [71, 73]]], 是, total_statistic_fibers_partition_sample_space)","explanation_zh":"Wave6第十層核對=([70, 71, 72, 73], [0, 1, 0, 1], [[0, [70, 72]], [1, [71, 73]]], 是, total_statistic_fibers_partition_sample_space)；依完整明示資料獨立重算；zero-mass conditional保持undefined，nonsufficient需明示witness；identity/constant boundaries分開且不使用factorization theorem或宣稱估計品質。"},"difficulty":{"band":"undergraduate_core","level":1,"skills":["有限模型充分統計量"]},"variant":{"family_id":"qf-mod47-suff-fibers","seed":202611165008,"parameters":{"theta_values":["a7","b7"],"samples":[70,71,72,73],"probability_rows":[[[2,5],[1,10],[2,5],[1,10]],[[1,10],[2,5],[1,10],[2,5]]],"statistic":[0,1,0,1],"domain":"Exact_finite_sufficient_statistic","operation":"suff-fibers","semantic_template":"qf-mod47-suff-fibers/{\"probability_rows\":[[[2,5],[1,10],[2,5],[1,10]],[[1,10],[2,5],[1,10],[2,5]]],\"samples\":[70,71,72,73],\"statistic\":[0,1,0,1],\"theta_values\":[\"a7\",\"b7\"]}"}},"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、一般Banach／IVT／Taylor證明、MLE漸近性、factorization theorem、一般DAG iff或primitive-root主張、Lean或Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-15","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261015-advance-20261116-r05-finite-sufficient-statistic-0009","batch_id":"batch-20261015-advance-20261116-r05-finite-sufficient-statistic-foundations","language":"zh-Hant","source_mko_ids":["mko-finite-sufficient-statistic"],"title_zh":"有限模型充分統計量","stem_zh":"total statistic fibers與正質量conditional laws的完整theta-invariance責任。操作=suff-fibers；資料={\"theta_values\":[\"a8\",\"b8\"],\"samples\":[80,81,82,83],\"probability_rows\":[[[2,5],[1,10],[2,5],[1,10]],[[1,10],[2,5],[1,10],[2,5]]],\"statistic\":[0,1,0,1]}。請依 exact_ordered_tuple_declared_by_interface 欄序回答。","answer":{"kind":"expression","value":"([80, 81, 82, 83], [0, 1, 0, 1], [[0, [80, 82]], [1, [81, 83]]], 是, total_statistic_fibers_partition_sample_space)","explanation_zh":"Wave6第十層核對=([80, 81, 82, 83], [0, 1, 0, 1], [[0, [80, 82]], [1, [81, 83]]], 是, total_statistic_fibers_partition_sample_space)；依完整明示資料獨立重算；zero-mass conditional保持undefined，nonsufficient需明示witness；identity/constant boundaries分開且不使用factorization theorem或宣稱估計品質。"},"difficulty":{"band":"undergraduate_core","level":2,"skills":["有限模型充分統計量"]},"variant":{"family_id":"qf-mod47-suff-fibers","seed":202611165009,"parameters":{"theta_values":["a8","b8"],"samples":[80,81,82,83],"probability_rows":[[[2,5],[1,10],[2,5],[1,10]],[[1,10],[2,5],[1,10],[2,5]]],"statistic":[0,1,0,1],"domain":"Exact_finite_sufficient_statistic","operation":"suff-fibers","semantic_template":"qf-mod47-suff-fibers/{\"probability_rows\":[[[2,5],[1,10],[2,5],[1,10]],[[1,10],[2,5],[1,10],[2,5]]],\"samples\":[80,81,82,83],\"statistic\":[0,1,0,1],\"theta_values\":[\"a8\",\"b8\"]}"}},"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、一般Banach／IVT／Taylor證明、MLE漸近性、factorization theorem、一般DAG iff或primitive-root主張、Lean或Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-15","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261015-advance-20261116-r05-finite-sufficient-statistic-0010","batch_id":"batch-20261015-advance-20261116-r05-finite-sufficient-statistic-foundations","language":"zh-Hant","source_mko_ids":["mko-finite-sufficient-statistic"],"title_zh":"有限模型充分統計量","stem_zh":"total statistic fibers與正質量conditional laws的完整theta-invariance責任。操作=suff-fibers；資料={\"theta_values\":[\"a9\",\"b9\"],\"samples\":[90,91,92,93],\"probability_rows\":[[[2,5],[1,10],[2,5],[1,10]],[[1,10],[2,5],[1,10],[2,5]]],\"statistic\":[0,1,0,1]}。請依 exact_ordered_tuple_declared_by_interface 欄序回答。","answer":{"kind":"expression","value":"([90, 91, 92, 93], [0, 1, 0, 1], [[0, [90, 92]], [1, [91, 93]]], 是, total_statistic_fibers_partition_sample_space)","explanation_zh":"Wave6第十層核對=([90, 91, 92, 93], [0, 1, 0, 1], [[0, [90, 92]], [1, [91, 93]]], 是, total_statistic_fibers_partition_sample_space)；依完整明示資料獨立重算；zero-mass conditional保持undefined，nonsufficient需明示witness；identity/constant boundaries分開且不使用factorization theorem或宣稱估計品質。"},"difficulty":{"band":"undergraduate_core","level":2,"skills":["有限模型充分統計量"]},"variant":{"family_id":"qf-mod47-suff-fibers","seed":202611165010,"parameters":{"theta_values":["a9","b9"],"samples":[90,91,92,93],"probability_rows":[[[2,5],[1,10],[2,5],[1,10]],[[1,10],[2,5],[1,10],[2,5]]],"statistic":[0,1,0,1],"domain":"Exact_finite_sufficient_statistic","operation":"suff-fibers","semantic_template":"qf-mod47-suff-fibers/{\"probability_rows\":[[[2,5],[1,10],[2,5],[1,10]],[[1,10],[2,5],[1,10],[2,5]]],\"samples\":[90,91,92,93],\"statistic\":[0,1,0,1],\"theta_values\":[\"a9\",\"b9\"]}"}},"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、一般Banach／IVT／Taylor證明、MLE漸近性、factorization theorem、一般DAG iff或primitive-root主張、Lean或Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-15","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261015-advance-20261116-r05-finite-sufficient-statistic-0011","batch_id":"batch-20261015-advance-20261116-r05-finite-sufficient-statistic-foundations","language":"zh-Hant","source_mko_ids":["mko-finite-sufficient-statistic"],"title_zh":"有限模型充分統計量","stem_zh":"total statistic fibers與正質量conditional laws的完整theta-invariance責任。操作=suff-fibers；資料={\"theta_values\":[\"a10\",\"b10\"],\"samples\":[100,101,102,103],\"probability_rows\":[[[2,5],[1,10],[2,5],[1,10]],[[1,10],[2,5],[1,10],[2,5]]],\"statistic\":[0,1,0,1]}。請依 exact_ordered_tuple_declared_by_interface 欄序回答。","answer":{"kind":"expression","value":"([100, 101, 102, 103], [0, 1, 0, 1], [[0, [100, 102]], [1, [101, 103]]], 是, total_statistic_fibers_partition_sample_space)","explanation_zh":"Wave6第十層核對=([100, 101, 102, 103], [0, 1, 0, 1], [[0, [100, 102]], [1, [101, 103]]], 是, total_statistic_fibers_partition_sample_space)；依完整明示資料獨立重算；zero-mass conditional保持undefined，nonsufficient需明示witness；identity/constant boundaries分開且不使用factorization theorem或宣稱估計品質。"},"difficulty":{"band":"undergraduate_core","level":2,"skills":["有限模型充分統計量"]},"variant":{"family_id":"qf-mod47-suff-fibers","seed":202611165011,"parameters":{"theta_values":["a10","b10"],"samples":[100,101,102,103],"probability_rows":[[[2,5],[1,10],[2,5],[1,10]],[[1,10],[2,5],[1,10],[2,5]]],"statistic":[0,1,0,1],"domain":"Exact_finite_sufficient_statistic","operation":"suff-fibers","semantic_template":"qf-mod47-suff-fibers/{\"probability_rows\":[[[2,5],[1,10],[2,5],[1,10]],[[1,10],[2,5],[1,10],[2,5]]],\"samples\":[100,101,102,103],\"statistic\":[0,1,0,1],\"theta_values\":[\"a10\",\"b10\"]}"}},"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、一般Banach／IVT／Taylor證明、MLE漸近性、factorization theorem、一般DAG iff或primitive-root主張、Lean或Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-15","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261015-advance-20261116-r05-finite-sufficient-statistic-0012","batch_id":"batch-20261015-advance-20261116-r05-finite-sufficient-statistic-foundations","language":"zh-Hant","source_mko_ids":["mko-finite-sufficient-statistic"],"title_zh":"有限模型充分統計量","stem_zh":"total statistic fibers與正質量conditional laws的完整theta-invariance責任。操作=suff-fibers；資料={\"theta_values\":[\"a11\",\"b11\"],\"samples\":[110,111,112,113],\"probability_rows\":[[[2,5],[1,10],[2,5],[1,10]],[[1,10],[2,5],[1,10],[2,5]]],\"statistic\":[0,1,0,1]}。請依 exact_ordered_tuple_declared_by_interface 欄序回答。","answer":{"kind":"expression","value":"([110, 111, 112, 113], [0, 1, 0, 1], [[0, [110, 112]], [1, [111, 113]]], 是, total_statistic_fibers_partition_sample_space)","explanation_zh":"Wave6第十層核對=([110, 111, 112, 113], [0, 1, 0, 1], [[0, [110, 112]], [1, [111, 113]]], 是, total_statistic_fibers_partition_sample_space)；依完整明示資料獨立重算；zero-mass conditional保持undefined，nonsufficient需明示witness；identity/constant boundaries分開且不使用factorization theorem或宣稱估計品質。"},"difficulty":{"band":"undergraduate_core","level":2,"skills":["有限模型充分統計量"]},"variant":{"family_id":"qf-mod47-suff-fibers","seed":202611165012,"parameters":{"theta_values":["a11","b11"],"samples":[110,111,112,113],"probability_rows":[[[2,5],[1,10],[2,5],[1,10]],[[1,10],[2,5],[1,10],[2,5]]],"statistic":[0,1,0,1],"domain":"Exact_finite_sufficient_statistic","operation":"suff-fibers","semantic_template":"qf-mod47-suff-fibers/{\"probability_rows\":[[[2,5],[1,10],[2,5],[1,10]],[[1,10],[2,5],[1,10],[2,5]]],\"samples\":[110,111,112,113],\"statistic\":[0,1,0,1],\"theta_values\":[\"a11\",\"b11\"]}"}},"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、一般Banach／IVT／Taylor證明、MLE漸近性、factorization theorem、一般DAG iff或primitive-root主張、Lean或Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-15","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261015-advance-20261116-r05-finite-sufficient-statistic-0013","batch_id":"batch-20261015-advance-20261116-r05-finite-sufficient-statistic-foundations","language":"zh-Hant","source_mko_ids":["mko-finite-sufficient-statistic"],"title_zh":"有限模型充分統計量","stem_zh":"total statistic fibers與正質量conditional laws的完整theta-invariance責任。操作=suff-fibers；資料={\"theta_values\":[\"a12\",\"b12\"],\"samples\":[120,121,122,123],\"probability_rows\":[[[2,5],[1,10],[2,5],[1,10]],[[1,10],[2,5],[1,10],[2,5]]],\"statistic\":[0,1,0,1]}。請依 exact_ordered_tuple_declared_by_interface 欄序回答。","answer":{"kind":"expression","value":"([120, 121, 122, 123], [0, 1, 0, 1], [[0, [120, 122]], [1, [121, 123]]], 是, total_statistic_fibers_partition_sample_space)","explanation_zh":"Wave6第十層核對=([120, 121, 122, 123], [0, 1, 0, 1], [[0, [120, 122]], [1, [121, 123]]], 是, total_statistic_fibers_partition_sample_space)；依完整明示資料獨立重算；zero-mass conditional保持undefined，nonsufficient需明示witness；identity/constant boundaries分開且不使用factorization theorem或宣稱估計品質。"},"difficulty":{"band":"undergraduate_core","level":2,"skills":["有限模型充分統計量"]},"variant":{"family_id":"qf-mod47-suff-fibers","seed":202611165013,"parameters":{"theta_values":["a12","b12"],"samples":[120,121,122,123],"probability_rows":[[[2,5],[1,10],[2,5],[1,10]],[[1,10],[2,5],[1,10],[2,5]]],"statistic":[0,1,0,1],"domain":"Exact_finite_sufficient_statistic","operation":"suff-fibers","semantic_template":"qf-mod47-suff-fibers/{\"probability_rows\":[[[2,5],[1,10],[2,5],[1,10]],[[1,10],[2,5],[1,10],[2,5]]],\"samples\":[120,121,122,123],\"statistic\":[0,1,0,1],\"theta_values\":[\"a12\",\"b12\"]}"}},"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、一般Banach／IVT／Taylor證明、MLE漸近性、factorization theorem、一般DAG iff或primitive-root主張、Lean或Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-15","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261015-advance-20261116-r05-finite-sufficient-statistic-0014","batch_id":"batch-20261015-advance-20261116-r05-finite-sufficient-statistic-foundations","language":"zh-Hant","source_mko_ids":["mko-finite-sufficient-statistic"],"title_zh":"有限模型充分統計量","stem_zh":"total statistic fibers與正質量conditional laws的完整theta-invariance責任。操作=suff-fibers；資料={\"theta_values\":[\"a13\",\"b13\"],\"samples\":[130,131,132,133],\"probability_rows\":[[[2,5],[1,10],[2,5],[1,10]],[[1,10],[2,5],[1,10],[2,5]]],\"statistic\":[0,1,0,1]}。請依 exact_ordered_tuple_declared_by_interface 欄序回答。","answer":{"kind":"expression","value":"([130, 131, 132, 133], [0, 1, 0, 1], [[0, [130, 132]], [1, [131, 133]]], 是, total_statistic_fibers_partition_sample_space)","explanation_zh":"Wave6第十層核對=([130, 131, 132, 133], [0, 1, 0, 1], [[0, [130, 132]], [1, [131, 133]]], 是, total_statistic_fibers_partition_sample_space)；依完整明示資料獨立重算；zero-mass conditional保持undefined，nonsufficient需明示witness；identity/constant boundaries分開且不使用factorization theorem或宣稱估計品質。"},"difficulty":{"band":"undergraduate_core","level":2,"skills":["有限模型充分統計量"]},"variant":{"family_id":"qf-mod47-suff-fibers","seed":202611165014,"parameters":{"theta_values":["a13","b13"],"samples":[130,131,132,133],"probability_rows":[[[2,5],[1,10],[2,5],[1,10]],[[1,10],[2,5],[1,10],[2,5]]],"statistic":[0,1,0,1],"domain":"Exact_finite_sufficient_statistic","operation":"suff-fibers","semantic_template":"qf-mod47-suff-fibers/{\"probability_rows\":[[[2,5],[1,10],[2,5],[1,10]],[[1,10],[2,5],[1,10],[2,5]]],\"samples\":[130,131,132,133],\"statistic\":[0,1,0,1],\"theta_values\":[\"a13\",\"b13\"]}"}},"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、一般Banach／IVT／Taylor證明、MLE漸近性、factorization theorem、一般DAG iff或primitive-root主張、Lean或Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-15","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261015-advance-20261116-r05-finite-sufficient-statistic-0015","batch_id":"batch-20261015-advance-20261116-r05-finite-sufficient-statistic-foundations","language":"zh-Hant","source_mko_ids":["mko-finite-sufficient-statistic"],"title_zh":"有限模型充分統計量","stem_zh":"total statistic fibers與正質量conditional laws的完整theta-invariance責任。操作=suff-fibers；資料={\"theta_values\":[\"a14\",\"b14\"],\"samples\":[140,141,142,143],\"probability_rows\":[[[2,5],[1,10],[2,5],[1,10]],[[1,10],[2,5],[1,10],[2,5]]],\"statistic\":[0,1,0,1]}。請依 exact_ordered_tuple_declared_by_interface 欄序回答。","answer":{"kind":"expression","value":"([140, 141, 142, 143], [0, 1, 0, 1], [[0, [140, 142]], [1, [141, 143]]], 是, total_statistic_fibers_partition_sample_space)","explanation_zh":"Wave6第十層核對=([140, 141, 142, 143], [0, 1, 0, 1], [[0, [140, 142]], [1, [141, 143]]], 是, total_statistic_fibers_partition_sample_space)；依完整明示資料獨立重算；zero-mass conditional保持undefined，nonsufficient需明示witness；identity/constant boundaries分開且不使用factorization theorem或宣稱估計品質。"},"difficulty":{"band":"undergraduate_core","level":2,"skills":["有限模型充分統計量"]},"variant":{"family_id":"qf-mod47-suff-fibers","seed":202611165015,"parameters":{"theta_values":["a14","b14"],"samples":[140,141,142,143],"probability_rows":[[[2,5],[1,10],[2,5],[1,10]],[[1,10],[2,5],[1,10],[2,5]]],"statistic":[0,1,0,1],"domain":"Exact_finite_sufficient_statistic","operation":"suff-fibers","semantic_template":"qf-mod47-suff-fibers/{\"probability_rows\":[[[2,5],[1,10],[2,5],[1,10]],[[1,10],[2,5],[1,10],[2,5]]],\"samples\":[140,141,142,143],\"statistic\":[0,1,0,1],\"theta_values\":[\"a14\",\"b14\"]}"}},"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、一般Banach／IVT／Taylor證明、MLE漸近性、factorization theorem、一般DAG iff或primitive-root主張、Lean或Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-15","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261015-advance-20261116-r05-finite-sufficient-statistic-0016","batch_id":"batch-20261015-advance-20261116-r05-finite-sufficient-statistic-foundations","language":"zh-Hant","source_mko_ids":["mko-finite-sufficient-statistic"],"title_zh":"有限模型充分統計量","stem_zh":"total statistic fibers與正質量conditional laws的完整theta-invariance責任。操作=suff-fibers；資料={\"theta_values\":[\"a15\",\"b15\"],\"samples\":[150,151,152,153],\"probability_rows\":[[[2,5],[1,10],[2,5],[1,10]],[[1,10],[2,5],[1,10],[2,5]]],\"statistic\":[0,1,0,1]}。請依 exact_ordered_tuple_declared_by_interface 欄序回答。","answer":{"kind":"expression","value":"([150, 151, 152, 153], [0, 1, 0, 1], [[0, [150, 152]], [1, [151, 153]]], 是, total_statistic_fibers_partition_sample_space)","explanation_zh":"Wave6第十層核對=([150, 151, 152, 153], [0, 1, 0, 1], [[0, [150, 152]], [1, [151, 153]]], 是, total_statistic_fibers_partition_sample_space)；依完整明示資料獨立重算；zero-mass conditional保持undefined，nonsufficient需明示witness；identity/constant boundaries分開且不使用factorization theorem或宣稱估計品質。"},"difficulty":{"band":"undergraduate_core","level":2,"skills":["有限模型充分統計量"]},"variant":{"family_id":"qf-mod47-suff-fibers","seed":202611165016,"parameters":{"theta_values":["a15","b15"],"samples":[150,151,152,153],"probability_rows":[[[2,5],[1,10],[2,5],[1,10]],[[1,10],[2,5],[1,10],[2,5]]],"statistic":[0,1,0,1],"domain":"Exact_finite_sufficient_statistic","operation":"suff-fibers","semantic_template":"qf-mod47-suff-fibers/{\"probability_rows\":[[[2,5],[1,10],[2,5],[1,10]],[[1,10],[2,5],[1,10],[2,5]]],\"samples\":[150,151,152,153],\"statistic\":[0,1,0,1],\"theta_values\":[\"a15\",\"b15\"]}"}},"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、一般Banach／IVT／Taylor證明、MLE漸近性、factorization theorem、一般DAG iff或primitive-root主張、Lean或Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-15","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261015-advance-20261116-r05-finite-sufficient-statistic-0017","batch_id":"batch-20261015-advance-20261116-r05-finite-sufficient-statistic-foundations","language":"zh-Hant","source_mko_ids":["mko-finite-sufficient-statistic"],"title_zh":"有限模型充分統計量","stem_zh":"total statistic fibers與正質量conditional laws的完整theta-invariance責任。操作=suff-fibers；資料={\"theta_values\":[\"a16\",\"b16\"],\"samples\":[160,161,162,163],\"probability_rows\":[[[2,5],[1,10],[2,5],[1,10]],[[1,10],[2,5],[1,10],[2,5]]],\"statistic\":[0,1,0,1]}。請依 exact_ordered_tuple_declared_by_interface 欄序回答。","answer":{"kind":"expression","value":"([160, 161, 162, 163], [0, 1, 0, 1], [[0, [160, 162]], [1, [161, 163]]], 是, total_statistic_fibers_partition_sample_space)","explanation_zh":"Wave6第十層核對=([160, 161, 162, 163], [0, 1, 0, 1], [[0, [160, 162]], [1, [161, 163]]], 是, total_statistic_fibers_partition_sample_space)；依完整明示資料獨立重算；zero-mass conditional保持undefined，nonsufficient需明示witness；identity/constant boundaries分開且不使用factorization theorem或宣稱估計品質。"},"difficulty":{"band":"undergraduate_core","level":2,"skills":["有限模型充分統計量"]},"variant":{"family_id":"qf-mod47-suff-fibers","seed":202611165017,"parameters":{"theta_values":["a16","b16"],"samples":[160,161,162,163],"probability_rows":[[[2,5],[1,10],[2,5],[1,10]],[[1,10],[2,5],[1,10],[2,5]]],"statistic":[0,1,0,1],"domain":"Exact_finite_sufficient_statistic","operation":"suff-fibers","semantic_template":"qf-mod47-suff-fibers/{\"probability_rows\":[[[2,5],[1,10],[2,5],[1,10]],[[1,10],[2,5],[1,10],[2,5]]],\"samples\":[160,161,162,163],\"statistic\":[0,1,0,1],\"theta_values\":[\"a16\",\"b16\"]}"}},"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、一般Banach／IVT／Taylor證明、MLE漸近性、factorization theorem、一般DAG iff或primitive-root主張、Lean或Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-15","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261015-advance-20261116-r05-finite-sufficient-statistic-0018","batch_id":"batch-20261015-advance-20261116-r05-finite-sufficient-statistic-foundations","language":"zh-Hant","source_mko_ids":["mko-finite-sufficient-statistic"],"title_zh":"有限模型充分統計量","stem_zh":"total statistic fibers與正質量conditional laws的完整theta-invariance責任。操作=suff-fibers；資料={\"theta_values\":[\"a17\",\"b17\"],\"samples\":[170,171,172,173],\"probability_rows\":[[[2,5],[1,10],[2,5],[1,10]],[[1,10],[2,5],[1,10],[2,5]]],\"statistic\":[0,1,0,1]}。請依 exact_ordered_tuple_declared_by_interface 欄序回答。","answer":{"kind":"expression","value":"([170, 171, 172, 173], [0, 1, 0, 1], [[0, [170, 172]], [1, [171, 173]]], 是, total_statistic_fibers_partition_sample_space)","explanation_zh":"Wave6第十層核對=([170, 171, 172, 173], [0, 1, 0, 1], [[0, [170, 172]], [1, [171, 173]]], 是, total_statistic_fibers_partition_sample_space)；依完整明示資料獨立重算；zero-mass conditional保持undefined，nonsufficient需明示witness；identity/constant boundaries分開且不使用factorization theorem或宣稱估計品質。"},"difficulty":{"band":"undergraduate_core","level":3,"skills":["有限模型充分統計量"]},"variant":{"family_id":"qf-mod47-suff-fibers","seed":202611165018,"parameters":{"theta_values":["a17","b17"],"samples":[170,171,172,173],"probability_rows":[[[2,5],[1,10],[2,5],[1,10]],[[1,10],[2,5],[1,10],[2,5]]],"statistic":[0,1,0,1],"domain":"Exact_finite_sufficient_statistic","operation":"suff-fibers","semantic_template":"qf-mod47-suff-fibers/{\"probability_rows\":[[[2,5],[1,10],[2,5],[1,10]],[[1,10],[2,5],[1,10],[2,5]]],\"samples\":[170,171,172,173],\"statistic\":[0,1,0,1],\"theta_values\":[\"a17\",\"b17\"]}"}},"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、一般Banach／IVT／Taylor證明、MLE漸近性、factorization theorem、一般DAG iff或primitive-root主張、Lean或Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-15","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261015-advance-20261116-r05-finite-sufficient-statistic-0019","batch_id":"batch-20261015-advance-20261116-r05-finite-sufficient-statistic-foundations","language":"zh-Hant","source_mko_ids":["mko-finite-sufficient-statistic"],"title_zh":"有限模型充分統計量","stem_zh":"total statistic fibers與正質量conditional laws的完整theta-invariance責任。操作=suff-fibers；資料={\"theta_values\":[\"a18\",\"b18\"],\"samples\":[180,181,182,183],\"probability_rows\":[[[2,5],[1,10],[2,5],[1,10]],[[1,10],[2,5],[1,10],[2,5]]],\"statistic\":[0,1,0,1]}。請依 exact_ordered_tuple_declared_by_interface 欄序回答。","answer":{"kind":"expression","value":"([180, 181, 182, 183], [0, 1, 0, 1], [[0, [180, 182]], [1, [181, 183]]], 是, total_statistic_fibers_partition_sample_space)","explanation_zh":"Wave6第十層核對=([180, 181, 182, 183], [0, 1, 0, 1], [[0, [180, 182]], [1, [181, 183]]], 是, total_statistic_fibers_partition_sample_space)；依完整明示資料獨立重算；zero-mass conditional保持undefined，nonsufficient需明示witness；identity/constant boundaries分開且不使用factorization theorem或宣稱估計品質。"},"difficulty":{"band":"undergraduate_core","level":3,"skills":["有限模型充分統計量"]},"variant":{"family_id":"qf-mod47-suff-fibers","seed":202611165019,"parameters":{"theta_values":["a18","b18"],"samples":[180,181,182,183],"probability_rows":[[[2,5],[1,10],[2,5],[1,10]],[[1,10],[2,5],[1,10],[2,5]]],"statistic":[0,1,0,1],"domain":"Exact_finite_sufficient_statistic","operation":"suff-fibers","semantic_template":"qf-mod47-suff-fibers/{\"probability_rows\":[[[2,5],[1,10],[2,5],[1,10]],[[1,10],[2,5],[1,10],[2,5]]],\"samples\":[180,181,182,183],\"statistic\":[0,1,0,1],\"theta_values\":[\"a18\",\"b18\"]}"}},"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、一般Banach／IVT／Taylor證明、MLE漸近性、factorization theorem、一般DAG iff或primitive-root主張、Lean或Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-15","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261015-advance-20261116-r05-finite-sufficient-statistic-0020","batch_id":"batch-20261015-advance-20261116-r05-finite-sufficient-statistic-foundations","language":"zh-Hant","source_mko_ids":["mko-finite-sufficient-statistic"],"title_zh":"有限模型充分統計量","stem_zh":"total statistic fibers與正質量conditional laws的完整theta-invariance責任。操作=suff-fibers；資料={\"theta_values\":[\"a19\",\"b19\"],\"samples\":[190,191,192,193],\"probability_rows\":[[[2,5],[1,10],[2,5],[1,10]],[[1,10],[2,5],[1,10],[2,5]]],\"statistic\":[0,1,0,1]}。請依 exact_ordered_tuple_declared_by_interface 欄序回答。","answer":{"kind":"expression","value":"([190, 191, 192, 193], [0, 1, 0, 1], [[0, [190, 192]], [1, [191, 193]]], 是, total_statistic_fibers_partition_sample_space)","explanation_zh":"Wave6第十層核對=([190, 191, 192, 193], [0, 1, 0, 1], [[0, [190, 192]], [1, [191, 193]]], 是, total_statistic_fibers_partition_sample_space)；依完整明示資料獨立重算；zero-mass conditional保持undefined，nonsufficient需明示witness；identity/constant boundaries分開且不使用factorization theorem或宣稱估計品質。"},"difficulty":{"band":"undergraduate_core","level":3,"skills":["有限模型充分統計量"]},"variant":{"family_id":"qf-mod47-suff-fibers","seed":202611165020,"parameters":{"theta_values":["a19","b19"],"samples":[190,191,192,193],"probability_rows":[[[2,5],[1,10],[2,5],[1,10]],[[1,10],[2,5],[1,10],[2,5]]],"statistic":[0,1,0,1],"domain":"Exact_finite_sufficient_statistic","operation":"suff-fibers","semantic_template":"qf-mod47-suff-fibers/{\"probability_rows\":[[[2,5],[1,10],[2,5],[1,10]],[[1,10],[2,5],[1,10],[2,5]]],\"samples\":[190,191,192,193],\"statistic\":[0,1,0,1],\"theta_values\":[\"a19\",\"b19\"]}"}},"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、一般Banach／IVT／Taylor證明、MLE漸近性、factorization theorem、一般DAG iff或primitive-root主張、Lean或Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-15","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261015-advance-20261116-r05-finite-sufficient-statistic-0021","batch_id":"batch-20261015-advance-20261116-r05-finite-sufficient-statistic-foundations","language":"zh-Hant","source_mko_ids":["mko-finite-sufficient-statistic"],"title_zh":"有限模型充分統計量","stem_zh":"total statistic fibers與正質量conditional laws的完整theta-invariance責任。操作=suff-fibers；資料={\"theta_values\":[\"a20\",\"b20\"],\"samples\":[200,201,202,203],\"probability_rows\":[[[2,5],[1,10],[2,5],[1,10]],[[1,10],[2,5],[1,10],[2,5]]],\"statistic\":[0,1,0,1]}。請依 exact_ordered_tuple_declared_by_interface 欄序回答。","answer":{"kind":"expression","value":"([200, 201, 202, 203], [0, 1, 0, 1], [[0, [200, 202]], [1, [201, 203]]], 是, total_statistic_fibers_partition_sample_space)","explanation_zh":"Wave6第十層核對=([200, 201, 202, 203], [0, 1, 0, 1], [[0, [200, 202]], [1, [201, 203]]], 是, total_statistic_fibers_partition_sample_space)；依完整明示資料獨立重算；zero-mass conditional保持undefined，nonsufficient需明示witness；identity/constant boundaries分開且不使用factorization theorem或宣稱估計品質。"},"difficulty":{"band":"undergraduate_core","level":3,"skills":["有限模型充分統計量"]},"variant":{"family_id":"qf-mod47-suff-fibers","seed":202611165021,"parameters":{"theta_values":["a20","b20"],"samples":[200,201,202,203],"probability_rows":[[[2,5],[1,10],[2,5],[1,10]],[[1,10],[2,5],[1,10],[2,5]]],"statistic":[0,1,0,1],"domain":"Exact_finite_sufficient_statistic","operation":"suff-fibers","semantic_template":"qf-mod47-suff-fibers/{\"probability_rows\":[[[2,5],[1,10],[2,5],[1,10]],[[1,10],[2,5],[1,10],[2,5]]],\"samples\":[200,201,202,203],\"statistic\":[0,1,0,1],\"theta_values\":[\"a20\",\"b20\"]}"}},"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、一般Banach／IVT／Taylor證明、MLE漸近性、factorization theorem、一般DAG iff或primitive-root主張、Lean或Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-15","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261015-advance-20261116-r05-finite-sufficient-statistic-0022","batch_id":"batch-20261015-advance-20261116-r05-finite-sufficient-statistic-foundations","language":"zh-Hant","source_mko_ids":["mko-finite-sufficient-statistic"],"title_zh":"有限模型充分統計量","stem_zh":"total statistic fibers與正質量conditional laws的完整theta-invariance責任。操作=suff-fibers；資料={\"theta_values\":[\"a21\",\"b21\"],\"samples\":[210,211,212,213],\"probability_rows\":[[[2,5],[1,10],[2,5],[1,10]],[[1,10],[2,5],[1,10],[2,5]]],\"statistic\":[0,1,0,1]}。請依 exact_ordered_tuple_declared_by_interface 欄序回答。","answer":{"kind":"expression","value":"([210, 211, 212, 213], [0, 1, 0, 1], [[0, [210, 212]], [1, [211, 213]]], 是, total_statistic_fibers_partition_sample_space)","explanation_zh":"Wave6第十層核對=([210, 211, 212, 213], [0, 1, 0, 1], [[0, [210, 212]], [1, [211, 213]]], 是, total_statistic_fibers_partition_sample_space)；依完整明示資料獨立重算；zero-mass conditional保持undefined，nonsufficient需明示witness；identity/constant boundaries分開且不使用factorization theorem或宣稱估計品質。"},"difficulty":{"band":"undergraduate_core","level":3,"skills":["有限模型充分統計量"]},"variant":{"family_id":"qf-mod47-suff-fibers","seed":202611165022,"parameters":{"theta_values":["a21","b21"],"samples":[210,211,212,213],"probability_rows":[[[2,5],[1,10],[2,5],[1,10]],[[1,10],[2,5],[1,10],[2,5]]],"statistic":[0,1,0,1],"domain":"Exact_finite_sufficient_statistic","operation":"suff-fibers","semantic_template":"qf-mod47-suff-fibers/{\"probability_rows\":[[[2,5],[1,10],[2,5],[1,10]],[[1,10],[2,5],[1,10],[2,5]]],\"samples\":[210,211,212,213],\"statistic\":[0,1,0,1],\"theta_values\":[\"a21\",\"b21\"]}"}},"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、一般Banach／IVT／Taylor證明、MLE漸近性、factorization theorem、一般DAG iff或primitive-root主張、Lean或Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-15","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261015-advance-20261116-r05-finite-sufficient-statistic-0023","batch_id":"batch-20261015-advance-20261116-r05-finite-sufficient-statistic-foundations","language":"zh-Hant","source_mko_ids":["mko-finite-sufficient-statistic"],"title_zh":"有限模型充分統計量","stem_zh":"total statistic fibers與正質量conditional laws的完整theta-invariance責任。操作=suff-fibers；資料={\"theta_values\":[\"a22\",\"b22\"],\"samples\":[220,221,222,223],\"probability_rows\":[[[2,5],[1,10],[2,5],[1,10]],[[1,10],[2,5],[1,10],[2,5]]],\"statistic\":[0,1,0,1]}。請依 exact_ordered_tuple_declared_by_interface 欄序回答。","answer":{"kind":"expression","value":"([220, 221, 222, 223], [0, 1, 0, 1], [[0, [220, 222]], [1, [221, 223]]], 是, total_statistic_fibers_partition_sample_space)","explanation_zh":"Wave6第十層核對=([220, 221, 222, 223], [0, 1, 0, 1], [[0, [220, 222]], [1, [221, 223]]], 是, total_statistic_fibers_partition_sample_space)；依完整明示資料獨立重算；zero-mass conditional保持undefined，nonsufficient需明示witness；identity/constant boundaries分開且不使用factorization theorem或宣稱估計品質。"},"difficulty":{"band":"undergraduate_core","level":3,"skills":["有限模型充分統計量"]},"variant":{"family_id":"qf-mod47-suff-fibers","seed":202611165023,"parameters":{"theta_values":["a22","b22"],"samples":[220,221,222,223],"probability_rows":[[[2,5],[1,10],[2,5],[1,10]],[[1,10],[2,5],[1,10],[2,5]]],"statistic":[0,1,0,1],"domain":"Exact_finite_sufficient_statistic","operation":"suff-fibers","semantic_template":"qf-mod47-suff-fibers/{\"probability_rows\":[[[2,5],[1,10],[2,5],[1,10]],[[1,10],[2,5],[1,10],[2,5]]],\"samples\":[220,221,222,223],\"statistic\":[0,1,0,1],\"theta_values\":[\"a22\",\"b22\"]}"}},"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、一般Banach／IVT／Taylor證明、MLE漸近性、factorization theorem、一般DAG iff或primitive-root主張、Lean或Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-15","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261015-advance-20261116-r05-finite-sufficient-statistic-0024","batch_id":"batch-20261015-advance-20261116-r05-finite-sufficient-statistic-foundations","language":"zh-Hant","source_mko_ids":["mko-finite-sufficient-statistic"],"title_zh":"有限模型充分統計量","stem_zh":"total statistic fibers與正質量conditional laws的完整theta-invariance責任。操作=suff-fibers；資料={\"theta_values\":[\"a23\",\"b23\"],\"samples\":[230,231,232,233],\"probability_rows\":[[[2,5],[1,10],[2,5],[1,10]],[[1,10],[2,5],[1,10],[2,5]]],\"statistic\":[0,1,0,1]}。請依 exact_ordered_tuple_declared_by_interface 欄序回答。","answer":{"kind":"expression","value":"([230, 231, 232, 233], [0, 1, 0, 1], [[0, [230, 232]], [1, [231, 233]]], 是, total_statistic_fibers_partition_sample_space)","explanation_zh":"Wave6第十層核對=([230, 231, 232, 233], [0, 1, 0, 1], [[0, [230, 232]], [1, [231, 233]]], 是, total_statistic_fibers_partition_sample_space)；依完整明示資料獨立重算；zero-mass conditional保持undefined，nonsufficient需明示witness；identity/constant boundaries分開且不使用factorization theorem或宣稱估計品質。"},"difficulty":{"band":"undergraduate_core","level":3,"skills":["有限模型充分統計量"]},"variant":{"family_id":"qf-mod47-suff-fibers","seed":202611165024,"parameters":{"theta_values":["a23","b23"],"samples":[230,231,232,233],"probability_rows":[[[2,5],[1,10],[2,5],[1,10]],[[1,10],[2,5],[1,10],[2,5]]],"statistic":[0,1,0,1],"domain":"Exact_finite_sufficient_statistic","operation":"suff-fibers","semantic_template":"qf-mod47-suff-fibers/{\"probability_rows\":[[[2,5],[1,10],[2,5],[1,10]],[[1,10],[2,5],[1,10],[2,5]]],\"samples\":[230,231,232,233],\"statistic\":[0,1,0,1],\"theta_values\":[\"a23\",\"b23\"]}"}},"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、一般Banach／IVT／Taylor證明、MLE漸近性、factorization theorem、一般DAG iff或primitive-root主張、Lean或Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-15","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261015-advance-20261116-r05-finite-sufficient-statistic-0025","batch_id":"batch-20261015-advance-20261116-r05-finite-sufficient-statistic-foundations","language":"zh-Hant","source_mko_ids":["mko-finite-sufficient-statistic"],"title_zh":"有限模型充分統計量","stem_zh":"total statistic fibers與正質量conditional laws的完整theta-invariance責任。操作=suff-fibers；資料={\"theta_values\":[\"a24\",\"b24\"],\"samples\":[240,241,242,243],\"probability_rows\":[[[2,5],[1,10],[2,5],[1,10]],[[1,10],[2,5],[1,10],[2,5]]],\"statistic\":[0,1,0,1]}。請依 exact_ordered_tuple_declared_by_interface 欄序回答。","answer":{"kind":"expression","value":"([240, 241, 242, 243], [0, 1, 0, 1], [[0, [240, 242]], [1, [241, 243]]], 是, total_statistic_fibers_partition_sample_space)","explanation_zh":"Wave6第十層核對=([240, 241, 242, 243], [0, 1, 0, 1], [[0, [240, 242]], [1, [241, 243]]], 是, total_statistic_fibers_partition_sample_space)；依完整明示資料獨立重算；zero-mass conditional保持undefined，nonsufficient需明示witness；identity/constant boundaries分開且不使用factorization theorem或宣稱估計品質。"},"difficulty":{"band":"undergraduate_core","level":3,"skills":["有限模型充分統計量"]},"variant":{"family_id":"qf-mod47-suff-fibers","seed":202611165025,"parameters":{"theta_values":["a24","b24"],"samples":[240,241,242,243],"probability_rows":[[[2,5],[1,10],[2,5],[1,10]],[[1,10],[2,5],[1,10],[2,5]]],"statistic":[0,1,0,1],"domain":"Exact_finite_sufficient_statistic","operation":"suff-fibers","semantic_template":"qf-mod47-suff-fibers/{\"probability_rows\":[[[2,5],[1,10],[2,5],[1,10]],[[1,10],[2,5],[1,10],[2,5]]],\"samples\":[240,241,242,243],\"statistic\":[0,1,0,1],\"theta_values\":[\"a24\",\"b24\"]}"}},"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、一般Banach／IVT／Taylor證明、MLE漸近性、factorization theorem、一般DAG iff或primitive-root主張、Lean或Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-15","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261015-advance-20261116-r05-finite-sufficient-statistic-0026","batch_id":"batch-20261015-advance-20261116-r05-finite-sufficient-statistic-foundations","language":"zh-Hant","source_mko_ids":["mko-finite-sufficient-statistic"],"title_zh":"有限模型充分統計量","stem_zh":"total statistic fibers與正質量conditional laws的完整theta-invariance責任。操作=suff-conditional-table；資料={\"theta_values\":[\"a0\",\"b0\"],\"samples\":[0,1,2,3],\"probability_rows\":[[[2,5],[1,10],[2,5],[1,10]],[[1,10],[2,5],[1,10],[2,5]]],\"statistic\":[0,1,0,1]}。請依 exact_ordered_tuple_declared_by_interface 欄序回答。","answer":{"kind":"expression","value":"([[a0, 0, 4/5, [[0, 1/2], [2, 1/2]]], [a0, 1, 1/5, [[1, 1/2], [3, 1/2]]], [b0, 0, 1/5, [[0, 1/2], [2, 1/2]]], [b0, 1, 4/5, [[1, 1/2], [3, 1/2]]]], zero_mass_cells_remain_undefined)","explanation_zh":"Wave6第十層核對=([[a0, 0, 4/5, [[0, 1/2], [2, 1/2]]], [a0, 1, 1/5, [[1, 1/2], [3, 1/2]]], [b0, 0, 1/5, [[0, 1/2], [2, 1/2]]], [b0, 1, 4/5, [[1, 1/2], [3, 1/2]]]], zero_mass_cells_remain_undefined)；依完整明示資料獨立重算；zero-mass conditional保持undefined，nonsufficient需明示witness；identity/constant boundaries分開且不使用factorization theorem或宣稱估計品質。"},"difficulty":{"band":"undergraduate_core","level":1,"skills":["有限模型充分統計量"]},"variant":{"family_id":"qf-mod47-suff-conditional-table","seed":202611165026,"parameters":{"theta_values":["a0","b0"],"samples":[0,1,2,3],"probability_rows":[[[2,5],[1,10],[2,5],[1,10]],[[1,10],[2,5],[1,10],[2,5]]],"statistic":[0,1,0,1],"domain":"Exact_finite_sufficient_statistic","operation":"suff-conditional-table","semantic_template":"qf-mod47-suff-conditional-table/{\"probability_rows\":[[[2,5],[1,10],[2,5],[1,10]],[[1,10],[2,5],[1,10],[2,5]]],\"samples\":[0,1,2,3],\"statistic\":[0,1,0,1],\"theta_values\":[\"a0\",\"b0\"]}"}},"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、一般Banach／IVT／Taylor證明、MLE漸近性、factorization theorem、一般DAG iff或primitive-root主張、Lean或Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-15","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261015-advance-20261116-r05-finite-sufficient-statistic-0027","batch_id":"batch-20261015-advance-20261116-r05-finite-sufficient-statistic-foundations","language":"zh-Hant","source_mko_ids":["mko-finite-sufficient-statistic"],"title_zh":"有限模型充分統計量","stem_zh":"total statistic fibers與正質量conditional laws的完整theta-invariance責任。操作=suff-conditional-table；資料={\"theta_values\":[\"a1\",\"b1\"],\"samples\":[10,11,12,13],\"probability_rows\":[[[2,5],[1,10],[2,5],[1,10]],[[1,10],[2,5],[1,10],[2,5]]],\"statistic\":[0,1,0,1]}。請依 exact_ordered_tuple_declared_by_interface 欄序回答。","answer":{"kind":"expression","value":"([[a1, 0, 4/5, [[10, 1/2], [12, 1/2]]], [a1, 1, 1/5, [[11, 1/2], [13, 1/2]]], [b1, 0, 1/5, [[10, 1/2], [12, 1/2]]], [b1, 1, 4/5, [[11, 1/2], [13, 1/2]]]], zero_mass_cells_remain_undefined)","explanation_zh":"Wave6第十層核對=([[a1, 0, 4/5, [[10, 1/2], [12, 1/2]]], [a1, 1, 1/5, [[11, 1/2], [13, 1/2]]], [b1, 0, 1/5, [[10, 1/2], [12, 1/2]]], [b1, 1, 4/5, [[11, 1/2], [13, 1/2]]]], zero_mass_cells_remain_undefined)；依完整明示資料獨立重算；zero-mass conditional保持undefined，nonsufficient需明示witness；identity/constant boundaries分開且不使用factorization theorem或宣稱估計品質。"},"difficulty":{"band":"undergraduate_core","level":1,"skills":["有限模型充分統計量"]},"variant":{"family_id":"qf-mod47-suff-conditional-table","seed":202611165027,"parameters":{"theta_values":["a1","b1"],"samples":[10,11,12,13],"probability_rows":[[[2,5],[1,10],[2,5],[1,10]],[[1,10],[2,5],[1,10],[2,5]]],"statistic":[0,1,0,1],"domain":"Exact_finite_sufficient_statistic","operation":"suff-conditional-table","semantic_template":"qf-mod47-suff-conditional-table/{\"probability_rows\":[[[2,5],[1,10],[2,5],[1,10]],[[1,10],[2,5],[1,10],[2,5]]],\"samples\":[10,11,12,13],\"statistic\":[0,1,0,1],\"theta_values\":[\"a1\",\"b1\"]}"}},"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、一般Banach／IVT／Taylor證明、MLE漸近性、factorization theorem、一般DAG iff或primitive-root主張、Lean或Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-15","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261015-advance-20261116-r05-finite-sufficient-statistic-0028","batch_id":"batch-20261015-advance-20261116-r05-finite-sufficient-statistic-foundations","language":"zh-Hant","source_mko_ids":["mko-finite-sufficient-statistic"],"title_zh":"有限模型充分統計量","stem_zh":"total statistic fibers與正質量conditional laws的完整theta-invariance責任。操作=suff-conditional-table；資料={\"theta_values\":[\"a2\",\"b2\"],\"samples\":[20,21,22,23],\"probability_rows\":[[[2,5],[1,10],[2,5],[1,10]],[[1,10],[2,5],[1,10],[2,5]]],\"statistic\":[0,1,0,1]}。請依 exact_ordered_tuple_declared_by_interface 欄序回答。","answer":{"kind":"expression","value":"([[a2, 0, 4/5, [[20, 1/2], [22, 1/2]]], [a2, 1, 1/5, [[21, 1/2], [23, 1/2]]], [b2, 0, 1/5, [[20, 1/2], [22, 1/2]]], [b2, 1, 4/5, [[21, 1/2], [23, 1/2]]]], zero_mass_cells_remain_undefined)","explanation_zh":"Wave6第十層核對=([[a2, 0, 4/5, [[20, 1/2], [22, 1/2]]], [a2, 1, 1/5, [[21, 1/2], [23, 1/2]]], [b2, 0, 1/5, [[20, 1/2], [22, 1/2]]], [b2, 1, 4/5, [[21, 1/2], [23, 1/2]]]], zero_mass_cells_remain_undefined)；依完整明示資料獨立重算；zero-mass conditional保持undefined，nonsufficient需明示witness；identity/constant boundaries分開且不使用factorization theorem或宣稱估計品質。"},"difficulty":{"band":"undergraduate_core","level":1,"skills":["有限模型充分統計量"]},"variant":{"family_id":"qf-mod47-suff-conditional-table","seed":202611165028,"parameters":{"theta_values":["a2","b2"],"samples":[20,21,22,23],"probability_rows":[[[2,5],[1,10],[2,5],[1,10]],[[1,10],[2,5],[1,10],[2,5]]],"statistic":[0,1,0,1],"domain":"Exact_finite_sufficient_statistic","operation":"suff-conditional-table","semantic_template":"qf-mod47-suff-conditional-table/{\"probability_rows\":[[[2,5],[1,10],[2,5],[1,10]],[[1,10],[2,5],[1,10],[2,5]]],\"samples\":[20,21,22,23],\"statistic\":[0,1,0,1],\"theta_values\":[\"a2\",\"b2\"]}"}},"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、一般Banach／IVT／Taylor證明、MLE漸近性、factorization theorem、一般DAG iff或primitive-root主張、Lean或Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-15","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261015-advance-20261116-r05-finite-sufficient-statistic-0029","batch_id":"batch-20261015-advance-20261116-r05-finite-sufficient-statistic-foundations","language":"zh-Hant","source_mko_ids":["mko-finite-sufficient-statistic"],"title_zh":"有限模型充分統計量","stem_zh":"total statistic fibers與正質量conditional laws的完整theta-invariance責任。操作=suff-conditional-table；資料={\"theta_values\":[\"a3\",\"b3\"],\"samples\":[30,31,32,33],\"probability_rows\":[[[2,5],[1,10],[2,5],[1,10]],[[1,10],[2,5],[1,10],[2,5]]],\"statistic\":[0,1,0,1]}。請依 exact_ordered_tuple_declared_by_interface 欄序回答。","answer":{"kind":"expression","value":"([[a3, 0, 4/5, [[30, 1/2], [32, 1/2]]], [a3, 1, 1/5, [[31, 1/2], [33, 1/2]]], [b3, 0, 1/5, [[30, 1/2], [32, 1/2]]], [b3, 1, 4/5, [[31, 1/2], [33, 1/2]]]], zero_mass_cells_remain_undefined)","explanation_zh":"Wave6第十層核對=([[a3, 0, 4/5, [[30, 1/2], [32, 1/2]]], [a3, 1, 1/5, [[31, 1/2], [33, 1/2]]], [b3, 0, 1/5, [[30, 1/2], [32, 1/2]]], [b3, 1, 4/5, [[31, 1/2], [33, 1/2]]]], zero_mass_cells_remain_undefined)；依完整明示資料獨立重算；zero-mass conditional保持undefined，nonsufficient需明示witness；identity/constant boundaries分開且不使用factorization theorem或宣稱估計品質。"},"difficulty":{"band":"undergraduate_core","level":1,"skills":["有限模型充分統計量"]},"variant":{"family_id":"qf-mod47-suff-conditional-table","seed":202611165029,"parameters":{"theta_values":["a3","b3"],"samples":[30,31,32,33],"probability_rows":[[[2,5],[1,10],[2,5],[1,10]],[[1,10],[2,5],[1,10],[2,5]]],"statistic":[0,1,0,1],"domain":"Exact_finite_sufficient_statistic","operation":"suff-conditional-table","semantic_template":"qf-mod47-suff-conditional-table/{\"probability_rows\":[[[2,5],[1,10],[2,5],[1,10]],[[1,10],[2,5],[1,10],[2,5]]],\"samples\":[30,31,32,33],\"statistic\":[0,1,0,1],\"theta_values\":[\"a3\",\"b3\"]}"}},"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、一般Banach／IVT／Taylor證明、MLE漸近性、factorization theorem、一般DAG iff或primitive-root主張、Lean或Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-15","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261015-advance-20261116-r05-finite-sufficient-statistic-0030","batch_id":"batch-20261015-advance-20261116-r05-finite-sufficient-statistic-foundations","language":"zh-Hant","source_mko_ids":["mko-finite-sufficient-statistic"],"title_zh":"有限模型充分統計量","stem_zh":"total statistic fibers與正質量conditional laws的完整theta-invariance責任。操作=suff-conditional-table；資料={\"theta_values\":[\"a4\",\"b4\"],\"samples\":[40,41,42,43],\"probability_rows\":[[[2,5],[1,10],[2,5],[1,10]],[[1,10],[2,5],[1,10],[2,5]]],\"statistic\":[0,1,0,1]}。請依 exact_ordered_tuple_declared_by_interface 欄序回答。","answer":{"kind":"expression","value":"([[a4, 0, 4/5, [[40, 1/2], [42, 1/2]]], [a4, 1, 1/5, [[41, 1/2], [43, 1/2]]], [b4, 0, 1/5, [[40, 1/2], [42, 1/2]]], [b4, 1, 4/5, [[41, 1/2], [43, 1/2]]]], zero_mass_cells_remain_undefined)","explanation_zh":"Wave6第十層核對=([[a4, 0, 4/5, [[40, 1/2], [42, 1/2]]], [a4, 1, 1/5, [[41, 1/2], [43, 1/2]]], [b4, 0, 1/5, [[40, 1/2], [42, 1/2]]], [b4, 1, 4/5, [[41, 1/2], [43, 1/2]]]], zero_mass_cells_remain_undefined)；依完整明示資料獨立重算；zero-mass conditional保持undefined，nonsufficient需明示witness；identity/constant boundaries分開且不使用factorization theorem或宣稱估計品質。"},"difficulty":{"band":"undergraduate_core","level":1,"skills":["有限模型充分統計量"]},"variant":{"family_id":"qf-mod47-suff-conditional-table","seed":202611165030,"parameters":{"theta_values":["a4","b4"],"samples":[40,41,42,43],"probability_rows":[[[2,5],[1,10],[2,5],[1,10]],[[1,10],[2,5],[1,10],[2,5]]],"statistic":[0,1,0,1],"domain":"Exact_finite_sufficient_statistic","operation":"suff-conditional-table","semantic_template":"qf-mod47-suff-conditional-table/{\"probability_rows\":[[[2,5],[1,10],[2,5],[1,10]],[[1,10],[2,5],[1,10],[2,5]]],\"samples\":[40,41,42,43],\"statistic\":[0,1,0,1],\"theta_values\":[\"a4\",\"b4\"]}"}},"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、一般Banach／IVT／Taylor證明、MLE漸近性、factorization theorem、一般DAG iff或primitive-root主張、Lean或Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-15","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261015-advance-20261116-r05-finite-sufficient-statistic-0031","batch_id":"batch-20261015-advance-20261116-r05-finite-sufficient-statistic-foundations","language":"zh-Hant","source_mko_ids":["mko-finite-sufficient-statistic"],"title_zh":"有限模型充分統計量","stem_zh":"total statistic fibers與正質量conditional laws的完整theta-invariance責任。操作=suff-conditional-table；資料={\"theta_values\":[\"a5\",\"b5\"],\"samples\":[50,51,52,53],\"probability_rows\":[[[2,5],[1,10],[2,5],[1,10]],[[1,10],[2,5],[1,10],[2,5]]],\"statistic\":[0,1,0,1]}。請依 exact_ordered_tuple_declared_by_interface 欄序回答。","answer":{"kind":"expression","value":"([[a5, 0, 4/5, [[50, 1/2], [52, 1/2]]], [a5, 1, 1/5, [[51, 1/2], [53, 1/2]]], [b5, 0, 1/5, [[50, 1/2], [52, 1/2]]], [b5, 1, 4/5, [[51, 1/2], [53, 1/2]]]], zero_mass_cells_remain_undefined)","explanation_zh":"Wave6第十層核對=([[a5, 0, 4/5, [[50, 1/2], [52, 1/2]]], [a5, 1, 1/5, [[51, 1/2], [53, 1/2]]], [b5, 0, 1/5, [[50, 1/2], [52, 1/2]]], [b5, 1, 4/5, [[51, 1/2], [53, 1/2]]]], zero_mass_cells_remain_undefined)；依完整明示資料獨立重算；zero-mass conditional保持undefined，nonsufficient需明示witness；identity/constant boundaries分開且不使用factorization theorem或宣稱估計品質。"},"difficulty":{"band":"undergraduate_core","level":1,"skills":["有限模型充分統計量"]},"variant":{"family_id":"qf-mod47-suff-conditional-table","seed":202611165031,"parameters":{"theta_values":["a5","b5"],"samples":[50,51,52,53],"probability_rows":[[[2,5],[1,10],[2,5],[1,10]],[[1,10],[2,5],[1,10],[2,5]]],"statistic":[0,1,0,1],"domain":"Exact_finite_sufficient_statistic","operation":"suff-conditional-table","semantic_template":"qf-mod47-suff-conditional-table/{\"probability_rows\":[[[2,5],[1,10],[2,5],[1,10]],[[1,10],[2,5],[1,10],[2,5]]],\"samples\":[50,51,52,53],\"statistic\":[0,1,0,1],\"theta_values\":[\"a5\",\"b5\"]}"}},"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、一般Banach／IVT／Taylor證明、MLE漸近性、factorization theorem、一般DAG iff或primitive-root主張、Lean或Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-15","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261015-advance-20261116-r05-finite-sufficient-statistic-0032","batch_id":"batch-20261015-advance-20261116-r05-finite-sufficient-statistic-foundations","language":"zh-Hant","source_mko_ids":["mko-finite-sufficient-statistic"],"title_zh":"有限模型充分統計量","stem_zh":"total statistic fibers與正質量conditional laws的完整theta-invariance責任。操作=suff-conditional-table；資料={\"theta_values\":[\"a6\",\"b6\"],\"samples\":[60,61,62,63],\"probability_rows\":[[[2,5],[1,10],[2,5],[1,10]],[[1,10],[2,5],[1,10],[2,5]]],\"statistic\":[0,1,0,1]}。請依 exact_ordered_tuple_declared_by_interface 欄序回答。","answer":{"kind":"expression","value":"([[a6, 0, 4/5, [[60, 1/2], [62, 1/2]]], [a6, 1, 1/5, [[61, 1/2], [63, 1/2]]], [b6, 0, 1/5, [[60, 1/2], [62, 1/2]]], [b6, 1, 4/5, [[61, 1/2], [63, 1/2]]]], zero_mass_cells_remain_undefined)","explanation_zh":"Wave6第十層核對=([[a6, 0, 4/5, [[60, 1/2], [62, 1/2]]], [a6, 1, 1/5, [[61, 1/2], [63, 1/2]]], [b6, 0, 1/5, [[60, 1/2], [62, 1/2]]], [b6, 1, 4/5, [[61, 1/2], [63, 1/2]]]], zero_mass_cells_remain_undefined)；依完整明示資料獨立重算；zero-mass conditional保持undefined，nonsufficient需明示witness；identity/constant boundaries分開且不使用factorization theorem或宣稱估計品質。"},"difficulty":{"band":"undergraduate_core","level":1,"skills":["有限模型充分統計量"]},"variant":{"family_id":"qf-mod47-suff-conditional-table","seed":202611165032,"parameters":{"theta_values":["a6","b6"],"samples":[60,61,62,63],"probability_rows":[[[2,5],[1,10],[2,5],[1,10]],[[1,10],[2,5],[1,10],[2,5]]],"statistic":[0,1,0,1],"domain":"Exact_finite_sufficient_statistic","operation":"suff-conditional-table","semantic_template":"qf-mod47-suff-conditional-table/{\"probability_rows\":[[[2,5],[1,10],[2,5],[1,10]],[[1,10],[2,5],[1,10],[2,5]]],\"samples\":[60,61,62,63],\"statistic\":[0,1,0,1],\"theta_values\":[\"a6\",\"b6\"]}"}},"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、一般Banach／IVT／Taylor證明、MLE漸近性、factorization theorem、一般DAG iff或primitive-root主張、Lean或Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-15","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261015-advance-20261116-r05-finite-sufficient-statistic-0033","batch_id":"batch-20261015-advance-20261116-r05-finite-sufficient-statistic-foundations","language":"zh-Hant","source_mko_ids":["mko-finite-sufficient-statistic"],"title_zh":"有限模型充分統計量","stem_zh":"total statistic fibers與正質量conditional laws的完整theta-invariance責任。操作=suff-conditional-table；資料={\"theta_values\":[\"a7\",\"b7\"],\"samples\":[70,71,72,73],\"probability_rows\":[[[2,5],[1,10],[2,5],[1,10]],[[1,10],[2,5],[1,10],[2,5]]],\"statistic\":[0,1,0,1]}。請依 exact_ordered_tuple_declared_by_interface 欄序回答。","answer":{"kind":"expression","value":"([[a7, 0, 4/5, [[70, 1/2], [72, 1/2]]], [a7, 1, 1/5, [[71, 1/2], [73, 1/2]]], [b7, 0, 1/5, [[70, 1/2], [72, 1/2]]], [b7, 1, 4/5, [[71, 1/2], [73, 1/2]]]], zero_mass_cells_remain_undefined)","explanation_zh":"Wave6第十層核對=([[a7, 0, 4/5, [[70, 1/2], [72, 1/2]]], [a7, 1, 1/5, [[71, 1/2], [73, 1/2]]], [b7, 0, 1/5, [[70, 1/2], [72, 1/2]]], [b7, 1, 4/5, [[71, 1/2], [73, 1/2]]]], zero_mass_cells_remain_undefined)；依完整明示資料獨立重算；zero-mass conditional保持undefined，nonsufficient需明示witness；identity/constant boundaries分開且不使用factorization theorem或宣稱估計品質。"},"difficulty":{"band":"undergraduate_core","level":1,"skills":["有限模型充分統計量"]},"variant":{"family_id":"qf-mod47-suff-conditional-table","seed":202611165033,"parameters":{"theta_values":["a7","b7"],"samples":[70,71,72,73],"probability_rows":[[[2,5],[1,10],[2,5],[1,10]],[[1,10],[2,5],[1,10],[2,5]]],"statistic":[0,1,0,1],"domain":"Exact_finite_sufficient_statistic","operation":"suff-conditional-table","semantic_template":"qf-mod47-suff-conditional-table/{\"probability_rows\":[[[2,5],[1,10],[2,5],[1,10]],[[1,10],[2,5],[1,10],[2,5]]],\"samples\":[70,71,72,73],\"statistic\":[0,1,0,1],\"theta_values\":[\"a7\",\"b7\"]}"}},"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、一般Banach／IVT／Taylor證明、MLE漸近性、factorization theorem、一般DAG iff或primitive-root主張、Lean或Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-15","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261015-advance-20261116-r05-finite-sufficient-statistic-0034","batch_id":"batch-20261015-advance-20261116-r05-finite-sufficient-statistic-foundations","language":"zh-Hant","source_mko_ids":["mko-finite-sufficient-statistic"],"title_zh":"有限模型充分統計量","stem_zh":"total statistic fibers與正質量conditional laws的完整theta-invariance責任。操作=suff-conditional-table；資料={\"theta_values\":[\"a8\",\"b8\"],\"samples\":[80,81,82,83],\"probability_rows\":[[[2,5],[1,10],[2,5],[1,10]],[[1,10],[2,5],[1,10],[2,5]]],\"statistic\":[0,1,0,1]}。請依 exact_ordered_tuple_declared_by_interface 欄序回答。","answer":{"kind":"expression","value":"([[a8, 0, 4/5, [[80, 1/2], [82, 1/2]]], [a8, 1, 1/5, [[81, 1/2], [83, 1/2]]], [b8, 0, 1/5, [[80, 1/2], [82, 1/2]]], [b8, 1, 4/5, [[81, 1/2], [83, 1/2]]]], zero_mass_cells_remain_undefined)","explanation_zh":"Wave6第十層核對=([[a8, 0, 4/5, [[80, 1/2], [82, 1/2]]], [a8, 1, 1/5, [[81, 1/2], [83, 1/2]]], [b8, 0, 1/5, [[80, 1/2], [82, 1/2]]], [b8, 1, 4/5, [[81, 1/2], [83, 1/2]]]], zero_mass_cells_remain_undefined)；依完整明示資料獨立重算；zero-mass conditional保持undefined，nonsufficient需明示witness；identity/constant boundaries分開且不使用factorization theorem或宣稱估計品質。"},"difficulty":{"band":"undergraduate_core","level":2,"skills":["有限模型充分統計量"]},"variant":{"family_id":"qf-mod47-suff-conditional-table","seed":202611165034,"parameters":{"theta_values":["a8","b8"],"samples":[80,81,82,83],"probability_rows":[[[2,5],[1,10],[2,5],[1,10]],[[1,10],[2,5],[1,10],[2,5]]],"statistic":[0,1,0,1],"domain":"Exact_finite_sufficient_statistic","operation":"suff-conditional-table","semantic_template":"qf-mod47-suff-conditional-table/{\"probability_rows\":[[[2,5],[1,10],[2,5],[1,10]],[[1,10],[2,5],[1,10],[2,5]]],\"samples\":[80,81,82,83],\"statistic\":[0,1,0,1],\"theta_values\":[\"a8\",\"b8\"]}"}},"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、一般Banach／IVT／Taylor證明、MLE漸近性、factorization theorem、一般DAG iff或primitive-root主張、Lean或Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-15","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261015-advance-20261116-r05-finite-sufficient-statistic-0035","batch_id":"batch-20261015-advance-20261116-r05-finite-sufficient-statistic-foundations","language":"zh-Hant","source_mko_ids":["mko-finite-sufficient-statistic"],"title_zh":"有限模型充分統計量","stem_zh":"total statistic fibers與正質量conditional laws的完整theta-invariance責任。操作=suff-conditional-table；資料={\"theta_values\":[\"a9\",\"b9\"],\"samples\":[90,91,92,93],\"probability_rows\":[[[2,5],[1,10],[2,5],[1,10]],[[1,10],[2,5],[1,10],[2,5]]],\"statistic\":[0,1,0,1]}。請依 exact_ordered_tuple_declared_by_interface 欄序回答。","answer":{"kind":"expression","value":"([[a9, 0, 4/5, [[90, 1/2], [92, 1/2]]], [a9, 1, 1/5, [[91, 1/2], [93, 1/2]]], [b9, 0, 1/5, [[90, 1/2], [92, 1/2]]], [b9, 1, 4/5, [[91, 1/2], [93, 1/2]]]], zero_mass_cells_remain_undefined)","explanation_zh":"Wave6第十層核對=([[a9, 0, 4/5, [[90, 1/2], [92, 1/2]]], [a9, 1, 1/5, [[91, 1/2], [93, 1/2]]], [b9, 0, 1/5, [[90, 1/2], [92, 1/2]]], [b9, 1, 4/5, [[91, 1/2], [93, 1/2]]]], zero_mass_cells_remain_undefined)；依完整明示資料獨立重算；zero-mass conditional保持undefined，nonsufficient需明示witness；identity/constant boundaries分開且不使用factorization theorem或宣稱估計品質。"},"difficulty":{"band":"undergraduate_core","level":2,"skills":["有限模型充分統計量"]},"variant":{"family_id":"qf-mod47-suff-conditional-table","seed":202611165035,"parameters":{"theta_values":["a9","b9"],"samples":[90,91,92,93],"probability_rows":[[[2,5],[1,10],[2,5],[1,10]],[[1,10],[2,5],[1,10],[2,5]]],"statistic":[0,1,0,1],"domain":"Exact_finite_sufficient_statistic","operation":"suff-conditional-table","semantic_template":"qf-mod47-suff-conditional-table/{\"probability_rows\":[[[2,5],[1,10],[2,5],[1,10]],[[1,10],[2,5],[1,10],[2,5]]],\"samples\":[90,91,92,93],\"statistic\":[0,1,0,1],\"theta_values\":[\"a9\",\"b9\"]}"}},"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、一般Banach／IVT／Taylor證明、MLE漸近性、factorization theorem、一般DAG iff或primitive-root主張、Lean或Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-15","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261015-advance-20261116-r05-finite-sufficient-statistic-0036","batch_id":"batch-20261015-advance-20261116-r05-finite-sufficient-statistic-foundations","language":"zh-Hant","source_mko_ids":["mko-finite-sufficient-statistic"],"title_zh":"有限模型充分統計量","stem_zh":"total statistic fibers與正質量conditional laws的完整theta-invariance責任。操作=suff-conditional-table；資料={\"theta_values\":[\"a10\",\"b10\"],\"samples\":[100,101,102,103],\"probability_rows\":[[[2,5],[1,10],[2,5],[1,10]],[[1,10],[2,5],[1,10],[2,5]]],\"statistic\":[0,1,0,1]}。請依 exact_ordered_tuple_declared_by_interface 欄序回答。","answer":{"kind":"expression","value":"([[a10, 0, 4/5, [[100, 1/2], [102, 1/2]]], [a10, 1, 1/5, [[101, 1/2], [103, 1/2]]], [b10, 0, 1/5, [[100, 1/2], [102, 1/2]]], [b10, 1, 4/5, [[101, 1/2], [103, 1/2]]]], zero_mass_cells_remain_undefined)","explanation_zh":"Wave6第十層核對=([[a10, 0, 4/5, [[100, 1/2], [102, 1/2]]], [a10, 1, 1/5, [[101, 1/2], [103, 1/2]]], [b10, 0, 1/5, [[100, 1/2], [102, 1/2]]], [b10, 1, 4/5, [[101, 1/2], [103, 1/2]]]], zero_mass_cells_remain_undefined)；依完整明示資料獨立重算；zero-mass conditional保持undefined，nonsufficient需明示witness；identity/constant boundaries分開且不使用factorization theorem或宣稱估計品質。"},"difficulty":{"band":"undergraduate_core","level":2,"skills":["有限模型充分統計量"]},"variant":{"family_id":"qf-mod47-suff-conditional-table","seed":202611165036,"parameters":{"theta_values":["a10","b10"],"samples":[100,101,102,103],"probability_rows":[[[2,5],[1,10],[2,5],[1,10]],[[1,10],[2,5],[1,10],[2,5]]],"statistic":[0,1,0,1],"domain":"Exact_finite_sufficient_statistic","operation":"suff-conditional-table","semantic_template":"qf-mod47-suff-conditional-table/{\"probability_rows\":[[[2,5],[1,10],[2,5],[1,10]],[[1,10],[2,5],[1,10],[2,5]]],\"samples\":[100,101,102,103],\"statistic\":[0,1,0,1],\"theta_values\":[\"a10\",\"b10\"]}"}},"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、一般Banach／IVT／Taylor證明、MLE漸近性、factorization theorem、一般DAG iff或primitive-root主張、Lean或Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-15","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261015-advance-20261116-r05-finite-sufficient-statistic-0037","batch_id":"batch-20261015-advance-20261116-r05-finite-sufficient-statistic-foundations","language":"zh-Hant","source_mko_ids":["mko-finite-sufficient-statistic"],"title_zh":"有限模型充分統計量","stem_zh":"total statistic fibers與正質量conditional laws的完整theta-invariance責任。操作=suff-conditional-table；資料={\"theta_values\":[\"a11\",\"b11\"],\"samples\":[110,111,112,113],\"probability_rows\":[[[2,5],[1,10],[2,5],[1,10]],[[1,10],[2,5],[1,10],[2,5]]],\"statistic\":[0,1,0,1]}。請依 exact_ordered_tuple_declared_by_interface 欄序回答。","answer":{"kind":"expression","value":"([[a11, 0, 4/5, [[110, 1/2], [112, 1/2]]], [a11, 1, 1/5, [[111, 1/2], [113, 1/2]]], [b11, 0, 1/5, [[110, 1/2], [112, 1/2]]], [b11, 1, 4/5, [[111, 1/2], [113, 1/2]]]], zero_mass_cells_remain_undefined)","explanation_zh":"Wave6第十層核對=([[a11, 0, 4/5, [[110, 1/2], [112, 1/2]]], [a11, 1, 1/5, [[111, 1/2], [113, 1/2]]], [b11, 0, 1/5, [[110, 1/2], [112, 1/2]]], [b11, 1, 4/5, [[111, 1/2], [113, 1/2]]]], zero_mass_cells_remain_undefined)；依完整明示資料獨立重算；zero-mass conditional保持undefined，nonsufficient需明示witness；identity/constant boundaries分開且不使用factorization theorem或宣稱估計品質。"},"difficulty":{"band":"undergraduate_core","level":2,"skills":["有限模型充分統計量"]},"variant":{"family_id":"qf-mod47-suff-conditional-table","seed":202611165037,"parameters":{"theta_values":["a11","b11"],"samples":[110,111,112,113],"probability_rows":[[[2,5],[1,10],[2,5],[1,10]],[[1,10],[2,5],[1,10],[2,5]]],"statistic":[0,1,0,1],"domain":"Exact_finite_sufficient_statistic","operation":"suff-conditional-table","semantic_template":"qf-mod47-suff-conditional-table/{\"probability_rows\":[[[2,5],[1,10],[2,5],[1,10]],[[1,10],[2,5],[1,10],[2,5]]],\"samples\":[110,111,112,113],\"statistic\":[0,1,0,1],\"theta_values\":[\"a11\",\"b11\"]}"}},"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、一般Banach／IVT／Taylor證明、MLE漸近性、factorization theorem、一般DAG iff或primitive-root主張、Lean或Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-15","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261015-advance-20261116-r05-finite-sufficient-statistic-0038","batch_id":"batch-20261015-advance-20261116-r05-finite-sufficient-statistic-foundations","language":"zh-Hant","source_mko_ids":["mko-finite-sufficient-statistic"],"title_zh":"有限模型充分統計量","stem_zh":"total statistic fibers與正質量conditional laws的完整theta-invariance責任。操作=suff-conditional-table；資料={\"theta_values\":[\"a12\",\"b12\"],\"samples\":[120,121,122,123],\"probability_rows\":[[[2,5],[1,10],[2,5],[1,10]],[[1,10],[2,5],[1,10],[2,5]]],\"statistic\":[0,1,0,1]}。請依 exact_ordered_tuple_declared_by_interface 欄序回答。","answer":{"kind":"expression","value":"([[a12, 0, 4/5, [[120, 1/2], [122, 1/2]]], [a12, 1, 1/5, [[121, 1/2], [123, 1/2]]], [b12, 0, 1/5, [[120, 1/2], [122, 1/2]]], [b12, 1, 4/5, [[121, 1/2], [123, 1/2]]]], zero_mass_cells_remain_undefined)","explanation_zh":"Wave6第十層核對=([[a12, 0, 4/5, [[120, 1/2], [122, 1/2]]], [a12, 1, 1/5, [[121, 1/2], [123, 1/2]]], [b12, 0, 1/5, [[120, 1/2], [122, 1/2]]], [b12, 1, 4/5, [[121, 1/2], [123, 1/2]]]], zero_mass_cells_remain_undefined)；依完整明示資料獨立重算；zero-mass conditional保持undefined，nonsufficient需明示witness；identity/constant boundaries分開且不使用factorization theorem或宣稱估計品質。"},"difficulty":{"band":"undergraduate_core","level":2,"skills":["有限模型充分統計量"]},"variant":{"family_id":"qf-mod47-suff-conditional-table","seed":202611165038,"parameters":{"theta_values":["a12","b12"],"samples":[120,121,122,123],"probability_rows":[[[2,5],[1,10],[2,5],[1,10]],[[1,10],[2,5],[1,10],[2,5]]],"statistic":[0,1,0,1],"domain":"Exact_finite_sufficient_statistic","operation":"suff-conditional-table","semantic_template":"qf-mod47-suff-conditional-table/{\"probability_rows\":[[[2,5],[1,10],[2,5],[1,10]],[[1,10],[2,5],[1,10],[2,5]]],\"samples\":[120,121,122,123],\"statistic\":[0,1,0,1],\"theta_values\":[\"a12\",\"b12\"]}"}},"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、一般Banach／IVT／Taylor證明、MLE漸近性、factorization theorem、一般DAG iff或primitive-root主張、Lean或Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-15","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261015-advance-20261116-r05-finite-sufficient-statistic-0039","batch_id":"batch-20261015-advance-20261116-r05-finite-sufficient-statistic-foundations","language":"zh-Hant","source_mko_ids":["mko-finite-sufficient-statistic"],"title_zh":"有限模型充分統計量","stem_zh":"total statistic fibers與正質量conditional laws的完整theta-invariance責任。操作=suff-conditional-table；資料={\"theta_values\":[\"a13\",\"b13\"],\"samples\":[130,131,132,133],\"probability_rows\":[[[2,5],[1,10],[2,5],[1,10]],[[1,10],[2,5],[1,10],[2,5]]],\"statistic\":[0,1,0,1]}。請依 exact_ordered_tuple_declared_by_interface 欄序回答。","answer":{"kind":"expression","value":"([[a13, 0, 4/5, [[130, 1/2], [132, 1/2]]], [a13, 1, 1/5, [[131, 1/2], [133, 1/2]]], [b13, 0, 1/5, [[130, 1/2], [132, 1/2]]], [b13, 1, 4/5, [[131, 1/2], [133, 1/2]]]], zero_mass_cells_remain_undefined)","explanation_zh":"Wave6第十層核對=([[a13, 0, 4/5, [[130, 1/2], [132, 1/2]]], [a13, 1, 1/5, [[131, 1/2], [133, 1/2]]], [b13, 0, 1/5, [[130, 1/2], [132, 1/2]]], [b13, 1, 4/5, [[131, 1/2], [133, 1/2]]]], zero_mass_cells_remain_undefined)；依完整明示資料獨立重算；zero-mass conditional保持undefined，nonsufficient需明示witness；identity/constant boundaries分開且不使用factorization theorem或宣稱估計品質。"},"difficulty":{"band":"undergraduate_core","level":2,"skills":["有限模型充分統計量"]},"variant":{"family_id":"qf-mod47-suff-conditional-table","seed":202611165039,"parameters":{"theta_values":["a13","b13"],"samples":[130,131,132,133],"probability_rows":[[[2,5],[1,10],[2,5],[1,10]],[[1,10],[2,5],[1,10],[2,5]]],"statistic":[0,1,0,1],"domain":"Exact_finite_sufficient_statistic","operation":"suff-conditional-table","semantic_template":"qf-mod47-suff-conditional-table/{\"probability_rows\":[[[2,5],[1,10],[2,5],[1,10]],[[1,10],[2,5],[1,10],[2,5]]],\"samples\":[130,131,132,133],\"statistic\":[0,1,0,1],\"theta_values\":[\"a13\",\"b13\"]}"}},"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、一般Banach／IVT／Taylor證明、MLE漸近性、factorization theorem、一般DAG iff或primitive-root主張、Lean或Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-15","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261015-advance-20261116-r05-finite-sufficient-statistic-0040","batch_id":"batch-20261015-advance-20261116-r05-finite-sufficient-statistic-foundations","language":"zh-Hant","source_mko_ids":["mko-finite-sufficient-statistic"],"title_zh":"有限模型充分統計量","stem_zh":"total statistic fibers與正質量conditional laws的完整theta-invariance責任。操作=suff-conditional-table；資料={\"theta_values\":[\"a14\",\"b14\"],\"samples\":[140,141,142,143],\"probability_rows\":[[[2,5],[1,10],[2,5],[1,10]],[[1,10],[2,5],[1,10],[2,5]]],\"statistic\":[0,1,0,1]}。請依 exact_ordered_tuple_declared_by_interface 欄序回答。","answer":{"kind":"expression","value":"([[a14, 0, 4/5, [[140, 1/2], [142, 1/2]]], [a14, 1, 1/5, [[141, 1/2], [143, 1/2]]], [b14, 0, 1/5, [[140, 1/2], [142, 1/2]]], [b14, 1, 4/5, [[141, 1/2], [143, 1/2]]]], zero_mass_cells_remain_undefined)","explanation_zh":"Wave6第十層核對=([[a14, 0, 4/5, [[140, 1/2], [142, 1/2]]], [a14, 1, 1/5, [[141, 1/2], [143, 1/2]]], [b14, 0, 1/5, [[140, 1/2], [142, 1/2]]], [b14, 1, 4/5, [[141, 1/2], [143, 1/2]]]], zero_mass_cells_remain_undefined)；依完整明示資料獨立重算；zero-mass conditional保持undefined，nonsufficient需明示witness；identity/constant boundaries分開且不使用factorization theorem或宣稱估計品質。"},"difficulty":{"band":"undergraduate_core","level":2,"skills":["有限模型充分統計量"]},"variant":{"family_id":"qf-mod47-suff-conditional-table","seed":202611165040,"parameters":{"theta_values":["a14","b14"],"samples":[140,141,142,143],"probability_rows":[[[2,5],[1,10],[2,5],[1,10]],[[1,10],[2,5],[1,10],[2,5]]],"statistic":[0,1,0,1],"domain":"Exact_finite_sufficient_statistic","operation":"suff-conditional-table","semantic_template":"qf-mod47-suff-conditional-table/{\"probability_rows\":[[[2,5],[1,10],[2,5],[1,10]],[[1,10],[2,5],[1,10],[2,5]]],\"samples\":[140,141,142,143],\"statistic\":[0,1,0,1],\"theta_values\":[\"a14\",\"b14\"]}"}},"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、一般Banach／IVT／Taylor證明、MLE漸近性、factorization theorem、一般DAG iff或primitive-root主張、Lean或Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-15","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261015-advance-20261116-r05-finite-sufficient-statistic-0041","batch_id":"batch-20261015-advance-20261116-r05-finite-sufficient-statistic-foundations","language":"zh-Hant","source_mko_ids":["mko-finite-sufficient-statistic"],"title_zh":"有限模型充分統計量","stem_zh":"total statistic fibers與正質量conditional laws的完整theta-invariance責任。操作=suff-conditional-table；資料={\"theta_values\":[\"a15\",\"b15\"],\"samples\":[150,151,152,153],\"probability_rows\":[[[2,5],[1,10],[2,5],[1,10]],[[1,10],[2,5],[1,10],[2,5]]],\"statistic\":[0,1,0,1]}。請依 exact_ordered_tuple_declared_by_interface 欄序回答。","answer":{"kind":"expression","value":"([[a15, 0, 4/5, [[150, 1/2], [152, 1/2]]], [a15, 1, 1/5, [[151, 1/2], [153, 1/2]]], [b15, 0, 1/5, [[150, 1/2], [152, 1/2]]], [b15, 1, 4/5, [[151, 1/2], [153, 1/2]]]], zero_mass_cells_remain_undefined)","explanation_zh":"Wave6第十層核對=([[a15, 0, 4/5, [[150, 1/2], [152, 1/2]]], [a15, 1, 1/5, [[151, 1/2], [153, 1/2]]], [b15, 0, 1/5, [[150, 1/2], [152, 1/2]]], [b15, 1, 4/5, [[151, 1/2], [153, 1/2]]]], zero_mass_cells_remain_undefined)；依完整明示資料獨立重算；zero-mass conditional保持undefined，nonsufficient需明示witness；identity/constant boundaries分開且不使用factorization theorem或宣稱估計品質。"},"difficulty":{"band":"undergraduate_core","level":2,"skills":["有限模型充分統計量"]},"variant":{"family_id":"qf-mod47-suff-conditional-table","seed":202611165041,"parameters":{"theta_values":["a15","b15"],"samples":[150,151,152,153],"probability_rows":[[[2,5],[1,10],[2,5],[1,10]],[[1,10],[2,5],[1,10],[2,5]]],"statistic":[0,1,0,1],"domain":"Exact_finite_sufficient_statistic","operation":"suff-conditional-table","semantic_template":"qf-mod47-suff-conditional-table/{\"probability_rows\":[[[2,5],[1,10],[2,5],[1,10]],[[1,10],[2,5],[1,10],[2,5]]],\"samples\":[150,151,152,153],\"statistic\":[0,1,0,1],\"theta_values\":[\"a15\",\"b15\"]}"}},"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、一般Banach／IVT／Taylor證明、MLE漸近性、factorization theorem、一般DAG iff或primitive-root主張、Lean或Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-15","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261015-advance-20261116-r05-finite-sufficient-statistic-0042","batch_id":"batch-20261015-advance-20261116-r05-finite-sufficient-statistic-foundations","language":"zh-Hant","source_mko_ids":["mko-finite-sufficient-statistic"],"title_zh":"有限模型充分統計量","stem_zh":"total statistic fibers與正質量conditional laws的完整theta-invariance責任。操作=suff-conditional-table；資料={\"theta_values\":[\"a16\",\"b16\"],\"samples\":[160,161,162,163],\"probability_rows\":[[[2,5],[1,10],[2,5],[1,10]],[[1,10],[2,5],[1,10],[2,5]]],\"statistic\":[0,1,0,1]}。請依 exact_ordered_tuple_declared_by_interface 欄序回答。","answer":{"kind":"expression","value":"([[a16, 0, 4/5, [[160, 1/2], [162, 1/2]]], [a16, 1, 1/5, [[161, 1/2], [163, 1/2]]], [b16, 0, 1/5, [[160, 1/2], [162, 1/2]]], [b16, 1, 4/5, [[161, 1/2], [163, 1/2]]]], zero_mass_cells_remain_undefined)","explanation_zh":"Wave6第十層核對=([[a16, 0, 4/5, [[160, 1/2], [162, 1/2]]], [a16, 1, 1/5, [[161, 1/2], [163, 1/2]]], [b16, 0, 1/5, [[160, 1/2], [162, 1/2]]], [b16, 1, 4/5, [[161, 1/2], [163, 1/2]]]], zero_mass_cells_remain_undefined)；依完整明示資料獨立重算；zero-mass conditional保持undefined，nonsufficient需明示witness；identity/constant boundaries分開且不使用factorization theorem或宣稱估計品質。"},"difficulty":{"band":"undergraduate_core","level":2,"skills":["有限模型充分統計量"]},"variant":{"family_id":"qf-mod47-suff-conditional-table","seed":202611165042,"parameters":{"theta_values":["a16","b16"],"samples":[160,161,162,163],"probability_rows":[[[2,5],[1,10],[2,5],[1,10]],[[1,10],[2,5],[1,10],[2,5]]],"statistic":[0,1,0,1],"domain":"Exact_finite_sufficient_statistic","operation":"suff-conditional-table","semantic_template":"qf-mod47-suff-conditional-table/{\"probability_rows\":[[[2,5],[1,10],[2,5],[1,10]],[[1,10],[2,5],[1,10],[2,5]]],\"samples\":[160,161,162,163],\"statistic\":[0,1,0,1],\"theta_values\":[\"a16\",\"b16\"]}"}},"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、一般Banach／IVT／Taylor證明、MLE漸近性、factorization theorem、一般DAG iff或primitive-root主張、Lean或Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-15","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261015-advance-20261116-r05-finite-sufficient-statistic-0043","batch_id":"batch-20261015-advance-20261116-r05-finite-sufficient-statistic-foundations","language":"zh-Hant","source_mko_ids":["mko-finite-sufficient-statistic"],"title_zh":"有限模型充分統計量","stem_zh":"total statistic fibers與正質量conditional laws的完整theta-invariance責任。操作=suff-conditional-table；資料={\"theta_values\":[\"a17\",\"b17\"],\"samples\":[170,171,172,173],\"probability_rows\":[[[2,5],[1,10],[2,5],[1,10]],[[1,10],[2,5],[1,10],[2,5]]],\"statistic\":[0,1,0,1]}。請依 exact_ordered_tuple_declared_by_interface 欄序回答。","answer":{"kind":"expression","value":"([[a17, 0, 4/5, [[170, 1/2], [172, 1/2]]], [a17, 1, 1/5, [[171, 1/2], [173, 1/2]]], [b17, 0, 1/5, [[170, 1/2], [172, 1/2]]], [b17, 1, 4/5, [[171, 1/2], [173, 1/2]]]], zero_mass_cells_remain_undefined)","explanation_zh":"Wave6第十層核對=([[a17, 0, 4/5, [[170, 1/2], [172, 1/2]]], [a17, 1, 1/5, [[171, 1/2], [173, 1/2]]], [b17, 0, 1/5, [[170, 1/2], [172, 1/2]]], [b17, 1, 4/5, [[171, 1/2], [173, 1/2]]]], zero_mass_cells_remain_undefined)；依完整明示資料獨立重算；zero-mass conditional保持undefined，nonsufficient需明示witness；identity/constant boundaries分開且不使用factorization theorem或宣稱估計品質。"},"difficulty":{"band":"undergraduate_core","level":3,"skills":["有限模型充分統計量"]},"variant":{"family_id":"qf-mod47-suff-conditional-table","seed":202611165043,"parameters":{"theta_values":["a17","b17"],"samples":[170,171,172,173],"probability_rows":[[[2,5],[1,10],[2,5],[1,10]],[[1,10],[2,5],[1,10],[2,5]]],"statistic":[0,1,0,1],"domain":"Exact_finite_sufficient_statistic","operation":"suff-conditional-table","semantic_template":"qf-mod47-suff-conditional-table/{\"probability_rows\":[[[2,5],[1,10],[2,5],[1,10]],[[1,10],[2,5],[1,10],[2,5]]],\"samples\":[170,171,172,173],\"statistic\":[0,1,0,1],\"theta_values\":[\"a17\",\"b17\"]}"}},"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、一般Banach／IVT／Taylor證明、MLE漸近性、factorization theorem、一般DAG iff或primitive-root主張、Lean或Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-15","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261015-advance-20261116-r05-finite-sufficient-statistic-0044","batch_id":"batch-20261015-advance-20261116-r05-finite-sufficient-statistic-foundations","language":"zh-Hant","source_mko_ids":["mko-finite-sufficient-statistic"],"title_zh":"有限模型充分統計量","stem_zh":"total statistic fibers與正質量conditional laws的完整theta-invariance責任。操作=suff-conditional-table；資料={\"theta_values\":[\"a18\",\"b18\"],\"samples\":[180,181,182,183],\"probability_rows\":[[[2,5],[1,10],[2,5],[1,10]],[[1,10],[2,5],[1,10],[2,5]]],\"statistic\":[0,1,0,1]}。請依 exact_ordered_tuple_declared_by_interface 欄序回答。","answer":{"kind":"expression","value":"([[a18, 0, 4/5, [[180, 1/2], [182, 1/2]]], [a18, 1, 1/5, [[181, 1/2], [183, 1/2]]], [b18, 0, 1/5, [[180, 1/2], [182, 1/2]]], [b18, 1, 4/5, [[181, 1/2], [183, 1/2]]]], zero_mass_cells_remain_undefined)","explanation_zh":"Wave6第十層核對=([[a18, 0, 4/5, [[180, 1/2], [182, 1/2]]], [a18, 1, 1/5, [[181, 1/2], [183, 1/2]]], [b18, 0, 1/5, [[180, 1/2], [182, 1/2]]], [b18, 1, 4/5, [[181, 1/2], [183, 1/2]]]], zero_mass_cells_remain_undefined)；依完整明示資料獨立重算；zero-mass conditional保持undefined，nonsufficient需明示witness；identity/constant boundaries分開且不使用factorization theorem或宣稱估計品質。"},"difficulty":{"band":"undergraduate_core","level":3,"skills":["有限模型充分統計量"]},"variant":{"family_id":"qf-mod47-suff-conditional-table","seed":202611165044,"parameters":{"theta_values":["a18","b18"],"samples":[180,181,182,183],"probability_rows":[[[2,5],[1,10],[2,5],[1,10]],[[1,10],[2,5],[1,10],[2,5]]],"statistic":[0,1,0,1],"domain":"Exact_finite_sufficient_statistic","operation":"suff-conditional-table","semantic_template":"qf-mod47-suff-conditional-table/{\"probability_rows\":[[[2,5],[1,10],[2,5],[1,10]],[[1,10],[2,5],[1,10],[2,5]]],\"samples\":[180,181,182,183],\"statistic\":[0,1,0,1],\"theta_values\":[\"a18\",\"b18\"]}"}},"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、一般Banach／IVT／Taylor證明、MLE漸近性、factorization theorem、一般DAG iff或primitive-root主張、Lean或Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-15","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261015-advance-20261116-r05-finite-sufficient-statistic-0045","batch_id":"batch-20261015-advance-20261116-r05-finite-sufficient-statistic-foundations","language":"zh-Hant","source_mko_ids":["mko-finite-sufficient-statistic"],"title_zh":"有限模型充分統計量","stem_zh":"total statistic fibers與正質量conditional laws的完整theta-invariance責任。操作=suff-conditional-table；資料={\"theta_values\":[\"a19\",\"b19\"],\"samples\":[190,191,192,193],\"probability_rows\":[[[2,5],[1,10],[2,5],[1,10]],[[1,10],[2,5],[1,10],[2,5]]],\"statistic\":[0,1,0,1]}。請依 exact_ordered_tuple_declared_by_interface 欄序回答。","answer":{"kind":"expression","value":"([[a19, 0, 4/5, [[190, 1/2], [192, 1/2]]], [a19, 1, 1/5, [[191, 1/2], [193, 1/2]]], [b19, 0, 1/5, [[190, 1/2], [192, 1/2]]], [b19, 1, 4/5, [[191, 1/2], [193, 1/2]]]], zero_mass_cells_remain_undefined)","explanation_zh":"Wave6第十層核對=([[a19, 0, 4/5, [[190, 1/2], [192, 1/2]]], [a19, 1, 1/5, [[191, 1/2], [193, 1/2]]], [b19, 0, 1/5, [[190, 1/2], [192, 1/2]]], [b19, 1, 4/5, [[191, 1/2], [193, 1/2]]]], zero_mass_cells_remain_undefined)；依完整明示資料獨立重算；zero-mass conditional保持undefined，nonsufficient需明示witness；identity/constant boundaries分開且不使用factorization theorem或宣稱估計品質。"},"difficulty":{"band":"undergraduate_core","level":3,"skills":["有限模型充分統計量"]},"variant":{"family_id":"qf-mod47-suff-conditional-table","seed":202611165045,"parameters":{"theta_values":["a19","b19"],"samples":[190,191,192,193],"probability_rows":[[[2,5],[1,10],[2,5],[1,10]],[[1,10],[2,5],[1,10],[2,5]]],"statistic":[0,1,0,1],"domain":"Exact_finite_sufficient_statistic","operation":"suff-conditional-table","semantic_template":"qf-mod47-suff-conditional-table/{\"probability_rows\":[[[2,5],[1,10],[2,5],[1,10]],[[1,10],[2,5],[1,10],[2,5]]],\"samples\":[190,191,192,193],\"statistic\":[0,1,0,1],\"theta_values\":[\"a19\",\"b19\"]}"}},"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、一般Banach／IVT／Taylor證明、MLE漸近性、factorization theorem、一般DAG iff或primitive-root主張、Lean或Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-15","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261015-advance-20261116-r05-finite-sufficient-statistic-0046","batch_id":"batch-20261015-advance-20261116-r05-finite-sufficient-statistic-foundations","language":"zh-Hant","source_mko_ids":["mko-finite-sufficient-statistic"],"title_zh":"有限模型充分統計量","stem_zh":"total statistic fibers與正質量conditional laws的完整theta-invariance責任。操作=suff-conditional-table；資料={\"theta_values\":[\"a20\",\"b20\"],\"samples\":[200,201,202,203],\"probability_rows\":[[[2,5],[1,10],[2,5],[1,10]],[[1,10],[2,5],[1,10],[2,5]]],\"statistic\":[0,1,0,1]}。請依 exact_ordered_tuple_declared_by_interface 欄序回答。","answer":{"kind":"expression","value":"([[a20, 0, 4/5, [[200, 1/2], [202, 1/2]]], [a20, 1, 1/5, [[201, 1/2], [203, 1/2]]], [b20, 0, 1/5, [[200, 1/2], [202, 1/2]]], [b20, 1, 4/5, [[201, 1/2], [203, 1/2]]]], zero_mass_cells_remain_undefined)","explanation_zh":"Wave6第十層核對=([[a20, 0, 4/5, [[200, 1/2], [202, 1/2]]], [a20, 1, 1/5, [[201, 1/2], [203, 1/2]]], [b20, 0, 1/5, [[200, 1/2], [202, 1/2]]], [b20, 1, 4/5, [[201, 1/2], [203, 1/2]]]], zero_mass_cells_remain_undefined)；依完整明示資料獨立重算；zero-mass conditional保持undefined，nonsufficient需明示witness；identity/constant boundaries分開且不使用factorization theorem或宣稱估計品質。"},"difficulty":{"band":"undergraduate_core","level":3,"skills":["有限模型充分統計量"]},"variant":{"family_id":"qf-mod47-suff-conditional-table","seed":202611165046,"parameters":{"theta_values":["a20","b20"],"samples":[200,201,202,203],"probability_rows":[[[2,5],[1,10],[2,5],[1,10]],[[1,10],[2,5],[1,10],[2,5]]],"statistic":[0,1,0,1],"domain":"Exact_finite_sufficient_statistic","operation":"suff-conditional-table","semantic_template":"qf-mod47-suff-conditional-table/{\"probability_rows\":[[[2,5],[1,10],[2,5],[1,10]],[[1,10],[2,5],[1,10],[2,5]]],\"samples\":[200,201,202,203],\"statistic\":[0,1,0,1],\"theta_values\":[\"a20\",\"b20\"]}"}},"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、一般Banach／IVT／Taylor證明、MLE漸近性、factorization theorem、一般DAG iff或primitive-root主張、Lean或Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-15","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261015-advance-20261116-r05-finite-sufficient-statistic-0047","batch_id":"batch-20261015-advance-20261116-r05-finite-sufficient-statistic-foundations","language":"zh-Hant","source_mko_ids":["mko-finite-sufficient-statistic"],"title_zh":"有限模型充分統計量","stem_zh":"total statistic fibers與正質量conditional laws的完整theta-invariance責任。操作=suff-conditional-table；資料={\"theta_values\":[\"a21\",\"b21\"],\"samples\":[210,211,212,213],\"probability_rows\":[[[2,5],[1,10],[2,5],[1,10]],[[1,10],[2,5],[1,10],[2,5]]],\"statistic\":[0,1,0,1]}。請依 exact_ordered_tuple_declared_by_interface 欄序回答。","answer":{"kind":"expression","value":"([[a21, 0, 4/5, [[210, 1/2], [212, 1/2]]], [a21, 1, 1/5, [[211, 1/2], [213, 1/2]]], [b21, 0, 1/5, [[210, 1/2], [212, 1/2]]], [b21, 1, 4/5, [[211, 1/2], [213, 1/2]]]], zero_mass_cells_remain_undefined)","explanation_zh":"Wave6第十層核對=([[a21, 0, 4/5, [[210, 1/2], [212, 1/2]]], [a21, 1, 1/5, [[211, 1/2], [213, 1/2]]], [b21, 0, 1/5, [[210, 1/2], [212, 1/2]]], [b21, 1, 4/5, [[211, 1/2], [213, 1/2]]]], zero_mass_cells_remain_undefined)；依完整明示資料獨立重算；zero-mass conditional保持undefined，nonsufficient需明示witness；identity/constant boundaries分開且不使用factorization theorem或宣稱估計品質。"},"difficulty":{"band":"undergraduate_core","level":3,"skills":["有限模型充分統計量"]},"variant":{"family_id":"qf-mod47-suff-conditional-table","seed":202611165047,"parameters":{"theta_values":["a21","b21"],"samples":[210,211,212,213],"probability_rows":[[[2,5],[1,10],[2,5],[1,10]],[[1,10],[2,5],[1,10],[2,5]]],"statistic":[0,1,0,1],"domain":"Exact_finite_sufficient_statistic","operation":"suff-conditional-table","semantic_template":"qf-mod47-suff-conditional-table/{\"probability_rows\":[[[2,5],[1,10],[2,5],[1,10]],[[1,10],[2,5],[1,10],[2,5]]],\"samples\":[210,211,212,213],\"statistic\":[0,1,0,1],\"theta_values\":[\"a21\",\"b21\"]}"}},"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、一般Banach／IVT／Taylor證明、MLE漸近性、factorization theorem、一般DAG iff或primitive-root主張、Lean或Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-15","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261015-advance-20261116-r05-finite-sufficient-statistic-0048","batch_id":"batch-20261015-advance-20261116-r05-finite-sufficient-statistic-foundations","language":"zh-Hant","source_mko_ids":["mko-finite-sufficient-statistic"],"title_zh":"有限模型充分統計量","stem_zh":"total statistic fibers與正質量conditional laws的完整theta-invariance責任。操作=suff-conditional-table；資料={\"theta_values\":[\"a22\",\"b22\"],\"samples\":[220,221,222,223],\"probability_rows\":[[[2,5],[1,10],[2,5],[1,10]],[[1,10],[2,5],[1,10],[2,5]]],\"statistic\":[0,1,0,1]}。請依 exact_ordered_tuple_declared_by_interface 欄序回答。","answer":{"kind":"expression","value":"([[a22, 0, 4/5, [[220, 1/2], [222, 1/2]]], [a22, 1, 1/5, [[221, 1/2], [223, 1/2]]], [b22, 0, 1/5, [[220, 1/2], [222, 1/2]]], [b22, 1, 4/5, [[221, 1/2], [223, 1/2]]]], zero_mass_cells_remain_undefined)","explanation_zh":"Wave6第十層核對=([[a22, 0, 4/5, [[220, 1/2], [222, 1/2]]], [a22, 1, 1/5, [[221, 1/2], [223, 1/2]]], [b22, 0, 1/5, [[220, 1/2], [222, 1/2]]], [b22, 1, 4/5, [[221, 1/2], [223, 1/2]]]], zero_mass_cells_remain_undefined)；依完整明示資料獨立重算；zero-mass conditional保持undefined，nonsufficient需明示witness；identity/constant boundaries分開且不使用factorization theorem或宣稱估計品質。"},"difficulty":{"band":"undergraduate_core","level":3,"skills":["有限模型充分統計量"]},"variant":{"family_id":"qf-mod47-suff-conditional-table","seed":202611165048,"parameters":{"theta_values":["a22","b22"],"samples":[220,221,222,223],"probability_rows":[[[2,5],[1,10],[2,5],[1,10]],[[1,10],[2,5],[1,10],[2,5]]],"statistic":[0,1,0,1],"domain":"Exact_finite_sufficient_statistic","operation":"suff-conditional-table","semantic_template":"qf-mod47-suff-conditional-table/{\"probability_rows\":[[[2,5],[1,10],[2,5],[1,10]],[[1,10],[2,5],[1,10],[2,5]]],\"samples\":[220,221,222,223],\"statistic\":[0,1,0,1],\"theta_values\":[\"a22\",\"b22\"]}"}},"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、一般Banach／IVT／Taylor證明、MLE漸近性、factorization theorem、一般DAG iff或primitive-root主張、Lean或Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-15","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261015-advance-20261116-r05-finite-sufficient-statistic-0049","batch_id":"batch-20261015-advance-20261116-r05-finite-sufficient-statistic-foundations","language":"zh-Hant","source_mko_ids":["mko-finite-sufficient-statistic"],"title_zh":"有限模型充分統計量","stem_zh":"total statistic fibers與正質量conditional laws的完整theta-invariance責任。操作=suff-conditional-table；資料={\"theta_values\":[\"a23\",\"b23\"],\"samples\":[230,231,232,233],\"probability_rows\":[[[2,5],[1,10],[2,5],[1,10]],[[1,10],[2,5],[1,10],[2,5]]],\"statistic\":[0,1,0,1]}。請依 exact_ordered_tuple_declared_by_interface 欄序回答。","answer":{"kind":"expression","value":"([[a23, 0, 4/5, [[230, 1/2], [232, 1/2]]], [a23, 1, 1/5, [[231, 1/2], [233, 1/2]]], [b23, 0, 1/5, [[230, 1/2], [232, 1/2]]], [b23, 1, 4/5, [[231, 1/2], [233, 1/2]]]], zero_mass_cells_remain_undefined)","explanation_zh":"Wave6第十層核對=([[a23, 0, 4/5, [[230, 1/2], [232, 1/2]]], [a23, 1, 1/5, [[231, 1/2], [233, 1/2]]], [b23, 0, 1/5, [[230, 1/2], [232, 1/2]]], [b23, 1, 4/5, [[231, 1/2], [233, 1/2]]]], zero_mass_cells_remain_undefined)；依完整明示資料獨立重算；zero-mass conditional保持undefined，nonsufficient需明示witness；identity/constant boundaries分開且不使用factorization theorem或宣稱估計品質。"},"difficulty":{"band":"undergraduate_core","level":3,"skills":["有限模型充分統計量"]},"variant":{"family_id":"qf-mod47-suff-conditional-table","seed":202611165049,"parameters":{"theta_values":["a23","b23"],"samples":[230,231,232,233],"probability_rows":[[[2,5],[1,10],[2,5],[1,10]],[[1,10],[2,5],[1,10],[2,5]]],"statistic":[0,1,0,1],"domain":"Exact_finite_sufficient_statistic","operation":"suff-conditional-table","semantic_template":"qf-mod47-suff-conditional-table/{\"probability_rows\":[[[2,5],[1,10],[2,5],[1,10]],[[1,10],[2,5],[1,10],[2,5]]],\"samples\":[230,231,232,233],\"statistic\":[0,1,0,1],\"theta_values\":[\"a23\",\"b23\"]}"}},"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、一般Banach／IVT／Taylor證明、MLE漸近性、factorization theorem、一般DAG iff或primitive-root主張、Lean或Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-15","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261015-advance-20261116-r05-finite-sufficient-statistic-0050","batch_id":"batch-20261015-advance-20261116-r05-finite-sufficient-statistic-foundations","language":"zh-Hant","source_mko_ids":["mko-finite-sufficient-statistic"],"title_zh":"有限模型充分統計量","stem_zh":"total statistic fibers與正質量conditional laws的完整theta-invariance責任。操作=suff-conditional-table；資料={\"theta_values\":[\"a24\",\"b24\"],\"samples\":[240,241,242,243],\"probability_rows\":[[[2,5],[1,10],[2,5],[1,10]],[[1,10],[2,5],[1,10],[2,5]]],\"statistic\":[0,1,0,1]}。請依 exact_ordered_tuple_declared_by_interface 欄序回答。","answer":{"kind":"expression","value":"([[a24, 0, 4/5, [[240, 1/2], [242, 1/2]]], [a24, 1, 1/5, [[241, 1/2], [243, 1/2]]], [b24, 0, 1/5, [[240, 1/2], [242, 1/2]]], [b24, 1, 4/5, [[241, 1/2], [243, 1/2]]]], zero_mass_cells_remain_undefined)","explanation_zh":"Wave6第十層核對=([[a24, 0, 4/5, [[240, 1/2], [242, 1/2]]], [a24, 1, 1/5, [[241, 1/2], [243, 1/2]]], [b24, 0, 1/5, [[240, 1/2], [242, 1/2]]], [b24, 1, 4/5, [[241, 1/2], [243, 1/2]]]], zero_mass_cells_remain_undefined)；依完整明示資料獨立重算；zero-mass conditional保持undefined，nonsufficient需明示witness；identity/constant boundaries分開且不使用factorization theorem或宣稱估計品質。"},"difficulty":{"band":"undergraduate_core","level":3,"skills":["有限模型充分統計量"]},"variant":{"family_id":"qf-mod47-suff-conditional-table","seed":202611165050,"parameters":{"theta_values":["a24","b24"],"samples":[240,241,242,243],"probability_rows":[[[2,5],[1,10],[2,5],[1,10]],[[1,10],[2,5],[1,10],[2,5]]],"statistic":[0,1,0,1],"domain":"Exact_finite_sufficient_statistic","operation":"suff-conditional-table","semantic_template":"qf-mod47-suff-conditional-table/{\"probability_rows\":[[[2,5],[1,10],[2,5],[1,10]],[[1,10],[2,5],[1,10],[2,5]]],\"samples\":[240,241,242,243],\"statistic\":[0,1,0,1],\"theta_values\":[\"a24\",\"b24\"]}"}},"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、一般Banach／IVT／Taylor證明、MLE漸近性、factorization theorem、一般DAG iff或primitive-root主張、Lean或Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-15","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261015-advance-20261116-r05-finite-sufficient-statistic-0051","batch_id":"batch-20261015-advance-20261116-r05-finite-sufficient-statistic-foundations","language":"zh-Hant","source_mko_ids":["mko-finite-sufficient-statistic"],"title_zh":"有限模型充分統計量","stem_zh":"total statistic fibers與正質量conditional laws的完整theta-invariance責任。操作=suff-invariance；資料={\"theta_values\":[\"a0\",\"b0\"],\"samples\":[0,1,2,3],\"probability_rows\":[[[2,5],[1,10],[2,5],[1,10]],[[1,10],[2,5],[1,10],[2,5]]],\"statistic\":[0,1,0,1]}。請依 exact_ordered_tuple_declared_by_interface 欄序回答。","answer":{"kind":"expression","value":"([[0, [[a0, [[0, 1/2], [2, 1/2]]], [b0, [[0, 1/2], [2, 1/2]]]], 是], [1, [[a0, [[1, 1/2], [3, 1/2]]], [b0, [[1, 1/2], [3, 1/2]]]], 是]], 是, conditional_law_must_be_theta_independent_on_every_positive_mass_cell)","explanation_zh":"Wave6第十層核對=([[0, [[a0, [[0, 1/2], [2, 1/2]]], [b0, [[0, 1/2], [2, 1/2]]]], 是], [1, [[a0, [[1, 1/2], [3, 1/2]]], [b0, [[1, 1/2], [3, 1/2]]]], 是]], 是, conditional_law_must_be_theta_independent_on_every_positive_mass_cell)；依完整明示資料獨立重算；zero-mass conditional保持undefined，nonsufficient需明示witness；identity/constant boundaries分開且不使用factorization theorem或宣稱估計品質。"},"difficulty":{"band":"undergraduate_core","level":1,"skills":["有限模型充分統計量"]},"variant":{"family_id":"qf-mod47-suff-invariance","seed":202611165051,"parameters":{"theta_values":["a0","b0"],"samples":[0,1,2,3],"probability_rows":[[[2,5],[1,10],[2,5],[1,10]],[[1,10],[2,5],[1,10],[2,5]]],"statistic":[0,1,0,1],"domain":"Exact_finite_sufficient_statistic","operation":"suff-invariance","semantic_template":"qf-mod47-suff-invariance/{\"probability_rows\":[[[2,5],[1,10],[2,5],[1,10]],[[1,10],[2,5],[1,10],[2,5]]],\"samples\":[0,1,2,3],\"statistic\":[0,1,0,1],\"theta_values\":[\"a0\",\"b0\"]}"}},"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、一般Banach／IVT／Taylor證明、MLE漸近性、factorization theorem、一般DAG iff或primitive-root主張、Lean或Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-15","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261015-advance-20261116-r05-finite-sufficient-statistic-0052","batch_id":"batch-20261015-advance-20261116-r05-finite-sufficient-statistic-foundations","language":"zh-Hant","source_mko_ids":["mko-finite-sufficient-statistic"],"title_zh":"有限模型充分統計量","stem_zh":"total statistic fibers與正質量conditional laws的完整theta-invariance責任。操作=suff-invariance；資料={\"theta_values\":[\"a1\",\"b1\"],\"samples\":[10,11,12,13],\"probability_rows\":[[[2,5],[1,10],[2,5],[1,10]],[[1,10],[2,5],[1,10],[2,5]]],\"statistic\":[0,1,0,1]}。請依 exact_ordered_tuple_declared_by_interface 欄序回答。","answer":{"kind":"expression","value":"([[0, [[a1, [[10, 1/2], [12, 1/2]]], [b1, [[10, 1/2], [12, 1/2]]]], 是], [1, [[a1, [[11, 1/2], [13, 1/2]]], [b1, [[11, 1/2], [13, 1/2]]]], 是]], 是, conditional_law_must_be_theta_independent_on_every_positive_mass_cell)","explanation_zh":"Wave6第十層核對=([[0, [[a1, [[10, 1/2], [12, 1/2]]], [b1, [[10, 1/2], [12, 1/2]]]], 是], [1, [[a1, [[11, 1/2], [13, 1/2]]], [b1, [[11, 1/2], [13, 1/2]]]], 是]], 是, conditional_law_must_be_theta_independent_on_every_positive_mass_cell)；依完整明示資料獨立重算；zero-mass conditional保持undefined，nonsufficient需明示witness；identity/constant boundaries分開且不使用factorization theorem或宣稱估計品質。"},"difficulty":{"band":"undergraduate_core","level":1,"skills":["有限模型充分統計量"]},"variant":{"family_id":"qf-mod47-suff-invariance","seed":202611165052,"parameters":{"theta_values":["a1","b1"],"samples":[10,11,12,13],"probability_rows":[[[2,5],[1,10],[2,5],[1,10]],[[1,10],[2,5],[1,10],[2,5]]],"statistic":[0,1,0,1],"domain":"Exact_finite_sufficient_statistic","operation":"suff-invariance","semantic_template":"qf-mod47-suff-invariance/{\"probability_rows\":[[[2,5],[1,10],[2,5],[1,10]],[[1,10],[2,5],[1,10],[2,5]]],\"samples\":[10,11,12,13],\"statistic\":[0,1,0,1],\"theta_values\":[\"a1\",\"b1\"]}"}},"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、一般Banach／IVT／Taylor證明、MLE漸近性、factorization theorem、一般DAG iff或primitive-root主張、Lean或Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-15","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261015-advance-20261116-r05-finite-sufficient-statistic-0053","batch_id":"batch-20261015-advance-20261116-r05-finite-sufficient-statistic-foundations","language":"zh-Hant","source_mko_ids":["mko-finite-sufficient-statistic"],"title_zh":"有限模型充分統計量","stem_zh":"total statistic fibers與正質量conditional laws的完整theta-invariance責任。操作=suff-invariance；資料={\"theta_values\":[\"a2\",\"b2\"],\"samples\":[20,21,22,23],\"probability_rows\":[[[2,5],[1,10],[2,5],[1,10]],[[1,10],[2,5],[1,10],[2,5]]],\"statistic\":[0,1,0,1]}。請依 exact_ordered_tuple_declared_by_interface 欄序回答。","answer":{"kind":"expression","value":"([[0, [[a2, [[20, 1/2], [22, 1/2]]], [b2, [[20, 1/2], [22, 1/2]]]], 是], [1, [[a2, [[21, 1/2], [23, 1/2]]], [b2, [[21, 1/2], [23, 1/2]]]], 是]], 是, conditional_law_must_be_theta_independent_on_every_positive_mass_cell)","explanation_zh":"Wave6第十層核對=([[0, [[a2, [[20, 1/2], [22, 1/2]]], [b2, [[20, 1/2], [22, 1/2]]]], 是], [1, [[a2, [[21, 1/2], [23, 1/2]]], [b2, [[21, 1/2], [23, 1/2]]]], 是]], 是, conditional_law_must_be_theta_independent_on_every_positive_mass_cell)；依完整明示資料獨立重算；zero-mass conditional保持undefined，nonsufficient需明示witness；identity/constant boundaries分開且不使用factorization theorem或宣稱估計品質。"},"difficulty":{"band":"undergraduate_core","level":1,"skills":["有限模型充分統計量"]},"variant":{"family_id":"qf-mod47-suff-invariance","seed":202611165053,"parameters":{"theta_values":["a2","b2"],"samples":[20,21,22,23],"probability_rows":[[[2,5],[1,10],[2,5],[1,10]],[[1,10],[2,5],[1,10],[2,5]]],"statistic":[0,1,0,1],"domain":"Exact_finite_sufficient_statistic","operation":"suff-invariance","semantic_template":"qf-mod47-suff-invariance/{\"probability_rows\":[[[2,5],[1,10],[2,5],[1,10]],[[1,10],[2,5],[1,10],[2,5]]],\"samples\":[20,21,22,23],\"statistic\":[0,1,0,1],\"theta_values\":[\"a2\",\"b2\"]}"}},"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、一般Banach／IVT／Taylor證明、MLE漸近性、factorization theorem、一般DAG iff或primitive-root主張、Lean或Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-15","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261015-advance-20261116-r05-finite-sufficient-statistic-0054","batch_id":"batch-20261015-advance-20261116-r05-finite-sufficient-statistic-foundations","language":"zh-Hant","source_mko_ids":["mko-finite-sufficient-statistic"],"title_zh":"有限模型充分統計量","stem_zh":"total statistic fibers與正質量conditional laws的完整theta-invariance責任。操作=suff-invariance；資料={\"theta_values\":[\"a3\",\"b3\"],\"samples\":[30,31,32,33],\"probability_rows\":[[[2,5],[1,10],[2,5],[1,10]],[[1,10],[2,5],[1,10],[2,5]]],\"statistic\":[0,1,0,1]}。請依 exact_ordered_tuple_declared_by_interface 欄序回答。","answer":{"kind":"expression","value":"([[0, [[a3, [[30, 1/2], [32, 1/2]]], [b3, [[30, 1/2], [32, 1/2]]]], 是], [1, [[a3, [[31, 1/2], [33, 1/2]]], [b3, [[31, 1/2], [33, 1/2]]]], 是]], 是, conditional_law_must_be_theta_independent_on_every_positive_mass_cell)","explanation_zh":"Wave6第十層核對=([[0, [[a3, [[30, 1/2], [32, 1/2]]], [b3, [[30, 1/2], [32, 1/2]]]], 是], [1, [[a3, [[31, 1/2], [33, 1/2]]], [b3, [[31, 1/2], [33, 1/2]]]], 是]], 是, conditional_law_must_be_theta_independent_on_every_positive_mass_cell)；依完整明示資料獨立重算；zero-mass conditional保持undefined，nonsufficient需明示witness；identity/constant boundaries分開且不使用factorization theorem或宣稱估計品質。"},"difficulty":{"band":"undergraduate_core","level":1,"skills":["有限模型充分統計量"]},"variant":{"family_id":"qf-mod47-suff-invariance","seed":202611165054,"parameters":{"theta_values":["a3","b3"],"samples":[30,31,32,33],"probability_rows":[[[2,5],[1,10],[2,5],[1,10]],[[1,10],[2,5],[1,10],[2,5]]],"statistic":[0,1,0,1],"domain":"Exact_finite_sufficient_statistic","operation":"suff-invariance","semantic_template":"qf-mod47-suff-invariance/{\"probability_rows\":[[[2,5],[1,10],[2,5],[1,10]],[[1,10],[2,5],[1,10],[2,5]]],\"samples\":[30,31,32,33],\"statistic\":[0,1,0,1],\"theta_values\":[\"a3\",\"b3\"]}"}},"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、一般Banach／IVT／Taylor證明、MLE漸近性、factorization theorem、一般DAG iff或primitive-root主張、Lean或Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-15","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261015-advance-20261116-r05-finite-sufficient-statistic-0055","batch_id":"batch-20261015-advance-20261116-r05-finite-sufficient-statistic-foundations","language":"zh-Hant","source_mko_ids":["mko-finite-sufficient-statistic"],"title_zh":"有限模型充分統計量","stem_zh":"total statistic fibers與正質量conditional laws的完整theta-invariance責任。操作=suff-invariance；資料={\"theta_values\":[\"a4\",\"b4\"],\"samples\":[40,41,42,43],\"probability_rows\":[[[2,5],[1,10],[2,5],[1,10]],[[1,10],[2,5],[1,10],[2,5]]],\"statistic\":[0,1,0,1]}。請依 exact_ordered_tuple_declared_by_interface 欄序回答。","answer":{"kind":"expression","value":"([[0, [[a4, [[40, 1/2], [42, 1/2]]], [b4, [[40, 1/2], [42, 1/2]]]], 是], [1, [[a4, [[41, 1/2], [43, 1/2]]], [b4, [[41, 1/2], [43, 1/2]]]], 是]], 是, conditional_law_must_be_theta_independent_on_every_positive_mass_cell)","explanation_zh":"Wave6第十層核對=([[0, [[a4, [[40, 1/2], [42, 1/2]]], [b4, [[40, 1/2], [42, 1/2]]]], 是], [1, [[a4, [[41, 1/2], [43, 1/2]]], [b4, [[41, 1/2], [43, 1/2]]]], 是]], 是, conditional_law_must_be_theta_independent_on_every_positive_mass_cell)；依完整明示資料獨立重算；zero-mass conditional保持undefined，nonsufficient需明示witness；identity/constant boundaries分開且不使用factorization theorem或宣稱估計品質。"},"difficulty":{"band":"undergraduate_core","level":1,"skills":["有限模型充分統計量"]},"variant":{"family_id":"qf-mod47-suff-invariance","seed":202611165055,"parameters":{"theta_values":["a4","b4"],"samples":[40,41,42,43],"probability_rows":[[[2,5],[1,10],[2,5],[1,10]],[[1,10],[2,5],[1,10],[2,5]]],"statistic":[0,1,0,1],"domain":"Exact_finite_sufficient_statistic","operation":"suff-invariance","semantic_template":"qf-mod47-suff-invariance/{\"probability_rows\":[[[2,5],[1,10],[2,5],[1,10]],[[1,10],[2,5],[1,10],[2,5]]],\"samples\":[40,41,42,43],\"statistic\":[0,1,0,1],\"theta_values\":[\"a4\",\"b4\"]}"}},"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、一般Banach／IVT／Taylor證明、MLE漸近性、factorization theorem、一般DAG iff或primitive-root主張、Lean或Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-15","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261015-advance-20261116-r05-finite-sufficient-statistic-0056","batch_id":"batch-20261015-advance-20261116-r05-finite-sufficient-statistic-foundations","language":"zh-Hant","source_mko_ids":["mko-finite-sufficient-statistic"],"title_zh":"有限模型充分統計量","stem_zh":"total statistic fibers與正質量conditional laws的完整theta-invariance責任。操作=suff-invariance；資料={\"theta_values\":[\"a5\",\"b5\"],\"samples\":[50,51,52,53],\"probability_rows\":[[[2,5],[1,10],[2,5],[1,10]],[[1,10],[2,5],[1,10],[2,5]]],\"statistic\":[0,1,0,1]}。請依 exact_ordered_tuple_declared_by_interface 欄序回答。","answer":{"kind":"expression","value":"([[0, [[a5, [[50, 1/2], [52, 1/2]]], [b5, [[50, 1/2], [52, 1/2]]]], 是], [1, [[a5, [[51, 1/2], [53, 1/2]]], [b5, [[51, 1/2], [53, 1/2]]]], 是]], 是, conditional_law_must_be_theta_independent_on_every_positive_mass_cell)","explanation_zh":"Wave6第十層核對=([[0, [[a5, [[50, 1/2], [52, 1/2]]], [b5, [[50, 1/2], [52, 1/2]]]], 是], [1, [[a5, [[51, 1/2], [53, 1/2]]], [b5, [[51, 1/2], [53, 1/2]]]], 是]], 是, conditional_law_must_be_theta_independent_on_every_positive_mass_cell)；依完整明示資料獨立重算；zero-mass conditional保持undefined，nonsufficient需明示witness；identity/constant boundaries分開且不使用factorization theorem或宣稱估計品質。"},"difficulty":{"band":"undergraduate_core","level":1,"skills":["有限模型充分統計量"]},"variant":{"family_id":"qf-mod47-suff-invariance","seed":202611165056,"parameters":{"theta_values":["a5","b5"],"samples":[50,51,52,53],"probability_rows":[[[2,5],[1,10],[2,5],[1,10]],[[1,10],[2,5],[1,10],[2,5]]],"statistic":[0,1,0,1],"domain":"Exact_finite_sufficient_statistic","operation":"suff-invariance","semantic_template":"qf-mod47-suff-invariance/{\"probability_rows\":[[[2,5],[1,10],[2,5],[1,10]],[[1,10],[2,5],[1,10],[2,5]]],\"samples\":[50,51,52,53],\"statistic\":[0,1,0,1],\"theta_values\":[\"a5\",\"b5\"]}"}},"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、一般Banach／IVT／Taylor證明、MLE漸近性、factorization theorem、一般DAG iff或primitive-root主張、Lean或Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-15","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261015-advance-20261116-r05-finite-sufficient-statistic-0057","batch_id":"batch-20261015-advance-20261116-r05-finite-sufficient-statistic-foundations","language":"zh-Hant","source_mko_ids":["mko-finite-sufficient-statistic"],"title_zh":"有限模型充分統計量","stem_zh":"total statistic fibers與正質量conditional laws的完整theta-invariance責任。操作=suff-invariance；資料={\"theta_values\":[\"a6\",\"b6\"],\"samples\":[60,61,62,63],\"probability_rows\":[[[2,5],[1,10],[2,5],[1,10]],[[1,10],[2,5],[1,10],[2,5]]],\"statistic\":[0,1,0,1]}。請依 exact_ordered_tuple_declared_by_interface 欄序回答。","answer":{"kind":"expression","value":"([[0, [[a6, [[60, 1/2], [62, 1/2]]], [b6, [[60, 1/2], [62, 1/2]]]], 是], [1, [[a6, [[61, 1/2], [63, 1/2]]], [b6, [[61, 1/2], [63, 1/2]]]], 是]], 是, conditional_law_must_be_theta_independent_on_every_positive_mass_cell)","explanation_zh":"Wave6第十層核對=([[0, [[a6, [[60, 1/2], [62, 1/2]]], [b6, [[60, 1/2], [62, 1/2]]]], 是], [1, [[a6, [[61, 1/2], [63, 1/2]]], [b6, [[61, 1/2], [63, 1/2]]]], 是]], 是, conditional_law_must_be_theta_independent_on_every_positive_mass_cell)；依完整明示資料獨立重算；zero-mass conditional保持undefined，nonsufficient需明示witness；identity/constant boundaries分開且不使用factorization theorem或宣稱估計品質。"},"difficulty":{"band":"undergraduate_core","level":1,"skills":["有限模型充分統計量"]},"variant":{"family_id":"qf-mod47-suff-invariance","seed":202611165057,"parameters":{"theta_values":["a6","b6"],"samples":[60,61,62,63],"probability_rows":[[[2,5],[1,10],[2,5],[1,10]],[[1,10],[2,5],[1,10],[2,5]]],"statistic":[0,1,0,1],"domain":"Exact_finite_sufficient_statistic","operation":"suff-invariance","semantic_template":"qf-mod47-suff-invariance/{\"probability_rows\":[[[2,5],[1,10],[2,5],[1,10]],[[1,10],[2,5],[1,10],[2,5]]],\"samples\":[60,61,62,63],\"statistic\":[0,1,0,1],\"theta_values\":[\"a6\",\"b6\"]}"}},"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、一般Banach／IVT／Taylor證明、MLE漸近性、factorization theorem、一般DAG iff或primitive-root主張、Lean或Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-15","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261015-advance-20261116-r05-finite-sufficient-statistic-0058","batch_id":"batch-20261015-advance-20261116-r05-finite-sufficient-statistic-foundations","language":"zh-Hant","source_mko_ids":["mko-finite-sufficient-statistic"],"title_zh":"有限模型充分統計量","stem_zh":"total statistic fibers與正質量conditional laws的完整theta-invariance責任。操作=suff-invariance；資料={\"theta_values\":[\"a7\",\"b7\"],\"samples\":[70,71,72,73],\"probability_rows\":[[[2,5],[1,10],[2,5],[1,10]],[[1,10],[2,5],[1,10],[2,5]]],\"statistic\":[0,1,0,1]}。請依 exact_ordered_tuple_declared_by_interface 欄序回答。","answer":{"kind":"expression","value":"([[0, [[a7, [[70, 1/2], [72, 1/2]]], [b7, [[70, 1/2], [72, 1/2]]]], 是], [1, [[a7, [[71, 1/2], [73, 1/2]]], [b7, [[71, 1/2], [73, 1/2]]]], 是]], 是, conditional_law_must_be_theta_independent_on_every_positive_mass_cell)","explanation_zh":"Wave6第十層核對=([[0, [[a7, [[70, 1/2], [72, 1/2]]], [b7, [[70, 1/2], [72, 1/2]]]], 是], [1, [[a7, [[71, 1/2], [73, 1/2]]], [b7, [[71, 1/2], [73, 1/2]]]], 是]], 是, conditional_law_must_be_theta_independent_on_every_positive_mass_cell)；依完整明示資料獨立重算；zero-mass conditional保持undefined，nonsufficient需明示witness；identity/constant boundaries分開且不使用factorization theorem或宣稱估計品質。"},"difficulty":{"band":"undergraduate_core","level":1,"skills":["有限模型充分統計量"]},"variant":{"family_id":"qf-mod47-suff-invariance","seed":202611165058,"parameters":{"theta_values":["a7","b7"],"samples":[70,71,72,73],"probability_rows":[[[2,5],[1,10],[2,5],[1,10]],[[1,10],[2,5],[1,10],[2,5]]],"statistic":[0,1,0,1],"domain":"Exact_finite_sufficient_statistic","operation":"suff-invariance","semantic_template":"qf-mod47-suff-invariance/{\"probability_rows\":[[[2,5],[1,10],[2,5],[1,10]],[[1,10],[2,5],[1,10],[2,5]]],\"samples\":[70,71,72,73],\"statistic\":[0,1,0,1],\"theta_values\":[\"a7\",\"b7\"]}"}},"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、一般Banach／IVT／Taylor證明、MLE漸近性、factorization theorem、一般DAG iff或primitive-root主張、Lean或Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-15","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261015-advance-20261116-r05-finite-sufficient-statistic-0059","batch_id":"batch-20261015-advance-20261116-r05-finite-sufficient-statistic-foundations","language":"zh-Hant","source_mko_ids":["mko-finite-sufficient-statistic"],"title_zh":"有限模型充分統計量","stem_zh":"total statistic fibers與正質量conditional laws的完整theta-invariance責任。操作=suff-invariance；資料={\"theta_values\":[\"a8\",\"b8\"],\"samples\":[80,81,82,83],\"probability_rows\":[[[2,5],[1,10],[2,5],[1,10]],[[1,10],[2,5],[1,10],[2,5]]],\"statistic\":[0,1,0,1]}。請依 exact_ordered_tuple_declared_by_interface 欄序回答。","answer":{"kind":"expression","value":"([[0, [[a8, [[80, 1/2], [82, 1/2]]], [b8, [[80, 1/2], [82, 1/2]]]], 是], [1, [[a8, [[81, 1/2], [83, 1/2]]], [b8, [[81, 1/2], [83, 1/2]]]], 是]], 是, conditional_law_must_be_theta_independent_on_every_positive_mass_cell)","explanation_zh":"Wave6第十層核對=([[0, [[a8, [[80, 1/2], [82, 1/2]]], [b8, [[80, 1/2], [82, 1/2]]]], 是], [1, [[a8, [[81, 1/2], [83, 1/2]]], [b8, [[81, 1/2], [83, 1/2]]]], 是]], 是, conditional_law_must_be_theta_independent_on_every_positive_mass_cell)；依完整明示資料獨立重算；zero-mass conditional保持undefined，nonsufficient需明示witness；identity/constant boundaries分開且不使用factorization theorem或宣稱估計品質。"},"difficulty":{"band":"undergraduate_core","level":2,"skills":["有限模型充分統計量"]},"variant":{"family_id":"qf-mod47-suff-invariance","seed":202611165059,"parameters":{"theta_values":["a8","b8"],"samples":[80,81,82,83],"probability_rows":[[[2,5],[1,10],[2,5],[1,10]],[[1,10],[2,5],[1,10],[2,5]]],"statistic":[0,1,0,1],"domain":"Exact_finite_sufficient_statistic","operation":"suff-invariance","semantic_template":"qf-mod47-suff-invariance/{\"probability_rows\":[[[2,5],[1,10],[2,5],[1,10]],[[1,10],[2,5],[1,10],[2,5]]],\"samples\":[80,81,82,83],\"statistic\":[0,1,0,1],\"theta_values\":[\"a8\",\"b8\"]}"}},"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、一般Banach／IVT／Taylor證明、MLE漸近性、factorization theorem、一般DAG iff或primitive-root主張、Lean或Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-15","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261015-advance-20261116-r05-finite-sufficient-statistic-0060","batch_id":"batch-20261015-advance-20261116-r05-finite-sufficient-statistic-foundations","language":"zh-Hant","source_mko_ids":["mko-finite-sufficient-statistic"],"title_zh":"有限模型充分統計量","stem_zh":"total statistic fibers與正質量conditional laws的完整theta-invariance責任。操作=suff-invariance；資料={\"theta_values\":[\"a9\",\"b9\"],\"samples\":[90,91,92,93],\"probability_rows\":[[[2,5],[1,10],[2,5],[1,10]],[[1,10],[2,5],[1,10],[2,5]]],\"statistic\":[0,1,0,1]}。請依 exact_ordered_tuple_declared_by_interface 欄序回答。","answer":{"kind":"expression","value":"([[0, [[a9, [[90, 1/2], [92, 1/2]]], [b9, [[90, 1/2], [92, 1/2]]]], 是], [1, [[a9, [[91, 1/2], [93, 1/2]]], [b9, [[91, 1/2], [93, 1/2]]]], 是]], 是, conditional_law_must_be_theta_independent_on_every_positive_mass_cell)","explanation_zh":"Wave6第十層核對=([[0, [[a9, [[90, 1/2], [92, 1/2]]], [b9, [[90, 1/2], [92, 1/2]]]], 是], [1, [[a9, [[91, 1/2], [93, 1/2]]], [b9, [[91, 1/2], [93, 1/2]]]], 是]], 是, conditional_law_must_be_theta_independent_on_every_positive_mass_cell)；依完整明示資料獨立重算；zero-mass conditional保持undefined，nonsufficient需明示witness；identity/constant boundaries分開且不使用factorization theorem或宣稱估計品質。"},"difficulty":{"band":"undergraduate_core","level":2,"skills":["有限模型充分統計量"]},"variant":{"family_id":"qf-mod47-suff-invariance","seed":202611165060,"parameters":{"theta_values":["a9","b9"],"samples":[90,91,92,93],"probability_rows":[[[2,5],[1,10],[2,5],[1,10]],[[1,10],[2,5],[1,10],[2,5]]],"statistic":[0,1,0,1],"domain":"Exact_finite_sufficient_statistic","operation":"suff-invariance","semantic_template":"qf-mod47-suff-invariance/{\"probability_rows\":[[[2,5],[1,10],[2,5],[1,10]],[[1,10],[2,5],[1,10],[2,5]]],\"samples\":[90,91,92,93],\"statistic\":[0,1,0,1],\"theta_values\":[\"a9\",\"b9\"]}"}},"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、一般Banach／IVT／Taylor證明、MLE漸近性、factorization theorem、一般DAG iff或primitive-root主張、Lean或Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-15","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261015-advance-20261116-r05-finite-sufficient-statistic-0061","batch_id":"batch-20261015-advance-20261116-r05-finite-sufficient-statistic-foundations","language":"zh-Hant","source_mko_ids":["mko-finite-sufficient-statistic"],"title_zh":"有限模型充分統計量","stem_zh":"total statistic fibers與正質量conditional laws的完整theta-invariance責任。操作=suff-invariance；資料={\"theta_values\":[\"a10\",\"b10\"],\"samples\":[100,101,102,103],\"probability_rows\":[[[2,5],[1,10],[2,5],[1,10]],[[1,10],[2,5],[1,10],[2,5]]],\"statistic\":[0,1,0,1]}。請依 exact_ordered_tuple_declared_by_interface 欄序回答。","answer":{"kind":"expression","value":"([[0, [[a10, [[100, 1/2], [102, 1/2]]], [b10, [[100, 1/2], [102, 1/2]]]], 是], [1, [[a10, [[101, 1/2], [103, 1/2]]], [b10, [[101, 1/2], [103, 1/2]]]], 是]], 是, conditional_law_must_be_theta_independent_on_every_positive_mass_cell)","explanation_zh":"Wave6第十層核對=([[0, [[a10, [[100, 1/2], [102, 1/2]]], [b10, [[100, 1/2], [102, 1/2]]]], 是], [1, [[a10, [[101, 1/2], [103, 1/2]]], [b10, [[101, 1/2], [103, 1/2]]]], 是]], 是, conditional_law_must_be_theta_independent_on_every_positive_mass_cell)；依完整明示資料獨立重算；zero-mass conditional保持undefined，nonsufficient需明示witness；identity/constant boundaries分開且不使用factorization theorem或宣稱估計品質。"},"difficulty":{"band":"undergraduate_core","level":2,"skills":["有限模型充分統計量"]},"variant":{"family_id":"qf-mod47-suff-invariance","seed":202611165061,"parameters":{"theta_values":["a10","b10"],"samples":[100,101,102,103],"probability_rows":[[[2,5],[1,10],[2,5],[1,10]],[[1,10],[2,5],[1,10],[2,5]]],"statistic":[0,1,0,1],"domain":"Exact_finite_sufficient_statistic","operation":"suff-invariance","semantic_template":"qf-mod47-suff-invariance/{\"probability_rows\":[[[2,5],[1,10],[2,5],[1,10]],[[1,10],[2,5],[1,10],[2,5]]],\"samples\":[100,101,102,103],\"statistic\":[0,1,0,1],\"theta_values\":[\"a10\",\"b10\"]}"}},"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、一般Banach／IVT／Taylor證明、MLE漸近性、factorization theorem、一般DAG iff或primitive-root主張、Lean或Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-15","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261015-advance-20261116-r05-finite-sufficient-statistic-0062","batch_id":"batch-20261015-advance-20261116-r05-finite-sufficient-statistic-foundations","language":"zh-Hant","source_mko_ids":["mko-finite-sufficient-statistic"],"title_zh":"有限模型充分統計量","stem_zh":"total statistic fibers與正質量conditional laws的完整theta-invariance責任。操作=suff-invariance；資料={\"theta_values\":[\"a11\",\"b11\"],\"samples\":[110,111,112,113],\"probability_rows\":[[[2,5],[1,10],[2,5],[1,10]],[[1,10],[2,5],[1,10],[2,5]]],\"statistic\":[0,1,0,1]}。請依 exact_ordered_tuple_declared_by_interface 欄序回答。","answer":{"kind":"expression","value":"([[0, [[a11, [[110, 1/2], [112, 1/2]]], [b11, [[110, 1/2], [112, 1/2]]]], 是], [1, [[a11, [[111, 1/2], [113, 1/2]]], [b11, [[111, 1/2], [113, 1/2]]]], 是]], 是, conditional_law_must_be_theta_independent_on_every_positive_mass_cell)","explanation_zh":"Wave6第十層核對=([[0, [[a11, [[110, 1/2], [112, 1/2]]], [b11, [[110, 1/2], [112, 1/2]]]], 是], [1, [[a11, [[111, 1/2], [113, 1/2]]], [b11, [[111, 1/2], [113, 1/2]]]], 是]], 是, conditional_law_must_be_theta_independent_on_every_positive_mass_cell)；依完整明示資料獨立重算；zero-mass conditional保持undefined，nonsufficient需明示witness；identity/constant boundaries分開且不使用factorization theorem或宣稱估計品質。"},"difficulty":{"band":"undergraduate_core","level":2,"skills":["有限模型充分統計量"]},"variant":{"family_id":"qf-mod47-suff-invariance","seed":202611165062,"parameters":{"theta_values":["a11","b11"],"samples":[110,111,112,113],"probability_rows":[[[2,5],[1,10],[2,5],[1,10]],[[1,10],[2,5],[1,10],[2,5]]],"statistic":[0,1,0,1],"domain":"Exact_finite_sufficient_statistic","operation":"suff-invariance","semantic_template":"qf-mod47-suff-invariance/{\"probability_rows\":[[[2,5],[1,10],[2,5],[1,10]],[[1,10],[2,5],[1,10],[2,5]]],\"samples\":[110,111,112,113],\"statistic\":[0,1,0,1],\"theta_values\":[\"a11\",\"b11\"]}"}},"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、一般Banach／IVT／Taylor證明、MLE漸近性、factorization theorem、一般DAG iff或primitive-root主張、Lean或Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-15","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261015-advance-20261116-r05-finite-sufficient-statistic-0063","batch_id":"batch-20261015-advance-20261116-r05-finite-sufficient-statistic-foundations","language":"zh-Hant","source_mko_ids":["mko-finite-sufficient-statistic"],"title_zh":"有限模型充分統計量","stem_zh":"total statistic fibers與正質量conditional laws的完整theta-invariance責任。操作=suff-invariance；資料={\"theta_values\":[\"a12\",\"b12\"],\"samples\":[120,121,122,123],\"probability_rows\":[[[2,5],[1,10],[2,5],[1,10]],[[1,10],[2,5],[1,10],[2,5]]],\"statistic\":[0,1,0,1]}。請依 exact_ordered_tuple_declared_by_interface 欄序回答。","answer":{"kind":"expression","value":"([[0, [[a12, [[120, 1/2], [122, 1/2]]], [b12, [[120, 1/2], [122, 1/2]]]], 是], [1, [[a12, [[121, 1/2], [123, 1/2]]], [b12, [[121, 1/2], [123, 1/2]]]], 是]], 是, conditional_law_must_be_theta_independent_on_every_positive_mass_cell)","explanation_zh":"Wave6第十層核對=([[0, [[a12, [[120, 1/2], [122, 1/2]]], [b12, [[120, 1/2], [122, 1/2]]]], 是], [1, [[a12, [[121, 1/2], [123, 1/2]]], [b12, [[121, 1/2], [123, 1/2]]]], 是]], 是, conditional_law_must_be_theta_independent_on_every_positive_mass_cell)；依完整明示資料獨立重算；zero-mass conditional保持undefined，nonsufficient需明示witness；identity/constant boundaries分開且不使用factorization theorem或宣稱估計品質。"},"difficulty":{"band":"undergraduate_core","level":2,"skills":["有限模型充分統計量"]},"variant":{"family_id":"qf-mod47-suff-invariance","seed":202611165063,"parameters":{"theta_values":["a12","b12"],"samples":[120,121,122,123],"probability_rows":[[[2,5],[1,10],[2,5],[1,10]],[[1,10],[2,5],[1,10],[2,5]]],"statistic":[0,1,0,1],"domain":"Exact_finite_sufficient_statistic","operation":"suff-invariance","semantic_template":"qf-mod47-suff-invariance/{\"probability_rows\":[[[2,5],[1,10],[2,5],[1,10]],[[1,10],[2,5],[1,10],[2,5]]],\"samples\":[120,121,122,123],\"statistic\":[0,1,0,1],\"theta_values\":[\"a12\",\"b12\"]}"}},"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、一般Banach／IVT／Taylor證明、MLE漸近性、factorization theorem、一般DAG iff或primitive-root主張、Lean或Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-15","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261015-advance-20261116-r05-finite-sufficient-statistic-0064","batch_id":"batch-20261015-advance-20261116-r05-finite-sufficient-statistic-foundations","language":"zh-Hant","source_mko_ids":["mko-finite-sufficient-statistic"],"title_zh":"有限模型充分統計量","stem_zh":"total statistic fibers與正質量conditional laws的完整theta-invariance責任。操作=suff-invariance；資料={\"theta_values\":[\"a13\",\"b13\"],\"samples\":[130,131,132,133],\"probability_rows\":[[[2,5],[1,10],[2,5],[1,10]],[[1,10],[2,5],[1,10],[2,5]]],\"statistic\":[0,1,0,1]}。請依 exact_ordered_tuple_declared_by_interface 欄序回答。","answer":{"kind":"expression","value":"([[0, [[a13, [[130, 1/2], [132, 1/2]]], [b13, [[130, 1/2], [132, 1/2]]]], 是], [1, [[a13, [[131, 1/2], [133, 1/2]]], [b13, [[131, 1/2], [133, 1/2]]]], 是]], 是, conditional_law_must_be_theta_independent_on_every_positive_mass_cell)","explanation_zh":"Wave6第十層核對=([[0, [[a13, [[130, 1/2], [132, 1/2]]], [b13, [[130, 1/2], [132, 1/2]]]], 是], [1, [[a13, [[131, 1/2], [133, 1/2]]], [b13, [[131, 1/2], [133, 1/2]]]], 是]], 是, conditional_law_must_be_theta_independent_on_every_positive_mass_cell)；依完整明示資料獨立重算；zero-mass conditional保持undefined，nonsufficient需明示witness；identity/constant boundaries分開且不使用factorization theorem或宣稱估計品質。"},"difficulty":{"band":"undergraduate_core","level":2,"skills":["有限模型充分統計量"]},"variant":{"family_id":"qf-mod47-suff-invariance","seed":202611165064,"parameters":{"theta_values":["a13","b13"],"samples":[130,131,132,133],"probability_rows":[[[2,5],[1,10],[2,5],[1,10]],[[1,10],[2,5],[1,10],[2,5]]],"statistic":[0,1,0,1],"domain":"Exact_finite_sufficient_statistic","operation":"suff-invariance","semantic_template":"qf-mod47-suff-invariance/{\"probability_rows\":[[[2,5],[1,10],[2,5],[1,10]],[[1,10],[2,5],[1,10],[2,5]]],\"samples\":[130,131,132,133],\"statistic\":[0,1,0,1],\"theta_values\":[\"a13\",\"b13\"]}"}},"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、一般Banach／IVT／Taylor證明、MLE漸近性、factorization theorem、一般DAG iff或primitive-root主張、Lean或Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-15","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261015-advance-20261116-r05-finite-sufficient-statistic-0065","batch_id":"batch-20261015-advance-20261116-r05-finite-sufficient-statistic-foundations","language":"zh-Hant","source_mko_ids":["mko-finite-sufficient-statistic"],"title_zh":"有限模型充分統計量","stem_zh":"total statistic fibers與正質量conditional laws的完整theta-invariance責任。操作=suff-invariance；資料={\"theta_values\":[\"a14\",\"b14\"],\"samples\":[140,141,142,143],\"probability_rows\":[[[2,5],[1,10],[2,5],[1,10]],[[1,10],[2,5],[1,10],[2,5]]],\"statistic\":[0,1,0,1]}。請依 exact_ordered_tuple_declared_by_interface 欄序回答。","answer":{"kind":"expression","value":"([[0, [[a14, [[140, 1/2], [142, 1/2]]], [b14, [[140, 1/2], [142, 1/2]]]], 是], [1, [[a14, [[141, 1/2], [143, 1/2]]], [b14, [[141, 1/2], [143, 1/2]]]], 是]], 是, conditional_law_must_be_theta_independent_on_every_positive_mass_cell)","explanation_zh":"Wave6第十層核對=([[0, [[a14, [[140, 1/2], [142, 1/2]]], [b14, [[140, 1/2], [142, 1/2]]]], 是], [1, [[a14, [[141, 1/2], [143, 1/2]]], [b14, [[141, 1/2], [143, 1/2]]]], 是]], 是, conditional_law_must_be_theta_independent_on_every_positive_mass_cell)；依完整明示資料獨立重算；zero-mass conditional保持undefined，nonsufficient需明示witness；identity/constant boundaries分開且不使用factorization theorem或宣稱估計品質。"},"difficulty":{"band":"undergraduate_core","level":2,"skills":["有限模型充分統計量"]},"variant":{"family_id":"qf-mod47-suff-invariance","seed":202611165065,"parameters":{"theta_values":["a14","b14"],"samples":[140,141,142,143],"probability_rows":[[[2,5],[1,10],[2,5],[1,10]],[[1,10],[2,5],[1,10],[2,5]]],"statistic":[0,1,0,1],"domain":"Exact_finite_sufficient_statistic","operation":"suff-invariance","semantic_template":"qf-mod47-suff-invariance/{\"probability_rows\":[[[2,5],[1,10],[2,5],[1,10]],[[1,10],[2,5],[1,10],[2,5]]],\"samples\":[140,141,142,143],\"statistic\":[0,1,0,1],\"theta_values\":[\"a14\",\"b14\"]}"}},"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、一般Banach／IVT／Taylor證明、MLE漸近性、factorization theorem、一般DAG iff或primitive-root主張、Lean或Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-15","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261015-advance-20261116-r05-finite-sufficient-statistic-0066","batch_id":"batch-20261015-advance-20261116-r05-finite-sufficient-statistic-foundations","language":"zh-Hant","source_mko_ids":["mko-finite-sufficient-statistic"],"title_zh":"有限模型充分統計量","stem_zh":"total statistic fibers與正質量conditional laws的完整theta-invariance責任。操作=suff-invariance；資料={\"theta_values\":[\"a15\",\"b15\"],\"samples\":[150,151,152,153],\"probability_rows\":[[[2,5],[1,10],[2,5],[1,10]],[[1,10],[2,5],[1,10],[2,5]]],\"statistic\":[0,1,0,1]}。請依 exact_ordered_tuple_declared_by_interface 欄序回答。","answer":{"kind":"expression","value":"([[0, [[a15, [[150, 1/2], [152, 1/2]]], [b15, [[150, 1/2], [152, 1/2]]]], 是], [1, [[a15, [[151, 1/2], [153, 1/2]]], [b15, [[151, 1/2], [153, 1/2]]]], 是]], 是, conditional_law_must_be_theta_independent_on_every_positive_mass_cell)","explanation_zh":"Wave6第十層核對=([[0, [[a15, [[150, 1/2], [152, 1/2]]], [b15, [[150, 1/2], [152, 1/2]]]], 是], [1, [[a15, [[151, 1/2], [153, 1/2]]], [b15, [[151, 1/2], [153, 1/2]]]], 是]], 是, conditional_law_must_be_theta_independent_on_every_positive_mass_cell)；依完整明示資料獨立重算；zero-mass conditional保持undefined，nonsufficient需明示witness；identity/constant boundaries分開且不使用factorization theorem或宣稱估計品質。"},"difficulty":{"band":"undergraduate_core","level":2,"skills":["有限模型充分統計量"]},"variant":{"family_id":"qf-mod47-suff-invariance","seed":202611165066,"parameters":{"theta_values":["a15","b15"],"samples":[150,151,152,153],"probability_rows":[[[2,5],[1,10],[2,5],[1,10]],[[1,10],[2,5],[1,10],[2,5]]],"statistic":[0,1,0,1],"domain":"Exact_finite_sufficient_statistic","operation":"suff-invariance","semantic_template":"qf-mod47-suff-invariance/{\"probability_rows\":[[[2,5],[1,10],[2,5],[1,10]],[[1,10],[2,5],[1,10],[2,5]]],\"samples\":[150,151,152,153],\"statistic\":[0,1,0,1],\"theta_values\":[\"a15\",\"b15\"]}"}},"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、一般Banach／IVT／Taylor證明、MLE漸近性、factorization theorem、一般DAG iff或primitive-root主張、Lean或Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-15","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261015-advance-20261116-r05-finite-sufficient-statistic-0067","batch_id":"batch-20261015-advance-20261116-r05-finite-sufficient-statistic-foundations","language":"zh-Hant","source_mko_ids":["mko-finite-sufficient-statistic"],"title_zh":"有限模型充分統計量","stem_zh":"total statistic fibers與正質量conditional laws的完整theta-invariance責任。操作=suff-invariance；資料={\"theta_values\":[\"a16\",\"b16\"],\"samples\":[160,161,162,163],\"probability_rows\":[[[2,5],[1,10],[2,5],[1,10]],[[1,10],[2,5],[1,10],[2,5]]],\"statistic\":[0,1,0,1]}。請依 exact_ordered_tuple_declared_by_interface 欄序回答。","answer":{"kind":"expression","value":"([[0, [[a16, [[160, 1/2], [162, 1/2]]], [b16, [[160, 1/2], [162, 1/2]]]], 是], [1, [[a16, [[161, 1/2], [163, 1/2]]], [b16, [[161, 1/2], [163, 1/2]]]], 是]], 是, conditional_law_must_be_theta_independent_on_every_positive_mass_cell)","explanation_zh":"Wave6第十層核對=([[0, [[a16, [[160, 1/2], [162, 1/2]]], [b16, [[160, 1/2], [162, 1/2]]]], 是], [1, [[a16, [[161, 1/2], [163, 1/2]]], [b16, [[161, 1/2], [163, 1/2]]]], 是]], 是, conditional_law_must_be_theta_independent_on_every_positive_mass_cell)；依完整明示資料獨立重算；zero-mass conditional保持undefined，nonsufficient需明示witness；identity/constant boundaries分開且不使用factorization theorem或宣稱估計品質。"},"difficulty":{"band":"undergraduate_core","level":2,"skills":["有限模型充分統計量"]},"variant":{"family_id":"qf-mod47-suff-invariance","seed":202611165067,"parameters":{"theta_values":["a16","b16"],"samples":[160,161,162,163],"probability_rows":[[[2,5],[1,10],[2,5],[1,10]],[[1,10],[2,5],[1,10],[2,5]]],"statistic":[0,1,0,1],"domain":"Exact_finite_sufficient_statistic","operation":"suff-invariance","semantic_template":"qf-mod47-suff-invariance/{\"probability_rows\":[[[2,5],[1,10],[2,5],[1,10]],[[1,10],[2,5],[1,10],[2,5]]],\"samples\":[160,161,162,163],\"statistic\":[0,1,0,1],\"theta_values\":[\"a16\",\"b16\"]}"}},"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、一般Banach／IVT／Taylor證明、MLE漸近性、factorization theorem、一般DAG iff或primitive-root主張、Lean或Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-15","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261015-advance-20261116-r05-finite-sufficient-statistic-0068","batch_id":"batch-20261015-advance-20261116-r05-finite-sufficient-statistic-foundations","language":"zh-Hant","source_mko_ids":["mko-finite-sufficient-statistic"],"title_zh":"有限模型充分統計量","stem_zh":"total statistic fibers與正質量conditional laws的完整theta-invariance責任。操作=suff-invariance；資料={\"theta_values\":[\"a17\",\"b17\"],\"samples\":[170,171,172,173],\"probability_rows\":[[[2,5],[1,10],[2,5],[1,10]],[[1,10],[2,5],[1,10],[2,5]]],\"statistic\":[0,1,0,1]}。請依 exact_ordered_tuple_declared_by_interface 欄序回答。","answer":{"kind":"expression","value":"([[0, [[a17, [[170, 1/2], [172, 1/2]]], [b17, [[170, 1/2], [172, 1/2]]]], 是], [1, [[a17, [[171, 1/2], [173, 1/2]]], [b17, [[171, 1/2], [173, 1/2]]]], 是]], 是, conditional_law_must_be_theta_independent_on_every_positive_mass_cell)","explanation_zh":"Wave6第十層核對=([[0, [[a17, [[170, 1/2], [172, 1/2]]], [b17, [[170, 1/2], [172, 1/2]]]], 是], [1, [[a17, [[171, 1/2], [173, 1/2]]], [b17, [[171, 1/2], [173, 1/2]]]], 是]], 是, conditional_law_must_be_theta_independent_on_every_positive_mass_cell)；依完整明示資料獨立重算；zero-mass conditional保持undefined，nonsufficient需明示witness；identity/constant boundaries分開且不使用factorization theorem或宣稱估計品質。"},"difficulty":{"band":"undergraduate_core","level":3,"skills":["有限模型充分統計量"]},"variant":{"family_id":"qf-mod47-suff-invariance","seed":202611165068,"parameters":{"theta_values":["a17","b17"],"samples":[170,171,172,173],"probability_rows":[[[2,5],[1,10],[2,5],[1,10]],[[1,10],[2,5],[1,10],[2,5]]],"statistic":[0,1,0,1],"domain":"Exact_finite_sufficient_statistic","operation":"suff-invariance","semantic_template":"qf-mod47-suff-invariance/{\"probability_rows\":[[[2,5],[1,10],[2,5],[1,10]],[[1,10],[2,5],[1,10],[2,5]]],\"samples\":[170,171,172,173],\"statistic\":[0,1,0,1],\"theta_values\":[\"a17\",\"b17\"]}"}},"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、一般Banach／IVT／Taylor證明、MLE漸近性、factorization theorem、一般DAG iff或primitive-root主張、Lean或Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-15","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261015-advance-20261116-r05-finite-sufficient-statistic-0069","batch_id":"batch-20261015-advance-20261116-r05-finite-sufficient-statistic-foundations","language":"zh-Hant","source_mko_ids":["mko-finite-sufficient-statistic"],"title_zh":"有限模型充分統計量","stem_zh":"total statistic fibers與正質量conditional laws的完整theta-invariance責任。操作=suff-invariance；資料={\"theta_values\":[\"a18\",\"b18\"],\"samples\":[180,181,182,183],\"probability_rows\":[[[2,5],[1,10],[2,5],[1,10]],[[1,10],[2,5],[1,10],[2,5]]],\"statistic\":[0,1,0,1]}。請依 exact_ordered_tuple_declared_by_interface 欄序回答。","answer":{"kind":"expression","value":"([[0, [[a18, [[180, 1/2], [182, 1/2]]], [b18, [[180, 1/2], [182, 1/2]]]], 是], [1, [[a18, [[181, 1/2], [183, 1/2]]], [b18, [[181, 1/2], [183, 1/2]]]], 是]], 是, conditional_law_must_be_theta_independent_on_every_positive_mass_cell)","explanation_zh":"Wave6第十層核對=([[0, [[a18, [[180, 1/2], [182, 1/2]]], [b18, [[180, 1/2], [182, 1/2]]]], 是], [1, [[a18, [[181, 1/2], [183, 1/2]]], [b18, [[181, 1/2], [183, 1/2]]]], 是]], 是, conditional_law_must_be_theta_independent_on_every_positive_mass_cell)；依完整明示資料獨立重算；zero-mass conditional保持undefined，nonsufficient需明示witness；identity/constant boundaries分開且不使用factorization theorem或宣稱估計品質。"},"difficulty":{"band":"undergraduate_core","level":3,"skills":["有限模型充分統計量"]},"variant":{"family_id":"qf-mod47-suff-invariance","seed":202611165069,"parameters":{"theta_values":["a18","b18"],"samples":[180,181,182,183],"probability_rows":[[[2,5],[1,10],[2,5],[1,10]],[[1,10],[2,5],[1,10],[2,5]]],"statistic":[0,1,0,1],"domain":"Exact_finite_sufficient_statistic","operation":"suff-invariance","semantic_template":"qf-mod47-suff-invariance/{\"probability_rows\":[[[2,5],[1,10],[2,5],[1,10]],[[1,10],[2,5],[1,10],[2,5]]],\"samples\":[180,181,182,183],\"statistic\":[0,1,0,1],\"theta_values\":[\"a18\",\"b18\"]}"}},"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、一般Banach／IVT／Taylor證明、MLE漸近性、factorization theorem、一般DAG iff或primitive-root主張、Lean或Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-15","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261015-advance-20261116-r05-finite-sufficient-statistic-0070","batch_id":"batch-20261015-advance-20261116-r05-finite-sufficient-statistic-foundations","language":"zh-Hant","source_mko_ids":["mko-finite-sufficient-statistic"],"title_zh":"有限模型充分統計量","stem_zh":"total statistic fibers與正質量conditional laws的完整theta-invariance責任。操作=suff-invariance；資料={\"theta_values\":[\"a19\",\"b19\"],\"samples\":[190,191,192,193],\"probability_rows\":[[[2,5],[1,10],[2,5],[1,10]],[[1,10],[2,5],[1,10],[2,5]]],\"statistic\":[0,1,0,1]}。請依 exact_ordered_tuple_declared_by_interface 欄序回答。","answer":{"kind":"expression","value":"([[0, [[a19, [[190, 1/2], [192, 1/2]]], [b19, [[190, 1/2], [192, 1/2]]]], 是], [1, [[a19, [[191, 1/2], [193, 1/2]]], [b19, [[191, 1/2], [193, 1/2]]]], 是]], 是, conditional_law_must_be_theta_independent_on_every_positive_mass_cell)","explanation_zh":"Wave6第十層核對=([[0, [[a19, [[190, 1/2], [192, 1/2]]], [b19, [[190, 1/2], [192, 1/2]]]], 是], [1, [[a19, [[191, 1/2], [193, 1/2]]], [b19, [[191, 1/2], [193, 1/2]]]], 是]], 是, conditional_law_must_be_theta_independent_on_every_positive_mass_cell)；依完整明示資料獨立重算；zero-mass conditional保持undefined，nonsufficient需明示witness；identity/constant boundaries分開且不使用factorization theorem或宣稱估計品質。"},"difficulty":{"band":"undergraduate_core","level":3,"skills":["有限模型充分統計量"]},"variant":{"family_id":"qf-mod47-suff-invariance","seed":202611165070,"parameters":{"theta_values":["a19","b19"],"samples":[190,191,192,193],"probability_rows":[[[2,5],[1,10],[2,5],[1,10]],[[1,10],[2,5],[1,10],[2,5]]],"statistic":[0,1,0,1],"domain":"Exact_finite_sufficient_statistic","operation":"suff-invariance","semantic_template":"qf-mod47-suff-invariance/{\"probability_rows\":[[[2,5],[1,10],[2,5],[1,10]],[[1,10],[2,5],[1,10],[2,5]]],\"samples\":[190,191,192,193],\"statistic\":[0,1,0,1],\"theta_values\":[\"a19\",\"b19\"]}"}},"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、一般Banach／IVT／Taylor證明、MLE漸近性、factorization theorem、一般DAG iff或primitive-root主張、Lean或Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-15","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261015-advance-20261116-r05-finite-sufficient-statistic-0071","batch_id":"batch-20261015-advance-20261116-r05-finite-sufficient-statistic-foundations","language":"zh-Hant","source_mko_ids":["mko-finite-sufficient-statistic"],"title_zh":"有限模型充分統計量","stem_zh":"total statistic fibers與正質量conditional laws的完整theta-invariance責任。操作=suff-invariance；資料={\"theta_values\":[\"a20\",\"b20\"],\"samples\":[200,201,202,203],\"probability_rows\":[[[2,5],[1,10],[2,5],[1,10]],[[1,10],[2,5],[1,10],[2,5]]],\"statistic\":[0,1,0,1]}。請依 exact_ordered_tuple_declared_by_interface 欄序回答。","answer":{"kind":"expression","value":"([[0, [[a20, [[200, 1/2], [202, 1/2]]], [b20, [[200, 1/2], [202, 1/2]]]], 是], [1, [[a20, [[201, 1/2], [203, 1/2]]], [b20, [[201, 1/2], [203, 1/2]]]], 是]], 是, conditional_law_must_be_theta_independent_on_every_positive_mass_cell)","explanation_zh":"Wave6第十層核對=([[0, [[a20, [[200, 1/2], [202, 1/2]]], [b20, [[200, 1/2], [202, 1/2]]]], 是], [1, [[a20, [[201, 1/2], [203, 1/2]]], [b20, [[201, 1/2], [203, 1/2]]]], 是]], 是, conditional_law_must_be_theta_independent_on_every_positive_mass_cell)；依完整明示資料獨立重算；zero-mass conditional保持undefined，nonsufficient需明示witness；identity/constant boundaries分開且不使用factorization theorem或宣稱估計品質。"},"difficulty":{"band":"undergraduate_core","level":3,"skills":["有限模型充分統計量"]},"variant":{"family_id":"qf-mod47-suff-invariance","seed":202611165071,"parameters":{"theta_values":["a20","b20"],"samples":[200,201,202,203],"probability_rows":[[[2,5],[1,10],[2,5],[1,10]],[[1,10],[2,5],[1,10],[2,5]]],"statistic":[0,1,0,1],"domain":"Exact_finite_sufficient_statistic","operation":"suff-invariance","semantic_template":"qf-mod47-suff-invariance/{\"probability_rows\":[[[2,5],[1,10],[2,5],[1,10]],[[1,10],[2,5],[1,10],[2,5]]],\"samples\":[200,201,202,203],\"statistic\":[0,1,0,1],\"theta_values\":[\"a20\",\"b20\"]}"}},"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、一般Banach／IVT／Taylor證明、MLE漸近性、factorization theorem、一般DAG iff或primitive-root主張、Lean或Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-15","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261015-advance-20261116-r05-finite-sufficient-statistic-0072","batch_id":"batch-20261015-advance-20261116-r05-finite-sufficient-statistic-foundations","language":"zh-Hant","source_mko_ids":["mko-finite-sufficient-statistic"],"title_zh":"有限模型充分統計量","stem_zh":"total statistic fibers與正質量conditional laws的完整theta-invariance責任。操作=suff-invariance；資料={\"theta_values\":[\"a21\",\"b21\"],\"samples\":[210,211,212,213],\"probability_rows\":[[[2,5],[1,10],[2,5],[1,10]],[[1,10],[2,5],[1,10],[2,5]]],\"statistic\":[0,1,0,1]}。請依 exact_ordered_tuple_declared_by_interface 欄序回答。","answer":{"kind":"expression","value":"([[0, [[a21, [[210, 1/2], [212, 1/2]]], [b21, [[210, 1/2], [212, 1/2]]]], 是], [1, [[a21, [[211, 1/2], [213, 1/2]]], [b21, [[211, 1/2], [213, 1/2]]]], 是]], 是, conditional_law_must_be_theta_independent_on_every_positive_mass_cell)","explanation_zh":"Wave6第十層核對=([[0, [[a21, [[210, 1/2], [212, 1/2]]], [b21, [[210, 1/2], [212, 1/2]]]], 是], [1, [[a21, [[211, 1/2], [213, 1/2]]], [b21, [[211, 1/2], [213, 1/2]]]], 是]], 是, conditional_law_must_be_theta_independent_on_every_positive_mass_cell)；依完整明示資料獨立重算；zero-mass conditional保持undefined，nonsufficient需明示witness；identity/constant boundaries分開且不使用factorization theorem或宣稱估計品質。"},"difficulty":{"band":"undergraduate_core","level":3,"skills":["有限模型充分統計量"]},"variant":{"family_id":"qf-mod47-suff-invariance","seed":202611165072,"parameters":{"theta_values":["a21","b21"],"samples":[210,211,212,213],"probability_rows":[[[2,5],[1,10],[2,5],[1,10]],[[1,10],[2,5],[1,10],[2,5]]],"statistic":[0,1,0,1],"domain":"Exact_finite_sufficient_statistic","operation":"suff-invariance","semantic_template":"qf-mod47-suff-invariance/{\"probability_rows\":[[[2,5],[1,10],[2,5],[1,10]],[[1,10],[2,5],[1,10],[2,5]]],\"samples\":[210,211,212,213],\"statistic\":[0,1,0,1],\"theta_values\":[\"a21\",\"b21\"]}"}},"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、一般Banach／IVT／Taylor證明、MLE漸近性、factorization theorem、一般DAG iff或primitive-root主張、Lean或Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-15","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261015-advance-20261116-r05-finite-sufficient-statistic-0073","batch_id":"batch-20261015-advance-20261116-r05-finite-sufficient-statistic-foundations","language":"zh-Hant","source_mko_ids":["mko-finite-sufficient-statistic"],"title_zh":"有限模型充分統計量","stem_zh":"total statistic fibers與正質量conditional laws的完整theta-invariance責任。操作=suff-invariance；資料={\"theta_values\":[\"a22\",\"b22\"],\"samples\":[220,221,222,223],\"probability_rows\":[[[2,5],[1,10],[2,5],[1,10]],[[1,10],[2,5],[1,10],[2,5]]],\"statistic\":[0,1,0,1]}。請依 exact_ordered_tuple_declared_by_interface 欄序回答。","answer":{"kind":"expression","value":"([[0, [[a22, [[220, 1/2], [222, 1/2]]], [b22, [[220, 1/2], [222, 1/2]]]], 是], [1, [[a22, [[221, 1/2], [223, 1/2]]], [b22, [[221, 1/2], [223, 1/2]]]], 是]], 是, conditional_law_must_be_theta_independent_on_every_positive_mass_cell)","explanation_zh":"Wave6第十層核對=([[0, [[a22, [[220, 1/2], [222, 1/2]]], [b22, [[220, 1/2], [222, 1/2]]]], 是], [1, [[a22, [[221, 1/2], [223, 1/2]]], [b22, [[221, 1/2], [223, 1/2]]]], 是]], 是, conditional_law_must_be_theta_independent_on_every_positive_mass_cell)；依完整明示資料獨立重算；zero-mass conditional保持undefined，nonsufficient需明示witness；identity/constant boundaries分開且不使用factorization theorem或宣稱估計品質。"},"difficulty":{"band":"undergraduate_core","level":3,"skills":["有限模型充分統計量"]},"variant":{"family_id":"qf-mod47-suff-invariance","seed":202611165073,"parameters":{"theta_values":["a22","b22"],"samples":[220,221,222,223],"probability_rows":[[[2,5],[1,10],[2,5],[1,10]],[[1,10],[2,5],[1,10],[2,5]]],"statistic":[0,1,0,1],"domain":"Exact_finite_sufficient_statistic","operation":"suff-invariance","semantic_template":"qf-mod47-suff-invariance/{\"probability_rows\":[[[2,5],[1,10],[2,5],[1,10]],[[1,10],[2,5],[1,10],[2,5]]],\"samples\":[220,221,222,223],\"statistic\":[0,1,0,1],\"theta_values\":[\"a22\",\"b22\"]}"}},"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、一般Banach／IVT／Taylor證明、MLE漸近性、factorization theorem、一般DAG iff或primitive-root主張、Lean或Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-15","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261015-advance-20261116-r05-finite-sufficient-statistic-0074","batch_id":"batch-20261015-advance-20261116-r05-finite-sufficient-statistic-foundations","language":"zh-Hant","source_mko_ids":["mko-finite-sufficient-statistic"],"title_zh":"有限模型充分統計量","stem_zh":"total statistic fibers與正質量conditional laws的完整theta-invariance責任。操作=suff-invariance；資料={\"theta_values\":[\"a23\",\"b23\"],\"samples\":[230,231,232,233],\"probability_rows\":[[[2,5],[1,10],[2,5],[1,10]],[[1,10],[2,5],[1,10],[2,5]]],\"statistic\":[0,1,0,1]}。請依 exact_ordered_tuple_declared_by_interface 欄序回答。","answer":{"kind":"expression","value":"([[0, [[a23, [[230, 1/2], [232, 1/2]]], [b23, [[230, 1/2], [232, 1/2]]]], 是], [1, [[a23, [[231, 1/2], [233, 1/2]]], [b23, [[231, 1/2], [233, 1/2]]]], 是]], 是, conditional_law_must_be_theta_independent_on_every_positive_mass_cell)","explanation_zh":"Wave6第十層核對=([[0, [[a23, [[230, 1/2], [232, 1/2]]], [b23, [[230, 1/2], [232, 1/2]]]], 是], [1, [[a23, [[231, 1/2], [233, 1/2]]], [b23, [[231, 1/2], [233, 1/2]]]], 是]], 是, conditional_law_must_be_theta_independent_on_every_positive_mass_cell)；依完整明示資料獨立重算；zero-mass conditional保持undefined，nonsufficient需明示witness；identity/constant boundaries分開且不使用factorization theorem或宣稱估計品質。"},"difficulty":{"band":"undergraduate_core","level":3,"skills":["有限模型充分統計量"]},"variant":{"family_id":"qf-mod47-suff-invariance","seed":202611165074,"parameters":{"theta_values":["a23","b23"],"samples":[230,231,232,233],"probability_rows":[[[2,5],[1,10],[2,5],[1,10]],[[1,10],[2,5],[1,10],[2,5]]],"statistic":[0,1,0,1],"domain":"Exact_finite_sufficient_statistic","operation":"suff-invariance","semantic_template":"qf-mod47-suff-invariance/{\"probability_rows\":[[[2,5],[1,10],[2,5],[1,10]],[[1,10],[2,5],[1,10],[2,5]]],\"samples\":[230,231,232,233],\"statistic\":[0,1,0,1],\"theta_values\":[\"a23\",\"b23\"]}"}},"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、一般Banach／IVT／Taylor證明、MLE漸近性、factorization theorem、一般DAG iff或primitive-root主張、Lean或Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-15","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261015-advance-20261116-r05-finite-sufficient-statistic-0075","batch_id":"batch-20261015-advance-20261116-r05-finite-sufficient-statistic-foundations","language":"zh-Hant","source_mko_ids":["mko-finite-sufficient-statistic"],"title_zh":"有限模型充分統計量","stem_zh":"total statistic fibers與正質量conditional laws的完整theta-invariance責任。操作=suff-invariance；資料={\"theta_values\":[\"a24\",\"b24\"],\"samples\":[240,241,242,243],\"probability_rows\":[[[2,5],[1,10],[2,5],[1,10]],[[1,10],[2,5],[1,10],[2,5]]],\"statistic\":[0,1,0,1]}。請依 exact_ordered_tuple_declared_by_interface 欄序回答。","answer":{"kind":"expression","value":"([[0, [[a24, [[240, 1/2], [242, 1/2]]], [b24, [[240, 1/2], [242, 1/2]]]], 是], [1, [[a24, [[241, 1/2], [243, 1/2]]], [b24, [[241, 1/2], [243, 1/2]]]], 是]], 是, conditional_law_must_be_theta_independent_on_every_positive_mass_cell)","explanation_zh":"Wave6第十層核對=([[0, [[a24, [[240, 1/2], [242, 1/2]]], [b24, [[240, 1/2], [242, 1/2]]]], 是], [1, [[a24, [[241, 1/2], [243, 1/2]]], [b24, [[241, 1/2], [243, 1/2]]]], 是]], 是, conditional_law_must_be_theta_independent_on_every_positive_mass_cell)；依完整明示資料獨立重算；zero-mass conditional保持undefined，nonsufficient需明示witness；identity/constant boundaries分開且不使用factorization theorem或宣稱估計品質。"},"difficulty":{"band":"undergraduate_core","level":3,"skills":["有限模型充分統計量"]},"variant":{"family_id":"qf-mod47-suff-invariance","seed":202611165075,"parameters":{"theta_values":["a24","b24"],"samples":[240,241,242,243],"probability_rows":[[[2,5],[1,10],[2,5],[1,10]],[[1,10],[2,5],[1,10],[2,5]]],"statistic":[0,1,0,1],"domain":"Exact_finite_sufficient_statistic","operation":"suff-invariance","semantic_template":"qf-mod47-suff-invariance/{\"probability_rows\":[[[2,5],[1,10],[2,5],[1,10]],[[1,10],[2,5],[1,10],[2,5]]],\"samples\":[240,241,242,243],\"statistic\":[0,1,0,1],\"theta_values\":[\"a24\",\"b24\"]}"}},"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、一般Banach／IVT／Taylor證明、MLE漸近性、factorization theorem、一般DAG iff或primitive-root主張、Lean或Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-15","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261015-advance-20261116-r05-finite-sufficient-statistic-0076","batch_id":"batch-20261015-advance-20261116-r05-finite-sufficient-statistic-foundations","language":"zh-Hant","source_mko_ids":["mko-finite-sufficient-statistic"],"title_zh":"有限模型充分統計量","stem_zh":"total statistic fibers與正質量conditional laws的完整theta-invariance責任。操作=suff-nonsufficient-zero-boundary；資料={\"mode\":\"nonsufficient\",\"theta_values\":[\"a0\",\"b0\"],\"samples\":[0,1,2,3],\"probability_rows\":[[[3,5],[1,10],[1,5],[1,10]],[[1,10],[2,5],[1,10],[2,5]]],\"statistic\":[0,1,0,1]}。請依 exact_ordered_tuple_declared_by_interface 欄序回答。","answer":{"kind":"expression","value":"(nonsufficient, [[0, [[a0, [[0, 3/4], [2, 1/4]]], [b0, [[0, 1/2], [2, 1/2]]]], 否], [1, [[a0, [[1, 1/2], [3, 1/2]]], [b0, [[1, 1/2], [3, 1/2]]]], 是]], 否, [], [0, [[a0, [[0, 3/4], [2, 1/4]]], [b0, [[0, 1/2], [2, 1/2]]]], 否], 否, 否, 否, 是, 否, identity_is_sufficient_constant_is_sufficient_exactly_when_theta_laws_match_no_factorization_or_estimator_quality_claim)","explanation_zh":"Wave6第十層核對=(nonsufficient, [[0, [[a0, [[0, 3/4], [2, 1/4]]], [b0, [[0, 1/2], [2, 1/2]]]], 否], [1, [[a0, [[1, 1/2], [3, 1/2]]], [b0, [[1, 1/2], [3, 1/2]]]], 是]], 否, [], [0, [[a0, [[0, 3/4], [2, 1/4]]], [b0, [[0, 1/2], [2, 1/2]]]], 否], 否, 否, 否, 是, 否, identity_is_sufficient_constant_is_sufficient_exactly_when_theta_laws_match_no_factorization_or_estimator_quality_claim)；依完整明示資料獨立重算；zero-mass conditional保持undefined，nonsufficient需明示witness；identity/constant boundaries分開且不使用factorization theorem或宣稱估計品質。"},"difficulty":{"band":"undergraduate_core","level":1,"skills":["有限模型充分統計量"]},"variant":{"family_id":"qf-mod47-suff-nonsufficient-zero-boundary","seed":202611165076,"parameters":{"mode":"nonsufficient","theta_values":["a0","b0"],"samples":[0,1,2,3],"probability_rows":[[[3,5],[1,10],[1,5],[1,10]],[[1,10],[2,5],[1,10],[2,5]]],"statistic":[0,1,0,1],"domain":"Exact_finite_sufficient_statistic","operation":"suff-nonsufficient-zero-boundary","semantic_template":"qf-mod47-suff-nonsufficient-zero-boundary/{\"mode\":\"nonsufficient\",\"probability_rows\":[[[3,5],[1,10],[1,5],[1,10]],[[1,10],[2,5],[1,10],[2,5]]],\"samples\":[0,1,2,3],\"statistic\":[0,1,0,1],\"theta_values\":[\"a0\",\"b0\"]}"}},"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、一般Banach／IVT／Taylor證明、MLE漸近性、factorization theorem、一般DAG iff或primitive-root主張、Lean或Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-15","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261015-advance-20261116-r05-finite-sufficient-statistic-0077","batch_id":"batch-20261015-advance-20261116-r05-finite-sufficient-statistic-foundations","language":"zh-Hant","source_mko_ids":["mko-finite-sufficient-statistic"],"title_zh":"有限模型充分統計量","stem_zh":"total statistic fibers與正質量conditional laws的完整theta-invariance責任。操作=suff-nonsufficient-zero-boundary；資料={\"mode\":\"zero_mass\",\"theta_values\":[\"a1\",\"b1\"],\"samples\":[10,11,12,13],\"probability_rows\":[[[1,2],0,[1,2],0],[0,[1,2],0,[1,2]]],\"statistic\":[0,1,0,1]}。請依 exact_ordered_tuple_declared_by_interface 欄序回答。","answer":{"kind":"expression","value":"(zero_mass, [[0, [[a1, [[10, 1/2], [12, 1/2]]]], 是], [1, [[b1, [[11, 1/2], [13, 1/2]]]], 是]], 是, [[a1, 1, 0, null], [b1, 0, 0, null]], null, 否, 否, 否, 是, 否, identity_is_sufficient_constant_is_sufficient_exactly_when_theta_laws_match_no_factorization_or_estimator_quality_claim)","explanation_zh":"Wave6第十層核對=(zero_mass, [[0, [[a1, [[10, 1/2], [12, 1/2]]]], 是], [1, [[b1, [[11, 1/2], [13, 1/2]]]], 是]], 是, [[a1, 1, 0, null], [b1, 0, 0, null]], null, 否, 否, 否, 是, 否, identity_is_sufficient_constant_is_sufficient_exactly_when_theta_laws_match_no_factorization_or_estimator_quality_claim)；依完整明示資料獨立重算；zero-mass conditional保持undefined，nonsufficient需明示witness；identity/constant boundaries分開且不使用factorization theorem或宣稱估計品質。"},"difficulty":{"band":"undergraduate_core","level":1,"skills":["有限模型充分統計量"]},"variant":{"family_id":"qf-mod47-suff-nonsufficient-zero-boundary","seed":202611165077,"parameters":{"mode":"zero_mass","theta_values":["a1","b1"],"samples":[10,11,12,13],"probability_rows":[[[1,2],0,[1,2],0],[0,[1,2],0,[1,2]]],"statistic":[0,1,0,1],"domain":"Exact_finite_sufficient_statistic","operation":"suff-nonsufficient-zero-boundary","semantic_template":"qf-mod47-suff-nonsufficient-zero-boundary/{\"mode\":\"zero_mass\",\"probability_rows\":[[[1,2],[0,1],[1,2],[0,1]],[[0,1],[1,2],[0,1],[1,2]]],\"samples\":[10,11,12,13],\"statistic\":[0,1,0,1],\"theta_values\":[\"a1\",\"b1\"]}"}},"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、一般Banach／IVT／Taylor證明、MLE漸近性、factorization theorem、一般DAG iff或primitive-root主張、Lean或Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-15","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261015-advance-20261116-r05-finite-sufficient-statistic-0078","batch_id":"batch-20261015-advance-20261116-r05-finite-sufficient-statistic-foundations","language":"zh-Hant","source_mko_ids":["mko-finite-sufficient-statistic"],"title_zh":"有限模型充分統計量","stem_zh":"total statistic fibers與正質量conditional laws的完整theta-invariance責任。操作=suff-nonsufficient-zero-boundary；資料={\"mode\":\"identity\",\"theta_values\":[\"a2\",\"b2\"],\"samples\":[20,21,22,23],\"probability_rows\":[[[2,5],[1,10],[2,5],[1,10]],[[1,10],[2,5],[1,10],[2,5]]],\"statistic\":[0,1,2,3]}。請依 exact_ordered_tuple_declared_by_interface 欄序回答。","answer":{"kind":"expression","value":"(identity, [[0, [[a2, [[20, 1]]], [b2, [[20, 1]]]], 是], [1, [[a2, [[21, 1]]], [b2, [[21, 1]]]], 是], [2, [[a2, [[22, 1]]], [b2, [[22, 1]]]], 是], [3, [[a2, [[23, 1]]], [b2, [[23, 1]]]], 是]], 是, [], null, 是, 否, 否, 是, 否, identity_is_sufficient_constant_is_sufficient_exactly_when_theta_laws_match_no_factorization_or_estimator_quality_claim)","explanation_zh":"Wave6第十層核對=(identity, [[0, [[a2, [[20, 1]]], [b2, [[20, 1]]]], 是], [1, [[a2, [[21, 1]]], [b2, [[21, 1]]]], 是], [2, [[a2, [[22, 1]]], [b2, [[22, 1]]]], 是], [3, [[a2, [[23, 1]]], [b2, [[23, 1]]]], 是]], 是, [], null, 是, 否, 否, 是, 否, identity_is_sufficient_constant_is_sufficient_exactly_when_theta_laws_match_no_factorization_or_estimator_quality_claim)；依完整明示資料獨立重算；zero-mass conditional保持undefined，nonsufficient需明示witness；identity/constant boundaries分開且不使用factorization theorem或宣稱估計品質。"},"difficulty":{"band":"undergraduate_core","level":1,"skills":["有限模型充分統計量"]},"variant":{"family_id":"qf-mod47-suff-nonsufficient-zero-boundary","seed":202611165078,"parameters":{"mode":"identity","theta_values":["a2","b2"],"samples":[20,21,22,23],"probability_rows":[[[2,5],[1,10],[2,5],[1,10]],[[1,10],[2,5],[1,10],[2,5]]],"statistic":[0,1,2,3],"domain":"Exact_finite_sufficient_statistic","operation":"suff-nonsufficient-zero-boundary","semantic_template":"qf-mod47-suff-nonsufficient-zero-boundary/{\"mode\":\"identity\",\"probability_rows\":[[[2,5],[1,10],[2,5],[1,10]],[[1,10],[2,5],[1,10],[2,5]]],\"samples\":[20,21,22,23],\"statistic\":[0,1,2,3],\"theta_values\":[\"a2\",\"b2\"]}"}},"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、一般Banach／IVT／Taylor證明、MLE漸近性、factorization theorem、一般DAG iff或primitive-root主張、Lean或Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-15","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261015-advance-20261116-r05-finite-sufficient-statistic-0079","batch_id":"batch-20261015-advance-20261116-r05-finite-sufficient-statistic-foundations","language":"zh-Hant","source_mko_ids":["mko-finite-sufficient-statistic"],"title_zh":"有限模型充分統計量","stem_zh":"total statistic fibers與正質量conditional laws的完整theta-invariance責任。操作=suff-nonsufficient-zero-boundary；資料={\"mode\":\"constant\",\"theta_values\":[\"a3\",\"b3\"],\"samples\":[30,31,32,33],\"probability_rows\":[[[2,5],[1,10],[2,5],[1,10]],[[1,10],[2,5],[1,10],[2,5]]],\"statistic\":[0,0,0,0]}。請依 exact_ordered_tuple_declared_by_interface 欄序回答。","answer":{"kind":"expression","value":"(constant, [[0, [[a3, [[30, 2/5], [31, 1/10], [32, 2/5], [33, 1/10]]], [b3, [[30, 1/10], [31, 2/5], [32, 1/10], [33, 2/5]]]], 否]], 否, [], null, 否, 是, 否, 是, 否, identity_is_sufficient_constant_is_sufficient_exactly_when_theta_laws_match_no_factorization_or_estimator_quality_claim)","explanation_zh":"Wave6第十層核對=(constant, [[0, [[a3, [[30, 2/5], [31, 1/10], [32, 2/5], [33, 1/10]]], [b3, [[30, 1/10], [31, 2/5], [32, 1/10], [33, 2/5]]]], 否]], 否, [], null, 否, 是, 否, 是, 否, identity_is_sufficient_constant_is_sufficient_exactly_when_theta_laws_match_no_factorization_or_estimator_quality_claim)；依完整明示資料獨立重算；zero-mass conditional保持undefined，nonsufficient需明示witness；identity/constant boundaries分開且不使用factorization theorem或宣稱估計品質。"},"difficulty":{"band":"undergraduate_core","level":1,"skills":["有限模型充分統計量"]},"variant":{"family_id":"qf-mod47-suff-nonsufficient-zero-boundary","seed":202611165079,"parameters":{"mode":"constant","theta_values":["a3","b3"],"samples":[30,31,32,33],"probability_rows":[[[2,5],[1,10],[2,5],[1,10]],[[1,10],[2,5],[1,10],[2,5]]],"statistic":[0,0,0,0],"domain":"Exact_finite_sufficient_statistic","operation":"suff-nonsufficient-zero-boundary","semantic_template":"qf-mod47-suff-nonsufficient-zero-boundary/{\"mode\":\"constant\",\"probability_rows\":[[[2,5],[1,10],[2,5],[1,10]],[[1,10],[2,5],[1,10],[2,5]]],\"samples\":[30,31,32,33],\"statistic\":[0,0,0,0],\"theta_values\":[\"a3\",\"b3\"]}"}},"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、一般Banach／IVT／Taylor證明、MLE漸近性、factorization theorem、一般DAG iff或primitive-root主張、Lean或Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-15","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261015-advance-20261116-r05-finite-sufficient-statistic-0080","batch_id":"batch-20261015-advance-20261116-r05-finite-sufficient-statistic-foundations","language":"zh-Hant","source_mko_ids":["mko-finite-sufficient-statistic"],"title_zh":"有限模型充分統計量","stem_zh":"total statistic fibers與正質量conditional laws的完整theta-invariance責任。操作=suff-nonsufficient-zero-boundary；資料={\"mode\":\"nonsufficient\",\"theta_values\":[\"a4\",\"b4\"],\"samples\":[40,41,42,43],\"probability_rows\":[[[3,5],[1,10],[1,5],[1,10]],[[1,10],[2,5],[1,10],[2,5]]],\"statistic\":[0,1,0,1]}。請依 exact_ordered_tuple_declared_by_interface 欄序回答。","answer":{"kind":"expression","value":"(nonsufficient, [[0, [[a4, [[40, 3/4], [42, 1/4]]], [b4, [[40, 1/2], [42, 1/2]]]], 否], [1, [[a4, [[41, 1/2], [43, 1/2]]], [b4, [[41, 1/2], [43, 1/2]]]], 是]], 否, [], [0, [[a4, [[40, 3/4], [42, 1/4]]], [b4, [[40, 1/2], [42, 1/2]]]], 否], 否, 否, 否, 是, 否, identity_is_sufficient_constant_is_sufficient_exactly_when_theta_laws_match_no_factorization_or_estimator_quality_claim)","explanation_zh":"Wave6第十層核對=(nonsufficient, [[0, [[a4, [[40, 3/4], [42, 1/4]]], [b4, [[40, 1/2], [42, 1/2]]]], 否], [1, [[a4, [[41, 1/2], [43, 1/2]]], [b4, [[41, 1/2], [43, 1/2]]]], 是]], 否, [], [0, [[a4, [[40, 3/4], [42, 1/4]]], [b4, [[40, 1/2], [42, 1/2]]]], 否], 否, 否, 否, 是, 否, identity_is_sufficient_constant_is_sufficient_exactly_when_theta_laws_match_no_factorization_or_estimator_quality_claim)；依完整明示資料獨立重算；zero-mass conditional保持undefined，nonsufficient需明示witness；identity/constant boundaries分開且不使用factorization theorem或宣稱估計品質。"},"difficulty":{"band":"undergraduate_core","level":1,"skills":["有限模型充分統計量"]},"variant":{"family_id":"qf-mod47-suff-nonsufficient-zero-boundary","seed":202611165080,"parameters":{"mode":"nonsufficient","theta_values":["a4","b4"],"samples":[40,41,42,43],"probability_rows":[[[3,5],[1,10],[1,5],[1,10]],[[1,10],[2,5],[1,10],[2,5]]],"statistic":[0,1,0,1],"domain":"Exact_finite_sufficient_statistic","operation":"suff-nonsufficient-zero-boundary","semantic_template":"qf-mod47-suff-nonsufficient-zero-boundary/{\"mode\":\"nonsufficient\",\"probability_rows\":[[[3,5],[1,10],[1,5],[1,10]],[[1,10],[2,5],[1,10],[2,5]]],\"samples\":[40,41,42,43],\"statistic\":[0,1,0,1],\"theta_values\":[\"a4\",\"b4\"]}"}},"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、一般Banach／IVT／Taylor證明、MLE漸近性、factorization theorem、一般DAG iff或primitive-root主張、Lean或Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-15","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261015-advance-20261116-r05-finite-sufficient-statistic-0081","batch_id":"batch-20261015-advance-20261116-r05-finite-sufficient-statistic-foundations","language":"zh-Hant","source_mko_ids":["mko-finite-sufficient-statistic"],"title_zh":"有限模型充分統計量","stem_zh":"total statistic fibers與正質量conditional laws的完整theta-invariance責任。操作=suff-nonsufficient-zero-boundary；資料={\"mode\":\"zero_mass\",\"theta_values\":[\"a5\",\"b5\"],\"samples\":[50,51,52,53],\"probability_rows\":[[[1,2],0,[1,2],0],[0,[1,2],0,[1,2]]],\"statistic\":[0,1,0,1]}。請依 exact_ordered_tuple_declared_by_interface 欄序回答。","answer":{"kind":"expression","value":"(zero_mass, [[0, [[a5, [[50, 1/2], [52, 1/2]]]], 是], [1, [[b5, [[51, 1/2], [53, 1/2]]]], 是]], 是, [[a5, 1, 0, null], [b5, 0, 0, null]], null, 否, 否, 否, 是, 否, identity_is_sufficient_constant_is_sufficient_exactly_when_theta_laws_match_no_factorization_or_estimator_quality_claim)","explanation_zh":"Wave6第十層核對=(zero_mass, [[0, [[a5, [[50, 1/2], [52, 1/2]]]], 是], [1, [[b5, [[51, 1/2], [53, 1/2]]]], 是]], 是, [[a5, 1, 0, null], [b5, 0, 0, null]], null, 否, 否, 否, 是, 否, identity_is_sufficient_constant_is_sufficient_exactly_when_theta_laws_match_no_factorization_or_estimator_quality_claim)；依完整明示資料獨立重算；zero-mass conditional保持undefined，nonsufficient需明示witness；identity/constant boundaries分開且不使用factorization theorem或宣稱估計品質。"},"difficulty":{"band":"undergraduate_core","level":1,"skills":["有限模型充分統計量"]},"variant":{"family_id":"qf-mod47-suff-nonsufficient-zero-boundary","seed":202611165081,"parameters":{"mode":"zero_mass","theta_values":["a5","b5"],"samples":[50,51,52,53],"probability_rows":[[[1,2],0,[1,2],0],[0,[1,2],0,[1,2]]],"statistic":[0,1,0,1],"domain":"Exact_finite_sufficient_statistic","operation":"suff-nonsufficient-zero-boundary","semantic_template":"qf-mod47-suff-nonsufficient-zero-boundary/{\"mode\":\"zero_mass\",\"probability_rows\":[[[1,2],[0,1],[1,2],[0,1]],[[0,1],[1,2],[0,1],[1,2]]],\"samples\":[50,51,52,53],\"statistic\":[0,1,0,1],\"theta_values\":[\"a5\",\"b5\"]}"}},"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、一般Banach／IVT／Taylor證明、MLE漸近性、factorization theorem、一般DAG iff或primitive-root主張、Lean或Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-15","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261015-advance-20261116-r05-finite-sufficient-statistic-0082","batch_id":"batch-20261015-advance-20261116-r05-finite-sufficient-statistic-foundations","language":"zh-Hant","source_mko_ids":["mko-finite-sufficient-statistic"],"title_zh":"有限模型充分統計量","stem_zh":"total statistic fibers與正質量conditional laws的完整theta-invariance責任。操作=suff-nonsufficient-zero-boundary；資料={\"mode\":\"identity\",\"theta_values\":[\"a6\",\"b6\"],\"samples\":[60,61,62,63],\"probability_rows\":[[[2,5],[1,10],[2,5],[1,10]],[[1,10],[2,5],[1,10],[2,5]]],\"statistic\":[0,1,2,3]}。請依 exact_ordered_tuple_declared_by_interface 欄序回答。","answer":{"kind":"expression","value":"(identity, [[0, [[a6, [[60, 1]]], [b6, [[60, 1]]]], 是], [1, [[a6, [[61, 1]]], [b6, [[61, 1]]]], 是], [2, [[a6, [[62, 1]]], [b6, [[62, 1]]]], 是], [3, [[a6, [[63, 1]]], [b6, [[63, 1]]]], 是]], 是, [], null, 是, 否, 否, 是, 否, identity_is_sufficient_constant_is_sufficient_exactly_when_theta_laws_match_no_factorization_or_estimator_quality_claim)","explanation_zh":"Wave6第十層核對=(identity, [[0, [[a6, [[60, 1]]], [b6, [[60, 1]]]], 是], [1, [[a6, [[61, 1]]], [b6, [[61, 1]]]], 是], [2, [[a6, [[62, 1]]], [b6, [[62, 1]]]], 是], [3, [[a6, [[63, 1]]], [b6, [[63, 1]]]], 是]], 是, [], null, 是, 否, 否, 是, 否, identity_is_sufficient_constant_is_sufficient_exactly_when_theta_laws_match_no_factorization_or_estimator_quality_claim)；依完整明示資料獨立重算；zero-mass conditional保持undefined，nonsufficient需明示witness；identity/constant boundaries分開且不使用factorization theorem或宣稱估計品質。"},"difficulty":{"band":"undergraduate_core","level":1,"skills":["有限模型充分統計量"]},"variant":{"family_id":"qf-mod47-suff-nonsufficient-zero-boundary","seed":202611165082,"parameters":{"mode":"identity","theta_values":["a6","b6"],"samples":[60,61,62,63],"probability_rows":[[[2,5],[1,10],[2,5],[1,10]],[[1,10],[2,5],[1,10],[2,5]]],"statistic":[0,1,2,3],"domain":"Exact_finite_sufficient_statistic","operation":"suff-nonsufficient-zero-boundary","semantic_template":"qf-mod47-suff-nonsufficient-zero-boundary/{\"mode\":\"identity\",\"probability_rows\":[[[2,5],[1,10],[2,5],[1,10]],[[1,10],[2,5],[1,10],[2,5]]],\"samples\":[60,61,62,63],\"statistic\":[0,1,2,3],\"theta_values\":[\"a6\",\"b6\"]}"}},"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、一般Banach／IVT／Taylor證明、MLE漸近性、factorization theorem、一般DAG iff或primitive-root主張、Lean或Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-15","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261015-advance-20261116-r05-finite-sufficient-statistic-0083","batch_id":"batch-20261015-advance-20261116-r05-finite-sufficient-statistic-foundations","language":"zh-Hant","source_mko_ids":["mko-finite-sufficient-statistic"],"title_zh":"有限模型充分統計量","stem_zh":"total statistic fibers與正質量conditional laws的完整theta-invariance責任。操作=suff-nonsufficient-zero-boundary；資料={\"mode\":\"constant\",\"theta_values\":[\"a7\",\"b7\"],\"samples\":[70,71,72,73],\"probability_rows\":[[[2,5],[1,10],[2,5],[1,10]],[[1,10],[2,5],[1,10],[2,5]]],\"statistic\":[0,0,0,0]}。請依 exact_ordered_tuple_declared_by_interface 欄序回答。","answer":{"kind":"expression","value":"(constant, [[0, [[a7, [[70, 2/5], [71, 1/10], [72, 2/5], [73, 1/10]]], [b7, [[70, 1/10], [71, 2/5], [72, 1/10], [73, 2/5]]]], 否]], 否, [], null, 否, 是, 否, 是, 否, identity_is_sufficient_constant_is_sufficient_exactly_when_theta_laws_match_no_factorization_or_estimator_quality_claim)","explanation_zh":"Wave6第十層核對=(constant, [[0, [[a7, [[70, 2/5], [71, 1/10], [72, 2/5], [73, 1/10]]], [b7, [[70, 1/10], [71, 2/5], [72, 1/10], [73, 2/5]]]], 否]], 否, [], null, 否, 是, 否, 是, 否, identity_is_sufficient_constant_is_sufficient_exactly_when_theta_laws_match_no_factorization_or_estimator_quality_claim)；依完整明示資料獨立重算；zero-mass conditional保持undefined，nonsufficient需明示witness；identity/constant boundaries分開且不使用factorization theorem或宣稱估計品質。"},"difficulty":{"band":"undergraduate_core","level":1,"skills":["有限模型充分統計量"]},"variant":{"family_id":"qf-mod47-suff-nonsufficient-zero-boundary","seed":202611165083,"parameters":{"mode":"constant","theta_values":["a7","b7"],"samples":[70,71,72,73],"probability_rows":[[[2,5],[1,10],[2,5],[1,10]],[[1,10],[2,5],[1,10],[2,5]]],"statistic":[0,0,0,0],"domain":"Exact_finite_sufficient_statistic","operation":"suff-nonsufficient-zero-boundary","semantic_template":"qf-mod47-suff-nonsufficient-zero-boundary/{\"mode\":\"constant\",\"probability_rows\":[[[2,5],[1,10],[2,5],[1,10]],[[1,10],[2,5],[1,10],[2,5]]],\"samples\":[70,71,72,73],\"statistic\":[0,0,0,0],\"theta_values\":[\"a7\",\"b7\"]}"}},"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、一般Banach／IVT／Taylor證明、MLE漸近性、factorization theorem、一般DAG iff或primitive-root主張、Lean或Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-15","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261015-advance-20261116-r05-finite-sufficient-statistic-0084","batch_id":"batch-20261015-advance-20261116-r05-finite-sufficient-statistic-foundations","language":"zh-Hant","source_mko_ids":["mko-finite-sufficient-statistic"],"title_zh":"有限模型充分統計量","stem_zh":"total statistic fibers與正質量conditional laws的完整theta-invariance責任。操作=suff-nonsufficient-zero-boundary；資料={\"mode\":\"nonsufficient\",\"theta_values\":[\"a8\",\"b8\"],\"samples\":[80,81,82,83],\"probability_rows\":[[[3,5],[1,10],[1,5],[1,10]],[[1,10],[2,5],[1,10],[2,5]]],\"statistic\":[0,1,0,1]}。請依 exact_ordered_tuple_declared_by_interface 欄序回答。","answer":{"kind":"expression","value":"(nonsufficient, [[0, [[a8, [[80, 3/4], [82, 1/4]]], [b8, [[80, 1/2], [82, 1/2]]]], 否], [1, [[a8, [[81, 1/2], [83, 1/2]]], [b8, [[81, 1/2], [83, 1/2]]]], 是]], 否, [], [0, [[a8, [[80, 3/4], [82, 1/4]]], [b8, [[80, 1/2], [82, 1/2]]]], 否], 否, 否, 否, 是, 否, identity_is_sufficient_constant_is_sufficient_exactly_when_theta_laws_match_no_factorization_or_estimator_quality_claim)","explanation_zh":"Wave6第十層核對=(nonsufficient, [[0, [[a8, [[80, 3/4], [82, 1/4]]], [b8, [[80, 1/2], [82, 1/2]]]], 否], [1, [[a8, [[81, 1/2], [83, 1/2]]], [b8, [[81, 1/2], [83, 1/2]]]], 是]], 否, [], [0, [[a8, [[80, 3/4], [82, 1/4]]], [b8, [[80, 1/2], [82, 1/2]]]], 否], 否, 否, 否, 是, 否, identity_is_sufficient_constant_is_sufficient_exactly_when_theta_laws_match_no_factorization_or_estimator_quality_claim)；依完整明示資料獨立重算；zero-mass conditional保持undefined，nonsufficient需明示witness；identity/constant boundaries分開且不使用factorization theorem或宣稱估計品質。"},"difficulty":{"band":"undergraduate_core","level":2,"skills":["有限模型充分統計量"]},"variant":{"family_id":"qf-mod47-suff-nonsufficient-zero-boundary","seed":202611165084,"parameters":{"mode":"nonsufficient","theta_values":["a8","b8"],"samples":[80,81,82,83],"probability_rows":[[[3,5],[1,10],[1,5],[1,10]],[[1,10],[2,5],[1,10],[2,5]]],"statistic":[0,1,0,1],"domain":"Exact_finite_sufficient_statistic","operation":"suff-nonsufficient-zero-boundary","semantic_template":"qf-mod47-suff-nonsufficient-zero-boundary/{\"mode\":\"nonsufficient\",\"probability_rows\":[[[3,5],[1,10],[1,5],[1,10]],[[1,10],[2,5],[1,10],[2,5]]],\"samples\":[80,81,82,83],\"statistic\":[0,1,0,1],\"theta_values\":[\"a8\",\"b8\"]}"}},"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、一般Banach／IVT／Taylor證明、MLE漸近性、factorization theorem、一般DAG iff或primitive-root主張、Lean或Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-15","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261015-advance-20261116-r05-finite-sufficient-statistic-0085","batch_id":"batch-20261015-advance-20261116-r05-finite-sufficient-statistic-foundations","language":"zh-Hant","source_mko_ids":["mko-finite-sufficient-statistic"],"title_zh":"有限模型充分統計量","stem_zh":"total statistic fibers與正質量conditional laws的完整theta-invariance責任。操作=suff-nonsufficient-zero-boundary；資料={\"mode\":\"zero_mass\",\"theta_values\":[\"a9\",\"b9\"],\"samples\":[90,91,92,93],\"probability_rows\":[[[1,2],0,[1,2],0],[0,[1,2],0,[1,2]]],\"statistic\":[0,1,0,1]}。請依 exact_ordered_tuple_declared_by_interface 欄序回答。","answer":{"kind":"expression","value":"(zero_mass, [[0, [[a9, [[90, 1/2], [92, 1/2]]]], 是], [1, [[b9, [[91, 1/2], [93, 1/2]]]], 是]], 是, [[a9, 1, 0, null], [b9, 0, 0, null]], null, 否, 否, 否, 是, 否, identity_is_sufficient_constant_is_sufficient_exactly_when_theta_laws_match_no_factorization_or_estimator_quality_claim)","explanation_zh":"Wave6第十層核對=(zero_mass, [[0, [[a9, [[90, 1/2], [92, 1/2]]]], 是], [1, [[b9, [[91, 1/2], [93, 1/2]]]], 是]], 是, [[a9, 1, 0, null], [b9, 0, 0, null]], null, 否, 否, 否, 是, 否, identity_is_sufficient_constant_is_sufficient_exactly_when_theta_laws_match_no_factorization_or_estimator_quality_claim)；依完整明示資料獨立重算；zero-mass conditional保持undefined，nonsufficient需明示witness；identity/constant boundaries分開且不使用factorization theorem或宣稱估計品質。"},"difficulty":{"band":"undergraduate_core","level":2,"skills":["有限模型充分統計量"]},"variant":{"family_id":"qf-mod47-suff-nonsufficient-zero-boundary","seed":202611165085,"parameters":{"mode":"zero_mass","theta_values":["a9","b9"],"samples":[90,91,92,93],"probability_rows":[[[1,2],0,[1,2],0],[0,[1,2],0,[1,2]]],"statistic":[0,1,0,1],"domain":"Exact_finite_sufficient_statistic","operation":"suff-nonsufficient-zero-boundary","semantic_template":"qf-mod47-suff-nonsufficient-zero-boundary/{\"mode\":\"zero_mass\",\"probability_rows\":[[[1,2],[0,1],[1,2],[0,1]],[[0,1],[1,2],[0,1],[1,2]]],\"samples\":[90,91,92,93],\"statistic\":[0,1,0,1],\"theta_values\":[\"a9\",\"b9\"]}"}},"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、一般Banach／IVT／Taylor證明、MLE漸近性、factorization theorem、一般DAG iff或primitive-root主張、Lean或Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-15","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261015-advance-20261116-r05-finite-sufficient-statistic-0086","batch_id":"batch-20261015-advance-20261116-r05-finite-sufficient-statistic-foundations","language":"zh-Hant","source_mko_ids":["mko-finite-sufficient-statistic"],"title_zh":"有限模型充分統計量","stem_zh":"total statistic fibers與正質量conditional laws的完整theta-invariance責任。操作=suff-nonsufficient-zero-boundary；資料={\"mode\":\"identity\",\"theta_values\":[\"a10\",\"b10\"],\"samples\":[100,101,102,103],\"probability_rows\":[[[2,5],[1,10],[2,5],[1,10]],[[1,10],[2,5],[1,10],[2,5]]],\"statistic\":[0,1,2,3]}。請依 exact_ordered_tuple_declared_by_interface 欄序回答。","answer":{"kind":"expression","value":"(identity, [[0, [[a10, [[100, 1]]], [b10, [[100, 1]]]], 是], [1, [[a10, [[101, 1]]], [b10, [[101, 1]]]], 是], [2, [[a10, [[102, 1]]], [b10, [[102, 1]]]], 是], [3, [[a10, [[103, 1]]], [b10, [[103, 1]]]], 是]], 是, [], null, 是, 否, 否, 是, 否, identity_is_sufficient_constant_is_sufficient_exactly_when_theta_laws_match_no_factorization_or_estimator_quality_claim)","explanation_zh":"Wave6第十層核對=(identity, [[0, [[a10, [[100, 1]]], [b10, [[100, 1]]]], 是], [1, [[a10, [[101, 1]]], [b10, [[101, 1]]]], 是], [2, [[a10, [[102, 1]]], [b10, [[102, 1]]]], 是], [3, [[a10, [[103, 1]]], [b10, [[103, 1]]]], 是]], 是, [], null, 是, 否, 否, 是, 否, identity_is_sufficient_constant_is_sufficient_exactly_when_theta_laws_match_no_factorization_or_estimator_quality_claim)；依完整明示資料獨立重算；zero-mass conditional保持undefined，nonsufficient需明示witness；identity/constant boundaries分開且不使用factorization theorem或宣稱估計品質。"},"difficulty":{"band":"undergraduate_core","level":2,"skills":["有限模型充分統計量"]},"variant":{"family_id":"qf-mod47-suff-nonsufficient-zero-boundary","seed":202611165086,"parameters":{"mode":"identity","theta_values":["a10","b10"],"samples":[100,101,102,103],"probability_rows":[[[2,5],[1,10],[2,5],[1,10]],[[1,10],[2,5],[1,10],[2,5]]],"statistic":[0,1,2,3],"domain":"Exact_finite_sufficient_statistic","operation":"suff-nonsufficient-zero-boundary","semantic_template":"qf-mod47-suff-nonsufficient-zero-boundary/{\"mode\":\"identity\",\"probability_rows\":[[[2,5],[1,10],[2,5],[1,10]],[[1,10],[2,5],[1,10],[2,5]]],\"samples\":[100,101,102,103],\"statistic\":[0,1,2,3],\"theta_values\":[\"a10\",\"b10\"]}"}},"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、一般Banach／IVT／Taylor證明、MLE漸近性、factorization theorem、一般DAG iff或primitive-root主張、Lean或Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-15","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261015-advance-20261116-r05-finite-sufficient-statistic-0087","batch_id":"batch-20261015-advance-20261116-r05-finite-sufficient-statistic-foundations","language":"zh-Hant","source_mko_ids":["mko-finite-sufficient-statistic"],"title_zh":"有限模型充分統計量","stem_zh":"total statistic fibers與正質量conditional laws的完整theta-invariance責任。操作=suff-nonsufficient-zero-boundary；資料={\"mode\":\"constant\",\"theta_values\":[\"a11\",\"b11\"],\"samples\":[110,111,112,113],\"probability_rows\":[[[2,5],[1,10],[2,5],[1,10]],[[1,10],[2,5],[1,10],[2,5]]],\"statistic\":[0,0,0,0]}。請依 exact_ordered_tuple_declared_by_interface 欄序回答。","answer":{"kind":"expression","value":"(constant, [[0, [[a11, [[110, 2/5], [111, 1/10], [112, 2/5], [113, 1/10]]], [b11, [[110, 1/10], [111, 2/5], [112, 1/10], [113, 2/5]]]], 否]], 否, [], null, 否, 是, 否, 是, 否, identity_is_sufficient_constant_is_sufficient_exactly_when_theta_laws_match_no_factorization_or_estimator_quality_claim)","explanation_zh":"Wave6第十層核對=(constant, [[0, [[a11, [[110, 2/5], [111, 1/10], [112, 2/5], [113, 1/10]]], [b11, [[110, 1/10], [111, 2/5], [112, 1/10], [113, 2/5]]]], 否]], 否, [], null, 否, 是, 否, 是, 否, identity_is_sufficient_constant_is_sufficient_exactly_when_theta_laws_match_no_factorization_or_estimator_quality_claim)；依完整明示資料獨立重算；zero-mass conditional保持undefined，nonsufficient需明示witness；identity/constant boundaries分開且不使用factorization theorem或宣稱估計品質。"},"difficulty":{"band":"undergraduate_core","level":2,"skills":["有限模型充分統計量"]},"variant":{"family_id":"qf-mod47-suff-nonsufficient-zero-boundary","seed":202611165087,"parameters":{"mode":"constant","theta_values":["a11","b11"],"samples":[110,111,112,113],"probability_rows":[[[2,5],[1,10],[2,5],[1,10]],[[1,10],[2,5],[1,10],[2,5]]],"statistic":[0,0,0,0],"domain":"Exact_finite_sufficient_statistic","operation":"suff-nonsufficient-zero-boundary","semantic_template":"qf-mod47-suff-nonsufficient-zero-boundary/{\"mode\":\"constant\",\"probability_rows\":[[[2,5],[1,10],[2,5],[1,10]],[[1,10],[2,5],[1,10],[2,5]]],\"samples\":[110,111,112,113],\"statistic\":[0,0,0,0],\"theta_values\":[\"a11\",\"b11\"]}"}},"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、一般Banach／IVT／Taylor證明、MLE漸近性、factorization theorem、一般DAG iff或primitive-root主張、Lean或Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-15","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261015-advance-20261116-r05-finite-sufficient-statistic-0088","batch_id":"batch-20261015-advance-20261116-r05-finite-sufficient-statistic-foundations","language":"zh-Hant","source_mko_ids":["mko-finite-sufficient-statistic"],"title_zh":"有限模型充分統計量","stem_zh":"total statistic fibers與正質量conditional laws的完整theta-invariance責任。操作=suff-nonsufficient-zero-boundary；資料={\"mode\":\"nonsufficient\",\"theta_values\":[\"a12\",\"b12\"],\"samples\":[120,121,122,123],\"probability_rows\":[[[3,5],[1,10],[1,5],[1,10]],[[1,10],[2,5],[1,10],[2,5]]],\"statistic\":[0,1,0,1]}。請依 exact_ordered_tuple_declared_by_interface 欄序回答。","answer":{"kind":"expression","value":"(nonsufficient, [[0, [[a12, [[120, 3/4], [122, 1/4]]], [b12, [[120, 1/2], [122, 1/2]]]], 否], [1, [[a12, [[121, 1/2], [123, 1/2]]], [b12, [[121, 1/2], [123, 1/2]]]], 是]], 否, [], [0, [[a12, [[120, 3/4], [122, 1/4]]], [b12, [[120, 1/2], [122, 1/2]]]], 否], 否, 否, 否, 是, 否, identity_is_sufficient_constant_is_sufficient_exactly_when_theta_laws_match_no_factorization_or_estimator_quality_claim)","explanation_zh":"Wave6第十層核對=(nonsufficient, [[0, [[a12, [[120, 3/4], [122, 1/4]]], [b12, [[120, 1/2], [122, 1/2]]]], 否], [1, [[a12, [[121, 1/2], [123, 1/2]]], [b12, [[121, 1/2], [123, 1/2]]]], 是]], 否, [], [0, [[a12, [[120, 3/4], [122, 1/4]]], [b12, [[120, 1/2], [122, 1/2]]]], 否], 否, 否, 否, 是, 否, identity_is_sufficient_constant_is_sufficient_exactly_when_theta_laws_match_no_factorization_or_estimator_quality_claim)；依完整明示資料獨立重算；zero-mass conditional保持undefined，nonsufficient需明示witness；identity/constant boundaries分開且不使用factorization theorem或宣稱估計品質。"},"difficulty":{"band":"undergraduate_core","level":2,"skills":["有限模型充分統計量"]},"variant":{"family_id":"qf-mod47-suff-nonsufficient-zero-boundary","seed":202611165088,"parameters":{"mode":"nonsufficient","theta_values":["a12","b12"],"samples":[120,121,122,123],"probability_rows":[[[3,5],[1,10],[1,5],[1,10]],[[1,10],[2,5],[1,10],[2,5]]],"statistic":[0,1,0,1],"domain":"Exact_finite_sufficient_statistic","operation":"suff-nonsufficient-zero-boundary","semantic_template":"qf-mod47-suff-nonsufficient-zero-boundary/{\"mode\":\"nonsufficient\",\"probability_rows\":[[[3,5],[1,10],[1,5],[1,10]],[[1,10],[2,5],[1,10],[2,5]]],\"samples\":[120,121,122,123],\"statistic\":[0,1,0,1],\"theta_values\":[\"a12\",\"b12\"]}"}},"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、一般Banach／IVT／Taylor證明、MLE漸近性、factorization theorem、一般DAG iff或primitive-root主張、Lean或Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-15","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261015-advance-20261116-r05-finite-sufficient-statistic-0089","batch_id":"batch-20261015-advance-20261116-r05-finite-sufficient-statistic-foundations","language":"zh-Hant","source_mko_ids":["mko-finite-sufficient-statistic"],"title_zh":"有限模型充分統計量","stem_zh":"total statistic fibers與正質量conditional laws的完整theta-invariance責任。操作=suff-nonsufficient-zero-boundary；資料={\"mode\":\"zero_mass\",\"theta_values\":[\"a13\",\"b13\"],\"samples\":[130,131,132,133],\"probability_rows\":[[[1,2],0,[1,2],0],[0,[1,2],0,[1,2]]],\"statistic\":[0,1,0,1]}。請依 exact_ordered_tuple_declared_by_interface 欄序回答。","answer":{"kind":"expression","value":"(zero_mass, [[0, [[a13, [[130, 1/2], [132, 1/2]]]], 是], [1, [[b13, [[131, 1/2], [133, 1/2]]]], 是]], 是, [[a13, 1, 0, null], [b13, 0, 0, null]], null, 否, 否, 否, 是, 否, identity_is_sufficient_constant_is_sufficient_exactly_when_theta_laws_match_no_factorization_or_estimator_quality_claim)","explanation_zh":"Wave6第十層核對=(zero_mass, [[0, [[a13, [[130, 1/2], [132, 1/2]]]], 是], [1, [[b13, [[131, 1/2], [133, 1/2]]]], 是]], 是, [[a13, 1, 0, null], [b13, 0, 0, null]], null, 否, 否, 否, 是, 否, identity_is_sufficient_constant_is_sufficient_exactly_when_theta_laws_match_no_factorization_or_estimator_quality_claim)；依完整明示資料獨立重算；zero-mass conditional保持undefined，nonsufficient需明示witness；identity/constant boundaries分開且不使用factorization theorem或宣稱估計品質。"},"difficulty":{"band":"undergraduate_core","level":2,"skills":["有限模型充分統計量"]},"variant":{"family_id":"qf-mod47-suff-nonsufficient-zero-boundary","seed":202611165089,"parameters":{"mode":"zero_mass","theta_values":["a13","b13"],"samples":[130,131,132,133],"probability_rows":[[[1,2],0,[1,2],0],[0,[1,2],0,[1,2]]],"statistic":[0,1,0,1],"domain":"Exact_finite_sufficient_statistic","operation":"suff-nonsufficient-zero-boundary","semantic_template":"qf-mod47-suff-nonsufficient-zero-boundary/{\"mode\":\"zero_mass\",\"probability_rows\":[[[1,2],[0,1],[1,2],[0,1]],[[0,1],[1,2],[0,1],[1,2]]],\"samples\":[130,131,132,133],\"statistic\":[0,1,0,1],\"theta_values\":[\"a13\",\"b13\"]}"}},"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、一般Banach／IVT／Taylor證明、MLE漸近性、factorization theorem、一般DAG iff或primitive-root主張、Lean或Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-15","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261015-advance-20261116-r05-finite-sufficient-statistic-0090","batch_id":"batch-20261015-advance-20261116-r05-finite-sufficient-statistic-foundations","language":"zh-Hant","source_mko_ids":["mko-finite-sufficient-statistic"],"title_zh":"有限模型充分統計量","stem_zh":"total statistic fibers與正質量conditional laws的完整theta-invariance責任。操作=suff-nonsufficient-zero-boundary；資料={\"mode\":\"identity\",\"theta_values\":[\"a14\",\"b14\"],\"samples\":[140,141,142,143],\"probability_rows\":[[[2,5],[1,10],[2,5],[1,10]],[[1,10],[2,5],[1,10],[2,5]]],\"statistic\":[0,1,2,3]}。請依 exact_ordered_tuple_declared_by_interface 欄序回答。","answer":{"kind":"expression","value":"(identity, [[0, [[a14, [[140, 1]]], [b14, [[140, 1]]]], 是], [1, [[a14, [[141, 1]]], [b14, [[141, 1]]]], 是], [2, [[a14, [[142, 1]]], [b14, [[142, 1]]]], 是], [3, [[a14, [[143, 1]]], [b14, [[143, 1]]]], 是]], 是, [], null, 是, 否, 否, 是, 否, identity_is_sufficient_constant_is_sufficient_exactly_when_theta_laws_match_no_factorization_or_estimator_quality_claim)","explanation_zh":"Wave6第十層核對=(identity, [[0, [[a14, [[140, 1]]], [b14, [[140, 1]]]], 是], [1, [[a14, [[141, 1]]], [b14, [[141, 1]]]], 是], [2, [[a14, [[142, 1]]], [b14, [[142, 1]]]], 是], [3, [[a14, [[143, 1]]], [b14, [[143, 1]]]], 是]], 是, [], null, 是, 否, 否, 是, 否, identity_is_sufficient_constant_is_sufficient_exactly_when_theta_laws_match_no_factorization_or_estimator_quality_claim)；依完整明示資料獨立重算；zero-mass conditional保持undefined，nonsufficient需明示witness；identity/constant boundaries分開且不使用factorization theorem或宣稱估計品質。"},"difficulty":{"band":"undergraduate_core","level":2,"skills":["有限模型充分統計量"]},"variant":{"family_id":"qf-mod47-suff-nonsufficient-zero-boundary","seed":202611165090,"parameters":{"mode":"identity","theta_values":["a14","b14"],"samples":[140,141,142,143],"probability_rows":[[[2,5],[1,10],[2,5],[1,10]],[[1,10],[2,5],[1,10],[2,5]]],"statistic":[0,1,2,3],"domain":"Exact_finite_sufficient_statistic","operation":"suff-nonsufficient-zero-boundary","semantic_template":"qf-mod47-suff-nonsufficient-zero-boundary/{\"mode\":\"identity\",\"probability_rows\":[[[2,5],[1,10],[2,5],[1,10]],[[1,10],[2,5],[1,10],[2,5]]],\"samples\":[140,141,142,143],\"statistic\":[0,1,2,3],\"theta_values\":[\"a14\",\"b14\"]}"}},"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、一般Banach／IVT／Taylor證明、MLE漸近性、factorization theorem、一般DAG iff或primitive-root主張、Lean或Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-15","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261015-advance-20261116-r05-finite-sufficient-statistic-0091","batch_id":"batch-20261015-advance-20261116-r05-finite-sufficient-statistic-foundations","language":"zh-Hant","source_mko_ids":["mko-finite-sufficient-statistic"],"title_zh":"有限模型充分統計量","stem_zh":"total statistic fibers與正質量conditional laws的完整theta-invariance責任。操作=suff-nonsufficient-zero-boundary；資料={\"mode\":\"constant\",\"theta_values\":[\"a15\",\"b15\"],\"samples\":[150,151,152,153],\"probability_rows\":[[[2,5],[1,10],[2,5],[1,10]],[[1,10],[2,5],[1,10],[2,5]]],\"statistic\":[0,0,0,0]}。請依 exact_ordered_tuple_declared_by_interface 欄序回答。","answer":{"kind":"expression","value":"(constant, [[0, [[a15, [[150, 2/5], [151, 1/10], [152, 2/5], [153, 1/10]]], [b15, [[150, 1/10], [151, 2/5], [152, 1/10], [153, 2/5]]]], 否]], 否, [], null, 否, 是, 否, 是, 否, identity_is_sufficient_constant_is_sufficient_exactly_when_theta_laws_match_no_factorization_or_estimator_quality_claim)","explanation_zh":"Wave6第十層核對=(constant, [[0, [[a15, [[150, 2/5], [151, 1/10], [152, 2/5], [153, 1/10]]], [b15, [[150, 1/10], [151, 2/5], [152, 1/10], [153, 2/5]]]], 否]], 否, [], null, 否, 是, 否, 是, 否, identity_is_sufficient_constant_is_sufficient_exactly_when_theta_laws_match_no_factorization_or_estimator_quality_claim)；依完整明示資料獨立重算；zero-mass conditional保持undefined，nonsufficient需明示witness；identity/constant boundaries分開且不使用factorization theorem或宣稱估計品質。"},"difficulty":{"band":"undergraduate_core","level":2,"skills":["有限模型充分統計量"]},"variant":{"family_id":"qf-mod47-suff-nonsufficient-zero-boundary","seed":202611165091,"parameters":{"mode":"constant","theta_values":["a15","b15"],"samples":[150,151,152,153],"probability_rows":[[[2,5],[1,10],[2,5],[1,10]],[[1,10],[2,5],[1,10],[2,5]]],"statistic":[0,0,0,0],"domain":"Exact_finite_sufficient_statistic","operation":"suff-nonsufficient-zero-boundary","semantic_template":"qf-mod47-suff-nonsufficient-zero-boundary/{\"mode\":\"constant\",\"probability_rows\":[[[2,5],[1,10],[2,5],[1,10]],[[1,10],[2,5],[1,10],[2,5]]],\"samples\":[150,151,152,153],\"statistic\":[0,0,0,0],\"theta_values\":[\"a15\",\"b15\"]}"}},"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、一般Banach／IVT／Taylor證明、MLE漸近性、factorization theorem、一般DAG iff或primitive-root主張、Lean或Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-15","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261015-advance-20261116-r05-finite-sufficient-statistic-0092","batch_id":"batch-20261015-advance-20261116-r05-finite-sufficient-statistic-foundations","language":"zh-Hant","source_mko_ids":["mko-finite-sufficient-statistic"],"title_zh":"有限模型充分統計量","stem_zh":"total statistic fibers與正質量conditional laws的完整theta-invariance責任。操作=suff-nonsufficient-zero-boundary；資料={\"mode\":\"nonsufficient\",\"theta_values\":[\"a16\",\"b16\"],\"samples\":[160,161,162,163],\"probability_rows\":[[[3,5],[1,10],[1,5],[1,10]],[[1,10],[2,5],[1,10],[2,5]]],\"statistic\":[0,1,0,1]}。請依 exact_ordered_tuple_declared_by_interface 欄序回答。","answer":{"kind":"expression","value":"(nonsufficient, [[0, [[a16, [[160, 3/4], [162, 1/4]]], [b16, [[160, 1/2], [162, 1/2]]]], 否], [1, [[a16, [[161, 1/2], [163, 1/2]]], [b16, [[161, 1/2], [163, 1/2]]]], 是]], 否, [], [0, [[a16, [[160, 3/4], [162, 1/4]]], [b16, [[160, 1/2], [162, 1/2]]]], 否], 否, 否, 否, 是, 否, identity_is_sufficient_constant_is_sufficient_exactly_when_theta_laws_match_no_factorization_or_estimator_quality_claim)","explanation_zh":"Wave6第十層核對=(nonsufficient, [[0, [[a16, [[160, 3/4], [162, 1/4]]], [b16, [[160, 1/2], [162, 1/2]]]], 否], [1, [[a16, [[161, 1/2], [163, 1/2]]], [b16, [[161, 1/2], [163, 1/2]]]], 是]], 否, [], [0, [[a16, [[160, 3/4], [162, 1/4]]], [b16, [[160, 1/2], [162, 1/2]]]], 否], 否, 否, 否, 是, 否, identity_is_sufficient_constant_is_sufficient_exactly_when_theta_laws_match_no_factorization_or_estimator_quality_claim)；依完整明示資料獨立重算；zero-mass conditional保持undefined，nonsufficient需明示witness；identity/constant boundaries分開且不使用factorization theorem或宣稱估計品質。"},"difficulty":{"band":"undergraduate_core","level":2,"skills":["有限模型充分統計量"]},"variant":{"family_id":"qf-mod47-suff-nonsufficient-zero-boundary","seed":202611165092,"parameters":{"mode":"nonsufficient","theta_values":["a16","b16"],"samples":[160,161,162,163],"probability_rows":[[[3,5],[1,10],[1,5],[1,10]],[[1,10],[2,5],[1,10],[2,5]]],"statistic":[0,1,0,1],"domain":"Exact_finite_sufficient_statistic","operation":"suff-nonsufficient-zero-boundary","semantic_template":"qf-mod47-suff-nonsufficient-zero-boundary/{\"mode\":\"nonsufficient\",\"probability_rows\":[[[3,5],[1,10],[1,5],[1,10]],[[1,10],[2,5],[1,10],[2,5]]],\"samples\":[160,161,162,163],\"statistic\":[0,1,0,1],\"theta_values\":[\"a16\",\"b16\"]}"}},"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、一般Banach／IVT／Taylor證明、MLE漸近性、factorization theorem、一般DAG iff或primitive-root主張、Lean或Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-15","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261015-advance-20261116-r05-finite-sufficient-statistic-0093","batch_id":"batch-20261015-advance-20261116-r05-finite-sufficient-statistic-foundations","language":"zh-Hant","source_mko_ids":["mko-finite-sufficient-statistic"],"title_zh":"有限模型充分統計量","stem_zh":"total statistic fibers與正質量conditional laws的完整theta-invariance責任。操作=suff-nonsufficient-zero-boundary；資料={\"mode\":\"zero_mass\",\"theta_values\":[\"a17\",\"b17\"],\"samples\":[170,171,172,173],\"probability_rows\":[[[1,2],0,[1,2],0],[0,[1,2],0,[1,2]]],\"statistic\":[0,1,0,1]}。請依 exact_ordered_tuple_declared_by_interface 欄序回答。","answer":{"kind":"expression","value":"(zero_mass, [[0, [[a17, [[170, 1/2], [172, 1/2]]]], 是], [1, [[b17, [[171, 1/2], [173, 1/2]]]], 是]], 是, [[a17, 1, 0, null], [b17, 0, 0, null]], null, 否, 否, 否, 是, 否, identity_is_sufficient_constant_is_sufficient_exactly_when_theta_laws_match_no_factorization_or_estimator_quality_claim)","explanation_zh":"Wave6第十層核對=(zero_mass, [[0, [[a17, [[170, 1/2], [172, 1/2]]]], 是], [1, [[b17, [[171, 1/2], [173, 1/2]]]], 是]], 是, [[a17, 1, 0, null], [b17, 0, 0, null]], null, 否, 否, 否, 是, 否, identity_is_sufficient_constant_is_sufficient_exactly_when_theta_laws_match_no_factorization_or_estimator_quality_claim)；依完整明示資料獨立重算；zero-mass conditional保持undefined，nonsufficient需明示witness；identity/constant boundaries分開且不使用factorization theorem或宣稱估計品質。"},"difficulty":{"band":"undergraduate_core","level":3,"skills":["有限模型充分統計量"]},"variant":{"family_id":"qf-mod47-suff-nonsufficient-zero-boundary","seed":202611165093,"parameters":{"mode":"zero_mass","theta_values":["a17","b17"],"samples":[170,171,172,173],"probability_rows":[[[1,2],0,[1,2],0],[0,[1,2],0,[1,2]]],"statistic":[0,1,0,1],"domain":"Exact_finite_sufficient_statistic","operation":"suff-nonsufficient-zero-boundary","semantic_template":"qf-mod47-suff-nonsufficient-zero-boundary/{\"mode\":\"zero_mass\",\"probability_rows\":[[[1,2],[0,1],[1,2],[0,1]],[[0,1],[1,2],[0,1],[1,2]]],\"samples\":[170,171,172,173],\"statistic\":[0,1,0,1],\"theta_values\":[\"a17\",\"b17\"]}"}},"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、一般Banach／IVT／Taylor證明、MLE漸近性、factorization theorem、一般DAG iff或primitive-root主張、Lean或Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-15","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261015-advance-20261116-r05-finite-sufficient-statistic-0094","batch_id":"batch-20261015-advance-20261116-r05-finite-sufficient-statistic-foundations","language":"zh-Hant","source_mko_ids":["mko-finite-sufficient-statistic"],"title_zh":"有限模型充分統計量","stem_zh":"total statistic fibers與正質量conditional laws的完整theta-invariance責任。操作=suff-nonsufficient-zero-boundary；資料={\"mode\":\"identity\",\"theta_values\":[\"a18\",\"b18\"],\"samples\":[180,181,182,183],\"probability_rows\":[[[2,5],[1,10],[2,5],[1,10]],[[1,10],[2,5],[1,10],[2,5]]],\"statistic\":[0,1,2,3]}。請依 exact_ordered_tuple_declared_by_interface 欄序回答。","answer":{"kind":"expression","value":"(identity, [[0, [[a18, [[180, 1]]], [b18, [[180, 1]]]], 是], [1, [[a18, [[181, 1]]], [b18, [[181, 1]]]], 是], [2, [[a18, [[182, 1]]], [b18, [[182, 1]]]], 是], [3, [[a18, [[183, 1]]], [b18, [[183, 1]]]], 是]], 是, [], null, 是, 否, 否, 是, 否, identity_is_sufficient_constant_is_sufficient_exactly_when_theta_laws_match_no_factorization_or_estimator_quality_claim)","explanation_zh":"Wave6第十層核對=(identity, [[0, [[a18, [[180, 1]]], [b18, [[180, 1]]]], 是], [1, [[a18, [[181, 1]]], [b18, [[181, 1]]]], 是], [2, [[a18, [[182, 1]]], [b18, [[182, 1]]]], 是], [3, [[a18, [[183, 1]]], [b18, [[183, 1]]]], 是]], 是, [], null, 是, 否, 否, 是, 否, identity_is_sufficient_constant_is_sufficient_exactly_when_theta_laws_match_no_factorization_or_estimator_quality_claim)；依完整明示資料獨立重算；zero-mass conditional保持undefined，nonsufficient需明示witness；identity/constant boundaries分開且不使用factorization theorem或宣稱估計品質。"},"difficulty":{"band":"undergraduate_core","level":3,"skills":["有限模型充分統計量"]},"variant":{"family_id":"qf-mod47-suff-nonsufficient-zero-boundary","seed":202611165094,"parameters":{"mode":"identity","theta_values":["a18","b18"],"samples":[180,181,182,183],"probability_rows":[[[2,5],[1,10],[2,5],[1,10]],[[1,10],[2,5],[1,10],[2,5]]],"statistic":[0,1,2,3],"domain":"Exact_finite_sufficient_statistic","operation":"suff-nonsufficient-zero-boundary","semantic_template":"qf-mod47-suff-nonsufficient-zero-boundary/{\"mode\":\"identity\",\"probability_rows\":[[[2,5],[1,10],[2,5],[1,10]],[[1,10],[2,5],[1,10],[2,5]]],\"samples\":[180,181,182,183],\"statistic\":[0,1,2,3],\"theta_values\":[\"a18\",\"b18\"]}"}},"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、一般Banach／IVT／Taylor證明、MLE漸近性、factorization theorem、一般DAG iff或primitive-root主張、Lean或Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-15","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261015-advance-20261116-r05-finite-sufficient-statistic-0095","batch_id":"batch-20261015-advance-20261116-r05-finite-sufficient-statistic-foundations","language":"zh-Hant","source_mko_ids":["mko-finite-sufficient-statistic"],"title_zh":"有限模型充分統計量","stem_zh":"total statistic fibers與正質量conditional laws的完整theta-invariance責任。操作=suff-nonsufficient-zero-boundary；資料={\"mode\":\"constant\",\"theta_values\":[\"a19\",\"b19\"],\"samples\":[190,191,192,193],\"probability_rows\":[[[2,5],[1,10],[2,5],[1,10]],[[1,10],[2,5],[1,10],[2,5]]],\"statistic\":[0,0,0,0]}。請依 exact_ordered_tuple_declared_by_interface 欄序回答。","answer":{"kind":"expression","value":"(constant, [[0, [[a19, [[190, 2/5], [191, 1/10], [192, 2/5], [193, 1/10]]], [b19, [[190, 1/10], [191, 2/5], [192, 1/10], [193, 2/5]]]], 否]], 否, [], null, 否, 是, 否, 是, 否, identity_is_sufficient_constant_is_sufficient_exactly_when_theta_laws_match_no_factorization_or_estimator_quality_claim)","explanation_zh":"Wave6第十層核對=(constant, [[0, [[a19, [[190, 2/5], [191, 1/10], [192, 2/5], [193, 1/10]]], [b19, [[190, 1/10], [191, 2/5], [192, 1/10], [193, 2/5]]]], 否]], 否, [], null, 否, 是, 否, 是, 否, identity_is_sufficient_constant_is_sufficient_exactly_when_theta_laws_match_no_factorization_or_estimator_quality_claim)；依完整明示資料獨立重算；zero-mass conditional保持undefined，nonsufficient需明示witness；identity/constant boundaries分開且不使用factorization theorem或宣稱估計品質。"},"difficulty":{"band":"undergraduate_core","level":3,"skills":["有限模型充分統計量"]},"variant":{"family_id":"qf-mod47-suff-nonsufficient-zero-boundary","seed":202611165095,"parameters":{"mode":"constant","theta_values":["a19","b19"],"samples":[190,191,192,193],"probability_rows":[[[2,5],[1,10],[2,5],[1,10]],[[1,10],[2,5],[1,10],[2,5]]],"statistic":[0,0,0,0],"domain":"Exact_finite_sufficient_statistic","operation":"suff-nonsufficient-zero-boundary","semantic_template":"qf-mod47-suff-nonsufficient-zero-boundary/{\"mode\":\"constant\",\"probability_rows\":[[[2,5],[1,10],[2,5],[1,10]],[[1,10],[2,5],[1,10],[2,5]]],\"samples\":[190,191,192,193],\"statistic\":[0,0,0,0],\"theta_values\":[\"a19\",\"b19\"]}"}},"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、一般Banach／IVT／Taylor證明、MLE漸近性、factorization theorem、一般DAG iff或primitive-root主張、Lean或Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-15","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261015-advance-20261116-r05-finite-sufficient-statistic-0096","batch_id":"batch-20261015-advance-20261116-r05-finite-sufficient-statistic-foundations","language":"zh-Hant","source_mko_ids":["mko-finite-sufficient-statistic"],"title_zh":"有限模型充分統計量","stem_zh":"total statistic fibers與正質量conditional laws的完整theta-invariance責任。操作=suff-nonsufficient-zero-boundary；資料={\"mode\":\"nonsufficient\",\"theta_values\":[\"a20\",\"b20\"],\"samples\":[200,201,202,203],\"probability_rows\":[[[3,5],[1,10],[1,5],[1,10]],[[1,10],[2,5],[1,10],[2,5]]],\"statistic\":[0,1,0,1]}。請依 exact_ordered_tuple_declared_by_interface 欄序回答。","answer":{"kind":"expression","value":"(nonsufficient, [[0, [[a20, [[200, 3/4], [202, 1/4]]], [b20, [[200, 1/2], [202, 1/2]]]], 否], [1, [[a20, [[201, 1/2], [203, 1/2]]], [b20, [[201, 1/2], [203, 1/2]]]], 是]], 否, [], [0, [[a20, [[200, 3/4], [202, 1/4]]], [b20, [[200, 1/2], [202, 1/2]]]], 否], 否, 否, 否, 是, 否, identity_is_sufficient_constant_is_sufficient_exactly_when_theta_laws_match_no_factorization_or_estimator_quality_claim)","explanation_zh":"Wave6第十層核對=(nonsufficient, [[0, [[a20, [[200, 3/4], [202, 1/4]]], [b20, [[200, 1/2], [202, 1/2]]]], 否], [1, [[a20, [[201, 1/2], [203, 1/2]]], [b20, [[201, 1/2], [203, 1/2]]]], 是]], 否, [], [0, [[a20, [[200, 3/4], [202, 1/4]]], [b20, [[200, 1/2], [202, 1/2]]]], 否], 否, 否, 否, 是, 否, identity_is_sufficient_constant_is_sufficient_exactly_when_theta_laws_match_no_factorization_or_estimator_quality_claim)；依完整明示資料獨立重算；zero-mass conditional保持undefined，nonsufficient需明示witness；identity/constant boundaries分開且不使用factorization theorem或宣稱估計品質。"},"difficulty":{"band":"undergraduate_core","level":3,"skills":["有限模型充分統計量"]},"variant":{"family_id":"qf-mod47-suff-nonsufficient-zero-boundary","seed":202611165096,"parameters":{"mode":"nonsufficient","theta_values":["a20","b20"],"samples":[200,201,202,203],"probability_rows":[[[3,5],[1,10],[1,5],[1,10]],[[1,10],[2,5],[1,10],[2,5]]],"statistic":[0,1,0,1],"domain":"Exact_finite_sufficient_statistic","operation":"suff-nonsufficient-zero-boundary","semantic_template":"qf-mod47-suff-nonsufficient-zero-boundary/{\"mode\":\"nonsufficient\",\"probability_rows\":[[[3,5],[1,10],[1,5],[1,10]],[[1,10],[2,5],[1,10],[2,5]]],\"samples\":[200,201,202,203],\"statistic\":[0,1,0,1],\"theta_values\":[\"a20\",\"b20\"]}"}},"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、一般Banach／IVT／Taylor證明、MLE漸近性、factorization theorem、一般DAG iff或primitive-root主張、Lean或Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-15","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261015-advance-20261116-r05-finite-sufficient-statistic-0097","batch_id":"batch-20261015-advance-20261116-r05-finite-sufficient-statistic-foundations","language":"zh-Hant","source_mko_ids":["mko-finite-sufficient-statistic"],"title_zh":"有限模型充分統計量","stem_zh":"total statistic fibers與正質量conditional laws的完整theta-invariance責任。操作=suff-nonsufficient-zero-boundary；資料={\"mode\":\"zero_mass\",\"theta_values\":[\"a21\",\"b21\"],\"samples\":[210,211,212,213],\"probability_rows\":[[[1,2],0,[1,2],0],[0,[1,2],0,[1,2]]],\"statistic\":[0,1,0,1]}。請依 exact_ordered_tuple_declared_by_interface 欄序回答。","answer":{"kind":"expression","value":"(zero_mass, [[0, [[a21, [[210, 1/2], [212, 1/2]]]], 是], [1, [[b21, [[211, 1/2], [213, 1/2]]]], 是]], 是, [[a21, 1, 0, null], [b21, 0, 0, null]], null, 否, 否, 否, 是, 否, identity_is_sufficient_constant_is_sufficient_exactly_when_theta_laws_match_no_factorization_or_estimator_quality_claim)","explanation_zh":"Wave6第十層核對=(zero_mass, [[0, [[a21, [[210, 1/2], [212, 1/2]]]], 是], [1, [[b21, [[211, 1/2], [213, 1/2]]]], 是]], 是, [[a21, 1, 0, null], [b21, 0, 0, null]], null, 否, 否, 否, 是, 否, identity_is_sufficient_constant_is_sufficient_exactly_when_theta_laws_match_no_factorization_or_estimator_quality_claim)；依完整明示資料獨立重算；zero-mass conditional保持undefined，nonsufficient需明示witness；identity/constant boundaries分開且不使用factorization theorem或宣稱估計品質。"},"difficulty":{"band":"undergraduate_core","level":3,"skills":["有限模型充分統計量"]},"variant":{"family_id":"qf-mod47-suff-nonsufficient-zero-boundary","seed":202611165097,"parameters":{"mode":"zero_mass","theta_values":["a21","b21"],"samples":[210,211,212,213],"probability_rows":[[[1,2],0,[1,2],0],[0,[1,2],0,[1,2]]],"statistic":[0,1,0,1],"domain":"Exact_finite_sufficient_statistic","operation":"suff-nonsufficient-zero-boundary","semantic_template":"qf-mod47-suff-nonsufficient-zero-boundary/{\"mode\":\"zero_mass\",\"probability_rows\":[[[1,2],[0,1],[1,2],[0,1]],[[0,1],[1,2],[0,1],[1,2]]],\"samples\":[210,211,212,213],\"statistic\":[0,1,0,1],\"theta_values\":[\"a21\",\"b21\"]}"}},"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、一般Banach／IVT／Taylor證明、MLE漸近性、factorization theorem、一般DAG iff或primitive-root主張、Lean或Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-15","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261015-advance-20261116-r05-finite-sufficient-statistic-0098","batch_id":"batch-20261015-advance-20261116-r05-finite-sufficient-statistic-foundations","language":"zh-Hant","source_mko_ids":["mko-finite-sufficient-statistic"],"title_zh":"有限模型充分統計量","stem_zh":"total statistic fibers與正質量conditional laws的完整theta-invariance責任。操作=suff-nonsufficient-zero-boundary；資料={\"mode\":\"identity\",\"theta_values\":[\"a22\",\"b22\"],\"samples\":[220,221,222,223],\"probability_rows\":[[[2,5],[1,10],[2,5],[1,10]],[[1,10],[2,5],[1,10],[2,5]]],\"statistic\":[0,1,2,3]}。請依 exact_ordered_tuple_declared_by_interface 欄序回答。","answer":{"kind":"expression","value":"(identity, [[0, [[a22, [[220, 1]]], [b22, [[220, 1]]]], 是], [1, [[a22, [[221, 1]]], [b22, [[221, 1]]]], 是], [2, [[a22, [[222, 1]]], [b22, [[222, 1]]]], 是], [3, [[a22, [[223, 1]]], [b22, [[223, 1]]]], 是]], 是, [], null, 是, 否, 否, 是, 否, identity_is_sufficient_constant_is_sufficient_exactly_when_theta_laws_match_no_factorization_or_estimator_quality_claim)","explanation_zh":"Wave6第十層核對=(identity, [[0, [[a22, [[220, 1]]], [b22, [[220, 1]]]], 是], [1, [[a22, [[221, 1]]], [b22, [[221, 1]]]], 是], [2, [[a22, [[222, 1]]], [b22, [[222, 1]]]], 是], [3, [[a22, [[223, 1]]], [b22, [[223, 1]]]], 是]], 是, [], null, 是, 否, 否, 是, 否, identity_is_sufficient_constant_is_sufficient_exactly_when_theta_laws_match_no_factorization_or_estimator_quality_claim)；依完整明示資料獨立重算；zero-mass conditional保持undefined，nonsufficient需明示witness；identity/constant boundaries分開且不使用factorization theorem或宣稱估計品質。"},"difficulty":{"band":"undergraduate_core","level":3,"skills":["有限模型充分統計量"]},"variant":{"family_id":"qf-mod47-suff-nonsufficient-zero-boundary","seed":202611165098,"parameters":{"mode":"identity","theta_values":["a22","b22"],"samples":[220,221,222,223],"probability_rows":[[[2,5],[1,10],[2,5],[1,10]],[[1,10],[2,5],[1,10],[2,5]]],"statistic":[0,1,2,3],"domain":"Exact_finite_sufficient_statistic","operation":"suff-nonsufficient-zero-boundary","semantic_template":"qf-mod47-suff-nonsufficient-zero-boundary/{\"mode\":\"identity\",\"probability_rows\":[[[2,5],[1,10],[2,5],[1,10]],[[1,10],[2,5],[1,10],[2,5]]],\"samples\":[220,221,222,223],\"statistic\":[0,1,2,3],\"theta_values\":[\"a22\",\"b22\"]}"}},"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、一般Banach／IVT／Taylor證明、MLE漸近性、factorization theorem、一般DAG iff或primitive-root主張、Lean或Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-15","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261015-advance-20261116-r05-finite-sufficient-statistic-0099","batch_id":"batch-20261015-advance-20261116-r05-finite-sufficient-statistic-foundations","language":"zh-Hant","source_mko_ids":["mko-finite-sufficient-statistic"],"title_zh":"有限模型充分統計量","stem_zh":"total statistic fibers與正質量conditional laws的完整theta-invariance責任。操作=suff-nonsufficient-zero-boundary；資料={\"mode\":\"constant\",\"theta_values\":[\"a23\",\"b23\"],\"samples\":[230,231,232,233],\"probability_rows\":[[[2,5],[1,10],[2,5],[1,10]],[[1,10],[2,5],[1,10],[2,5]]],\"statistic\":[0,0,0,0]}。請依 exact_ordered_tuple_declared_by_interface 欄序回答。","answer":{"kind":"expression","value":"(constant, [[0, [[a23, [[230, 2/5], [231, 1/10], [232, 2/5], [233, 1/10]]], [b23, [[230, 1/10], [231, 2/5], [232, 1/10], [233, 2/5]]]], 否]], 否, [], null, 否, 是, 否, 是, 否, identity_is_sufficient_constant_is_sufficient_exactly_when_theta_laws_match_no_factorization_or_estimator_quality_claim)","explanation_zh":"Wave6第十層核對=(constant, [[0, [[a23, [[230, 2/5], [231, 1/10], [232, 2/5], [233, 1/10]]], [b23, [[230, 1/10], [231, 2/5], [232, 1/10], [233, 2/5]]]], 否]], 否, [], null, 否, 是, 否, 是, 否, identity_is_sufficient_constant_is_sufficient_exactly_when_theta_laws_match_no_factorization_or_estimator_quality_claim)；依完整明示資料獨立重算；zero-mass conditional保持undefined，nonsufficient需明示witness；identity/constant boundaries分開且不使用factorization theorem或宣稱估計品質。"},"difficulty":{"band":"undergraduate_core","level":3,"skills":["有限模型充分統計量"]},"variant":{"family_id":"qf-mod47-suff-nonsufficient-zero-boundary","seed":202611165099,"parameters":{"mode":"constant","theta_values":["a23","b23"],"samples":[230,231,232,233],"probability_rows":[[[2,5],[1,10],[2,5],[1,10]],[[1,10],[2,5],[1,10],[2,5]]],"statistic":[0,0,0,0],"domain":"Exact_finite_sufficient_statistic","operation":"suff-nonsufficient-zero-boundary","semantic_template":"qf-mod47-suff-nonsufficient-zero-boundary/{\"mode\":\"constant\",\"probability_rows\":[[[2,5],[1,10],[2,5],[1,10]],[[1,10],[2,5],[1,10],[2,5]]],\"samples\":[230,231,232,233],\"statistic\":[0,0,0,0],\"theta_values\":[\"a23\",\"b23\"]}"}},"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、一般Banach／IVT／Taylor證明、MLE漸近性、factorization theorem、一般DAG iff或primitive-root主張、Lean或Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-15","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261015-advance-20261116-r05-finite-sufficient-statistic-0100","batch_id":"batch-20261015-advance-20261116-r05-finite-sufficient-statistic-foundations","language":"zh-Hant","source_mko_ids":["mko-finite-sufficient-statistic"],"title_zh":"有限模型充分統計量","stem_zh":"total statistic fibers與正質量conditional laws的完整theta-invariance責任。操作=suff-nonsufficient-zero-boundary；資料={\"mode\":\"nonsufficient\",\"theta_values\":[\"a24\",\"b24\"],\"samples\":[240,241,242,243],\"probability_rows\":[[[3,5],[1,10],[1,5],[1,10]],[[1,10],[2,5],[1,10],[2,5]]],\"statistic\":[0,1,0,1]}。請依 exact_ordered_tuple_declared_by_interface 欄序回答。","answer":{"kind":"expression","value":"(nonsufficient, [[0, [[a24, [[240, 3/4], [242, 1/4]]], [b24, [[240, 1/2], [242, 1/2]]]], 否], [1, [[a24, [[241, 1/2], [243, 1/2]]], [b24, [[241, 1/2], [243, 1/2]]]], 是]], 否, [], [0, [[a24, [[240, 3/4], [242, 1/4]]], [b24, [[240, 1/2], [242, 1/2]]]], 否], 否, 否, 否, 是, 否, identity_is_sufficient_constant_is_sufficient_exactly_when_theta_laws_match_no_factorization_or_estimator_quality_claim)","explanation_zh":"Wave6第十層核對=(nonsufficient, [[0, [[a24, [[240, 3/4], [242, 1/4]]], [b24, [[240, 1/2], [242, 1/2]]]], 否], [1, [[a24, [[241, 1/2], [243, 1/2]]], [b24, [[241, 1/2], [243, 1/2]]]], 是]], 否, [], [0, [[a24, [[240, 3/4], [242, 1/4]]], [b24, [[240, 1/2], [242, 1/2]]]], 否], 否, 否, 否, 是, 否, identity_is_sufficient_constant_is_sufficient_exactly_when_theta_laws_match_no_factorization_or_estimator_quality_claim)；依完整明示資料獨立重算；zero-mass conditional保持undefined，nonsufficient需明示witness；identity/constant boundaries分開且不使用factorization theorem或宣稱估計品質。"},"difficulty":{"band":"undergraduate_core","level":3,"skills":["有限模型充分統計量"]},"variant":{"family_id":"qf-mod47-suff-nonsufficient-zero-boundary","seed":202611165100,"parameters":{"mode":"nonsufficient","theta_values":["a24","b24"],"samples":[240,241,242,243],"probability_rows":[[[3,5],[1,10],[1,5],[1,10]],[[1,10],[2,5],[1,10],[2,5]]],"statistic":[0,1,0,1],"domain":"Exact_finite_sufficient_statistic","operation":"suff-nonsufficient-zero-boundary","semantic_template":"qf-mod47-suff-nonsufficient-zero-boundary/{\"mode\":\"nonsufficient\",\"probability_rows\":[[[3,5],[1,10],[1,5],[1,10]],[[1,10],[2,5],[1,10],[2,5]]],\"samples\":[240,241,242,243],\"statistic\":[0,1,0,1],\"theta_values\":[\"a24\",\"b24\"]}"}},"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、一般Banach／IVT／Taylor證明、MLE漸近性、factorization theorem、一般DAG iff或primitive-root主張、Lean或Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-15","contract_version":"ocme-question-factory-v0.1"}}