{"schema_version":"ocme-question-v0.1","id":"q-20261014-advance-20261105-r07-weak-law-large-numbers-0001","batch_id":"batch-20261014-advance-20261105-r07-weak-law-large-numbers-foundations","language":"zh-Hant","source_mko_ids":["mko-weak-law-large-numbers"],"title_zh":"弱大數律","stem_zh":"IID通用證書、共同有限mean與variance及exact Chebyshev tail。操作=wlln-variance-average；資料={\"mean\":[0,1],\"variance\":[1,2],\"n\":5,\"iid_certificate\":\"symbolic_all_finite_subfamilies\"}。請依 exact_ordered_tuple_declared_by_interface 欄序回答。","answer":{"kind":"expression","value":"(0, 1/2, 5, 1/10, independence_gives_variance_sigma_squared_over_n)","explanation_zh":"Wave5第五層核對=(0, 1/2, 5, 1/10, independence_gives_variance_sigma_squared_over_n)；依完整明示資料獨立重算；independence給Var(sample mean)=sigma squared/n並以forall n大於等於N證依機率收斂；有限樣本或模擬不足，且不宣稱almost sure、CLT或有限n已等於極限。"},"difficulty":{"band":"undergraduate_core","level":1,"skills":["弱大數律"]},"variant":{"family_id":"qf-mod36-wlln-variance-average","seed":202611057001,"parameters":{"mean":[0,1],"variance":[1,2],"n":5,"iid_certificate":"symbolic_all_finite_subfamilies","domain":"Symbolic_iid_Chebyshev_WLLN","operation":"wlln-variance-average","semantic_template":"qf-mod36-wlln-variance-average/{\"iid_certificate\":\"symbolic_all_finite_subfamilies\",\"mean\":[0,1],\"n\":5,\"variance\":[1,2]}"}},"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、有限取樣全稱證明、V與dual典範識別、Hamilton結論、一般continuous-bijection捷徑、統計性質、strong law、CLT、Lean或Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-14","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261014-advance-20261105-r07-weak-law-large-numbers-0002","batch_id":"batch-20261014-advance-20261105-r07-weak-law-large-numbers-foundations","language":"zh-Hant","source_mko_ids":["mko-weak-law-large-numbers"],"title_zh":"弱大數律","stem_zh":"IID通用證書、共同有限mean與variance及exact Chebyshev tail。操作=wlln-variance-average；資料={\"mean\":[1,2],\"variance\":[2,3],\"n\":6,\"iid_certificate\":\"symbolic_all_finite_subfamilies\"}。請依 exact_ordered_tuple_declared_by_interface 欄序回答。","answer":{"kind":"expression","value":"(1/2, 2/3, 6, 1/9, independence_gives_variance_sigma_squared_over_n)","explanation_zh":"Wave5第五層核對=(1/2, 2/3, 6, 1/9, independence_gives_variance_sigma_squared_over_n)；依完整明示資料獨立重算；independence給Var(sample mean)=sigma squared/n並以forall n大於等於N證依機率收斂；有限樣本或模擬不足，且不宣稱almost sure、CLT或有限n已等於極限。"},"difficulty":{"band":"undergraduate_core","level":1,"skills":["弱大數律"]},"variant":{"family_id":"qf-mod36-wlln-variance-average","seed":202611057002,"parameters":{"mean":[1,2],"variance":[2,3],"n":6,"iid_certificate":"symbolic_all_finite_subfamilies","domain":"Symbolic_iid_Chebyshev_WLLN","operation":"wlln-variance-average","semantic_template":"qf-mod36-wlln-variance-average/{\"iid_certificate\":\"symbolic_all_finite_subfamilies\",\"mean\":[1,2],\"n\":6,\"variance\":[2,3]}"}},"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、有限取樣全稱證明、V與dual典範識別、Hamilton結論、一般continuous-bijection捷徑、統計性質、strong law、CLT、Lean或Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-14","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261014-advance-20261105-r07-weak-law-large-numbers-0003","batch_id":"batch-20261014-advance-20261105-r07-weak-law-large-numbers-foundations","language":"zh-Hant","source_mko_ids":["mko-weak-law-large-numbers"],"title_zh":"弱大數律","stem_zh":"IID通用證書、共同有限mean與variance及exact Chebyshev tail。操作=wlln-variance-average；資料={\"mean\":[2,3],\"variance\":[3,4],\"n\":7,\"iid_certificate\":\"symbolic_all_finite_subfamilies\"}。請依 exact_ordered_tuple_declared_by_interface 欄序回答。","answer":{"kind":"expression","value":"(2/3, 3/4, 7, 3/28, independence_gives_variance_sigma_squared_over_n)","explanation_zh":"Wave5第五層核對=(2/3, 3/4, 7, 3/28, independence_gives_variance_sigma_squared_over_n)；依完整明示資料獨立重算；independence給Var(sample mean)=sigma squared/n並以forall n大於等於N證依機率收斂；有限樣本或模擬不足，且不宣稱almost sure、CLT或有限n已等於極限。"},"difficulty":{"band":"undergraduate_core","level":1,"skills":["弱大數律"]},"variant":{"family_id":"qf-mod36-wlln-variance-average","seed":202611057003,"parameters":{"mean":[2,3],"variance":[3,4],"n":7,"iid_certificate":"symbolic_all_finite_subfamilies","domain":"Symbolic_iid_Chebyshev_WLLN","operation":"wlln-variance-average","semantic_template":"qf-mod36-wlln-variance-average/{\"iid_certificate\":\"symbolic_all_finite_subfamilies\",\"mean\":[2,3],\"n\":7,\"variance\":[3,4]}"}},"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、有限取樣全稱證明、V與dual典範識別、Hamilton結論、一般continuous-bijection捷徑、統計性質、strong law、CLT、Lean或Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-14","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261014-advance-20261105-r07-weak-law-large-numbers-0004","batch_id":"batch-20261014-advance-20261105-r07-weak-law-large-numbers-foundations","language":"zh-Hant","source_mko_ids":["mko-weak-law-large-numbers"],"title_zh":"弱大數律","stem_zh":"IID通用證書、共同有限mean與variance及exact Chebyshev tail。操作=wlln-variance-average；資料={\"mean\":[3,4],\"variance\":[4,5],\"n\":8,\"iid_certificate\":\"symbolic_all_finite_subfamilies\"}。請依 exact_ordered_tuple_declared_by_interface 欄序回答。","answer":{"kind":"expression","value":"(3/4, 4/5, 8, 1/10, independence_gives_variance_sigma_squared_over_n)","explanation_zh":"Wave5第五層核對=(3/4, 4/5, 8, 1/10, independence_gives_variance_sigma_squared_over_n)；依完整明示資料獨立重算；independence給Var(sample mean)=sigma squared/n並以forall n大於等於N證依機率收斂；有限樣本或模擬不足，且不宣稱almost sure、CLT或有限n已等於極限。"},"difficulty":{"band":"undergraduate_core","level":1,"skills":["弱大數律"]},"variant":{"family_id":"qf-mod36-wlln-variance-average","seed":202611057004,"parameters":{"mean":[3,4],"variance":[4,5],"n":8,"iid_certificate":"symbolic_all_finite_subfamilies","domain":"Symbolic_iid_Chebyshev_WLLN","operation":"wlln-variance-average","semantic_template":"qf-mod36-wlln-variance-average/{\"iid_certificate\":\"symbolic_all_finite_subfamilies\",\"mean\":[3,4],\"n\":8,\"variance\":[4,5]}"}},"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、有限取樣全稱證明、V與dual典範識別、Hamilton結論、一般continuous-bijection捷徑、統計性質、strong law、CLT、Lean或Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-14","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261014-advance-20261105-r07-weak-law-large-numbers-0005","batch_id":"batch-20261014-advance-20261105-r07-weak-law-large-numbers-foundations","language":"zh-Hant","source_mko_ids":["mko-weak-law-large-numbers"],"title_zh":"弱大數律","stem_zh":"IID通用證書、共同有限mean與variance及exact Chebyshev tail。操作=wlln-variance-average；資料={\"mean\":[4,5],\"variance\":[5,6],\"n\":9,\"iid_certificate\":\"symbolic_all_finite_subfamilies\"}。請依 exact_ordered_tuple_declared_by_interface 欄序回答。","answer":{"kind":"expression","value":"(4/5, 5/6, 9, 5/54, independence_gives_variance_sigma_squared_over_n)","explanation_zh":"Wave5第五層核對=(4/5, 5/6, 9, 5/54, independence_gives_variance_sigma_squared_over_n)；依完整明示資料獨立重算；independence給Var(sample mean)=sigma squared/n並以forall n大於等於N證依機率收斂；有限樣本或模擬不足，且不宣稱almost sure、CLT或有限n已等於極限。"},"difficulty":{"band":"undergraduate_core","level":1,"skills":["弱大數律"]},"variant":{"family_id":"qf-mod36-wlln-variance-average","seed":202611057005,"parameters":{"mean":[4,5],"variance":[5,6],"n":9,"iid_certificate":"symbolic_all_finite_subfamilies","domain":"Symbolic_iid_Chebyshev_WLLN","operation":"wlln-variance-average","semantic_template":"qf-mod36-wlln-variance-average/{\"iid_certificate\":\"symbolic_all_finite_subfamilies\",\"mean\":[4,5],\"n\":9,\"variance\":[5,6]}"}},"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、有限取樣全稱證明、V與dual典範識別、Hamilton結論、一般continuous-bijection捷徑、統計性質、strong law、CLT、Lean或Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-14","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261014-advance-20261105-r07-weak-law-large-numbers-0006","batch_id":"batch-20261014-advance-20261105-r07-weak-law-large-numbers-foundations","language":"zh-Hant","source_mko_ids":["mko-weak-law-large-numbers"],"title_zh":"弱大數律","stem_zh":"IID通用證書、共同有限mean與variance及exact Chebyshev tail。操作=wlln-variance-average；資料={\"mean\":[5,6],\"variance\":[6,7],\"n\":10,\"iid_certificate\":\"symbolic_all_finite_subfamilies\"}。請依 exact_ordered_tuple_declared_by_interface 欄序回答。","answer":{"kind":"expression","value":"(5/6, 6/7, 10, 3/35, independence_gives_variance_sigma_squared_over_n)","explanation_zh":"Wave5第五層核對=(5/6, 6/7, 10, 3/35, independence_gives_variance_sigma_squared_over_n)；依完整明示資料獨立重算；independence給Var(sample mean)=sigma squared/n並以forall n大於等於N證依機率收斂；有限樣本或模擬不足，且不宣稱almost sure、CLT或有限n已等於極限。"},"difficulty":{"band":"undergraduate_core","level":1,"skills":["弱大數律"]},"variant":{"family_id":"qf-mod36-wlln-variance-average","seed":202611057006,"parameters":{"mean":[5,6],"variance":[6,7],"n":10,"iid_certificate":"symbolic_all_finite_subfamilies","domain":"Symbolic_iid_Chebyshev_WLLN","operation":"wlln-variance-average","semantic_template":"qf-mod36-wlln-variance-average/{\"iid_certificate\":\"symbolic_all_finite_subfamilies\",\"mean\":[5,6],\"n\":10,\"variance\":[6,7]}"}},"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、有限取樣全稱證明、V與dual典範識別、Hamilton結論、一般continuous-bijection捷徑、統計性質、strong law、CLT、Lean或Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-14","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261014-advance-20261105-r07-weak-law-large-numbers-0007","batch_id":"batch-20261014-advance-20261105-r07-weak-law-large-numbers-foundations","language":"zh-Hant","source_mko_ids":["mko-weak-law-large-numbers"],"title_zh":"弱大數律","stem_zh":"IID通用證書、共同有限mean與variance及exact Chebyshev tail。操作=wlln-variance-average；資料={\"mean\":[6,7],\"variance\":[7,8],\"n\":11,\"iid_certificate\":\"symbolic_all_finite_subfamilies\"}。請依 exact_ordered_tuple_declared_by_interface 欄序回答。","answer":{"kind":"expression","value":"(6/7, 7/8, 11, 7/88, independence_gives_variance_sigma_squared_over_n)","explanation_zh":"Wave5第五層核對=(6/7, 7/8, 11, 7/88, independence_gives_variance_sigma_squared_over_n)；依完整明示資料獨立重算；independence給Var(sample mean)=sigma squared/n並以forall n大於等於N證依機率收斂；有限樣本或模擬不足，且不宣稱almost sure、CLT或有限n已等於極限。"},"difficulty":{"band":"undergraduate_core","level":1,"skills":["弱大數律"]},"variant":{"family_id":"qf-mod36-wlln-variance-average","seed":202611057007,"parameters":{"mean":[6,7],"variance":[7,8],"n":11,"iid_certificate":"symbolic_all_finite_subfamilies","domain":"Symbolic_iid_Chebyshev_WLLN","operation":"wlln-variance-average","semantic_template":"qf-mod36-wlln-variance-average/{\"iid_certificate\":\"symbolic_all_finite_subfamilies\",\"mean\":[6,7],\"n\":11,\"variance\":[7,8]}"}},"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、有限取樣全稱證明、V與dual典範識別、Hamilton結論、一般continuous-bijection捷徑、統計性質、strong law、CLT、Lean或Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-14","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261014-advance-20261105-r07-weak-law-large-numbers-0008","batch_id":"batch-20261014-advance-20261105-r07-weak-law-large-numbers-foundations","language":"zh-Hant","source_mko_ids":["mko-weak-law-large-numbers"],"title_zh":"弱大數律","stem_zh":"IID通用證書、共同有限mean與variance及exact Chebyshev tail。操作=wlln-variance-average；資料={\"mean\":[7,8],\"variance\":[8,9],\"n\":12,\"iid_certificate\":\"symbolic_all_finite_subfamilies\"}。請依 exact_ordered_tuple_declared_by_interface 欄序回答。","answer":{"kind":"expression","value":"(7/8, 8/9, 12, 2/27, independence_gives_variance_sigma_squared_over_n)","explanation_zh":"Wave5第五層核對=(7/8, 8/9, 12, 2/27, independence_gives_variance_sigma_squared_over_n)；依完整明示資料獨立重算；independence給Var(sample mean)=sigma squared/n並以forall n大於等於N證依機率收斂；有限樣本或模擬不足，且不宣稱almost sure、CLT或有限n已等於極限。"},"difficulty":{"band":"undergraduate_core","level":1,"skills":["弱大數律"]},"variant":{"family_id":"qf-mod36-wlln-variance-average","seed":202611057008,"parameters":{"mean":[7,8],"variance":[8,9],"n":12,"iid_certificate":"symbolic_all_finite_subfamilies","domain":"Symbolic_iid_Chebyshev_WLLN","operation":"wlln-variance-average","semantic_template":"qf-mod36-wlln-variance-average/{\"iid_certificate\":\"symbolic_all_finite_subfamilies\",\"mean\":[7,8],\"n\":12,\"variance\":[8,9]}"}},"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、有限取樣全稱證明、V與dual典範識別、Hamilton結論、一般continuous-bijection捷徑、統計性質、strong law、CLT、Lean或Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-14","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261014-advance-20261105-r07-weak-law-large-numbers-0009","batch_id":"batch-20261014-advance-20261105-r07-weak-law-large-numbers-foundations","language":"zh-Hant","source_mko_ids":["mko-weak-law-large-numbers"],"title_zh":"弱大數律","stem_zh":"IID通用證書、共同有限mean與variance及exact Chebyshev tail。操作=wlln-variance-average；資料={\"mean\":[8,9],\"variance\":[9,10],\"n\":13,\"iid_certificate\":\"symbolic_all_finite_subfamilies\"}。請依 exact_ordered_tuple_declared_by_interface 欄序回答。","answer":{"kind":"expression","value":"(8/9, 9/10, 13, 9/130, independence_gives_variance_sigma_squared_over_n)","explanation_zh":"Wave5第五層核對=(8/9, 9/10, 13, 9/130, independence_gives_variance_sigma_squared_over_n)；依完整明示資料獨立重算；independence給Var(sample mean)=sigma squared/n並以forall n大於等於N證依機率收斂；有限樣本或模擬不足，且不宣稱almost sure、CLT或有限n已等於極限。"},"difficulty":{"band":"undergraduate_core","level":2,"skills":["弱大數律"]},"variant":{"family_id":"qf-mod36-wlln-variance-average","seed":202611057009,"parameters":{"mean":[8,9],"variance":[9,10],"n":13,"iid_certificate":"symbolic_all_finite_subfamilies","domain":"Symbolic_iid_Chebyshev_WLLN","operation":"wlln-variance-average","semantic_template":"qf-mod36-wlln-variance-average/{\"iid_certificate\":\"symbolic_all_finite_subfamilies\",\"mean\":[8,9],\"n\":13,\"variance\":[9,10]}"}},"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、有限取樣全稱證明、V與dual典範識別、Hamilton結論、一般continuous-bijection捷徑、統計性質、strong law、CLT、Lean或Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-14","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261014-advance-20261105-r07-weak-law-large-numbers-0010","batch_id":"batch-20261014-advance-20261105-r07-weak-law-large-numbers-foundations","language":"zh-Hant","source_mko_ids":["mko-weak-law-large-numbers"],"title_zh":"弱大數律","stem_zh":"IID通用證書、共同有限mean與variance及exact Chebyshev tail。操作=wlln-variance-average；資料={\"mean\":[9,10],\"variance\":[10,11],\"n\":14,\"iid_certificate\":\"symbolic_all_finite_subfamilies\"}。請依 exact_ordered_tuple_declared_by_interface 欄序回答。","answer":{"kind":"expression","value":"(9/10, 10/11, 14, 5/77, independence_gives_variance_sigma_squared_over_n)","explanation_zh":"Wave5第五層核對=(9/10, 10/11, 14, 5/77, independence_gives_variance_sigma_squared_over_n)；依完整明示資料獨立重算；independence給Var(sample mean)=sigma squared/n並以forall n大於等於N證依機率收斂；有限樣本或模擬不足，且不宣稱almost sure、CLT或有限n已等於極限。"},"difficulty":{"band":"undergraduate_core","level":2,"skills":["弱大數律"]},"variant":{"family_id":"qf-mod36-wlln-variance-average","seed":202611057010,"parameters":{"mean":[9,10],"variance":[10,11],"n":14,"iid_certificate":"symbolic_all_finite_subfamilies","domain":"Symbolic_iid_Chebyshev_WLLN","operation":"wlln-variance-average","semantic_template":"qf-mod36-wlln-variance-average/{\"iid_certificate\":\"symbolic_all_finite_subfamilies\",\"mean\":[9,10],\"n\":14,\"variance\":[10,11]}"}},"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、有限取樣全稱證明、V與dual典範識別、Hamilton結論、一般continuous-bijection捷徑、統計性質、strong law、CLT、Lean或Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-14","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261014-advance-20261105-r07-weak-law-large-numbers-0011","batch_id":"batch-20261014-advance-20261105-r07-weak-law-large-numbers-foundations","language":"zh-Hant","source_mko_ids":["mko-weak-law-large-numbers"],"title_zh":"弱大數律","stem_zh":"IID通用證書、共同有限mean與variance及exact Chebyshev tail。操作=wlln-variance-average；資料={\"mean\":[10,11],\"variance\":[11,12],\"n\":15,\"iid_certificate\":\"symbolic_all_finite_subfamilies\"}。請依 exact_ordered_tuple_declared_by_interface 欄序回答。","answer":{"kind":"expression","value":"(10/11, 11/12, 15, 11/180, independence_gives_variance_sigma_squared_over_n)","explanation_zh":"Wave5第五層核對=(10/11, 11/12, 15, 11/180, independence_gives_variance_sigma_squared_over_n)；依完整明示資料獨立重算；independence給Var(sample mean)=sigma squared/n並以forall n大於等於N證依機率收斂；有限樣本或模擬不足，且不宣稱almost sure、CLT或有限n已等於極限。"},"difficulty":{"band":"undergraduate_core","level":2,"skills":["弱大數律"]},"variant":{"family_id":"qf-mod36-wlln-variance-average","seed":202611057011,"parameters":{"mean":[10,11],"variance":[11,12],"n":15,"iid_certificate":"symbolic_all_finite_subfamilies","domain":"Symbolic_iid_Chebyshev_WLLN","operation":"wlln-variance-average","semantic_template":"qf-mod36-wlln-variance-average/{\"iid_certificate\":\"symbolic_all_finite_subfamilies\",\"mean\":[10,11],\"n\":15,\"variance\":[11,12]}"}},"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、有限取樣全稱證明、V與dual典範識別、Hamilton結論、一般continuous-bijection捷徑、統計性質、strong law、CLT、Lean或Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-14","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261014-advance-20261105-r07-weak-law-large-numbers-0012","batch_id":"batch-20261014-advance-20261105-r07-weak-law-large-numbers-foundations","language":"zh-Hant","source_mko_ids":["mko-weak-law-large-numbers"],"title_zh":"弱大數律","stem_zh":"IID通用證書、共同有限mean與variance及exact Chebyshev tail。操作=wlln-variance-average；資料={\"mean\":[11,12],\"variance\":[12,13],\"n\":16,\"iid_certificate\":\"symbolic_all_finite_subfamilies\"}。請依 exact_ordered_tuple_declared_by_interface 欄序回答。","answer":{"kind":"expression","value":"(11/12, 12/13, 16, 3/52, independence_gives_variance_sigma_squared_over_n)","explanation_zh":"Wave5第五層核對=(11/12, 12/13, 16, 3/52, independence_gives_variance_sigma_squared_over_n)；依完整明示資料獨立重算；independence給Var(sample mean)=sigma squared/n並以forall n大於等於N證依機率收斂；有限樣本或模擬不足，且不宣稱almost sure、CLT或有限n已等於極限。"},"difficulty":{"band":"undergraduate_core","level":2,"skills":["弱大數律"]},"variant":{"family_id":"qf-mod36-wlln-variance-average","seed":202611057012,"parameters":{"mean":[11,12],"variance":[12,13],"n":16,"iid_certificate":"symbolic_all_finite_subfamilies","domain":"Symbolic_iid_Chebyshev_WLLN","operation":"wlln-variance-average","semantic_template":"qf-mod36-wlln-variance-average/{\"iid_certificate\":\"symbolic_all_finite_subfamilies\",\"mean\":[11,12],\"n\":16,\"variance\":[12,13]}"}},"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、有限取樣全稱證明、V與dual典範識別、Hamilton結論、一般continuous-bijection捷徑、統計性質、strong law、CLT、Lean或Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-14","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261014-advance-20261105-r07-weak-law-large-numbers-0013","batch_id":"batch-20261014-advance-20261105-r07-weak-law-large-numbers-foundations","language":"zh-Hant","source_mko_ids":["mko-weak-law-large-numbers"],"title_zh":"弱大數律","stem_zh":"IID通用證書、共同有限mean與variance及exact Chebyshev tail。操作=wlln-variance-average；資料={\"mean\":[12,13],\"variance\":[13,14],\"n\":17,\"iid_certificate\":\"symbolic_all_finite_subfamilies\"}。請依 exact_ordered_tuple_declared_by_interface 欄序回答。","answer":{"kind":"expression","value":"(12/13, 13/14, 17, 13/238, independence_gives_variance_sigma_squared_over_n)","explanation_zh":"Wave5第五層核對=(12/13, 13/14, 17, 13/238, independence_gives_variance_sigma_squared_over_n)；依完整明示資料獨立重算；independence給Var(sample mean)=sigma squared/n並以forall n大於等於N證依機率收斂；有限樣本或模擬不足，且不宣稱almost sure、CLT或有限n已等於極限。"},"difficulty":{"band":"undergraduate_core","level":2,"skills":["弱大數律"]},"variant":{"family_id":"qf-mod36-wlln-variance-average","seed":202611057013,"parameters":{"mean":[12,13],"variance":[13,14],"n":17,"iid_certificate":"symbolic_all_finite_subfamilies","domain":"Symbolic_iid_Chebyshev_WLLN","operation":"wlln-variance-average","semantic_template":"qf-mod36-wlln-variance-average/{\"iid_certificate\":\"symbolic_all_finite_subfamilies\",\"mean\":[12,13],\"n\":17,\"variance\":[13,14]}"}},"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、有限取樣全稱證明、V與dual典範識別、Hamilton結論、一般continuous-bijection捷徑、統計性質、strong law、CLT、Lean或Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-14","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261014-advance-20261105-r07-weak-law-large-numbers-0014","batch_id":"batch-20261014-advance-20261105-r07-weak-law-large-numbers-foundations","language":"zh-Hant","source_mko_ids":["mko-weak-law-large-numbers"],"title_zh":"弱大數律","stem_zh":"IID通用證書、共同有限mean與variance及exact Chebyshev tail。操作=wlln-variance-average；資料={\"mean\":[13,14],\"variance\":[14,15],\"n\":18,\"iid_certificate\":\"symbolic_all_finite_subfamilies\"}。請依 exact_ordered_tuple_declared_by_interface 欄序回答。","answer":{"kind":"expression","value":"(13/14, 14/15, 18, 7/135, independence_gives_variance_sigma_squared_over_n)","explanation_zh":"Wave5第五層核對=(13/14, 14/15, 18, 7/135, independence_gives_variance_sigma_squared_over_n)；依完整明示資料獨立重算；independence給Var(sample mean)=sigma squared/n並以forall n大於等於N證依機率收斂；有限樣本或模擬不足，且不宣稱almost sure、CLT或有限n已等於極限。"},"difficulty":{"band":"undergraduate_core","level":2,"skills":["弱大數律"]},"variant":{"family_id":"qf-mod36-wlln-variance-average","seed":202611057014,"parameters":{"mean":[13,14],"variance":[14,15],"n":18,"iid_certificate":"symbolic_all_finite_subfamilies","domain":"Symbolic_iid_Chebyshev_WLLN","operation":"wlln-variance-average","semantic_template":"qf-mod36-wlln-variance-average/{\"iid_certificate\":\"symbolic_all_finite_subfamilies\",\"mean\":[13,14],\"n\":18,\"variance\":[14,15]}"}},"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、有限取樣全稱證明、V與dual典範識別、Hamilton結論、一般continuous-bijection捷徑、統計性質、strong law、CLT、Lean或Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-14","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261014-advance-20261105-r07-weak-law-large-numbers-0015","batch_id":"batch-20261014-advance-20261105-r07-weak-law-large-numbers-foundations","language":"zh-Hant","source_mko_ids":["mko-weak-law-large-numbers"],"title_zh":"弱大數律","stem_zh":"IID通用證書、共同有限mean與variance及exact Chebyshev tail。操作=wlln-variance-average；資料={\"mean\":[14,15],\"variance\":[15,16],\"n\":19,\"iid_certificate\":\"symbolic_all_finite_subfamilies\"}。請依 exact_ordered_tuple_declared_by_interface 欄序回答。","answer":{"kind":"expression","value":"(14/15, 15/16, 19, 15/304, independence_gives_variance_sigma_squared_over_n)","explanation_zh":"Wave5第五層核對=(14/15, 15/16, 19, 15/304, independence_gives_variance_sigma_squared_over_n)；依完整明示資料獨立重算；independence給Var(sample mean)=sigma squared/n並以forall n大於等於N證依機率收斂；有限樣本或模擬不足，且不宣稱almost sure、CLT或有限n已等於極限。"},"difficulty":{"band":"undergraduate_core","level":2,"skills":["弱大數律"]},"variant":{"family_id":"qf-mod36-wlln-variance-average","seed":202611057015,"parameters":{"mean":[14,15],"variance":[15,16],"n":19,"iid_certificate":"symbolic_all_finite_subfamilies","domain":"Symbolic_iid_Chebyshev_WLLN","operation":"wlln-variance-average","semantic_template":"qf-mod36-wlln-variance-average/{\"iid_certificate\":\"symbolic_all_finite_subfamilies\",\"mean\":[14,15],\"n\":19,\"variance\":[15,16]}"}},"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、有限取樣全稱證明、V與dual典範識別、Hamilton結論、一般continuous-bijection捷徑、統計性質、strong law、CLT、Lean或Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-14","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261014-advance-20261105-r07-weak-law-large-numbers-0016","batch_id":"batch-20261014-advance-20261105-r07-weak-law-large-numbers-foundations","language":"zh-Hant","source_mko_ids":["mko-weak-law-large-numbers"],"title_zh":"弱大數律","stem_zh":"IID通用證書、共同有限mean與variance及exact Chebyshev tail。操作=wlln-variance-average；資料={\"mean\":[15,16],\"variance\":[16,17],\"n\":20,\"iid_certificate\":\"symbolic_all_finite_subfamilies\"}。請依 exact_ordered_tuple_declared_by_interface 欄序回答。","answer":{"kind":"expression","value":"(15/16, 16/17, 20, 4/85, independence_gives_variance_sigma_squared_over_n)","explanation_zh":"Wave5第五層核對=(15/16, 16/17, 20, 4/85, independence_gives_variance_sigma_squared_over_n)；依完整明示資料獨立重算；independence給Var(sample mean)=sigma squared/n並以forall n大於等於N證依機率收斂；有限樣本或模擬不足，且不宣稱almost sure、CLT或有限n已等於極限。"},"difficulty":{"band":"undergraduate_core","level":2,"skills":["弱大數律"]},"variant":{"family_id":"qf-mod36-wlln-variance-average","seed":202611057016,"parameters":{"mean":[15,16],"variance":[16,17],"n":20,"iid_certificate":"symbolic_all_finite_subfamilies","domain":"Symbolic_iid_Chebyshev_WLLN","operation":"wlln-variance-average","semantic_template":"qf-mod36-wlln-variance-average/{\"iid_certificate\":\"symbolic_all_finite_subfamilies\",\"mean\":[15,16],\"n\":20,\"variance\":[16,17]}"}},"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、有限取樣全稱證明、V與dual典範識別、Hamilton結論、一般continuous-bijection捷徑、統計性質、strong law、CLT、Lean或Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-14","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261014-advance-20261105-r07-weak-law-large-numbers-0017","batch_id":"batch-20261014-advance-20261105-r07-weak-law-large-numbers-foundations","language":"zh-Hant","source_mko_ids":["mko-weak-law-large-numbers"],"title_zh":"弱大數律","stem_zh":"IID通用證書、共同有限mean與variance及exact Chebyshev tail。操作=wlln-variance-average；資料={\"mean\":[16,17],\"variance\":[17,18],\"n\":21,\"iid_certificate\":\"symbolic_all_finite_subfamilies\"}。請依 exact_ordered_tuple_declared_by_interface 欄序回答。","answer":{"kind":"expression","value":"(16/17, 17/18, 21, 17/378, independence_gives_variance_sigma_squared_over_n)","explanation_zh":"Wave5第五層核對=(16/17, 17/18, 21, 17/378, independence_gives_variance_sigma_squared_over_n)；依完整明示資料獨立重算；independence給Var(sample mean)=sigma squared/n並以forall n大於等於N證依機率收斂；有限樣本或模擬不足，且不宣稱almost sure、CLT或有限n已等於極限。"},"difficulty":{"band":"undergraduate_core","level":2,"skills":["弱大數律"]},"variant":{"family_id":"qf-mod36-wlln-variance-average","seed":202611057017,"parameters":{"mean":[16,17],"variance":[17,18],"n":21,"iid_certificate":"symbolic_all_finite_subfamilies","domain":"Symbolic_iid_Chebyshev_WLLN","operation":"wlln-variance-average","semantic_template":"qf-mod36-wlln-variance-average/{\"iid_certificate\":\"symbolic_all_finite_subfamilies\",\"mean\":[16,17],\"n\":21,\"variance\":[17,18]}"}},"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、有限取樣全稱證明、V與dual典範識別、Hamilton結論、一般continuous-bijection捷徑、統計性質、strong law、CLT、Lean或Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-14","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261014-advance-20261105-r07-weak-law-large-numbers-0018","batch_id":"batch-20261014-advance-20261105-r07-weak-law-large-numbers-foundations","language":"zh-Hant","source_mko_ids":["mko-weak-law-large-numbers"],"title_zh":"弱大數律","stem_zh":"IID通用證書、共同有限mean與variance及exact Chebyshev tail。操作=wlln-variance-average；資料={\"mean\":[17,18],\"variance\":[18,19],\"n\":22,\"iid_certificate\":\"symbolic_all_finite_subfamilies\"}。請依 exact_ordered_tuple_declared_by_interface 欄序回答。","answer":{"kind":"expression","value":"(17/18, 18/19, 22, 9/209, independence_gives_variance_sigma_squared_over_n)","explanation_zh":"Wave5第五層核對=(17/18, 18/19, 22, 9/209, independence_gives_variance_sigma_squared_over_n)；依完整明示資料獨立重算；independence給Var(sample mean)=sigma squared/n並以forall n大於等於N證依機率收斂；有限樣本或模擬不足，且不宣稱almost sure、CLT或有限n已等於極限。"},"difficulty":{"band":"undergraduate_core","level":3,"skills":["弱大數律"]},"variant":{"family_id":"qf-mod36-wlln-variance-average","seed":202611057018,"parameters":{"mean":[17,18],"variance":[18,19],"n":22,"iid_certificate":"symbolic_all_finite_subfamilies","domain":"Symbolic_iid_Chebyshev_WLLN","operation":"wlln-variance-average","semantic_template":"qf-mod36-wlln-variance-average/{\"iid_certificate\":\"symbolic_all_finite_subfamilies\",\"mean\":[17,18],\"n\":22,\"variance\":[18,19]}"}},"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、有限取樣全稱證明、V與dual典範識別、Hamilton結論、一般continuous-bijection捷徑、統計性質、strong law、CLT、Lean或Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-14","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261014-advance-20261105-r07-weak-law-large-numbers-0019","batch_id":"batch-20261014-advance-20261105-r07-weak-law-large-numbers-foundations","language":"zh-Hant","source_mko_ids":["mko-weak-law-large-numbers"],"title_zh":"弱大數律","stem_zh":"IID通用證書、共同有限mean與variance及exact Chebyshev tail。操作=wlln-variance-average；資料={\"mean\":[18,19],\"variance\":[19,20],\"n\":23,\"iid_certificate\":\"symbolic_all_finite_subfamilies\"}。請依 exact_ordered_tuple_declared_by_interface 欄序回答。","answer":{"kind":"expression","value":"(18/19, 19/20, 23, 19/460, independence_gives_variance_sigma_squared_over_n)","explanation_zh":"Wave5第五層核對=(18/19, 19/20, 23, 19/460, independence_gives_variance_sigma_squared_over_n)；依完整明示資料獨立重算；independence給Var(sample mean)=sigma squared/n並以forall n大於等於N證依機率收斂；有限樣本或模擬不足，且不宣稱almost sure、CLT或有限n已等於極限。"},"difficulty":{"band":"undergraduate_core","level":3,"skills":["弱大數律"]},"variant":{"family_id":"qf-mod36-wlln-variance-average","seed":202611057019,"parameters":{"mean":[18,19],"variance":[19,20],"n":23,"iid_certificate":"symbolic_all_finite_subfamilies","domain":"Symbolic_iid_Chebyshev_WLLN","operation":"wlln-variance-average","semantic_template":"qf-mod36-wlln-variance-average/{\"iid_certificate\":\"symbolic_all_finite_subfamilies\",\"mean\":[18,19],\"n\":23,\"variance\":[19,20]}"}},"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、有限取樣全稱證明、V與dual典範識別、Hamilton結論、一般continuous-bijection捷徑、統計性質、strong law、CLT、Lean或Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-14","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261014-advance-20261105-r07-weak-law-large-numbers-0020","batch_id":"batch-20261014-advance-20261105-r07-weak-law-large-numbers-foundations","language":"zh-Hant","source_mko_ids":["mko-weak-law-large-numbers"],"title_zh":"弱大數律","stem_zh":"IID通用證書、共同有限mean與variance及exact Chebyshev tail。操作=wlln-variance-average；資料={\"mean\":[19,20],\"variance\":[20,21],\"n\":24,\"iid_certificate\":\"symbolic_all_finite_subfamilies\"}。請依 exact_ordered_tuple_declared_by_interface 欄序回答。","answer":{"kind":"expression","value":"(19/20, 20/21, 24, 5/126, independence_gives_variance_sigma_squared_over_n)","explanation_zh":"Wave5第五層核對=(19/20, 20/21, 24, 5/126, independence_gives_variance_sigma_squared_over_n)；依完整明示資料獨立重算；independence給Var(sample mean)=sigma squared/n並以forall n大於等於N證依機率收斂；有限樣本或模擬不足，且不宣稱almost sure、CLT或有限n已等於極限。"},"difficulty":{"band":"undergraduate_core","level":3,"skills":["弱大數律"]},"variant":{"family_id":"qf-mod36-wlln-variance-average","seed":202611057020,"parameters":{"mean":[19,20],"variance":[20,21],"n":24,"iid_certificate":"symbolic_all_finite_subfamilies","domain":"Symbolic_iid_Chebyshev_WLLN","operation":"wlln-variance-average","semantic_template":"qf-mod36-wlln-variance-average/{\"iid_certificate\":\"symbolic_all_finite_subfamilies\",\"mean\":[19,20],\"n\":24,\"variance\":[20,21]}"}},"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、有限取樣全稱證明、V與dual典範識別、Hamilton結論、一般continuous-bijection捷徑、統計性質、strong law、CLT、Lean或Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-14","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261014-advance-20261105-r07-weak-law-large-numbers-0021","batch_id":"batch-20261014-advance-20261105-r07-weak-law-large-numbers-foundations","language":"zh-Hant","source_mko_ids":["mko-weak-law-large-numbers"],"title_zh":"弱大數律","stem_zh":"IID通用證書、共同有限mean與variance及exact Chebyshev tail。操作=wlln-variance-average；資料={\"mean\":[20,21],\"variance\":[21,22],\"n\":25,\"iid_certificate\":\"symbolic_all_finite_subfamilies\"}。請依 exact_ordered_tuple_declared_by_interface 欄序回答。","answer":{"kind":"expression","value":"(20/21, 21/22, 25, 21/550, independence_gives_variance_sigma_squared_over_n)","explanation_zh":"Wave5第五層核對=(20/21, 21/22, 25, 21/550, independence_gives_variance_sigma_squared_over_n)；依完整明示資料獨立重算；independence給Var(sample mean)=sigma squared/n並以forall n大於等於N證依機率收斂；有限樣本或模擬不足，且不宣稱almost sure、CLT或有限n已等於極限。"},"difficulty":{"band":"undergraduate_core","level":3,"skills":["弱大數律"]},"variant":{"family_id":"qf-mod36-wlln-variance-average","seed":202611057021,"parameters":{"mean":[20,21],"variance":[21,22],"n":25,"iid_certificate":"symbolic_all_finite_subfamilies","domain":"Symbolic_iid_Chebyshev_WLLN","operation":"wlln-variance-average","semantic_template":"qf-mod36-wlln-variance-average/{\"iid_certificate\":\"symbolic_all_finite_subfamilies\",\"mean\":[20,21],\"n\":25,\"variance\":[21,22]}"}},"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、有限取樣全稱證明、V與dual典範識別、Hamilton結論、一般continuous-bijection捷徑、統計性質、strong law、CLT、Lean或Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-14","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261014-advance-20261105-r07-weak-law-large-numbers-0022","batch_id":"batch-20261014-advance-20261105-r07-weak-law-large-numbers-foundations","language":"zh-Hant","source_mko_ids":["mko-weak-law-large-numbers"],"title_zh":"弱大數律","stem_zh":"IID通用證書、共同有限mean與variance及exact Chebyshev tail。操作=wlln-variance-average；資料={\"mean\":[21,22],\"variance\":[22,23],\"n\":26,\"iid_certificate\":\"symbolic_all_finite_subfamilies\"}。請依 exact_ordered_tuple_declared_by_interface 欄序回答。","answer":{"kind":"expression","value":"(21/22, 22/23, 26, 11/299, independence_gives_variance_sigma_squared_over_n)","explanation_zh":"Wave5第五層核對=(21/22, 22/23, 26, 11/299, independence_gives_variance_sigma_squared_over_n)；依完整明示資料獨立重算；independence給Var(sample mean)=sigma squared/n並以forall n大於等於N證依機率收斂；有限樣本或模擬不足，且不宣稱almost sure、CLT或有限n已等於極限。"},"difficulty":{"band":"undergraduate_core","level":3,"skills":["弱大數律"]},"variant":{"family_id":"qf-mod36-wlln-variance-average","seed":202611057022,"parameters":{"mean":[21,22],"variance":[22,23],"n":26,"iid_certificate":"symbolic_all_finite_subfamilies","domain":"Symbolic_iid_Chebyshev_WLLN","operation":"wlln-variance-average","semantic_template":"qf-mod36-wlln-variance-average/{\"iid_certificate\":\"symbolic_all_finite_subfamilies\",\"mean\":[21,22],\"n\":26,\"variance\":[22,23]}"}},"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、有限取樣全稱證明、V與dual典範識別、Hamilton結論、一般continuous-bijection捷徑、統計性質、strong law、CLT、Lean或Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-14","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261014-advance-20261105-r07-weak-law-large-numbers-0023","batch_id":"batch-20261014-advance-20261105-r07-weak-law-large-numbers-foundations","language":"zh-Hant","source_mko_ids":["mko-weak-law-large-numbers"],"title_zh":"弱大數律","stem_zh":"IID通用證書、共同有限mean與variance及exact Chebyshev tail。操作=wlln-variance-average；資料={\"mean\":[22,23],\"variance\":[23,24],\"n\":27,\"iid_certificate\":\"symbolic_all_finite_subfamilies\"}。請依 exact_ordered_tuple_declared_by_interface 欄序回答。","answer":{"kind":"expression","value":"(22/23, 23/24, 27, 23/648, independence_gives_variance_sigma_squared_over_n)","explanation_zh":"Wave5第五層核對=(22/23, 23/24, 27, 23/648, independence_gives_variance_sigma_squared_over_n)；依完整明示資料獨立重算；independence給Var(sample mean)=sigma squared/n並以forall n大於等於N證依機率收斂；有限樣本或模擬不足，且不宣稱almost sure、CLT或有限n已等於極限。"},"difficulty":{"band":"undergraduate_core","level":3,"skills":["弱大數律"]},"variant":{"family_id":"qf-mod36-wlln-variance-average","seed":202611057023,"parameters":{"mean":[22,23],"variance":[23,24],"n":27,"iid_certificate":"symbolic_all_finite_subfamilies","domain":"Symbolic_iid_Chebyshev_WLLN","operation":"wlln-variance-average","semantic_template":"qf-mod36-wlln-variance-average/{\"iid_certificate\":\"symbolic_all_finite_subfamilies\",\"mean\":[22,23],\"n\":27,\"variance\":[23,24]}"}},"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、有限取樣全稱證明、V與dual典範識別、Hamilton結論、一般continuous-bijection捷徑、統計性質、strong law、CLT、Lean或Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-14","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261014-advance-20261105-r07-weak-law-large-numbers-0024","batch_id":"batch-20261014-advance-20261105-r07-weak-law-large-numbers-foundations","language":"zh-Hant","source_mko_ids":["mko-weak-law-large-numbers"],"title_zh":"弱大數律","stem_zh":"IID通用證書、共同有限mean與variance及exact Chebyshev tail。操作=wlln-variance-average；資料={\"mean\":[23,24],\"variance\":[24,25],\"n\":28,\"iid_certificate\":\"symbolic_all_finite_subfamilies\"}。請依 exact_ordered_tuple_declared_by_interface 欄序回答。","answer":{"kind":"expression","value":"(23/24, 24/25, 28, 6/175, independence_gives_variance_sigma_squared_over_n)","explanation_zh":"Wave5第五層核對=(23/24, 24/25, 28, 6/175, independence_gives_variance_sigma_squared_over_n)；依完整明示資料獨立重算；independence給Var(sample mean)=sigma squared/n並以forall n大於等於N證依機率收斂；有限樣本或模擬不足，且不宣稱almost sure、CLT或有限n已等於極限。"},"difficulty":{"band":"undergraduate_core","level":3,"skills":["弱大數律"]},"variant":{"family_id":"qf-mod36-wlln-variance-average","seed":202611057024,"parameters":{"mean":[23,24],"variance":[24,25],"n":28,"iid_certificate":"symbolic_all_finite_subfamilies","domain":"Symbolic_iid_Chebyshev_WLLN","operation":"wlln-variance-average","semantic_template":"qf-mod36-wlln-variance-average/{\"iid_certificate\":\"symbolic_all_finite_subfamilies\",\"mean\":[23,24],\"n\":28,\"variance\":[24,25]}"}},"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、有限取樣全稱證明、V與dual典範識別、Hamilton結論、一般continuous-bijection捷徑、統計性質、strong law、CLT、Lean或Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-14","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261014-advance-20261105-r07-weak-law-large-numbers-0025","batch_id":"batch-20261014-advance-20261105-r07-weak-law-large-numbers-foundations","language":"zh-Hant","source_mko_ids":["mko-weak-law-large-numbers"],"title_zh":"弱大數律","stem_zh":"IID通用證書、共同有限mean與variance及exact Chebyshev tail。操作=wlln-variance-average；資料={\"mean\":[24,25],\"variance\":[25,26],\"n\":29,\"iid_certificate\":\"symbolic_all_finite_subfamilies\"}。請依 exact_ordered_tuple_declared_by_interface 欄序回答。","answer":{"kind":"expression","value":"(24/25, 25/26, 29, 25/754, independence_gives_variance_sigma_squared_over_n)","explanation_zh":"Wave5第五層核對=(24/25, 25/26, 29, 25/754, independence_gives_variance_sigma_squared_over_n)；依完整明示資料獨立重算；independence給Var(sample mean)=sigma squared/n並以forall n大於等於N證依機率收斂；有限樣本或模擬不足，且不宣稱almost sure、CLT或有限n已等於極限。"},"difficulty":{"band":"undergraduate_core","level":3,"skills":["弱大數律"]},"variant":{"family_id":"qf-mod36-wlln-variance-average","seed":202611057025,"parameters":{"mean":[24,25],"variance":[25,26],"n":29,"iid_certificate":"symbolic_all_finite_subfamilies","domain":"Symbolic_iid_Chebyshev_WLLN","operation":"wlln-variance-average","semantic_template":"qf-mod36-wlln-variance-average/{\"iid_certificate\":\"symbolic_all_finite_subfamilies\",\"mean\":[24,25],\"n\":29,\"variance\":[25,26]}"}},"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、有限取樣全稱證明、V與dual典範識別、Hamilton結論、一般continuous-bijection捷徑、統計性質、strong law、CLT、Lean或Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-14","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261014-advance-20261105-r07-weak-law-large-numbers-0026","batch_id":"batch-20261014-advance-20261105-r07-weak-law-large-numbers-foundations","language":"zh-Hant","source_mko_ids":["mko-weak-law-large-numbers"],"title_zh":"弱大數律","stem_zh":"IID通用證書、共同有限mean與variance及exact Chebyshev tail。操作=wlln-chebyshev-bound；資料={\"mean\":[0,1],\"variance\":[1,2],\"epsilon\":[1,2],\"n\":20,\"iid_certificate\":\"symbolic_all_finite_subfamilies\"}。請依 exact_ordered_tuple_declared_by_interface 欄序回答。","answer":{"kind":"expression","value":"(0, 1/2, 20, 1/10, 是, probability_upper_bound_not_finite_n_equality)","explanation_zh":"Wave5第五層核對=(0, 1/2, 20, 1/10, 是, probability_upper_bound_not_finite_n_equality)；依完整明示資料獨立重算；independence給Var(sample mean)=sigma squared/n並以forall n大於等於N證依機率收斂；有限樣本或模擬不足，且不宣稱almost sure、CLT或有限n已等於極限。"},"difficulty":{"band":"undergraduate_core","level":1,"skills":["弱大數律"]},"variant":{"family_id":"qf-mod36-wlln-chebyshev-bound","seed":202611057026,"parameters":{"mean":[0,1],"variance":[1,2],"epsilon":[1,2],"n":20,"iid_certificate":"symbolic_all_finite_subfamilies","domain":"Symbolic_iid_Chebyshev_WLLN","operation":"wlln-chebyshev-bound","semantic_template":"qf-mod36-wlln-chebyshev-bound/{\"epsilon\":[1,2],\"iid_certificate\":\"symbolic_all_finite_subfamilies\",\"mean\":[0,1],\"n\":20,\"variance\":[1,2]}"}},"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、有限取樣全稱證明、V與dual典範識別、Hamilton結論、一般continuous-bijection捷徑、統計性質、strong law、CLT、Lean或Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-14","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261014-advance-20261105-r07-weak-law-large-numbers-0027","batch_id":"batch-20261014-advance-20261105-r07-weak-law-large-numbers-foundations","language":"zh-Hant","source_mko_ids":["mko-weak-law-large-numbers"],"title_zh":"弱大數律","stem_zh":"IID通用證書、共同有限mean與variance及exact Chebyshev tail。操作=wlln-chebyshev-bound；資料={\"mean\":[1,2],\"variance\":[2,3],\"epsilon\":[1,3],\"n\":21,\"iid_certificate\":\"symbolic_all_finite_subfamilies\"}。請依 exact_ordered_tuple_declared_by_interface 欄序回答。","answer":{"kind":"expression","value":"(1/2, 1/3, 21, 2/7, 是, probability_upper_bound_not_finite_n_equality)","explanation_zh":"Wave5第五層核對=(1/2, 1/3, 21, 2/7, 是, probability_upper_bound_not_finite_n_equality)；依完整明示資料獨立重算；independence給Var(sample mean)=sigma squared/n並以forall n大於等於N證依機率收斂；有限樣本或模擬不足，且不宣稱almost sure、CLT或有限n已等於極限。"},"difficulty":{"band":"undergraduate_core","level":1,"skills":["弱大數律"]},"variant":{"family_id":"qf-mod36-wlln-chebyshev-bound","seed":202611057027,"parameters":{"mean":[1,2],"variance":[2,3],"epsilon":[1,3],"n":21,"iid_certificate":"symbolic_all_finite_subfamilies","domain":"Symbolic_iid_Chebyshev_WLLN","operation":"wlln-chebyshev-bound","semantic_template":"qf-mod36-wlln-chebyshev-bound/{\"epsilon\":[1,3],\"iid_certificate\":\"symbolic_all_finite_subfamilies\",\"mean\":[1,2],\"n\":21,\"variance\":[2,3]}"}},"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、有限取樣全稱證明、V與dual典範識別、Hamilton結論、一般continuous-bijection捷徑、統計性質、strong law、CLT、Lean或Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-14","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261014-advance-20261105-r07-weak-law-large-numbers-0028","batch_id":"batch-20261014-advance-20261105-r07-weak-law-large-numbers-foundations","language":"zh-Hant","source_mko_ids":["mko-weak-law-large-numbers"],"title_zh":"弱大數律","stem_zh":"IID通用證書、共同有限mean與variance及exact Chebyshev tail。操作=wlln-chebyshev-bound；資料={\"mean\":[2,3],\"variance\":[3,4],\"epsilon\":[1,4],\"n\":22,\"iid_certificate\":\"symbolic_all_finite_subfamilies\"}。請依 exact_ordered_tuple_declared_by_interface 欄序回答。","answer":{"kind":"expression","value":"(2/3, 1/4, 22, 6/11, 是, probability_upper_bound_not_finite_n_equality)","explanation_zh":"Wave5第五層核對=(2/3, 1/4, 22, 6/11, 是, probability_upper_bound_not_finite_n_equality)；依完整明示資料獨立重算；independence給Var(sample mean)=sigma squared/n並以forall n大於等於N證依機率收斂；有限樣本或模擬不足，且不宣稱almost sure、CLT或有限n已等於極限。"},"difficulty":{"band":"undergraduate_core","level":1,"skills":["弱大數律"]},"variant":{"family_id":"qf-mod36-wlln-chebyshev-bound","seed":202611057028,"parameters":{"mean":[2,3],"variance":[3,4],"epsilon":[1,4],"n":22,"iid_certificate":"symbolic_all_finite_subfamilies","domain":"Symbolic_iid_Chebyshev_WLLN","operation":"wlln-chebyshev-bound","semantic_template":"qf-mod36-wlln-chebyshev-bound/{\"epsilon\":[1,4],\"iid_certificate\":\"symbolic_all_finite_subfamilies\",\"mean\":[2,3],\"n\":22,\"variance\":[3,4]}"}},"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、有限取樣全稱證明、V與dual典範識別、Hamilton結論、一般continuous-bijection捷徑、統計性質、strong law、CLT、Lean或Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-14","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261014-advance-20261105-r07-weak-law-large-numbers-0029","batch_id":"batch-20261014-advance-20261105-r07-weak-law-large-numbers-foundations","language":"zh-Hant","source_mko_ids":["mko-weak-law-large-numbers"],"title_zh":"弱大數律","stem_zh":"IID通用證書、共同有限mean與variance及exact Chebyshev tail。操作=wlln-chebyshev-bound；資料={\"mean\":[3,4],\"variance\":[4,5],\"epsilon\":[1,5],\"n\":23,\"iid_certificate\":\"symbolic_all_finite_subfamilies\"}。請依 exact_ordered_tuple_declared_by_interface 欄序回答。","answer":{"kind":"expression","value":"(3/4, 1/5, 23, 20/23, 是, probability_upper_bound_not_finite_n_equality)","explanation_zh":"Wave5第五層核對=(3/4, 1/5, 23, 20/23, 是, probability_upper_bound_not_finite_n_equality)；依完整明示資料獨立重算；independence給Var(sample mean)=sigma squared/n並以forall n大於等於N證依機率收斂；有限樣本或模擬不足，且不宣稱almost sure、CLT或有限n已等於極限。"},"difficulty":{"band":"undergraduate_core","level":1,"skills":["弱大數律"]},"variant":{"family_id":"qf-mod36-wlln-chebyshev-bound","seed":202611057029,"parameters":{"mean":[3,4],"variance":[4,5],"epsilon":[1,5],"n":23,"iid_certificate":"symbolic_all_finite_subfamilies","domain":"Symbolic_iid_Chebyshev_WLLN","operation":"wlln-chebyshev-bound","semantic_template":"qf-mod36-wlln-chebyshev-bound/{\"epsilon\":[1,5],\"iid_certificate\":\"symbolic_all_finite_subfamilies\",\"mean\":[3,4],\"n\":23,\"variance\":[4,5]}"}},"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、有限取樣全稱證明、V與dual典範識別、Hamilton結論、一般continuous-bijection捷徑、統計性質、strong law、CLT、Lean或Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-14","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261014-advance-20261105-r07-weak-law-large-numbers-0030","batch_id":"batch-20261014-advance-20261105-r07-weak-law-large-numbers-foundations","language":"zh-Hant","source_mko_ids":["mko-weak-law-large-numbers"],"title_zh":"弱大數律","stem_zh":"IID通用證書、共同有限mean與variance及exact Chebyshev tail。操作=wlln-chebyshev-bound；資料={\"mean\":[4,5],\"variance\":[5,6],\"epsilon\":[1,6],\"n\":24,\"iid_certificate\":\"symbolic_all_finite_subfamilies\"}。請依 exact_ordered_tuple_declared_by_interface 欄序回答。","answer":{"kind":"expression","value":"(4/5, 1/6, 24, 5/4, 是, probability_upper_bound_not_finite_n_equality)","explanation_zh":"Wave5第五層核對=(4/5, 1/6, 24, 5/4, 是, probability_upper_bound_not_finite_n_equality)；依完整明示資料獨立重算；independence給Var(sample mean)=sigma squared/n並以forall n大於等於N證依機率收斂；有限樣本或模擬不足，且不宣稱almost sure、CLT或有限n已等於極限。"},"difficulty":{"band":"undergraduate_core","level":1,"skills":["弱大數律"]},"variant":{"family_id":"qf-mod36-wlln-chebyshev-bound","seed":202611057030,"parameters":{"mean":[4,5],"variance":[5,6],"epsilon":[1,6],"n":24,"iid_certificate":"symbolic_all_finite_subfamilies","domain":"Symbolic_iid_Chebyshev_WLLN","operation":"wlln-chebyshev-bound","semantic_template":"qf-mod36-wlln-chebyshev-bound/{\"epsilon\":[1,6],\"iid_certificate\":\"symbolic_all_finite_subfamilies\",\"mean\":[4,5],\"n\":24,\"variance\":[5,6]}"}},"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、有限取樣全稱證明、V與dual典範識別、Hamilton結論、一般continuous-bijection捷徑、統計性質、strong law、CLT、Lean或Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-14","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261014-advance-20261105-r07-weak-law-large-numbers-0031","batch_id":"batch-20261014-advance-20261105-r07-weak-law-large-numbers-foundations","language":"zh-Hant","source_mko_ids":["mko-weak-law-large-numbers"],"title_zh":"弱大數律","stem_zh":"IID通用證書、共同有限mean與variance及exact Chebyshev tail。操作=wlln-chebyshev-bound；資料={\"mean\":[5,6],\"variance\":[6,7],\"epsilon\":[1,7],\"n\":25,\"iid_certificate\":\"symbolic_all_finite_subfamilies\"}。請依 exact_ordered_tuple_declared_by_interface 欄序回答。","answer":{"kind":"expression","value":"(5/6, 1/7, 25, 42/25, 是, probability_upper_bound_not_finite_n_equality)","explanation_zh":"Wave5第五層核對=(5/6, 1/7, 25, 42/25, 是, probability_upper_bound_not_finite_n_equality)；依完整明示資料獨立重算；independence給Var(sample mean)=sigma squared/n並以forall n大於等於N證依機率收斂；有限樣本或模擬不足，且不宣稱almost sure、CLT或有限n已等於極限。"},"difficulty":{"band":"undergraduate_core","level":1,"skills":["弱大數律"]},"variant":{"family_id":"qf-mod36-wlln-chebyshev-bound","seed":202611057031,"parameters":{"mean":[5,6],"variance":[6,7],"epsilon":[1,7],"n":25,"iid_certificate":"symbolic_all_finite_subfamilies","domain":"Symbolic_iid_Chebyshev_WLLN","operation":"wlln-chebyshev-bound","semantic_template":"qf-mod36-wlln-chebyshev-bound/{\"epsilon\":[1,7],\"iid_certificate\":\"symbolic_all_finite_subfamilies\",\"mean\":[5,6],\"n\":25,\"variance\":[6,7]}"}},"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、有限取樣全稱證明、V與dual典範識別、Hamilton結論、一般continuous-bijection捷徑、統計性質、strong law、CLT、Lean或Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-14","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261014-advance-20261105-r07-weak-law-large-numbers-0032","batch_id":"batch-20261014-advance-20261105-r07-weak-law-large-numbers-foundations","language":"zh-Hant","source_mko_ids":["mko-weak-law-large-numbers"],"title_zh":"弱大數律","stem_zh":"IID通用證書、共同有限mean與variance及exact Chebyshev tail。操作=wlln-chebyshev-bound；資料={\"mean\":[6,7],\"variance\":[7,8],\"epsilon\":[1,8],\"n\":26,\"iid_certificate\":\"symbolic_all_finite_subfamilies\"}。請依 exact_ordered_tuple_declared_by_interface 欄序回答。","answer":{"kind":"expression","value":"(6/7, 1/8, 26, 28/13, 是, probability_upper_bound_not_finite_n_equality)","explanation_zh":"Wave5第五層核對=(6/7, 1/8, 26, 28/13, 是, probability_upper_bound_not_finite_n_equality)；依完整明示資料獨立重算；independence給Var(sample mean)=sigma squared/n並以forall n大於等於N證依機率收斂；有限樣本或模擬不足，且不宣稱almost sure、CLT或有限n已等於極限。"},"difficulty":{"band":"undergraduate_core","level":1,"skills":["弱大數律"]},"variant":{"family_id":"qf-mod36-wlln-chebyshev-bound","seed":202611057032,"parameters":{"mean":[6,7],"variance":[7,8],"epsilon":[1,8],"n":26,"iid_certificate":"symbolic_all_finite_subfamilies","domain":"Symbolic_iid_Chebyshev_WLLN","operation":"wlln-chebyshev-bound","semantic_template":"qf-mod36-wlln-chebyshev-bound/{\"epsilon\":[1,8],\"iid_certificate\":\"symbolic_all_finite_subfamilies\",\"mean\":[6,7],\"n\":26,\"variance\":[7,8]}"}},"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、有限取樣全稱證明、V與dual典範識別、Hamilton結論、一般continuous-bijection捷徑、統計性質、strong law、CLT、Lean或Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-14","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261014-advance-20261105-r07-weak-law-large-numbers-0033","batch_id":"batch-20261014-advance-20261105-r07-weak-law-large-numbers-foundations","language":"zh-Hant","source_mko_ids":["mko-weak-law-large-numbers"],"title_zh":"弱大數律","stem_zh":"IID通用證書、共同有限mean與variance及exact Chebyshev tail。操作=wlln-chebyshev-bound；資料={\"mean\":[7,8],\"variance\":[8,9],\"epsilon\":[1,9],\"n\":27,\"iid_certificate\":\"symbolic_all_finite_subfamilies\"}。請依 exact_ordered_tuple_declared_by_interface 欄序回答。","answer":{"kind":"expression","value":"(7/8, 1/9, 27, 8/3, 是, probability_upper_bound_not_finite_n_equality)","explanation_zh":"Wave5第五層核對=(7/8, 1/9, 27, 8/3, 是, probability_upper_bound_not_finite_n_equality)；依完整明示資料獨立重算；independence給Var(sample mean)=sigma squared/n並以forall n大於等於N證依機率收斂；有限樣本或模擬不足，且不宣稱almost sure、CLT或有限n已等於極限。"},"difficulty":{"band":"undergraduate_core","level":1,"skills":["弱大數律"]},"variant":{"family_id":"qf-mod36-wlln-chebyshev-bound","seed":202611057033,"parameters":{"mean":[7,8],"variance":[8,9],"epsilon":[1,9],"n":27,"iid_certificate":"symbolic_all_finite_subfamilies","domain":"Symbolic_iid_Chebyshev_WLLN","operation":"wlln-chebyshev-bound","semantic_template":"qf-mod36-wlln-chebyshev-bound/{\"epsilon\":[1,9],\"iid_certificate\":\"symbolic_all_finite_subfamilies\",\"mean\":[7,8],\"n\":27,\"variance\":[8,9]}"}},"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、有限取樣全稱證明、V與dual典範識別、Hamilton結論、一般continuous-bijection捷徑、統計性質、strong law、CLT、Lean或Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-14","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261014-advance-20261105-r07-weak-law-large-numbers-0034","batch_id":"batch-20261014-advance-20261105-r07-weak-law-large-numbers-foundations","language":"zh-Hant","source_mko_ids":["mko-weak-law-large-numbers"],"title_zh":"弱大數律","stem_zh":"IID通用證書、共同有限mean與variance及exact Chebyshev tail。操作=wlln-chebyshev-bound；資料={\"mean\":[8,9],\"variance\":[9,10],\"epsilon\":[1,10],\"n\":28,\"iid_certificate\":\"symbolic_all_finite_subfamilies\"}。請依 exact_ordered_tuple_declared_by_interface 欄序回答。","answer":{"kind":"expression","value":"(8/9, 1/10, 28, 45/14, 是, probability_upper_bound_not_finite_n_equality)","explanation_zh":"Wave5第五層核對=(8/9, 1/10, 28, 45/14, 是, probability_upper_bound_not_finite_n_equality)；依完整明示資料獨立重算；independence給Var(sample mean)=sigma squared/n並以forall n大於等於N證依機率收斂；有限樣本或模擬不足，且不宣稱almost sure、CLT或有限n已等於極限。"},"difficulty":{"band":"undergraduate_core","level":2,"skills":["弱大數律"]},"variant":{"family_id":"qf-mod36-wlln-chebyshev-bound","seed":202611057034,"parameters":{"mean":[8,9],"variance":[9,10],"epsilon":[1,10],"n":28,"iid_certificate":"symbolic_all_finite_subfamilies","domain":"Symbolic_iid_Chebyshev_WLLN","operation":"wlln-chebyshev-bound","semantic_template":"qf-mod36-wlln-chebyshev-bound/{\"epsilon\":[1,10],\"iid_certificate\":\"symbolic_all_finite_subfamilies\",\"mean\":[8,9],\"n\":28,\"variance\":[9,10]}"}},"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、有限取樣全稱證明、V與dual典範識別、Hamilton結論、一般continuous-bijection捷徑、統計性質、strong law、CLT、Lean或Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-14","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261014-advance-20261105-r07-weak-law-large-numbers-0035","batch_id":"batch-20261014-advance-20261105-r07-weak-law-large-numbers-foundations","language":"zh-Hant","source_mko_ids":["mko-weak-law-large-numbers"],"title_zh":"弱大數律","stem_zh":"IID通用證書、共同有限mean與variance及exact Chebyshev tail。操作=wlln-chebyshev-bound；資料={\"mean\":[9,10],\"variance\":[10,11],\"epsilon\":[1,11],\"n\":29,\"iid_certificate\":\"symbolic_all_finite_subfamilies\"}。請依 exact_ordered_tuple_declared_by_interface 欄序回答。","answer":{"kind":"expression","value":"(9/10, 1/11, 29, 110/29, 是, probability_upper_bound_not_finite_n_equality)","explanation_zh":"Wave5第五層核對=(9/10, 1/11, 29, 110/29, 是, probability_upper_bound_not_finite_n_equality)；依完整明示資料獨立重算；independence給Var(sample mean)=sigma squared/n並以forall n大於等於N證依機率收斂；有限樣本或模擬不足，且不宣稱almost sure、CLT或有限n已等於極限。"},"difficulty":{"band":"undergraduate_core","level":2,"skills":["弱大數律"]},"variant":{"family_id":"qf-mod36-wlln-chebyshev-bound","seed":202611057035,"parameters":{"mean":[9,10],"variance":[10,11],"epsilon":[1,11],"n":29,"iid_certificate":"symbolic_all_finite_subfamilies","domain":"Symbolic_iid_Chebyshev_WLLN","operation":"wlln-chebyshev-bound","semantic_template":"qf-mod36-wlln-chebyshev-bound/{\"epsilon\":[1,11],\"iid_certificate\":\"symbolic_all_finite_subfamilies\",\"mean\":[9,10],\"n\":29,\"variance\":[10,11]}"}},"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、有限取樣全稱證明、V與dual典範識別、Hamilton結論、一般continuous-bijection捷徑、統計性質、strong law、CLT、Lean或Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-14","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261014-advance-20261105-r07-weak-law-large-numbers-0036","batch_id":"batch-20261014-advance-20261105-r07-weak-law-large-numbers-foundations","language":"zh-Hant","source_mko_ids":["mko-weak-law-large-numbers"],"title_zh":"弱大數律","stem_zh":"IID通用證書、共同有限mean與variance及exact Chebyshev tail。操作=wlln-chebyshev-bound；資料={\"mean\":[10,11],\"variance\":[11,12],\"epsilon\":[1,12],\"n\":30,\"iid_certificate\":\"symbolic_all_finite_subfamilies\"}。請依 exact_ordered_tuple_declared_by_interface 欄序回答。","answer":{"kind":"expression","value":"(10/11, 1/12, 30, 22/5, 是, probability_upper_bound_not_finite_n_equality)","explanation_zh":"Wave5第五層核對=(10/11, 1/12, 30, 22/5, 是, probability_upper_bound_not_finite_n_equality)；依完整明示資料獨立重算；independence給Var(sample mean)=sigma squared/n並以forall n大於等於N證依機率收斂；有限樣本或模擬不足，且不宣稱almost sure、CLT或有限n已等於極限。"},"difficulty":{"band":"undergraduate_core","level":2,"skills":["弱大數律"]},"variant":{"family_id":"qf-mod36-wlln-chebyshev-bound","seed":202611057036,"parameters":{"mean":[10,11],"variance":[11,12],"epsilon":[1,12],"n":30,"iid_certificate":"symbolic_all_finite_subfamilies","domain":"Symbolic_iid_Chebyshev_WLLN","operation":"wlln-chebyshev-bound","semantic_template":"qf-mod36-wlln-chebyshev-bound/{\"epsilon\":[1,12],\"iid_certificate\":\"symbolic_all_finite_subfamilies\",\"mean\":[10,11],\"n\":30,\"variance\":[11,12]}"}},"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、有限取樣全稱證明、V與dual典範識別、Hamilton結論、一般continuous-bijection捷徑、統計性質、strong law、CLT、Lean或Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-14","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261014-advance-20261105-r07-weak-law-large-numbers-0037","batch_id":"batch-20261014-advance-20261105-r07-weak-law-large-numbers-foundations","language":"zh-Hant","source_mko_ids":["mko-weak-law-large-numbers"],"title_zh":"弱大數律","stem_zh":"IID通用證書、共同有限mean與variance及exact Chebyshev tail。操作=wlln-chebyshev-bound；資料={\"mean\":[11,12],\"variance\":[12,13],\"epsilon\":[1,13],\"n\":31,\"iid_certificate\":\"symbolic_all_finite_subfamilies\"}。請依 exact_ordered_tuple_declared_by_interface 欄序回答。","answer":{"kind":"expression","value":"(11/12, 1/13, 31, 156/31, 是, probability_upper_bound_not_finite_n_equality)","explanation_zh":"Wave5第五層核對=(11/12, 1/13, 31, 156/31, 是, probability_upper_bound_not_finite_n_equality)；依完整明示資料獨立重算；independence給Var(sample mean)=sigma squared/n並以forall n大於等於N證依機率收斂；有限樣本或模擬不足，且不宣稱almost sure、CLT或有限n已等於極限。"},"difficulty":{"band":"undergraduate_core","level":2,"skills":["弱大數律"]},"variant":{"family_id":"qf-mod36-wlln-chebyshev-bound","seed":202611057037,"parameters":{"mean":[11,12],"variance":[12,13],"epsilon":[1,13],"n":31,"iid_certificate":"symbolic_all_finite_subfamilies","domain":"Symbolic_iid_Chebyshev_WLLN","operation":"wlln-chebyshev-bound","semantic_template":"qf-mod36-wlln-chebyshev-bound/{\"epsilon\":[1,13],\"iid_certificate\":\"symbolic_all_finite_subfamilies\",\"mean\":[11,12],\"n\":31,\"variance\":[12,13]}"}},"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、有限取樣全稱證明、V與dual典範識別、Hamilton結論、一般continuous-bijection捷徑、統計性質、strong law、CLT、Lean或Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-14","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261014-advance-20261105-r07-weak-law-large-numbers-0038","batch_id":"batch-20261014-advance-20261105-r07-weak-law-large-numbers-foundations","language":"zh-Hant","source_mko_ids":["mko-weak-law-large-numbers"],"title_zh":"弱大數律","stem_zh":"IID通用證書、共同有限mean與variance及exact Chebyshev tail。操作=wlln-chebyshev-bound；資料={\"mean\":[12,13],\"variance\":[13,14],\"epsilon\":[1,14],\"n\":32,\"iid_certificate\":\"symbolic_all_finite_subfamilies\"}。請依 exact_ordered_tuple_declared_by_interface 欄序回答。","answer":{"kind":"expression","value":"(12/13, 1/14, 32, 91/16, 是, probability_upper_bound_not_finite_n_equality)","explanation_zh":"Wave5第五層核對=(12/13, 1/14, 32, 91/16, 是, probability_upper_bound_not_finite_n_equality)；依完整明示資料獨立重算；independence給Var(sample mean)=sigma squared/n並以forall n大於等於N證依機率收斂；有限樣本或模擬不足，且不宣稱almost sure、CLT或有限n已等於極限。"},"difficulty":{"band":"undergraduate_core","level":2,"skills":["弱大數律"]},"variant":{"family_id":"qf-mod36-wlln-chebyshev-bound","seed":202611057038,"parameters":{"mean":[12,13],"variance":[13,14],"epsilon":[1,14],"n":32,"iid_certificate":"symbolic_all_finite_subfamilies","domain":"Symbolic_iid_Chebyshev_WLLN","operation":"wlln-chebyshev-bound","semantic_template":"qf-mod36-wlln-chebyshev-bound/{\"epsilon\":[1,14],\"iid_certificate\":\"symbolic_all_finite_subfamilies\",\"mean\":[12,13],\"n\":32,\"variance\":[13,14]}"}},"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、有限取樣全稱證明、V與dual典範識別、Hamilton結論、一般continuous-bijection捷徑、統計性質、strong law、CLT、Lean或Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-14","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261014-advance-20261105-r07-weak-law-large-numbers-0039","batch_id":"batch-20261014-advance-20261105-r07-weak-law-large-numbers-foundations","language":"zh-Hant","source_mko_ids":["mko-weak-law-large-numbers"],"title_zh":"弱大數律","stem_zh":"IID通用證書、共同有限mean與variance及exact Chebyshev tail。操作=wlln-chebyshev-bound；資料={\"mean\":[13,14],\"variance\":[14,15],\"epsilon\":[1,15],\"n\":33,\"iid_certificate\":\"symbolic_all_finite_subfamilies\"}。請依 exact_ordered_tuple_declared_by_interface 欄序回答。","answer":{"kind":"expression","value":"(13/14, 1/15, 33, 70/11, 是, probability_upper_bound_not_finite_n_equality)","explanation_zh":"Wave5第五層核對=(13/14, 1/15, 33, 70/11, 是, probability_upper_bound_not_finite_n_equality)；依完整明示資料獨立重算；independence給Var(sample mean)=sigma squared/n並以forall n大於等於N證依機率收斂；有限樣本或模擬不足，且不宣稱almost sure、CLT或有限n已等於極限。"},"difficulty":{"band":"undergraduate_core","level":2,"skills":["弱大數律"]},"variant":{"family_id":"qf-mod36-wlln-chebyshev-bound","seed":202611057039,"parameters":{"mean":[13,14],"variance":[14,15],"epsilon":[1,15],"n":33,"iid_certificate":"symbolic_all_finite_subfamilies","domain":"Symbolic_iid_Chebyshev_WLLN","operation":"wlln-chebyshev-bound","semantic_template":"qf-mod36-wlln-chebyshev-bound/{\"epsilon\":[1,15],\"iid_certificate\":\"symbolic_all_finite_subfamilies\",\"mean\":[13,14],\"n\":33,\"variance\":[14,15]}"}},"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、有限取樣全稱證明、V與dual典範識別、Hamilton結論、一般continuous-bijection捷徑、統計性質、strong law、CLT、Lean或Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-14","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261014-advance-20261105-r07-weak-law-large-numbers-0040","batch_id":"batch-20261014-advance-20261105-r07-weak-law-large-numbers-foundations","language":"zh-Hant","source_mko_ids":["mko-weak-law-large-numbers"],"title_zh":"弱大數律","stem_zh":"IID通用證書、共同有限mean與variance及exact Chebyshev tail。操作=wlln-chebyshev-bound；資料={\"mean\":[14,15],\"variance\":[15,16],\"epsilon\":[1,16],\"n\":34,\"iid_certificate\":\"symbolic_all_finite_subfamilies\"}。請依 exact_ordered_tuple_declared_by_interface 欄序回答。","answer":{"kind":"expression","value":"(14/15, 1/16, 34, 120/17, 是, probability_upper_bound_not_finite_n_equality)","explanation_zh":"Wave5第五層核對=(14/15, 1/16, 34, 120/17, 是, probability_upper_bound_not_finite_n_equality)；依完整明示資料獨立重算；independence給Var(sample mean)=sigma squared/n並以forall n大於等於N證依機率收斂；有限樣本或模擬不足，且不宣稱almost sure、CLT或有限n已等於極限。"},"difficulty":{"band":"undergraduate_core","level":2,"skills":["弱大數律"]},"variant":{"family_id":"qf-mod36-wlln-chebyshev-bound","seed":202611057040,"parameters":{"mean":[14,15],"variance":[15,16],"epsilon":[1,16],"n":34,"iid_certificate":"symbolic_all_finite_subfamilies","domain":"Symbolic_iid_Chebyshev_WLLN","operation":"wlln-chebyshev-bound","semantic_template":"qf-mod36-wlln-chebyshev-bound/{\"epsilon\":[1,16],\"iid_certificate\":\"symbolic_all_finite_subfamilies\",\"mean\":[14,15],\"n\":34,\"variance\":[15,16]}"}},"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、有限取樣全稱證明、V與dual典範識別、Hamilton結論、一般continuous-bijection捷徑、統計性質、strong law、CLT、Lean或Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-14","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261014-advance-20261105-r07-weak-law-large-numbers-0041","batch_id":"batch-20261014-advance-20261105-r07-weak-law-large-numbers-foundations","language":"zh-Hant","source_mko_ids":["mko-weak-law-large-numbers"],"title_zh":"弱大數律","stem_zh":"IID通用證書、共同有限mean與variance及exact Chebyshev tail。操作=wlln-chebyshev-bound；資料={\"mean\":[15,16],\"variance\":[16,17],\"epsilon\":[1,17],\"n\":35,\"iid_certificate\":\"symbolic_all_finite_subfamilies\"}。請依 exact_ordered_tuple_declared_by_interface 欄序回答。","answer":{"kind":"expression","value":"(15/16, 1/17, 35, 272/35, 是, probability_upper_bound_not_finite_n_equality)","explanation_zh":"Wave5第五層核對=(15/16, 1/17, 35, 272/35, 是, probability_upper_bound_not_finite_n_equality)；依完整明示資料獨立重算；independence給Var(sample mean)=sigma squared/n並以forall n大於等於N證依機率收斂；有限樣本或模擬不足，且不宣稱almost sure、CLT或有限n已等於極限。"},"difficulty":{"band":"undergraduate_core","level":2,"skills":["弱大數律"]},"variant":{"family_id":"qf-mod36-wlln-chebyshev-bound","seed":202611057041,"parameters":{"mean":[15,16],"variance":[16,17],"epsilon":[1,17],"n":35,"iid_certificate":"symbolic_all_finite_subfamilies","domain":"Symbolic_iid_Chebyshev_WLLN","operation":"wlln-chebyshev-bound","semantic_template":"qf-mod36-wlln-chebyshev-bound/{\"epsilon\":[1,17],\"iid_certificate\":\"symbolic_all_finite_subfamilies\",\"mean\":[15,16],\"n\":35,\"variance\":[16,17]}"}},"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、有限取樣全稱證明、V與dual典範識別、Hamilton結論、一般continuous-bijection捷徑、統計性質、strong law、CLT、Lean或Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-14","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261014-advance-20261105-r07-weak-law-large-numbers-0042","batch_id":"batch-20261014-advance-20261105-r07-weak-law-large-numbers-foundations","language":"zh-Hant","source_mko_ids":["mko-weak-law-large-numbers"],"title_zh":"弱大數律","stem_zh":"IID通用證書、共同有限mean與variance及exact Chebyshev tail。操作=wlln-chebyshev-bound；資料={\"mean\":[16,17],\"variance\":[17,18],\"epsilon\":[1,18],\"n\":36,\"iid_certificate\":\"symbolic_all_finite_subfamilies\"}。請依 exact_ordered_tuple_declared_by_interface 欄序回答。","answer":{"kind":"expression","value":"(16/17, 1/18, 36, 17/2, 是, probability_upper_bound_not_finite_n_equality)","explanation_zh":"Wave5第五層核對=(16/17, 1/18, 36, 17/2, 是, probability_upper_bound_not_finite_n_equality)；依完整明示資料獨立重算；independence給Var(sample mean)=sigma squared/n並以forall n大於等於N證依機率收斂；有限樣本或模擬不足，且不宣稱almost sure、CLT或有限n已等於極限。"},"difficulty":{"band":"undergraduate_core","level":2,"skills":["弱大數律"]},"variant":{"family_id":"qf-mod36-wlln-chebyshev-bound","seed":202611057042,"parameters":{"mean":[16,17],"variance":[17,18],"epsilon":[1,18],"n":36,"iid_certificate":"symbolic_all_finite_subfamilies","domain":"Symbolic_iid_Chebyshev_WLLN","operation":"wlln-chebyshev-bound","semantic_template":"qf-mod36-wlln-chebyshev-bound/{\"epsilon\":[1,18],\"iid_certificate\":\"symbolic_all_finite_subfamilies\",\"mean\":[16,17],\"n\":36,\"variance\":[17,18]}"}},"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、有限取樣全稱證明、V與dual典範識別、Hamilton結論、一般continuous-bijection捷徑、統計性質、strong law、CLT、Lean或Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-14","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261014-advance-20261105-r07-weak-law-large-numbers-0043","batch_id":"batch-20261014-advance-20261105-r07-weak-law-large-numbers-foundations","language":"zh-Hant","source_mko_ids":["mko-weak-law-large-numbers"],"title_zh":"弱大數律","stem_zh":"IID通用證書、共同有限mean與variance及exact Chebyshev tail。操作=wlln-chebyshev-bound；資料={\"mean\":[17,18],\"variance\":[18,19],\"epsilon\":[1,19],\"n\":37,\"iid_certificate\":\"symbolic_all_finite_subfamilies\"}。請依 exact_ordered_tuple_declared_by_interface 欄序回答。","answer":{"kind":"expression","value":"(17/18, 1/19, 37, 342/37, 是, probability_upper_bound_not_finite_n_equality)","explanation_zh":"Wave5第五層核對=(17/18, 1/19, 37, 342/37, 是, probability_upper_bound_not_finite_n_equality)；依完整明示資料獨立重算；independence給Var(sample mean)=sigma squared/n並以forall n大於等於N證依機率收斂；有限樣本或模擬不足，且不宣稱almost sure、CLT或有限n已等於極限。"},"difficulty":{"band":"undergraduate_core","level":3,"skills":["弱大數律"]},"variant":{"family_id":"qf-mod36-wlln-chebyshev-bound","seed":202611057043,"parameters":{"mean":[17,18],"variance":[18,19],"epsilon":[1,19],"n":37,"iid_certificate":"symbolic_all_finite_subfamilies","domain":"Symbolic_iid_Chebyshev_WLLN","operation":"wlln-chebyshev-bound","semantic_template":"qf-mod36-wlln-chebyshev-bound/{\"epsilon\":[1,19],\"iid_certificate\":\"symbolic_all_finite_subfamilies\",\"mean\":[17,18],\"n\":37,\"variance\":[18,19]}"}},"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、有限取樣全稱證明、V與dual典範識別、Hamilton結論、一般continuous-bijection捷徑、統計性質、strong law、CLT、Lean或Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-14","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261014-advance-20261105-r07-weak-law-large-numbers-0044","batch_id":"batch-20261014-advance-20261105-r07-weak-law-large-numbers-foundations","language":"zh-Hant","source_mko_ids":["mko-weak-law-large-numbers"],"title_zh":"弱大數律","stem_zh":"IID通用證書、共同有限mean與variance及exact Chebyshev tail。操作=wlln-chebyshev-bound；資料={\"mean\":[18,19],\"variance\":[19,20],\"epsilon\":[1,20],\"n\":38,\"iid_certificate\":\"symbolic_all_finite_subfamilies\"}。請依 exact_ordered_tuple_declared_by_interface 欄序回答。","answer":{"kind":"expression","value":"(18/19, 1/20, 38, 10, 是, probability_upper_bound_not_finite_n_equality)","explanation_zh":"Wave5第五層核對=(18/19, 1/20, 38, 10, 是, probability_upper_bound_not_finite_n_equality)；依完整明示資料獨立重算；independence給Var(sample mean)=sigma squared/n並以forall n大於等於N證依機率收斂；有限樣本或模擬不足，且不宣稱almost sure、CLT或有限n已等於極限。"},"difficulty":{"band":"undergraduate_core","level":3,"skills":["弱大數律"]},"variant":{"family_id":"qf-mod36-wlln-chebyshev-bound","seed":202611057044,"parameters":{"mean":[18,19],"variance":[19,20],"epsilon":[1,20],"n":38,"iid_certificate":"symbolic_all_finite_subfamilies","domain":"Symbolic_iid_Chebyshev_WLLN","operation":"wlln-chebyshev-bound","semantic_template":"qf-mod36-wlln-chebyshev-bound/{\"epsilon\":[1,20],\"iid_certificate\":\"symbolic_all_finite_subfamilies\",\"mean\":[18,19],\"n\":38,\"variance\":[19,20]}"}},"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、有限取樣全稱證明、V與dual典範識別、Hamilton結論、一般continuous-bijection捷徑、統計性質、strong law、CLT、Lean或Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-14","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261014-advance-20261105-r07-weak-law-large-numbers-0045","batch_id":"batch-20261014-advance-20261105-r07-weak-law-large-numbers-foundations","language":"zh-Hant","source_mko_ids":["mko-weak-law-large-numbers"],"title_zh":"弱大數律","stem_zh":"IID通用證書、共同有限mean與variance及exact Chebyshev tail。操作=wlln-chebyshev-bound；資料={\"mean\":[19,20],\"variance\":[20,21],\"epsilon\":[1,21],\"n\":39,\"iid_certificate\":\"symbolic_all_finite_subfamilies\"}。請依 exact_ordered_tuple_declared_by_interface 欄序回答。","answer":{"kind":"expression","value":"(19/20, 1/21, 39, 140/13, 是, probability_upper_bound_not_finite_n_equality)","explanation_zh":"Wave5第五層核對=(19/20, 1/21, 39, 140/13, 是, probability_upper_bound_not_finite_n_equality)；依完整明示資料獨立重算；independence給Var(sample mean)=sigma squared/n並以forall n大於等於N證依機率收斂；有限樣本或模擬不足，且不宣稱almost sure、CLT或有限n已等於極限。"},"difficulty":{"band":"undergraduate_core","level":3,"skills":["弱大數律"]},"variant":{"family_id":"qf-mod36-wlln-chebyshev-bound","seed":202611057045,"parameters":{"mean":[19,20],"variance":[20,21],"epsilon":[1,21],"n":39,"iid_certificate":"symbolic_all_finite_subfamilies","domain":"Symbolic_iid_Chebyshev_WLLN","operation":"wlln-chebyshev-bound","semantic_template":"qf-mod36-wlln-chebyshev-bound/{\"epsilon\":[1,21],\"iid_certificate\":\"symbolic_all_finite_subfamilies\",\"mean\":[19,20],\"n\":39,\"variance\":[20,21]}"}},"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、有限取樣全稱證明、V與dual典範識別、Hamilton結論、一般continuous-bijection捷徑、統計性質、strong law、CLT、Lean或Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-14","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261014-advance-20261105-r07-weak-law-large-numbers-0046","batch_id":"batch-20261014-advance-20261105-r07-weak-law-large-numbers-foundations","language":"zh-Hant","source_mko_ids":["mko-weak-law-large-numbers"],"title_zh":"弱大數律","stem_zh":"IID通用證書、共同有限mean與variance及exact Chebyshev tail。操作=wlln-chebyshev-bound；資料={\"mean\":[20,21],\"variance\":[21,22],\"epsilon\":[1,22],\"n\":40,\"iid_certificate\":\"symbolic_all_finite_subfamilies\"}。請依 exact_ordered_tuple_declared_by_interface 欄序回答。","answer":{"kind":"expression","value":"(20/21, 1/22, 40, 231/20, 是, probability_upper_bound_not_finite_n_equality)","explanation_zh":"Wave5第五層核對=(20/21, 1/22, 40, 231/20, 是, probability_upper_bound_not_finite_n_equality)；依完整明示資料獨立重算；independence給Var(sample mean)=sigma squared/n並以forall n大於等於N證依機率收斂；有限樣本或模擬不足，且不宣稱almost sure、CLT或有限n已等於極限。"},"difficulty":{"band":"undergraduate_core","level":3,"skills":["弱大數律"]},"variant":{"family_id":"qf-mod36-wlln-chebyshev-bound","seed":202611057046,"parameters":{"mean":[20,21],"variance":[21,22],"epsilon":[1,22],"n":40,"iid_certificate":"symbolic_all_finite_subfamilies","domain":"Symbolic_iid_Chebyshev_WLLN","operation":"wlln-chebyshev-bound","semantic_template":"qf-mod36-wlln-chebyshev-bound/{\"epsilon\":[1,22],\"iid_certificate\":\"symbolic_all_finite_subfamilies\",\"mean\":[20,21],\"n\":40,\"variance\":[21,22]}"}},"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、有限取樣全稱證明、V與dual典範識別、Hamilton結論、一般continuous-bijection捷徑、統計性質、strong law、CLT、Lean或Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-14","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261014-advance-20261105-r07-weak-law-large-numbers-0047","batch_id":"batch-20261014-advance-20261105-r07-weak-law-large-numbers-foundations","language":"zh-Hant","source_mko_ids":["mko-weak-law-large-numbers"],"title_zh":"弱大數律","stem_zh":"IID通用證書、共同有限mean與variance及exact Chebyshev tail。操作=wlln-chebyshev-bound；資料={\"mean\":[21,22],\"variance\":[22,23],\"epsilon\":[1,23],\"n\":41,\"iid_certificate\":\"symbolic_all_finite_subfamilies\"}。請依 exact_ordered_tuple_declared_by_interface 欄序回答。","answer":{"kind":"expression","value":"(21/22, 1/23, 41, 506/41, 是, probability_upper_bound_not_finite_n_equality)","explanation_zh":"Wave5第五層核對=(21/22, 1/23, 41, 506/41, 是, probability_upper_bound_not_finite_n_equality)；依完整明示資料獨立重算；independence給Var(sample mean)=sigma squared/n並以forall n大於等於N證依機率收斂；有限樣本或模擬不足，且不宣稱almost sure、CLT或有限n已等於極限。"},"difficulty":{"band":"undergraduate_core","level":3,"skills":["弱大數律"]},"variant":{"family_id":"qf-mod36-wlln-chebyshev-bound","seed":202611057047,"parameters":{"mean":[21,22],"variance":[22,23],"epsilon":[1,23],"n":41,"iid_certificate":"symbolic_all_finite_subfamilies","domain":"Symbolic_iid_Chebyshev_WLLN","operation":"wlln-chebyshev-bound","semantic_template":"qf-mod36-wlln-chebyshev-bound/{\"epsilon\":[1,23],\"iid_certificate\":\"symbolic_all_finite_subfamilies\",\"mean\":[21,22],\"n\":41,\"variance\":[22,23]}"}},"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、有限取樣全稱證明、V與dual典範識別、Hamilton結論、一般continuous-bijection捷徑、統計性質、strong law、CLT、Lean或Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-14","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261014-advance-20261105-r07-weak-law-large-numbers-0048","batch_id":"batch-20261014-advance-20261105-r07-weak-law-large-numbers-foundations","language":"zh-Hant","source_mko_ids":["mko-weak-law-large-numbers"],"title_zh":"弱大數律","stem_zh":"IID通用證書、共同有限mean與variance及exact Chebyshev tail。操作=wlln-chebyshev-bound；資料={\"mean\":[22,23],\"variance\":[23,24],\"epsilon\":[1,24],\"n\":42,\"iid_certificate\":\"symbolic_all_finite_subfamilies\"}。請依 exact_ordered_tuple_declared_by_interface 欄序回答。","answer":{"kind":"expression","value":"(22/23, 1/24, 42, 92/7, 是, probability_upper_bound_not_finite_n_equality)","explanation_zh":"Wave5第五層核對=(22/23, 1/24, 42, 92/7, 是, probability_upper_bound_not_finite_n_equality)；依完整明示資料獨立重算；independence給Var(sample mean)=sigma squared/n並以forall n大於等於N證依機率收斂；有限樣本或模擬不足，且不宣稱almost sure、CLT或有限n已等於極限。"},"difficulty":{"band":"undergraduate_core","level":3,"skills":["弱大數律"]},"variant":{"family_id":"qf-mod36-wlln-chebyshev-bound","seed":202611057048,"parameters":{"mean":[22,23],"variance":[23,24],"epsilon":[1,24],"n":42,"iid_certificate":"symbolic_all_finite_subfamilies","domain":"Symbolic_iid_Chebyshev_WLLN","operation":"wlln-chebyshev-bound","semantic_template":"qf-mod36-wlln-chebyshev-bound/{\"epsilon\":[1,24],\"iid_certificate\":\"symbolic_all_finite_subfamilies\",\"mean\":[22,23],\"n\":42,\"variance\":[23,24]}"}},"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、有限取樣全稱證明、V與dual典範識別、Hamilton結論、一般continuous-bijection捷徑、統計性質、strong law、CLT、Lean或Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-14","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261014-advance-20261105-r07-weak-law-large-numbers-0049","batch_id":"batch-20261014-advance-20261105-r07-weak-law-large-numbers-foundations","language":"zh-Hant","source_mko_ids":["mko-weak-law-large-numbers"],"title_zh":"弱大數律","stem_zh":"IID通用證書、共同有限mean與variance及exact Chebyshev tail。操作=wlln-chebyshev-bound；資料={\"mean\":[23,24],\"variance\":[24,25],\"epsilon\":[1,25],\"n\":43,\"iid_certificate\":\"symbolic_all_finite_subfamilies\"}。請依 exact_ordered_tuple_declared_by_interface 欄序回答。","answer":{"kind":"expression","value":"(23/24, 1/25, 43, 600/43, 是, probability_upper_bound_not_finite_n_equality)","explanation_zh":"Wave5第五層核對=(23/24, 1/25, 43, 600/43, 是, probability_upper_bound_not_finite_n_equality)；依完整明示資料獨立重算；independence給Var(sample mean)=sigma squared/n並以forall n大於等於N證依機率收斂；有限樣本或模擬不足，且不宣稱almost sure、CLT或有限n已等於極限。"},"difficulty":{"band":"undergraduate_core","level":3,"skills":["弱大數律"]},"variant":{"family_id":"qf-mod36-wlln-chebyshev-bound","seed":202611057049,"parameters":{"mean":[23,24],"variance":[24,25],"epsilon":[1,25],"n":43,"iid_certificate":"symbolic_all_finite_subfamilies","domain":"Symbolic_iid_Chebyshev_WLLN","operation":"wlln-chebyshev-bound","semantic_template":"qf-mod36-wlln-chebyshev-bound/{\"epsilon\":[1,25],\"iid_certificate\":\"symbolic_all_finite_subfamilies\",\"mean\":[23,24],\"n\":43,\"variance\":[24,25]}"}},"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、有限取樣全稱證明、V與dual典範識別、Hamilton結論、一般continuous-bijection捷徑、統計性質、strong law、CLT、Lean或Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-14","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261014-advance-20261105-r07-weak-law-large-numbers-0050","batch_id":"batch-20261014-advance-20261105-r07-weak-law-large-numbers-foundations","language":"zh-Hant","source_mko_ids":["mko-weak-law-large-numbers"],"title_zh":"弱大數律","stem_zh":"IID通用證書、共同有限mean與variance及exact Chebyshev tail。操作=wlln-chebyshev-bound；資料={\"mean\":[24,25],\"variance\":[25,26],\"epsilon\":[1,26],\"n\":44,\"iid_certificate\":\"symbolic_all_finite_subfamilies\"}。請依 exact_ordered_tuple_declared_by_interface 欄序回答。","answer":{"kind":"expression","value":"(24/25, 1/26, 44, 325/22, 是, probability_upper_bound_not_finite_n_equality)","explanation_zh":"Wave5第五層核對=(24/25, 1/26, 44, 325/22, 是, probability_upper_bound_not_finite_n_equality)；依完整明示資料獨立重算；independence給Var(sample mean)=sigma squared/n並以forall n大於等於N證依機率收斂；有限樣本或模擬不足，且不宣稱almost sure、CLT或有限n已等於極限。"},"difficulty":{"band":"undergraduate_core","level":3,"skills":["弱大數律"]},"variant":{"family_id":"qf-mod36-wlln-chebyshev-bound","seed":202611057050,"parameters":{"mean":[24,25],"variance":[25,26],"epsilon":[1,26],"n":44,"iid_certificate":"symbolic_all_finite_subfamilies","domain":"Symbolic_iid_Chebyshev_WLLN","operation":"wlln-chebyshev-bound","semantic_template":"qf-mod36-wlln-chebyshev-bound/{\"epsilon\":[1,26],\"iid_certificate\":\"symbolic_all_finite_subfamilies\",\"mean\":[24,25],\"n\":44,\"variance\":[25,26]}"}},"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、有限取樣全稱證明、V與dual典範識別、Hamilton結論、一般continuous-bijection捷徑、統計性質、strong law、CLT、Lean或Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-14","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261014-advance-20261105-r07-weak-law-large-numbers-0051","batch_id":"batch-20261014-advance-20261105-r07-weak-law-large-numbers-foundations","language":"zh-Hant","source_mko_ids":["mko-weak-law-large-numbers"],"title_zh":"弱大數律","stem_zh":"IID通用證書、共同有限mean與variance及exact Chebyshev tail。操作=wlln-epsilon-delta-witness；資料={\"mean\":[0,1],\"variance\":[1,2],\"epsilon\":[1,2],\"delta\":[1,10],\"iid_certificate\":\"symbolic_all_finite_subfamilies\"}。請依 exact_ordered_tuple_declared_by_interface 欄序回答。","answer":{"kind":"expression","value":"(1/2, 1/10, 21, 2/21, 是, forall_n_ge_N_monotone_Chebyshev_tail)","explanation_zh":"Wave5第五層核對=(1/2, 1/10, 21, 2/21, 是, forall_n_ge_N_monotone_Chebyshev_tail)；依完整明示資料獨立重算；independence給Var(sample mean)=sigma squared/n並以forall n大於等於N證依機率收斂；有限樣本或模擬不足，且不宣稱almost sure、CLT或有限n已等於極限。"},"difficulty":{"band":"undergraduate_core","level":1,"skills":["弱大數律"]},"variant":{"family_id":"qf-mod36-wlln-epsilon-delta-witness","seed":202611057051,"parameters":{"mean":[0,1],"variance":[1,2],"epsilon":[1,2],"delta":[1,10],"iid_certificate":"symbolic_all_finite_subfamilies","domain":"Symbolic_iid_Chebyshev_WLLN","operation":"wlln-epsilon-delta-witness","semantic_template":"qf-mod36-wlln-epsilon-delta-witness/{\"delta\":[1,10],\"epsilon\":[1,2],\"iid_certificate\":\"symbolic_all_finite_subfamilies\",\"mean\":[0,1],\"variance\":[1,2]}"}},"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、有限取樣全稱證明、V與dual典範識別、Hamilton結論、一般continuous-bijection捷徑、統計性質、strong law、CLT、Lean或Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-14","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261014-advance-20261105-r07-weak-law-large-numbers-0052","batch_id":"batch-20261014-advance-20261105-r07-weak-law-large-numbers-foundations","language":"zh-Hant","source_mko_ids":["mko-weak-law-large-numbers"],"title_zh":"弱大數律","stem_zh":"IID通用證書、共同有限mean與variance及exact Chebyshev tail。操作=wlln-epsilon-delta-witness；資料={\"mean\":[1,2],\"variance\":[2,3],\"epsilon\":[1,3],\"delta\":[1,11],\"iid_certificate\":\"symbolic_all_finite_subfamilies\"}。請依 exact_ordered_tuple_declared_by_interface 欄序回答。","answer":{"kind":"expression","value":"(1/3, 1/11, 67, 6/67, 是, forall_n_ge_N_monotone_Chebyshev_tail)","explanation_zh":"Wave5第五層核對=(1/3, 1/11, 67, 6/67, 是, forall_n_ge_N_monotone_Chebyshev_tail)；依完整明示資料獨立重算；independence給Var(sample mean)=sigma squared/n並以forall n大於等於N證依機率收斂；有限樣本或模擬不足，且不宣稱almost sure、CLT或有限n已等於極限。"},"difficulty":{"band":"undergraduate_core","level":1,"skills":["弱大數律"]},"variant":{"family_id":"qf-mod36-wlln-epsilon-delta-witness","seed":202611057052,"parameters":{"mean":[1,2],"variance":[2,3],"epsilon":[1,3],"delta":[1,11],"iid_certificate":"symbolic_all_finite_subfamilies","domain":"Symbolic_iid_Chebyshev_WLLN","operation":"wlln-epsilon-delta-witness","semantic_template":"qf-mod36-wlln-epsilon-delta-witness/{\"delta\":[1,11],\"epsilon\":[1,3],\"iid_certificate\":\"symbolic_all_finite_subfamilies\",\"mean\":[1,2],\"variance\":[2,3]}"}},"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、有限取樣全稱證明、V與dual典範識別、Hamilton結論、一般continuous-bijection捷徑、統計性質、strong law、CLT、Lean或Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-14","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261014-advance-20261105-r07-weak-law-large-numbers-0053","batch_id":"batch-20261014-advance-20261105-r07-weak-law-large-numbers-foundations","language":"zh-Hant","source_mko_ids":["mko-weak-law-large-numbers"],"title_zh":"弱大數律","stem_zh":"IID通用證書、共同有限mean與variance及exact Chebyshev tail。操作=wlln-epsilon-delta-witness；資料={\"mean\":[2,3],\"variance\":[3,4],\"epsilon\":[1,4],\"delta\":[1,12],\"iid_certificate\":\"symbolic_all_finite_subfamilies\"}。請依 exact_ordered_tuple_declared_by_interface 欄序回答。","answer":{"kind":"expression","value":"(1/4, 1/12, 145, 12/145, 是, forall_n_ge_N_monotone_Chebyshev_tail)","explanation_zh":"Wave5第五層核對=(1/4, 1/12, 145, 12/145, 是, forall_n_ge_N_monotone_Chebyshev_tail)；依完整明示資料獨立重算；independence給Var(sample mean)=sigma squared/n並以forall n大於等於N證依機率收斂；有限樣本或模擬不足，且不宣稱almost sure、CLT或有限n已等於極限。"},"difficulty":{"band":"undergraduate_core","level":1,"skills":["弱大數律"]},"variant":{"family_id":"qf-mod36-wlln-epsilon-delta-witness","seed":202611057053,"parameters":{"mean":[2,3],"variance":[3,4],"epsilon":[1,4],"delta":[1,12],"iid_certificate":"symbolic_all_finite_subfamilies","domain":"Symbolic_iid_Chebyshev_WLLN","operation":"wlln-epsilon-delta-witness","semantic_template":"qf-mod36-wlln-epsilon-delta-witness/{\"delta\":[1,12],\"epsilon\":[1,4],\"iid_certificate\":\"symbolic_all_finite_subfamilies\",\"mean\":[2,3],\"variance\":[3,4]}"}},"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、有限取樣全稱證明、V與dual典範識別、Hamilton結論、一般continuous-bijection捷徑、統計性質、strong law、CLT、Lean或Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-14","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261014-advance-20261105-r07-weak-law-large-numbers-0054","batch_id":"batch-20261014-advance-20261105-r07-weak-law-large-numbers-foundations","language":"zh-Hant","source_mko_ids":["mko-weak-law-large-numbers"],"title_zh":"弱大數律","stem_zh":"IID通用證書、共同有限mean與variance及exact Chebyshev tail。操作=wlln-epsilon-delta-witness；資料={\"mean\":[3,4],\"variance\":[4,5],\"epsilon\":[1,5],\"delta\":[1,13],\"iid_certificate\":\"symbolic_all_finite_subfamilies\"}。請依 exact_ordered_tuple_declared_by_interface 欄序回答。","answer":{"kind":"expression","value":"(1/5, 1/13, 261, 20/261, 是, forall_n_ge_N_monotone_Chebyshev_tail)","explanation_zh":"Wave5第五層核對=(1/5, 1/13, 261, 20/261, 是, forall_n_ge_N_monotone_Chebyshev_tail)；依完整明示資料獨立重算；independence給Var(sample mean)=sigma squared/n並以forall n大於等於N證依機率收斂；有限樣本或模擬不足，且不宣稱almost sure、CLT或有限n已等於極限。"},"difficulty":{"band":"undergraduate_core","level":1,"skills":["弱大數律"]},"variant":{"family_id":"qf-mod36-wlln-epsilon-delta-witness","seed":202611057054,"parameters":{"mean":[3,4],"variance":[4,5],"epsilon":[1,5],"delta":[1,13],"iid_certificate":"symbolic_all_finite_subfamilies","domain":"Symbolic_iid_Chebyshev_WLLN","operation":"wlln-epsilon-delta-witness","semantic_template":"qf-mod36-wlln-epsilon-delta-witness/{\"delta\":[1,13],\"epsilon\":[1,5],\"iid_certificate\":\"symbolic_all_finite_subfamilies\",\"mean\":[3,4],\"variance\":[4,5]}"}},"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、有限取樣全稱證明、V與dual典範識別、Hamilton結論、一般continuous-bijection捷徑、統計性質、strong law、CLT、Lean或Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-14","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261014-advance-20261105-r07-weak-law-large-numbers-0055","batch_id":"batch-20261014-advance-20261105-r07-weak-law-large-numbers-foundations","language":"zh-Hant","source_mko_ids":["mko-weak-law-large-numbers"],"title_zh":"弱大數律","stem_zh":"IID通用證書、共同有限mean與variance及exact Chebyshev tail。操作=wlln-epsilon-delta-witness；資料={\"mean\":[4,5],\"variance\":[5,6],\"epsilon\":[1,6],\"delta\":[1,14],\"iid_certificate\":\"symbolic_all_finite_subfamilies\"}。請依 exact_ordered_tuple_declared_by_interface 欄序回答。","answer":{"kind":"expression","value":"(1/6, 1/14, 421, 30/421, 是, forall_n_ge_N_monotone_Chebyshev_tail)","explanation_zh":"Wave5第五層核對=(1/6, 1/14, 421, 30/421, 是, forall_n_ge_N_monotone_Chebyshev_tail)；依完整明示資料獨立重算；independence給Var(sample mean)=sigma squared/n並以forall n大於等於N證依機率收斂；有限樣本或模擬不足，且不宣稱almost sure、CLT或有限n已等於極限。"},"difficulty":{"band":"undergraduate_core","level":1,"skills":["弱大數律"]},"variant":{"family_id":"qf-mod36-wlln-epsilon-delta-witness","seed":202611057055,"parameters":{"mean":[4,5],"variance":[5,6],"epsilon":[1,6],"delta":[1,14],"iid_certificate":"symbolic_all_finite_subfamilies","domain":"Symbolic_iid_Chebyshev_WLLN","operation":"wlln-epsilon-delta-witness","semantic_template":"qf-mod36-wlln-epsilon-delta-witness/{\"delta\":[1,14],\"epsilon\":[1,6],\"iid_certificate\":\"symbolic_all_finite_subfamilies\",\"mean\":[4,5],\"variance\":[5,6]}"}},"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、有限取樣全稱證明、V與dual典範識別、Hamilton結論、一般continuous-bijection捷徑、統計性質、strong law、CLT、Lean或Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-14","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261014-advance-20261105-r07-weak-law-large-numbers-0056","batch_id":"batch-20261014-advance-20261105-r07-weak-law-large-numbers-foundations","language":"zh-Hant","source_mko_ids":["mko-weak-law-large-numbers"],"title_zh":"弱大數律","stem_zh":"IID通用證書、共同有限mean與variance及exact Chebyshev tail。操作=wlln-epsilon-delta-witness；資料={\"mean\":[5,6],\"variance\":[6,7],\"epsilon\":[1,7],\"delta\":[1,15],\"iid_certificate\":\"symbolic_all_finite_subfamilies\"}。請依 exact_ordered_tuple_declared_by_interface 欄序回答。","answer":{"kind":"expression","value":"(1/7, 1/15, 631, 42/631, 是, forall_n_ge_N_monotone_Chebyshev_tail)","explanation_zh":"Wave5第五層核對=(1/7, 1/15, 631, 42/631, 是, forall_n_ge_N_monotone_Chebyshev_tail)；依完整明示資料獨立重算；independence給Var(sample mean)=sigma squared/n並以forall n大於等於N證依機率收斂；有限樣本或模擬不足，且不宣稱almost sure、CLT或有限n已等於極限。"},"difficulty":{"band":"undergraduate_core","level":1,"skills":["弱大數律"]},"variant":{"family_id":"qf-mod36-wlln-epsilon-delta-witness","seed":202611057056,"parameters":{"mean":[5,6],"variance":[6,7],"epsilon":[1,7],"delta":[1,15],"iid_certificate":"symbolic_all_finite_subfamilies","domain":"Symbolic_iid_Chebyshev_WLLN","operation":"wlln-epsilon-delta-witness","semantic_template":"qf-mod36-wlln-epsilon-delta-witness/{\"delta\":[1,15],\"epsilon\":[1,7],\"iid_certificate\":\"symbolic_all_finite_subfamilies\",\"mean\":[5,6],\"variance\":[6,7]}"}},"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、有限取樣全稱證明、V與dual典範識別、Hamilton結論、一般continuous-bijection捷徑、統計性質、strong law、CLT、Lean或Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-14","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261014-advance-20261105-r07-weak-law-large-numbers-0057","batch_id":"batch-20261014-advance-20261105-r07-weak-law-large-numbers-foundations","language":"zh-Hant","source_mko_ids":["mko-weak-law-large-numbers"],"title_zh":"弱大數律","stem_zh":"IID通用證書、共同有限mean與variance及exact Chebyshev tail。操作=wlln-epsilon-delta-witness；資料={\"mean\":[6,7],\"variance\":[7,8],\"epsilon\":[1,8],\"delta\":[1,16],\"iid_certificate\":\"symbolic_all_finite_subfamilies\"}。請依 exact_ordered_tuple_declared_by_interface 欄序回答。","answer":{"kind":"expression","value":"(1/8, 1/16, 897, 56/897, 是, forall_n_ge_N_monotone_Chebyshev_tail)","explanation_zh":"Wave5第五層核對=(1/8, 1/16, 897, 56/897, 是, forall_n_ge_N_monotone_Chebyshev_tail)；依完整明示資料獨立重算；independence給Var(sample mean)=sigma squared/n並以forall n大於等於N證依機率收斂；有限樣本或模擬不足，且不宣稱almost sure、CLT或有限n已等於極限。"},"difficulty":{"band":"undergraduate_core","level":1,"skills":["弱大數律"]},"variant":{"family_id":"qf-mod36-wlln-epsilon-delta-witness","seed":202611057057,"parameters":{"mean":[6,7],"variance":[7,8],"epsilon":[1,8],"delta":[1,16],"iid_certificate":"symbolic_all_finite_subfamilies","domain":"Symbolic_iid_Chebyshev_WLLN","operation":"wlln-epsilon-delta-witness","semantic_template":"qf-mod36-wlln-epsilon-delta-witness/{\"delta\":[1,16],\"epsilon\":[1,8],\"iid_certificate\":\"symbolic_all_finite_subfamilies\",\"mean\":[6,7],\"variance\":[7,8]}"}},"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、有限取樣全稱證明、V與dual典範識別、Hamilton結論、一般continuous-bijection捷徑、統計性質、strong law、CLT、Lean或Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-14","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261014-advance-20261105-r07-weak-law-large-numbers-0058","batch_id":"batch-20261014-advance-20261105-r07-weak-law-large-numbers-foundations","language":"zh-Hant","source_mko_ids":["mko-weak-law-large-numbers"],"title_zh":"弱大數律","stem_zh":"IID通用證書、共同有限mean與variance及exact Chebyshev tail。操作=wlln-epsilon-delta-witness；資料={\"mean\":[7,8],\"variance\":[8,9],\"epsilon\":[1,9],\"delta\":[1,17],\"iid_certificate\":\"symbolic_all_finite_subfamilies\"}。請依 exact_ordered_tuple_declared_by_interface 欄序回答。","answer":{"kind":"expression","value":"(1/9, 1/17, 1225, 72/1225, 是, forall_n_ge_N_monotone_Chebyshev_tail)","explanation_zh":"Wave5第五層核對=(1/9, 1/17, 1225, 72/1225, 是, forall_n_ge_N_monotone_Chebyshev_tail)；依完整明示資料獨立重算；independence給Var(sample mean)=sigma squared/n並以forall n大於等於N證依機率收斂；有限樣本或模擬不足，且不宣稱almost sure、CLT或有限n已等於極限。"},"difficulty":{"band":"undergraduate_core","level":1,"skills":["弱大數律"]},"variant":{"family_id":"qf-mod36-wlln-epsilon-delta-witness","seed":202611057058,"parameters":{"mean":[7,8],"variance":[8,9],"epsilon":[1,9],"delta":[1,17],"iid_certificate":"symbolic_all_finite_subfamilies","domain":"Symbolic_iid_Chebyshev_WLLN","operation":"wlln-epsilon-delta-witness","semantic_template":"qf-mod36-wlln-epsilon-delta-witness/{\"delta\":[1,17],\"epsilon\":[1,9],\"iid_certificate\":\"symbolic_all_finite_subfamilies\",\"mean\":[7,8],\"variance\":[8,9]}"}},"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、有限取樣全稱證明、V與dual典範識別、Hamilton結論、一般continuous-bijection捷徑、統計性質、strong law、CLT、Lean或Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-14","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261014-advance-20261105-r07-weak-law-large-numbers-0059","batch_id":"batch-20261014-advance-20261105-r07-weak-law-large-numbers-foundations","language":"zh-Hant","source_mko_ids":["mko-weak-law-large-numbers"],"title_zh":"弱大數律","stem_zh":"IID通用證書、共同有限mean與variance及exact Chebyshev tail。操作=wlln-epsilon-delta-witness；資料={\"mean\":[8,9],\"variance\":[9,10],\"epsilon\":[1,10],\"delta\":[1,18],\"iid_certificate\":\"symbolic_all_finite_subfamilies\"}。請依 exact_ordered_tuple_declared_by_interface 欄序回答。","answer":{"kind":"expression","value":"(1/10, 1/18, 1621, 90/1621, 是, forall_n_ge_N_monotone_Chebyshev_tail)","explanation_zh":"Wave5第五層核對=(1/10, 1/18, 1621, 90/1621, 是, forall_n_ge_N_monotone_Chebyshev_tail)；依完整明示資料獨立重算；independence給Var(sample mean)=sigma squared/n並以forall n大於等於N證依機率收斂；有限樣本或模擬不足，且不宣稱almost sure、CLT或有限n已等於極限。"},"difficulty":{"band":"undergraduate_core","level":2,"skills":["弱大數律"]},"variant":{"family_id":"qf-mod36-wlln-epsilon-delta-witness","seed":202611057059,"parameters":{"mean":[8,9],"variance":[9,10],"epsilon":[1,10],"delta":[1,18],"iid_certificate":"symbolic_all_finite_subfamilies","domain":"Symbolic_iid_Chebyshev_WLLN","operation":"wlln-epsilon-delta-witness","semantic_template":"qf-mod36-wlln-epsilon-delta-witness/{\"delta\":[1,18],\"epsilon\":[1,10],\"iid_certificate\":\"symbolic_all_finite_subfamilies\",\"mean\":[8,9],\"variance\":[9,10]}"}},"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、有限取樣全稱證明、V與dual典範識別、Hamilton結論、一般continuous-bijection捷徑、統計性質、strong law、CLT、Lean或Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-14","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261014-advance-20261105-r07-weak-law-large-numbers-0060","batch_id":"batch-20261014-advance-20261105-r07-weak-law-large-numbers-foundations","language":"zh-Hant","source_mko_ids":["mko-weak-law-large-numbers"],"title_zh":"弱大數律","stem_zh":"IID通用證書、共同有限mean與variance及exact Chebyshev tail。操作=wlln-epsilon-delta-witness；資料={\"mean\":[9,10],\"variance\":[10,11],\"epsilon\":[1,11],\"delta\":[1,19],\"iid_certificate\":\"symbolic_all_finite_subfamilies\"}。請依 exact_ordered_tuple_declared_by_interface 欄序回答。","answer":{"kind":"expression","value":"(1/11, 1/19, 2091, 110/2091, 是, forall_n_ge_N_monotone_Chebyshev_tail)","explanation_zh":"Wave5第五層核對=(1/11, 1/19, 2091, 110/2091, 是, forall_n_ge_N_monotone_Chebyshev_tail)；依完整明示資料獨立重算；independence給Var(sample mean)=sigma squared/n並以forall n大於等於N證依機率收斂；有限樣本或模擬不足，且不宣稱almost sure、CLT或有限n已等於極限。"},"difficulty":{"band":"undergraduate_core","level":2,"skills":["弱大數律"]},"variant":{"family_id":"qf-mod36-wlln-epsilon-delta-witness","seed":202611057060,"parameters":{"mean":[9,10],"variance":[10,11],"epsilon":[1,11],"delta":[1,19],"iid_certificate":"symbolic_all_finite_subfamilies","domain":"Symbolic_iid_Chebyshev_WLLN","operation":"wlln-epsilon-delta-witness","semantic_template":"qf-mod36-wlln-epsilon-delta-witness/{\"delta\":[1,19],\"epsilon\":[1,11],\"iid_certificate\":\"symbolic_all_finite_subfamilies\",\"mean\":[9,10],\"variance\":[10,11]}"}},"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、有限取樣全稱證明、V與dual典範識別、Hamilton結論、一般continuous-bijection捷徑、統計性質、strong law、CLT、Lean或Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-14","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261014-advance-20261105-r07-weak-law-large-numbers-0061","batch_id":"batch-20261014-advance-20261105-r07-weak-law-large-numbers-foundations","language":"zh-Hant","source_mko_ids":["mko-weak-law-large-numbers"],"title_zh":"弱大數律","stem_zh":"IID通用證書、共同有限mean與variance及exact Chebyshev tail。操作=wlln-epsilon-delta-witness；資料={\"mean\":[10,11],\"variance\":[11,12],\"epsilon\":[1,12],\"delta\":[1,20],\"iid_certificate\":\"symbolic_all_finite_subfamilies\"}。請依 exact_ordered_tuple_declared_by_interface 欄序回答。","answer":{"kind":"expression","value":"(1/12, 1/20, 2641, 132/2641, 是, forall_n_ge_N_monotone_Chebyshev_tail)","explanation_zh":"Wave5第五層核對=(1/12, 1/20, 2641, 132/2641, 是, forall_n_ge_N_monotone_Chebyshev_tail)；依完整明示資料獨立重算；independence給Var(sample mean)=sigma squared/n並以forall n大於等於N證依機率收斂；有限樣本或模擬不足，且不宣稱almost sure、CLT或有限n已等於極限。"},"difficulty":{"band":"undergraduate_core","level":2,"skills":["弱大數律"]},"variant":{"family_id":"qf-mod36-wlln-epsilon-delta-witness","seed":202611057061,"parameters":{"mean":[10,11],"variance":[11,12],"epsilon":[1,12],"delta":[1,20],"iid_certificate":"symbolic_all_finite_subfamilies","domain":"Symbolic_iid_Chebyshev_WLLN","operation":"wlln-epsilon-delta-witness","semantic_template":"qf-mod36-wlln-epsilon-delta-witness/{\"delta\":[1,20],\"epsilon\":[1,12],\"iid_certificate\":\"symbolic_all_finite_subfamilies\",\"mean\":[10,11],\"variance\":[11,12]}"}},"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、有限取樣全稱證明、V與dual典範識別、Hamilton結論、一般continuous-bijection捷徑、統計性質、strong law、CLT、Lean或Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-14","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261014-advance-20261105-r07-weak-law-large-numbers-0062","batch_id":"batch-20261014-advance-20261105-r07-weak-law-large-numbers-foundations","language":"zh-Hant","source_mko_ids":["mko-weak-law-large-numbers"],"title_zh":"弱大數律","stem_zh":"IID通用證書、共同有限mean與variance及exact Chebyshev tail。操作=wlln-epsilon-delta-witness；資料={\"mean\":[11,12],\"variance\":[12,13],\"epsilon\":[1,13],\"delta\":[1,21],\"iid_certificate\":\"symbolic_all_finite_subfamilies\"}。請依 exact_ordered_tuple_declared_by_interface 欄序回答。","answer":{"kind":"expression","value":"(1/13, 1/21, 3277, 156/3277, 是, forall_n_ge_N_monotone_Chebyshev_tail)","explanation_zh":"Wave5第五層核對=(1/13, 1/21, 3277, 156/3277, 是, forall_n_ge_N_monotone_Chebyshev_tail)；依完整明示資料獨立重算；independence給Var(sample mean)=sigma squared/n並以forall n大於等於N證依機率收斂；有限樣本或模擬不足，且不宣稱almost sure、CLT或有限n已等於極限。"},"difficulty":{"band":"undergraduate_core","level":2,"skills":["弱大數律"]},"variant":{"family_id":"qf-mod36-wlln-epsilon-delta-witness","seed":202611057062,"parameters":{"mean":[11,12],"variance":[12,13],"epsilon":[1,13],"delta":[1,21],"iid_certificate":"symbolic_all_finite_subfamilies","domain":"Symbolic_iid_Chebyshev_WLLN","operation":"wlln-epsilon-delta-witness","semantic_template":"qf-mod36-wlln-epsilon-delta-witness/{\"delta\":[1,21],\"epsilon\":[1,13],\"iid_certificate\":\"symbolic_all_finite_subfamilies\",\"mean\":[11,12],\"variance\":[12,13]}"}},"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、有限取樣全稱證明、V與dual典範識別、Hamilton結論、一般continuous-bijection捷徑、統計性質、strong law、CLT、Lean或Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-14","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261014-advance-20261105-r07-weak-law-large-numbers-0063","batch_id":"batch-20261014-advance-20261105-r07-weak-law-large-numbers-foundations","language":"zh-Hant","source_mko_ids":["mko-weak-law-large-numbers"],"title_zh":"弱大數律","stem_zh":"IID通用證書、共同有限mean與variance及exact Chebyshev tail。操作=wlln-epsilon-delta-witness；資料={\"mean\":[12,13],\"variance\":[13,14],\"epsilon\":[1,14],\"delta\":[1,22],\"iid_certificate\":\"symbolic_all_finite_subfamilies\"}。請依 exact_ordered_tuple_declared_by_interface 欄序回答。","answer":{"kind":"expression","value":"(1/14, 1/22, 4005, 182/4005, 是, forall_n_ge_N_monotone_Chebyshev_tail)","explanation_zh":"Wave5第五層核對=(1/14, 1/22, 4005, 182/4005, 是, forall_n_ge_N_monotone_Chebyshev_tail)；依完整明示資料獨立重算；independence給Var(sample mean)=sigma squared/n並以forall n大於等於N證依機率收斂；有限樣本或模擬不足，且不宣稱almost sure、CLT或有限n已等於極限。"},"difficulty":{"band":"undergraduate_core","level":2,"skills":["弱大數律"]},"variant":{"family_id":"qf-mod36-wlln-epsilon-delta-witness","seed":202611057063,"parameters":{"mean":[12,13],"variance":[13,14],"epsilon":[1,14],"delta":[1,22],"iid_certificate":"symbolic_all_finite_subfamilies","domain":"Symbolic_iid_Chebyshev_WLLN","operation":"wlln-epsilon-delta-witness","semantic_template":"qf-mod36-wlln-epsilon-delta-witness/{\"delta\":[1,22],\"epsilon\":[1,14],\"iid_certificate\":\"symbolic_all_finite_subfamilies\",\"mean\":[12,13],\"variance\":[13,14]}"}},"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、有限取樣全稱證明、V與dual典範識別、Hamilton結論、一般continuous-bijection捷徑、統計性質、strong law、CLT、Lean或Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-14","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261014-advance-20261105-r07-weak-law-large-numbers-0064","batch_id":"batch-20261014-advance-20261105-r07-weak-law-large-numbers-foundations","language":"zh-Hant","source_mko_ids":["mko-weak-law-large-numbers"],"title_zh":"弱大數律","stem_zh":"IID通用證書、共同有限mean與variance及exact Chebyshev tail。操作=wlln-epsilon-delta-witness；資料={\"mean\":[13,14],\"variance\":[14,15],\"epsilon\":[1,15],\"delta\":[1,23],\"iid_certificate\":\"symbolic_all_finite_subfamilies\"}。請依 exact_ordered_tuple_declared_by_interface 欄序回答。","answer":{"kind":"expression","value":"(1/15, 1/23, 4831, 210/4831, 是, forall_n_ge_N_monotone_Chebyshev_tail)","explanation_zh":"Wave5第五層核對=(1/15, 1/23, 4831, 210/4831, 是, forall_n_ge_N_monotone_Chebyshev_tail)；依完整明示資料獨立重算；independence給Var(sample mean)=sigma squared/n並以forall n大於等於N證依機率收斂；有限樣本或模擬不足，且不宣稱almost sure、CLT或有限n已等於極限。"},"difficulty":{"band":"undergraduate_core","level":2,"skills":["弱大數律"]},"variant":{"family_id":"qf-mod36-wlln-epsilon-delta-witness","seed":202611057064,"parameters":{"mean":[13,14],"variance":[14,15],"epsilon":[1,15],"delta":[1,23],"iid_certificate":"symbolic_all_finite_subfamilies","domain":"Symbolic_iid_Chebyshev_WLLN","operation":"wlln-epsilon-delta-witness","semantic_template":"qf-mod36-wlln-epsilon-delta-witness/{\"delta\":[1,23],\"epsilon\":[1,15],\"iid_certificate\":\"symbolic_all_finite_subfamilies\",\"mean\":[13,14],\"variance\":[14,15]}"}},"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、有限取樣全稱證明、V與dual典範識別、Hamilton結論、一般continuous-bijection捷徑、統計性質、strong law、CLT、Lean或Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-14","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261014-advance-20261105-r07-weak-law-large-numbers-0065","batch_id":"batch-20261014-advance-20261105-r07-weak-law-large-numbers-foundations","language":"zh-Hant","source_mko_ids":["mko-weak-law-large-numbers"],"title_zh":"弱大數律","stem_zh":"IID通用證書、共同有限mean與variance及exact Chebyshev tail。操作=wlln-epsilon-delta-witness；資料={\"mean\":[14,15],\"variance\":[15,16],\"epsilon\":[1,16],\"delta\":[1,24],\"iid_certificate\":\"symbolic_all_finite_subfamilies\"}。請依 exact_ordered_tuple_declared_by_interface 欄序回答。","answer":{"kind":"expression","value":"(1/16, 1/24, 5761, 240/5761, 是, forall_n_ge_N_monotone_Chebyshev_tail)","explanation_zh":"Wave5第五層核對=(1/16, 1/24, 5761, 240/5761, 是, forall_n_ge_N_monotone_Chebyshev_tail)；依完整明示資料獨立重算；independence給Var(sample mean)=sigma squared/n並以forall n大於等於N證依機率收斂；有限樣本或模擬不足，且不宣稱almost sure、CLT或有限n已等於極限。"},"difficulty":{"band":"undergraduate_core","level":2,"skills":["弱大數律"]},"variant":{"family_id":"qf-mod36-wlln-epsilon-delta-witness","seed":202611057065,"parameters":{"mean":[14,15],"variance":[15,16],"epsilon":[1,16],"delta":[1,24],"iid_certificate":"symbolic_all_finite_subfamilies","domain":"Symbolic_iid_Chebyshev_WLLN","operation":"wlln-epsilon-delta-witness","semantic_template":"qf-mod36-wlln-epsilon-delta-witness/{\"delta\":[1,24],\"epsilon\":[1,16],\"iid_certificate\":\"symbolic_all_finite_subfamilies\",\"mean\":[14,15],\"variance\":[15,16]}"}},"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、有限取樣全稱證明、V與dual典範識別、Hamilton結論、一般continuous-bijection捷徑、統計性質、strong law、CLT、Lean或Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-14","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261014-advance-20261105-r07-weak-law-large-numbers-0066","batch_id":"batch-20261014-advance-20261105-r07-weak-law-large-numbers-foundations","language":"zh-Hant","source_mko_ids":["mko-weak-law-large-numbers"],"title_zh":"弱大數律","stem_zh":"IID通用證書、共同有限mean與variance及exact Chebyshev tail。操作=wlln-epsilon-delta-witness；資料={\"mean\":[15,16],\"variance\":[16,17],\"epsilon\":[1,17],\"delta\":[1,25],\"iid_certificate\":\"symbolic_all_finite_subfamilies\"}。請依 exact_ordered_tuple_declared_by_interface 欄序回答。","answer":{"kind":"expression","value":"(1/17, 1/25, 6801, 272/6801, 是, forall_n_ge_N_monotone_Chebyshev_tail)","explanation_zh":"Wave5第五層核對=(1/17, 1/25, 6801, 272/6801, 是, forall_n_ge_N_monotone_Chebyshev_tail)；依完整明示資料獨立重算；independence給Var(sample mean)=sigma squared/n並以forall n大於等於N證依機率收斂；有限樣本或模擬不足，且不宣稱almost sure、CLT或有限n已等於極限。"},"difficulty":{"band":"undergraduate_core","level":2,"skills":["弱大數律"]},"variant":{"family_id":"qf-mod36-wlln-epsilon-delta-witness","seed":202611057066,"parameters":{"mean":[15,16],"variance":[16,17],"epsilon":[1,17],"delta":[1,25],"iid_certificate":"symbolic_all_finite_subfamilies","domain":"Symbolic_iid_Chebyshev_WLLN","operation":"wlln-epsilon-delta-witness","semantic_template":"qf-mod36-wlln-epsilon-delta-witness/{\"delta\":[1,25],\"epsilon\":[1,17],\"iid_certificate\":\"symbolic_all_finite_subfamilies\",\"mean\":[15,16],\"variance\":[16,17]}"}},"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、有限取樣全稱證明、V與dual典範識別、Hamilton結論、一般continuous-bijection捷徑、統計性質、strong law、CLT、Lean或Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-14","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261014-advance-20261105-r07-weak-law-large-numbers-0067","batch_id":"batch-20261014-advance-20261105-r07-weak-law-large-numbers-foundations","language":"zh-Hant","source_mko_ids":["mko-weak-law-large-numbers"],"title_zh":"弱大數律","stem_zh":"IID通用證書、共同有限mean與variance及exact Chebyshev tail。操作=wlln-epsilon-delta-witness；資料={\"mean\":[16,17],\"variance\":[17,18],\"epsilon\":[1,18],\"delta\":[1,26],\"iid_certificate\":\"symbolic_all_finite_subfamilies\"}。請依 exact_ordered_tuple_declared_by_interface 欄序回答。","answer":{"kind":"expression","value":"(1/18, 1/26, 7957, 306/7957, 是, forall_n_ge_N_monotone_Chebyshev_tail)","explanation_zh":"Wave5第五層核對=(1/18, 1/26, 7957, 306/7957, 是, forall_n_ge_N_monotone_Chebyshev_tail)；依完整明示資料獨立重算；independence給Var(sample mean)=sigma squared/n並以forall n大於等於N證依機率收斂；有限樣本或模擬不足，且不宣稱almost sure、CLT或有限n已等於極限。"},"difficulty":{"band":"undergraduate_core","level":2,"skills":["弱大數律"]},"variant":{"family_id":"qf-mod36-wlln-epsilon-delta-witness","seed":202611057067,"parameters":{"mean":[16,17],"variance":[17,18],"epsilon":[1,18],"delta":[1,26],"iid_certificate":"symbolic_all_finite_subfamilies","domain":"Symbolic_iid_Chebyshev_WLLN","operation":"wlln-epsilon-delta-witness","semantic_template":"qf-mod36-wlln-epsilon-delta-witness/{\"delta\":[1,26],\"epsilon\":[1,18],\"iid_certificate\":\"symbolic_all_finite_subfamilies\",\"mean\":[16,17],\"variance\":[17,18]}"}},"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、有限取樣全稱證明、V與dual典範識別、Hamilton結論、一般continuous-bijection捷徑、統計性質、strong law、CLT、Lean或Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-14","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261014-advance-20261105-r07-weak-law-large-numbers-0068","batch_id":"batch-20261014-advance-20261105-r07-weak-law-large-numbers-foundations","language":"zh-Hant","source_mko_ids":["mko-weak-law-large-numbers"],"title_zh":"弱大數律","stem_zh":"IID通用證書、共同有限mean與variance及exact Chebyshev tail。操作=wlln-epsilon-delta-witness；資料={\"mean\":[17,18],\"variance\":[18,19],\"epsilon\":[1,19],\"delta\":[1,27],\"iid_certificate\":\"symbolic_all_finite_subfamilies\"}。請依 exact_ordered_tuple_declared_by_interface 欄序回答。","answer":{"kind":"expression","value":"(1/19, 1/27, 9235, 342/9235, 是, forall_n_ge_N_monotone_Chebyshev_tail)","explanation_zh":"Wave5第五層核對=(1/19, 1/27, 9235, 342/9235, 是, forall_n_ge_N_monotone_Chebyshev_tail)；依完整明示資料獨立重算；independence給Var(sample mean)=sigma squared/n並以forall n大於等於N證依機率收斂；有限樣本或模擬不足，且不宣稱almost sure、CLT或有限n已等於極限。"},"difficulty":{"band":"undergraduate_core","level":3,"skills":["弱大數律"]},"variant":{"family_id":"qf-mod36-wlln-epsilon-delta-witness","seed":202611057068,"parameters":{"mean":[17,18],"variance":[18,19],"epsilon":[1,19],"delta":[1,27],"iid_certificate":"symbolic_all_finite_subfamilies","domain":"Symbolic_iid_Chebyshev_WLLN","operation":"wlln-epsilon-delta-witness","semantic_template":"qf-mod36-wlln-epsilon-delta-witness/{\"delta\":[1,27],\"epsilon\":[1,19],\"iid_certificate\":\"symbolic_all_finite_subfamilies\",\"mean\":[17,18],\"variance\":[18,19]}"}},"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、有限取樣全稱證明、V與dual典範識別、Hamilton結論、一般continuous-bijection捷徑、統計性質、strong law、CLT、Lean或Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-14","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261014-advance-20261105-r07-weak-law-large-numbers-0069","batch_id":"batch-20261014-advance-20261105-r07-weak-law-large-numbers-foundations","language":"zh-Hant","source_mko_ids":["mko-weak-law-large-numbers"],"title_zh":"弱大數律","stem_zh":"IID通用證書、共同有限mean與variance及exact Chebyshev tail。操作=wlln-epsilon-delta-witness；資料={\"mean\":[18,19],\"variance\":[19,20],\"epsilon\":[1,20],\"delta\":[1,28],\"iid_certificate\":\"symbolic_all_finite_subfamilies\"}。請依 exact_ordered_tuple_declared_by_interface 欄序回答。","answer":{"kind":"expression","value":"(1/20, 1/28, 10641, 380/10641, 是, forall_n_ge_N_monotone_Chebyshev_tail)","explanation_zh":"Wave5第五層核對=(1/20, 1/28, 10641, 380/10641, 是, forall_n_ge_N_monotone_Chebyshev_tail)；依完整明示資料獨立重算；independence給Var(sample mean)=sigma squared/n並以forall n大於等於N證依機率收斂；有限樣本或模擬不足，且不宣稱almost sure、CLT或有限n已等於極限。"},"difficulty":{"band":"undergraduate_core","level":3,"skills":["弱大數律"]},"variant":{"family_id":"qf-mod36-wlln-epsilon-delta-witness","seed":202611057069,"parameters":{"mean":[18,19],"variance":[19,20],"epsilon":[1,20],"delta":[1,28],"iid_certificate":"symbolic_all_finite_subfamilies","domain":"Symbolic_iid_Chebyshev_WLLN","operation":"wlln-epsilon-delta-witness","semantic_template":"qf-mod36-wlln-epsilon-delta-witness/{\"delta\":[1,28],\"epsilon\":[1,20],\"iid_certificate\":\"symbolic_all_finite_subfamilies\",\"mean\":[18,19],\"variance\":[19,20]}"}},"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、有限取樣全稱證明、V與dual典範識別、Hamilton結論、一般continuous-bijection捷徑、統計性質、strong law、CLT、Lean或Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-14","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261014-advance-20261105-r07-weak-law-large-numbers-0070","batch_id":"batch-20261014-advance-20261105-r07-weak-law-large-numbers-foundations","language":"zh-Hant","source_mko_ids":["mko-weak-law-large-numbers"],"title_zh":"弱大數律","stem_zh":"IID通用證書、共同有限mean與variance及exact Chebyshev tail。操作=wlln-epsilon-delta-witness；資料={\"mean\":[19,20],\"variance\":[20,21],\"epsilon\":[1,21],\"delta\":[1,29],\"iid_certificate\":\"symbolic_all_finite_subfamilies\"}。請依 exact_ordered_tuple_declared_by_interface 欄序回答。","answer":{"kind":"expression","value":"(1/21, 1/29, 12181, 420/12181, 是, forall_n_ge_N_monotone_Chebyshev_tail)","explanation_zh":"Wave5第五層核對=(1/21, 1/29, 12181, 420/12181, 是, forall_n_ge_N_monotone_Chebyshev_tail)；依完整明示資料獨立重算；independence給Var(sample mean)=sigma squared/n並以forall n大於等於N證依機率收斂；有限樣本或模擬不足，且不宣稱almost sure、CLT或有限n已等於極限。"},"difficulty":{"band":"undergraduate_core","level":3,"skills":["弱大數律"]},"variant":{"family_id":"qf-mod36-wlln-epsilon-delta-witness","seed":202611057070,"parameters":{"mean":[19,20],"variance":[20,21],"epsilon":[1,21],"delta":[1,29],"iid_certificate":"symbolic_all_finite_subfamilies","domain":"Symbolic_iid_Chebyshev_WLLN","operation":"wlln-epsilon-delta-witness","semantic_template":"qf-mod36-wlln-epsilon-delta-witness/{\"delta\":[1,29],\"epsilon\":[1,21],\"iid_certificate\":\"symbolic_all_finite_subfamilies\",\"mean\":[19,20],\"variance\":[20,21]}"}},"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、有限取樣全稱證明、V與dual典範識別、Hamilton結論、一般continuous-bijection捷徑、統計性質、strong law、CLT、Lean或Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-14","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261014-advance-20261105-r07-weak-law-large-numbers-0071","batch_id":"batch-20261014-advance-20261105-r07-weak-law-large-numbers-foundations","language":"zh-Hant","source_mko_ids":["mko-weak-law-large-numbers"],"title_zh":"弱大數律","stem_zh":"IID通用證書、共同有限mean與variance及exact Chebyshev tail。操作=wlln-epsilon-delta-witness；資料={\"mean\":[20,21],\"variance\":[21,22],\"epsilon\":[1,22],\"delta\":[1,30],\"iid_certificate\":\"symbolic_all_finite_subfamilies\"}。請依 exact_ordered_tuple_declared_by_interface 欄序回答。","answer":{"kind":"expression","value":"(1/22, 1/30, 13861, 462/13861, 是, forall_n_ge_N_monotone_Chebyshev_tail)","explanation_zh":"Wave5第五層核對=(1/22, 1/30, 13861, 462/13861, 是, forall_n_ge_N_monotone_Chebyshev_tail)；依完整明示資料獨立重算；independence給Var(sample mean)=sigma squared/n並以forall n大於等於N證依機率收斂；有限樣本或模擬不足，且不宣稱almost sure、CLT或有限n已等於極限。"},"difficulty":{"band":"undergraduate_core","level":3,"skills":["弱大數律"]},"variant":{"family_id":"qf-mod36-wlln-epsilon-delta-witness","seed":202611057071,"parameters":{"mean":[20,21],"variance":[21,22],"epsilon":[1,22],"delta":[1,30],"iid_certificate":"symbolic_all_finite_subfamilies","domain":"Symbolic_iid_Chebyshev_WLLN","operation":"wlln-epsilon-delta-witness","semantic_template":"qf-mod36-wlln-epsilon-delta-witness/{\"delta\":[1,30],\"epsilon\":[1,22],\"iid_certificate\":\"symbolic_all_finite_subfamilies\",\"mean\":[20,21],\"variance\":[21,22]}"}},"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、有限取樣全稱證明、V與dual典範識別、Hamilton結論、一般continuous-bijection捷徑、統計性質、strong law、CLT、Lean或Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-14","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261014-advance-20261105-r07-weak-law-large-numbers-0072","batch_id":"batch-20261014-advance-20261105-r07-weak-law-large-numbers-foundations","language":"zh-Hant","source_mko_ids":["mko-weak-law-large-numbers"],"title_zh":"弱大數律","stem_zh":"IID通用證書、共同有限mean與variance及exact Chebyshev tail。操作=wlln-epsilon-delta-witness；資料={\"mean\":[21,22],\"variance\":[22,23],\"epsilon\":[1,23],\"delta\":[1,31],\"iid_certificate\":\"symbolic_all_finite_subfamilies\"}。請依 exact_ordered_tuple_declared_by_interface 欄序回答。","answer":{"kind":"expression","value":"(1/23, 1/31, 15687, 506/15687, 是, forall_n_ge_N_monotone_Chebyshev_tail)","explanation_zh":"Wave5第五層核對=(1/23, 1/31, 15687, 506/15687, 是, forall_n_ge_N_monotone_Chebyshev_tail)；依完整明示資料獨立重算；independence給Var(sample mean)=sigma squared/n並以forall n大於等於N證依機率收斂；有限樣本或模擬不足，且不宣稱almost sure、CLT或有限n已等於極限。"},"difficulty":{"band":"undergraduate_core","level":3,"skills":["弱大數律"]},"variant":{"family_id":"qf-mod36-wlln-epsilon-delta-witness","seed":202611057072,"parameters":{"mean":[21,22],"variance":[22,23],"epsilon":[1,23],"delta":[1,31],"iid_certificate":"symbolic_all_finite_subfamilies","domain":"Symbolic_iid_Chebyshev_WLLN","operation":"wlln-epsilon-delta-witness","semantic_template":"qf-mod36-wlln-epsilon-delta-witness/{\"delta\":[1,31],\"epsilon\":[1,23],\"iid_certificate\":\"symbolic_all_finite_subfamilies\",\"mean\":[21,22],\"variance\":[22,23]}"}},"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、有限取樣全稱證明、V與dual典範識別、Hamilton結論、一般continuous-bijection捷徑、統計性質、strong law、CLT、Lean或Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-14","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261014-advance-20261105-r07-weak-law-large-numbers-0073","batch_id":"batch-20261014-advance-20261105-r07-weak-law-large-numbers-foundations","language":"zh-Hant","source_mko_ids":["mko-weak-law-large-numbers"],"title_zh":"弱大數律","stem_zh":"IID通用證書、共同有限mean與variance及exact Chebyshev tail。操作=wlln-epsilon-delta-witness；資料={\"mean\":[22,23],\"variance\":[23,24],\"epsilon\":[1,24],\"delta\":[1,32],\"iid_certificate\":\"symbolic_all_finite_subfamilies\"}。請依 exact_ordered_tuple_declared_by_interface 欄序回答。","answer":{"kind":"expression","value":"(1/24, 1/32, 17665, 552/17665, 是, forall_n_ge_N_monotone_Chebyshev_tail)","explanation_zh":"Wave5第五層核對=(1/24, 1/32, 17665, 552/17665, 是, forall_n_ge_N_monotone_Chebyshev_tail)；依完整明示資料獨立重算；independence給Var(sample mean)=sigma squared/n並以forall n大於等於N證依機率收斂；有限樣本或模擬不足，且不宣稱almost sure、CLT或有限n已等於極限。"},"difficulty":{"band":"undergraduate_core","level":3,"skills":["弱大數律"]},"variant":{"family_id":"qf-mod36-wlln-epsilon-delta-witness","seed":202611057073,"parameters":{"mean":[22,23],"variance":[23,24],"epsilon":[1,24],"delta":[1,32],"iid_certificate":"symbolic_all_finite_subfamilies","domain":"Symbolic_iid_Chebyshev_WLLN","operation":"wlln-epsilon-delta-witness","semantic_template":"qf-mod36-wlln-epsilon-delta-witness/{\"delta\":[1,32],\"epsilon\":[1,24],\"iid_certificate\":\"symbolic_all_finite_subfamilies\",\"mean\":[22,23],\"variance\":[23,24]}"}},"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、有限取樣全稱證明、V與dual典範識別、Hamilton結論、一般continuous-bijection捷徑、統計性質、strong law、CLT、Lean或Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-14","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261014-advance-20261105-r07-weak-law-large-numbers-0074","batch_id":"batch-20261014-advance-20261105-r07-weak-law-large-numbers-foundations","language":"zh-Hant","source_mko_ids":["mko-weak-law-large-numbers"],"title_zh":"弱大數律","stem_zh":"IID通用證書、共同有限mean與variance及exact Chebyshev tail。操作=wlln-epsilon-delta-witness；資料={\"mean\":[23,24],\"variance\":[24,25],\"epsilon\":[1,25],\"delta\":[1,33],\"iid_certificate\":\"symbolic_all_finite_subfamilies\"}。請依 exact_ordered_tuple_declared_by_interface 欄序回答。","answer":{"kind":"expression","value":"(1/25, 1/33, 19801, 600/19801, 是, forall_n_ge_N_monotone_Chebyshev_tail)","explanation_zh":"Wave5第五層核對=(1/25, 1/33, 19801, 600/19801, 是, forall_n_ge_N_monotone_Chebyshev_tail)；依完整明示資料獨立重算；independence給Var(sample mean)=sigma squared/n並以forall n大於等於N證依機率收斂；有限樣本或模擬不足，且不宣稱almost sure、CLT或有限n已等於極限。"},"difficulty":{"band":"undergraduate_core","level":3,"skills":["弱大數律"]},"variant":{"family_id":"qf-mod36-wlln-epsilon-delta-witness","seed":202611057074,"parameters":{"mean":[23,24],"variance":[24,25],"epsilon":[1,25],"delta":[1,33],"iid_certificate":"symbolic_all_finite_subfamilies","domain":"Symbolic_iid_Chebyshev_WLLN","operation":"wlln-epsilon-delta-witness","semantic_template":"qf-mod36-wlln-epsilon-delta-witness/{\"delta\":[1,33],\"epsilon\":[1,25],\"iid_certificate\":\"symbolic_all_finite_subfamilies\",\"mean\":[23,24],\"variance\":[24,25]}"}},"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、有限取樣全稱證明、V與dual典範識別、Hamilton結論、一般continuous-bijection捷徑、統計性質、strong law、CLT、Lean或Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-14","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261014-advance-20261105-r07-weak-law-large-numbers-0075","batch_id":"batch-20261014-advance-20261105-r07-weak-law-large-numbers-foundations","language":"zh-Hant","source_mko_ids":["mko-weak-law-large-numbers"],"title_zh":"弱大數律","stem_zh":"IID通用證書、共同有限mean與variance及exact Chebyshev tail。操作=wlln-epsilon-delta-witness；資料={\"mean\":[24,25],\"variance\":[25,26],\"epsilon\":[1,26],\"delta\":[1,34],\"iid_certificate\":\"symbolic_all_finite_subfamilies\"}。請依 exact_ordered_tuple_declared_by_interface 欄序回答。","answer":{"kind":"expression","value":"(1/26, 1/34, 22101, 650/22101, 是, forall_n_ge_N_monotone_Chebyshev_tail)","explanation_zh":"Wave5第五層核對=(1/26, 1/34, 22101, 650/22101, 是, forall_n_ge_N_monotone_Chebyshev_tail)；依完整明示資料獨立重算；independence給Var(sample mean)=sigma squared/n並以forall n大於等於N證依機率收斂；有限樣本或模擬不足，且不宣稱almost sure、CLT或有限n已等於極限。"},"difficulty":{"band":"undergraduate_core","level":3,"skills":["弱大數律"]},"variant":{"family_id":"qf-mod36-wlln-epsilon-delta-witness","seed":202611057075,"parameters":{"mean":[24,25],"variance":[25,26],"epsilon":[1,26],"delta":[1,34],"iid_certificate":"symbolic_all_finite_subfamilies","domain":"Symbolic_iid_Chebyshev_WLLN","operation":"wlln-epsilon-delta-witness","semantic_template":"qf-mod36-wlln-epsilon-delta-witness/{\"delta\":[1,34],\"epsilon\":[1,26],\"iid_certificate\":\"symbolic_all_finite_subfamilies\",\"mean\":[24,25],\"variance\":[25,26]}"}},"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、有限取樣全稱證明、V與dual典範識別、Hamilton結論、一般continuous-bijection捷徑、統計性質、strong law、CLT、Lean或Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-14","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261014-advance-20261105-r07-weak-law-large-numbers-0076","batch_id":"batch-20261014-advance-20261105-r07-weak-law-large-numbers-foundations","language":"zh-Hant","source_mko_ids":["mko-weak-law-large-numbers"],"title_zh":"弱大數律","stem_zh":"IID通用證書、共同有限mean與variance及exact Chebyshev tail。操作=wlln-finite-simulation-boundary；資料={\"mean\":[0,1],\"variance\":[1,2],\"epsilon\":[1,2],\"prefix_sample_means\":[[1,2],[2,3],[3,4]],\"iid_certificate\":\"finite_simulation_only\"}。請依 exact_ordered_tuple_declared_by_interface 欄序回答。","answer":{"kind":"expression","value":"(0, 1/2, [1/2, 2/3, 3/4], 否, finite_simulation_not_IID_certificate_or_WLLN_proof)","explanation_zh":"Wave5第五層核對=(0, 1/2, [1/2, 2/3, 3/4], 否, finite_simulation_not_IID_certificate_or_WLLN_proof)；依完整明示資料獨立重算；independence給Var(sample mean)=sigma squared/n並以forall n大於等於N證依機率收斂；有限樣本或模擬不足，且不宣稱almost sure、CLT或有限n已等於極限。"},"difficulty":{"band":"undergraduate_core","level":1,"skills":["弱大數律"]},"variant":{"family_id":"qf-mod36-wlln-finite-simulation-boundary","seed":202611057076,"parameters":{"mean":[0,1],"variance":[1,2],"epsilon":[1,2],"prefix_sample_means":[[1,2],[2,3],[3,4]],"iid_certificate":"finite_simulation_only","domain":"Symbolic_iid_Chebyshev_WLLN","operation":"wlln-finite-simulation-boundary","semantic_template":"qf-mod36-wlln-finite-simulation-boundary/{\"epsilon\":[1,2],\"iid_certificate\":\"finite_simulation_only\",\"mean\":[0,1],\"prefix_sample_means\":[[1,2],[2,3],[3,4]],\"variance\":[1,2]}"}},"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、有限取樣全稱證明、V與dual典範識別、Hamilton結論、一般continuous-bijection捷徑、統計性質、strong law、CLT、Lean或Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-14","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261014-advance-20261105-r07-weak-law-large-numbers-0077","batch_id":"batch-20261014-advance-20261105-r07-weak-law-large-numbers-foundations","language":"zh-Hant","source_mko_ids":["mko-weak-law-large-numbers"],"title_zh":"弱大數律","stem_zh":"IID通用證書、共同有限mean與variance及exact Chebyshev tail。操作=wlln-finite-simulation-boundary；資料={\"mean\":[1,2],\"variance\":[2,3],\"epsilon\":[1,3],\"prefix_sample_means\":[[2,3],[3,4],[4,5]],\"iid_certificate\":\"finite_simulation_only\"}。請依 exact_ordered_tuple_declared_by_interface 欄序回答。","answer":{"kind":"expression","value":"(1/2, 1/3, [2/3, 3/4, 4/5], 否, finite_simulation_not_IID_certificate_or_WLLN_proof)","explanation_zh":"Wave5第五層核對=(1/2, 1/3, [2/3, 3/4, 4/5], 否, finite_simulation_not_IID_certificate_or_WLLN_proof)；依完整明示資料獨立重算；independence給Var(sample mean)=sigma squared/n並以forall n大於等於N證依機率收斂；有限樣本或模擬不足，且不宣稱almost sure、CLT或有限n已等於極限。"},"difficulty":{"band":"undergraduate_core","level":1,"skills":["弱大數律"]},"variant":{"family_id":"qf-mod36-wlln-finite-simulation-boundary","seed":202611057077,"parameters":{"mean":[1,2],"variance":[2,3],"epsilon":[1,3],"prefix_sample_means":[[2,3],[3,4],[4,5]],"iid_certificate":"finite_simulation_only","domain":"Symbolic_iid_Chebyshev_WLLN","operation":"wlln-finite-simulation-boundary","semantic_template":"qf-mod36-wlln-finite-simulation-boundary/{\"epsilon\":[1,3],\"iid_certificate\":\"finite_simulation_only\",\"mean\":[1,2],\"prefix_sample_means\":[[2,3],[3,4],[4,5]],\"variance\":[2,3]}"}},"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、有限取樣全稱證明、V與dual典範識別、Hamilton結論、一般continuous-bijection捷徑、統計性質、strong law、CLT、Lean或Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-14","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261014-advance-20261105-r07-weak-law-large-numbers-0078","batch_id":"batch-20261014-advance-20261105-r07-weak-law-large-numbers-foundations","language":"zh-Hant","source_mko_ids":["mko-weak-law-large-numbers"],"title_zh":"弱大數律","stem_zh":"IID通用證書、共同有限mean與variance及exact Chebyshev tail。操作=wlln-finite-simulation-boundary；資料={\"mean\":[2,3],\"variance\":[3,4],\"epsilon\":[1,4],\"prefix_sample_means\":[[3,4],[4,5],[5,6]],\"iid_certificate\":\"finite_simulation_only\"}。請依 exact_ordered_tuple_declared_by_interface 欄序回答。","answer":{"kind":"expression","value":"(2/3, 1/4, [3/4, 4/5, 5/6], 否, finite_simulation_not_IID_certificate_or_WLLN_proof)","explanation_zh":"Wave5第五層核對=(2/3, 1/4, [3/4, 4/5, 5/6], 否, finite_simulation_not_IID_certificate_or_WLLN_proof)；依完整明示資料獨立重算；independence給Var(sample mean)=sigma squared/n並以forall n大於等於N證依機率收斂；有限樣本或模擬不足，且不宣稱almost sure、CLT或有限n已等於極限。"},"difficulty":{"band":"undergraduate_core","level":1,"skills":["弱大數律"]},"variant":{"family_id":"qf-mod36-wlln-finite-simulation-boundary","seed":202611057078,"parameters":{"mean":[2,3],"variance":[3,4],"epsilon":[1,4],"prefix_sample_means":[[3,4],[4,5],[5,6]],"iid_certificate":"finite_simulation_only","domain":"Symbolic_iid_Chebyshev_WLLN","operation":"wlln-finite-simulation-boundary","semantic_template":"qf-mod36-wlln-finite-simulation-boundary/{\"epsilon\":[1,4],\"iid_certificate\":\"finite_simulation_only\",\"mean\":[2,3],\"prefix_sample_means\":[[3,4],[4,5],[5,6]],\"variance\":[3,4]}"}},"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、有限取樣全稱證明、V與dual典範識別、Hamilton結論、一般continuous-bijection捷徑、統計性質、strong law、CLT、Lean或Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-14","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261014-advance-20261105-r07-weak-law-large-numbers-0079","batch_id":"batch-20261014-advance-20261105-r07-weak-law-large-numbers-foundations","language":"zh-Hant","source_mko_ids":["mko-weak-law-large-numbers"],"title_zh":"弱大數律","stem_zh":"IID通用證書、共同有限mean與variance及exact Chebyshev tail。操作=wlln-finite-simulation-boundary；資料={\"mean\":[3,4],\"variance\":[4,5],\"epsilon\":[1,5],\"prefix_sample_means\":[[4,5],[5,6],[6,7]],\"iid_certificate\":\"finite_simulation_only\"}。請依 exact_ordered_tuple_declared_by_interface 欄序回答。","answer":{"kind":"expression","value":"(3/4, 1/5, [4/5, 5/6, 6/7], 否, finite_simulation_not_IID_certificate_or_WLLN_proof)","explanation_zh":"Wave5第五層核對=(3/4, 1/5, [4/5, 5/6, 6/7], 否, finite_simulation_not_IID_certificate_or_WLLN_proof)；依完整明示資料獨立重算；independence給Var(sample mean)=sigma squared/n並以forall n大於等於N證依機率收斂；有限樣本或模擬不足，且不宣稱almost sure、CLT或有限n已等於極限。"},"difficulty":{"band":"undergraduate_core","level":1,"skills":["弱大數律"]},"variant":{"family_id":"qf-mod36-wlln-finite-simulation-boundary","seed":202611057079,"parameters":{"mean":[3,4],"variance":[4,5],"epsilon":[1,5],"prefix_sample_means":[[4,5],[5,6],[6,7]],"iid_certificate":"finite_simulation_only","domain":"Symbolic_iid_Chebyshev_WLLN","operation":"wlln-finite-simulation-boundary","semantic_template":"qf-mod36-wlln-finite-simulation-boundary/{\"epsilon\":[1,5],\"iid_certificate\":\"finite_simulation_only\",\"mean\":[3,4],\"prefix_sample_means\":[[4,5],[5,6],[6,7]],\"variance\":[4,5]}"}},"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、有限取樣全稱證明、V與dual典範識別、Hamilton結論、一般continuous-bijection捷徑、統計性質、strong law、CLT、Lean或Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-14","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261014-advance-20261105-r07-weak-law-large-numbers-0080","batch_id":"batch-20261014-advance-20261105-r07-weak-law-large-numbers-foundations","language":"zh-Hant","source_mko_ids":["mko-weak-law-large-numbers"],"title_zh":"弱大數律","stem_zh":"IID通用證書、共同有限mean與variance及exact Chebyshev tail。操作=wlln-finite-simulation-boundary；資料={\"mean\":[4,5],\"variance\":[5,6],\"epsilon\":[1,6],\"prefix_sample_means\":[[5,6],[6,7],[7,8]],\"iid_certificate\":\"finite_simulation_only\"}。請依 exact_ordered_tuple_declared_by_interface 欄序回答。","answer":{"kind":"expression","value":"(4/5, 1/6, [5/6, 6/7, 7/8], 否, finite_simulation_not_IID_certificate_or_WLLN_proof)","explanation_zh":"Wave5第五層核對=(4/5, 1/6, [5/6, 6/7, 7/8], 否, finite_simulation_not_IID_certificate_or_WLLN_proof)；依完整明示資料獨立重算；independence給Var(sample mean)=sigma squared/n並以forall n大於等於N證依機率收斂；有限樣本或模擬不足，且不宣稱almost sure、CLT或有限n已等於極限。"},"difficulty":{"band":"undergraduate_core","level":1,"skills":["弱大數律"]},"variant":{"family_id":"qf-mod36-wlln-finite-simulation-boundary","seed":202611057080,"parameters":{"mean":[4,5],"variance":[5,6],"epsilon":[1,6],"prefix_sample_means":[[5,6],[6,7],[7,8]],"iid_certificate":"finite_simulation_only","domain":"Symbolic_iid_Chebyshev_WLLN","operation":"wlln-finite-simulation-boundary","semantic_template":"qf-mod36-wlln-finite-simulation-boundary/{\"epsilon\":[1,6],\"iid_certificate\":\"finite_simulation_only\",\"mean\":[4,5],\"prefix_sample_means\":[[5,6],[6,7],[7,8]],\"variance\":[5,6]}"}},"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、有限取樣全稱證明、V與dual典範識別、Hamilton結論、一般continuous-bijection捷徑、統計性質、strong law、CLT、Lean或Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-14","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261014-advance-20261105-r07-weak-law-large-numbers-0081","batch_id":"batch-20261014-advance-20261105-r07-weak-law-large-numbers-foundations","language":"zh-Hant","source_mko_ids":["mko-weak-law-large-numbers"],"title_zh":"弱大數律","stem_zh":"IID通用證書、共同有限mean與variance及exact Chebyshev tail。操作=wlln-finite-simulation-boundary；資料={\"mean\":[5,6],\"variance\":[6,7],\"epsilon\":[1,7],\"prefix_sample_means\":[[6,7],[7,8],[8,9]],\"iid_certificate\":\"finite_simulation_only\"}。請依 exact_ordered_tuple_declared_by_interface 欄序回答。","answer":{"kind":"expression","value":"(5/6, 1/7, [6/7, 7/8, 8/9], 否, finite_simulation_not_IID_certificate_or_WLLN_proof)","explanation_zh":"Wave5第五層核對=(5/6, 1/7, [6/7, 7/8, 8/9], 否, finite_simulation_not_IID_certificate_or_WLLN_proof)；依完整明示資料獨立重算；independence給Var(sample mean)=sigma squared/n並以forall n大於等於N證依機率收斂；有限樣本或模擬不足，且不宣稱almost sure、CLT或有限n已等於極限。"},"difficulty":{"band":"undergraduate_core","level":1,"skills":["弱大數律"]},"variant":{"family_id":"qf-mod36-wlln-finite-simulation-boundary","seed":202611057081,"parameters":{"mean":[5,6],"variance":[6,7],"epsilon":[1,7],"prefix_sample_means":[[6,7],[7,8],[8,9]],"iid_certificate":"finite_simulation_only","domain":"Symbolic_iid_Chebyshev_WLLN","operation":"wlln-finite-simulation-boundary","semantic_template":"qf-mod36-wlln-finite-simulation-boundary/{\"epsilon\":[1,7],\"iid_certificate\":\"finite_simulation_only\",\"mean\":[5,6],\"prefix_sample_means\":[[6,7],[7,8],[8,9]],\"variance\":[6,7]}"}},"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、有限取樣全稱證明、V與dual典範識別、Hamilton結論、一般continuous-bijection捷徑、統計性質、strong law、CLT、Lean或Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-14","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261014-advance-20261105-r07-weak-law-large-numbers-0082","batch_id":"batch-20261014-advance-20261105-r07-weak-law-large-numbers-foundations","language":"zh-Hant","source_mko_ids":["mko-weak-law-large-numbers"],"title_zh":"弱大數律","stem_zh":"IID通用證書、共同有限mean與variance及exact Chebyshev tail。操作=wlln-finite-simulation-boundary；資料={\"mean\":[6,7],\"variance\":[7,8],\"epsilon\":[1,8],\"prefix_sample_means\":[[7,8],[8,9],[9,10]],\"iid_certificate\":\"finite_simulation_only\"}。請依 exact_ordered_tuple_declared_by_interface 欄序回答。","answer":{"kind":"expression","value":"(6/7, 1/8, [7/8, 8/9, 9/10], 否, finite_simulation_not_IID_certificate_or_WLLN_proof)","explanation_zh":"Wave5第五層核對=(6/7, 1/8, [7/8, 8/9, 9/10], 否, finite_simulation_not_IID_certificate_or_WLLN_proof)；依完整明示資料獨立重算；independence給Var(sample mean)=sigma squared/n並以forall n大於等於N證依機率收斂；有限樣本或模擬不足，且不宣稱almost sure、CLT或有限n已等於極限。"},"difficulty":{"band":"undergraduate_core","level":1,"skills":["弱大數律"]},"variant":{"family_id":"qf-mod36-wlln-finite-simulation-boundary","seed":202611057082,"parameters":{"mean":[6,7],"variance":[7,8],"epsilon":[1,8],"prefix_sample_means":[[7,8],[8,9],[9,10]],"iid_certificate":"finite_simulation_only","domain":"Symbolic_iid_Chebyshev_WLLN","operation":"wlln-finite-simulation-boundary","semantic_template":"qf-mod36-wlln-finite-simulation-boundary/{\"epsilon\":[1,8],\"iid_certificate\":\"finite_simulation_only\",\"mean\":[6,7],\"prefix_sample_means\":[[7,8],[8,9],[9,10]],\"variance\":[7,8]}"}},"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、有限取樣全稱證明、V與dual典範識別、Hamilton結論、一般continuous-bijection捷徑、統計性質、strong law、CLT、Lean或Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-14","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261014-advance-20261105-r07-weak-law-large-numbers-0083","batch_id":"batch-20261014-advance-20261105-r07-weak-law-large-numbers-foundations","language":"zh-Hant","source_mko_ids":["mko-weak-law-large-numbers"],"title_zh":"弱大數律","stem_zh":"IID通用證書、共同有限mean與variance及exact Chebyshev tail。操作=wlln-finite-simulation-boundary；資料={\"mean\":[7,8],\"variance\":[8,9],\"epsilon\":[1,9],\"prefix_sample_means\":[[8,9],[9,10],[10,11]],\"iid_certificate\":\"finite_simulation_only\"}。請依 exact_ordered_tuple_declared_by_interface 欄序回答。","answer":{"kind":"expression","value":"(7/8, 1/9, [8/9, 9/10, 10/11], 否, finite_simulation_not_IID_certificate_or_WLLN_proof)","explanation_zh":"Wave5第五層核對=(7/8, 1/9, [8/9, 9/10, 10/11], 否, finite_simulation_not_IID_certificate_or_WLLN_proof)；依完整明示資料獨立重算；independence給Var(sample mean)=sigma squared/n並以forall n大於等於N證依機率收斂；有限樣本或模擬不足，且不宣稱almost sure、CLT或有限n已等於極限。"},"difficulty":{"band":"undergraduate_core","level":1,"skills":["弱大數律"]},"variant":{"family_id":"qf-mod36-wlln-finite-simulation-boundary","seed":202611057083,"parameters":{"mean":[7,8],"variance":[8,9],"epsilon":[1,9],"prefix_sample_means":[[8,9],[9,10],[10,11]],"iid_certificate":"finite_simulation_only","domain":"Symbolic_iid_Chebyshev_WLLN","operation":"wlln-finite-simulation-boundary","semantic_template":"qf-mod36-wlln-finite-simulation-boundary/{\"epsilon\":[1,9],\"iid_certificate\":\"finite_simulation_only\",\"mean\":[7,8],\"prefix_sample_means\":[[8,9],[9,10],[10,11]],\"variance\":[8,9]}"}},"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、有限取樣全稱證明、V與dual典範識別、Hamilton結論、一般continuous-bijection捷徑、統計性質、strong law、CLT、Lean或Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-14","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261014-advance-20261105-r07-weak-law-large-numbers-0084","batch_id":"batch-20261014-advance-20261105-r07-weak-law-large-numbers-foundations","language":"zh-Hant","source_mko_ids":["mko-weak-law-large-numbers"],"title_zh":"弱大數律","stem_zh":"IID通用證書、共同有限mean與variance及exact Chebyshev tail。操作=wlln-finite-simulation-boundary；資料={\"mean\":[8,9],\"variance\":[9,10],\"epsilon\":[1,10],\"prefix_sample_means\":[[9,10],[10,11],[11,12]],\"iid_certificate\":\"finite_simulation_only\"}。請依 exact_ordered_tuple_declared_by_interface 欄序回答。","answer":{"kind":"expression","value":"(8/9, 1/10, [9/10, 10/11, 11/12], 否, finite_simulation_not_IID_certificate_or_WLLN_proof)","explanation_zh":"Wave5第五層核對=(8/9, 1/10, [9/10, 10/11, 11/12], 否, finite_simulation_not_IID_certificate_or_WLLN_proof)；依完整明示資料獨立重算；independence給Var(sample mean)=sigma squared/n並以forall n大於等於N證依機率收斂；有限樣本或模擬不足，且不宣稱almost sure、CLT或有限n已等於極限。"},"difficulty":{"band":"undergraduate_core","level":2,"skills":["弱大數律"]},"variant":{"family_id":"qf-mod36-wlln-finite-simulation-boundary","seed":202611057084,"parameters":{"mean":[8,9],"variance":[9,10],"epsilon":[1,10],"prefix_sample_means":[[9,10],[10,11],[11,12]],"iid_certificate":"finite_simulation_only","domain":"Symbolic_iid_Chebyshev_WLLN","operation":"wlln-finite-simulation-boundary","semantic_template":"qf-mod36-wlln-finite-simulation-boundary/{\"epsilon\":[1,10],\"iid_certificate\":\"finite_simulation_only\",\"mean\":[8,9],\"prefix_sample_means\":[[9,10],[10,11],[11,12]],\"variance\":[9,10]}"}},"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、有限取樣全稱證明、V與dual典範識別、Hamilton結論、一般continuous-bijection捷徑、統計性質、strong law、CLT、Lean或Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-14","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261014-advance-20261105-r07-weak-law-large-numbers-0085","batch_id":"batch-20261014-advance-20261105-r07-weak-law-large-numbers-foundations","language":"zh-Hant","source_mko_ids":["mko-weak-law-large-numbers"],"title_zh":"弱大數律","stem_zh":"IID通用證書、共同有限mean與variance及exact Chebyshev tail。操作=wlln-finite-simulation-boundary；資料={\"mean\":[9,10],\"variance\":[10,11],\"epsilon\":[1,11],\"prefix_sample_means\":[[10,11],[11,12],[12,13]],\"iid_certificate\":\"finite_simulation_only\"}。請依 exact_ordered_tuple_declared_by_interface 欄序回答。","answer":{"kind":"expression","value":"(9/10, 1/11, [10/11, 11/12, 12/13], 否, finite_simulation_not_IID_certificate_or_WLLN_proof)","explanation_zh":"Wave5第五層核對=(9/10, 1/11, [10/11, 11/12, 12/13], 否, finite_simulation_not_IID_certificate_or_WLLN_proof)；依完整明示資料獨立重算；independence給Var(sample mean)=sigma squared/n並以forall n大於等於N證依機率收斂；有限樣本或模擬不足，且不宣稱almost sure、CLT或有限n已等於極限。"},"difficulty":{"band":"undergraduate_core","level":2,"skills":["弱大數律"]},"variant":{"family_id":"qf-mod36-wlln-finite-simulation-boundary","seed":202611057085,"parameters":{"mean":[9,10],"variance":[10,11],"epsilon":[1,11],"prefix_sample_means":[[10,11],[11,12],[12,13]],"iid_certificate":"finite_simulation_only","domain":"Symbolic_iid_Chebyshev_WLLN","operation":"wlln-finite-simulation-boundary","semantic_template":"qf-mod36-wlln-finite-simulation-boundary/{\"epsilon\":[1,11],\"iid_certificate\":\"finite_simulation_only\",\"mean\":[9,10],\"prefix_sample_means\":[[10,11],[11,12],[12,13]],\"variance\":[10,11]}"}},"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、有限取樣全稱證明、V與dual典範識別、Hamilton結論、一般continuous-bijection捷徑、統計性質、strong law、CLT、Lean或Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-14","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261014-advance-20261105-r07-weak-law-large-numbers-0086","batch_id":"batch-20261014-advance-20261105-r07-weak-law-large-numbers-foundations","language":"zh-Hant","source_mko_ids":["mko-weak-law-large-numbers"],"title_zh":"弱大數律","stem_zh":"IID通用證書、共同有限mean與variance及exact Chebyshev tail。操作=wlln-finite-simulation-boundary；資料={\"mean\":[10,11],\"variance\":[11,12],\"epsilon\":[1,12],\"prefix_sample_means\":[[11,12],[12,13],[13,14]],\"iid_certificate\":\"finite_simulation_only\"}。請依 exact_ordered_tuple_declared_by_interface 欄序回答。","answer":{"kind":"expression","value":"(10/11, 1/12, [11/12, 12/13, 13/14], 否, finite_simulation_not_IID_certificate_or_WLLN_proof)","explanation_zh":"Wave5第五層核對=(10/11, 1/12, [11/12, 12/13, 13/14], 否, finite_simulation_not_IID_certificate_or_WLLN_proof)；依完整明示資料獨立重算；independence給Var(sample mean)=sigma squared/n並以forall n大於等於N證依機率收斂；有限樣本或模擬不足，且不宣稱almost sure、CLT或有限n已等於極限。"},"difficulty":{"band":"undergraduate_core","level":2,"skills":["弱大數律"]},"variant":{"family_id":"qf-mod36-wlln-finite-simulation-boundary","seed":202611057086,"parameters":{"mean":[10,11],"variance":[11,12],"epsilon":[1,12],"prefix_sample_means":[[11,12],[12,13],[13,14]],"iid_certificate":"finite_simulation_only","domain":"Symbolic_iid_Chebyshev_WLLN","operation":"wlln-finite-simulation-boundary","semantic_template":"qf-mod36-wlln-finite-simulation-boundary/{\"epsilon\":[1,12],\"iid_certificate\":\"finite_simulation_only\",\"mean\":[10,11],\"prefix_sample_means\":[[11,12],[12,13],[13,14]],\"variance\":[11,12]}"}},"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、有限取樣全稱證明、V與dual典範識別、Hamilton結論、一般continuous-bijection捷徑、統計性質、strong law、CLT、Lean或Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-14","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261014-advance-20261105-r07-weak-law-large-numbers-0087","batch_id":"batch-20261014-advance-20261105-r07-weak-law-large-numbers-foundations","language":"zh-Hant","source_mko_ids":["mko-weak-law-large-numbers"],"title_zh":"弱大數律","stem_zh":"IID通用證書、共同有限mean與variance及exact Chebyshev tail。操作=wlln-finite-simulation-boundary；資料={\"mean\":[11,12],\"variance\":[12,13],\"epsilon\":[1,13],\"prefix_sample_means\":[[12,13],[13,14],[14,15]],\"iid_certificate\":\"finite_simulation_only\"}。請依 exact_ordered_tuple_declared_by_interface 欄序回答。","answer":{"kind":"expression","value":"(11/12, 1/13, [12/13, 13/14, 14/15], 否, finite_simulation_not_IID_certificate_or_WLLN_proof)","explanation_zh":"Wave5第五層核對=(11/12, 1/13, [12/13, 13/14, 14/15], 否, finite_simulation_not_IID_certificate_or_WLLN_proof)；依完整明示資料獨立重算；independence給Var(sample mean)=sigma squared/n並以forall n大於等於N證依機率收斂；有限樣本或模擬不足，且不宣稱almost sure、CLT或有限n已等於極限。"},"difficulty":{"band":"undergraduate_core","level":2,"skills":["弱大數律"]},"variant":{"family_id":"qf-mod36-wlln-finite-simulation-boundary","seed":202611057087,"parameters":{"mean":[11,12],"variance":[12,13],"epsilon":[1,13],"prefix_sample_means":[[12,13],[13,14],[14,15]],"iid_certificate":"finite_simulation_only","domain":"Symbolic_iid_Chebyshev_WLLN","operation":"wlln-finite-simulation-boundary","semantic_template":"qf-mod36-wlln-finite-simulation-boundary/{\"epsilon\":[1,13],\"iid_certificate\":\"finite_simulation_only\",\"mean\":[11,12],\"prefix_sample_means\":[[12,13],[13,14],[14,15]],\"variance\":[12,13]}"}},"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、有限取樣全稱證明、V與dual典範識別、Hamilton結論、一般continuous-bijection捷徑、統計性質、strong law、CLT、Lean或Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-14","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261014-advance-20261105-r07-weak-law-large-numbers-0088","batch_id":"batch-20261014-advance-20261105-r07-weak-law-large-numbers-foundations","language":"zh-Hant","source_mko_ids":["mko-weak-law-large-numbers"],"title_zh":"弱大數律","stem_zh":"IID通用證書、共同有限mean與variance及exact Chebyshev tail。操作=wlln-finite-simulation-boundary；資料={\"mean\":[12,13],\"variance\":[13,14],\"epsilon\":[1,14],\"prefix_sample_means\":[[13,14],[14,15],[15,16]],\"iid_certificate\":\"finite_simulation_only\"}。請依 exact_ordered_tuple_declared_by_interface 欄序回答。","answer":{"kind":"expression","value":"(12/13, 1/14, [13/14, 14/15, 15/16], 否, finite_simulation_not_IID_certificate_or_WLLN_proof)","explanation_zh":"Wave5第五層核對=(12/13, 1/14, [13/14, 14/15, 15/16], 否, finite_simulation_not_IID_certificate_or_WLLN_proof)；依完整明示資料獨立重算；independence給Var(sample mean)=sigma squared/n並以forall n大於等於N證依機率收斂；有限樣本或模擬不足，且不宣稱almost sure、CLT或有限n已等於極限。"},"difficulty":{"band":"undergraduate_core","level":2,"skills":["弱大數律"]},"variant":{"family_id":"qf-mod36-wlln-finite-simulation-boundary","seed":202611057088,"parameters":{"mean":[12,13],"variance":[13,14],"epsilon":[1,14],"prefix_sample_means":[[13,14],[14,15],[15,16]],"iid_certificate":"finite_simulation_only","domain":"Symbolic_iid_Chebyshev_WLLN","operation":"wlln-finite-simulation-boundary","semantic_template":"qf-mod36-wlln-finite-simulation-boundary/{\"epsilon\":[1,14],\"iid_certificate\":\"finite_simulation_only\",\"mean\":[12,13],\"prefix_sample_means\":[[13,14],[14,15],[15,16]],\"variance\":[13,14]}"}},"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、有限取樣全稱證明、V與dual典範識別、Hamilton結論、一般continuous-bijection捷徑、統計性質、strong law、CLT、Lean或Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-14","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261014-advance-20261105-r07-weak-law-large-numbers-0089","batch_id":"batch-20261014-advance-20261105-r07-weak-law-large-numbers-foundations","language":"zh-Hant","source_mko_ids":["mko-weak-law-large-numbers"],"title_zh":"弱大數律","stem_zh":"IID通用證書、共同有限mean與variance及exact Chebyshev tail。操作=wlln-finite-simulation-boundary；資料={\"mean\":[13,14],\"variance\":[14,15],\"epsilon\":[1,15],\"prefix_sample_means\":[[14,15],[15,16],[16,17]],\"iid_certificate\":\"finite_simulation_only\"}。請依 exact_ordered_tuple_declared_by_interface 欄序回答。","answer":{"kind":"expression","value":"(13/14, 1/15, [14/15, 15/16, 16/17], 否, finite_simulation_not_IID_certificate_or_WLLN_proof)","explanation_zh":"Wave5第五層核對=(13/14, 1/15, [14/15, 15/16, 16/17], 否, finite_simulation_not_IID_certificate_or_WLLN_proof)；依完整明示資料獨立重算；independence給Var(sample mean)=sigma squared/n並以forall n大於等於N證依機率收斂；有限樣本或模擬不足，且不宣稱almost sure、CLT或有限n已等於極限。"},"difficulty":{"band":"undergraduate_core","level":2,"skills":["弱大數律"]},"variant":{"family_id":"qf-mod36-wlln-finite-simulation-boundary","seed":202611057089,"parameters":{"mean":[13,14],"variance":[14,15],"epsilon":[1,15],"prefix_sample_means":[[14,15],[15,16],[16,17]],"iid_certificate":"finite_simulation_only","domain":"Symbolic_iid_Chebyshev_WLLN","operation":"wlln-finite-simulation-boundary","semantic_template":"qf-mod36-wlln-finite-simulation-boundary/{\"epsilon\":[1,15],\"iid_certificate\":\"finite_simulation_only\",\"mean\":[13,14],\"prefix_sample_means\":[[14,15],[15,16],[16,17]],\"variance\":[14,15]}"}},"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、有限取樣全稱證明、V與dual典範識別、Hamilton結論、一般continuous-bijection捷徑、統計性質、strong law、CLT、Lean或Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-14","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261014-advance-20261105-r07-weak-law-large-numbers-0090","batch_id":"batch-20261014-advance-20261105-r07-weak-law-large-numbers-foundations","language":"zh-Hant","source_mko_ids":["mko-weak-law-large-numbers"],"title_zh":"弱大數律","stem_zh":"IID通用證書、共同有限mean與variance及exact Chebyshev tail。操作=wlln-finite-simulation-boundary；資料={\"mean\":[14,15],\"variance\":[15,16],\"epsilon\":[1,16],\"prefix_sample_means\":[[15,16],[16,17],[17,18]],\"iid_certificate\":\"finite_simulation_only\"}。請依 exact_ordered_tuple_declared_by_interface 欄序回答。","answer":{"kind":"expression","value":"(14/15, 1/16, [15/16, 16/17, 17/18], 否, finite_simulation_not_IID_certificate_or_WLLN_proof)","explanation_zh":"Wave5第五層核對=(14/15, 1/16, [15/16, 16/17, 17/18], 否, finite_simulation_not_IID_certificate_or_WLLN_proof)；依完整明示資料獨立重算；independence給Var(sample mean)=sigma squared/n並以forall n大於等於N證依機率收斂；有限樣本或模擬不足，且不宣稱almost sure、CLT或有限n已等於極限。"},"difficulty":{"band":"undergraduate_core","level":2,"skills":["弱大數律"]},"variant":{"family_id":"qf-mod36-wlln-finite-simulation-boundary","seed":202611057090,"parameters":{"mean":[14,15],"variance":[15,16],"epsilon":[1,16],"prefix_sample_means":[[15,16],[16,17],[17,18]],"iid_certificate":"finite_simulation_only","domain":"Symbolic_iid_Chebyshev_WLLN","operation":"wlln-finite-simulation-boundary","semantic_template":"qf-mod36-wlln-finite-simulation-boundary/{\"epsilon\":[1,16],\"iid_certificate\":\"finite_simulation_only\",\"mean\":[14,15],\"prefix_sample_means\":[[15,16],[16,17],[17,18]],\"variance\":[15,16]}"}},"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、有限取樣全稱證明、V與dual典範識別、Hamilton結論、一般continuous-bijection捷徑、統計性質、strong law、CLT、Lean或Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-14","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261014-advance-20261105-r07-weak-law-large-numbers-0091","batch_id":"batch-20261014-advance-20261105-r07-weak-law-large-numbers-foundations","language":"zh-Hant","source_mko_ids":["mko-weak-law-large-numbers"],"title_zh":"弱大數律","stem_zh":"IID通用證書、共同有限mean與variance及exact Chebyshev tail。操作=wlln-finite-simulation-boundary；資料={\"mean\":[15,16],\"variance\":[16,17],\"epsilon\":[1,17],\"prefix_sample_means\":[[16,17],[17,18],[18,19]],\"iid_certificate\":\"finite_simulation_only\"}。請依 exact_ordered_tuple_declared_by_interface 欄序回答。","answer":{"kind":"expression","value":"(15/16, 1/17, [16/17, 17/18, 18/19], 否, finite_simulation_not_IID_certificate_or_WLLN_proof)","explanation_zh":"Wave5第五層核對=(15/16, 1/17, [16/17, 17/18, 18/19], 否, finite_simulation_not_IID_certificate_or_WLLN_proof)；依完整明示資料獨立重算；independence給Var(sample mean)=sigma squared/n並以forall n大於等於N證依機率收斂；有限樣本或模擬不足，且不宣稱almost sure、CLT或有限n已等於極限。"},"difficulty":{"band":"undergraduate_core","level":2,"skills":["弱大數律"]},"variant":{"family_id":"qf-mod36-wlln-finite-simulation-boundary","seed":202611057091,"parameters":{"mean":[15,16],"variance":[16,17],"epsilon":[1,17],"prefix_sample_means":[[16,17],[17,18],[18,19]],"iid_certificate":"finite_simulation_only","domain":"Symbolic_iid_Chebyshev_WLLN","operation":"wlln-finite-simulation-boundary","semantic_template":"qf-mod36-wlln-finite-simulation-boundary/{\"epsilon\":[1,17],\"iid_certificate\":\"finite_simulation_only\",\"mean\":[15,16],\"prefix_sample_means\":[[16,17],[17,18],[18,19]],\"variance\":[16,17]}"}},"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、有限取樣全稱證明、V與dual典範識別、Hamilton結論、一般continuous-bijection捷徑、統計性質、strong law、CLT、Lean或Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-14","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261014-advance-20261105-r07-weak-law-large-numbers-0092","batch_id":"batch-20261014-advance-20261105-r07-weak-law-large-numbers-foundations","language":"zh-Hant","source_mko_ids":["mko-weak-law-large-numbers"],"title_zh":"弱大數律","stem_zh":"IID通用證書、共同有限mean與variance及exact Chebyshev tail。操作=wlln-finite-simulation-boundary；資料={\"mean\":[16,17],\"variance\":[17,18],\"epsilon\":[1,18],\"prefix_sample_means\":[[17,18],[18,19],[19,20]],\"iid_certificate\":\"finite_simulation_only\"}。請依 exact_ordered_tuple_declared_by_interface 欄序回答。","answer":{"kind":"expression","value":"(16/17, 1/18, [17/18, 18/19, 19/20], 否, finite_simulation_not_IID_certificate_or_WLLN_proof)","explanation_zh":"Wave5第五層核對=(16/17, 1/18, [17/18, 18/19, 19/20], 否, finite_simulation_not_IID_certificate_or_WLLN_proof)；依完整明示資料獨立重算；independence給Var(sample mean)=sigma squared/n並以forall n大於等於N證依機率收斂；有限樣本或模擬不足，且不宣稱almost sure、CLT或有限n已等於極限。"},"difficulty":{"band":"undergraduate_core","level":2,"skills":["弱大數律"]},"variant":{"family_id":"qf-mod36-wlln-finite-simulation-boundary","seed":202611057092,"parameters":{"mean":[16,17],"variance":[17,18],"epsilon":[1,18],"prefix_sample_means":[[17,18],[18,19],[19,20]],"iid_certificate":"finite_simulation_only","domain":"Symbolic_iid_Chebyshev_WLLN","operation":"wlln-finite-simulation-boundary","semantic_template":"qf-mod36-wlln-finite-simulation-boundary/{\"epsilon\":[1,18],\"iid_certificate\":\"finite_simulation_only\",\"mean\":[16,17],\"prefix_sample_means\":[[17,18],[18,19],[19,20]],\"variance\":[17,18]}"}},"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、有限取樣全稱證明、V與dual典範識別、Hamilton結論、一般continuous-bijection捷徑、統計性質、strong law、CLT、Lean或Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-14","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261014-advance-20261105-r07-weak-law-large-numbers-0093","batch_id":"batch-20261014-advance-20261105-r07-weak-law-large-numbers-foundations","language":"zh-Hant","source_mko_ids":["mko-weak-law-large-numbers"],"title_zh":"弱大數律","stem_zh":"IID通用證書、共同有限mean與variance及exact Chebyshev tail。操作=wlln-finite-simulation-boundary；資料={\"mean\":[17,18],\"variance\":[18,19],\"epsilon\":[1,19],\"prefix_sample_means\":[[18,19],[19,20],[20,21]],\"iid_certificate\":\"finite_simulation_only\"}。請依 exact_ordered_tuple_declared_by_interface 欄序回答。","answer":{"kind":"expression","value":"(17/18, 1/19, [18/19, 19/20, 20/21], 否, finite_simulation_not_IID_certificate_or_WLLN_proof)","explanation_zh":"Wave5第五層核對=(17/18, 1/19, [18/19, 19/20, 20/21], 否, finite_simulation_not_IID_certificate_or_WLLN_proof)；依完整明示資料獨立重算；independence給Var(sample mean)=sigma squared/n並以forall n大於等於N證依機率收斂；有限樣本或模擬不足，且不宣稱almost sure、CLT或有限n已等於極限。"},"difficulty":{"band":"undergraduate_core","level":3,"skills":["弱大數律"]},"variant":{"family_id":"qf-mod36-wlln-finite-simulation-boundary","seed":202611057093,"parameters":{"mean":[17,18],"variance":[18,19],"epsilon":[1,19],"prefix_sample_means":[[18,19],[19,20],[20,21]],"iid_certificate":"finite_simulation_only","domain":"Symbolic_iid_Chebyshev_WLLN","operation":"wlln-finite-simulation-boundary","semantic_template":"qf-mod36-wlln-finite-simulation-boundary/{\"epsilon\":[1,19],\"iid_certificate\":\"finite_simulation_only\",\"mean\":[17,18],\"prefix_sample_means\":[[18,19],[19,20],[20,21]],\"variance\":[18,19]}"}},"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、有限取樣全稱證明、V與dual典範識別、Hamilton結論、一般continuous-bijection捷徑、統計性質、strong law、CLT、Lean或Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-14","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261014-advance-20261105-r07-weak-law-large-numbers-0094","batch_id":"batch-20261014-advance-20261105-r07-weak-law-large-numbers-foundations","language":"zh-Hant","source_mko_ids":["mko-weak-law-large-numbers"],"title_zh":"弱大數律","stem_zh":"IID通用證書、共同有限mean與variance及exact Chebyshev tail。操作=wlln-finite-simulation-boundary；資料={\"mean\":[18,19],\"variance\":[19,20],\"epsilon\":[1,20],\"prefix_sample_means\":[[19,20],[20,21],[21,22]],\"iid_certificate\":\"finite_simulation_only\"}。請依 exact_ordered_tuple_declared_by_interface 欄序回答。","answer":{"kind":"expression","value":"(18/19, 1/20, [19/20, 20/21, 21/22], 否, finite_simulation_not_IID_certificate_or_WLLN_proof)","explanation_zh":"Wave5第五層核對=(18/19, 1/20, [19/20, 20/21, 21/22], 否, finite_simulation_not_IID_certificate_or_WLLN_proof)；依完整明示資料獨立重算；independence給Var(sample mean)=sigma squared/n並以forall n大於等於N證依機率收斂；有限樣本或模擬不足，且不宣稱almost sure、CLT或有限n已等於極限。"},"difficulty":{"band":"undergraduate_core","level":3,"skills":["弱大數律"]},"variant":{"family_id":"qf-mod36-wlln-finite-simulation-boundary","seed":202611057094,"parameters":{"mean":[18,19],"variance":[19,20],"epsilon":[1,20],"prefix_sample_means":[[19,20],[20,21],[21,22]],"iid_certificate":"finite_simulation_only","domain":"Symbolic_iid_Chebyshev_WLLN","operation":"wlln-finite-simulation-boundary","semantic_template":"qf-mod36-wlln-finite-simulation-boundary/{\"epsilon\":[1,20],\"iid_certificate\":\"finite_simulation_only\",\"mean\":[18,19],\"prefix_sample_means\":[[19,20],[20,21],[21,22]],\"variance\":[19,20]}"}},"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、有限取樣全稱證明、V與dual典範識別、Hamilton結論、一般continuous-bijection捷徑、統計性質、strong law、CLT、Lean或Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-14","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261014-advance-20261105-r07-weak-law-large-numbers-0095","batch_id":"batch-20261014-advance-20261105-r07-weak-law-large-numbers-foundations","language":"zh-Hant","source_mko_ids":["mko-weak-law-large-numbers"],"title_zh":"弱大數律","stem_zh":"IID通用證書、共同有限mean與variance及exact Chebyshev tail。操作=wlln-finite-simulation-boundary；資料={\"mean\":[19,20],\"variance\":[20,21],\"epsilon\":[1,21],\"prefix_sample_means\":[[20,21],[21,22],[22,23]],\"iid_certificate\":\"finite_simulation_only\"}。請依 exact_ordered_tuple_declared_by_interface 欄序回答。","answer":{"kind":"expression","value":"(19/20, 1/21, [20/21, 21/22, 22/23], 否, finite_simulation_not_IID_certificate_or_WLLN_proof)","explanation_zh":"Wave5第五層核對=(19/20, 1/21, [20/21, 21/22, 22/23], 否, finite_simulation_not_IID_certificate_or_WLLN_proof)；依完整明示資料獨立重算；independence給Var(sample mean)=sigma squared/n並以forall n大於等於N證依機率收斂；有限樣本或模擬不足，且不宣稱almost sure、CLT或有限n已等於極限。"},"difficulty":{"band":"undergraduate_core","level":3,"skills":["弱大數律"]},"variant":{"family_id":"qf-mod36-wlln-finite-simulation-boundary","seed":202611057095,"parameters":{"mean":[19,20],"variance":[20,21],"epsilon":[1,21],"prefix_sample_means":[[20,21],[21,22],[22,23]],"iid_certificate":"finite_simulation_only","domain":"Symbolic_iid_Chebyshev_WLLN","operation":"wlln-finite-simulation-boundary","semantic_template":"qf-mod36-wlln-finite-simulation-boundary/{\"epsilon\":[1,21],\"iid_certificate\":\"finite_simulation_only\",\"mean\":[19,20],\"prefix_sample_means\":[[20,21],[21,22],[22,23]],\"variance\":[20,21]}"}},"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、有限取樣全稱證明、V與dual典範識別、Hamilton結論、一般continuous-bijection捷徑、統計性質、strong law、CLT、Lean或Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-14","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261014-advance-20261105-r07-weak-law-large-numbers-0096","batch_id":"batch-20261014-advance-20261105-r07-weak-law-large-numbers-foundations","language":"zh-Hant","source_mko_ids":["mko-weak-law-large-numbers"],"title_zh":"弱大數律","stem_zh":"IID通用證書、共同有限mean與variance及exact Chebyshev tail。操作=wlln-finite-simulation-boundary；資料={\"mean\":[20,21],\"variance\":[21,22],\"epsilon\":[1,22],\"prefix_sample_means\":[[21,22],[22,23],[23,24]],\"iid_certificate\":\"finite_simulation_only\"}。請依 exact_ordered_tuple_declared_by_interface 欄序回答。","answer":{"kind":"expression","value":"(20/21, 1/22, [21/22, 22/23, 23/24], 否, finite_simulation_not_IID_certificate_or_WLLN_proof)","explanation_zh":"Wave5第五層核對=(20/21, 1/22, [21/22, 22/23, 23/24], 否, finite_simulation_not_IID_certificate_or_WLLN_proof)；依完整明示資料獨立重算；independence給Var(sample mean)=sigma squared/n並以forall n大於等於N證依機率收斂；有限樣本或模擬不足，且不宣稱almost sure、CLT或有限n已等於極限。"},"difficulty":{"band":"undergraduate_core","level":3,"skills":["弱大數律"]},"variant":{"family_id":"qf-mod36-wlln-finite-simulation-boundary","seed":202611057096,"parameters":{"mean":[20,21],"variance":[21,22],"epsilon":[1,22],"prefix_sample_means":[[21,22],[22,23],[23,24]],"iid_certificate":"finite_simulation_only","domain":"Symbolic_iid_Chebyshev_WLLN","operation":"wlln-finite-simulation-boundary","semantic_template":"qf-mod36-wlln-finite-simulation-boundary/{\"epsilon\":[1,22],\"iid_certificate\":\"finite_simulation_only\",\"mean\":[20,21],\"prefix_sample_means\":[[21,22],[22,23],[23,24]],\"variance\":[21,22]}"}},"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、有限取樣全稱證明、V與dual典範識別、Hamilton結論、一般continuous-bijection捷徑、統計性質、strong law、CLT、Lean或Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-14","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261014-advance-20261105-r07-weak-law-large-numbers-0097","batch_id":"batch-20261014-advance-20261105-r07-weak-law-large-numbers-foundations","language":"zh-Hant","source_mko_ids":["mko-weak-law-large-numbers"],"title_zh":"弱大數律","stem_zh":"IID通用證書、共同有限mean與variance及exact Chebyshev tail。操作=wlln-finite-simulation-boundary；資料={\"mean\":[21,22],\"variance\":[22,23],\"epsilon\":[1,23],\"prefix_sample_means\":[[22,23],[23,24],[24,25]],\"iid_certificate\":\"finite_simulation_only\"}。請依 exact_ordered_tuple_declared_by_interface 欄序回答。","answer":{"kind":"expression","value":"(21/22, 1/23, [22/23, 23/24, 24/25], 否, finite_simulation_not_IID_certificate_or_WLLN_proof)","explanation_zh":"Wave5第五層核對=(21/22, 1/23, [22/23, 23/24, 24/25], 否, finite_simulation_not_IID_certificate_or_WLLN_proof)；依完整明示資料獨立重算；independence給Var(sample mean)=sigma squared/n並以forall n大於等於N證依機率收斂；有限樣本或模擬不足，且不宣稱almost sure、CLT或有限n已等於極限。"},"difficulty":{"band":"undergraduate_core","level":3,"skills":["弱大數律"]},"variant":{"family_id":"qf-mod36-wlln-finite-simulation-boundary","seed":202611057097,"parameters":{"mean":[21,22],"variance":[22,23],"epsilon":[1,23],"prefix_sample_means":[[22,23],[23,24],[24,25]],"iid_certificate":"finite_simulation_only","domain":"Symbolic_iid_Chebyshev_WLLN","operation":"wlln-finite-simulation-boundary","semantic_template":"qf-mod36-wlln-finite-simulation-boundary/{\"epsilon\":[1,23],\"iid_certificate\":\"finite_simulation_only\",\"mean\":[21,22],\"prefix_sample_means\":[[22,23],[23,24],[24,25]],\"variance\":[22,23]}"}},"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、有限取樣全稱證明、V與dual典範識別、Hamilton結論、一般continuous-bijection捷徑、統計性質、strong law、CLT、Lean或Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-14","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261014-advance-20261105-r07-weak-law-large-numbers-0098","batch_id":"batch-20261014-advance-20261105-r07-weak-law-large-numbers-foundations","language":"zh-Hant","source_mko_ids":["mko-weak-law-large-numbers"],"title_zh":"弱大數律","stem_zh":"IID通用證書、共同有限mean與variance及exact Chebyshev tail。操作=wlln-finite-simulation-boundary；資料={\"mean\":[22,23],\"variance\":[23,24],\"epsilon\":[1,24],\"prefix_sample_means\":[[23,24],[24,25],[25,26]],\"iid_certificate\":\"finite_simulation_only\"}。請依 exact_ordered_tuple_declared_by_interface 欄序回答。","answer":{"kind":"expression","value":"(22/23, 1/24, [23/24, 24/25, 25/26], 否, finite_simulation_not_IID_certificate_or_WLLN_proof)","explanation_zh":"Wave5第五層核對=(22/23, 1/24, [23/24, 24/25, 25/26], 否, finite_simulation_not_IID_certificate_or_WLLN_proof)；依完整明示資料獨立重算；independence給Var(sample mean)=sigma squared/n並以forall n大於等於N證依機率收斂；有限樣本或模擬不足，且不宣稱almost sure、CLT或有限n已等於極限。"},"difficulty":{"band":"undergraduate_core","level":3,"skills":["弱大數律"]},"variant":{"family_id":"qf-mod36-wlln-finite-simulation-boundary","seed":202611057098,"parameters":{"mean":[22,23],"variance":[23,24],"epsilon":[1,24],"prefix_sample_means":[[23,24],[24,25],[25,26]],"iid_certificate":"finite_simulation_only","domain":"Symbolic_iid_Chebyshev_WLLN","operation":"wlln-finite-simulation-boundary","semantic_template":"qf-mod36-wlln-finite-simulation-boundary/{\"epsilon\":[1,24],\"iid_certificate\":\"finite_simulation_only\",\"mean\":[22,23],\"prefix_sample_means\":[[23,24],[24,25],[25,26]],\"variance\":[23,24]}"}},"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、有限取樣全稱證明、V與dual典範識別、Hamilton結論、一般continuous-bijection捷徑、統計性質、strong law、CLT、Lean或Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-14","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261014-advance-20261105-r07-weak-law-large-numbers-0099","batch_id":"batch-20261014-advance-20261105-r07-weak-law-large-numbers-foundations","language":"zh-Hant","source_mko_ids":["mko-weak-law-large-numbers"],"title_zh":"弱大數律","stem_zh":"IID通用證書、共同有限mean與variance及exact Chebyshev tail。操作=wlln-finite-simulation-boundary；資料={\"mean\":[23,24],\"variance\":[24,25],\"epsilon\":[1,25],\"prefix_sample_means\":[[24,25],[25,26],[26,27]],\"iid_certificate\":\"finite_simulation_only\"}。請依 exact_ordered_tuple_declared_by_interface 欄序回答。","answer":{"kind":"expression","value":"(23/24, 1/25, [24/25, 25/26, 26/27], 否, finite_simulation_not_IID_certificate_or_WLLN_proof)","explanation_zh":"Wave5第五層核對=(23/24, 1/25, [24/25, 25/26, 26/27], 否, finite_simulation_not_IID_certificate_or_WLLN_proof)；依完整明示資料獨立重算；independence給Var(sample mean)=sigma squared/n並以forall n大於等於N證依機率收斂；有限樣本或模擬不足，且不宣稱almost sure、CLT或有限n已等於極限。"},"difficulty":{"band":"undergraduate_core","level":3,"skills":["弱大數律"]},"variant":{"family_id":"qf-mod36-wlln-finite-simulation-boundary","seed":202611057099,"parameters":{"mean":[23,24],"variance":[24,25],"epsilon":[1,25],"prefix_sample_means":[[24,25],[25,26],[26,27]],"iid_certificate":"finite_simulation_only","domain":"Symbolic_iid_Chebyshev_WLLN","operation":"wlln-finite-simulation-boundary","semantic_template":"qf-mod36-wlln-finite-simulation-boundary/{\"epsilon\":[1,25],\"iid_certificate\":\"finite_simulation_only\",\"mean\":[23,24],\"prefix_sample_means\":[[24,25],[25,26],[26,27]],\"variance\":[24,25]}"}},"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、有限取樣全稱證明、V與dual典範識別、Hamilton結論、一般continuous-bijection捷徑、統計性質、strong law、CLT、Lean或Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-14","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261014-advance-20261105-r07-weak-law-large-numbers-0100","batch_id":"batch-20261014-advance-20261105-r07-weak-law-large-numbers-foundations","language":"zh-Hant","source_mko_ids":["mko-weak-law-large-numbers"],"title_zh":"弱大數律","stem_zh":"IID通用證書、共同有限mean與variance及exact Chebyshev tail。操作=wlln-finite-simulation-boundary；資料={\"mean\":[24,25],\"variance\":[25,26],\"epsilon\":[1,26],\"prefix_sample_means\":[[25,26],[26,27],[27,28]],\"iid_certificate\":\"finite_simulation_only\"}。請依 exact_ordered_tuple_declared_by_interface 欄序回答。","answer":{"kind":"expression","value":"(24/25, 1/26, [25/26, 26/27, 27/28], 否, finite_simulation_not_IID_certificate_or_WLLN_proof)","explanation_zh":"Wave5第五層核對=(24/25, 1/26, [25/26, 26/27, 27/28], 否, finite_simulation_not_IID_certificate_or_WLLN_proof)；依完整明示資料獨立重算；independence給Var(sample mean)=sigma squared/n並以forall n大於等於N證依機率收斂；有限樣本或模擬不足，且不宣稱almost sure、CLT或有限n已等於極限。"},"difficulty":{"band":"undergraduate_core","level":3,"skills":["弱大數律"]},"variant":{"family_id":"qf-mod36-wlln-finite-simulation-boundary","seed":202611057100,"parameters":{"mean":[24,25],"variance":[25,26],"epsilon":[1,26],"prefix_sample_means":[[25,26],[26,27],[27,28]],"iid_certificate":"finite_simulation_only","domain":"Symbolic_iid_Chebyshev_WLLN","operation":"wlln-finite-simulation-boundary","semantic_template":"qf-mod36-wlln-finite-simulation-boundary/{\"epsilon\":[1,26],\"iid_certificate\":\"finite_simulation_only\",\"mean\":[24,25],\"prefix_sample_means\":[[25,26],[26,27],[27,28]],\"variance\":[25,26]}"}},"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、有限取樣全稱證明、V與dual典範識別、Hamilton結論、一般continuous-bijection捷徑、統計性質、strong law、CLT、Lean或Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-14","contract_version":"ocme-question-factory-v0.1"}}