{"schema_version":"ocme-question-v0.1","id":"q-20261014-advance-20261031-r03-convergence-in-distribution-0001","batch_id":"batch-20261014-advance-20261031-r03-convergence-in-distribution-foundations","language":"zh-Hant","source_mko_ids":["mko-convergence-in-distribution"],"title_zh":"依分布收斂","stem_zh":"Bernoulli symbolic tail與極限CDF。操作=convdist-bernoulli-cdf；資料={\"p\":[1,2],\"c\":[1,20],\"shift\":2,\"n\":1,\"threshold\":[-1,1]}。請依 [n,p_n,threshold,F_n,F,limit_CDF_continuity_point] 欄序回答。","answer":{"kind":"expression","value":"(1, 31/60, -1, 0, 0, 是)","explanation_zh":"Wave4收束核對=(1, 31/60, -1, 0, 0, 是)；依完整明示資料重算；只在極限CDF連續點要求收斂且有限prefix不足；不要求coupling且不推出依機率、幾乎處處或Lp收斂。"},"difficulty":{"band":"undergraduate_core","level":1,"skills":["依分布收斂"]},"variant":{"family_id":"qf-mod31-convdist-bernoulli-cdf","seed":202610313001,"parameters":{"p":[1,2],"c":[1,20],"shift":2,"n":1,"threshold":[-1,1],"domain":"Symbolic_Bernoulli_CDF_limit","operation":"convdist-bernoulli-cdf","semantic_template":"qf-mod31-convdist-bernoulli-cdf/{\"c\":[1,20],\"n\":1,\"p\":[1,2],\"shift\":2,\"threshold\":[-1,1]}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_model","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"候選須由主端獨立重算；不構成人工審定、一般不可數性／色數最優性／更強機率收斂／商域、optional stopping、Lean或形式Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-14","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261014-advance-20261031-r03-convergence-in-distribution-0002","batch_id":"batch-20261014-advance-20261031-r03-convergence-in-distribution-foundations","language":"zh-Hant","source_mko_ids":["mko-convergence-in-distribution"],"title_zh":"依分布收斂","stem_zh":"Bernoulli symbolic tail與極限CDF。操作=convdist-bernoulli-cdf；資料={\"p\":[1,2],\"c\":[2,20],\"shift\":3,\"n\":2,\"threshold\":[1,2]}。請依 [n,p_n,threshold,F_n,F,limit_CDF_continuity_point] 欄序回答。","answer":{"kind":"expression","value":"(2, 13/25, 1/2, 12/25, 1/2, 是)","explanation_zh":"Wave4收束核對=(2, 13/25, 1/2, 12/25, 1/2, 是)；依完整明示資料重算；只在極限CDF連續點要求收斂且有限prefix不足；不要求coupling且不推出依機率、幾乎處處或Lp收斂。"},"difficulty":{"band":"undergraduate_core","level":1,"skills":["依分布收斂"]},"variant":{"family_id":"qf-mod31-convdist-bernoulli-cdf","seed":202610313002,"parameters":{"p":[1,2],"c":[2,20],"shift":3,"n":2,"threshold":[1,2],"domain":"Symbolic_Bernoulli_CDF_limit","operation":"convdist-bernoulli-cdf","semantic_template":"qf-mod31-convdist-bernoulli-cdf/{\"c\":[2,20],\"n\":2,\"p\":[1,2],\"shift\":3,\"threshold\":[1,2]}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_model","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"候選須由主端獨立重算；不構成人工審定、一般不可數性／色數最優性／更強機率收斂／商域、optional stopping、Lean或形式Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-14","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261014-advance-20261031-r03-convergence-in-distribution-0003","batch_id":"batch-20261014-advance-20261031-r03-convergence-in-distribution-foundations","language":"zh-Hant","source_mko_ids":["mko-convergence-in-distribution"],"title_zh":"依分布收斂","stem_zh":"Bernoulli symbolic tail與極限CDF。操作=convdist-bernoulli-cdf；資料={\"p\":[1,2],\"c\":[3,20],\"shift\":4,\"n\":3,\"threshold\":[2,1]}。請依 [n,p_n,threshold,F_n,F,limit_CDF_continuity_point] 欄序回答。","answer":{"kind":"expression","value":"(3, 73/140, 2, 1, 1, 是)","explanation_zh":"Wave4收束核對=(3, 73/140, 2, 1, 1, 是)；依完整明示資料重算；只在極限CDF連續點要求收斂且有限prefix不足；不要求coupling且不推出依機率、幾乎處處或Lp收斂。"},"difficulty":{"band":"undergraduate_core","level":1,"skills":["依分布收斂"]},"variant":{"family_id":"qf-mod31-convdist-bernoulli-cdf","seed":202610313003,"parameters":{"p":[1,2],"c":[3,20],"shift":4,"n":3,"threshold":[2,1],"domain":"Symbolic_Bernoulli_CDF_limit","operation":"convdist-bernoulli-cdf","semantic_template":"qf-mod31-convdist-bernoulli-cdf/{\"c\":[3,20],\"n\":3,\"p\":[1,2],\"shift\":4,\"threshold\":[2,1]}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_model","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"候選須由主端獨立重算；不構成人工審定、一般不可數性／色數最優性／更強機率收斂／商域、optional stopping、Lean或形式Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-14","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261014-advance-20261031-r03-convergence-in-distribution-0004","batch_id":"batch-20261014-advance-20261031-r03-convergence-in-distribution-foundations","language":"zh-Hant","source_mko_ids":["mko-convergence-in-distribution"],"title_zh":"依分布收斂","stem_zh":"Bernoulli symbolic tail與極限CDF。操作=convdist-bernoulli-cdf；資料={\"p\":[1,2],\"c\":[4,20],\"shift\":5,\"n\":4,\"threshold\":[-1,1]}。請依 [n,p_n,threshold,F_n,F,limit_CDF_continuity_point] 欄序回答。","answer":{"kind":"expression","value":"(4, 47/90, -1, 0, 0, 是)","explanation_zh":"Wave4收束核對=(4, 47/90, -1, 0, 0, 是)；依完整明示資料重算；只在極限CDF連續點要求收斂且有限prefix不足；不要求coupling且不推出依機率、幾乎處處或Lp收斂。"},"difficulty":{"band":"undergraduate_core","level":1,"skills":["依分布收斂"]},"variant":{"family_id":"qf-mod31-convdist-bernoulli-cdf","seed":202610313004,"parameters":{"p":[1,2],"c":[4,20],"shift":5,"n":4,"threshold":[-1,1],"domain":"Symbolic_Bernoulli_CDF_limit","operation":"convdist-bernoulli-cdf","semantic_template":"qf-mod31-convdist-bernoulli-cdf/{\"c\":[4,20],\"n\":4,\"p\":[1,2],\"shift\":5,\"threshold\":[-1,1]}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_model","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"候選須由主端獨立重算；不構成人工審定、一般不可數性／色數最優性／更強機率收斂／商域、optional stopping、Lean或形式Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-14","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261014-advance-20261031-r03-convergence-in-distribution-0005","batch_id":"batch-20261014-advance-20261031-r03-convergence-in-distribution-foundations","language":"zh-Hant","source_mko_ids":["mko-convergence-in-distribution"],"title_zh":"依分布收斂","stem_zh":"Bernoulli symbolic tail與極限CDF。操作=convdist-bernoulli-cdf；資料={\"p\":[1,2],\"c\":[5,20],\"shift\":6,\"n\":5,\"threshold\":[1,2]}。請依 [n,p_n,threshold,F_n,F,limit_CDF_continuity_point] 欄序回答。","answer":{"kind":"expression","value":"(5, 23/44, 1/2, 21/44, 1/2, 是)","explanation_zh":"Wave4收束核對=(5, 23/44, 1/2, 21/44, 1/2, 是)；依完整明示資料重算；只在極限CDF連續點要求收斂且有限prefix不足；不要求coupling且不推出依機率、幾乎處處或Lp收斂。"},"difficulty":{"band":"undergraduate_core","level":1,"skills":["依分布收斂"]},"variant":{"family_id":"qf-mod31-convdist-bernoulli-cdf","seed":202610313005,"parameters":{"p":[1,2],"c":[5,20],"shift":6,"n":5,"threshold":[1,2],"domain":"Symbolic_Bernoulli_CDF_limit","operation":"convdist-bernoulli-cdf","semantic_template":"qf-mod31-convdist-bernoulli-cdf/{\"c\":[5,20],\"n\":5,\"p\":[1,2],\"shift\":6,\"threshold\":[1,2]}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_model","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"候選須由主端獨立重算；不構成人工審定、一般不可數性／色數最優性／更強機率收斂／商域、optional stopping、Lean或形式Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-14","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261014-advance-20261031-r03-convergence-in-distribution-0006","batch_id":"batch-20261014-advance-20261031-r03-convergence-in-distribution-foundations","language":"zh-Hant","source_mko_ids":["mko-convergence-in-distribution"],"title_zh":"依分布收斂","stem_zh":"Bernoulli symbolic tail與極限CDF。操作=convdist-bernoulli-cdf；資料={\"p\":[1,2],\"c\":[1,20],\"shift\":7,\"n\":6,\"threshold\":[2,1]}。請依 [n,p_n,threshold,F_n,F,limit_CDF_continuity_point] 欄序回答。","answer":{"kind":"expression","value":"(6, 131/260, 2, 1, 1, 是)","explanation_zh":"Wave4收束核對=(6, 131/260, 2, 1, 1, 是)；依完整明示資料重算；只在極限CDF連續點要求收斂且有限prefix不足；不要求coupling且不推出依機率、幾乎處處或Lp收斂。"},"difficulty":{"band":"undergraduate_core","level":1,"skills":["依分布收斂"]},"variant":{"family_id":"qf-mod31-convdist-bernoulli-cdf","seed":202610313006,"parameters":{"p":[1,2],"c":[1,20],"shift":7,"n":6,"threshold":[2,1],"domain":"Symbolic_Bernoulli_CDF_limit","operation":"convdist-bernoulli-cdf","semantic_template":"qf-mod31-convdist-bernoulli-cdf/{\"c\":[1,20],\"n\":6,\"p\":[1,2],\"shift\":7,\"threshold\":[2,1]}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_model","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"候選須由主端獨立重算；不構成人工審定、一般不可數性／色數最優性／更強機率收斂／商域、optional stopping、Lean或形式Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-14","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261014-advance-20261031-r03-convergence-in-distribution-0007","batch_id":"batch-20261014-advance-20261031-r03-convergence-in-distribution-foundations","language":"zh-Hant","source_mko_ids":["mko-convergence-in-distribution"],"title_zh":"依分布收斂","stem_zh":"Bernoulli symbolic tail與極限CDF。操作=convdist-bernoulli-cdf；資料={\"p\":[1,2],\"c\":[2,20],\"shift\":8,\"n\":7,\"threshold\":[-1,1]}。請依 [n,p_n,threshold,F_n,F,limit_CDF_continuity_point] 欄序回答。","answer":{"kind":"expression","value":"(7, 38/75, -1, 0, 0, 是)","explanation_zh":"Wave4收束核對=(7, 38/75, -1, 0, 0, 是)；依完整明示資料重算；只在極限CDF連續點要求收斂且有限prefix不足；不要求coupling且不推出依機率、幾乎處處或Lp收斂。"},"difficulty":{"band":"undergraduate_core","level":1,"skills":["依分布收斂"]},"variant":{"family_id":"qf-mod31-convdist-bernoulli-cdf","seed":202610313007,"parameters":{"p":[1,2],"c":[2,20],"shift":8,"n":7,"threshold":[-1,1],"domain":"Symbolic_Bernoulli_CDF_limit","operation":"convdist-bernoulli-cdf","semantic_template":"qf-mod31-convdist-bernoulli-cdf/{\"c\":[2,20],\"n\":7,\"p\":[1,2],\"shift\":8,\"threshold\":[-1,1]}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_model","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"候選須由主端獨立重算；不構成人工審定、一般不可數性／色數最優性／更強機率收斂／商域、optional stopping、Lean或形式Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-14","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261014-advance-20261031-r03-convergence-in-distribution-0008","batch_id":"batch-20261014-advance-20261031-r03-convergence-in-distribution-foundations","language":"zh-Hant","source_mko_ids":["mko-convergence-in-distribution"],"title_zh":"依分布收斂","stem_zh":"Bernoulli symbolic tail與極限CDF。操作=convdist-bernoulli-cdf；資料={\"p\":[1,2],\"c\":[3,20],\"shift\":9,\"n\":8,\"threshold\":[1,2]}。請依 [n,p_n,threshold,F_n,F,limit_CDF_continuity_point] 欄序回答。","answer":{"kind":"expression","value":"(8, 173/340, 1/2, 167/340, 1/2, 是)","explanation_zh":"Wave4收束核對=(8, 173/340, 1/2, 167/340, 1/2, 是)；依完整明示資料重算；只在極限CDF連續點要求收斂且有限prefix不足；不要求coupling且不推出依機率、幾乎處處或Lp收斂。"},"difficulty":{"band":"undergraduate_core","level":1,"skills":["依分布收斂"]},"variant":{"family_id":"qf-mod31-convdist-bernoulli-cdf","seed":202610313008,"parameters":{"p":[1,2],"c":[3,20],"shift":9,"n":8,"threshold":[1,2],"domain":"Symbolic_Bernoulli_CDF_limit","operation":"convdist-bernoulli-cdf","semantic_template":"qf-mod31-convdist-bernoulli-cdf/{\"c\":[3,20],\"n\":8,\"p\":[1,2],\"shift\":9,\"threshold\":[1,2]}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_model","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"候選須由主端獨立重算；不構成人工審定、一般不可數性／色數最優性／更強機率收斂／商域、optional stopping、Lean或形式Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-14","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261014-advance-20261031-r03-convergence-in-distribution-0009","batch_id":"batch-20261014-advance-20261031-r03-convergence-in-distribution-foundations","language":"zh-Hant","source_mko_ids":["mko-convergence-in-distribution"],"title_zh":"依分布收斂","stem_zh":"Bernoulli symbolic tail與極限CDF。操作=convdist-bernoulli-cdf；資料={\"p\":[1,2],\"c\":[4,20],\"shift\":10,\"n\":9,\"threshold\":[2,1]}。請依 [n,p_n,threshold,F_n,F,limit_CDF_continuity_point] 欄序回答。","answer":{"kind":"expression","value":"(9, 97/190, 2, 1, 1, 是)","explanation_zh":"Wave4收束核對=(9, 97/190, 2, 1, 1, 是)；依完整明示資料重算；只在極限CDF連續點要求收斂且有限prefix不足；不要求coupling且不推出依機率、幾乎處處或Lp收斂。"},"difficulty":{"band":"undergraduate_core","level":2,"skills":["依分布收斂"]},"variant":{"family_id":"qf-mod31-convdist-bernoulli-cdf","seed":202610313009,"parameters":{"p":[1,2],"c":[4,20],"shift":10,"n":9,"threshold":[2,1],"domain":"Symbolic_Bernoulli_CDF_limit","operation":"convdist-bernoulli-cdf","semantic_template":"qf-mod31-convdist-bernoulli-cdf/{\"c\":[4,20],\"n\":9,\"p\":[1,2],\"shift\":10,\"threshold\":[2,1]}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_model","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"候選須由主端獨立重算；不構成人工審定、一般不可數性／色數最優性／更強機率收斂／商域、optional stopping、Lean或形式Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-14","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261014-advance-20261031-r03-convergence-in-distribution-0010","batch_id":"batch-20261014-advance-20261031-r03-convergence-in-distribution-foundations","language":"zh-Hant","source_mko_ids":["mko-convergence-in-distribution"],"title_zh":"依分布收斂","stem_zh":"Bernoulli symbolic tail與極限CDF。操作=convdist-bernoulli-cdf；資料={\"p\":[1,2],\"c\":[5,20],\"shift\":11,\"n\":10,\"threshold\":[-1,1]}。請依 [n,p_n,threshold,F_n,F,limit_CDF_continuity_point] 欄序回答。","answer":{"kind":"expression","value":"(10, 43/84, -1, 0, 0, 是)","explanation_zh":"Wave4收束核對=(10, 43/84, -1, 0, 0, 是)；依完整明示資料重算；只在極限CDF連續點要求收斂且有限prefix不足；不要求coupling且不推出依機率、幾乎處處或Lp收斂。"},"difficulty":{"band":"undergraduate_core","level":2,"skills":["依分布收斂"]},"variant":{"family_id":"qf-mod31-convdist-bernoulli-cdf","seed":202610313010,"parameters":{"p":[1,2],"c":[5,20],"shift":11,"n":10,"threshold":[-1,1],"domain":"Symbolic_Bernoulli_CDF_limit","operation":"convdist-bernoulli-cdf","semantic_template":"qf-mod31-convdist-bernoulli-cdf/{\"c\":[5,20],\"n\":10,\"p\":[1,2],\"shift\":11,\"threshold\":[-1,1]}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_model","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"候選須由主端獨立重算；不構成人工審定、一般不可數性／色數最優性／更強機率收斂／商域、optional stopping、Lean或形式Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-14","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261014-advance-20261031-r03-convergence-in-distribution-0011","batch_id":"batch-20261014-advance-20261031-r03-convergence-in-distribution-foundations","language":"zh-Hant","source_mko_ids":["mko-convergence-in-distribution"],"title_zh":"依分布收斂","stem_zh":"Bernoulli symbolic tail與極限CDF。操作=convdist-bernoulli-cdf；資料={\"p\":[1,2],\"c\":[1,20],\"shift\":12,\"n\":11,\"threshold\":[1,2]}。請依 [n,p_n,threshold,F_n,F,limit_CDF_continuity_point] 欄序回答。","answer":{"kind":"expression","value":"(11, 231/460, 1/2, 229/460, 1/2, 是)","explanation_zh":"Wave4收束核對=(11, 231/460, 1/2, 229/460, 1/2, 是)；依完整明示資料重算；只在極限CDF連續點要求收斂且有限prefix不足；不要求coupling且不推出依機率、幾乎處處或Lp收斂。"},"difficulty":{"band":"undergraduate_core","level":2,"skills":["依分布收斂"]},"variant":{"family_id":"qf-mod31-convdist-bernoulli-cdf","seed":202610313011,"parameters":{"p":[1,2],"c":[1,20],"shift":12,"n":11,"threshold":[1,2],"domain":"Symbolic_Bernoulli_CDF_limit","operation":"convdist-bernoulli-cdf","semantic_template":"qf-mod31-convdist-bernoulli-cdf/{\"c\":[1,20],\"n\":11,\"p\":[1,2],\"shift\":12,\"threshold\":[1,2]}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_model","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"候選須由主端獨立重算；不構成人工審定、一般不可數性／色數最優性／更強機率收斂／商域、optional stopping、Lean或形式Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-14","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261014-advance-20261031-r03-convergence-in-distribution-0012","batch_id":"batch-20261014-advance-20261031-r03-convergence-in-distribution-foundations","language":"zh-Hant","source_mko_ids":["mko-convergence-in-distribution"],"title_zh":"依分布收斂","stem_zh":"Bernoulli symbolic tail與極限CDF。操作=convdist-bernoulli-cdf；資料={\"p\":[1,2],\"c\":[2,20],\"shift\":13,\"n\":12,\"threshold\":[2,1]}。請依 [n,p_n,threshold,F_n,F,limit_CDF_continuity_point] 欄序回答。","answer":{"kind":"expression","value":"(12, 63/125, 2, 1, 1, 是)","explanation_zh":"Wave4收束核對=(12, 63/125, 2, 1, 1, 是)；依完整明示資料重算；只在極限CDF連續點要求收斂且有限prefix不足；不要求coupling且不推出依機率、幾乎處處或Lp收斂。"},"difficulty":{"band":"undergraduate_core","level":2,"skills":["依分布收斂"]},"variant":{"family_id":"qf-mod31-convdist-bernoulli-cdf","seed":202610313012,"parameters":{"p":[1,2],"c":[2,20],"shift":13,"n":12,"threshold":[2,1],"domain":"Symbolic_Bernoulli_CDF_limit","operation":"convdist-bernoulli-cdf","semantic_template":"qf-mod31-convdist-bernoulli-cdf/{\"c\":[2,20],\"n\":12,\"p\":[1,2],\"shift\":13,\"threshold\":[2,1]}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_model","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"候選須由主端獨立重算；不構成人工審定、一般不可數性／色數最優性／更強機率收斂／商域、optional stopping、Lean或形式Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-14","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261014-advance-20261031-r03-convergence-in-distribution-0013","batch_id":"batch-20261014-advance-20261031-r03-convergence-in-distribution-foundations","language":"zh-Hant","source_mko_ids":["mko-convergence-in-distribution"],"title_zh":"依分布收斂","stem_zh":"Bernoulli symbolic tail與極限CDF。操作=convdist-bernoulli-cdf；資料={\"p\":[1,2],\"c\":[3,20],\"shift\":14,\"n\":13,\"threshold\":[-1,1]}。請依 [n,p_n,threshold,F_n,F,limit_CDF_continuity_point] 欄序回答。","answer":{"kind":"expression","value":"(13, 91/180, -1, 0, 0, 是)","explanation_zh":"Wave4收束核對=(13, 91/180, -1, 0, 0, 是)；依完整明示資料重算；只在極限CDF連續點要求收斂且有限prefix不足；不要求coupling且不推出依機率、幾乎處處或Lp收斂。"},"difficulty":{"band":"undergraduate_core","level":2,"skills":["依分布收斂"]},"variant":{"family_id":"qf-mod31-convdist-bernoulli-cdf","seed":202610313013,"parameters":{"p":[1,2],"c":[3,20],"shift":14,"n":13,"threshold":[-1,1],"domain":"Symbolic_Bernoulli_CDF_limit","operation":"convdist-bernoulli-cdf","semantic_template":"qf-mod31-convdist-bernoulli-cdf/{\"c\":[3,20],\"n\":13,\"p\":[1,2],\"shift\":14,\"threshold\":[-1,1]}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_model","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"候選須由主端獨立重算；不構成人工審定、一般不可數性／色數最優性／更強機率收斂／商域、optional stopping、Lean或形式Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-14","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261014-advance-20261031-r03-convergence-in-distribution-0014","batch_id":"batch-20261014-advance-20261031-r03-convergence-in-distribution-foundations","language":"zh-Hant","source_mko_ids":["mko-convergence-in-distribution"],"title_zh":"依分布收斂","stem_zh":"Bernoulli symbolic tail與極限CDF。操作=convdist-bernoulli-cdf；資料={\"p\":[1,2],\"c\":[4,20],\"shift\":15,\"n\":14,\"threshold\":[1,2]}。請依 [n,p_n,threshold,F_n,F,limit_CDF_continuity_point] 欄序回答。","answer":{"kind":"expression","value":"(14, 147/290, 1/2, 143/290, 1/2, 是)","explanation_zh":"Wave4收束核對=(14, 147/290, 1/2, 143/290, 1/2, 是)；依完整明示資料重算；只在極限CDF連續點要求收斂且有限prefix不足；不要求coupling且不推出依機率、幾乎處處或Lp收斂。"},"difficulty":{"band":"undergraduate_core","level":2,"skills":["依分布收斂"]},"variant":{"family_id":"qf-mod31-convdist-bernoulli-cdf","seed":202610313014,"parameters":{"p":[1,2],"c":[4,20],"shift":15,"n":14,"threshold":[1,2],"domain":"Symbolic_Bernoulli_CDF_limit","operation":"convdist-bernoulli-cdf","semantic_template":"qf-mod31-convdist-bernoulli-cdf/{\"c\":[4,20],\"n\":14,\"p\":[1,2],\"shift\":15,\"threshold\":[1,2]}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_model","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"候選須由主端獨立重算；不構成人工審定、一般不可數性／色數最優性／更強機率收斂／商域、optional stopping、Lean或形式Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-14","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261014-advance-20261031-r03-convergence-in-distribution-0015","batch_id":"batch-20261014-advance-20261031-r03-convergence-in-distribution-foundations","language":"zh-Hant","source_mko_ids":["mko-convergence-in-distribution"],"title_zh":"依分布收斂","stem_zh":"Bernoulli symbolic tail與極限CDF。操作=convdist-bernoulli-cdf；資料={\"p\":[1,2],\"c\":[5,20],\"shift\":16,\"n\":15,\"threshold\":[2,1]}。請依 [n,p_n,threshold,F_n,F,limit_CDF_continuity_point] 欄序回答。","answer":{"kind":"expression","value":"(15, 63/124, 2, 1, 1, 是)","explanation_zh":"Wave4收束核對=(15, 63/124, 2, 1, 1, 是)；依完整明示資料重算；只在極限CDF連續點要求收斂且有限prefix不足；不要求coupling且不推出依機率、幾乎處處或Lp收斂。"},"difficulty":{"band":"undergraduate_core","level":2,"skills":["依分布收斂"]},"variant":{"family_id":"qf-mod31-convdist-bernoulli-cdf","seed":202610313015,"parameters":{"p":[1,2],"c":[5,20],"shift":16,"n":15,"threshold":[2,1],"domain":"Symbolic_Bernoulli_CDF_limit","operation":"convdist-bernoulli-cdf","semantic_template":"qf-mod31-convdist-bernoulli-cdf/{\"c\":[5,20],\"n\":15,\"p\":[1,2],\"shift\":16,\"threshold\":[2,1]}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_model","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"候選須由主端獨立重算；不構成人工審定、一般不可數性／色數最優性／更強機率收斂／商域、optional stopping、Lean或形式Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-14","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261014-advance-20261031-r03-convergence-in-distribution-0016","batch_id":"batch-20261014-advance-20261031-r03-convergence-in-distribution-foundations","language":"zh-Hant","source_mko_ids":["mko-convergence-in-distribution"],"title_zh":"依分布收斂","stem_zh":"Bernoulli symbolic tail與極限CDF。操作=convdist-bernoulli-cdf；資料={\"p\":[1,2],\"c\":[1,20],\"shift\":17,\"n\":16,\"threshold\":[-1,1]}。請依 [n,p_n,threshold,F_n,F,limit_CDF_continuity_point] 欄序回答。","answer":{"kind":"expression","value":"(16, 331/660, -1, 0, 0, 是)","explanation_zh":"Wave4收束核對=(16, 331/660, -1, 0, 0, 是)；依完整明示資料重算；只在極限CDF連續點要求收斂且有限prefix不足；不要求coupling且不推出依機率、幾乎處處或Lp收斂。"},"difficulty":{"band":"undergraduate_core","level":2,"skills":["依分布收斂"]},"variant":{"family_id":"qf-mod31-convdist-bernoulli-cdf","seed":202610313016,"parameters":{"p":[1,2],"c":[1,20],"shift":17,"n":16,"threshold":[-1,1],"domain":"Symbolic_Bernoulli_CDF_limit","operation":"convdist-bernoulli-cdf","semantic_template":"qf-mod31-convdist-bernoulli-cdf/{\"c\":[1,20],\"n\":16,\"p\":[1,2],\"shift\":17,\"threshold\":[-1,1]}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_model","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"候選須由主端獨立重算；不構成人工審定、一般不可數性／色數最優性／更強機率收斂／商域、optional stopping、Lean或形式Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-14","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261014-advance-20261031-r03-convergence-in-distribution-0017","batch_id":"batch-20261014-advance-20261031-r03-convergence-in-distribution-foundations","language":"zh-Hant","source_mko_ids":["mko-convergence-in-distribution"],"title_zh":"依分布收斂","stem_zh":"Bernoulli symbolic tail與極限CDF。操作=convdist-bernoulli-cdf；資料={\"p\":[1,2],\"c\":[2,20],\"shift\":18,\"n\":17,\"threshold\":[1,2]}。請依 [n,p_n,threshold,F_n,F,limit_CDF_continuity_point] 欄序回答。","answer":{"kind":"expression","value":"(17, 88/175, 1/2, 87/175, 1/2, 是)","explanation_zh":"Wave4收束核對=(17, 88/175, 1/2, 87/175, 1/2, 是)；依完整明示資料重算；只在極限CDF連續點要求收斂且有限prefix不足；不要求coupling且不推出依機率、幾乎處處或Lp收斂。"},"difficulty":{"band":"undergraduate_core","level":2,"skills":["依分布收斂"]},"variant":{"family_id":"qf-mod31-convdist-bernoulli-cdf","seed":202610313017,"parameters":{"p":[1,2],"c":[2,20],"shift":18,"n":17,"threshold":[1,2],"domain":"Symbolic_Bernoulli_CDF_limit","operation":"convdist-bernoulli-cdf","semantic_template":"qf-mod31-convdist-bernoulli-cdf/{\"c\":[2,20],\"n\":17,\"p\":[1,2],\"shift\":18,\"threshold\":[1,2]}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_model","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"候選須由主端獨立重算；不構成人工審定、一般不可數性／色數最優性／更強機率收斂／商域、optional stopping、Lean或形式Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-14","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261014-advance-20261031-r03-convergence-in-distribution-0018","batch_id":"batch-20261014-advance-20261031-r03-convergence-in-distribution-foundations","language":"zh-Hant","source_mko_ids":["mko-convergence-in-distribution"],"title_zh":"依分布收斂","stem_zh":"Bernoulli symbolic tail與極限CDF。操作=convdist-bernoulli-cdf；資料={\"p\":[1,2],\"c\":[3,20],\"shift\":19,\"n\":18,\"threshold\":[2,1]}。請依 [n,p_n,threshold,F_n,F,limit_CDF_continuity_point] 欄序回答。","answer":{"kind":"expression","value":"(18, 373/740, 2, 1, 1, 是)","explanation_zh":"Wave4收束核對=(18, 373/740, 2, 1, 1, 是)；依完整明示資料重算；只在極限CDF連續點要求收斂且有限prefix不足；不要求coupling且不推出依機率、幾乎處處或Lp收斂。"},"difficulty":{"band":"undergraduate_core","level":3,"skills":["依分布收斂"]},"variant":{"family_id":"qf-mod31-convdist-bernoulli-cdf","seed":202610313018,"parameters":{"p":[1,2],"c":[3,20],"shift":19,"n":18,"threshold":[2,1],"domain":"Symbolic_Bernoulli_CDF_limit","operation":"convdist-bernoulli-cdf","semantic_template":"qf-mod31-convdist-bernoulli-cdf/{\"c\":[3,20],\"n\":18,\"p\":[1,2],\"shift\":19,\"threshold\":[2,1]}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_model","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"候選須由主端獨立重算；不構成人工審定、一般不可數性／色數最優性／更強機率收斂／商域、optional stopping、Lean或形式Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-14","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261014-advance-20261031-r03-convergence-in-distribution-0019","batch_id":"batch-20261014-advance-20261031-r03-convergence-in-distribution-foundations","language":"zh-Hant","source_mko_ids":["mko-convergence-in-distribution"],"title_zh":"依分布收斂","stem_zh":"Bernoulli symbolic tail與極限CDF。操作=convdist-bernoulli-cdf；資料={\"p\":[1,2],\"c\":[4,20],\"shift\":20,\"n\":19,\"threshold\":[-1,1]}。請依 [n,p_n,threshold,F_n,F,limit_CDF_continuity_point] 欄序回答。","answer":{"kind":"expression","value":"(19, 197/390, -1, 0, 0, 是)","explanation_zh":"Wave4收束核對=(19, 197/390, -1, 0, 0, 是)；依完整明示資料重算；只在極限CDF連續點要求收斂且有限prefix不足；不要求coupling且不推出依機率、幾乎處處或Lp收斂。"},"difficulty":{"band":"undergraduate_core","level":3,"skills":["依分布收斂"]},"variant":{"family_id":"qf-mod31-convdist-bernoulli-cdf","seed":202610313019,"parameters":{"p":[1,2],"c":[4,20],"shift":20,"n":19,"threshold":[-1,1],"domain":"Symbolic_Bernoulli_CDF_limit","operation":"convdist-bernoulli-cdf","semantic_template":"qf-mod31-convdist-bernoulli-cdf/{\"c\":[4,20],\"n\":19,\"p\":[1,2],\"shift\":20,\"threshold\":[-1,1]}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_model","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"候選須由主端獨立重算；不構成人工審定、一般不可數性／色數最優性／更強機率收斂／商域、optional stopping、Lean或形式Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-14","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261014-advance-20261031-r03-convergence-in-distribution-0020","batch_id":"batch-20261014-advance-20261031-r03-convergence-in-distribution-foundations","language":"zh-Hant","source_mko_ids":["mko-convergence-in-distribution"],"title_zh":"依分布收斂","stem_zh":"Bernoulli symbolic tail與極限CDF。操作=convdist-bernoulli-cdf；資料={\"p\":[1,2],\"c\":[5,20],\"shift\":21,\"n\":20,\"threshold\":[1,2]}。請依 [n,p_n,threshold,F_n,F,limit_CDF_continuity_point] 欄序回答。","answer":{"kind":"expression","value":"(20, 83/164, 1/2, 81/164, 1/2, 是)","explanation_zh":"Wave4收束核對=(20, 83/164, 1/2, 81/164, 1/2, 是)；依完整明示資料重算；只在極限CDF連續點要求收斂且有限prefix不足；不要求coupling且不推出依機率、幾乎處處或Lp收斂。"},"difficulty":{"band":"undergraduate_core","level":3,"skills":["依分布收斂"]},"variant":{"family_id":"qf-mod31-convdist-bernoulli-cdf","seed":202610313020,"parameters":{"p":[1,2],"c":[5,20],"shift":21,"n":20,"threshold":[1,2],"domain":"Symbolic_Bernoulli_CDF_limit","operation":"convdist-bernoulli-cdf","semantic_template":"qf-mod31-convdist-bernoulli-cdf/{\"c\":[5,20],\"n\":20,\"p\":[1,2],\"shift\":21,\"threshold\":[1,2]}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_model","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"候選須由主端獨立重算；不構成人工審定、一般不可數性／色數最優性／更強機率收斂／商域、optional stopping、Lean或形式Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-14","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261014-advance-20261031-r03-convergence-in-distribution-0021","batch_id":"batch-20261014-advance-20261031-r03-convergence-in-distribution-foundations","language":"zh-Hant","source_mko_ids":["mko-convergence-in-distribution"],"title_zh":"依分布收斂","stem_zh":"Bernoulli symbolic tail與極限CDF。操作=convdist-bernoulli-cdf；資料={\"p\":[1,2],\"c\":[1,20],\"shift\":22,\"n\":21,\"threshold\":[2,1]}。請依 [n,p_n,threshold,F_n,F,limit_CDF_continuity_point] 欄序回答。","answer":{"kind":"expression","value":"(21, 431/860, 2, 1, 1, 是)","explanation_zh":"Wave4收束核對=(21, 431/860, 2, 1, 1, 是)；依完整明示資料重算；只在極限CDF連續點要求收斂且有限prefix不足；不要求coupling且不推出依機率、幾乎處處或Lp收斂。"},"difficulty":{"band":"undergraduate_core","level":3,"skills":["依分布收斂"]},"variant":{"family_id":"qf-mod31-convdist-bernoulli-cdf","seed":202610313021,"parameters":{"p":[1,2],"c":[1,20],"shift":22,"n":21,"threshold":[2,1],"domain":"Symbolic_Bernoulli_CDF_limit","operation":"convdist-bernoulli-cdf","semantic_template":"qf-mod31-convdist-bernoulli-cdf/{\"c\":[1,20],\"n\":21,\"p\":[1,2],\"shift\":22,\"threshold\":[2,1]}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_model","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"候選須由主端獨立重算；不構成人工審定、一般不可數性／色數最優性／更強機率收斂／商域、optional stopping、Lean或形式Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-14","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261014-advance-20261031-r03-convergence-in-distribution-0022","batch_id":"batch-20261014-advance-20261031-r03-convergence-in-distribution-foundations","language":"zh-Hant","source_mko_ids":["mko-convergence-in-distribution"],"title_zh":"依分布收斂","stem_zh":"Bernoulli symbolic tail與極限CDF。操作=convdist-bernoulli-cdf；資料={\"p\":[1,2],\"c\":[2,20],\"shift\":23,\"n\":22,\"threshold\":[-1,1]}。請依 [n,p_n,threshold,F_n,F,limit_CDF_continuity_point] 欄序回答。","answer":{"kind":"expression","value":"(22, 113/225, -1, 0, 0, 是)","explanation_zh":"Wave4收束核對=(22, 113/225, -1, 0, 0, 是)；依完整明示資料重算；只在極限CDF連續點要求收斂且有限prefix不足；不要求coupling且不推出依機率、幾乎處處或Lp收斂。"},"difficulty":{"band":"undergraduate_core","level":3,"skills":["依分布收斂"]},"variant":{"family_id":"qf-mod31-convdist-bernoulli-cdf","seed":202610313022,"parameters":{"p":[1,2],"c":[2,20],"shift":23,"n":22,"threshold":[-1,1],"domain":"Symbolic_Bernoulli_CDF_limit","operation":"convdist-bernoulli-cdf","semantic_template":"qf-mod31-convdist-bernoulli-cdf/{\"c\":[2,20],\"n\":22,\"p\":[1,2],\"shift\":23,\"threshold\":[-1,1]}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_model","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"候選須由主端獨立重算；不構成人工審定、一般不可數性／色數最優性／更強機率收斂／商域、optional stopping、Lean或形式Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-14","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261014-advance-20261031-r03-convergence-in-distribution-0023","batch_id":"batch-20261014-advance-20261031-r03-convergence-in-distribution-foundations","language":"zh-Hant","source_mko_ids":["mko-convergence-in-distribution"],"title_zh":"依分布收斂","stem_zh":"Bernoulli symbolic tail與極限CDF。操作=convdist-bernoulli-cdf；資料={\"p\":[1,2],\"c\":[3,20],\"shift\":24,\"n\":23,\"threshold\":[1,2]}。請依 [n,p_n,threshold,F_n,F,limit_CDF_continuity_point] 欄序回答。","answer":{"kind":"expression","value":"(23, 473/940, 1/2, 467/940, 1/2, 是)","explanation_zh":"Wave4收束核對=(23, 473/940, 1/2, 467/940, 1/2, 是)；依完整明示資料重算；只在極限CDF連續點要求收斂且有限prefix不足；不要求coupling且不推出依機率、幾乎處處或Lp收斂。"},"difficulty":{"band":"undergraduate_core","level":3,"skills":["依分布收斂"]},"variant":{"family_id":"qf-mod31-convdist-bernoulli-cdf","seed":202610313023,"parameters":{"p":[1,2],"c":[3,20],"shift":24,"n":23,"threshold":[1,2],"domain":"Symbolic_Bernoulli_CDF_limit","operation":"convdist-bernoulli-cdf","semantic_template":"qf-mod31-convdist-bernoulli-cdf/{\"c\":[3,20],\"n\":23,\"p\":[1,2],\"shift\":24,\"threshold\":[1,2]}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_model","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"候選須由主端獨立重算；不構成人工審定、一般不可數性／色數最優性／更強機率收斂／商域、optional stopping、Lean或形式Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-14","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261014-advance-20261031-r03-convergence-in-distribution-0024","batch_id":"batch-20261014-advance-20261031-r03-convergence-in-distribution-foundations","language":"zh-Hant","source_mko_ids":["mko-convergence-in-distribution"],"title_zh":"依分布收斂","stem_zh":"Bernoulli symbolic tail與極限CDF。操作=convdist-bernoulli-cdf；資料={\"p\":[1,2],\"c\":[4,20],\"shift\":25,\"n\":24,\"threshold\":[2,1]}。請依 [n,p_n,threshold,F_n,F,limit_CDF_continuity_point] 欄序回答。","answer":{"kind":"expression","value":"(24, 247/490, 2, 1, 1, 是)","explanation_zh":"Wave4收束核對=(24, 247/490, 2, 1, 1, 是)；依完整明示資料重算；只在極限CDF連續點要求收斂且有限prefix不足；不要求coupling且不推出依機率、幾乎處處或Lp收斂。"},"difficulty":{"band":"undergraduate_core","level":3,"skills":["依分布收斂"]},"variant":{"family_id":"qf-mod31-convdist-bernoulli-cdf","seed":202610313024,"parameters":{"p":[1,2],"c":[4,20],"shift":25,"n":24,"threshold":[2,1],"domain":"Symbolic_Bernoulli_CDF_limit","operation":"convdist-bernoulli-cdf","semantic_template":"qf-mod31-convdist-bernoulli-cdf/{\"c\":[4,20],\"n\":24,\"p\":[1,2],\"shift\":25,\"threshold\":[2,1]}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_model","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"候選須由主端獨立重算；不構成人工審定、一般不可數性／色數最優性／更強機率收斂／商域、optional stopping、Lean或形式Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-14","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261014-advance-20261031-r03-convergence-in-distribution-0025","batch_id":"batch-20261014-advance-20261031-r03-convergence-in-distribution-foundations","language":"zh-Hant","source_mko_ids":["mko-convergence-in-distribution"],"title_zh":"依分布收斂","stem_zh":"Bernoulli symbolic tail與極限CDF。操作=convdist-bernoulli-cdf；資料={\"p\":[1,2],\"c\":[5,20],\"shift\":26,\"n\":25,\"threshold\":[-1,1]}。請依 [n,p_n,threshold,F_n,F,limit_CDF_continuity_point] 欄序回答。","answer":{"kind":"expression","value":"(25, 103/204, -1, 0, 0, 是)","explanation_zh":"Wave4收束核對=(25, 103/204, -1, 0, 0, 是)；依完整明示資料重算；只在極限CDF連續點要求收斂且有限prefix不足；不要求coupling且不推出依機率、幾乎處處或Lp收斂。"},"difficulty":{"band":"undergraduate_core","level":3,"skills":["依分布收斂"]},"variant":{"family_id":"qf-mod31-convdist-bernoulli-cdf","seed":202610313025,"parameters":{"p":[1,2],"c":[5,20],"shift":26,"n":25,"threshold":[-1,1],"domain":"Symbolic_Bernoulli_CDF_limit","operation":"convdist-bernoulli-cdf","semantic_template":"qf-mod31-convdist-bernoulli-cdf/{\"c\":[5,20],\"n\":25,\"p\":[1,2],\"shift\":26,\"threshold\":[-1,1]}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_model","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"候選須由主端獨立重算；不構成人工審定、一般不可數性／色數最優性／更強機率收斂／商域、optional stopping、Lean或形式Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-14","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261014-advance-20261031-r03-convergence-in-distribution-0026","batch_id":"batch-20261014-advance-20261031-r03-convergence-in-distribution-foundations","language":"zh-Hant","source_mko_ids":["mko-convergence-in-distribution"],"title_zh":"依分布收斂","stem_zh":"Bernoulli symbolic tail與極限CDF。操作=convdist-pointwise-gap；資料={\"p\":[1,2],\"c\":[1,20],\"shift\":2,\"n\":1,\"threshold\":[-1,1]}。請依 [n,threshold,absolute_gap,limit_CDF_continuity_point,symbolic_certificate] 欄序回答。","answer":{"kind":"expression","value":"(1, -1, 0, 是, gap_tends_to_zero_at_every_limit_CDF_continuity_point)","explanation_zh":"Wave4收束核對=(1, -1, 0, 是, gap_tends_to_zero_at_every_limit_CDF_continuity_point)；依完整明示資料重算；只在極限CDF連續點要求收斂且有限prefix不足；不要求coupling且不推出依機率、幾乎處處或Lp收斂。"},"difficulty":{"band":"undergraduate_core","level":1,"skills":["依分布收斂"]},"variant":{"family_id":"qf-mod31-convdist-pointwise-gap","seed":202610313026,"parameters":{"p":[1,2],"c":[1,20],"shift":2,"n":1,"threshold":[-1,1],"domain":"Symbolic_Bernoulli_CDF_limit","operation":"convdist-pointwise-gap","semantic_template":"qf-mod31-convdist-pointwise-gap/{\"c\":[1,20],\"n\":1,\"p\":[1,2],\"shift\":2,\"threshold\":[-1,1]}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_model","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"候選須由主端獨立重算；不構成人工審定、一般不可數性／色數最優性／更強機率收斂／商域、optional stopping、Lean或形式Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-14","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261014-advance-20261031-r03-convergence-in-distribution-0027","batch_id":"batch-20261014-advance-20261031-r03-convergence-in-distribution-foundations","language":"zh-Hant","source_mko_ids":["mko-convergence-in-distribution"],"title_zh":"依分布收斂","stem_zh":"Bernoulli symbolic tail與極限CDF。操作=convdist-pointwise-gap；資料={\"p\":[1,2],\"c\":[2,20],\"shift\":3,\"n\":2,\"threshold\":[1,2]}。請依 [n,threshold,absolute_gap,limit_CDF_continuity_point,symbolic_certificate] 欄序回答。","answer":{"kind":"expression","value":"(2, 1/2, 1/50, 是, gap_tends_to_zero_at_every_limit_CDF_continuity_point)","explanation_zh":"Wave4收束核對=(2, 1/2, 1/50, 是, gap_tends_to_zero_at_every_limit_CDF_continuity_point)；依完整明示資料重算；只在極限CDF連續點要求收斂且有限prefix不足；不要求coupling且不推出依機率、幾乎處處或Lp收斂。"},"difficulty":{"band":"undergraduate_core","level":1,"skills":["依分布收斂"]},"variant":{"family_id":"qf-mod31-convdist-pointwise-gap","seed":202610313027,"parameters":{"p":[1,2],"c":[2,20],"shift":3,"n":2,"threshold":[1,2],"domain":"Symbolic_Bernoulli_CDF_limit","operation":"convdist-pointwise-gap","semantic_template":"qf-mod31-convdist-pointwise-gap/{\"c\":[2,20],\"n\":2,\"p\":[1,2],\"shift\":3,\"threshold\":[1,2]}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_model","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"候選須由主端獨立重算；不構成人工審定、一般不可數性／色數最優性／更強機率收斂／商域、optional stopping、Lean或形式Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-14","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261014-advance-20261031-r03-convergence-in-distribution-0028","batch_id":"batch-20261014-advance-20261031-r03-convergence-in-distribution-foundations","language":"zh-Hant","source_mko_ids":["mko-convergence-in-distribution"],"title_zh":"依分布收斂","stem_zh":"Bernoulli symbolic tail與極限CDF。操作=convdist-pointwise-gap；資料={\"p\":[1,2],\"c\":[3,20],\"shift\":4,\"n\":3,\"threshold\":[2,1]}。請依 [n,threshold,absolute_gap,limit_CDF_continuity_point,symbolic_certificate] 欄序回答。","answer":{"kind":"expression","value":"(3, 2, 0, 是, gap_tends_to_zero_at_every_limit_CDF_continuity_point)","explanation_zh":"Wave4收束核對=(3, 2, 0, 是, gap_tends_to_zero_at_every_limit_CDF_continuity_point)；依完整明示資料重算；只在極限CDF連續點要求收斂且有限prefix不足；不要求coupling且不推出依機率、幾乎處處或Lp收斂。"},"difficulty":{"band":"undergraduate_core","level":1,"skills":["依分布收斂"]},"variant":{"family_id":"qf-mod31-convdist-pointwise-gap","seed":202610313028,"parameters":{"p":[1,2],"c":[3,20],"shift":4,"n":3,"threshold":[2,1],"domain":"Symbolic_Bernoulli_CDF_limit","operation":"convdist-pointwise-gap","semantic_template":"qf-mod31-convdist-pointwise-gap/{\"c\":[3,20],\"n\":3,\"p\":[1,2],\"shift\":4,\"threshold\":[2,1]}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_model","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"候選須由主端獨立重算；不構成人工審定、一般不可數性／色數最優性／更強機率收斂／商域、optional stopping、Lean或形式Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-14","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261014-advance-20261031-r03-convergence-in-distribution-0029","batch_id":"batch-20261014-advance-20261031-r03-convergence-in-distribution-foundations","language":"zh-Hant","source_mko_ids":["mko-convergence-in-distribution"],"title_zh":"依分布收斂","stem_zh":"Bernoulli symbolic tail與極限CDF。操作=convdist-pointwise-gap；資料={\"p\":[1,2],\"c\":[4,20],\"shift\":5,\"n\":4,\"threshold\":[-1,1]}。請依 [n,threshold,absolute_gap,limit_CDF_continuity_point,symbolic_certificate] 欄序回答。","answer":{"kind":"expression","value":"(4, -1, 0, 是, gap_tends_to_zero_at_every_limit_CDF_continuity_point)","explanation_zh":"Wave4收束核對=(4, -1, 0, 是, gap_tends_to_zero_at_every_limit_CDF_continuity_point)；依完整明示資料重算；只在極限CDF連續點要求收斂且有限prefix不足；不要求coupling且不推出依機率、幾乎處處或Lp收斂。"},"difficulty":{"band":"undergraduate_core","level":1,"skills":["依分布收斂"]},"variant":{"family_id":"qf-mod31-convdist-pointwise-gap","seed":202610313029,"parameters":{"p":[1,2],"c":[4,20],"shift":5,"n":4,"threshold":[-1,1],"domain":"Symbolic_Bernoulli_CDF_limit","operation":"convdist-pointwise-gap","semantic_template":"qf-mod31-convdist-pointwise-gap/{\"c\":[4,20],\"n\":4,\"p\":[1,2],\"shift\":5,\"threshold\":[-1,1]}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_model","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"候選須由主端獨立重算；不構成人工審定、一般不可數性／色數最優性／更強機率收斂／商域、optional stopping、Lean或形式Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-14","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261014-advance-20261031-r03-convergence-in-distribution-0030","batch_id":"batch-20261014-advance-20261031-r03-convergence-in-distribution-foundations","language":"zh-Hant","source_mko_ids":["mko-convergence-in-distribution"],"title_zh":"依分布收斂","stem_zh":"Bernoulli symbolic tail與極限CDF。操作=convdist-pointwise-gap；資料={\"p\":[1,2],\"c\":[5,20],\"shift\":6,\"n\":5,\"threshold\":[1,2]}。請依 [n,threshold,absolute_gap,limit_CDF_continuity_point,symbolic_certificate] 欄序回答。","answer":{"kind":"expression","value":"(5, 1/2, 1/44, 是, gap_tends_to_zero_at_every_limit_CDF_continuity_point)","explanation_zh":"Wave4收束核對=(5, 1/2, 1/44, 是, gap_tends_to_zero_at_every_limit_CDF_continuity_point)；依完整明示資料重算；只在極限CDF連續點要求收斂且有限prefix不足；不要求coupling且不推出依機率、幾乎處處或Lp收斂。"},"difficulty":{"band":"undergraduate_core","level":1,"skills":["依分布收斂"]},"variant":{"family_id":"qf-mod31-convdist-pointwise-gap","seed":202610313030,"parameters":{"p":[1,2],"c":[5,20],"shift":6,"n":5,"threshold":[1,2],"domain":"Symbolic_Bernoulli_CDF_limit","operation":"convdist-pointwise-gap","semantic_template":"qf-mod31-convdist-pointwise-gap/{\"c\":[5,20],\"n\":5,\"p\":[1,2],\"shift\":6,\"threshold\":[1,2]}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_model","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"候選須由主端獨立重算；不構成人工審定、一般不可數性／色數最優性／更強機率收斂／商域、optional stopping、Lean或形式Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-14","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261014-advance-20261031-r03-convergence-in-distribution-0031","batch_id":"batch-20261014-advance-20261031-r03-convergence-in-distribution-foundations","language":"zh-Hant","source_mko_ids":["mko-convergence-in-distribution"],"title_zh":"依分布收斂","stem_zh":"Bernoulli symbolic tail與極限CDF。操作=convdist-pointwise-gap；資料={\"p\":[1,2],\"c\":[1,20],\"shift\":7,\"n\":6,\"threshold\":[2,1]}。請依 [n,threshold,absolute_gap,limit_CDF_continuity_point,symbolic_certificate] 欄序回答。","answer":{"kind":"expression","value":"(6, 2, 0, 是, gap_tends_to_zero_at_every_limit_CDF_continuity_point)","explanation_zh":"Wave4收束核對=(6, 2, 0, 是, gap_tends_to_zero_at_every_limit_CDF_continuity_point)；依完整明示資料重算；只在極限CDF連續點要求收斂且有限prefix不足；不要求coupling且不推出依機率、幾乎處處或Lp收斂。"},"difficulty":{"band":"undergraduate_core","level":1,"skills":["依分布收斂"]},"variant":{"family_id":"qf-mod31-convdist-pointwise-gap","seed":202610313031,"parameters":{"p":[1,2],"c":[1,20],"shift":7,"n":6,"threshold":[2,1],"domain":"Symbolic_Bernoulli_CDF_limit","operation":"convdist-pointwise-gap","semantic_template":"qf-mod31-convdist-pointwise-gap/{\"c\":[1,20],\"n\":6,\"p\":[1,2],\"shift\":7,\"threshold\":[2,1]}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_model","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"候選須由主端獨立重算；不構成人工審定、一般不可數性／色數最優性／更強機率收斂／商域、optional stopping、Lean或形式Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-14","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261014-advance-20261031-r03-convergence-in-distribution-0032","batch_id":"batch-20261014-advance-20261031-r03-convergence-in-distribution-foundations","language":"zh-Hant","source_mko_ids":["mko-convergence-in-distribution"],"title_zh":"依分布收斂","stem_zh":"Bernoulli symbolic tail與極限CDF。操作=convdist-pointwise-gap；資料={\"p\":[1,2],\"c\":[2,20],\"shift\":8,\"n\":7,\"threshold\":[-1,1]}。請依 [n,threshold,absolute_gap,limit_CDF_continuity_point,symbolic_certificate] 欄序回答。","answer":{"kind":"expression","value":"(7, -1, 0, 是, gap_tends_to_zero_at_every_limit_CDF_continuity_point)","explanation_zh":"Wave4收束核對=(7, -1, 0, 是, gap_tends_to_zero_at_every_limit_CDF_continuity_point)；依完整明示資料重算；只在極限CDF連續點要求收斂且有限prefix不足；不要求coupling且不推出依機率、幾乎處處或Lp收斂。"},"difficulty":{"band":"undergraduate_core","level":1,"skills":["依分布收斂"]},"variant":{"family_id":"qf-mod31-convdist-pointwise-gap","seed":202610313032,"parameters":{"p":[1,2],"c":[2,20],"shift":8,"n":7,"threshold":[-1,1],"domain":"Symbolic_Bernoulli_CDF_limit","operation":"convdist-pointwise-gap","semantic_template":"qf-mod31-convdist-pointwise-gap/{\"c\":[2,20],\"n\":7,\"p\":[1,2],\"shift\":8,\"threshold\":[-1,1]}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_model","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"候選須由主端獨立重算；不構成人工審定、一般不可數性／色數最優性／更強機率收斂／商域、optional stopping、Lean或形式Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-14","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261014-advance-20261031-r03-convergence-in-distribution-0033","batch_id":"batch-20261014-advance-20261031-r03-convergence-in-distribution-foundations","language":"zh-Hant","source_mko_ids":["mko-convergence-in-distribution"],"title_zh":"依分布收斂","stem_zh":"Bernoulli symbolic tail與極限CDF。操作=convdist-pointwise-gap；資料={\"p\":[1,2],\"c\":[3,20],\"shift\":9,\"n\":8,\"threshold\":[1,2]}。請依 [n,threshold,absolute_gap,limit_CDF_continuity_point,symbolic_certificate] 欄序回答。","answer":{"kind":"expression","value":"(8, 1/2, 3/340, 是, gap_tends_to_zero_at_every_limit_CDF_continuity_point)","explanation_zh":"Wave4收束核對=(8, 1/2, 3/340, 是, gap_tends_to_zero_at_every_limit_CDF_continuity_point)；依完整明示資料重算；只在極限CDF連續點要求收斂且有限prefix不足；不要求coupling且不推出依機率、幾乎處處或Lp收斂。"},"difficulty":{"band":"undergraduate_core","level":1,"skills":["依分布收斂"]},"variant":{"family_id":"qf-mod31-convdist-pointwise-gap","seed":202610313033,"parameters":{"p":[1,2],"c":[3,20],"shift":9,"n":8,"threshold":[1,2],"domain":"Symbolic_Bernoulli_CDF_limit","operation":"convdist-pointwise-gap","semantic_template":"qf-mod31-convdist-pointwise-gap/{\"c\":[3,20],\"n\":8,\"p\":[1,2],\"shift\":9,\"threshold\":[1,2]}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_model","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"候選須由主端獨立重算；不構成人工審定、一般不可數性／色數最優性／更強機率收斂／商域、optional stopping、Lean或形式Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-14","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261014-advance-20261031-r03-convergence-in-distribution-0034","batch_id":"batch-20261014-advance-20261031-r03-convergence-in-distribution-foundations","language":"zh-Hant","source_mko_ids":["mko-convergence-in-distribution"],"title_zh":"依分布收斂","stem_zh":"Bernoulli symbolic tail與極限CDF。操作=convdist-pointwise-gap；資料={\"p\":[1,2],\"c\":[4,20],\"shift\":10,\"n\":9,\"threshold\":[2,1]}。請依 [n,threshold,absolute_gap,limit_CDF_continuity_point,symbolic_certificate] 欄序回答。","answer":{"kind":"expression","value":"(9, 2, 0, 是, gap_tends_to_zero_at_every_limit_CDF_continuity_point)","explanation_zh":"Wave4收束核對=(9, 2, 0, 是, gap_tends_to_zero_at_every_limit_CDF_continuity_point)；依完整明示資料重算；只在極限CDF連續點要求收斂且有限prefix不足；不要求coupling且不推出依機率、幾乎處處或Lp收斂。"},"difficulty":{"band":"undergraduate_core","level":2,"skills":["依分布收斂"]},"variant":{"family_id":"qf-mod31-convdist-pointwise-gap","seed":202610313034,"parameters":{"p":[1,2],"c":[4,20],"shift":10,"n":9,"threshold":[2,1],"domain":"Symbolic_Bernoulli_CDF_limit","operation":"convdist-pointwise-gap","semantic_template":"qf-mod31-convdist-pointwise-gap/{\"c\":[4,20],\"n\":9,\"p\":[1,2],\"shift\":10,\"threshold\":[2,1]}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_model","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"候選須由主端獨立重算；不構成人工審定、一般不可數性／色數最優性／更強機率收斂／商域、optional stopping、Lean或形式Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-14","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261014-advance-20261031-r03-convergence-in-distribution-0035","batch_id":"batch-20261014-advance-20261031-r03-convergence-in-distribution-foundations","language":"zh-Hant","source_mko_ids":["mko-convergence-in-distribution"],"title_zh":"依分布收斂","stem_zh":"Bernoulli symbolic tail與極限CDF。操作=convdist-pointwise-gap；資料={\"p\":[1,2],\"c\":[5,20],\"shift\":11,\"n\":10,\"threshold\":[-1,1]}。請依 [n,threshold,absolute_gap,limit_CDF_continuity_point,symbolic_certificate] 欄序回答。","answer":{"kind":"expression","value":"(10, -1, 0, 是, gap_tends_to_zero_at_every_limit_CDF_continuity_point)","explanation_zh":"Wave4收束核對=(10, -1, 0, 是, gap_tends_to_zero_at_every_limit_CDF_continuity_point)；依完整明示資料重算；只在極限CDF連續點要求收斂且有限prefix不足；不要求coupling且不推出依機率、幾乎處處或Lp收斂。"},"difficulty":{"band":"undergraduate_core","level":2,"skills":["依分布收斂"]},"variant":{"family_id":"qf-mod31-convdist-pointwise-gap","seed":202610313035,"parameters":{"p":[1,2],"c":[5,20],"shift":11,"n":10,"threshold":[-1,1],"domain":"Symbolic_Bernoulli_CDF_limit","operation":"convdist-pointwise-gap","semantic_template":"qf-mod31-convdist-pointwise-gap/{\"c\":[5,20],\"n\":10,\"p\":[1,2],\"shift\":11,\"threshold\":[-1,1]}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_model","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"候選須由主端獨立重算；不構成人工審定、一般不可數性／色數最優性／更強機率收斂／商域、optional stopping、Lean或形式Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-14","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261014-advance-20261031-r03-convergence-in-distribution-0036","batch_id":"batch-20261014-advance-20261031-r03-convergence-in-distribution-foundations","language":"zh-Hant","source_mko_ids":["mko-convergence-in-distribution"],"title_zh":"依分布收斂","stem_zh":"Bernoulli symbolic tail與極限CDF。操作=convdist-pointwise-gap；資料={\"p\":[1,2],\"c\":[1,20],\"shift\":12,\"n\":11,\"threshold\":[1,2]}。請依 [n,threshold,absolute_gap,limit_CDF_continuity_point,symbolic_certificate] 欄序回答。","answer":{"kind":"expression","value":"(11, 1/2, 1/460, 是, gap_tends_to_zero_at_every_limit_CDF_continuity_point)","explanation_zh":"Wave4收束核對=(11, 1/2, 1/460, 是, gap_tends_to_zero_at_every_limit_CDF_continuity_point)；依完整明示資料重算；只在極限CDF連續點要求收斂且有限prefix不足；不要求coupling且不推出依機率、幾乎處處或Lp收斂。"},"difficulty":{"band":"undergraduate_core","level":2,"skills":["依分布收斂"]},"variant":{"family_id":"qf-mod31-convdist-pointwise-gap","seed":202610313036,"parameters":{"p":[1,2],"c":[1,20],"shift":12,"n":11,"threshold":[1,2],"domain":"Symbolic_Bernoulli_CDF_limit","operation":"convdist-pointwise-gap","semantic_template":"qf-mod31-convdist-pointwise-gap/{\"c\":[1,20],\"n\":11,\"p\":[1,2],\"shift\":12,\"threshold\":[1,2]}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_model","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"候選須由主端獨立重算；不構成人工審定、一般不可數性／色數最優性／更強機率收斂／商域、optional stopping、Lean或形式Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-14","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261014-advance-20261031-r03-convergence-in-distribution-0037","batch_id":"batch-20261014-advance-20261031-r03-convergence-in-distribution-foundations","language":"zh-Hant","source_mko_ids":["mko-convergence-in-distribution"],"title_zh":"依分布收斂","stem_zh":"Bernoulli symbolic tail與極限CDF。操作=convdist-pointwise-gap；資料={\"p\":[1,2],\"c\":[2,20],\"shift\":13,\"n\":12,\"threshold\":[2,1]}。請依 [n,threshold,absolute_gap,limit_CDF_continuity_point,symbolic_certificate] 欄序回答。","answer":{"kind":"expression","value":"(12, 2, 0, 是, gap_tends_to_zero_at_every_limit_CDF_continuity_point)","explanation_zh":"Wave4收束核對=(12, 2, 0, 是, gap_tends_to_zero_at_every_limit_CDF_continuity_point)；依完整明示資料重算；只在極限CDF連續點要求收斂且有限prefix不足；不要求coupling且不推出依機率、幾乎處處或Lp收斂。"},"difficulty":{"band":"undergraduate_core","level":2,"skills":["依分布收斂"]},"variant":{"family_id":"qf-mod31-convdist-pointwise-gap","seed":202610313037,"parameters":{"p":[1,2],"c":[2,20],"shift":13,"n":12,"threshold":[2,1],"domain":"Symbolic_Bernoulli_CDF_limit","operation":"convdist-pointwise-gap","semantic_template":"qf-mod31-convdist-pointwise-gap/{\"c\":[2,20],\"n\":12,\"p\":[1,2],\"shift\":13,\"threshold\":[2,1]}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_model","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"候選須由主端獨立重算；不構成人工審定、一般不可數性／色數最優性／更強機率收斂／商域、optional stopping、Lean或形式Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-14","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261014-advance-20261031-r03-convergence-in-distribution-0038","batch_id":"batch-20261014-advance-20261031-r03-convergence-in-distribution-foundations","language":"zh-Hant","source_mko_ids":["mko-convergence-in-distribution"],"title_zh":"依分布收斂","stem_zh":"Bernoulli symbolic tail與極限CDF。操作=convdist-pointwise-gap；資料={\"p\":[1,2],\"c\":[3,20],\"shift\":14,\"n\":13,\"threshold\":[-1,1]}。請依 [n,threshold,absolute_gap,limit_CDF_continuity_point,symbolic_certificate] 欄序回答。","answer":{"kind":"expression","value":"(13, -1, 0, 是, gap_tends_to_zero_at_every_limit_CDF_continuity_point)","explanation_zh":"Wave4收束核對=(13, -1, 0, 是, gap_tends_to_zero_at_every_limit_CDF_continuity_point)；依完整明示資料重算；只在極限CDF連續點要求收斂且有限prefix不足；不要求coupling且不推出依機率、幾乎處處或Lp收斂。"},"difficulty":{"band":"undergraduate_core","level":2,"skills":["依分布收斂"]},"variant":{"family_id":"qf-mod31-convdist-pointwise-gap","seed":202610313038,"parameters":{"p":[1,2],"c":[3,20],"shift":14,"n":13,"threshold":[-1,1],"domain":"Symbolic_Bernoulli_CDF_limit","operation":"convdist-pointwise-gap","semantic_template":"qf-mod31-convdist-pointwise-gap/{\"c\":[3,20],\"n\":13,\"p\":[1,2],\"shift\":14,\"threshold\":[-1,1]}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_model","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"候選須由主端獨立重算；不構成人工審定、一般不可數性／色數最優性／更強機率收斂／商域、optional stopping、Lean或形式Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-14","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261014-advance-20261031-r03-convergence-in-distribution-0039","batch_id":"batch-20261014-advance-20261031-r03-convergence-in-distribution-foundations","language":"zh-Hant","source_mko_ids":["mko-convergence-in-distribution"],"title_zh":"依分布收斂","stem_zh":"Bernoulli symbolic tail與極限CDF。操作=convdist-pointwise-gap；資料={\"p\":[1,2],\"c\":[4,20],\"shift\":15,\"n\":14,\"threshold\":[1,2]}。請依 [n,threshold,absolute_gap,limit_CDF_continuity_point,symbolic_certificate] 欄序回答。","answer":{"kind":"expression","value":"(14, 1/2, 1/145, 是, gap_tends_to_zero_at_every_limit_CDF_continuity_point)","explanation_zh":"Wave4收束核對=(14, 1/2, 1/145, 是, gap_tends_to_zero_at_every_limit_CDF_continuity_point)；依完整明示資料重算；只在極限CDF連續點要求收斂且有限prefix不足；不要求coupling且不推出依機率、幾乎處處或Lp收斂。"},"difficulty":{"band":"undergraduate_core","level":2,"skills":["依分布收斂"]},"variant":{"family_id":"qf-mod31-convdist-pointwise-gap","seed":202610313039,"parameters":{"p":[1,2],"c":[4,20],"shift":15,"n":14,"threshold":[1,2],"domain":"Symbolic_Bernoulli_CDF_limit","operation":"convdist-pointwise-gap","semantic_template":"qf-mod31-convdist-pointwise-gap/{\"c\":[4,20],\"n\":14,\"p\":[1,2],\"shift\":15,\"threshold\":[1,2]}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_model","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"候選須由主端獨立重算；不構成人工審定、一般不可數性／色數最優性／更強機率收斂／商域、optional stopping、Lean或形式Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-14","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261014-advance-20261031-r03-convergence-in-distribution-0040","batch_id":"batch-20261014-advance-20261031-r03-convergence-in-distribution-foundations","language":"zh-Hant","source_mko_ids":["mko-convergence-in-distribution"],"title_zh":"依分布收斂","stem_zh":"Bernoulli symbolic tail與極限CDF。操作=convdist-pointwise-gap；資料={\"p\":[1,2],\"c\":[5,20],\"shift\":16,\"n\":15,\"threshold\":[2,1]}。請依 [n,threshold,absolute_gap,limit_CDF_continuity_point,symbolic_certificate] 欄序回答。","answer":{"kind":"expression","value":"(15, 2, 0, 是, gap_tends_to_zero_at_every_limit_CDF_continuity_point)","explanation_zh":"Wave4收束核對=(15, 2, 0, 是, gap_tends_to_zero_at_every_limit_CDF_continuity_point)；依完整明示資料重算；只在極限CDF連續點要求收斂且有限prefix不足；不要求coupling且不推出依機率、幾乎處處或Lp收斂。"},"difficulty":{"band":"undergraduate_core","level":2,"skills":["依分布收斂"]},"variant":{"family_id":"qf-mod31-convdist-pointwise-gap","seed":202610313040,"parameters":{"p":[1,2],"c":[5,20],"shift":16,"n":15,"threshold":[2,1],"domain":"Symbolic_Bernoulli_CDF_limit","operation":"convdist-pointwise-gap","semantic_template":"qf-mod31-convdist-pointwise-gap/{\"c\":[5,20],\"n\":15,\"p\":[1,2],\"shift\":16,\"threshold\":[2,1]}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_model","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"候選須由主端獨立重算；不構成人工審定、一般不可數性／色數最優性／更強機率收斂／商域、optional stopping、Lean或形式Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-14","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261014-advance-20261031-r03-convergence-in-distribution-0041","batch_id":"batch-20261014-advance-20261031-r03-convergence-in-distribution-foundations","language":"zh-Hant","source_mko_ids":["mko-convergence-in-distribution"],"title_zh":"依分布收斂","stem_zh":"Bernoulli symbolic tail與極限CDF。操作=convdist-pointwise-gap；資料={\"p\":[1,2],\"c\":[1,20],\"shift\":17,\"n\":16,\"threshold\":[-1,1]}。請依 [n,threshold,absolute_gap,limit_CDF_continuity_point,symbolic_certificate] 欄序回答。","answer":{"kind":"expression","value":"(16, -1, 0, 是, gap_tends_to_zero_at_every_limit_CDF_continuity_point)","explanation_zh":"Wave4收束核對=(16, -1, 0, 是, gap_tends_to_zero_at_every_limit_CDF_continuity_point)；依完整明示資料重算；只在極限CDF連續點要求收斂且有限prefix不足；不要求coupling且不推出依機率、幾乎處處或Lp收斂。"},"difficulty":{"band":"undergraduate_core","level":2,"skills":["依分布收斂"]},"variant":{"family_id":"qf-mod31-convdist-pointwise-gap","seed":202610313041,"parameters":{"p":[1,2],"c":[1,20],"shift":17,"n":16,"threshold":[-1,1],"domain":"Symbolic_Bernoulli_CDF_limit","operation":"convdist-pointwise-gap","semantic_template":"qf-mod31-convdist-pointwise-gap/{\"c\":[1,20],\"n\":16,\"p\":[1,2],\"shift\":17,\"threshold\":[-1,1]}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_model","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"候選須由主端獨立重算；不構成人工審定、一般不可數性／色數最優性／更強機率收斂／商域、optional stopping、Lean或形式Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-14","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261014-advance-20261031-r03-convergence-in-distribution-0042","batch_id":"batch-20261014-advance-20261031-r03-convergence-in-distribution-foundations","language":"zh-Hant","source_mko_ids":["mko-convergence-in-distribution"],"title_zh":"依分布收斂","stem_zh":"Bernoulli symbolic tail與極限CDF。操作=convdist-pointwise-gap；資料={\"p\":[1,2],\"c\":[2,20],\"shift\":18,\"n\":17,\"threshold\":[1,2]}。請依 [n,threshold,absolute_gap,limit_CDF_continuity_point,symbolic_certificate] 欄序回答。","answer":{"kind":"expression","value":"(17, 1/2, 1/350, 是, gap_tends_to_zero_at_every_limit_CDF_continuity_point)","explanation_zh":"Wave4收束核對=(17, 1/2, 1/350, 是, gap_tends_to_zero_at_every_limit_CDF_continuity_point)；依完整明示資料重算；只在極限CDF連續點要求收斂且有限prefix不足；不要求coupling且不推出依機率、幾乎處處或Lp收斂。"},"difficulty":{"band":"undergraduate_core","level":2,"skills":["依分布收斂"]},"variant":{"family_id":"qf-mod31-convdist-pointwise-gap","seed":202610313042,"parameters":{"p":[1,2],"c":[2,20],"shift":18,"n":17,"threshold":[1,2],"domain":"Symbolic_Bernoulli_CDF_limit","operation":"convdist-pointwise-gap","semantic_template":"qf-mod31-convdist-pointwise-gap/{\"c\":[2,20],\"n\":17,\"p\":[1,2],\"shift\":18,\"threshold\":[1,2]}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_model","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"候選須由主端獨立重算；不構成人工審定、一般不可數性／色數最優性／更強機率收斂／商域、optional stopping、Lean或形式Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-14","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261014-advance-20261031-r03-convergence-in-distribution-0043","batch_id":"batch-20261014-advance-20261031-r03-convergence-in-distribution-foundations","language":"zh-Hant","source_mko_ids":["mko-convergence-in-distribution"],"title_zh":"依分布收斂","stem_zh":"Bernoulli symbolic tail與極限CDF。操作=convdist-pointwise-gap；資料={\"p\":[1,2],\"c\":[3,20],\"shift\":19,\"n\":18,\"threshold\":[2,1]}。請依 [n,threshold,absolute_gap,limit_CDF_continuity_point,symbolic_certificate] 欄序回答。","answer":{"kind":"expression","value":"(18, 2, 0, 是, gap_tends_to_zero_at_every_limit_CDF_continuity_point)","explanation_zh":"Wave4收束核對=(18, 2, 0, 是, gap_tends_to_zero_at_every_limit_CDF_continuity_point)；依完整明示資料重算；只在極限CDF連續點要求收斂且有限prefix不足；不要求coupling且不推出依機率、幾乎處處或Lp收斂。"},"difficulty":{"band":"undergraduate_core","level":3,"skills":["依分布收斂"]},"variant":{"family_id":"qf-mod31-convdist-pointwise-gap","seed":202610313043,"parameters":{"p":[1,2],"c":[3,20],"shift":19,"n":18,"threshold":[2,1],"domain":"Symbolic_Bernoulli_CDF_limit","operation":"convdist-pointwise-gap","semantic_template":"qf-mod31-convdist-pointwise-gap/{\"c\":[3,20],\"n\":18,\"p\":[1,2],\"shift\":19,\"threshold\":[2,1]}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_model","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"候選須由主端獨立重算；不構成人工審定、一般不可數性／色數最優性／更強機率收斂／商域、optional stopping、Lean或形式Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-14","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261014-advance-20261031-r03-convergence-in-distribution-0044","batch_id":"batch-20261014-advance-20261031-r03-convergence-in-distribution-foundations","language":"zh-Hant","source_mko_ids":["mko-convergence-in-distribution"],"title_zh":"依分布收斂","stem_zh":"Bernoulli symbolic tail與極限CDF。操作=convdist-pointwise-gap；資料={\"p\":[1,2],\"c\":[4,20],\"shift\":20,\"n\":19,\"threshold\":[-1,1]}。請依 [n,threshold,absolute_gap,limit_CDF_continuity_point,symbolic_certificate] 欄序回答。","answer":{"kind":"expression","value":"(19, -1, 0, 是, gap_tends_to_zero_at_every_limit_CDF_continuity_point)","explanation_zh":"Wave4收束核對=(19, -1, 0, 是, gap_tends_to_zero_at_every_limit_CDF_continuity_point)；依完整明示資料重算；只在極限CDF連續點要求收斂且有限prefix不足；不要求coupling且不推出依機率、幾乎處處或Lp收斂。"},"difficulty":{"band":"undergraduate_core","level":3,"skills":["依分布收斂"]},"variant":{"family_id":"qf-mod31-convdist-pointwise-gap","seed":202610313044,"parameters":{"p":[1,2],"c":[4,20],"shift":20,"n":19,"threshold":[-1,1],"domain":"Symbolic_Bernoulli_CDF_limit","operation":"convdist-pointwise-gap","semantic_template":"qf-mod31-convdist-pointwise-gap/{\"c\":[4,20],\"n\":19,\"p\":[1,2],\"shift\":20,\"threshold\":[-1,1]}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_model","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"候選須由主端獨立重算；不構成人工審定、一般不可數性／色數最優性／更強機率收斂／商域、optional stopping、Lean或形式Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-14","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261014-advance-20261031-r03-convergence-in-distribution-0045","batch_id":"batch-20261014-advance-20261031-r03-convergence-in-distribution-foundations","language":"zh-Hant","source_mko_ids":["mko-convergence-in-distribution"],"title_zh":"依分布收斂","stem_zh":"Bernoulli symbolic tail與極限CDF。操作=convdist-pointwise-gap；資料={\"p\":[1,2],\"c\":[5,20],\"shift\":21,\"n\":20,\"threshold\":[1,2]}。請依 [n,threshold,absolute_gap,limit_CDF_continuity_point,symbolic_certificate] 欄序回答。","answer":{"kind":"expression","value":"(20, 1/2, 1/164, 是, gap_tends_to_zero_at_every_limit_CDF_continuity_point)","explanation_zh":"Wave4收束核對=(20, 1/2, 1/164, 是, gap_tends_to_zero_at_every_limit_CDF_continuity_point)；依完整明示資料重算；只在極限CDF連續點要求收斂且有限prefix不足；不要求coupling且不推出依機率、幾乎處處或Lp收斂。"},"difficulty":{"band":"undergraduate_core","level":3,"skills":["依分布收斂"]},"variant":{"family_id":"qf-mod31-convdist-pointwise-gap","seed":202610313045,"parameters":{"p":[1,2],"c":[5,20],"shift":21,"n":20,"threshold":[1,2],"domain":"Symbolic_Bernoulli_CDF_limit","operation":"convdist-pointwise-gap","semantic_template":"qf-mod31-convdist-pointwise-gap/{\"c\":[5,20],\"n\":20,\"p\":[1,2],\"shift\":21,\"threshold\":[1,2]}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_model","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"候選須由主端獨立重算；不構成人工審定、一般不可數性／色數最優性／更強機率收斂／商域、optional stopping、Lean或形式Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-14","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261014-advance-20261031-r03-convergence-in-distribution-0046","batch_id":"batch-20261014-advance-20261031-r03-convergence-in-distribution-foundations","language":"zh-Hant","source_mko_ids":["mko-convergence-in-distribution"],"title_zh":"依分布收斂","stem_zh":"Bernoulli symbolic tail與極限CDF。操作=convdist-pointwise-gap；資料={\"p\":[1,2],\"c\":[1,20],\"shift\":22,\"n\":21,\"threshold\":[2,1]}。請依 [n,threshold,absolute_gap,limit_CDF_continuity_point,symbolic_certificate] 欄序回答。","answer":{"kind":"expression","value":"(21, 2, 0, 是, gap_tends_to_zero_at_every_limit_CDF_continuity_point)","explanation_zh":"Wave4收束核對=(21, 2, 0, 是, gap_tends_to_zero_at_every_limit_CDF_continuity_point)；依完整明示資料重算；只在極限CDF連續點要求收斂且有限prefix不足；不要求coupling且不推出依機率、幾乎處處或Lp收斂。"},"difficulty":{"band":"undergraduate_core","level":3,"skills":["依分布收斂"]},"variant":{"family_id":"qf-mod31-convdist-pointwise-gap","seed":202610313046,"parameters":{"p":[1,2],"c":[1,20],"shift":22,"n":21,"threshold":[2,1],"domain":"Symbolic_Bernoulli_CDF_limit","operation":"convdist-pointwise-gap","semantic_template":"qf-mod31-convdist-pointwise-gap/{\"c\":[1,20],\"n\":21,\"p\":[1,2],\"shift\":22,\"threshold\":[2,1]}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_model","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"候選須由主端獨立重算；不構成人工審定、一般不可數性／色數最優性／更強機率收斂／商域、optional stopping、Lean或形式Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-14","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261014-advance-20261031-r03-convergence-in-distribution-0047","batch_id":"batch-20261014-advance-20261031-r03-convergence-in-distribution-foundations","language":"zh-Hant","source_mko_ids":["mko-convergence-in-distribution"],"title_zh":"依分布收斂","stem_zh":"Bernoulli symbolic tail與極限CDF。操作=convdist-pointwise-gap；資料={\"p\":[1,2],\"c\":[2,20],\"shift\":23,\"n\":22,\"threshold\":[-1,1]}。請依 [n,threshold,absolute_gap,limit_CDF_continuity_point,symbolic_certificate] 欄序回答。","answer":{"kind":"expression","value":"(22, -1, 0, 是, gap_tends_to_zero_at_every_limit_CDF_continuity_point)","explanation_zh":"Wave4收束核對=(22, -1, 0, 是, gap_tends_to_zero_at_every_limit_CDF_continuity_point)；依完整明示資料重算；只在極限CDF連續點要求收斂且有限prefix不足；不要求coupling且不推出依機率、幾乎處處或Lp收斂。"},"difficulty":{"band":"undergraduate_core","level":3,"skills":["依分布收斂"]},"variant":{"family_id":"qf-mod31-convdist-pointwise-gap","seed":202610313047,"parameters":{"p":[1,2],"c":[2,20],"shift":23,"n":22,"threshold":[-1,1],"domain":"Symbolic_Bernoulli_CDF_limit","operation":"convdist-pointwise-gap","semantic_template":"qf-mod31-convdist-pointwise-gap/{\"c\":[2,20],\"n\":22,\"p\":[1,2],\"shift\":23,\"threshold\":[-1,1]}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_model","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"候選須由主端獨立重算；不構成人工審定、一般不可數性／色數最優性／更強機率收斂／商域、optional stopping、Lean或形式Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-14","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261014-advance-20261031-r03-convergence-in-distribution-0048","batch_id":"batch-20261014-advance-20261031-r03-convergence-in-distribution-foundations","language":"zh-Hant","source_mko_ids":["mko-convergence-in-distribution"],"title_zh":"依分布收斂","stem_zh":"Bernoulli symbolic tail與極限CDF。操作=convdist-pointwise-gap；資料={\"p\":[1,2],\"c\":[3,20],\"shift\":24,\"n\":23,\"threshold\":[1,2]}。請依 [n,threshold,absolute_gap,limit_CDF_continuity_point,symbolic_certificate] 欄序回答。","answer":{"kind":"expression","value":"(23, 1/2, 3/940, 是, gap_tends_to_zero_at_every_limit_CDF_continuity_point)","explanation_zh":"Wave4收束核對=(23, 1/2, 3/940, 是, gap_tends_to_zero_at_every_limit_CDF_continuity_point)；依完整明示資料重算；只在極限CDF連續點要求收斂且有限prefix不足；不要求coupling且不推出依機率、幾乎處處或Lp收斂。"},"difficulty":{"band":"undergraduate_core","level":3,"skills":["依分布收斂"]},"variant":{"family_id":"qf-mod31-convdist-pointwise-gap","seed":202610313048,"parameters":{"p":[1,2],"c":[3,20],"shift":24,"n":23,"threshold":[1,2],"domain":"Symbolic_Bernoulli_CDF_limit","operation":"convdist-pointwise-gap","semantic_template":"qf-mod31-convdist-pointwise-gap/{\"c\":[3,20],\"n\":23,\"p\":[1,2],\"shift\":24,\"threshold\":[1,2]}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_model","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"候選須由主端獨立重算；不構成人工審定、一般不可數性／色數最優性／更強機率收斂／商域、optional stopping、Lean或形式Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-14","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261014-advance-20261031-r03-convergence-in-distribution-0049","batch_id":"batch-20261014-advance-20261031-r03-convergence-in-distribution-foundations","language":"zh-Hant","source_mko_ids":["mko-convergence-in-distribution"],"title_zh":"依分布收斂","stem_zh":"Bernoulli symbolic tail與極限CDF。操作=convdist-pointwise-gap；資料={\"p\":[1,2],\"c\":[4,20],\"shift\":25,\"n\":24,\"threshold\":[2,1]}。請依 [n,threshold,absolute_gap,limit_CDF_continuity_point,symbolic_certificate] 欄序回答。","answer":{"kind":"expression","value":"(24, 2, 0, 是, gap_tends_to_zero_at_every_limit_CDF_continuity_point)","explanation_zh":"Wave4收束核對=(24, 2, 0, 是, gap_tends_to_zero_at_every_limit_CDF_continuity_point)；依完整明示資料重算；只在極限CDF連續點要求收斂且有限prefix不足；不要求coupling且不推出依機率、幾乎處處或Lp收斂。"},"difficulty":{"band":"undergraduate_core","level":3,"skills":["依分布收斂"]},"variant":{"family_id":"qf-mod31-convdist-pointwise-gap","seed":202610313049,"parameters":{"p":[1,2],"c":[4,20],"shift":25,"n":24,"threshold":[2,1],"domain":"Symbolic_Bernoulli_CDF_limit","operation":"convdist-pointwise-gap","semantic_template":"qf-mod31-convdist-pointwise-gap/{\"c\":[4,20],\"n\":24,\"p\":[1,2],\"shift\":25,\"threshold\":[2,1]}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_model","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"候選須由主端獨立重算；不構成人工審定、一般不可數性／色數最優性／更強機率收斂／商域、optional stopping、Lean或形式Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-14","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261014-advance-20261031-r03-convergence-in-distribution-0050","batch_id":"batch-20261014-advance-20261031-r03-convergence-in-distribution-foundations","language":"zh-Hant","source_mko_ids":["mko-convergence-in-distribution"],"title_zh":"依分布收斂","stem_zh":"Bernoulli symbolic tail與極限CDF。操作=convdist-pointwise-gap；資料={\"p\":[1,2],\"c\":[5,20],\"shift\":26,\"n\":25,\"threshold\":[-1,1]}。請依 [n,threshold,absolute_gap,limit_CDF_continuity_point,symbolic_certificate] 欄序回答。","answer":{"kind":"expression","value":"(25, -1, 0, 是, gap_tends_to_zero_at_every_limit_CDF_continuity_point)","explanation_zh":"Wave4收束核對=(25, -1, 0, 是, gap_tends_to_zero_at_every_limit_CDF_continuity_point)；依完整明示資料重算；只在極限CDF連續點要求收斂且有限prefix不足；不要求coupling且不推出依機率、幾乎處處或Lp收斂。"},"difficulty":{"band":"undergraduate_core","level":3,"skills":["依分布收斂"]},"variant":{"family_id":"qf-mod31-convdist-pointwise-gap","seed":202610313050,"parameters":{"p":[1,2],"c":[5,20],"shift":26,"n":25,"threshold":[-1,1],"domain":"Symbolic_Bernoulli_CDF_limit","operation":"convdist-pointwise-gap","semantic_template":"qf-mod31-convdist-pointwise-gap/{\"c\":[5,20],\"n\":25,\"p\":[1,2],\"shift\":26,\"threshold\":[-1,1]}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_model","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"候選須由主端獨立重算；不構成人工審定、一般不可數性／色數最優性／更強機率收斂／商域、optional stopping、Lean或形式Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-14","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261014-advance-20261031-r03-convergence-in-distribution-0051","batch_id":"batch-20261014-advance-20261031-r03-convergence-in-distribution-foundations","language":"zh-Hant","source_mko_ids":["mko-convergence-in-distribution"],"title_zh":"依分布收斂","stem_zh":"Bernoulli symbolic tail與極限CDF。操作=convdist-continuity-obligation；資料={\"p\":[1,30],\"threshold\":[-12,7]}。請依 [p,threshold,continuity_point,definition_obligation] 欄序回答。","answer":{"kind":"expression","value":"(1/30, -12/7, 是, CDF_convergence_required_here)","explanation_zh":"Wave4收束核對=(1/30, -12/7, 是, CDF_convergence_required_here)；依完整明示資料重算；只在極限CDF連續點要求收斂且有限prefix不足；不要求coupling且不推出依機率、幾乎處處或Lp收斂。"},"difficulty":{"band":"undergraduate_core","level":1,"skills":["依分布收斂"]},"variant":{"family_id":"qf-mod31-convdist-continuity-obligation","seed":202610313051,"parameters":{"p":[1,30],"threshold":[-12,7],"domain":"Symbolic_Bernoulli_CDF_limit","operation":"convdist-continuity-obligation","semantic_template":"qf-mod31-convdist-continuity-obligation/{\"p\":[1,30],\"threshold\":[-12,7]}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_model","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"候選須由主端獨立重算；不構成人工審定、一般不可數性／色數最優性／更強機率收斂／商域、optional stopping、Lean或形式Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-14","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261014-advance-20261031-r03-convergence-in-distribution-0052","batch_id":"batch-20261014-advance-20261031-r03-convergence-in-distribution-foundations","language":"zh-Hant","source_mko_ids":["mko-convergence-in-distribution"],"title_zh":"依分布收斂","stem_zh":"Bernoulli symbolic tail與極限CDF。操作=convdist-continuity-obligation；資料={\"p\":[2,30],\"threshold\":[-11,7]}。請依 [p,threshold,continuity_point,definition_obligation] 欄序回答。","answer":{"kind":"expression","value":"(1/15, -11/7, 是, CDF_convergence_required_here)","explanation_zh":"Wave4收束核對=(1/15, -11/7, 是, CDF_convergence_required_here)；依完整明示資料重算；只在極限CDF連續點要求收斂且有限prefix不足；不要求coupling且不推出依機率、幾乎處處或Lp收斂。"},"difficulty":{"band":"undergraduate_core","level":1,"skills":["依分布收斂"]},"variant":{"family_id":"qf-mod31-convdist-continuity-obligation","seed":202610313052,"parameters":{"p":[2,30],"threshold":[-11,7],"domain":"Symbolic_Bernoulli_CDF_limit","operation":"convdist-continuity-obligation","semantic_template":"qf-mod31-convdist-continuity-obligation/{\"p\":[2,30],\"threshold\":[-11,7]}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_model","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"候選須由主端獨立重算；不構成人工審定、一般不可數性／色數最優性／更強機率收斂／商域、optional stopping、Lean或形式Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-14","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261014-advance-20261031-r03-convergence-in-distribution-0053","batch_id":"batch-20261014-advance-20261031-r03-convergence-in-distribution-foundations","language":"zh-Hant","source_mko_ids":["mko-convergence-in-distribution"],"title_zh":"依分布收斂","stem_zh":"Bernoulli symbolic tail與極限CDF。操作=convdist-continuity-obligation；資料={\"p\":[3,30],\"threshold\":[-10,7]}。請依 [p,threshold,continuity_point,definition_obligation] 欄序回答。","answer":{"kind":"expression","value":"(1/10, -10/7, 是, CDF_convergence_required_here)","explanation_zh":"Wave4收束核對=(1/10, -10/7, 是, CDF_convergence_required_here)；依完整明示資料重算；只在極限CDF連續點要求收斂且有限prefix不足；不要求coupling且不推出依機率、幾乎處處或Lp收斂。"},"difficulty":{"band":"undergraduate_core","level":1,"skills":["依分布收斂"]},"variant":{"family_id":"qf-mod31-convdist-continuity-obligation","seed":202610313053,"parameters":{"p":[3,30],"threshold":[-10,7],"domain":"Symbolic_Bernoulli_CDF_limit","operation":"convdist-continuity-obligation","semantic_template":"qf-mod31-convdist-continuity-obligation/{\"p\":[3,30],\"threshold\":[-10,7]}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_model","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"候選須由主端獨立重算；不構成人工審定、一般不可數性／色數最優性／更強機率收斂／商域、optional stopping、Lean或形式Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-14","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261014-advance-20261031-r03-convergence-in-distribution-0054","batch_id":"batch-20261014-advance-20261031-r03-convergence-in-distribution-foundations","language":"zh-Hant","source_mko_ids":["mko-convergence-in-distribution"],"title_zh":"依分布收斂","stem_zh":"Bernoulli symbolic tail與極限CDF。操作=convdist-continuity-obligation；資料={\"p\":[4,30],\"threshold\":[-9,7]}。請依 [p,threshold,continuity_point,definition_obligation] 欄序回答。","answer":{"kind":"expression","value":"(2/15, -9/7, 是, CDF_convergence_required_here)","explanation_zh":"Wave4收束核對=(2/15, -9/7, 是, CDF_convergence_required_here)；依完整明示資料重算；只在極限CDF連續點要求收斂且有限prefix不足；不要求coupling且不推出依機率、幾乎處處或Lp收斂。"},"difficulty":{"band":"undergraduate_core","level":1,"skills":["依分布收斂"]},"variant":{"family_id":"qf-mod31-convdist-continuity-obligation","seed":202610313054,"parameters":{"p":[4,30],"threshold":[-9,7],"domain":"Symbolic_Bernoulli_CDF_limit","operation":"convdist-continuity-obligation","semantic_template":"qf-mod31-convdist-continuity-obligation/{\"p\":[4,30],\"threshold\":[-9,7]}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_model","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"候選須由主端獨立重算；不構成人工審定、一般不可數性／色數最優性／更強機率收斂／商域、optional stopping、Lean或形式Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-14","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261014-advance-20261031-r03-convergence-in-distribution-0055","batch_id":"batch-20261014-advance-20261031-r03-convergence-in-distribution-foundations","language":"zh-Hant","source_mko_ids":["mko-convergence-in-distribution"],"title_zh":"依分布收斂","stem_zh":"Bernoulli symbolic tail與極限CDF。操作=convdist-continuity-obligation；資料={\"p\":[5,30],\"threshold\":[-8,7]}。請依 [p,threshold,continuity_point,definition_obligation] 欄序回答。","answer":{"kind":"expression","value":"(1/6, -8/7, 是, CDF_convergence_required_here)","explanation_zh":"Wave4收束核對=(1/6, -8/7, 是, CDF_convergence_required_here)；依完整明示資料重算；只在極限CDF連續點要求收斂且有限prefix不足；不要求coupling且不推出依機率、幾乎處處或Lp收斂。"},"difficulty":{"band":"undergraduate_core","level":1,"skills":["依分布收斂"]},"variant":{"family_id":"qf-mod31-convdist-continuity-obligation","seed":202610313055,"parameters":{"p":[5,30],"threshold":[-8,7],"domain":"Symbolic_Bernoulli_CDF_limit","operation":"convdist-continuity-obligation","semantic_template":"qf-mod31-convdist-continuity-obligation/{\"p\":[5,30],\"threshold\":[-8,7]}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_model","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"候選須由主端獨立重算；不構成人工審定、一般不可數性／色數最優性／更強機率收斂／商域、optional stopping、Lean或形式Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-14","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261014-advance-20261031-r03-convergence-in-distribution-0056","batch_id":"batch-20261014-advance-20261031-r03-convergence-in-distribution-foundations","language":"zh-Hant","source_mko_ids":["mko-convergence-in-distribution"],"title_zh":"依分布收斂","stem_zh":"Bernoulli symbolic tail與極限CDF。操作=convdist-continuity-obligation；資料={\"p\":[6,30],\"threshold\":[-7,7]}。請依 [p,threshold,continuity_point,definition_obligation] 欄序回答。","answer":{"kind":"expression","value":"(1/5, -1, 是, CDF_convergence_required_here)","explanation_zh":"Wave4收束核對=(1/5, -1, 是, CDF_convergence_required_here)；依完整明示資料重算；只在極限CDF連續點要求收斂且有限prefix不足；不要求coupling且不推出依機率、幾乎處處或Lp收斂。"},"difficulty":{"band":"undergraduate_core","level":1,"skills":["依分布收斂"]},"variant":{"family_id":"qf-mod31-convdist-continuity-obligation","seed":202610313056,"parameters":{"p":[6,30],"threshold":[-7,7],"domain":"Symbolic_Bernoulli_CDF_limit","operation":"convdist-continuity-obligation","semantic_template":"qf-mod31-convdist-continuity-obligation/{\"p\":[6,30],\"threshold\":[-7,7]}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_model","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"候選須由主端獨立重算；不構成人工審定、一般不可數性／色數最優性／更強機率收斂／商域、optional stopping、Lean或形式Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-14","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261014-advance-20261031-r03-convergence-in-distribution-0057","batch_id":"batch-20261014-advance-20261031-r03-convergence-in-distribution-foundations","language":"zh-Hant","source_mko_ids":["mko-convergence-in-distribution"],"title_zh":"依分布收斂","stem_zh":"Bernoulli symbolic tail與極限CDF。操作=convdist-continuity-obligation；資料={\"p\":[7,30],\"threshold\":[-6,7]}。請依 [p,threshold,continuity_point,definition_obligation] 欄序回答。","answer":{"kind":"expression","value":"(7/30, -6/7, 是, CDF_convergence_required_here)","explanation_zh":"Wave4收束核對=(7/30, -6/7, 是, CDF_convergence_required_here)；依完整明示資料重算；只在極限CDF連續點要求收斂且有限prefix不足；不要求coupling且不推出依機率、幾乎處處或Lp收斂。"},"difficulty":{"band":"undergraduate_core","level":1,"skills":["依分布收斂"]},"variant":{"family_id":"qf-mod31-convdist-continuity-obligation","seed":202610313057,"parameters":{"p":[7,30],"threshold":[-6,7],"domain":"Symbolic_Bernoulli_CDF_limit","operation":"convdist-continuity-obligation","semantic_template":"qf-mod31-convdist-continuity-obligation/{\"p\":[7,30],\"threshold\":[-6,7]}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_model","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"候選須由主端獨立重算；不構成人工審定、一般不可數性／色數最優性／更強機率收斂／商域、optional stopping、Lean或形式Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-14","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261014-advance-20261031-r03-convergence-in-distribution-0058","batch_id":"batch-20261014-advance-20261031-r03-convergence-in-distribution-foundations","language":"zh-Hant","source_mko_ids":["mko-convergence-in-distribution"],"title_zh":"依分布收斂","stem_zh":"Bernoulli symbolic tail與極限CDF。操作=convdist-continuity-obligation；資料={\"p\":[8,30],\"threshold\":[-5,7]}。請依 [p,threshold,continuity_point,definition_obligation] 欄序回答。","answer":{"kind":"expression","value":"(4/15, -5/7, 是, CDF_convergence_required_here)","explanation_zh":"Wave4收束核對=(4/15, -5/7, 是, CDF_convergence_required_here)；依完整明示資料重算；只在極限CDF連續點要求收斂且有限prefix不足；不要求coupling且不推出依機率、幾乎處處或Lp收斂。"},"difficulty":{"band":"undergraduate_core","level":1,"skills":["依分布收斂"]},"variant":{"family_id":"qf-mod31-convdist-continuity-obligation","seed":202610313058,"parameters":{"p":[8,30],"threshold":[-5,7],"domain":"Symbolic_Bernoulli_CDF_limit","operation":"convdist-continuity-obligation","semantic_template":"qf-mod31-convdist-continuity-obligation/{\"p\":[8,30],\"threshold\":[-5,7]}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_model","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"候選須由主端獨立重算；不構成人工審定、一般不可數性／色數最優性／更強機率收斂／商域、optional stopping、Lean或形式Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-14","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261014-advance-20261031-r03-convergence-in-distribution-0059","batch_id":"batch-20261014-advance-20261031-r03-convergence-in-distribution-foundations","language":"zh-Hant","source_mko_ids":["mko-convergence-in-distribution"],"title_zh":"依分布收斂","stem_zh":"Bernoulli symbolic tail與極限CDF。操作=convdist-continuity-obligation；資料={\"p\":[9,30],\"threshold\":[-4,7]}。請依 [p,threshold,continuity_point,definition_obligation] 欄序回答。","answer":{"kind":"expression","value":"(3/10, -4/7, 是, CDF_convergence_required_here)","explanation_zh":"Wave4收束核對=(3/10, -4/7, 是, CDF_convergence_required_here)；依完整明示資料重算；只在極限CDF連續點要求收斂且有限prefix不足；不要求coupling且不推出依機率、幾乎處處或Lp收斂。"},"difficulty":{"band":"undergraduate_core","level":2,"skills":["依分布收斂"]},"variant":{"family_id":"qf-mod31-convdist-continuity-obligation","seed":202610313059,"parameters":{"p":[9,30],"threshold":[-4,7],"domain":"Symbolic_Bernoulli_CDF_limit","operation":"convdist-continuity-obligation","semantic_template":"qf-mod31-convdist-continuity-obligation/{\"p\":[9,30],\"threshold\":[-4,7]}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_model","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"候選須由主端獨立重算；不構成人工審定、一般不可數性／色數最優性／更強機率收斂／商域、optional stopping、Lean或形式Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-14","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261014-advance-20261031-r03-convergence-in-distribution-0060","batch_id":"batch-20261014-advance-20261031-r03-convergence-in-distribution-foundations","language":"zh-Hant","source_mko_ids":["mko-convergence-in-distribution"],"title_zh":"依分布收斂","stem_zh":"Bernoulli symbolic tail與極限CDF。操作=convdist-continuity-obligation；資料={\"p\":[10,30],\"threshold\":[-3,7]}。請依 [p,threshold,continuity_point,definition_obligation] 欄序回答。","answer":{"kind":"expression","value":"(1/3, -3/7, 是, CDF_convergence_required_here)","explanation_zh":"Wave4收束核對=(1/3, -3/7, 是, CDF_convergence_required_here)；依完整明示資料重算；只在極限CDF連續點要求收斂且有限prefix不足；不要求coupling且不推出依機率、幾乎處處或Lp收斂。"},"difficulty":{"band":"undergraduate_core","level":2,"skills":["依分布收斂"]},"variant":{"family_id":"qf-mod31-convdist-continuity-obligation","seed":202610313060,"parameters":{"p":[10,30],"threshold":[-3,7],"domain":"Symbolic_Bernoulli_CDF_limit","operation":"convdist-continuity-obligation","semantic_template":"qf-mod31-convdist-continuity-obligation/{\"p\":[10,30],\"threshold\":[-3,7]}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_model","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"候選須由主端獨立重算；不構成人工審定、一般不可數性／色數最優性／更強機率收斂／商域、optional stopping、Lean或形式Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-14","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261014-advance-20261031-r03-convergence-in-distribution-0061","batch_id":"batch-20261014-advance-20261031-r03-convergence-in-distribution-foundations","language":"zh-Hant","source_mko_ids":["mko-convergence-in-distribution"],"title_zh":"依分布收斂","stem_zh":"Bernoulli symbolic tail與極限CDF。操作=convdist-continuity-obligation；資料={\"p\":[11,30],\"threshold\":[-2,7]}。請依 [p,threshold,continuity_point,definition_obligation] 欄序回答。","answer":{"kind":"expression","value":"(11/30, -2/7, 是, CDF_convergence_required_here)","explanation_zh":"Wave4收束核對=(11/30, -2/7, 是, CDF_convergence_required_here)；依完整明示資料重算；只在極限CDF連續點要求收斂且有限prefix不足；不要求coupling且不推出依機率、幾乎處處或Lp收斂。"},"difficulty":{"band":"undergraduate_core","level":2,"skills":["依分布收斂"]},"variant":{"family_id":"qf-mod31-convdist-continuity-obligation","seed":202610313061,"parameters":{"p":[11,30],"threshold":[-2,7],"domain":"Symbolic_Bernoulli_CDF_limit","operation":"convdist-continuity-obligation","semantic_template":"qf-mod31-convdist-continuity-obligation/{\"p\":[11,30],\"threshold\":[-2,7]}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_model","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"候選須由主端獨立重算；不構成人工審定、一般不可數性／色數最優性／更強機率收斂／商域、optional stopping、Lean或形式Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-14","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261014-advance-20261031-r03-convergence-in-distribution-0062","batch_id":"batch-20261014-advance-20261031-r03-convergence-in-distribution-foundations","language":"zh-Hant","source_mko_ids":["mko-convergence-in-distribution"],"title_zh":"依分布收斂","stem_zh":"Bernoulli symbolic tail與極限CDF。操作=convdist-continuity-obligation；資料={\"p\":[12,30],\"threshold\":[-1,7]}。請依 [p,threshold,continuity_point,definition_obligation] 欄序回答。","answer":{"kind":"expression","value":"(2/5, -1/7, 是, CDF_convergence_required_here)","explanation_zh":"Wave4收束核對=(2/5, -1/7, 是, CDF_convergence_required_here)；依完整明示資料重算；只在極限CDF連續點要求收斂且有限prefix不足；不要求coupling且不推出依機率、幾乎處處或Lp收斂。"},"difficulty":{"band":"undergraduate_core","level":2,"skills":["依分布收斂"]},"variant":{"family_id":"qf-mod31-convdist-continuity-obligation","seed":202610313062,"parameters":{"p":[12,30],"threshold":[-1,7],"domain":"Symbolic_Bernoulli_CDF_limit","operation":"convdist-continuity-obligation","semantic_template":"qf-mod31-convdist-continuity-obligation/{\"p\":[12,30],\"threshold\":[-1,7]}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_model","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"候選須由主端獨立重算；不構成人工審定、一般不可數性／色數最優性／更強機率收斂／商域、optional stopping、Lean或形式Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-14","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261014-advance-20261031-r03-convergence-in-distribution-0063","batch_id":"batch-20261014-advance-20261031-r03-convergence-in-distribution-foundations","language":"zh-Hant","source_mko_ids":["mko-convergence-in-distribution"],"title_zh":"依分布收斂","stem_zh":"Bernoulli symbolic tail與極限CDF。操作=convdist-continuity-obligation；資料={\"p\":[13,30],\"threshold\":[0,7]}。請依 [p,threshold,continuity_point,definition_obligation] 欄序回答。","answer":{"kind":"expression","value":"(13/30, 0, 否, limit_CDF_jump_no_requirement_from_definition)","explanation_zh":"Wave4收束核對=(13/30, 0, 否, limit_CDF_jump_no_requirement_from_definition)；依完整明示資料重算；只在極限CDF連續點要求收斂且有限prefix不足；不要求coupling且不推出依機率、幾乎處處或Lp收斂。"},"difficulty":{"band":"undergraduate_core","level":2,"skills":["依分布收斂"]},"variant":{"family_id":"qf-mod31-convdist-continuity-obligation","seed":202610313063,"parameters":{"p":[13,30],"threshold":[0,7],"domain":"Symbolic_Bernoulli_CDF_limit","operation":"convdist-continuity-obligation","semantic_template":"qf-mod31-convdist-continuity-obligation/{\"p\":[13,30],\"threshold\":[0,7]}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_model","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"候選須由主端獨立重算；不構成人工審定、一般不可數性／色數最優性／更強機率收斂／商域、optional stopping、Lean或形式Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-14","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261014-advance-20261031-r03-convergence-in-distribution-0064","batch_id":"batch-20261014-advance-20261031-r03-convergence-in-distribution-foundations","language":"zh-Hant","source_mko_ids":["mko-convergence-in-distribution"],"title_zh":"依分布收斂","stem_zh":"Bernoulli symbolic tail與極限CDF。操作=convdist-continuity-obligation；資料={\"p\":[14,30],\"threshold\":[1,7]}。請依 [p,threshold,continuity_point,definition_obligation] 欄序回答。","answer":{"kind":"expression","value":"(7/15, 1/7, 是, CDF_convergence_required_here)","explanation_zh":"Wave4收束核對=(7/15, 1/7, 是, CDF_convergence_required_here)；依完整明示資料重算；只在極限CDF連續點要求收斂且有限prefix不足；不要求coupling且不推出依機率、幾乎處處或Lp收斂。"},"difficulty":{"band":"undergraduate_core","level":2,"skills":["依分布收斂"]},"variant":{"family_id":"qf-mod31-convdist-continuity-obligation","seed":202610313064,"parameters":{"p":[14,30],"threshold":[1,7],"domain":"Symbolic_Bernoulli_CDF_limit","operation":"convdist-continuity-obligation","semantic_template":"qf-mod31-convdist-continuity-obligation/{\"p\":[14,30],\"threshold\":[1,7]}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_model","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"候選須由主端獨立重算；不構成人工審定、一般不可數性／色數最優性／更強機率收斂／商域、optional stopping、Lean或形式Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-14","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261014-advance-20261031-r03-convergence-in-distribution-0065","batch_id":"batch-20261014-advance-20261031-r03-convergence-in-distribution-foundations","language":"zh-Hant","source_mko_ids":["mko-convergence-in-distribution"],"title_zh":"依分布收斂","stem_zh":"Bernoulli symbolic tail與極限CDF。操作=convdist-continuity-obligation；資料={\"p\":[15,30],\"threshold\":[2,7]}。請依 [p,threshold,continuity_point,definition_obligation] 欄序回答。","answer":{"kind":"expression","value":"(1/2, 2/7, 是, CDF_convergence_required_here)","explanation_zh":"Wave4收束核對=(1/2, 2/7, 是, CDF_convergence_required_here)；依完整明示資料重算；只在極限CDF連續點要求收斂且有限prefix不足；不要求coupling且不推出依機率、幾乎處處或Lp收斂。"},"difficulty":{"band":"undergraduate_core","level":2,"skills":["依分布收斂"]},"variant":{"family_id":"qf-mod31-convdist-continuity-obligation","seed":202610313065,"parameters":{"p":[15,30],"threshold":[2,7],"domain":"Symbolic_Bernoulli_CDF_limit","operation":"convdist-continuity-obligation","semantic_template":"qf-mod31-convdist-continuity-obligation/{\"p\":[15,30],\"threshold\":[2,7]}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_model","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"候選須由主端獨立重算；不構成人工審定、一般不可數性／色數最優性／更強機率收斂／商域、optional stopping、Lean或形式Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-14","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261014-advance-20261031-r03-convergence-in-distribution-0066","batch_id":"batch-20261014-advance-20261031-r03-convergence-in-distribution-foundations","language":"zh-Hant","source_mko_ids":["mko-convergence-in-distribution"],"title_zh":"依分布收斂","stem_zh":"Bernoulli symbolic tail與極限CDF。操作=convdist-continuity-obligation；資料={\"p\":[16,30],\"threshold\":[3,7]}。請依 [p,threshold,continuity_point,definition_obligation] 欄序回答。","answer":{"kind":"expression","value":"(8/15, 3/7, 是, CDF_convergence_required_here)","explanation_zh":"Wave4收束核對=(8/15, 3/7, 是, CDF_convergence_required_here)；依完整明示資料重算；只在極限CDF連續點要求收斂且有限prefix不足；不要求coupling且不推出依機率、幾乎處處或Lp收斂。"},"difficulty":{"band":"undergraduate_core","level":2,"skills":["依分布收斂"]},"variant":{"family_id":"qf-mod31-convdist-continuity-obligation","seed":202610313066,"parameters":{"p":[16,30],"threshold":[3,7],"domain":"Symbolic_Bernoulli_CDF_limit","operation":"convdist-continuity-obligation","semantic_template":"qf-mod31-convdist-continuity-obligation/{\"p\":[16,30],\"threshold\":[3,7]}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_model","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"候選須由主端獨立重算；不構成人工審定、一般不可數性／色數最優性／更強機率收斂／商域、optional stopping、Lean或形式Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-14","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261014-advance-20261031-r03-convergence-in-distribution-0067","batch_id":"batch-20261014-advance-20261031-r03-convergence-in-distribution-foundations","language":"zh-Hant","source_mko_ids":["mko-convergence-in-distribution"],"title_zh":"依分布收斂","stem_zh":"Bernoulli symbolic tail與極限CDF。操作=convdist-continuity-obligation；資料={\"p\":[17,30],\"threshold\":[4,7]}。請依 [p,threshold,continuity_point,definition_obligation] 欄序回答。","answer":{"kind":"expression","value":"(17/30, 4/7, 是, CDF_convergence_required_here)","explanation_zh":"Wave4收束核對=(17/30, 4/7, 是, CDF_convergence_required_here)；依完整明示資料重算；只在極限CDF連續點要求收斂且有限prefix不足；不要求coupling且不推出依機率、幾乎處處或Lp收斂。"},"difficulty":{"band":"undergraduate_core","level":2,"skills":["依分布收斂"]},"variant":{"family_id":"qf-mod31-convdist-continuity-obligation","seed":202610313067,"parameters":{"p":[17,30],"threshold":[4,7],"domain":"Symbolic_Bernoulli_CDF_limit","operation":"convdist-continuity-obligation","semantic_template":"qf-mod31-convdist-continuity-obligation/{\"p\":[17,30],\"threshold\":[4,7]}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_model","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"候選須由主端獨立重算；不構成人工審定、一般不可數性／色數最優性／更強機率收斂／商域、optional stopping、Lean或形式Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-14","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261014-advance-20261031-r03-convergence-in-distribution-0068","batch_id":"batch-20261014-advance-20261031-r03-convergence-in-distribution-foundations","language":"zh-Hant","source_mko_ids":["mko-convergence-in-distribution"],"title_zh":"依分布收斂","stem_zh":"Bernoulli symbolic tail與極限CDF。操作=convdist-continuity-obligation；資料={\"p\":[18,30],\"threshold\":[5,7]}。請依 [p,threshold,continuity_point,definition_obligation] 欄序回答。","answer":{"kind":"expression","value":"(3/5, 5/7, 是, CDF_convergence_required_here)","explanation_zh":"Wave4收束核對=(3/5, 5/7, 是, CDF_convergence_required_here)；依完整明示資料重算；只在極限CDF連續點要求收斂且有限prefix不足；不要求coupling且不推出依機率、幾乎處處或Lp收斂。"},"difficulty":{"band":"undergraduate_core","level":3,"skills":["依分布收斂"]},"variant":{"family_id":"qf-mod31-convdist-continuity-obligation","seed":202610313068,"parameters":{"p":[18,30],"threshold":[5,7],"domain":"Symbolic_Bernoulli_CDF_limit","operation":"convdist-continuity-obligation","semantic_template":"qf-mod31-convdist-continuity-obligation/{\"p\":[18,30],\"threshold\":[5,7]}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_model","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"候選須由主端獨立重算；不構成人工審定、一般不可數性／色數最優性／更強機率收斂／商域、optional stopping、Lean或形式Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-14","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261014-advance-20261031-r03-convergence-in-distribution-0069","batch_id":"batch-20261014-advance-20261031-r03-convergence-in-distribution-foundations","language":"zh-Hant","source_mko_ids":["mko-convergence-in-distribution"],"title_zh":"依分布收斂","stem_zh":"Bernoulli symbolic tail與極限CDF。操作=convdist-continuity-obligation；資料={\"p\":[19,30],\"threshold\":[6,7]}。請依 [p,threshold,continuity_point,definition_obligation] 欄序回答。","answer":{"kind":"expression","value":"(19/30, 6/7, 是, CDF_convergence_required_here)","explanation_zh":"Wave4收束核對=(19/30, 6/7, 是, CDF_convergence_required_here)；依完整明示資料重算；只在極限CDF連續點要求收斂且有限prefix不足；不要求coupling且不推出依機率、幾乎處處或Lp收斂。"},"difficulty":{"band":"undergraduate_core","level":3,"skills":["依分布收斂"]},"variant":{"family_id":"qf-mod31-convdist-continuity-obligation","seed":202610313069,"parameters":{"p":[19,30],"threshold":[6,7],"domain":"Symbolic_Bernoulli_CDF_limit","operation":"convdist-continuity-obligation","semantic_template":"qf-mod31-convdist-continuity-obligation/{\"p\":[19,30],\"threshold\":[6,7]}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_model","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"候選須由主端獨立重算；不構成人工審定、一般不可數性／色數最優性／更強機率收斂／商域、optional stopping、Lean或形式Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-14","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261014-advance-20261031-r03-convergence-in-distribution-0070","batch_id":"batch-20261014-advance-20261031-r03-convergence-in-distribution-foundations","language":"zh-Hant","source_mko_ids":["mko-convergence-in-distribution"],"title_zh":"依分布收斂","stem_zh":"Bernoulli symbolic tail與極限CDF。操作=convdist-continuity-obligation；資料={\"p\":[20,30],\"threshold\":[7,7]}。請依 [p,threshold,continuity_point,definition_obligation] 欄序回答。","answer":{"kind":"expression","value":"(2/3, 1, 否, limit_CDF_jump_no_requirement_from_definition)","explanation_zh":"Wave4收束核對=(2/3, 1, 否, limit_CDF_jump_no_requirement_from_definition)；依完整明示資料重算；只在極限CDF連續點要求收斂且有限prefix不足；不要求coupling且不推出依機率、幾乎處處或Lp收斂。"},"difficulty":{"band":"undergraduate_core","level":3,"skills":["依分布收斂"]},"variant":{"family_id":"qf-mod31-convdist-continuity-obligation","seed":202610313070,"parameters":{"p":[20,30],"threshold":[7,7],"domain":"Symbolic_Bernoulli_CDF_limit","operation":"convdist-continuity-obligation","semantic_template":"qf-mod31-convdist-continuity-obligation/{\"p\":[20,30],\"threshold\":[7,7]}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_model","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"候選須由主端獨立重算；不構成人工審定、一般不可數性／色數最優性／更強機率收斂／商域、optional stopping、Lean或形式Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-14","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261014-advance-20261031-r03-convergence-in-distribution-0071","batch_id":"batch-20261014-advance-20261031-r03-convergence-in-distribution-foundations","language":"zh-Hant","source_mko_ids":["mko-convergence-in-distribution"],"title_zh":"依分布收斂","stem_zh":"Bernoulli symbolic tail與極限CDF。操作=convdist-continuity-obligation；資料={\"p\":[21,30],\"threshold\":[8,7]}。請依 [p,threshold,continuity_point,definition_obligation] 欄序回答。","answer":{"kind":"expression","value":"(7/10, 8/7, 是, CDF_convergence_required_here)","explanation_zh":"Wave4收束核對=(7/10, 8/7, 是, CDF_convergence_required_here)；依完整明示資料重算；只在極限CDF連續點要求收斂且有限prefix不足；不要求coupling且不推出依機率、幾乎處處或Lp收斂。"},"difficulty":{"band":"undergraduate_core","level":3,"skills":["依分布收斂"]},"variant":{"family_id":"qf-mod31-convdist-continuity-obligation","seed":202610313071,"parameters":{"p":[21,30],"threshold":[8,7],"domain":"Symbolic_Bernoulli_CDF_limit","operation":"convdist-continuity-obligation","semantic_template":"qf-mod31-convdist-continuity-obligation/{\"p\":[21,30],\"threshold\":[8,7]}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_model","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"候選須由主端獨立重算；不構成人工審定、一般不可數性／色數最優性／更強機率收斂／商域、optional stopping、Lean或形式Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-14","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261014-advance-20261031-r03-convergence-in-distribution-0072","batch_id":"batch-20261014-advance-20261031-r03-convergence-in-distribution-foundations","language":"zh-Hant","source_mko_ids":["mko-convergence-in-distribution"],"title_zh":"依分布收斂","stem_zh":"Bernoulli symbolic tail與極限CDF。操作=convdist-continuity-obligation；資料={\"p\":[22,30],\"threshold\":[9,7]}。請依 [p,threshold,continuity_point,definition_obligation] 欄序回答。","answer":{"kind":"expression","value":"(11/15, 9/7, 是, CDF_convergence_required_here)","explanation_zh":"Wave4收束核對=(11/15, 9/7, 是, CDF_convergence_required_here)；依完整明示資料重算；只在極限CDF連續點要求收斂且有限prefix不足；不要求coupling且不推出依機率、幾乎處處或Lp收斂。"},"difficulty":{"band":"undergraduate_core","level":3,"skills":["依分布收斂"]},"variant":{"family_id":"qf-mod31-convdist-continuity-obligation","seed":202610313072,"parameters":{"p":[22,30],"threshold":[9,7],"domain":"Symbolic_Bernoulli_CDF_limit","operation":"convdist-continuity-obligation","semantic_template":"qf-mod31-convdist-continuity-obligation/{\"p\":[22,30],\"threshold\":[9,7]}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_model","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"候選須由主端獨立重算；不構成人工審定、一般不可數性／色數最優性／更強機率收斂／商域、optional stopping、Lean或形式Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-14","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261014-advance-20261031-r03-convergence-in-distribution-0073","batch_id":"batch-20261014-advance-20261031-r03-convergence-in-distribution-foundations","language":"zh-Hant","source_mko_ids":["mko-convergence-in-distribution"],"title_zh":"依分布收斂","stem_zh":"Bernoulli symbolic tail與極限CDF。操作=convdist-continuity-obligation；資料={\"p\":[23,30],\"threshold\":[10,7]}。請依 [p,threshold,continuity_point,definition_obligation] 欄序回答。","answer":{"kind":"expression","value":"(23/30, 10/7, 是, CDF_convergence_required_here)","explanation_zh":"Wave4收束核對=(23/30, 10/7, 是, CDF_convergence_required_here)；依完整明示資料重算；只在極限CDF連續點要求收斂且有限prefix不足；不要求coupling且不推出依機率、幾乎處處或Lp收斂。"},"difficulty":{"band":"undergraduate_core","level":3,"skills":["依分布收斂"]},"variant":{"family_id":"qf-mod31-convdist-continuity-obligation","seed":202610313073,"parameters":{"p":[23,30],"threshold":[10,7],"domain":"Symbolic_Bernoulli_CDF_limit","operation":"convdist-continuity-obligation","semantic_template":"qf-mod31-convdist-continuity-obligation/{\"p\":[23,30],\"threshold\":[10,7]}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_model","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"候選須由主端獨立重算；不構成人工審定、一般不可數性／色數最優性／更強機率收斂／商域、optional stopping、Lean或形式Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-14","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261014-advance-20261031-r03-convergence-in-distribution-0074","batch_id":"batch-20261014-advance-20261031-r03-convergence-in-distribution-foundations","language":"zh-Hant","source_mko_ids":["mko-convergence-in-distribution"],"title_zh":"依分布收斂","stem_zh":"Bernoulli symbolic tail與極限CDF。操作=convdist-continuity-obligation；資料={\"p\":[24,30],\"threshold\":[11,7]}。請依 [p,threshold,continuity_point,definition_obligation] 欄序回答。","answer":{"kind":"expression","value":"(4/5, 11/7, 是, CDF_convergence_required_here)","explanation_zh":"Wave4收束核對=(4/5, 11/7, 是, CDF_convergence_required_here)；依完整明示資料重算；只在極限CDF連續點要求收斂且有限prefix不足；不要求coupling且不推出依機率、幾乎處處或Lp收斂。"},"difficulty":{"band":"undergraduate_core","level":3,"skills":["依分布收斂"]},"variant":{"family_id":"qf-mod31-convdist-continuity-obligation","seed":202610313074,"parameters":{"p":[24,30],"threshold":[11,7],"domain":"Symbolic_Bernoulli_CDF_limit","operation":"convdist-continuity-obligation","semantic_template":"qf-mod31-convdist-continuity-obligation/{\"p\":[24,30],\"threshold\":[11,7]}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_model","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"候選須由主端獨立重算；不構成人工審定、一般不可數性／色數最優性／更強機率收斂／商域、optional stopping、Lean或形式Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-14","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261014-advance-20261031-r03-convergence-in-distribution-0075","batch_id":"batch-20261014-advance-20261031-r03-convergence-in-distribution-foundations","language":"zh-Hant","source_mko_ids":["mko-convergence-in-distribution"],"title_zh":"依分布收斂","stem_zh":"Bernoulli symbolic tail與極限CDF。操作=convdist-continuity-obligation；資料={\"p\":[25,30],\"threshold\":[12,7]}。請依 [p,threshold,continuity_point,definition_obligation] 欄序回答。","answer":{"kind":"expression","value":"(5/6, 12/7, 是, CDF_convergence_required_here)","explanation_zh":"Wave4收束核對=(5/6, 12/7, 是, CDF_convergence_required_here)；依完整明示資料重算；只在極限CDF連續點要求收斂且有限prefix不足；不要求coupling且不推出依機率、幾乎處處或Lp收斂。"},"difficulty":{"band":"undergraduate_core","level":3,"skills":["依分布收斂"]},"variant":{"family_id":"qf-mod31-convdist-continuity-obligation","seed":202610313075,"parameters":{"p":[25,30],"threshold":[12,7],"domain":"Symbolic_Bernoulli_CDF_limit","operation":"convdist-continuity-obligation","semantic_template":"qf-mod31-convdist-continuity-obligation/{\"p\":[25,30],\"threshold\":[12,7]}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_model","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"候選須由主端獨立重算；不構成人工審定、一般不可數性／色數最優性／更強機率收斂／商域、optional stopping、Lean或形式Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-14","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261014-advance-20261031-r03-convergence-in-distribution-0076","batch_id":"batch-20261014-advance-20261031-r03-convergence-in-distribution-foundations","language":"zh-Hant","source_mko_ids":["mko-convergence-in-distribution"],"title_zh":"依分布收斂","stem_zh":"Bernoulli symbolic tail與極限CDF。操作=convdist-finite-prefix；資料={\"p\":[1,2],\"c\":[1,20],\"shift\":2,\"prefix_length\":1}。請依 [p,c,shift,prefix_length,sufficient,boundary] 欄序回答。","answer":{"kind":"expression","value":"(1/2, 1/20, 2, 1, 否, finite_prefix_not_convergence_certificate)","explanation_zh":"Wave4收束核對=(1/2, 1/20, 2, 1, 否, finite_prefix_not_convergence_certificate)；依完整明示資料重算；只在極限CDF連續點要求收斂且有限prefix不足；不要求coupling且不推出依機率、幾乎處處或Lp收斂。"},"difficulty":{"band":"undergraduate_core","level":1,"skills":["依分布收斂"]},"variant":{"family_id":"qf-mod31-convdist-finite-prefix","seed":202610313076,"parameters":{"p":[1,2],"c":[1,20],"shift":2,"prefix_length":1,"domain":"Symbolic_Bernoulli_CDF_limit","operation":"convdist-finite-prefix","semantic_template":"qf-mod31-convdist-finite-prefix/{\"c\":[1,20],\"p\":[1,2],\"prefix_length\":1,\"shift\":2}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_model","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"候選須由主端獨立重算；不構成人工審定、一般不可數性／色數最優性／更強機率收斂／商域、optional stopping、Lean或形式Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-14","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261014-advance-20261031-r03-convergence-in-distribution-0077","batch_id":"batch-20261014-advance-20261031-r03-convergence-in-distribution-foundations","language":"zh-Hant","source_mko_ids":["mko-convergence-in-distribution"],"title_zh":"依分布收斂","stem_zh":"Bernoulli symbolic tail與極限CDF。操作=convdist-finite-prefix；資料={\"p\":[1,2],\"c\":[2,20],\"shift\":3,\"prefix_length\":2}。請依 [p,c,shift,prefix_length,sufficient,boundary] 欄序回答。","answer":{"kind":"expression","value":"(1/2, 1/10, 3, 2, 否, finite_prefix_not_convergence_certificate)","explanation_zh":"Wave4收束核對=(1/2, 1/10, 3, 2, 否, finite_prefix_not_convergence_certificate)；依完整明示資料重算；只在極限CDF連續點要求收斂且有限prefix不足；不要求coupling且不推出依機率、幾乎處處或Lp收斂。"},"difficulty":{"band":"undergraduate_core","level":1,"skills":["依分布收斂"]},"variant":{"family_id":"qf-mod31-convdist-finite-prefix","seed":202610313077,"parameters":{"p":[1,2],"c":[2,20],"shift":3,"prefix_length":2,"domain":"Symbolic_Bernoulli_CDF_limit","operation":"convdist-finite-prefix","semantic_template":"qf-mod31-convdist-finite-prefix/{\"c\":[2,20],\"p\":[1,2],\"prefix_length\":2,\"shift\":3}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_model","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"候選須由主端獨立重算；不構成人工審定、一般不可數性／色數最優性／更強機率收斂／商域、optional stopping、Lean或形式Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-14","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261014-advance-20261031-r03-convergence-in-distribution-0078","batch_id":"batch-20261014-advance-20261031-r03-convergence-in-distribution-foundations","language":"zh-Hant","source_mko_ids":["mko-convergence-in-distribution"],"title_zh":"依分布收斂","stem_zh":"Bernoulli symbolic tail與極限CDF。操作=convdist-finite-prefix；資料={\"p\":[1,2],\"c\":[3,20],\"shift\":4,\"prefix_length\":3}。請依 [p,c,shift,prefix_length,sufficient,boundary] 欄序回答。","answer":{"kind":"expression","value":"(1/2, 3/20, 4, 3, 否, finite_prefix_not_convergence_certificate)","explanation_zh":"Wave4收束核對=(1/2, 3/20, 4, 3, 否, finite_prefix_not_convergence_certificate)；依完整明示資料重算；只在極限CDF連續點要求收斂且有限prefix不足；不要求coupling且不推出依機率、幾乎處處或Lp收斂。"},"difficulty":{"band":"undergraduate_core","level":1,"skills":["依分布收斂"]},"variant":{"family_id":"qf-mod31-convdist-finite-prefix","seed":202610313078,"parameters":{"p":[1,2],"c":[3,20],"shift":4,"prefix_length":3,"domain":"Symbolic_Bernoulli_CDF_limit","operation":"convdist-finite-prefix","semantic_template":"qf-mod31-convdist-finite-prefix/{\"c\":[3,20],\"p\":[1,2],\"prefix_length\":3,\"shift\":4}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_model","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"候選須由主端獨立重算；不構成人工審定、一般不可數性／色數最優性／更強機率收斂／商域、optional stopping、Lean或形式Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-14","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261014-advance-20261031-r03-convergence-in-distribution-0079","batch_id":"batch-20261014-advance-20261031-r03-convergence-in-distribution-foundations","language":"zh-Hant","source_mko_ids":["mko-convergence-in-distribution"],"title_zh":"依分布收斂","stem_zh":"Bernoulli symbolic tail與極限CDF。操作=convdist-finite-prefix；資料={\"p\":[1,2],\"c\":[4,20],\"shift\":5,\"prefix_length\":4}。請依 [p,c,shift,prefix_length,sufficient,boundary] 欄序回答。","answer":{"kind":"expression","value":"(1/2, 1/5, 5, 4, 否, finite_prefix_not_convergence_certificate)","explanation_zh":"Wave4收束核對=(1/2, 1/5, 5, 4, 否, finite_prefix_not_convergence_certificate)；依完整明示資料重算；只在極限CDF連續點要求收斂且有限prefix不足；不要求coupling且不推出依機率、幾乎處處或Lp收斂。"},"difficulty":{"band":"undergraduate_core","level":1,"skills":["依分布收斂"]},"variant":{"family_id":"qf-mod31-convdist-finite-prefix","seed":202610313079,"parameters":{"p":[1,2],"c":[4,20],"shift":5,"prefix_length":4,"domain":"Symbolic_Bernoulli_CDF_limit","operation":"convdist-finite-prefix","semantic_template":"qf-mod31-convdist-finite-prefix/{\"c\":[4,20],\"p\":[1,2],\"prefix_length\":4,\"shift\":5}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_model","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"候選須由主端獨立重算；不構成人工審定、一般不可數性／色數最優性／更強機率收斂／商域、optional stopping、Lean或形式Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-14","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261014-advance-20261031-r03-convergence-in-distribution-0080","batch_id":"batch-20261014-advance-20261031-r03-convergence-in-distribution-foundations","language":"zh-Hant","source_mko_ids":["mko-convergence-in-distribution"],"title_zh":"依分布收斂","stem_zh":"Bernoulli symbolic tail與極限CDF。操作=convdist-finite-prefix；資料={\"p\":[1,2],\"c\":[5,20],\"shift\":6,\"prefix_length\":5}。請依 [p,c,shift,prefix_length,sufficient,boundary] 欄序回答。","answer":{"kind":"expression","value":"(1/2, 1/4, 6, 5, 否, finite_prefix_not_convergence_certificate)","explanation_zh":"Wave4收束核對=(1/2, 1/4, 6, 5, 否, finite_prefix_not_convergence_certificate)；依完整明示資料重算；只在極限CDF連續點要求收斂且有限prefix不足；不要求coupling且不推出依機率、幾乎處處或Lp收斂。"},"difficulty":{"band":"undergraduate_core","level":1,"skills":["依分布收斂"]},"variant":{"family_id":"qf-mod31-convdist-finite-prefix","seed":202610313080,"parameters":{"p":[1,2],"c":[5,20],"shift":6,"prefix_length":5,"domain":"Symbolic_Bernoulli_CDF_limit","operation":"convdist-finite-prefix","semantic_template":"qf-mod31-convdist-finite-prefix/{\"c\":[5,20],\"p\":[1,2],\"prefix_length\":5,\"shift\":6}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_model","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"候選須由主端獨立重算；不構成人工審定、一般不可數性／色數最優性／更強機率收斂／商域、optional stopping、Lean或形式Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-14","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261014-advance-20261031-r03-convergence-in-distribution-0081","batch_id":"batch-20261014-advance-20261031-r03-convergence-in-distribution-foundations","language":"zh-Hant","source_mko_ids":["mko-convergence-in-distribution"],"title_zh":"依分布收斂","stem_zh":"Bernoulli symbolic tail與極限CDF。操作=convdist-finite-prefix；資料={\"p\":[1,2],\"c\":[1,20],\"shift\":7,\"prefix_length\":6}。請依 [p,c,shift,prefix_length,sufficient,boundary] 欄序回答。","answer":{"kind":"expression","value":"(1/2, 1/20, 7, 6, 否, finite_prefix_not_convergence_certificate)","explanation_zh":"Wave4收束核對=(1/2, 1/20, 7, 6, 否, finite_prefix_not_convergence_certificate)；依完整明示資料重算；只在極限CDF連續點要求收斂且有限prefix不足；不要求coupling且不推出依機率、幾乎處處或Lp收斂。"},"difficulty":{"band":"undergraduate_core","level":1,"skills":["依分布收斂"]},"variant":{"family_id":"qf-mod31-convdist-finite-prefix","seed":202610313081,"parameters":{"p":[1,2],"c":[1,20],"shift":7,"prefix_length":6,"domain":"Symbolic_Bernoulli_CDF_limit","operation":"convdist-finite-prefix","semantic_template":"qf-mod31-convdist-finite-prefix/{\"c\":[1,20],\"p\":[1,2],\"prefix_length\":6,\"shift\":7}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_model","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"候選須由主端獨立重算；不構成人工審定、一般不可數性／色數最優性／更強機率收斂／商域、optional stopping、Lean或形式Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-14","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261014-advance-20261031-r03-convergence-in-distribution-0082","batch_id":"batch-20261014-advance-20261031-r03-convergence-in-distribution-foundations","language":"zh-Hant","source_mko_ids":["mko-convergence-in-distribution"],"title_zh":"依分布收斂","stem_zh":"Bernoulli symbolic tail與極限CDF。操作=convdist-finite-prefix；資料={\"p\":[1,2],\"c\":[2,20],\"shift\":8,\"prefix_length\":7}。請依 [p,c,shift,prefix_length,sufficient,boundary] 欄序回答。","answer":{"kind":"expression","value":"(1/2, 1/10, 8, 7, 否, finite_prefix_not_convergence_certificate)","explanation_zh":"Wave4收束核對=(1/2, 1/10, 8, 7, 否, finite_prefix_not_convergence_certificate)；依完整明示資料重算；只在極限CDF連續點要求收斂且有限prefix不足；不要求coupling且不推出依機率、幾乎處處或Lp收斂。"},"difficulty":{"band":"undergraduate_core","level":1,"skills":["依分布收斂"]},"variant":{"family_id":"qf-mod31-convdist-finite-prefix","seed":202610313082,"parameters":{"p":[1,2],"c":[2,20],"shift":8,"prefix_length":7,"domain":"Symbolic_Bernoulli_CDF_limit","operation":"convdist-finite-prefix","semantic_template":"qf-mod31-convdist-finite-prefix/{\"c\":[2,20],\"p\":[1,2],\"prefix_length\":7,\"shift\":8}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_model","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"候選須由主端獨立重算；不構成人工審定、一般不可數性／色數最優性／更強機率收斂／商域、optional stopping、Lean或形式Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-14","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261014-advance-20261031-r03-convergence-in-distribution-0083","batch_id":"batch-20261014-advance-20261031-r03-convergence-in-distribution-foundations","language":"zh-Hant","source_mko_ids":["mko-convergence-in-distribution"],"title_zh":"依分布收斂","stem_zh":"Bernoulli symbolic tail與極限CDF。操作=convdist-finite-prefix；資料={\"p\":[1,2],\"c\":[3,20],\"shift\":9,\"prefix_length\":8}。請依 [p,c,shift,prefix_length,sufficient,boundary] 欄序回答。","answer":{"kind":"expression","value":"(1/2, 3/20, 9, 8, 否, finite_prefix_not_convergence_certificate)","explanation_zh":"Wave4收束核對=(1/2, 3/20, 9, 8, 否, finite_prefix_not_convergence_certificate)；依完整明示資料重算；只在極限CDF連續點要求收斂且有限prefix不足；不要求coupling且不推出依機率、幾乎處處或Lp收斂。"},"difficulty":{"band":"undergraduate_core","level":1,"skills":["依分布收斂"]},"variant":{"family_id":"qf-mod31-convdist-finite-prefix","seed":202610313083,"parameters":{"p":[1,2],"c":[3,20],"shift":9,"prefix_length":8,"domain":"Symbolic_Bernoulli_CDF_limit","operation":"convdist-finite-prefix","semantic_template":"qf-mod31-convdist-finite-prefix/{\"c\":[3,20],\"p\":[1,2],\"prefix_length\":8,\"shift\":9}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_model","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"候選須由主端獨立重算；不構成人工審定、一般不可數性／色數最優性／更強機率收斂／商域、optional stopping、Lean或形式Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-14","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261014-advance-20261031-r03-convergence-in-distribution-0084","batch_id":"batch-20261014-advance-20261031-r03-convergence-in-distribution-foundations","language":"zh-Hant","source_mko_ids":["mko-convergence-in-distribution"],"title_zh":"依分布收斂","stem_zh":"Bernoulli symbolic tail與極限CDF。操作=convdist-finite-prefix；資料={\"p\":[1,2],\"c\":[4,20],\"shift\":10,\"prefix_length\":9}。請依 [p,c,shift,prefix_length,sufficient,boundary] 欄序回答。","answer":{"kind":"expression","value":"(1/2, 1/5, 10, 9, 否, finite_prefix_not_convergence_certificate)","explanation_zh":"Wave4收束核對=(1/2, 1/5, 10, 9, 否, finite_prefix_not_convergence_certificate)；依完整明示資料重算；只在極限CDF連續點要求收斂且有限prefix不足；不要求coupling且不推出依機率、幾乎處處或Lp收斂。"},"difficulty":{"band":"undergraduate_core","level":2,"skills":["依分布收斂"]},"variant":{"family_id":"qf-mod31-convdist-finite-prefix","seed":202610313084,"parameters":{"p":[1,2],"c":[4,20],"shift":10,"prefix_length":9,"domain":"Symbolic_Bernoulli_CDF_limit","operation":"convdist-finite-prefix","semantic_template":"qf-mod31-convdist-finite-prefix/{\"c\":[4,20],\"p\":[1,2],\"prefix_length\":9,\"shift\":10}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_model","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"候選須由主端獨立重算；不構成人工審定、一般不可數性／色數最優性／更強機率收斂／商域、optional stopping、Lean或形式Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-14","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261014-advance-20261031-r03-convergence-in-distribution-0085","batch_id":"batch-20261014-advance-20261031-r03-convergence-in-distribution-foundations","language":"zh-Hant","source_mko_ids":["mko-convergence-in-distribution"],"title_zh":"依分布收斂","stem_zh":"Bernoulli symbolic tail與極限CDF。操作=convdist-finite-prefix；資料={\"p\":[1,2],\"c\":[5,20],\"shift\":11,\"prefix_length\":10}。請依 [p,c,shift,prefix_length,sufficient,boundary] 欄序回答。","answer":{"kind":"expression","value":"(1/2, 1/4, 11, 10, 否, finite_prefix_not_convergence_certificate)","explanation_zh":"Wave4收束核對=(1/2, 1/4, 11, 10, 否, finite_prefix_not_convergence_certificate)；依完整明示資料重算；只在極限CDF連續點要求收斂且有限prefix不足；不要求coupling且不推出依機率、幾乎處處或Lp收斂。"},"difficulty":{"band":"undergraduate_core","level":2,"skills":["依分布收斂"]},"variant":{"family_id":"qf-mod31-convdist-finite-prefix","seed":202610313085,"parameters":{"p":[1,2],"c":[5,20],"shift":11,"prefix_length":10,"domain":"Symbolic_Bernoulli_CDF_limit","operation":"convdist-finite-prefix","semantic_template":"qf-mod31-convdist-finite-prefix/{\"c\":[5,20],\"p\":[1,2],\"prefix_length\":10,\"shift\":11}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_model","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"候選須由主端獨立重算；不構成人工審定、一般不可數性／色數最優性／更強機率收斂／商域、optional stopping、Lean或形式Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-14","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261014-advance-20261031-r03-convergence-in-distribution-0086","batch_id":"batch-20261014-advance-20261031-r03-convergence-in-distribution-foundations","language":"zh-Hant","source_mko_ids":["mko-convergence-in-distribution"],"title_zh":"依分布收斂","stem_zh":"Bernoulli symbolic tail與極限CDF。操作=convdist-finite-prefix；資料={\"p\":[1,2],\"c\":[1,20],\"shift\":12,\"prefix_length\":11}。請依 [p,c,shift,prefix_length,sufficient,boundary] 欄序回答。","answer":{"kind":"expression","value":"(1/2, 1/20, 12, 11, 否, finite_prefix_not_convergence_certificate)","explanation_zh":"Wave4收束核對=(1/2, 1/20, 12, 11, 否, finite_prefix_not_convergence_certificate)；依完整明示資料重算；只在極限CDF連續點要求收斂且有限prefix不足；不要求coupling且不推出依機率、幾乎處處或Lp收斂。"},"difficulty":{"band":"undergraduate_core","level":2,"skills":["依分布收斂"]},"variant":{"family_id":"qf-mod31-convdist-finite-prefix","seed":202610313086,"parameters":{"p":[1,2],"c":[1,20],"shift":12,"prefix_length":11,"domain":"Symbolic_Bernoulli_CDF_limit","operation":"convdist-finite-prefix","semantic_template":"qf-mod31-convdist-finite-prefix/{\"c\":[1,20],\"p\":[1,2],\"prefix_length\":11,\"shift\":12}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_model","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"候選須由主端獨立重算；不構成人工審定、一般不可數性／色數最優性／更強機率收斂／商域、optional stopping、Lean或形式Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-14","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261014-advance-20261031-r03-convergence-in-distribution-0087","batch_id":"batch-20261014-advance-20261031-r03-convergence-in-distribution-foundations","language":"zh-Hant","source_mko_ids":["mko-convergence-in-distribution"],"title_zh":"依分布收斂","stem_zh":"Bernoulli symbolic tail與極限CDF。操作=convdist-finite-prefix；資料={\"p\":[1,2],\"c\":[2,20],\"shift\":13,\"prefix_length\":12}。請依 [p,c,shift,prefix_length,sufficient,boundary] 欄序回答。","answer":{"kind":"expression","value":"(1/2, 1/10, 13, 12, 否, finite_prefix_not_convergence_certificate)","explanation_zh":"Wave4收束核對=(1/2, 1/10, 13, 12, 否, finite_prefix_not_convergence_certificate)；依完整明示資料重算；只在極限CDF連續點要求收斂且有限prefix不足；不要求coupling且不推出依機率、幾乎處處或Lp收斂。"},"difficulty":{"band":"undergraduate_core","level":2,"skills":["依分布收斂"]},"variant":{"family_id":"qf-mod31-convdist-finite-prefix","seed":202610313087,"parameters":{"p":[1,2],"c":[2,20],"shift":13,"prefix_length":12,"domain":"Symbolic_Bernoulli_CDF_limit","operation":"convdist-finite-prefix","semantic_template":"qf-mod31-convdist-finite-prefix/{\"c\":[2,20],\"p\":[1,2],\"prefix_length\":12,\"shift\":13}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_model","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"候選須由主端獨立重算；不構成人工審定、一般不可數性／色數最優性／更強機率收斂／商域、optional stopping、Lean或形式Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-14","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261014-advance-20261031-r03-convergence-in-distribution-0088","batch_id":"batch-20261014-advance-20261031-r03-convergence-in-distribution-foundations","language":"zh-Hant","source_mko_ids":["mko-convergence-in-distribution"],"title_zh":"依分布收斂","stem_zh":"Bernoulli symbolic tail與極限CDF。操作=convdist-finite-prefix；資料={\"p\":[1,2],\"c\":[3,20],\"shift\":14,\"prefix_length\":13}。請依 [p,c,shift,prefix_length,sufficient,boundary] 欄序回答。","answer":{"kind":"expression","value":"(1/2, 3/20, 14, 13, 否, finite_prefix_not_convergence_certificate)","explanation_zh":"Wave4收束核對=(1/2, 3/20, 14, 13, 否, finite_prefix_not_convergence_certificate)；依完整明示資料重算；只在極限CDF連續點要求收斂且有限prefix不足；不要求coupling且不推出依機率、幾乎處處或Lp收斂。"},"difficulty":{"band":"undergraduate_core","level":2,"skills":["依分布收斂"]},"variant":{"family_id":"qf-mod31-convdist-finite-prefix","seed":202610313088,"parameters":{"p":[1,2],"c":[3,20],"shift":14,"prefix_length":13,"domain":"Symbolic_Bernoulli_CDF_limit","operation":"convdist-finite-prefix","semantic_template":"qf-mod31-convdist-finite-prefix/{\"c\":[3,20],\"p\":[1,2],\"prefix_length\":13,\"shift\":14}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_model","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"候選須由主端獨立重算；不構成人工審定、一般不可數性／色數最優性／更強機率收斂／商域、optional stopping、Lean或形式Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-14","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261014-advance-20261031-r03-convergence-in-distribution-0089","batch_id":"batch-20261014-advance-20261031-r03-convergence-in-distribution-foundations","language":"zh-Hant","source_mko_ids":["mko-convergence-in-distribution"],"title_zh":"依分布收斂","stem_zh":"Bernoulli symbolic tail與極限CDF。操作=convdist-finite-prefix；資料={\"p\":[1,2],\"c\":[4,20],\"shift\":15,\"prefix_length\":14}。請依 [p,c,shift,prefix_length,sufficient,boundary] 欄序回答。","answer":{"kind":"expression","value":"(1/2, 1/5, 15, 14, 否, finite_prefix_not_convergence_certificate)","explanation_zh":"Wave4收束核對=(1/2, 1/5, 15, 14, 否, finite_prefix_not_convergence_certificate)；依完整明示資料重算；只在極限CDF連續點要求收斂且有限prefix不足；不要求coupling且不推出依機率、幾乎處處或Lp收斂。"},"difficulty":{"band":"undergraduate_core","level":2,"skills":["依分布收斂"]},"variant":{"family_id":"qf-mod31-convdist-finite-prefix","seed":202610313089,"parameters":{"p":[1,2],"c":[4,20],"shift":15,"prefix_length":14,"domain":"Symbolic_Bernoulli_CDF_limit","operation":"convdist-finite-prefix","semantic_template":"qf-mod31-convdist-finite-prefix/{\"c\":[4,20],\"p\":[1,2],\"prefix_length\":14,\"shift\":15}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_model","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"候選須由主端獨立重算；不構成人工審定、一般不可數性／色數最優性／更強機率收斂／商域、optional stopping、Lean或形式Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-14","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261014-advance-20261031-r03-convergence-in-distribution-0090","batch_id":"batch-20261014-advance-20261031-r03-convergence-in-distribution-foundations","language":"zh-Hant","source_mko_ids":["mko-convergence-in-distribution"],"title_zh":"依分布收斂","stem_zh":"Bernoulli symbolic tail與極限CDF。操作=convdist-finite-prefix；資料={\"p\":[1,2],\"c\":[5,20],\"shift\":16,\"prefix_length\":15}。請依 [p,c,shift,prefix_length,sufficient,boundary] 欄序回答。","answer":{"kind":"expression","value":"(1/2, 1/4, 16, 15, 否, finite_prefix_not_convergence_certificate)","explanation_zh":"Wave4收束核對=(1/2, 1/4, 16, 15, 否, finite_prefix_not_convergence_certificate)；依完整明示資料重算；只在極限CDF連續點要求收斂且有限prefix不足；不要求coupling且不推出依機率、幾乎處處或Lp收斂。"},"difficulty":{"band":"undergraduate_core","level":2,"skills":["依分布收斂"]},"variant":{"family_id":"qf-mod31-convdist-finite-prefix","seed":202610313090,"parameters":{"p":[1,2],"c":[5,20],"shift":16,"prefix_length":15,"domain":"Symbolic_Bernoulli_CDF_limit","operation":"convdist-finite-prefix","semantic_template":"qf-mod31-convdist-finite-prefix/{\"c\":[5,20],\"p\":[1,2],\"prefix_length\":15,\"shift\":16}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_model","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"候選須由主端獨立重算；不構成人工審定、一般不可數性／色數最優性／更強機率收斂／商域、optional stopping、Lean或形式Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-14","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261014-advance-20261031-r03-convergence-in-distribution-0091","batch_id":"batch-20261014-advance-20261031-r03-convergence-in-distribution-foundations","language":"zh-Hant","source_mko_ids":["mko-convergence-in-distribution"],"title_zh":"依分布收斂","stem_zh":"Bernoulli symbolic tail與極限CDF。操作=convdist-finite-prefix；資料={\"p\":[1,2],\"c\":[1,20],\"shift\":17,\"prefix_length\":16}。請依 [p,c,shift,prefix_length,sufficient,boundary] 欄序回答。","answer":{"kind":"expression","value":"(1/2, 1/20, 17, 16, 否, finite_prefix_not_convergence_certificate)","explanation_zh":"Wave4收束核對=(1/2, 1/20, 17, 16, 否, finite_prefix_not_convergence_certificate)；依完整明示資料重算；只在極限CDF連續點要求收斂且有限prefix不足；不要求coupling且不推出依機率、幾乎處處或Lp收斂。"},"difficulty":{"band":"undergraduate_core","level":2,"skills":["依分布收斂"]},"variant":{"family_id":"qf-mod31-convdist-finite-prefix","seed":202610313091,"parameters":{"p":[1,2],"c":[1,20],"shift":17,"prefix_length":16,"domain":"Symbolic_Bernoulli_CDF_limit","operation":"convdist-finite-prefix","semantic_template":"qf-mod31-convdist-finite-prefix/{\"c\":[1,20],\"p\":[1,2],\"prefix_length\":16,\"shift\":17}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_model","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"候選須由主端獨立重算；不構成人工審定、一般不可數性／色數最優性／更強機率收斂／商域、optional stopping、Lean或形式Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-14","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261014-advance-20261031-r03-convergence-in-distribution-0092","batch_id":"batch-20261014-advance-20261031-r03-convergence-in-distribution-foundations","language":"zh-Hant","source_mko_ids":["mko-convergence-in-distribution"],"title_zh":"依分布收斂","stem_zh":"Bernoulli symbolic tail與極限CDF。操作=convdist-finite-prefix；資料={\"p\":[1,2],\"c\":[2,20],\"shift\":18,\"prefix_length\":17}。請依 [p,c,shift,prefix_length,sufficient,boundary] 欄序回答。","answer":{"kind":"expression","value":"(1/2, 1/10, 18, 17, 否, finite_prefix_not_convergence_certificate)","explanation_zh":"Wave4收束核對=(1/2, 1/10, 18, 17, 否, finite_prefix_not_convergence_certificate)；依完整明示資料重算；只在極限CDF連續點要求收斂且有限prefix不足；不要求coupling且不推出依機率、幾乎處處或Lp收斂。"},"difficulty":{"band":"undergraduate_core","level":2,"skills":["依分布收斂"]},"variant":{"family_id":"qf-mod31-convdist-finite-prefix","seed":202610313092,"parameters":{"p":[1,2],"c":[2,20],"shift":18,"prefix_length":17,"domain":"Symbolic_Bernoulli_CDF_limit","operation":"convdist-finite-prefix","semantic_template":"qf-mod31-convdist-finite-prefix/{\"c\":[2,20],\"p\":[1,2],\"prefix_length\":17,\"shift\":18}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_model","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"候選須由主端獨立重算；不構成人工審定、一般不可數性／色數最優性／更強機率收斂／商域、optional stopping、Lean或形式Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-14","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261014-advance-20261031-r03-convergence-in-distribution-0093","batch_id":"batch-20261014-advance-20261031-r03-convergence-in-distribution-foundations","language":"zh-Hant","source_mko_ids":["mko-convergence-in-distribution"],"title_zh":"依分布收斂","stem_zh":"Bernoulli symbolic tail與極限CDF。操作=convdist-finite-prefix；資料={\"p\":[1,2],\"c\":[3,20],\"shift\":19,\"prefix_length\":18}。請依 [p,c,shift,prefix_length,sufficient,boundary] 欄序回答。","answer":{"kind":"expression","value":"(1/2, 3/20, 19, 18, 否, finite_prefix_not_convergence_certificate)","explanation_zh":"Wave4收束核對=(1/2, 3/20, 19, 18, 否, finite_prefix_not_convergence_certificate)；依完整明示資料重算；只在極限CDF連續點要求收斂且有限prefix不足；不要求coupling且不推出依機率、幾乎處處或Lp收斂。"},"difficulty":{"band":"undergraduate_core","level":3,"skills":["依分布收斂"]},"variant":{"family_id":"qf-mod31-convdist-finite-prefix","seed":202610313093,"parameters":{"p":[1,2],"c":[3,20],"shift":19,"prefix_length":18,"domain":"Symbolic_Bernoulli_CDF_limit","operation":"convdist-finite-prefix","semantic_template":"qf-mod31-convdist-finite-prefix/{\"c\":[3,20],\"p\":[1,2],\"prefix_length\":18,\"shift\":19}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_model","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"候選須由主端獨立重算；不構成人工審定、一般不可數性／色數最優性／更強機率收斂／商域、optional stopping、Lean或形式Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-14","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261014-advance-20261031-r03-convergence-in-distribution-0094","batch_id":"batch-20261014-advance-20261031-r03-convergence-in-distribution-foundations","language":"zh-Hant","source_mko_ids":["mko-convergence-in-distribution"],"title_zh":"依分布收斂","stem_zh":"Bernoulli symbolic tail與極限CDF。操作=convdist-finite-prefix；資料={\"p\":[1,2],\"c\":[4,20],\"shift\":20,\"prefix_length\":19}。請依 [p,c,shift,prefix_length,sufficient,boundary] 欄序回答。","answer":{"kind":"expression","value":"(1/2, 1/5, 20, 19, 否, finite_prefix_not_convergence_certificate)","explanation_zh":"Wave4收束核對=(1/2, 1/5, 20, 19, 否, finite_prefix_not_convergence_certificate)；依完整明示資料重算；只在極限CDF連續點要求收斂且有限prefix不足；不要求coupling且不推出依機率、幾乎處處或Lp收斂。"},"difficulty":{"band":"undergraduate_core","level":3,"skills":["依分布收斂"]},"variant":{"family_id":"qf-mod31-convdist-finite-prefix","seed":202610313094,"parameters":{"p":[1,2],"c":[4,20],"shift":20,"prefix_length":19,"domain":"Symbolic_Bernoulli_CDF_limit","operation":"convdist-finite-prefix","semantic_template":"qf-mod31-convdist-finite-prefix/{\"c\":[4,20],\"p\":[1,2],\"prefix_length\":19,\"shift\":20}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_model","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"候選須由主端獨立重算；不構成人工審定、一般不可數性／色數最優性／更強機率收斂／商域、optional stopping、Lean或形式Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-14","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261014-advance-20261031-r03-convergence-in-distribution-0095","batch_id":"batch-20261014-advance-20261031-r03-convergence-in-distribution-foundations","language":"zh-Hant","source_mko_ids":["mko-convergence-in-distribution"],"title_zh":"依分布收斂","stem_zh":"Bernoulli symbolic tail與極限CDF。操作=convdist-finite-prefix；資料={\"p\":[1,2],\"c\":[5,20],\"shift\":21,\"prefix_length\":20}。請依 [p,c,shift,prefix_length,sufficient,boundary] 欄序回答。","answer":{"kind":"expression","value":"(1/2, 1/4, 21, 20, 否, finite_prefix_not_convergence_certificate)","explanation_zh":"Wave4收束核對=(1/2, 1/4, 21, 20, 否, finite_prefix_not_convergence_certificate)；依完整明示資料重算；只在極限CDF連續點要求收斂且有限prefix不足；不要求coupling且不推出依機率、幾乎處處或Lp收斂。"},"difficulty":{"band":"undergraduate_core","level":3,"skills":["依分布收斂"]},"variant":{"family_id":"qf-mod31-convdist-finite-prefix","seed":202610313095,"parameters":{"p":[1,2],"c":[5,20],"shift":21,"prefix_length":20,"domain":"Symbolic_Bernoulli_CDF_limit","operation":"convdist-finite-prefix","semantic_template":"qf-mod31-convdist-finite-prefix/{\"c\":[5,20],\"p\":[1,2],\"prefix_length\":20,\"shift\":21}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_model","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"候選須由主端獨立重算；不構成人工審定、一般不可數性／色數最優性／更強機率收斂／商域、optional stopping、Lean或形式Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-14","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261014-advance-20261031-r03-convergence-in-distribution-0096","batch_id":"batch-20261014-advance-20261031-r03-convergence-in-distribution-foundations","language":"zh-Hant","source_mko_ids":["mko-convergence-in-distribution"],"title_zh":"依分布收斂","stem_zh":"Bernoulli symbolic tail與極限CDF。操作=convdist-finite-prefix；資料={\"p\":[1,2],\"c\":[1,20],\"shift\":22,\"prefix_length\":21}。請依 [p,c,shift,prefix_length,sufficient,boundary] 欄序回答。","answer":{"kind":"expression","value":"(1/2, 1/20, 22, 21, 否, finite_prefix_not_convergence_certificate)","explanation_zh":"Wave4收束核對=(1/2, 1/20, 22, 21, 否, finite_prefix_not_convergence_certificate)；依完整明示資料重算；只在極限CDF連續點要求收斂且有限prefix不足；不要求coupling且不推出依機率、幾乎處處或Lp收斂。"},"difficulty":{"band":"undergraduate_core","level":3,"skills":["依分布收斂"]},"variant":{"family_id":"qf-mod31-convdist-finite-prefix","seed":202610313096,"parameters":{"p":[1,2],"c":[1,20],"shift":22,"prefix_length":21,"domain":"Symbolic_Bernoulli_CDF_limit","operation":"convdist-finite-prefix","semantic_template":"qf-mod31-convdist-finite-prefix/{\"c\":[1,20],\"p\":[1,2],\"prefix_length\":21,\"shift\":22}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_model","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"候選須由主端獨立重算；不構成人工審定、一般不可數性／色數最優性／更強機率收斂／商域、optional stopping、Lean或形式Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-14","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261014-advance-20261031-r03-convergence-in-distribution-0097","batch_id":"batch-20261014-advance-20261031-r03-convergence-in-distribution-foundations","language":"zh-Hant","source_mko_ids":["mko-convergence-in-distribution"],"title_zh":"依分布收斂","stem_zh":"Bernoulli symbolic tail與極限CDF。操作=convdist-finite-prefix；資料={\"p\":[1,2],\"c\":[2,20],\"shift\":23,\"prefix_length\":22}。請依 [p,c,shift,prefix_length,sufficient,boundary] 欄序回答。","answer":{"kind":"expression","value":"(1/2, 1/10, 23, 22, 否, finite_prefix_not_convergence_certificate)","explanation_zh":"Wave4收束核對=(1/2, 1/10, 23, 22, 否, finite_prefix_not_convergence_certificate)；依完整明示資料重算；只在極限CDF連續點要求收斂且有限prefix不足；不要求coupling且不推出依機率、幾乎處處或Lp收斂。"},"difficulty":{"band":"undergraduate_core","level":3,"skills":["依分布收斂"]},"variant":{"family_id":"qf-mod31-convdist-finite-prefix","seed":202610313097,"parameters":{"p":[1,2],"c":[2,20],"shift":23,"prefix_length":22,"domain":"Symbolic_Bernoulli_CDF_limit","operation":"convdist-finite-prefix","semantic_template":"qf-mod31-convdist-finite-prefix/{\"c\":[2,20],\"p\":[1,2],\"prefix_length\":22,\"shift\":23}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_model","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"候選須由主端獨立重算；不構成人工審定、一般不可數性／色數最優性／更強機率收斂／商域、optional stopping、Lean或形式Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-14","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261014-advance-20261031-r03-convergence-in-distribution-0098","batch_id":"batch-20261014-advance-20261031-r03-convergence-in-distribution-foundations","language":"zh-Hant","source_mko_ids":["mko-convergence-in-distribution"],"title_zh":"依分布收斂","stem_zh":"Bernoulli symbolic tail與極限CDF。操作=convdist-finite-prefix；資料={\"p\":[1,2],\"c\":[3,20],\"shift\":24,\"prefix_length\":23}。請依 [p,c,shift,prefix_length,sufficient,boundary] 欄序回答。","answer":{"kind":"expression","value":"(1/2, 3/20, 24, 23, 否, finite_prefix_not_convergence_certificate)","explanation_zh":"Wave4收束核對=(1/2, 3/20, 24, 23, 否, finite_prefix_not_convergence_certificate)；依完整明示資料重算；只在極限CDF連續點要求收斂且有限prefix不足；不要求coupling且不推出依機率、幾乎處處或Lp收斂。"},"difficulty":{"band":"undergraduate_core","level":3,"skills":["依分布收斂"]},"variant":{"family_id":"qf-mod31-convdist-finite-prefix","seed":202610313098,"parameters":{"p":[1,2],"c":[3,20],"shift":24,"prefix_length":23,"domain":"Symbolic_Bernoulli_CDF_limit","operation":"convdist-finite-prefix","semantic_template":"qf-mod31-convdist-finite-prefix/{\"c\":[3,20],\"p\":[1,2],\"prefix_length\":23,\"shift\":24}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_model","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"候選須由主端獨立重算；不構成人工審定、一般不可數性／色數最優性／更強機率收斂／商域、optional stopping、Lean或形式Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-14","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261014-advance-20261031-r03-convergence-in-distribution-0099","batch_id":"batch-20261014-advance-20261031-r03-convergence-in-distribution-foundations","language":"zh-Hant","source_mko_ids":["mko-convergence-in-distribution"],"title_zh":"依分布收斂","stem_zh":"Bernoulli symbolic tail與極限CDF。操作=convdist-finite-prefix；資料={\"p\":[1,2],\"c\":[4,20],\"shift\":25,\"prefix_length\":24}。請依 [p,c,shift,prefix_length,sufficient,boundary] 欄序回答。","answer":{"kind":"expression","value":"(1/2, 1/5, 25, 24, 否, finite_prefix_not_convergence_certificate)","explanation_zh":"Wave4收束核對=(1/2, 1/5, 25, 24, 否, finite_prefix_not_convergence_certificate)；依完整明示資料重算；只在極限CDF連續點要求收斂且有限prefix不足；不要求coupling且不推出依機率、幾乎處處或Lp收斂。"},"difficulty":{"band":"undergraduate_core","level":3,"skills":["依分布收斂"]},"variant":{"family_id":"qf-mod31-convdist-finite-prefix","seed":202610313099,"parameters":{"p":[1,2],"c":[4,20],"shift":25,"prefix_length":24,"domain":"Symbolic_Bernoulli_CDF_limit","operation":"convdist-finite-prefix","semantic_template":"qf-mod31-convdist-finite-prefix/{\"c\":[4,20],\"p\":[1,2],\"prefix_length\":24,\"shift\":25}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_model","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"候選須由主端獨立重算；不構成人工審定、一般不可數性／色數最優性／更強機率收斂／商域、optional stopping、Lean或形式Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-14","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261014-advance-20261031-r03-convergence-in-distribution-0100","batch_id":"batch-20261014-advance-20261031-r03-convergence-in-distribution-foundations","language":"zh-Hant","source_mko_ids":["mko-convergence-in-distribution"],"title_zh":"依分布收斂","stem_zh":"Bernoulli symbolic tail與極限CDF。操作=convdist-finite-prefix；資料={\"p\":[1,2],\"c\":[5,20],\"shift\":26,\"prefix_length\":25}。請依 [p,c,shift,prefix_length,sufficient,boundary] 欄序回答。","answer":{"kind":"expression","value":"(1/2, 1/4, 26, 25, 否, finite_prefix_not_convergence_certificate)","explanation_zh":"Wave4收束核對=(1/2, 1/4, 26, 25, 否, finite_prefix_not_convergence_certificate)；依完整明示資料重算；只在極限CDF連續點要求收斂且有限prefix不足；不要求coupling且不推出依機率、幾乎處處或Lp收斂。"},"difficulty":{"band":"undergraduate_core","level":3,"skills":["依分布收斂"]},"variant":{"family_id":"qf-mod31-convdist-finite-prefix","seed":202610313100,"parameters":{"p":[1,2],"c":[5,20],"shift":26,"prefix_length":25,"domain":"Symbolic_Bernoulli_CDF_limit","operation":"convdist-finite-prefix","semantic_template":"qf-mod31-convdist-finite-prefix/{\"c\":[5,20],\"p\":[1,2],\"prefix_length\":25,\"shift\":26}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_model","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"候選須由主端獨立重算；不構成人工審定、一般不可數性／色數最優性／更強機率收斂／商域、optional stopping、Lean或形式Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-14","contract_version":"ocme-question-factory-v0.1"}}