{"schema_version":"ocme-question-v0.1","id":"q-20261014-advance-20261030-r07-convergence-in-probability-0001","batch_id":"batch-20261014-advance-20261030-r07-convergence-in-probability-foundations","language":"zh-Hant","source_mko_ids":["mko-convergence-in-probability"],"title_zh":"依機率收斂","stem_zh":"共同機率空間與forall epsilon tail責任。操作=convprob-deviation-probability；資料={\"numerator\":1,\"shift\":2,\"n\":1}。請依 [numerator,shift,n,probability] 欄序回答。","answer":{"kind":"expression","value":"(1, 2, 1, 1/3)","explanation_zh":"Wave4第四層核對=(1, 2, 1, 1/3)；依完整明示資料重算；完整有限／symbolic tail證書不自動升格為未聲明的一般定理；finite prefix不足且只接受symbolic tail或eventual equality；不混同almost sure Lp或distribution convergence。"},"difficulty":{"band":"undergraduate_core","level":1,"skills":["依機率收斂"]},"variant":{"family_id":"qf-mod30-convprob-deviation-probability","seed":202610307001,"parameters":{"numerator":1,"shift":2,"n":1,"domain":"Symbolic_deviation_probability_tail","operation":"convprob-deviation-probability","semantic_template":"qf-mod30-convprob-deviation-probability/{\"n\":1,\"numerator\":1,\"shift\":2}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_model","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"候選須主端重算；不構成人工審定、一般域／Hilbert／martingale／無限基數／一般收斂、Lean或Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-14","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261014-advance-20261030-r07-convergence-in-probability-0002","batch_id":"batch-20261014-advance-20261030-r07-convergence-in-probability-foundations","language":"zh-Hant","source_mko_ids":["mko-convergence-in-probability"],"title_zh":"依機率收斂","stem_zh":"共同機率空間與forall epsilon tail責任。操作=convprob-deviation-probability；資料={\"numerator\":2,\"shift\":3,\"n\":2}。請依 [numerator,shift,n,probability] 欄序回答。","answer":{"kind":"expression","value":"(2, 3, 2, 2/5)","explanation_zh":"Wave4第四層核對=(2, 3, 2, 2/5)；依完整明示資料重算；完整有限／symbolic tail證書不自動升格為未聲明的一般定理；finite prefix不足且只接受symbolic tail或eventual equality；不混同almost sure Lp或distribution convergence。"},"difficulty":{"band":"undergraduate_core","level":1,"skills":["依機率收斂"]},"variant":{"family_id":"qf-mod30-convprob-deviation-probability","seed":202610307002,"parameters":{"numerator":2,"shift":3,"n":2,"domain":"Symbolic_deviation_probability_tail","operation":"convprob-deviation-probability","semantic_template":"qf-mod30-convprob-deviation-probability/{\"n\":2,\"numerator\":2,\"shift\":3}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_model","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"候選須主端重算；不構成人工審定、一般域／Hilbert／martingale／無限基數／一般收斂、Lean或Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-14","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261014-advance-20261030-r07-convergence-in-probability-0003","batch_id":"batch-20261014-advance-20261030-r07-convergence-in-probability-foundations","language":"zh-Hant","source_mko_ids":["mko-convergence-in-probability"],"title_zh":"依機率收斂","stem_zh":"共同機率空間與forall epsilon tail責任。操作=convprob-deviation-probability；資料={\"numerator\":3,\"shift\":4,\"n\":3}。請依 [numerator,shift,n,probability] 欄序回答。","answer":{"kind":"expression","value":"(3, 4, 3, 3/7)","explanation_zh":"Wave4第四層核對=(3, 4, 3, 3/7)；依完整明示資料重算；完整有限／symbolic tail證書不自動升格為未聲明的一般定理；finite prefix不足且只接受symbolic tail或eventual equality；不混同almost sure Lp或distribution convergence。"},"difficulty":{"band":"undergraduate_core","level":1,"skills":["依機率收斂"]},"variant":{"family_id":"qf-mod30-convprob-deviation-probability","seed":202610307003,"parameters":{"numerator":3,"shift":4,"n":3,"domain":"Symbolic_deviation_probability_tail","operation":"convprob-deviation-probability","semantic_template":"qf-mod30-convprob-deviation-probability/{\"n\":3,\"numerator\":3,\"shift\":4}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_model","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"候選須主端重算；不構成人工審定、一般域／Hilbert／martingale／無限基數／一般收斂、Lean或Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-14","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261014-advance-20261030-r07-convergence-in-probability-0004","batch_id":"batch-20261014-advance-20261030-r07-convergence-in-probability-foundations","language":"zh-Hant","source_mko_ids":["mko-convergence-in-probability"],"title_zh":"依機率收斂","stem_zh":"共同機率空間與forall epsilon tail責任。操作=convprob-deviation-probability；資料={\"numerator\":4,\"shift\":5,\"n\":4}。請依 [numerator,shift,n,probability] 欄序回答。","answer":{"kind":"expression","value":"(4, 5, 4, 4/9)","explanation_zh":"Wave4第四層核對=(4, 5, 4, 4/9)；依完整明示資料重算；完整有限／symbolic tail證書不自動升格為未聲明的一般定理；finite prefix不足且只接受symbolic tail或eventual equality；不混同almost sure Lp或distribution convergence。"},"difficulty":{"band":"undergraduate_core","level":1,"skills":["依機率收斂"]},"variant":{"family_id":"qf-mod30-convprob-deviation-probability","seed":202610307004,"parameters":{"numerator":4,"shift":5,"n":4,"domain":"Symbolic_deviation_probability_tail","operation":"convprob-deviation-probability","semantic_template":"qf-mod30-convprob-deviation-probability/{\"n\":4,\"numerator\":4,\"shift\":5}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_model","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"候選須主端重算；不構成人工審定、一般域／Hilbert／martingale／無限基數／一般收斂、Lean或Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-14","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261014-advance-20261030-r07-convergence-in-probability-0005","batch_id":"batch-20261014-advance-20261030-r07-convergence-in-probability-foundations","language":"zh-Hant","source_mko_ids":["mko-convergence-in-probability"],"title_zh":"依機率收斂","stem_zh":"共同機率空間與forall epsilon tail責任。操作=convprob-deviation-probability；資料={\"numerator\":5,\"shift\":6,\"n\":5}。請依 [numerator,shift,n,probability] 欄序回答。","answer":{"kind":"expression","value":"(5, 6, 5, 5/11)","explanation_zh":"Wave4第四層核對=(5, 6, 5, 5/11)；依完整明示資料重算；完整有限／symbolic tail證書不自動升格為未聲明的一般定理；finite prefix不足且只接受symbolic tail或eventual equality；不混同almost sure Lp或distribution convergence。"},"difficulty":{"band":"undergraduate_core","level":1,"skills":["依機率收斂"]},"variant":{"family_id":"qf-mod30-convprob-deviation-probability","seed":202610307005,"parameters":{"numerator":5,"shift":6,"n":5,"domain":"Symbolic_deviation_probability_tail","operation":"convprob-deviation-probability","semantic_template":"qf-mod30-convprob-deviation-probability/{\"n\":5,\"numerator\":5,\"shift\":6}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_model","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"候選須主端重算；不構成人工審定、一般域／Hilbert／martingale／無限基數／一般收斂、Lean或Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-14","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261014-advance-20261030-r07-convergence-in-probability-0006","batch_id":"batch-20261014-advance-20261030-r07-convergence-in-probability-foundations","language":"zh-Hant","source_mko_ids":["mko-convergence-in-probability"],"title_zh":"依機率收斂","stem_zh":"共同機率空間與forall epsilon tail責任。操作=convprob-deviation-probability；資料={\"numerator\":1,\"shift\":7,\"n\":6}。請依 [numerator,shift,n,probability] 欄序回答。","answer":{"kind":"expression","value":"(1, 7, 6, 1/13)","explanation_zh":"Wave4第四層核對=(1, 7, 6, 1/13)；依完整明示資料重算；完整有限／symbolic tail證書不自動升格為未聲明的一般定理；finite prefix不足且只接受symbolic tail或eventual equality；不混同almost sure Lp或distribution convergence。"},"difficulty":{"band":"undergraduate_core","level":1,"skills":["依機率收斂"]},"variant":{"family_id":"qf-mod30-convprob-deviation-probability","seed":202610307006,"parameters":{"numerator":1,"shift":7,"n":6,"domain":"Symbolic_deviation_probability_tail","operation":"convprob-deviation-probability","semantic_template":"qf-mod30-convprob-deviation-probability/{\"n\":6,\"numerator\":1,\"shift\":7}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_model","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"候選須主端重算；不構成人工審定、一般域／Hilbert／martingale／無限基數／一般收斂、Lean或Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-14","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261014-advance-20261030-r07-convergence-in-probability-0007","batch_id":"batch-20261014-advance-20261030-r07-convergence-in-probability-foundations","language":"zh-Hant","source_mko_ids":["mko-convergence-in-probability"],"title_zh":"依機率收斂","stem_zh":"共同機率空間與forall epsilon tail責任。操作=convprob-deviation-probability；資料={\"numerator\":2,\"shift\":8,\"n\":7}。請依 [numerator,shift,n,probability] 欄序回答。","answer":{"kind":"expression","value":"(2, 8, 7, 2/15)","explanation_zh":"Wave4第四層核對=(2, 8, 7, 2/15)；依完整明示資料重算；完整有限／symbolic tail證書不自動升格為未聲明的一般定理；finite prefix不足且只接受symbolic tail或eventual equality；不混同almost sure Lp或distribution convergence。"},"difficulty":{"band":"undergraduate_core","level":1,"skills":["依機率收斂"]},"variant":{"family_id":"qf-mod30-convprob-deviation-probability","seed":202610307007,"parameters":{"numerator":2,"shift":8,"n":7,"domain":"Symbolic_deviation_probability_tail","operation":"convprob-deviation-probability","semantic_template":"qf-mod30-convprob-deviation-probability/{\"n\":7,\"numerator\":2,\"shift\":8}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_model","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"候選須主端重算；不構成人工審定、一般域／Hilbert／martingale／無限基數／一般收斂、Lean或Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-14","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261014-advance-20261030-r07-convergence-in-probability-0008","batch_id":"batch-20261014-advance-20261030-r07-convergence-in-probability-foundations","language":"zh-Hant","source_mko_ids":["mko-convergence-in-probability"],"title_zh":"依機率收斂","stem_zh":"共同機率空間與forall epsilon tail責任。操作=convprob-deviation-probability；資料={\"numerator\":3,\"shift\":2,\"n\":8}。請依 [numerator,shift,n,probability] 欄序回答。","answer":{"kind":"expression","value":"(3, 2, 8, 3/10)","explanation_zh":"Wave4第四層核對=(3, 2, 8, 3/10)；依完整明示資料重算；完整有限／symbolic tail證書不自動升格為未聲明的一般定理；finite prefix不足且只接受symbolic tail或eventual equality；不混同almost sure Lp或distribution convergence。"},"difficulty":{"band":"undergraduate_core","level":1,"skills":["依機率收斂"]},"variant":{"family_id":"qf-mod30-convprob-deviation-probability","seed":202610307008,"parameters":{"numerator":3,"shift":2,"n":8,"domain":"Symbolic_deviation_probability_tail","operation":"convprob-deviation-probability","semantic_template":"qf-mod30-convprob-deviation-probability/{\"n\":8,\"numerator\":3,\"shift\":2}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_model","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"候選須主端重算；不構成人工審定、一般域／Hilbert／martingale／無限基數／一般收斂、Lean或Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-14","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261014-advance-20261030-r07-convergence-in-probability-0009","batch_id":"batch-20261014-advance-20261030-r07-convergence-in-probability-foundations","language":"zh-Hant","source_mko_ids":["mko-convergence-in-probability"],"title_zh":"依機率收斂","stem_zh":"共同機率空間與forall epsilon tail責任。操作=convprob-deviation-probability；資料={\"numerator\":4,\"shift\":3,\"n\":9}。請依 [numerator,shift,n,probability] 欄序回答。","answer":{"kind":"expression","value":"(4, 3, 9, 1/3)","explanation_zh":"Wave4第四層核對=(4, 3, 9, 1/3)；依完整明示資料重算；完整有限／symbolic tail證書不自動升格為未聲明的一般定理；finite prefix不足且只接受symbolic tail或eventual equality；不混同almost sure Lp或distribution convergence。"},"difficulty":{"band":"undergraduate_core","level":2,"skills":["依機率收斂"]},"variant":{"family_id":"qf-mod30-convprob-deviation-probability","seed":202610307009,"parameters":{"numerator":4,"shift":3,"n":9,"domain":"Symbolic_deviation_probability_tail","operation":"convprob-deviation-probability","semantic_template":"qf-mod30-convprob-deviation-probability/{\"n\":9,\"numerator\":4,\"shift\":3}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_model","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"候選須主端重算；不構成人工審定、一般域／Hilbert／martingale／無限基數／一般收斂、Lean或Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-14","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261014-advance-20261030-r07-convergence-in-probability-0010","batch_id":"batch-20261014-advance-20261030-r07-convergence-in-probability-foundations","language":"zh-Hant","source_mko_ids":["mko-convergence-in-probability"],"title_zh":"依機率收斂","stem_zh":"共同機率空間與forall epsilon tail責任。操作=convprob-deviation-probability；資料={\"numerator\":5,\"shift\":4,\"n\":10}。請依 [numerator,shift,n,probability] 欄序回答。","answer":{"kind":"expression","value":"(5, 4, 10, 5/14)","explanation_zh":"Wave4第四層核對=(5, 4, 10, 5/14)；依完整明示資料重算；完整有限／symbolic tail證書不自動升格為未聲明的一般定理；finite prefix不足且只接受symbolic tail或eventual equality；不混同almost sure Lp或distribution convergence。"},"difficulty":{"band":"undergraduate_core","level":2,"skills":["依機率收斂"]},"variant":{"family_id":"qf-mod30-convprob-deviation-probability","seed":202610307010,"parameters":{"numerator":5,"shift":4,"n":10,"domain":"Symbolic_deviation_probability_tail","operation":"convprob-deviation-probability","semantic_template":"qf-mod30-convprob-deviation-probability/{\"n\":10,\"numerator\":5,\"shift\":4}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_model","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"候選須主端重算；不構成人工審定、一般域／Hilbert／martingale／無限基數／一般收斂、Lean或Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-14","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261014-advance-20261030-r07-convergence-in-probability-0011","batch_id":"batch-20261014-advance-20261030-r07-convergence-in-probability-foundations","language":"zh-Hant","source_mko_ids":["mko-convergence-in-probability"],"title_zh":"依機率收斂","stem_zh":"共同機率空間與forall epsilon tail責任。操作=convprob-deviation-probability；資料={\"numerator\":1,\"shift\":5,\"n\":11}。請依 [numerator,shift,n,probability] 欄序回答。","answer":{"kind":"expression","value":"(1, 5, 11, 1/16)","explanation_zh":"Wave4第四層核對=(1, 5, 11, 1/16)；依完整明示資料重算；完整有限／symbolic tail證書不自動升格為未聲明的一般定理；finite prefix不足且只接受symbolic tail或eventual equality；不混同almost sure Lp或distribution convergence。"},"difficulty":{"band":"undergraduate_core","level":2,"skills":["依機率收斂"]},"variant":{"family_id":"qf-mod30-convprob-deviation-probability","seed":202610307011,"parameters":{"numerator":1,"shift":5,"n":11,"domain":"Symbolic_deviation_probability_tail","operation":"convprob-deviation-probability","semantic_template":"qf-mod30-convprob-deviation-probability/{\"n\":11,\"numerator\":1,\"shift\":5}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_model","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"候選須主端重算；不構成人工審定、一般域／Hilbert／martingale／無限基數／一般收斂、Lean或Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-14","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261014-advance-20261030-r07-convergence-in-probability-0012","batch_id":"batch-20261014-advance-20261030-r07-convergence-in-probability-foundations","language":"zh-Hant","source_mko_ids":["mko-convergence-in-probability"],"title_zh":"依機率收斂","stem_zh":"共同機率空間與forall epsilon tail責任。操作=convprob-deviation-probability；資料={\"numerator\":2,\"shift\":6,\"n\":12}。請依 [numerator,shift,n,probability] 欄序回答。","answer":{"kind":"expression","value":"(2, 6, 12, 1/9)","explanation_zh":"Wave4第四層核對=(2, 6, 12, 1/9)；依完整明示資料重算；完整有限／symbolic tail證書不自動升格為未聲明的一般定理；finite prefix不足且只接受symbolic tail或eventual equality；不混同almost sure Lp或distribution convergence。"},"difficulty":{"band":"undergraduate_core","level":2,"skills":["依機率收斂"]},"variant":{"family_id":"qf-mod30-convprob-deviation-probability","seed":202610307012,"parameters":{"numerator":2,"shift":6,"n":12,"domain":"Symbolic_deviation_probability_tail","operation":"convprob-deviation-probability","semantic_template":"qf-mod30-convprob-deviation-probability/{\"n\":12,\"numerator\":2,\"shift\":6}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_model","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"候選須主端重算；不構成人工審定、一般域／Hilbert／martingale／無限基數／一般收斂、Lean或Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-14","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261014-advance-20261030-r07-convergence-in-probability-0013","batch_id":"batch-20261014-advance-20261030-r07-convergence-in-probability-foundations","language":"zh-Hant","source_mko_ids":["mko-convergence-in-probability"],"title_zh":"依機率收斂","stem_zh":"共同機率空間與forall epsilon tail責任。操作=convprob-deviation-probability；資料={\"numerator\":3,\"shift\":7,\"n\":13}。請依 [numerator,shift,n,probability] 欄序回答。","answer":{"kind":"expression","value":"(3, 7, 13, 3/20)","explanation_zh":"Wave4第四層核對=(3, 7, 13, 3/20)；依完整明示資料重算；完整有限／symbolic tail證書不自動升格為未聲明的一般定理；finite prefix不足且只接受symbolic tail或eventual equality；不混同almost sure Lp或distribution convergence。"},"difficulty":{"band":"undergraduate_core","level":2,"skills":["依機率收斂"]},"variant":{"family_id":"qf-mod30-convprob-deviation-probability","seed":202610307013,"parameters":{"numerator":3,"shift":7,"n":13,"domain":"Symbolic_deviation_probability_tail","operation":"convprob-deviation-probability","semantic_template":"qf-mod30-convprob-deviation-probability/{\"n\":13,\"numerator\":3,\"shift\":7}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_model","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"候選須主端重算；不構成人工審定、一般域／Hilbert／martingale／無限基數／一般收斂、Lean或Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-14","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261014-advance-20261030-r07-convergence-in-probability-0014","batch_id":"batch-20261014-advance-20261030-r07-convergence-in-probability-foundations","language":"zh-Hant","source_mko_ids":["mko-convergence-in-probability"],"title_zh":"依機率收斂","stem_zh":"共同機率空間與forall epsilon tail責任。操作=convprob-deviation-probability；資料={\"numerator\":4,\"shift\":8,\"n\":14}。請依 [numerator,shift,n,probability] 欄序回答。","answer":{"kind":"expression","value":"(4, 8, 14, 2/11)","explanation_zh":"Wave4第四層核對=(4, 8, 14, 2/11)；依完整明示資料重算；完整有限／symbolic tail證書不自動升格為未聲明的一般定理；finite prefix不足且只接受symbolic tail或eventual equality；不混同almost sure Lp或distribution convergence。"},"difficulty":{"band":"undergraduate_core","level":2,"skills":["依機率收斂"]},"variant":{"family_id":"qf-mod30-convprob-deviation-probability","seed":202610307014,"parameters":{"numerator":4,"shift":8,"n":14,"domain":"Symbolic_deviation_probability_tail","operation":"convprob-deviation-probability","semantic_template":"qf-mod30-convprob-deviation-probability/{\"n\":14,\"numerator\":4,\"shift\":8}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_model","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"候選須主端重算；不構成人工審定、一般域／Hilbert／martingale／無限基數／一般收斂、Lean或Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-14","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261014-advance-20261030-r07-convergence-in-probability-0015","batch_id":"batch-20261014-advance-20261030-r07-convergence-in-probability-foundations","language":"zh-Hant","source_mko_ids":["mko-convergence-in-probability"],"title_zh":"依機率收斂","stem_zh":"共同機率空間與forall epsilon tail責任。操作=convprob-deviation-probability；資料={\"numerator\":5,\"shift\":2,\"n\":15}。請依 [numerator,shift,n,probability] 欄序回答。","answer":{"kind":"expression","value":"(5, 2, 15, 5/17)","explanation_zh":"Wave4第四層核對=(5, 2, 15, 5/17)；依完整明示資料重算；完整有限／symbolic tail證書不自動升格為未聲明的一般定理；finite prefix不足且只接受symbolic tail或eventual equality；不混同almost sure Lp或distribution convergence。"},"difficulty":{"band":"undergraduate_core","level":2,"skills":["依機率收斂"]},"variant":{"family_id":"qf-mod30-convprob-deviation-probability","seed":202610307015,"parameters":{"numerator":5,"shift":2,"n":15,"domain":"Symbolic_deviation_probability_tail","operation":"convprob-deviation-probability","semantic_template":"qf-mod30-convprob-deviation-probability/{\"n\":15,\"numerator\":5,\"shift\":2}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_model","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"候選須主端重算；不構成人工審定、一般域／Hilbert／martingale／無限基數／一般收斂、Lean或Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-14","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261014-advance-20261030-r07-convergence-in-probability-0016","batch_id":"batch-20261014-advance-20261030-r07-convergence-in-probability-foundations","language":"zh-Hant","source_mko_ids":["mko-convergence-in-probability"],"title_zh":"依機率收斂","stem_zh":"共同機率空間與forall epsilon tail責任。操作=convprob-deviation-probability；資料={\"numerator\":1,\"shift\":3,\"n\":16}。請依 [numerator,shift,n,probability] 欄序回答。","answer":{"kind":"expression","value":"(1, 3, 16, 1/19)","explanation_zh":"Wave4第四層核對=(1, 3, 16, 1/19)；依完整明示資料重算；完整有限／symbolic tail證書不自動升格為未聲明的一般定理；finite prefix不足且只接受symbolic tail或eventual equality；不混同almost sure Lp或distribution convergence。"},"difficulty":{"band":"undergraduate_core","level":2,"skills":["依機率收斂"]},"variant":{"family_id":"qf-mod30-convprob-deviation-probability","seed":202610307016,"parameters":{"numerator":1,"shift":3,"n":16,"domain":"Symbolic_deviation_probability_tail","operation":"convprob-deviation-probability","semantic_template":"qf-mod30-convprob-deviation-probability/{\"n\":16,\"numerator\":1,\"shift\":3}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_model","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"候選須主端重算；不構成人工審定、一般域／Hilbert／martingale／無限基數／一般收斂、Lean或Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-14","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261014-advance-20261030-r07-convergence-in-probability-0017","batch_id":"batch-20261014-advance-20261030-r07-convergence-in-probability-foundations","language":"zh-Hant","source_mko_ids":["mko-convergence-in-probability"],"title_zh":"依機率收斂","stem_zh":"共同機率空間與forall epsilon tail責任。操作=convprob-deviation-probability；資料={\"numerator\":2,\"shift\":4,\"n\":17}。請依 [numerator,shift,n,probability] 欄序回答。","answer":{"kind":"expression","value":"(2, 4, 17, 2/21)","explanation_zh":"Wave4第四層核對=(2, 4, 17, 2/21)；依完整明示資料重算；完整有限／symbolic tail證書不自動升格為未聲明的一般定理；finite prefix不足且只接受symbolic tail或eventual equality；不混同almost sure Lp或distribution convergence。"},"difficulty":{"band":"undergraduate_core","level":2,"skills":["依機率收斂"]},"variant":{"family_id":"qf-mod30-convprob-deviation-probability","seed":202610307017,"parameters":{"numerator":2,"shift":4,"n":17,"domain":"Symbolic_deviation_probability_tail","operation":"convprob-deviation-probability","semantic_template":"qf-mod30-convprob-deviation-probability/{\"n\":17,\"numerator\":2,\"shift\":4}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_model","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"候選須主端重算；不構成人工審定、一般域／Hilbert／martingale／無限基數／一般收斂、Lean或Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-14","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261014-advance-20261030-r07-convergence-in-probability-0018","batch_id":"batch-20261014-advance-20261030-r07-convergence-in-probability-foundations","language":"zh-Hant","source_mko_ids":["mko-convergence-in-probability"],"title_zh":"依機率收斂","stem_zh":"共同機率空間與forall epsilon tail責任。操作=convprob-deviation-probability；資料={\"numerator\":3,\"shift\":5,\"n\":18}。請依 [numerator,shift,n,probability] 欄序回答。","answer":{"kind":"expression","value":"(3, 5, 18, 3/23)","explanation_zh":"Wave4第四層核對=(3, 5, 18, 3/23)；依完整明示資料重算；完整有限／symbolic tail證書不自動升格為未聲明的一般定理；finite prefix不足且只接受symbolic tail或eventual equality；不混同almost sure Lp或distribution convergence。"},"difficulty":{"band":"undergraduate_core","level":3,"skills":["依機率收斂"]},"variant":{"family_id":"qf-mod30-convprob-deviation-probability","seed":202610307018,"parameters":{"numerator":3,"shift":5,"n":18,"domain":"Symbolic_deviation_probability_tail","operation":"convprob-deviation-probability","semantic_template":"qf-mod30-convprob-deviation-probability/{\"n\":18,\"numerator\":3,\"shift\":5}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_model","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"候選須主端重算；不構成人工審定、一般域／Hilbert／martingale／無限基數／一般收斂、Lean或Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-14","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261014-advance-20261030-r07-convergence-in-probability-0019","batch_id":"batch-20261014-advance-20261030-r07-convergence-in-probability-foundations","language":"zh-Hant","source_mko_ids":["mko-convergence-in-probability"],"title_zh":"依機率收斂","stem_zh":"共同機率空間與forall epsilon tail責任。操作=convprob-deviation-probability；資料={\"numerator\":4,\"shift\":6,\"n\":19}。請依 [numerator,shift,n,probability] 欄序回答。","answer":{"kind":"expression","value":"(4, 6, 19, 4/25)","explanation_zh":"Wave4第四層核對=(4, 6, 19, 4/25)；依完整明示資料重算；完整有限／symbolic tail證書不自動升格為未聲明的一般定理；finite prefix不足且只接受symbolic tail或eventual equality；不混同almost sure Lp或distribution convergence。"},"difficulty":{"band":"undergraduate_core","level":3,"skills":["依機率收斂"]},"variant":{"family_id":"qf-mod30-convprob-deviation-probability","seed":202610307019,"parameters":{"numerator":4,"shift":6,"n":19,"domain":"Symbolic_deviation_probability_tail","operation":"convprob-deviation-probability","semantic_template":"qf-mod30-convprob-deviation-probability/{\"n\":19,\"numerator\":4,\"shift\":6}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_model","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"候選須主端重算；不構成人工審定、一般域／Hilbert／martingale／無限基數／一般收斂、Lean或Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-14","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261014-advance-20261030-r07-convergence-in-probability-0020","batch_id":"batch-20261014-advance-20261030-r07-convergence-in-probability-foundations","language":"zh-Hant","source_mko_ids":["mko-convergence-in-probability"],"title_zh":"依機率收斂","stem_zh":"共同機率空間與forall epsilon tail責任。操作=convprob-deviation-probability；資料={\"numerator\":5,\"shift\":7,\"n\":20}。請依 [numerator,shift,n,probability] 欄序回答。","answer":{"kind":"expression","value":"(5, 7, 20, 5/27)","explanation_zh":"Wave4第四層核對=(5, 7, 20, 5/27)；依完整明示資料重算；完整有限／symbolic tail證書不自動升格為未聲明的一般定理；finite prefix不足且只接受symbolic tail或eventual equality；不混同almost sure Lp或distribution convergence。"},"difficulty":{"band":"undergraduate_core","level":3,"skills":["依機率收斂"]},"variant":{"family_id":"qf-mod30-convprob-deviation-probability","seed":202610307020,"parameters":{"numerator":5,"shift":7,"n":20,"domain":"Symbolic_deviation_probability_tail","operation":"convprob-deviation-probability","semantic_template":"qf-mod30-convprob-deviation-probability/{\"n\":20,\"numerator\":5,\"shift\":7}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_model","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"候選須主端重算；不構成人工審定、一般域／Hilbert／martingale／無限基數／一般收斂、Lean或Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-14","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261014-advance-20261030-r07-convergence-in-probability-0021","batch_id":"batch-20261014-advance-20261030-r07-convergence-in-probability-foundations","language":"zh-Hant","source_mko_ids":["mko-convergence-in-probability"],"title_zh":"依機率收斂","stem_zh":"共同機率空間與forall epsilon tail責任。操作=convprob-deviation-probability；資料={\"numerator\":1,\"shift\":8,\"n\":21}。請依 [numerator,shift,n,probability] 欄序回答。","answer":{"kind":"expression","value":"(1, 8, 21, 1/29)","explanation_zh":"Wave4第四層核對=(1, 8, 21, 1/29)；依完整明示資料重算；完整有限／symbolic tail證書不自動升格為未聲明的一般定理；finite prefix不足且只接受symbolic tail或eventual equality；不混同almost sure Lp或distribution convergence。"},"difficulty":{"band":"undergraduate_core","level":3,"skills":["依機率收斂"]},"variant":{"family_id":"qf-mod30-convprob-deviation-probability","seed":202610307021,"parameters":{"numerator":1,"shift":8,"n":21,"domain":"Symbolic_deviation_probability_tail","operation":"convprob-deviation-probability","semantic_template":"qf-mod30-convprob-deviation-probability/{\"n\":21,\"numerator\":1,\"shift\":8}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_model","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"候選須主端重算；不構成人工審定、一般域／Hilbert／martingale／無限基數／一般收斂、Lean或Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-14","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261014-advance-20261030-r07-convergence-in-probability-0022","batch_id":"batch-20261014-advance-20261030-r07-convergence-in-probability-foundations","language":"zh-Hant","source_mko_ids":["mko-convergence-in-probability"],"title_zh":"依機率收斂","stem_zh":"共同機率空間與forall epsilon tail責任。操作=convprob-deviation-probability；資料={\"numerator\":2,\"shift\":2,\"n\":22}。請依 [numerator,shift,n,probability] 欄序回答。","answer":{"kind":"expression","value":"(2, 2, 22, 1/12)","explanation_zh":"Wave4第四層核對=(2, 2, 22, 1/12)；依完整明示資料重算；完整有限／symbolic tail證書不自動升格為未聲明的一般定理；finite prefix不足且只接受symbolic tail或eventual equality；不混同almost sure Lp或distribution convergence。"},"difficulty":{"band":"undergraduate_core","level":3,"skills":["依機率收斂"]},"variant":{"family_id":"qf-mod30-convprob-deviation-probability","seed":202610307022,"parameters":{"numerator":2,"shift":2,"n":22,"domain":"Symbolic_deviation_probability_tail","operation":"convprob-deviation-probability","semantic_template":"qf-mod30-convprob-deviation-probability/{\"n\":22,\"numerator\":2,\"shift\":2}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_model","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"候選須主端重算；不構成人工審定、一般域／Hilbert／martingale／無限基數／一般收斂、Lean或Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-14","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261014-advance-20261030-r07-convergence-in-probability-0023","batch_id":"batch-20261014-advance-20261030-r07-convergence-in-probability-foundations","language":"zh-Hant","source_mko_ids":["mko-convergence-in-probability"],"title_zh":"依機率收斂","stem_zh":"共同機率空間與forall epsilon tail責任。操作=convprob-deviation-probability；資料={\"numerator\":3,\"shift\":3,\"n\":23}。請依 [numerator,shift,n,probability] 欄序回答。","answer":{"kind":"expression","value":"(3, 3, 23, 3/26)","explanation_zh":"Wave4第四層核對=(3, 3, 23, 3/26)；依完整明示資料重算；完整有限／symbolic tail證書不自動升格為未聲明的一般定理；finite prefix不足且只接受symbolic tail或eventual equality；不混同almost sure Lp或distribution convergence。"},"difficulty":{"band":"undergraduate_core","level":3,"skills":["依機率收斂"]},"variant":{"family_id":"qf-mod30-convprob-deviation-probability","seed":202610307023,"parameters":{"numerator":3,"shift":3,"n":23,"domain":"Symbolic_deviation_probability_tail","operation":"convprob-deviation-probability","semantic_template":"qf-mod30-convprob-deviation-probability/{\"n\":23,\"numerator\":3,\"shift\":3}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_model","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"候選須主端重算；不構成人工審定、一般域／Hilbert／martingale／無限基數／一般收斂、Lean或Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-14","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261014-advance-20261030-r07-convergence-in-probability-0024","batch_id":"batch-20261014-advance-20261030-r07-convergence-in-probability-foundations","language":"zh-Hant","source_mko_ids":["mko-convergence-in-probability"],"title_zh":"依機率收斂","stem_zh":"共同機率空間與forall epsilon tail責任。操作=convprob-deviation-probability；資料={\"numerator\":4,\"shift\":4,\"n\":24}。請依 [numerator,shift,n,probability] 欄序回答。","answer":{"kind":"expression","value":"(4, 4, 24, 1/7)","explanation_zh":"Wave4第四層核對=(4, 4, 24, 1/7)；依完整明示資料重算；完整有限／symbolic tail證書不自動升格為未聲明的一般定理；finite prefix不足且只接受symbolic tail或eventual equality；不混同almost sure Lp或distribution convergence。"},"difficulty":{"band":"undergraduate_core","level":3,"skills":["依機率收斂"]},"variant":{"family_id":"qf-mod30-convprob-deviation-probability","seed":202610307024,"parameters":{"numerator":4,"shift":4,"n":24,"domain":"Symbolic_deviation_probability_tail","operation":"convprob-deviation-probability","semantic_template":"qf-mod30-convprob-deviation-probability/{\"n\":24,\"numerator\":4,\"shift\":4}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_model","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"候選須主端重算；不構成人工審定、一般域／Hilbert／martingale／無限基數／一般收斂、Lean或Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-14","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261014-advance-20261030-r07-convergence-in-probability-0025","batch_id":"batch-20261014-advance-20261030-r07-convergence-in-probability-foundations","language":"zh-Hant","source_mko_ids":["mko-convergence-in-probability"],"title_zh":"依機率收斂","stem_zh":"共同機率空間與forall epsilon tail責任。操作=convprob-deviation-probability；資料={\"numerator\":5,\"shift\":5,\"n\":25}。請依 [numerator,shift,n,probability] 欄序回答。","answer":{"kind":"expression","value":"(5, 5, 25, 1/6)","explanation_zh":"Wave4第四層核對=(5, 5, 25, 1/6)；依完整明示資料重算；完整有限／symbolic tail證書不自動升格為未聲明的一般定理；finite prefix不足且只接受symbolic tail或eventual equality；不混同almost sure Lp或distribution convergence。"},"difficulty":{"band":"undergraduate_core","level":3,"skills":["依機率收斂"]},"variant":{"family_id":"qf-mod30-convprob-deviation-probability","seed":202610307025,"parameters":{"numerator":5,"shift":5,"n":25,"domain":"Symbolic_deviation_probability_tail","operation":"convprob-deviation-probability","semantic_template":"qf-mod30-convprob-deviation-probability/{\"n\":25,\"numerator\":5,\"shift\":5}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_model","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"候選須主端重算；不構成人工審定、一般域／Hilbert／martingale／無限基數／一般收斂、Lean或Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-14","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261014-advance-20261030-r07-convergence-in-probability-0026","batch_id":"batch-20261014-advance-20261030-r07-convergence-in-probability-foundations","language":"zh-Hant","source_mko_ids":["mko-convergence-in-probability"],"title_zh":"依機率收斂","stem_zh":"共同機率空間與forall epsilon tail責任。操作=convprob-epsilon-witness；資料={\"numerator\":1,\"shift\":2,\"delta\":[1,10]}。請依 [numerator,shift,delta,N,bound,pass,certificate] 欄序回答。","answer":{"kind":"expression","value":"(1, 2, 1/10, 9, 1/11, 是, forall_n_ge_N_tail_bound)","explanation_zh":"Wave4第四層核對=(1, 2, 1/10, 9, 1/11, 是, forall_n_ge_N_tail_bound)；依完整明示資料重算；完整有限／symbolic tail證書不自動升格為未聲明的一般定理；finite prefix不足且只接受symbolic tail或eventual equality；不混同almost sure Lp或distribution convergence。"},"difficulty":{"band":"undergraduate_core","level":1,"skills":["依機率收斂"]},"variant":{"family_id":"qf-mod30-convprob-epsilon-witness","seed":202610307026,"parameters":{"numerator":1,"shift":2,"delta":[1,10],"domain":"Symbolic_deviation_probability_tail","operation":"convprob-epsilon-witness","semantic_template":"qf-mod30-convprob-epsilon-witness/{\"delta\":[1,10],\"numerator\":1,\"shift\":2}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_model","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"候選須主端重算；不構成人工審定、一般域／Hilbert／martingale／無限基數／一般收斂、Lean或Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-14","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261014-advance-20261030-r07-convergence-in-probability-0027","batch_id":"batch-20261014-advance-20261030-r07-convergence-in-probability-foundations","language":"zh-Hant","source_mko_ids":["mko-convergence-in-probability"],"title_zh":"依機率收斂","stem_zh":"共同機率空間與forall epsilon tail責任。操作=convprob-epsilon-witness；資料={\"numerator\":2,\"shift\":3,\"delta\":[1,11]}。請依 [numerator,shift,delta,N,bound,pass,certificate] 欄序回答。","answer":{"kind":"expression","value":"(2, 3, 1/11, 20, 2/23, 是, forall_n_ge_N_tail_bound)","explanation_zh":"Wave4第四層核對=(2, 3, 1/11, 20, 2/23, 是, forall_n_ge_N_tail_bound)；依完整明示資料重算；完整有限／symbolic tail證書不自動升格為未聲明的一般定理；finite prefix不足且只接受symbolic tail或eventual equality；不混同almost sure Lp或distribution convergence。"},"difficulty":{"band":"undergraduate_core","level":1,"skills":["依機率收斂"]},"variant":{"family_id":"qf-mod30-convprob-epsilon-witness","seed":202610307027,"parameters":{"numerator":2,"shift":3,"delta":[1,11],"domain":"Symbolic_deviation_probability_tail","operation":"convprob-epsilon-witness","semantic_template":"qf-mod30-convprob-epsilon-witness/{\"delta\":[1,11],\"numerator\":2,\"shift\":3}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_model","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"候選須主端重算；不構成人工審定、一般域／Hilbert／martingale／無限基數／一般收斂、Lean或Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-14","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261014-advance-20261030-r07-convergence-in-probability-0028","batch_id":"batch-20261014-advance-20261030-r07-convergence-in-probability-foundations","language":"zh-Hant","source_mko_ids":["mko-convergence-in-probability"],"title_zh":"依機率收斂","stem_zh":"共同機率空間與forall epsilon tail責任。操作=convprob-epsilon-witness；資料={\"numerator\":3,\"shift\":4,\"delta\":[1,12]}。請依 [numerator,shift,delta,N,bound,pass,certificate] 欄序回答。","answer":{"kind":"expression","value":"(3, 4, 1/12, 33, 3/37, 是, forall_n_ge_N_tail_bound)","explanation_zh":"Wave4第四層核對=(3, 4, 1/12, 33, 3/37, 是, forall_n_ge_N_tail_bound)；依完整明示資料重算；完整有限／symbolic tail證書不自動升格為未聲明的一般定理；finite prefix不足且只接受symbolic tail或eventual equality；不混同almost sure Lp或distribution convergence。"},"difficulty":{"band":"undergraduate_core","level":1,"skills":["依機率收斂"]},"variant":{"family_id":"qf-mod30-convprob-epsilon-witness","seed":202610307028,"parameters":{"numerator":3,"shift":4,"delta":[1,12],"domain":"Symbolic_deviation_probability_tail","operation":"convprob-epsilon-witness","semantic_template":"qf-mod30-convprob-epsilon-witness/{\"delta\":[1,12],\"numerator\":3,\"shift\":4}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_model","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"候選須主端重算；不構成人工審定、一般域／Hilbert／martingale／無限基數／一般收斂、Lean或Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-14","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261014-advance-20261030-r07-convergence-in-probability-0029","batch_id":"batch-20261014-advance-20261030-r07-convergence-in-probability-foundations","language":"zh-Hant","source_mko_ids":["mko-convergence-in-probability"],"title_zh":"依機率收斂","stem_zh":"共同機率空間與forall epsilon tail責任。操作=convprob-epsilon-witness；資料={\"numerator\":4,\"shift\":5,\"delta\":[1,13]}。請依 [numerator,shift,delta,N,bound,pass,certificate] 欄序回答。","answer":{"kind":"expression","value":"(4, 5, 1/13, 48, 4/53, 是, forall_n_ge_N_tail_bound)","explanation_zh":"Wave4第四層核對=(4, 5, 1/13, 48, 4/53, 是, forall_n_ge_N_tail_bound)；依完整明示資料重算；完整有限／symbolic tail證書不自動升格為未聲明的一般定理；finite prefix不足且只接受symbolic tail或eventual equality；不混同almost sure Lp或distribution convergence。"},"difficulty":{"band":"undergraduate_core","level":1,"skills":["依機率收斂"]},"variant":{"family_id":"qf-mod30-convprob-epsilon-witness","seed":202610307029,"parameters":{"numerator":4,"shift":5,"delta":[1,13],"domain":"Symbolic_deviation_probability_tail","operation":"convprob-epsilon-witness","semantic_template":"qf-mod30-convprob-epsilon-witness/{\"delta\":[1,13],\"numerator\":4,\"shift\":5}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_model","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"候選須主端重算；不構成人工審定、一般域／Hilbert／martingale／無限基數／一般收斂、Lean或Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-14","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261014-advance-20261030-r07-convergence-in-probability-0030","batch_id":"batch-20261014-advance-20261030-r07-convergence-in-probability-foundations","language":"zh-Hant","source_mko_ids":["mko-convergence-in-probability"],"title_zh":"依機率收斂","stem_zh":"共同機率空間與forall epsilon tail責任。操作=convprob-epsilon-witness；資料={\"numerator\":5,\"shift\":6,\"delta\":[1,14]}。請依 [numerator,shift,delta,N,bound,pass,certificate] 欄序回答。","answer":{"kind":"expression","value":"(5, 6, 1/14, 65, 5/71, 是, forall_n_ge_N_tail_bound)","explanation_zh":"Wave4第四層核對=(5, 6, 1/14, 65, 5/71, 是, forall_n_ge_N_tail_bound)；依完整明示資料重算；完整有限／symbolic tail證書不自動升格為未聲明的一般定理；finite prefix不足且只接受symbolic tail或eventual equality；不混同almost sure Lp或distribution convergence。"},"difficulty":{"band":"undergraduate_core","level":1,"skills":["依機率收斂"]},"variant":{"family_id":"qf-mod30-convprob-epsilon-witness","seed":202610307030,"parameters":{"numerator":5,"shift":6,"delta":[1,14],"domain":"Symbolic_deviation_probability_tail","operation":"convprob-epsilon-witness","semantic_template":"qf-mod30-convprob-epsilon-witness/{\"delta\":[1,14],\"numerator\":5,\"shift\":6}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_model","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"候選須主端重算；不構成人工審定、一般域／Hilbert／martingale／無限基數／一般收斂、Lean或Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-14","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261014-advance-20261030-r07-convergence-in-probability-0031","batch_id":"batch-20261014-advance-20261030-r07-convergence-in-probability-foundations","language":"zh-Hant","source_mko_ids":["mko-convergence-in-probability"],"title_zh":"依機率收斂","stem_zh":"共同機率空間與forall epsilon tail責任。操作=convprob-epsilon-witness；資料={\"numerator\":1,\"shift\":7,\"delta\":[1,15]}。請依 [numerator,shift,delta,N,bound,pass,certificate] 欄序回答。","answer":{"kind":"expression","value":"(1, 7, 1/15, 9, 1/16, 是, forall_n_ge_N_tail_bound)","explanation_zh":"Wave4第四層核對=(1, 7, 1/15, 9, 1/16, 是, forall_n_ge_N_tail_bound)；依完整明示資料重算；完整有限／symbolic tail證書不自動升格為未聲明的一般定理；finite prefix不足且只接受symbolic tail或eventual equality；不混同almost sure Lp或distribution convergence。"},"difficulty":{"band":"undergraduate_core","level":1,"skills":["依機率收斂"]},"variant":{"family_id":"qf-mod30-convprob-epsilon-witness","seed":202610307031,"parameters":{"numerator":1,"shift":7,"delta":[1,15],"domain":"Symbolic_deviation_probability_tail","operation":"convprob-epsilon-witness","semantic_template":"qf-mod30-convprob-epsilon-witness/{\"delta\":[1,15],\"numerator\":1,\"shift\":7}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_model","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"候選須主端重算；不構成人工審定、一般域／Hilbert／martingale／無限基數／一般收斂、Lean或Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-14","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261014-advance-20261030-r07-convergence-in-probability-0032","batch_id":"batch-20261014-advance-20261030-r07-convergence-in-probability-foundations","language":"zh-Hant","source_mko_ids":["mko-convergence-in-probability"],"title_zh":"依機率收斂","stem_zh":"共同機率空間與forall epsilon tail責任。操作=convprob-epsilon-witness；資料={\"numerator\":2,\"shift\":8,\"delta\":[1,16]}。請依 [numerator,shift,delta,N,bound,pass,certificate] 欄序回答。","answer":{"kind":"expression","value":"(2, 8, 1/16, 25, 2/33, 是, forall_n_ge_N_tail_bound)","explanation_zh":"Wave4第四層核對=(2, 8, 1/16, 25, 2/33, 是, forall_n_ge_N_tail_bound)；依完整明示資料重算；完整有限／symbolic tail證書不自動升格為未聲明的一般定理；finite prefix不足且只接受symbolic tail或eventual equality；不混同almost sure Lp或distribution convergence。"},"difficulty":{"band":"undergraduate_core","level":1,"skills":["依機率收斂"]},"variant":{"family_id":"qf-mod30-convprob-epsilon-witness","seed":202610307032,"parameters":{"numerator":2,"shift":8,"delta":[1,16],"domain":"Symbolic_deviation_probability_tail","operation":"convprob-epsilon-witness","semantic_template":"qf-mod30-convprob-epsilon-witness/{\"delta\":[1,16],\"numerator\":2,\"shift\":8}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_model","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"候選須主端重算；不構成人工審定、一般域／Hilbert／martingale／無限基數／一般收斂、Lean或Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-14","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261014-advance-20261030-r07-convergence-in-probability-0033","batch_id":"batch-20261014-advance-20261030-r07-convergence-in-probability-foundations","language":"zh-Hant","source_mko_ids":["mko-convergence-in-probability"],"title_zh":"依機率收斂","stem_zh":"共同機率空間與forall epsilon tail責任。操作=convprob-epsilon-witness；資料={\"numerator\":3,\"shift\":2,\"delta\":[1,17]}。請依 [numerator,shift,delta,N,bound,pass,certificate] 欄序回答。","answer":{"kind":"expression","value":"(3, 2, 1/17, 50, 3/52, 是, forall_n_ge_N_tail_bound)","explanation_zh":"Wave4第四層核對=(3, 2, 1/17, 50, 3/52, 是, forall_n_ge_N_tail_bound)；依完整明示資料重算；完整有限／symbolic tail證書不自動升格為未聲明的一般定理；finite prefix不足且只接受symbolic tail或eventual equality；不混同almost sure Lp或distribution convergence。"},"difficulty":{"band":"undergraduate_core","level":1,"skills":["依機率收斂"]},"variant":{"family_id":"qf-mod30-convprob-epsilon-witness","seed":202610307033,"parameters":{"numerator":3,"shift":2,"delta":[1,17],"domain":"Symbolic_deviation_probability_tail","operation":"convprob-epsilon-witness","semantic_template":"qf-mod30-convprob-epsilon-witness/{\"delta\":[1,17],\"numerator\":3,\"shift\":2}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_model","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"候選須主端重算；不構成人工審定、一般域／Hilbert／martingale／無限基數／一般收斂、Lean或Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-14","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261014-advance-20261030-r07-convergence-in-probability-0034","batch_id":"batch-20261014-advance-20261030-r07-convergence-in-probability-foundations","language":"zh-Hant","source_mko_ids":["mko-convergence-in-probability"],"title_zh":"依機率收斂","stem_zh":"共同機率空間與forall epsilon tail責任。操作=convprob-epsilon-witness；資料={\"numerator\":4,\"shift\":3,\"delta\":[1,18]}。請依 [numerator,shift,delta,N,bound,pass,certificate] 欄序回答。","answer":{"kind":"expression","value":"(4, 3, 1/18, 70, 4/73, 是, forall_n_ge_N_tail_bound)","explanation_zh":"Wave4第四層核對=(4, 3, 1/18, 70, 4/73, 是, forall_n_ge_N_tail_bound)；依完整明示資料重算；完整有限／symbolic tail證書不自動升格為未聲明的一般定理；finite prefix不足且只接受symbolic tail或eventual equality；不混同almost sure Lp或distribution convergence。"},"difficulty":{"band":"undergraduate_core","level":2,"skills":["依機率收斂"]},"variant":{"family_id":"qf-mod30-convprob-epsilon-witness","seed":202610307034,"parameters":{"numerator":4,"shift":3,"delta":[1,18],"domain":"Symbolic_deviation_probability_tail","operation":"convprob-epsilon-witness","semantic_template":"qf-mod30-convprob-epsilon-witness/{\"delta\":[1,18],\"numerator\":4,\"shift\":3}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_model","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"候選須主端重算；不構成人工審定、一般域／Hilbert／martingale／無限基數／一般收斂、Lean或Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-14","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261014-advance-20261030-r07-convergence-in-probability-0035","batch_id":"batch-20261014-advance-20261030-r07-convergence-in-probability-foundations","language":"zh-Hant","source_mko_ids":["mko-convergence-in-probability"],"title_zh":"依機率收斂","stem_zh":"共同機率空間與forall epsilon tail責任。操作=convprob-epsilon-witness；資料={\"numerator\":5,\"shift\":4,\"delta\":[1,19]}。請依 [numerator,shift,delta,N,bound,pass,certificate] 欄序回答。","answer":{"kind":"expression","value":"(5, 4, 1/19, 92, 5/96, 是, forall_n_ge_N_tail_bound)","explanation_zh":"Wave4第四層核對=(5, 4, 1/19, 92, 5/96, 是, forall_n_ge_N_tail_bound)；依完整明示資料重算；完整有限／symbolic tail證書不自動升格為未聲明的一般定理；finite prefix不足且只接受symbolic tail或eventual equality；不混同almost sure Lp或distribution convergence。"},"difficulty":{"band":"undergraduate_core","level":2,"skills":["依機率收斂"]},"variant":{"family_id":"qf-mod30-convprob-epsilon-witness","seed":202610307035,"parameters":{"numerator":5,"shift":4,"delta":[1,19],"domain":"Symbolic_deviation_probability_tail","operation":"convprob-epsilon-witness","semantic_template":"qf-mod30-convprob-epsilon-witness/{\"delta\":[1,19],\"numerator\":5,\"shift\":4}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_model","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"候選須主端重算；不構成人工審定、一般域／Hilbert／martingale／無限基數／一般收斂、Lean或Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-14","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261014-advance-20261030-r07-convergence-in-probability-0036","batch_id":"batch-20261014-advance-20261030-r07-convergence-in-probability-foundations","language":"zh-Hant","source_mko_ids":["mko-convergence-in-probability"],"title_zh":"依機率收斂","stem_zh":"共同機率空間與forall epsilon tail責任。操作=convprob-epsilon-witness；資料={\"numerator\":1,\"shift\":5,\"delta\":[1,20]}。請依 [numerator,shift,delta,N,bound,pass,certificate] 欄序回答。","answer":{"kind":"expression","value":"(1, 5, 1/20, 16, 1/21, 是, forall_n_ge_N_tail_bound)","explanation_zh":"Wave4第四層核對=(1, 5, 1/20, 16, 1/21, 是, forall_n_ge_N_tail_bound)；依完整明示資料重算；完整有限／symbolic tail證書不自動升格為未聲明的一般定理；finite prefix不足且只接受symbolic tail或eventual equality；不混同almost sure Lp或distribution convergence。"},"difficulty":{"band":"undergraduate_core","level":2,"skills":["依機率收斂"]},"variant":{"family_id":"qf-mod30-convprob-epsilon-witness","seed":202610307036,"parameters":{"numerator":1,"shift":5,"delta":[1,20],"domain":"Symbolic_deviation_probability_tail","operation":"convprob-epsilon-witness","semantic_template":"qf-mod30-convprob-epsilon-witness/{\"delta\":[1,20],\"numerator\":1,\"shift\":5}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_model","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"候選須主端重算；不構成人工審定、一般域／Hilbert／martingale／無限基數／一般收斂、Lean或Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-14","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261014-advance-20261030-r07-convergence-in-probability-0037","batch_id":"batch-20261014-advance-20261030-r07-convergence-in-probability-foundations","language":"zh-Hant","source_mko_ids":["mko-convergence-in-probability"],"title_zh":"依機率收斂","stem_zh":"共同機率空間與forall epsilon tail責任。操作=convprob-epsilon-witness；資料={\"numerator\":2,\"shift\":6,\"delta\":[1,21]}。請依 [numerator,shift,delta,N,bound,pass,certificate] 欄序回答。","answer":{"kind":"expression","value":"(2, 6, 1/21, 37, 2/43, 是, forall_n_ge_N_tail_bound)","explanation_zh":"Wave4第四層核對=(2, 6, 1/21, 37, 2/43, 是, forall_n_ge_N_tail_bound)；依完整明示資料重算；完整有限／symbolic tail證書不自動升格為未聲明的一般定理；finite prefix不足且只接受symbolic tail或eventual equality；不混同almost sure Lp或distribution convergence。"},"difficulty":{"band":"undergraduate_core","level":2,"skills":["依機率收斂"]},"variant":{"family_id":"qf-mod30-convprob-epsilon-witness","seed":202610307037,"parameters":{"numerator":2,"shift":6,"delta":[1,21],"domain":"Symbolic_deviation_probability_tail","operation":"convprob-epsilon-witness","semantic_template":"qf-mod30-convprob-epsilon-witness/{\"delta\":[1,21],\"numerator\":2,\"shift\":6}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_model","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"候選須主端重算；不構成人工審定、一般域／Hilbert／martingale／無限基數／一般收斂、Lean或Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-14","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261014-advance-20261030-r07-convergence-in-probability-0038","batch_id":"batch-20261014-advance-20261030-r07-convergence-in-probability-foundations","language":"zh-Hant","source_mko_ids":["mko-convergence-in-probability"],"title_zh":"依機率收斂","stem_zh":"共同機率空間與forall epsilon tail責任。操作=convprob-epsilon-witness；資料={\"numerator\":3,\"shift\":7,\"delta\":[1,22]}。請依 [numerator,shift,delta,N,bound,pass,certificate] 欄序回答。","answer":{"kind":"expression","value":"(3, 7, 1/22, 60, 3/67, 是, forall_n_ge_N_tail_bound)","explanation_zh":"Wave4第四層核對=(3, 7, 1/22, 60, 3/67, 是, forall_n_ge_N_tail_bound)；依完整明示資料重算；完整有限／symbolic tail證書不自動升格為未聲明的一般定理；finite prefix不足且只接受symbolic tail或eventual equality；不混同almost sure Lp或distribution convergence。"},"difficulty":{"band":"undergraduate_core","level":2,"skills":["依機率收斂"]},"variant":{"family_id":"qf-mod30-convprob-epsilon-witness","seed":202610307038,"parameters":{"numerator":3,"shift":7,"delta":[1,22],"domain":"Symbolic_deviation_probability_tail","operation":"convprob-epsilon-witness","semantic_template":"qf-mod30-convprob-epsilon-witness/{\"delta\":[1,22],\"numerator\":3,\"shift\":7}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_model","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"候選須主端重算；不構成人工審定、一般域／Hilbert／martingale／無限基數／一般收斂、Lean或Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-14","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261014-advance-20261030-r07-convergence-in-probability-0039","batch_id":"batch-20261014-advance-20261030-r07-convergence-in-probability-foundations","language":"zh-Hant","source_mko_ids":["mko-convergence-in-probability"],"title_zh":"依機率收斂","stem_zh":"共同機率空間與forall epsilon tail責任。操作=convprob-epsilon-witness；資料={\"numerator\":4,\"shift\":8,\"delta\":[1,23]}。請依 [numerator,shift,delta,N,bound,pass,certificate] 欄序回答。","answer":{"kind":"expression","value":"(4, 8, 1/23, 85, 4/93, 是, forall_n_ge_N_tail_bound)","explanation_zh":"Wave4第四層核對=(4, 8, 1/23, 85, 4/93, 是, forall_n_ge_N_tail_bound)；依完整明示資料重算；完整有限／symbolic tail證書不自動升格為未聲明的一般定理；finite prefix不足且只接受symbolic tail或eventual equality；不混同almost sure Lp或distribution convergence。"},"difficulty":{"band":"undergraduate_core","level":2,"skills":["依機率收斂"]},"variant":{"family_id":"qf-mod30-convprob-epsilon-witness","seed":202610307039,"parameters":{"numerator":4,"shift":8,"delta":[1,23],"domain":"Symbolic_deviation_probability_tail","operation":"convprob-epsilon-witness","semantic_template":"qf-mod30-convprob-epsilon-witness/{\"delta\":[1,23],\"numerator\":4,\"shift\":8}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_model","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"候選須主端重算；不構成人工審定、一般域／Hilbert／martingale／無限基數／一般收斂、Lean或Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-14","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261014-advance-20261030-r07-convergence-in-probability-0040","batch_id":"batch-20261014-advance-20261030-r07-convergence-in-probability-foundations","language":"zh-Hant","source_mko_ids":["mko-convergence-in-probability"],"title_zh":"依機率收斂","stem_zh":"共同機率空間與forall epsilon tail責任。操作=convprob-epsilon-witness；資料={\"numerator\":5,\"shift\":2,\"delta\":[1,24]}。請依 [numerator,shift,delta,N,bound,pass,certificate] 欄序回答。","answer":{"kind":"expression","value":"(5, 2, 1/24, 119, 5/121, 是, forall_n_ge_N_tail_bound)","explanation_zh":"Wave4第四層核對=(5, 2, 1/24, 119, 5/121, 是, forall_n_ge_N_tail_bound)；依完整明示資料重算；完整有限／symbolic tail證書不自動升格為未聲明的一般定理；finite prefix不足且只接受symbolic tail或eventual equality；不混同almost sure Lp或distribution convergence。"},"difficulty":{"band":"undergraduate_core","level":2,"skills":["依機率收斂"]},"variant":{"family_id":"qf-mod30-convprob-epsilon-witness","seed":202610307040,"parameters":{"numerator":5,"shift":2,"delta":[1,24],"domain":"Symbolic_deviation_probability_tail","operation":"convprob-epsilon-witness","semantic_template":"qf-mod30-convprob-epsilon-witness/{\"delta\":[1,24],\"numerator\":5,\"shift\":2}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_model","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"候選須主端重算；不構成人工審定、一般域／Hilbert／martingale／無限基數／一般收斂、Lean或Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-14","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261014-advance-20261030-r07-convergence-in-probability-0041","batch_id":"batch-20261014-advance-20261030-r07-convergence-in-probability-foundations","language":"zh-Hant","source_mko_ids":["mko-convergence-in-probability"],"title_zh":"依機率收斂","stem_zh":"共同機率空間與forall epsilon tail責任。操作=convprob-epsilon-witness；資料={\"numerator\":1,\"shift\":3,\"delta\":[1,25]}。請依 [numerator,shift,delta,N,bound,pass,certificate] 欄序回答。","answer":{"kind":"expression","value":"(1, 3, 1/25, 23, 1/26, 是, forall_n_ge_N_tail_bound)","explanation_zh":"Wave4第四層核對=(1, 3, 1/25, 23, 1/26, 是, forall_n_ge_N_tail_bound)；依完整明示資料重算；完整有限／symbolic tail證書不自動升格為未聲明的一般定理；finite prefix不足且只接受symbolic tail或eventual equality；不混同almost sure Lp或distribution convergence。"},"difficulty":{"band":"undergraduate_core","level":2,"skills":["依機率收斂"]},"variant":{"family_id":"qf-mod30-convprob-epsilon-witness","seed":202610307041,"parameters":{"numerator":1,"shift":3,"delta":[1,25],"domain":"Symbolic_deviation_probability_tail","operation":"convprob-epsilon-witness","semantic_template":"qf-mod30-convprob-epsilon-witness/{\"delta\":[1,25],\"numerator\":1,\"shift\":3}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_model","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"候選須主端重算；不構成人工審定、一般域／Hilbert／martingale／無限基數／一般收斂、Lean或Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-14","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261014-advance-20261030-r07-convergence-in-probability-0042","batch_id":"batch-20261014-advance-20261030-r07-convergence-in-probability-foundations","language":"zh-Hant","source_mko_ids":["mko-convergence-in-probability"],"title_zh":"依機率收斂","stem_zh":"共同機率空間與forall epsilon tail責任。操作=convprob-epsilon-witness；資料={\"numerator\":2,\"shift\":4,\"delta\":[1,26]}。請依 [numerator,shift,delta,N,bound,pass,certificate] 欄序回答。","answer":{"kind":"expression","value":"(2, 4, 1/26, 49, 2/53, 是, forall_n_ge_N_tail_bound)","explanation_zh":"Wave4第四層核對=(2, 4, 1/26, 49, 2/53, 是, forall_n_ge_N_tail_bound)；依完整明示資料重算；完整有限／symbolic tail證書不自動升格為未聲明的一般定理；finite prefix不足且只接受symbolic tail或eventual equality；不混同almost sure Lp或distribution convergence。"},"difficulty":{"band":"undergraduate_core","level":2,"skills":["依機率收斂"]},"variant":{"family_id":"qf-mod30-convprob-epsilon-witness","seed":202610307042,"parameters":{"numerator":2,"shift":4,"delta":[1,26],"domain":"Symbolic_deviation_probability_tail","operation":"convprob-epsilon-witness","semantic_template":"qf-mod30-convprob-epsilon-witness/{\"delta\":[1,26],\"numerator\":2,\"shift\":4}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_model","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"候選須主端重算；不構成人工審定、一般域／Hilbert／martingale／無限基數／一般收斂、Lean或Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-14","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261014-advance-20261030-r07-convergence-in-probability-0043","batch_id":"batch-20261014-advance-20261030-r07-convergence-in-probability-foundations","language":"zh-Hant","source_mko_ids":["mko-convergence-in-probability"],"title_zh":"依機率收斂","stem_zh":"共同機率空間與forall epsilon tail責任。操作=convprob-epsilon-witness；資料={\"numerator\":3,\"shift\":5,\"delta\":[1,27]}。請依 [numerator,shift,delta,N,bound,pass,certificate] 欄序回答。","answer":{"kind":"expression","value":"(3, 5, 1/27, 77, 3/82, 是, forall_n_ge_N_tail_bound)","explanation_zh":"Wave4第四層核對=(3, 5, 1/27, 77, 3/82, 是, forall_n_ge_N_tail_bound)；依完整明示資料重算；完整有限／symbolic tail證書不自動升格為未聲明的一般定理；finite prefix不足且只接受symbolic tail或eventual equality；不混同almost sure Lp或distribution convergence。"},"difficulty":{"band":"undergraduate_core","level":3,"skills":["依機率收斂"]},"variant":{"family_id":"qf-mod30-convprob-epsilon-witness","seed":202610307043,"parameters":{"numerator":3,"shift":5,"delta":[1,27],"domain":"Symbolic_deviation_probability_tail","operation":"convprob-epsilon-witness","semantic_template":"qf-mod30-convprob-epsilon-witness/{\"delta\":[1,27],\"numerator\":3,\"shift\":5}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_model","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"候選須主端重算；不構成人工審定、一般域／Hilbert／martingale／無限基數／一般收斂、Lean或Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-14","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261014-advance-20261030-r07-convergence-in-probability-0044","batch_id":"batch-20261014-advance-20261030-r07-convergence-in-probability-foundations","language":"zh-Hant","source_mko_ids":["mko-convergence-in-probability"],"title_zh":"依機率收斂","stem_zh":"共同機率空間與forall epsilon tail責任。操作=convprob-epsilon-witness；資料={\"numerator\":4,\"shift\":6,\"delta\":[1,28]}。請依 [numerator,shift,delta,N,bound,pass,certificate] 欄序回答。","answer":{"kind":"expression","value":"(4, 6, 1/28, 107, 4/113, 是, forall_n_ge_N_tail_bound)","explanation_zh":"Wave4第四層核對=(4, 6, 1/28, 107, 4/113, 是, forall_n_ge_N_tail_bound)；依完整明示資料重算；完整有限／symbolic tail證書不自動升格為未聲明的一般定理；finite prefix不足且只接受symbolic tail或eventual equality；不混同almost sure Lp或distribution convergence。"},"difficulty":{"band":"undergraduate_core","level":3,"skills":["依機率收斂"]},"variant":{"family_id":"qf-mod30-convprob-epsilon-witness","seed":202610307044,"parameters":{"numerator":4,"shift":6,"delta":[1,28],"domain":"Symbolic_deviation_probability_tail","operation":"convprob-epsilon-witness","semantic_template":"qf-mod30-convprob-epsilon-witness/{\"delta\":[1,28],\"numerator\":4,\"shift\":6}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_model","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"候選須主端重算；不構成人工審定、一般域／Hilbert／martingale／無限基數／一般收斂、Lean或Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-14","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261014-advance-20261030-r07-convergence-in-probability-0045","batch_id":"batch-20261014-advance-20261030-r07-convergence-in-probability-foundations","language":"zh-Hant","source_mko_ids":["mko-convergence-in-probability"],"title_zh":"依機率收斂","stem_zh":"共同機率空間與forall epsilon tail責任。操作=convprob-epsilon-witness；資料={\"numerator\":5,\"shift\":7,\"delta\":[1,29]}。請依 [numerator,shift,delta,N,bound,pass,certificate] 欄序回答。","answer":{"kind":"expression","value":"(5, 7, 1/29, 139, 5/146, 是, forall_n_ge_N_tail_bound)","explanation_zh":"Wave4第四層核對=(5, 7, 1/29, 139, 5/146, 是, forall_n_ge_N_tail_bound)；依完整明示資料重算；完整有限／symbolic tail證書不自動升格為未聲明的一般定理；finite prefix不足且只接受symbolic tail或eventual equality；不混同almost sure Lp或distribution convergence。"},"difficulty":{"band":"undergraduate_core","level":3,"skills":["依機率收斂"]},"variant":{"family_id":"qf-mod30-convprob-epsilon-witness","seed":202610307045,"parameters":{"numerator":5,"shift":7,"delta":[1,29],"domain":"Symbolic_deviation_probability_tail","operation":"convprob-epsilon-witness","semantic_template":"qf-mod30-convprob-epsilon-witness/{\"delta\":[1,29],\"numerator\":5,\"shift\":7}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_model","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"候選須主端重算；不構成人工審定、一般域／Hilbert／martingale／無限基數／一般收斂、Lean或Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-14","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261014-advance-20261030-r07-convergence-in-probability-0046","batch_id":"batch-20261014-advance-20261030-r07-convergence-in-probability-foundations","language":"zh-Hant","source_mko_ids":["mko-convergence-in-probability"],"title_zh":"依機率收斂","stem_zh":"共同機率空間與forall epsilon tail責任。操作=convprob-epsilon-witness；資料={\"numerator\":1,\"shift\":8,\"delta\":[1,30]}。請依 [numerator,shift,delta,N,bound,pass,certificate] 欄序回答。","answer":{"kind":"expression","value":"(1, 8, 1/30, 23, 1/31, 是, forall_n_ge_N_tail_bound)","explanation_zh":"Wave4第四層核對=(1, 8, 1/30, 23, 1/31, 是, forall_n_ge_N_tail_bound)；依完整明示資料重算；完整有限／symbolic tail證書不自動升格為未聲明的一般定理；finite prefix不足且只接受symbolic tail或eventual equality；不混同almost sure Lp或distribution convergence。"},"difficulty":{"band":"undergraduate_core","level":3,"skills":["依機率收斂"]},"variant":{"family_id":"qf-mod30-convprob-epsilon-witness","seed":202610307046,"parameters":{"numerator":1,"shift":8,"delta":[1,30],"domain":"Symbolic_deviation_probability_tail","operation":"convprob-epsilon-witness","semantic_template":"qf-mod30-convprob-epsilon-witness/{\"delta\":[1,30],\"numerator\":1,\"shift\":8}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_model","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"候選須主端重算；不構成人工審定、一般域／Hilbert／martingale／無限基數／一般收斂、Lean或Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-14","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261014-advance-20261030-r07-convergence-in-probability-0047","batch_id":"batch-20261014-advance-20261030-r07-convergence-in-probability-foundations","language":"zh-Hant","source_mko_ids":["mko-convergence-in-probability"],"title_zh":"依機率收斂","stem_zh":"共同機率空間與forall epsilon tail責任。操作=convprob-epsilon-witness；資料={\"numerator\":2,\"shift\":2,\"delta\":[1,31]}。請依 [numerator,shift,delta,N,bound,pass,certificate] 欄序回答。","answer":{"kind":"expression","value":"(2, 2, 1/31, 61, 2/63, 是, forall_n_ge_N_tail_bound)","explanation_zh":"Wave4第四層核對=(2, 2, 1/31, 61, 2/63, 是, forall_n_ge_N_tail_bound)；依完整明示資料重算；完整有限／symbolic tail證書不自動升格為未聲明的一般定理；finite prefix不足且只接受symbolic tail或eventual equality；不混同almost sure Lp或distribution convergence。"},"difficulty":{"band":"undergraduate_core","level":3,"skills":["依機率收斂"]},"variant":{"family_id":"qf-mod30-convprob-epsilon-witness","seed":202610307047,"parameters":{"numerator":2,"shift":2,"delta":[1,31],"domain":"Symbolic_deviation_probability_tail","operation":"convprob-epsilon-witness","semantic_template":"qf-mod30-convprob-epsilon-witness/{\"delta\":[1,31],\"numerator\":2,\"shift\":2}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_model","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"候選須主端重算；不構成人工審定、一般域／Hilbert／martingale／無限基數／一般收斂、Lean或Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-14","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261014-advance-20261030-r07-convergence-in-probability-0048","batch_id":"batch-20261014-advance-20261030-r07-convergence-in-probability-foundations","language":"zh-Hant","source_mko_ids":["mko-convergence-in-probability"],"title_zh":"依機率收斂","stem_zh":"共同機率空間與forall epsilon tail責任。操作=convprob-epsilon-witness；資料={\"numerator\":3,\"shift\":3,\"delta\":[1,32]}。請依 [numerator,shift,delta,N,bound,pass,certificate] 欄序回答。","answer":{"kind":"expression","value":"(3, 3, 1/32, 94, 3/97, 是, forall_n_ge_N_tail_bound)","explanation_zh":"Wave4第四層核對=(3, 3, 1/32, 94, 3/97, 是, forall_n_ge_N_tail_bound)；依完整明示資料重算；完整有限／symbolic tail證書不自動升格為未聲明的一般定理；finite prefix不足且只接受symbolic tail或eventual equality；不混同almost sure Lp或distribution convergence。"},"difficulty":{"band":"undergraduate_core","level":3,"skills":["依機率收斂"]},"variant":{"family_id":"qf-mod30-convprob-epsilon-witness","seed":202610307048,"parameters":{"numerator":3,"shift":3,"delta":[1,32],"domain":"Symbolic_deviation_probability_tail","operation":"convprob-epsilon-witness","semantic_template":"qf-mod30-convprob-epsilon-witness/{\"delta\":[1,32],\"numerator\":3,\"shift\":3}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_model","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"候選須主端重算；不構成人工審定、一般域／Hilbert／martingale／無限基數／一般收斂、Lean或Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-14","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261014-advance-20261030-r07-convergence-in-probability-0049","batch_id":"batch-20261014-advance-20261030-r07-convergence-in-probability-foundations","language":"zh-Hant","source_mko_ids":["mko-convergence-in-probability"],"title_zh":"依機率收斂","stem_zh":"共同機率空間與forall epsilon tail責任。操作=convprob-epsilon-witness；資料={\"numerator\":4,\"shift\":4,\"delta\":[1,33]}。請依 [numerator,shift,delta,N,bound,pass,certificate] 欄序回答。","answer":{"kind":"expression","value":"(4, 4, 1/33, 129, 4/133, 是, forall_n_ge_N_tail_bound)","explanation_zh":"Wave4第四層核對=(4, 4, 1/33, 129, 4/133, 是, forall_n_ge_N_tail_bound)；依完整明示資料重算；完整有限／symbolic tail證書不自動升格為未聲明的一般定理；finite prefix不足且只接受symbolic tail或eventual equality；不混同almost sure Lp或distribution convergence。"},"difficulty":{"band":"undergraduate_core","level":3,"skills":["依機率收斂"]},"variant":{"family_id":"qf-mod30-convprob-epsilon-witness","seed":202610307049,"parameters":{"numerator":4,"shift":4,"delta":[1,33],"domain":"Symbolic_deviation_probability_tail","operation":"convprob-epsilon-witness","semantic_template":"qf-mod30-convprob-epsilon-witness/{\"delta\":[1,33],\"numerator\":4,\"shift\":4}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_model","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"候選須主端重算；不構成人工審定、一般域／Hilbert／martingale／無限基數／一般收斂、Lean或Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-14","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261014-advance-20261030-r07-convergence-in-probability-0050","batch_id":"batch-20261014-advance-20261030-r07-convergence-in-probability-foundations","language":"zh-Hant","source_mko_ids":["mko-convergence-in-probability"],"title_zh":"依機率收斂","stem_zh":"共同機率空間與forall epsilon tail責任。操作=convprob-epsilon-witness；資料={\"numerator\":5,\"shift\":5,\"delta\":[1,34]}。請依 [numerator,shift,delta,N,bound,pass,certificate] 欄序回答。","answer":{"kind":"expression","value":"(5, 5, 1/34, 166, 5/171, 是, forall_n_ge_N_tail_bound)","explanation_zh":"Wave4第四層核對=(5, 5, 1/34, 166, 5/171, 是, forall_n_ge_N_tail_bound)；依完整明示資料重算；完整有限／symbolic tail證書不自動升格為未聲明的一般定理；finite prefix不足且只接受symbolic tail或eventual equality；不混同almost sure Lp或distribution convergence。"},"difficulty":{"band":"undergraduate_core","level":3,"skills":["依機率收斂"]},"variant":{"family_id":"qf-mod30-convprob-epsilon-witness","seed":202610307050,"parameters":{"numerator":5,"shift":5,"delta":[1,34],"domain":"Symbolic_deviation_probability_tail","operation":"convprob-epsilon-witness","semantic_template":"qf-mod30-convprob-epsilon-witness/{\"delta\":[1,34],\"numerator\":5,\"shift\":5}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_model","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"候選須主端重算；不構成人工審定、一般域／Hilbert／martingale／無限基數／一般收斂、Lean或Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-14","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261014-advance-20261030-r07-convergence-in-probability-0051","batch_id":"batch-20261014-advance-20261030-r07-convergence-in-probability-foundations","language":"zh-Hant","source_mko_ids":["mko-convergence-in-probability"],"title_zh":"依機率收斂","stem_zh":"共同機率空間與forall epsilon tail責任。操作=convprob-finite-prefix-boundary；資料={\"numerator\":1,\"shift\":2,\"prefix_length\":1}。請依 [numerator,shift,prefix_length,values,convergence_proved,boundary] 欄序回答。","answer":{"kind":"expression","value":"(1, 2, 1, [1/2], 否, finite_prefix_not_convergence_certificate)","explanation_zh":"Wave4第四層核對=(1, 2, 1, [1/2], 否, finite_prefix_not_convergence_certificate)；依完整明示資料重算；完整有限／symbolic tail證書不自動升格為未聲明的一般定理；finite prefix不足且只接受symbolic tail或eventual equality；不混同almost sure Lp或distribution convergence。"},"difficulty":{"band":"undergraduate_core","level":1,"skills":["依機率收斂"]},"variant":{"family_id":"qf-mod30-convprob-finite-prefix-boundary","seed":202610307051,"parameters":{"numerator":1,"shift":2,"prefix_length":1,"domain":"Symbolic_deviation_probability_tail","operation":"convprob-finite-prefix-boundary","semantic_template":"qf-mod30-convprob-finite-prefix-boundary/{\"numerator\":1,\"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":"候選須主端重算；不構成人工審定、一般域／Hilbert／martingale／無限基數／一般收斂、Lean或Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-14","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261014-advance-20261030-r07-convergence-in-probability-0052","batch_id":"batch-20261014-advance-20261030-r07-convergence-in-probability-foundations","language":"zh-Hant","source_mko_ids":["mko-convergence-in-probability"],"title_zh":"依機率收斂","stem_zh":"共同機率空間與forall epsilon tail責任。操作=convprob-finite-prefix-boundary；資料={\"numerator\":2,\"shift\":3,\"prefix_length\":2}。請依 [numerator,shift,prefix_length,values,convergence_proved,boundary] 欄序回答。","answer":{"kind":"expression","value":"(2, 3, 2, [2/3, 1/2], 否, finite_prefix_not_convergence_certificate)","explanation_zh":"Wave4第四層核對=(2, 3, 2, [2/3, 1/2], 否, finite_prefix_not_convergence_certificate)；依完整明示資料重算；完整有限／symbolic tail證書不自動升格為未聲明的一般定理；finite prefix不足且只接受symbolic tail或eventual equality；不混同almost sure Lp或distribution convergence。"},"difficulty":{"band":"undergraduate_core","level":1,"skills":["依機率收斂"]},"variant":{"family_id":"qf-mod30-convprob-finite-prefix-boundary","seed":202610307052,"parameters":{"numerator":2,"shift":3,"prefix_length":2,"domain":"Symbolic_deviation_probability_tail","operation":"convprob-finite-prefix-boundary","semantic_template":"qf-mod30-convprob-finite-prefix-boundary/{\"numerator\":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":"候選須主端重算；不構成人工審定、一般域／Hilbert／martingale／無限基數／一般收斂、Lean或Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-14","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261014-advance-20261030-r07-convergence-in-probability-0053","batch_id":"batch-20261014-advance-20261030-r07-convergence-in-probability-foundations","language":"zh-Hant","source_mko_ids":["mko-convergence-in-probability"],"title_zh":"依機率收斂","stem_zh":"共同機率空間與forall epsilon tail責任。操作=convprob-finite-prefix-boundary；資料={\"numerator\":3,\"shift\":4,\"prefix_length\":3}。請依 [numerator,shift,prefix_length,values,convergence_proved,boundary] 欄序回答。","answer":{"kind":"expression","value":"(3, 4, 3, [3/4, 3/5, 1/2], 否, finite_prefix_not_convergence_certificate)","explanation_zh":"Wave4第四層核對=(3, 4, 3, [3/4, 3/5, 1/2], 否, finite_prefix_not_convergence_certificate)；依完整明示資料重算；完整有限／symbolic tail證書不自動升格為未聲明的一般定理；finite prefix不足且只接受symbolic tail或eventual equality；不混同almost sure Lp或distribution convergence。"},"difficulty":{"band":"undergraduate_core","level":1,"skills":["依機率收斂"]},"variant":{"family_id":"qf-mod30-convprob-finite-prefix-boundary","seed":202610307053,"parameters":{"numerator":3,"shift":4,"prefix_length":3,"domain":"Symbolic_deviation_probability_tail","operation":"convprob-finite-prefix-boundary","semantic_template":"qf-mod30-convprob-finite-prefix-boundary/{\"numerator\":3,\"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":"候選須主端重算；不構成人工審定、一般域／Hilbert／martingale／無限基數／一般收斂、Lean或Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-14","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261014-advance-20261030-r07-convergence-in-probability-0054","batch_id":"batch-20261014-advance-20261030-r07-convergence-in-probability-foundations","language":"zh-Hant","source_mko_ids":["mko-convergence-in-probability"],"title_zh":"依機率收斂","stem_zh":"共同機率空間與forall epsilon tail責任。操作=convprob-finite-prefix-boundary；資料={\"numerator\":4,\"shift\":5,\"prefix_length\":4}。請依 [numerator,shift,prefix_length,values,convergence_proved,boundary] 欄序回答。","answer":{"kind":"expression","value":"(4, 5, 4, [4/5, 2/3, 4/7, 1/2], 否, finite_prefix_not_convergence_certificate)","explanation_zh":"Wave4第四層核對=(4, 5, 4, [4/5, 2/3, 4/7, 1/2], 否, finite_prefix_not_convergence_certificate)；依完整明示資料重算；完整有限／symbolic tail證書不自動升格為未聲明的一般定理；finite prefix不足且只接受symbolic tail或eventual equality；不混同almost sure Lp或distribution convergence。"},"difficulty":{"band":"undergraduate_core","level":1,"skills":["依機率收斂"]},"variant":{"family_id":"qf-mod30-convprob-finite-prefix-boundary","seed":202610307054,"parameters":{"numerator":4,"shift":5,"prefix_length":4,"domain":"Symbolic_deviation_probability_tail","operation":"convprob-finite-prefix-boundary","semantic_template":"qf-mod30-convprob-finite-prefix-boundary/{\"numerator\":4,\"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":"候選須主端重算；不構成人工審定、一般域／Hilbert／martingale／無限基數／一般收斂、Lean或Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-14","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261014-advance-20261030-r07-convergence-in-probability-0055","batch_id":"batch-20261014-advance-20261030-r07-convergence-in-probability-foundations","language":"zh-Hant","source_mko_ids":["mko-convergence-in-probability"],"title_zh":"依機率收斂","stem_zh":"共同機率空間與forall epsilon tail責任。操作=convprob-finite-prefix-boundary；資料={\"numerator\":5,\"shift\":6,\"prefix_length\":5}。請依 [numerator,shift,prefix_length,values,convergence_proved,boundary] 欄序回答。","answer":{"kind":"expression","value":"(5, 6, 5, [5/6, 5/7, 5/8, 5/9, 1/2], 否, finite_prefix_not_convergence_certificate)","explanation_zh":"Wave4第四層核對=(5, 6, 5, [5/6, 5/7, 5/8, 5/9, 1/2], 否, finite_prefix_not_convergence_certificate)；依完整明示資料重算；完整有限／symbolic tail證書不自動升格為未聲明的一般定理；finite prefix不足且只接受symbolic tail或eventual equality；不混同almost sure Lp或distribution convergence。"},"difficulty":{"band":"undergraduate_core","level":1,"skills":["依機率收斂"]},"variant":{"family_id":"qf-mod30-convprob-finite-prefix-boundary","seed":202610307055,"parameters":{"numerator":5,"shift":6,"prefix_length":5,"domain":"Symbolic_deviation_probability_tail","operation":"convprob-finite-prefix-boundary","semantic_template":"qf-mod30-convprob-finite-prefix-boundary/{\"numerator\":5,\"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":"候選須主端重算；不構成人工審定、一般域／Hilbert／martingale／無限基數／一般收斂、Lean或Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-14","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261014-advance-20261030-r07-convergence-in-probability-0056","batch_id":"batch-20261014-advance-20261030-r07-convergence-in-probability-foundations","language":"zh-Hant","source_mko_ids":["mko-convergence-in-probability"],"title_zh":"依機率收斂","stem_zh":"共同機率空間與forall epsilon tail責任。操作=convprob-finite-prefix-boundary；資料={\"numerator\":1,\"shift\":7,\"prefix_length\":6}。請依 [numerator,shift,prefix_length,values,convergence_proved,boundary] 欄序回答。","answer":{"kind":"expression","value":"(1, 7, 6, [1/7, 1/8, 1/9, 1/10, 1/11, 1/12], 否, finite_prefix_not_convergence_certificate)","explanation_zh":"Wave4第四層核對=(1, 7, 6, [1/7, 1/8, 1/9, 1/10, 1/11, 1/12], 否, finite_prefix_not_convergence_certificate)；依完整明示資料重算；完整有限／symbolic tail證書不自動升格為未聲明的一般定理；finite prefix不足且只接受symbolic tail或eventual equality；不混同almost sure Lp或distribution convergence。"},"difficulty":{"band":"undergraduate_core","level":1,"skills":["依機率收斂"]},"variant":{"family_id":"qf-mod30-convprob-finite-prefix-boundary","seed":202610307056,"parameters":{"numerator":1,"shift":7,"prefix_length":6,"domain":"Symbolic_deviation_probability_tail","operation":"convprob-finite-prefix-boundary","semantic_template":"qf-mod30-convprob-finite-prefix-boundary/{\"numerator\":1,\"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":"候選須主端重算；不構成人工審定、一般域／Hilbert／martingale／無限基數／一般收斂、Lean或Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-14","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261014-advance-20261030-r07-convergence-in-probability-0057","batch_id":"batch-20261014-advance-20261030-r07-convergence-in-probability-foundations","language":"zh-Hant","source_mko_ids":["mko-convergence-in-probability"],"title_zh":"依機率收斂","stem_zh":"共同機率空間與forall epsilon tail責任。操作=convprob-finite-prefix-boundary；資料={\"numerator\":2,\"shift\":8,\"prefix_length\":7}。請依 [numerator,shift,prefix_length,values,convergence_proved,boundary] 欄序回答。","answer":{"kind":"expression","value":"(2, 8, 7, [1/4, 2/9, 1/5, 2/11, 1/6, 2/13, 1/7], 否, finite_prefix_not_convergence_certificate)","explanation_zh":"Wave4第四層核對=(2, 8, 7, [1/4, 2/9, 1/5, 2/11, 1/6, 2/13, 1/7], 否, finite_prefix_not_convergence_certificate)；依完整明示資料重算；完整有限／symbolic tail證書不自動升格為未聲明的一般定理；finite prefix不足且只接受symbolic tail或eventual equality；不混同almost sure Lp或distribution convergence。"},"difficulty":{"band":"undergraduate_core","level":1,"skills":["依機率收斂"]},"variant":{"family_id":"qf-mod30-convprob-finite-prefix-boundary","seed":202610307057,"parameters":{"numerator":2,"shift":8,"prefix_length":7,"domain":"Symbolic_deviation_probability_tail","operation":"convprob-finite-prefix-boundary","semantic_template":"qf-mod30-convprob-finite-prefix-boundary/{\"numerator\":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":"候選須主端重算；不構成人工審定、一般域／Hilbert／martingale／無限基數／一般收斂、Lean或Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-14","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261014-advance-20261030-r07-convergence-in-probability-0058","batch_id":"batch-20261014-advance-20261030-r07-convergence-in-probability-foundations","language":"zh-Hant","source_mko_ids":["mko-convergence-in-probability"],"title_zh":"依機率收斂","stem_zh":"共同機率空間與forall epsilon tail責任。操作=convprob-finite-prefix-boundary；資料={\"numerator\":3,\"shift\":3,\"prefix_length\":8}。請依 [numerator,shift,prefix_length,values,convergence_proved,boundary] 欄序回答。","answer":{"kind":"expression","value":"(3, 3, 8, [1, 3/4, 3/5, 1/2, 3/7, 3/8, 1/3, 3/10], 否, finite_prefix_not_convergence_certificate)","explanation_zh":"Wave4第四層核對=(3, 3, 8, [1, 3/4, 3/5, 1/2, 3/7, 3/8, 1/3, 3/10], 否, finite_prefix_not_convergence_certificate)；依完整明示資料重算；完整有限／symbolic tail證書不自動升格為未聲明的一般定理；finite prefix不足且只接受symbolic tail或eventual equality；不混同almost sure Lp或distribution convergence。"},"difficulty":{"band":"undergraduate_core","level":1,"skills":["依機率收斂"]},"variant":{"family_id":"qf-mod30-convprob-finite-prefix-boundary","seed":202610307058,"parameters":{"numerator":3,"shift":3,"prefix_length":8,"domain":"Symbolic_deviation_probability_tail","operation":"convprob-finite-prefix-boundary","semantic_template":"qf-mod30-convprob-finite-prefix-boundary/{\"numerator\":3,\"prefix_length\":8,\"shift\":3}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_model","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"候選須主端重算；不構成人工審定、一般域／Hilbert／martingale／無限基數／一般收斂、Lean或Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-14","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261014-advance-20261030-r07-convergence-in-probability-0059","batch_id":"batch-20261014-advance-20261030-r07-convergence-in-probability-foundations","language":"zh-Hant","source_mko_ids":["mko-convergence-in-probability"],"title_zh":"依機率收斂","stem_zh":"共同機率空間與forall epsilon tail責任。操作=convprob-finite-prefix-boundary；資料={\"numerator\":4,\"shift\":4,\"prefix_length\":9}。請依 [numerator,shift,prefix_length,values,convergence_proved,boundary] 欄序回答。","answer":{"kind":"expression","value":"(4, 4, 9, [1, 4/5, 2/3, 4/7, 1/2, 4/9, 2/5, 4/11, 1/3], 否, finite_prefix_not_convergence_certificate)","explanation_zh":"Wave4第四層核對=(4, 4, 9, [1, 4/5, 2/3, 4/7, 1/2, 4/9, 2/5, 4/11, 1/3], 否, finite_prefix_not_convergence_certificate)；依完整明示資料重算；完整有限／symbolic tail證書不自動升格為未聲明的一般定理；finite prefix不足且只接受symbolic tail或eventual equality；不混同almost sure Lp或distribution convergence。"},"difficulty":{"band":"undergraduate_core","level":2,"skills":["依機率收斂"]},"variant":{"family_id":"qf-mod30-convprob-finite-prefix-boundary","seed":202610307059,"parameters":{"numerator":4,"shift":4,"prefix_length":9,"domain":"Symbolic_deviation_probability_tail","operation":"convprob-finite-prefix-boundary","semantic_template":"qf-mod30-convprob-finite-prefix-boundary/{\"numerator\":4,\"prefix_length\":9,\"shift\":4}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_model","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"候選須主端重算；不構成人工審定、一般域／Hilbert／martingale／無限基數／一般收斂、Lean或Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-14","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261014-advance-20261030-r07-convergence-in-probability-0060","batch_id":"batch-20261014-advance-20261030-r07-convergence-in-probability-foundations","language":"zh-Hant","source_mko_ids":["mko-convergence-in-probability"],"title_zh":"依機率收斂","stem_zh":"共同機率空間與forall epsilon tail責任。操作=convprob-finite-prefix-boundary；資料={\"numerator\":5,\"shift\":5,\"prefix_length\":10}。請依 [numerator,shift,prefix_length,values,convergence_proved,boundary] 欄序回答。","answer":{"kind":"expression","value":"(5, 5, 10, [1, 5/6, 5/7, 5/8, 5/9, 1/2, 5/11, 5/12, 5/13, 5/14], 否, finite_prefix_not_convergence_certificate)","explanation_zh":"Wave4第四層核對=(5, 5, 10, [1, 5/6, 5/7, 5/8, 5/9, 1/2, 5/11, 5/12, 5/13, 5/14], 否, finite_prefix_not_convergence_certificate)；依完整明示資料重算；完整有限／symbolic tail證書不自動升格為未聲明的一般定理；finite prefix不足且只接受symbolic tail或eventual equality；不混同almost sure Lp或distribution convergence。"},"difficulty":{"band":"undergraduate_core","level":2,"skills":["依機率收斂"]},"variant":{"family_id":"qf-mod30-convprob-finite-prefix-boundary","seed":202610307060,"parameters":{"numerator":5,"shift":5,"prefix_length":10,"domain":"Symbolic_deviation_probability_tail","operation":"convprob-finite-prefix-boundary","semantic_template":"qf-mod30-convprob-finite-prefix-boundary/{\"numerator\":5,\"prefix_length\":10,\"shift\":5}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_model","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"候選須主端重算；不構成人工審定、一般域／Hilbert／martingale／無限基數／一般收斂、Lean或Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-14","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261014-advance-20261030-r07-convergence-in-probability-0061","batch_id":"batch-20261014-advance-20261030-r07-convergence-in-probability-foundations","language":"zh-Hant","source_mko_ids":["mko-convergence-in-probability"],"title_zh":"依機率收斂","stem_zh":"共同機率空間與forall epsilon tail責任。操作=convprob-finite-prefix-boundary；資料={\"numerator\":1,\"shift\":5,\"prefix_length\":11}。請依 [numerator,shift,prefix_length,values,convergence_proved,boundary] 欄序回答。","answer":{"kind":"expression","value":"(1, 5, 11, [1/5, 1/6, 1/7, 1/8, 1/9, 1/10, 1/11, 1/12, 1/13, 1/14, 1/15], 否, finite_prefix_not_convergence_certificate)","explanation_zh":"Wave4第四層核對=(1, 5, 11, [1/5, 1/6, 1/7, 1/8, 1/9, 1/10, 1/11, 1/12, 1/13, 1/14, 1/15], 否, finite_prefix_not_convergence_certificate)；依完整明示資料重算；完整有限／symbolic tail證書不自動升格為未聲明的一般定理；finite prefix不足且只接受symbolic tail或eventual equality；不混同almost sure Lp或distribution convergence。"},"difficulty":{"band":"undergraduate_core","level":2,"skills":["依機率收斂"]},"variant":{"family_id":"qf-mod30-convprob-finite-prefix-boundary","seed":202610307061,"parameters":{"numerator":1,"shift":5,"prefix_length":11,"domain":"Symbolic_deviation_probability_tail","operation":"convprob-finite-prefix-boundary","semantic_template":"qf-mod30-convprob-finite-prefix-boundary/{\"numerator\":1,\"prefix_length\":11,\"shift\":5}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_model","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"候選須主端重算；不構成人工審定、一般域／Hilbert／martingale／無限基數／一般收斂、Lean或Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-14","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261014-advance-20261030-r07-convergence-in-probability-0062","batch_id":"batch-20261014-advance-20261030-r07-convergence-in-probability-foundations","language":"zh-Hant","source_mko_ids":["mko-convergence-in-probability"],"title_zh":"依機率收斂","stem_zh":"共同機率空間與forall epsilon tail責任。操作=convprob-finite-prefix-boundary；資料={\"numerator\":2,\"shift\":6,\"prefix_length\":12}。請依 [numerator,shift,prefix_length,values,convergence_proved,boundary] 欄序回答。","answer":{"kind":"expression","value":"(2, 6, 12, [1/3, 2/7, 1/4, 2/9, 1/5, 2/11, 1/6, 2/13, 1/7, 2/15, 1/8, 2/17], 否, finite_prefix_not_convergence_certificate)","explanation_zh":"Wave4第四層核對=(2, 6, 12, [1/3, 2/7, 1/4, 2/9, 1/5, 2/11, 1/6, 2/13, 1/7, 2/15, 1/8, 2/17], 否, finite_prefix_not_convergence_certificate)；依完整明示資料重算；完整有限／symbolic tail證書不自動升格為未聲明的一般定理；finite prefix不足且只接受symbolic tail或eventual equality；不混同almost sure Lp或distribution convergence。"},"difficulty":{"band":"undergraduate_core","level":2,"skills":["依機率收斂"]},"variant":{"family_id":"qf-mod30-convprob-finite-prefix-boundary","seed":202610307062,"parameters":{"numerator":2,"shift":6,"prefix_length":12,"domain":"Symbolic_deviation_probability_tail","operation":"convprob-finite-prefix-boundary","semantic_template":"qf-mod30-convprob-finite-prefix-boundary/{\"numerator\":2,\"prefix_length\":12,\"shift\":6}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_model","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"候選須主端重算；不構成人工審定、一般域／Hilbert／martingale／無限基數／一般收斂、Lean或Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-14","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261014-advance-20261030-r07-convergence-in-probability-0063","batch_id":"batch-20261014-advance-20261030-r07-convergence-in-probability-foundations","language":"zh-Hant","source_mko_ids":["mko-convergence-in-probability"],"title_zh":"依機率收斂","stem_zh":"共同機率空間與forall epsilon tail責任。操作=convprob-finite-prefix-boundary；資料={\"numerator\":3,\"shift\":7,\"prefix_length\":13}。請依 [numerator,shift,prefix_length,values,convergence_proved,boundary] 欄序回答。","answer":{"kind":"expression","value":"(3, 7, 13, [3/7, 3/8, 1/3, 3/10, 3/11, 1/4, 3/13, 3/14, 1/5, 3/16, 3/17, 1/6, 3/19], 否, finite_prefix_not_convergence_certificate)","explanation_zh":"Wave4第四層核對=(3, 7, 13, [3/7, 3/8, 1/3, 3/10, 3/11, 1/4, 3/13, 3/14, 1/5, 3/16, 3/17, 1/6, 3/19], 否, finite_prefix_not_convergence_certificate)；依完整明示資料重算；完整有限／symbolic tail證書不自動升格為未聲明的一般定理；finite prefix不足且只接受symbolic tail或eventual equality；不混同almost sure Lp或distribution convergence。"},"difficulty":{"band":"undergraduate_core","level":2,"skills":["依機率收斂"]},"variant":{"family_id":"qf-mod30-convprob-finite-prefix-boundary","seed":202610307063,"parameters":{"numerator":3,"shift":7,"prefix_length":13,"domain":"Symbolic_deviation_probability_tail","operation":"convprob-finite-prefix-boundary","semantic_template":"qf-mod30-convprob-finite-prefix-boundary/{\"numerator\":3,\"prefix_length\":13,\"shift\":7}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_model","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"候選須主端重算；不構成人工審定、一般域／Hilbert／martingale／無限基數／一般收斂、Lean或Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-14","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261014-advance-20261030-r07-convergence-in-probability-0064","batch_id":"batch-20261014-advance-20261030-r07-convergence-in-probability-foundations","language":"zh-Hant","source_mko_ids":["mko-convergence-in-probability"],"title_zh":"依機率收斂","stem_zh":"共同機率空間與forall epsilon tail責任。操作=convprob-finite-prefix-boundary；資料={\"numerator\":4,\"shift\":8,\"prefix_length\":14}。請依 [numerator,shift,prefix_length,values,convergence_proved,boundary] 欄序回答。","answer":{"kind":"expression","value":"(4, 8, 14, [1/2, 4/9, 2/5, 4/11, 1/3, 4/13, 2/7, 4/15, 1/4, 4/17, 2/9, 4/19, 1/5, 4/21], 否, finite_prefix_not_convergence_certificate)","explanation_zh":"Wave4第四層核對=(4, 8, 14, [1/2, 4/9, 2/5, 4/11, 1/3, 4/13, 2/7, 4/15, 1/4, 4/17, 2/9, 4/19, 1/5, 4/21], 否, finite_prefix_not_convergence_certificate)；依完整明示資料重算；完整有限／symbolic tail證書不自動升格為未聲明的一般定理；finite prefix不足且只接受symbolic tail或eventual equality；不混同almost sure Lp或distribution convergence。"},"difficulty":{"band":"undergraduate_core","level":2,"skills":["依機率收斂"]},"variant":{"family_id":"qf-mod30-convprob-finite-prefix-boundary","seed":202610307064,"parameters":{"numerator":4,"shift":8,"prefix_length":14,"domain":"Symbolic_deviation_probability_tail","operation":"convprob-finite-prefix-boundary","semantic_template":"qf-mod30-convprob-finite-prefix-boundary/{\"numerator\":4,\"prefix_length\":14,\"shift\":8}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_model","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"候選須主端重算；不構成人工審定、一般域／Hilbert／martingale／無限基數／一般收斂、Lean或Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-14","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261014-advance-20261030-r07-convergence-in-probability-0065","batch_id":"batch-20261014-advance-20261030-r07-convergence-in-probability-foundations","language":"zh-Hant","source_mko_ids":["mko-convergence-in-probability"],"title_zh":"依機率收斂","stem_zh":"共同機率空間與forall epsilon tail責任。操作=convprob-finite-prefix-boundary；資料={\"numerator\":5,\"shift\":5,\"prefix_length\":15}。請依 [numerator,shift,prefix_length,values,convergence_proved,boundary] 欄序回答。","answer":{"kind":"expression","value":"(5, 5, 15, [1, 5/6, 5/7, 5/8, 5/9, 1/2, 5/11, 5/12, 5/13, 5/14, 1/3, 5/16, 5/17, 5/18, 5/19], 否, finite_prefix_not_convergence_certificate)","explanation_zh":"Wave4第四層核對=(5, 5, 15, [1, 5/6, 5/7, 5/8, 5/9, 1/2, 5/11, 5/12, 5/13, 5/14, 1/3, 5/16, 5/17, 5/18, 5/19], 否, finite_prefix_not_convergence_certificate)；依完整明示資料重算；完整有限／symbolic tail證書不自動升格為未聲明的一般定理；finite prefix不足且只接受symbolic tail或eventual equality；不混同almost sure Lp或distribution convergence。"},"difficulty":{"band":"undergraduate_core","level":2,"skills":["依機率收斂"]},"variant":{"family_id":"qf-mod30-convprob-finite-prefix-boundary","seed":202610307065,"parameters":{"numerator":5,"shift":5,"prefix_length":15,"domain":"Symbolic_deviation_probability_tail","operation":"convprob-finite-prefix-boundary","semantic_template":"qf-mod30-convprob-finite-prefix-boundary/{\"numerator\":5,\"prefix_length\":15,\"shift\":5}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_model","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"候選須主端重算；不構成人工審定、一般域／Hilbert／martingale／無限基數／一般收斂、Lean或Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-14","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261014-advance-20261030-r07-convergence-in-probability-0066","batch_id":"batch-20261014-advance-20261030-r07-convergence-in-probability-foundations","language":"zh-Hant","source_mko_ids":["mko-convergence-in-probability"],"title_zh":"依機率收斂","stem_zh":"共同機率空間與forall epsilon tail責任。操作=convprob-finite-prefix-boundary；資料={\"numerator\":1,\"shift\":3,\"prefix_length\":16}。請依 [numerator,shift,prefix_length,values,convergence_proved,boundary] 欄序回答。","answer":{"kind":"expression","value":"(1, 3, 16, [1/3, 1/4, 1/5, 1/6, 1/7, 1/8, 1/9, 1/10, 1/11, 1/12, 1/13, 1/14, 1/15, 1/16, 1/17, 1/18], 否, finite_prefix_not_convergence_certificate)","explanation_zh":"Wave4第四層核對=(1, 3, 16, [1/3, 1/4, 1/5, 1/6, 1/7, 1/8, 1/9, 1/10, 1/11, 1/12, 1/13, 1/14, 1/15, 1/16, 1/17, 1/18], 否, finite_prefix_not_convergence_certificate)；依完整明示資料重算；完整有限／symbolic tail證書不自動升格為未聲明的一般定理；finite prefix不足且只接受symbolic tail或eventual equality；不混同almost sure Lp或distribution convergence。"},"difficulty":{"band":"undergraduate_core","level":2,"skills":["依機率收斂"]},"variant":{"family_id":"qf-mod30-convprob-finite-prefix-boundary","seed":202610307066,"parameters":{"numerator":1,"shift":3,"prefix_length":16,"domain":"Symbolic_deviation_probability_tail","operation":"convprob-finite-prefix-boundary","semantic_template":"qf-mod30-convprob-finite-prefix-boundary/{\"numerator\":1,\"prefix_length\":16,\"shift\":3}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_model","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"候選須主端重算；不構成人工審定、一般域／Hilbert／martingale／無限基數／一般收斂、Lean或Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-14","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261014-advance-20261030-r07-convergence-in-probability-0067","batch_id":"batch-20261014-advance-20261030-r07-convergence-in-probability-foundations","language":"zh-Hant","source_mko_ids":["mko-convergence-in-probability"],"title_zh":"依機率收斂","stem_zh":"共同機率空間與forall epsilon tail責任。操作=convprob-finite-prefix-boundary；資料={\"numerator\":2,\"shift\":4,\"prefix_length\":17}。請依 [numerator,shift,prefix_length,values,convergence_proved,boundary] 欄序回答。","answer":{"kind":"expression","value":"(2, 4, 17, [1/2, 2/5, 1/3, 2/7, 1/4, 2/9, 1/5, 2/11, 1/6, 2/13, 1/7, 2/15, 1/8, 2/17, 1/9, 2/19, 1/10], 否, finite_prefix_not_convergence_certificate)","explanation_zh":"Wave4第四層核對=(2, 4, 17, [1/2, 2/5, 1/3, 2/7, 1/4, 2/9, 1/5, 2/11, 1/6, 2/13, 1/7, 2/15, 1/8, 2/17, 1/9, 2/19, 1/10], 否, finite_prefix_not_convergence_certificate)；依完整明示資料重算；完整有限／symbolic tail證書不自動升格為未聲明的一般定理；finite prefix不足且只接受symbolic tail或eventual equality；不混同almost sure Lp或distribution convergence。"},"difficulty":{"band":"undergraduate_core","level":2,"skills":["依機率收斂"]},"variant":{"family_id":"qf-mod30-convprob-finite-prefix-boundary","seed":202610307067,"parameters":{"numerator":2,"shift":4,"prefix_length":17,"domain":"Symbolic_deviation_probability_tail","operation":"convprob-finite-prefix-boundary","semantic_template":"qf-mod30-convprob-finite-prefix-boundary/{\"numerator\":2,\"prefix_length\":17,\"shift\":4}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_model","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"候選須主端重算；不構成人工審定、一般域／Hilbert／martingale／無限基數／一般收斂、Lean或Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-14","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261014-advance-20261030-r07-convergence-in-probability-0068","batch_id":"batch-20261014-advance-20261030-r07-convergence-in-probability-foundations","language":"zh-Hant","source_mko_ids":["mko-convergence-in-probability"],"title_zh":"依機率收斂","stem_zh":"共同機率空間與forall epsilon tail責任。操作=convprob-finite-prefix-boundary；資料={\"numerator\":3,\"shift\":5,\"prefix_length\":18}。請依 [numerator,shift,prefix_length,values,convergence_proved,boundary] 欄序回答。","answer":{"kind":"expression","value":"(3, 5, 18, [3/5, 1/2, 3/7, 3/8, 1/3, 3/10, 3/11, 1/4, 3/13, 3/14, 1/5, 3/16, 3/17, 1/6, 3/19, 3/20, 1/7, 3/22], 否, finite_prefix_not_convergence_certificate)","explanation_zh":"Wave4第四層核對=(3, 5, 18, [3/5, 1/2, 3/7, 3/8, 1/3, 3/10, 3/11, 1/4, 3/13, 3/14, 1/5, 3/16, 3/17, 1/6, 3/19, 3/20, 1/7, 3/22], 否, finite_prefix_not_convergence_certificate)；依完整明示資料重算；完整有限／symbolic tail證書不自動升格為未聲明的一般定理；finite prefix不足且只接受symbolic tail或eventual equality；不混同almost sure Lp或distribution convergence。"},"difficulty":{"band":"undergraduate_core","level":3,"skills":["依機率收斂"]},"variant":{"family_id":"qf-mod30-convprob-finite-prefix-boundary","seed":202610307068,"parameters":{"numerator":3,"shift":5,"prefix_length":18,"domain":"Symbolic_deviation_probability_tail","operation":"convprob-finite-prefix-boundary","semantic_template":"qf-mod30-convprob-finite-prefix-boundary/{\"numerator\":3,\"prefix_length\":18,\"shift\":5}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_model","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"候選須主端重算；不構成人工審定、一般域／Hilbert／martingale／無限基數／一般收斂、Lean或Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-14","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261014-advance-20261030-r07-convergence-in-probability-0069","batch_id":"batch-20261014-advance-20261030-r07-convergence-in-probability-foundations","language":"zh-Hant","source_mko_ids":["mko-convergence-in-probability"],"title_zh":"依機率收斂","stem_zh":"共同機率空間與forall epsilon tail責任。操作=convprob-finite-prefix-boundary；資料={\"numerator\":4,\"shift\":6,\"prefix_length\":19}。請依 [numerator,shift,prefix_length,values,convergence_proved,boundary] 欄序回答。","answer":{"kind":"expression","value":"(4, 6, 19, [2/3, 4/7, 1/2, 4/9, 2/5, 4/11, 1/3, 4/13, 2/7, 4/15, 1/4, 4/17, 2/9, 4/19, 1/5, 4/21, 2/11, 4/23, 1/6], 否, finite_prefix_not_convergence_certificate)","explanation_zh":"Wave4第四層核對=(4, 6, 19, [2/3, 4/7, 1/2, 4/9, 2/5, 4/11, 1/3, 4/13, 2/7, 4/15, 1/4, 4/17, 2/9, 4/19, 1/5, 4/21, 2/11, 4/23, 1/6], 否, finite_prefix_not_convergence_certificate)；依完整明示資料重算；完整有限／symbolic tail證書不自動升格為未聲明的一般定理；finite prefix不足且只接受symbolic tail或eventual equality；不混同almost sure Lp或distribution convergence。"},"difficulty":{"band":"undergraduate_core","level":3,"skills":["依機率收斂"]},"variant":{"family_id":"qf-mod30-convprob-finite-prefix-boundary","seed":202610307069,"parameters":{"numerator":4,"shift":6,"prefix_length":19,"domain":"Symbolic_deviation_probability_tail","operation":"convprob-finite-prefix-boundary","semantic_template":"qf-mod30-convprob-finite-prefix-boundary/{\"numerator\":4,\"prefix_length\":19,\"shift\":6}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_model","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"候選須主端重算；不構成人工審定、一般域／Hilbert／martingale／無限基數／一般收斂、Lean或Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-14","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261014-advance-20261030-r07-convergence-in-probability-0070","batch_id":"batch-20261014-advance-20261030-r07-convergence-in-probability-foundations","language":"zh-Hant","source_mko_ids":["mko-convergence-in-probability"],"title_zh":"依機率收斂","stem_zh":"共同機率空間與forall epsilon tail責任。操作=convprob-finite-prefix-boundary；資料={\"numerator\":5,\"shift\":7,\"prefix_length\":20}。請依 [numerator,shift,prefix_length,values,convergence_proved,boundary] 欄序回答。","answer":{"kind":"expression","value":"(5, 7, 20, [5/7, 5/8, 5/9, 1/2, 5/11, 5/12, 5/13, 5/14, 1/3, 5/16, 5/17, 5/18, 5/19, 1/4, 5/21, 5/22, 5/23, 5/24, 1/5, 5/26], 否, finite_prefix_not_convergence_certificate)","explanation_zh":"Wave4第四層核對=(5, 7, 20, [5/7, 5/8, 5/9, 1/2, 5/11, 5/12, 5/13, 5/14, 1/3, 5/16, 5/17, 5/18, 5/19, 1/4, 5/21, 5/22, 5/23, 5/24, 1/5, 5/26], 否, finite_prefix_not_convergence_certificate)；依完整明示資料重算；完整有限／symbolic tail證書不自動升格為未聲明的一般定理；finite prefix不足且只接受symbolic tail或eventual equality；不混同almost sure Lp或distribution convergence。"},"difficulty":{"band":"undergraduate_core","level":3,"skills":["依機率收斂"]},"variant":{"family_id":"qf-mod30-convprob-finite-prefix-boundary","seed":202610307070,"parameters":{"numerator":5,"shift":7,"prefix_length":20,"domain":"Symbolic_deviation_probability_tail","operation":"convprob-finite-prefix-boundary","semantic_template":"qf-mod30-convprob-finite-prefix-boundary/{\"numerator\":5,\"prefix_length\":20,\"shift\":7}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_model","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"候選須主端重算；不構成人工審定、一般域／Hilbert／martingale／無限基數／一般收斂、Lean或Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-14","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261014-advance-20261030-r07-convergence-in-probability-0071","batch_id":"batch-20261014-advance-20261030-r07-convergence-in-probability-foundations","language":"zh-Hant","source_mko_ids":["mko-convergence-in-probability"],"title_zh":"依機率收斂","stem_zh":"共同機率空間與forall epsilon tail責任。操作=convprob-finite-prefix-boundary；資料={\"numerator\":1,\"shift\":8,\"prefix_length\":21}。請依 [numerator,shift,prefix_length,values,convergence_proved,boundary] 欄序回答。","answer":{"kind":"expression","value":"(1, 8, 21, [1/8, 1/9, 1/10, 1/11, 1/12, 1/13, 1/14, 1/15, 1/16, 1/17, 1/18, 1/19, 1/20, 1/21, 1/22, 1/23, 1/24, 1/25, 1/26, 1/27, 1/28], 否, finite_prefix_not_convergence_certificate)","explanation_zh":"Wave4第四層核對=(1, 8, 21, [1/8, 1/9, 1/10, 1/11, 1/12, 1/13, 1/14, 1/15, 1/16, 1/17, 1/18, 1/19, 1/20, 1/21, 1/22, 1/23, 1/24, 1/25, 1/26, 1/27, 1/28], 否, finite_prefix_not_convergence_certificate)；依完整明示資料重算；完整有限／symbolic tail證書不自動升格為未聲明的一般定理；finite prefix不足且只接受symbolic tail或eventual equality；不混同almost sure Lp或distribution convergence。"},"difficulty":{"band":"undergraduate_core","level":3,"skills":["依機率收斂"]},"variant":{"family_id":"qf-mod30-convprob-finite-prefix-boundary","seed":202610307071,"parameters":{"numerator":1,"shift":8,"prefix_length":21,"domain":"Symbolic_deviation_probability_tail","operation":"convprob-finite-prefix-boundary","semantic_template":"qf-mod30-convprob-finite-prefix-boundary/{\"numerator\":1,\"prefix_length\":21,\"shift\":8}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_model","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"候選須主端重算；不構成人工審定、一般域／Hilbert／martingale／無限基數／一般收斂、Lean或Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-14","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261014-advance-20261030-r07-convergence-in-probability-0072","batch_id":"batch-20261014-advance-20261030-r07-convergence-in-probability-foundations","language":"zh-Hant","source_mko_ids":["mko-convergence-in-probability"],"title_zh":"依機率收斂","stem_zh":"共同機率空間與forall epsilon tail責任。操作=convprob-finite-prefix-boundary；資料={\"numerator\":2,\"shift\":2,\"prefix_length\":22}。請依 [numerator,shift,prefix_length,values,convergence_proved,boundary] 欄序回答。","answer":{"kind":"expression","value":"(2, 2, 22, [1, 2/3, 1/2, 2/5, 1/3, 2/7, 1/4, 2/9, 1/5, 2/11, 1/6, 2/13, 1/7, 2/15, 1/8, 2/17, 1/9, 2/19, 1/10, 2/21, 1/11, 2/23], 否, finite_prefix_not_convergence_certificate)","explanation_zh":"Wave4第四層核對=(2, 2, 22, [1, 2/3, 1/2, 2/5, 1/3, 2/7, 1/4, 2/9, 1/5, 2/11, 1/6, 2/13, 1/7, 2/15, 1/8, 2/17, 1/9, 2/19, 1/10, 2/21, 1/11, 2/23], 否, finite_prefix_not_convergence_certificate)；依完整明示資料重算；完整有限／symbolic tail證書不自動升格為未聲明的一般定理；finite prefix不足且只接受symbolic tail或eventual equality；不混同almost sure Lp或distribution convergence。"},"difficulty":{"band":"undergraduate_core","level":3,"skills":["依機率收斂"]},"variant":{"family_id":"qf-mod30-convprob-finite-prefix-boundary","seed":202610307072,"parameters":{"numerator":2,"shift":2,"prefix_length":22,"domain":"Symbolic_deviation_probability_tail","operation":"convprob-finite-prefix-boundary","semantic_template":"qf-mod30-convprob-finite-prefix-boundary/{\"numerator\":2,\"prefix_length\":22,\"shift\":2}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_model","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"候選須主端重算；不構成人工審定、一般域／Hilbert／martingale／無限基數／一般收斂、Lean或Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-14","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261014-advance-20261030-r07-convergence-in-probability-0073","batch_id":"batch-20261014-advance-20261030-r07-convergence-in-probability-foundations","language":"zh-Hant","source_mko_ids":["mko-convergence-in-probability"],"title_zh":"依機率收斂","stem_zh":"共同機率空間與forall epsilon tail責任。操作=convprob-finite-prefix-boundary；資料={\"numerator\":3,\"shift\":3,\"prefix_length\":23}。請依 [numerator,shift,prefix_length,values,convergence_proved,boundary] 欄序回答。","answer":{"kind":"expression","value":"(3, 3, 23, [1, 3/4, 3/5, 1/2, 3/7, 3/8, 1/3, 3/10, 3/11, 1/4, 3/13, 3/14, 1/5, 3/16, 3/17, 1/6, 3/19, 3/20, 1/7, 3/22, 3/23, 1/8, 3/25], 否, finite_prefix_not_convergence_certificate)","explanation_zh":"Wave4第四層核對=(3, 3, 23, [1, 3/4, 3/5, 1/2, 3/7, 3/8, 1/3, 3/10, 3/11, 1/4, 3/13, 3/14, 1/5, 3/16, 3/17, 1/6, 3/19, 3/20, 1/7, 3/22, 3/23, 1/8, 3/25], 否, finite_prefix_not_convergence_certificate)；依完整明示資料重算；完整有限／symbolic tail證書不自動升格為未聲明的一般定理；finite prefix不足且只接受symbolic tail或eventual equality；不混同almost sure Lp或distribution convergence。"},"difficulty":{"band":"undergraduate_core","level":3,"skills":["依機率收斂"]},"variant":{"family_id":"qf-mod30-convprob-finite-prefix-boundary","seed":202610307073,"parameters":{"numerator":3,"shift":3,"prefix_length":23,"domain":"Symbolic_deviation_probability_tail","operation":"convprob-finite-prefix-boundary","semantic_template":"qf-mod30-convprob-finite-prefix-boundary/{\"numerator\":3,\"prefix_length\":23,\"shift\":3}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_model","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"候選須主端重算；不構成人工審定、一般域／Hilbert／martingale／無限基數／一般收斂、Lean或Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-14","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261014-advance-20261030-r07-convergence-in-probability-0074","batch_id":"batch-20261014-advance-20261030-r07-convergence-in-probability-foundations","language":"zh-Hant","source_mko_ids":["mko-convergence-in-probability"],"title_zh":"依機率收斂","stem_zh":"共同機率空間與forall epsilon tail責任。操作=convprob-finite-prefix-boundary；資料={\"numerator\":4,\"shift\":4,\"prefix_length\":24}。請依 [numerator,shift,prefix_length,values,convergence_proved,boundary] 欄序回答。","answer":{"kind":"expression","value":"(4, 4, 24, [1, 4/5, 2/3, 4/7, 1/2, 4/9, 2/5, 4/11, 1/3, 4/13, 2/7, 4/15, 1/4, 4/17, 2/9, 4/19, 1/5, 4/21, 2/11, 4/23, 1/6, 4/25, 2/13, 4/27], 否, finite_prefix_not_convergence_certificate)","explanation_zh":"Wave4第四層核對=(4, 4, 24, [1, 4/5, 2/3, 4/7, 1/2, 4/9, 2/5, 4/11, 1/3, 4/13, 2/7, 4/15, 1/4, 4/17, 2/9, 4/19, 1/5, 4/21, 2/11, 4/23, 1/6, 4/25, 2/13, 4/27], 否, finite_prefix_not_convergence_certificate)；依完整明示資料重算；完整有限／symbolic tail證書不自動升格為未聲明的一般定理；finite prefix不足且只接受symbolic tail或eventual equality；不混同almost sure Lp或distribution convergence。"},"difficulty":{"band":"undergraduate_core","level":3,"skills":["依機率收斂"]},"variant":{"family_id":"qf-mod30-convprob-finite-prefix-boundary","seed":202610307074,"parameters":{"numerator":4,"shift":4,"prefix_length":24,"domain":"Symbolic_deviation_probability_tail","operation":"convprob-finite-prefix-boundary","semantic_template":"qf-mod30-convprob-finite-prefix-boundary/{\"numerator\":4,\"prefix_length\":24,\"shift\":4}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_model","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"候選須主端重算；不構成人工審定、一般域／Hilbert／martingale／無限基數／一般收斂、Lean或Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-14","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261014-advance-20261030-r07-convergence-in-probability-0075","batch_id":"batch-20261014-advance-20261030-r07-convergence-in-probability-foundations","language":"zh-Hant","source_mko_ids":["mko-convergence-in-probability"],"title_zh":"依機率收斂","stem_zh":"共同機率空間與forall epsilon tail責任。操作=convprob-finite-prefix-boundary；資料={\"numerator\":5,\"shift\":5,\"prefix_length\":25}。請依 [numerator,shift,prefix_length,values,convergence_proved,boundary] 欄序回答。","answer":{"kind":"expression","value":"(5, 5, 25, [1, 5/6, 5/7, 5/8, 5/9, 1/2, 5/11, 5/12, 5/13, 5/14, 1/3, 5/16, 5/17, 5/18, 5/19, 1/4, 5/21, 5/22, 5/23, 5/24, 1/5, 5/26, 5/27, 5/28, 5/29], 否, finite_prefix_not_convergence_certificate)","explanation_zh":"Wave4第四層核對=(5, 5, 25, [1, 5/6, 5/7, 5/8, 5/9, 1/2, 5/11, 5/12, 5/13, 5/14, 1/3, 5/16, 5/17, 5/18, 5/19, 1/4, 5/21, 5/22, 5/23, 5/24, 1/5, 5/26, 5/27, 5/28, 5/29], 否, finite_prefix_not_convergence_certificate)；依完整明示資料重算；完整有限／symbolic tail證書不自動升格為未聲明的一般定理；finite prefix不足且只接受symbolic tail或eventual equality；不混同almost sure Lp或distribution convergence。"},"difficulty":{"band":"undergraduate_core","level":3,"skills":["依機率收斂"]},"variant":{"family_id":"qf-mod30-convprob-finite-prefix-boundary","seed":202610307075,"parameters":{"numerator":5,"shift":5,"prefix_length":25,"domain":"Symbolic_deviation_probability_tail","operation":"convprob-finite-prefix-boundary","semantic_template":"qf-mod30-convprob-finite-prefix-boundary/{\"numerator\":5,\"prefix_length\":25,\"shift\":5}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_model","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"候選須主端重算；不構成人工審定、一般域／Hilbert／martingale／無限基數／一般收斂、Lean或Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-14","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261014-advance-20261030-r07-convergence-in-probability-0076","batch_id":"batch-20261014-advance-20261030-r07-convergence-in-probability-foundations","language":"zh-Hant","source_mko_ids":["mko-convergence-in-probability"],"title_zh":"依機率收斂","stem_zh":"共同機率空間與forall epsilon tail責任。操作=convprob-eventual-equality；資料={\"settling_index\":1,\"n\":0}。請依 [settling_index,n,deviation_probability,converges,certificate] 欄序回答。","answer":{"kind":"expression","value":"(1, 0, not_yet_zero, 是, eventual_equality_universal_tail_certificate)","explanation_zh":"Wave4第四層核對=(1, 0, not_yet_zero, 是, eventual_equality_universal_tail_certificate)；依完整明示資料重算；完整有限／symbolic tail證書不自動升格為未聲明的一般定理；finite prefix不足且只接受symbolic tail或eventual equality；不混同almost sure Lp或distribution convergence。"},"difficulty":{"band":"undergraduate_core","level":1,"skills":["依機率收斂"]},"variant":{"family_id":"qf-mod30-convprob-eventual-equality","seed":202610307076,"parameters":{"settling_index":1,"n":0,"domain":"Symbolic_deviation_probability_tail","operation":"convprob-eventual-equality","semantic_template":"qf-mod30-convprob-eventual-equality/{\"n\":0,\"settling_index\":1}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_model","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"候選須主端重算；不構成人工審定、一般域／Hilbert／martingale／無限基數／一般收斂、Lean或Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-14","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261014-advance-20261030-r07-convergence-in-probability-0077","batch_id":"batch-20261014-advance-20261030-r07-convergence-in-probability-foundations","language":"zh-Hant","source_mko_ids":["mko-convergence-in-probability"],"title_zh":"依機率收斂","stem_zh":"共同機率空間與forall epsilon tail責任。操作=convprob-eventual-equality；資料={\"settling_index\":2,\"n\":1}。請依 [settling_index,n,deviation_probability,converges,certificate] 欄序回答。","answer":{"kind":"expression","value":"(2, 1, not_yet_zero, 是, eventual_equality_universal_tail_certificate)","explanation_zh":"Wave4第四層核對=(2, 1, not_yet_zero, 是, eventual_equality_universal_tail_certificate)；依完整明示資料重算；完整有限／symbolic tail證書不自動升格為未聲明的一般定理；finite prefix不足且只接受symbolic tail或eventual equality；不混同almost sure Lp或distribution convergence。"},"difficulty":{"band":"undergraduate_core","level":1,"skills":["依機率收斂"]},"variant":{"family_id":"qf-mod30-convprob-eventual-equality","seed":202610307077,"parameters":{"settling_index":2,"n":1,"domain":"Symbolic_deviation_probability_tail","operation":"convprob-eventual-equality","semantic_template":"qf-mod30-convprob-eventual-equality/{\"n\":1,\"settling_index\":2}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_model","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"候選須主端重算；不構成人工審定、一般域／Hilbert／martingale／無限基數／一般收斂、Lean或Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-14","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261014-advance-20261030-r07-convergence-in-probability-0078","batch_id":"batch-20261014-advance-20261030-r07-convergence-in-probability-foundations","language":"zh-Hant","source_mko_ids":["mko-convergence-in-probability"],"title_zh":"依機率收斂","stem_zh":"共同機率空間與forall epsilon tail責任。操作=convprob-eventual-equality；資料={\"settling_index\":3,\"n\":2}。請依 [settling_index,n,deviation_probability,converges,certificate] 欄序回答。","answer":{"kind":"expression","value":"(3, 2, not_yet_zero, 是, eventual_equality_universal_tail_certificate)","explanation_zh":"Wave4第四層核對=(3, 2, not_yet_zero, 是, eventual_equality_universal_tail_certificate)；依完整明示資料重算；完整有限／symbolic tail證書不自動升格為未聲明的一般定理；finite prefix不足且只接受symbolic tail或eventual equality；不混同almost sure Lp或distribution convergence。"},"difficulty":{"band":"undergraduate_core","level":1,"skills":["依機率收斂"]},"variant":{"family_id":"qf-mod30-convprob-eventual-equality","seed":202610307078,"parameters":{"settling_index":3,"n":2,"domain":"Symbolic_deviation_probability_tail","operation":"convprob-eventual-equality","semantic_template":"qf-mod30-convprob-eventual-equality/{\"n\":2,\"settling_index\":3}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_model","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"候選須主端重算；不構成人工審定、一般域／Hilbert／martingale／無限基數／一般收斂、Lean或Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-14","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261014-advance-20261030-r07-convergence-in-probability-0079","batch_id":"batch-20261014-advance-20261030-r07-convergence-in-probability-foundations","language":"zh-Hant","source_mko_ids":["mko-convergence-in-probability"],"title_zh":"依機率收斂","stem_zh":"共同機率空間與forall epsilon tail責任。操作=convprob-eventual-equality；資料={\"settling_index\":4,\"n\":4}。請依 [settling_index,n,deviation_probability,converges,certificate] 欄序回答。","answer":{"kind":"expression","value":"(4, 4, 0, 是, eventual_equality_universal_tail_certificate)","explanation_zh":"Wave4第四層核對=(4, 4, 0, 是, eventual_equality_universal_tail_certificate)；依完整明示資料重算；完整有限／symbolic tail證書不自動升格為未聲明的一般定理；finite prefix不足且只接受symbolic tail或eventual equality；不混同almost sure Lp或distribution convergence。"},"difficulty":{"band":"undergraduate_core","level":1,"skills":["依機率收斂"]},"variant":{"family_id":"qf-mod30-convprob-eventual-equality","seed":202610307079,"parameters":{"settling_index":4,"n":4,"domain":"Symbolic_deviation_probability_tail","operation":"convprob-eventual-equality","semantic_template":"qf-mod30-convprob-eventual-equality/{\"n\":4,\"settling_index\":4}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_model","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"候選須主端重算；不構成人工審定、一般域／Hilbert／martingale／無限基數／一般收斂、Lean或Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-14","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261014-advance-20261030-r07-convergence-in-probability-0080","batch_id":"batch-20261014-advance-20261030-r07-convergence-in-probability-foundations","language":"zh-Hant","source_mko_ids":["mko-convergence-in-probability"],"title_zh":"依機率收斂","stem_zh":"共同機率空間與forall epsilon tail責任。操作=convprob-eventual-equality；資料={\"settling_index\":5,\"n\":5}。請依 [settling_index,n,deviation_probability,converges,certificate] 欄序回答。","answer":{"kind":"expression","value":"(5, 5, 0, 是, eventual_equality_universal_tail_certificate)","explanation_zh":"Wave4第四層核對=(5, 5, 0, 是, eventual_equality_universal_tail_certificate)；依完整明示資料重算；完整有限／symbolic tail證書不自動升格為未聲明的一般定理；finite prefix不足且只接受symbolic tail或eventual equality；不混同almost sure Lp或distribution convergence。"},"difficulty":{"band":"undergraduate_core","level":1,"skills":["依機率收斂"]},"variant":{"family_id":"qf-mod30-convprob-eventual-equality","seed":202610307080,"parameters":{"settling_index":5,"n":5,"domain":"Symbolic_deviation_probability_tail","operation":"convprob-eventual-equality","semantic_template":"qf-mod30-convprob-eventual-equality/{\"n\":5,\"settling_index\":5}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_model","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"候選須主端重算；不構成人工審定、一般域／Hilbert／martingale／無限基數／一般收斂、Lean或Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-14","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261014-advance-20261030-r07-convergence-in-probability-0081","batch_id":"batch-20261014-advance-20261030-r07-convergence-in-probability-foundations","language":"zh-Hant","source_mko_ids":["mko-convergence-in-probability"],"title_zh":"依機率收斂","stem_zh":"共同機率空間與forall epsilon tail責任。操作=convprob-eventual-equality；資料={\"settling_index\":6,\"n\":6}。請依 [settling_index,n,deviation_probability,converges,certificate] 欄序回答。","answer":{"kind":"expression","value":"(6, 6, 0, 是, eventual_equality_universal_tail_certificate)","explanation_zh":"Wave4第四層核對=(6, 6, 0, 是, eventual_equality_universal_tail_certificate)；依完整明示資料重算；完整有限／symbolic tail證書不自動升格為未聲明的一般定理；finite prefix不足且只接受symbolic tail或eventual equality；不混同almost sure Lp或distribution convergence。"},"difficulty":{"band":"undergraduate_core","level":1,"skills":["依機率收斂"]},"variant":{"family_id":"qf-mod30-convprob-eventual-equality","seed":202610307081,"parameters":{"settling_index":6,"n":6,"domain":"Symbolic_deviation_probability_tail","operation":"convprob-eventual-equality","semantic_template":"qf-mod30-convprob-eventual-equality/{\"n\":6,\"settling_index\":6}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_model","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"候選須主端重算；不構成人工審定、一般域／Hilbert／martingale／無限基數／一般收斂、Lean或Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-14","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261014-advance-20261030-r07-convergence-in-probability-0082","batch_id":"batch-20261014-advance-20261030-r07-convergence-in-probability-foundations","language":"zh-Hant","source_mko_ids":["mko-convergence-in-probability"],"title_zh":"依機率收斂","stem_zh":"共同機率空間與forall epsilon tail責任。操作=convprob-eventual-equality；資料={\"settling_index\":7,\"n\":8}。請依 [settling_index,n,deviation_probability,converges,certificate] 欄序回答。","answer":{"kind":"expression","value":"(7, 8, 0, 是, eventual_equality_universal_tail_certificate)","explanation_zh":"Wave4第四層核對=(7, 8, 0, 是, eventual_equality_universal_tail_certificate)；依完整明示資料重算；完整有限／symbolic tail證書不自動升格為未聲明的一般定理；finite prefix不足且只接受symbolic tail或eventual equality；不混同almost sure Lp或distribution convergence。"},"difficulty":{"band":"undergraduate_core","level":1,"skills":["依機率收斂"]},"variant":{"family_id":"qf-mod30-convprob-eventual-equality","seed":202610307082,"parameters":{"settling_index":7,"n":8,"domain":"Symbolic_deviation_probability_tail","operation":"convprob-eventual-equality","semantic_template":"qf-mod30-convprob-eventual-equality/{\"n\":8,\"settling_index\":7}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_model","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"候選須主端重算；不構成人工審定、一般域／Hilbert／martingale／無限基數／一般收斂、Lean或Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-14","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261014-advance-20261030-r07-convergence-in-probability-0083","batch_id":"batch-20261014-advance-20261030-r07-convergence-in-probability-foundations","language":"zh-Hant","source_mko_ids":["mko-convergence-in-probability"],"title_zh":"依機率收斂","stem_zh":"共同機率空間與forall epsilon tail責任。操作=convprob-eventual-equality；資料={\"settling_index\":8,\"n\":9}。請依 [settling_index,n,deviation_probability,converges,certificate] 欄序回答。","answer":{"kind":"expression","value":"(8, 9, 0, 是, eventual_equality_universal_tail_certificate)","explanation_zh":"Wave4第四層核對=(8, 9, 0, 是, eventual_equality_universal_tail_certificate)；依完整明示資料重算；完整有限／symbolic tail證書不自動升格為未聲明的一般定理；finite prefix不足且只接受symbolic tail或eventual equality；不混同almost sure Lp或distribution convergence。"},"difficulty":{"band":"undergraduate_core","level":1,"skills":["依機率收斂"]},"variant":{"family_id":"qf-mod30-convprob-eventual-equality","seed":202610307083,"parameters":{"settling_index":8,"n":9,"domain":"Symbolic_deviation_probability_tail","operation":"convprob-eventual-equality","semantic_template":"qf-mod30-convprob-eventual-equality/{\"n\":9,\"settling_index\":8}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_model","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"候選須主端重算；不構成人工審定、一般域／Hilbert／martingale／無限基數／一般收斂、Lean或Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-14","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261014-advance-20261030-r07-convergence-in-probability-0084","batch_id":"batch-20261014-advance-20261030-r07-convergence-in-probability-foundations","language":"zh-Hant","source_mko_ids":["mko-convergence-in-probability"],"title_zh":"依機率收斂","stem_zh":"共同機率空間與forall epsilon tail責任。操作=convprob-eventual-equality；資料={\"settling_index\":9,\"n\":10}。請依 [settling_index,n,deviation_probability,converges,certificate] 欄序回答。","answer":{"kind":"expression","value":"(9, 10, 0, 是, eventual_equality_universal_tail_certificate)","explanation_zh":"Wave4第四層核對=(9, 10, 0, 是, eventual_equality_universal_tail_certificate)；依完整明示資料重算；完整有限／symbolic tail證書不自動升格為未聲明的一般定理；finite prefix不足且只接受symbolic tail或eventual equality；不混同almost sure Lp或distribution convergence。"},"difficulty":{"band":"undergraduate_core","level":2,"skills":["依機率收斂"]},"variant":{"family_id":"qf-mod30-convprob-eventual-equality","seed":202610307084,"parameters":{"settling_index":9,"n":10,"domain":"Symbolic_deviation_probability_tail","operation":"convprob-eventual-equality","semantic_template":"qf-mod30-convprob-eventual-equality/{\"n\":10,\"settling_index\":9}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_model","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"候選須主端重算；不構成人工審定、一般域／Hilbert／martingale／無限基數／一般收斂、Lean或Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-14","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261014-advance-20261030-r07-convergence-in-probability-0085","batch_id":"batch-20261014-advance-20261030-r07-convergence-in-probability-foundations","language":"zh-Hant","source_mko_ids":["mko-convergence-in-probability"],"title_zh":"依機率收斂","stem_zh":"共同機率空間與forall epsilon tail責任。操作=convprob-eventual-equality；資料={\"settling_index\":10,\"n\":12}。請依 [settling_index,n,deviation_probability,converges,certificate] 欄序回答。","answer":{"kind":"expression","value":"(10, 12, 0, 是, eventual_equality_universal_tail_certificate)","explanation_zh":"Wave4第四層核對=(10, 12, 0, 是, eventual_equality_universal_tail_certificate)；依完整明示資料重算；完整有限／symbolic tail證書不自動升格為未聲明的一般定理；finite prefix不足且只接受symbolic tail或eventual equality；不混同almost sure Lp或distribution convergence。"},"difficulty":{"band":"undergraduate_core","level":2,"skills":["依機率收斂"]},"variant":{"family_id":"qf-mod30-convprob-eventual-equality","seed":202610307085,"parameters":{"settling_index":10,"n":12,"domain":"Symbolic_deviation_probability_tail","operation":"convprob-eventual-equality","semantic_template":"qf-mod30-convprob-eventual-equality/{\"n\":12,\"settling_index\":10}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_model","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"候選須主端重算；不構成人工審定、一般域／Hilbert／martingale／無限基數／一般收斂、Lean或Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-14","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261014-advance-20261030-r07-convergence-in-probability-0086","batch_id":"batch-20261014-advance-20261030-r07-convergence-in-probability-foundations","language":"zh-Hant","source_mko_ids":["mko-convergence-in-probability"],"title_zh":"依機率收斂","stem_zh":"共同機率空間與forall epsilon tail責任。操作=convprob-eventual-equality；資料={\"settling_index\":11,\"n\":13}。請依 [settling_index,n,deviation_probability,converges,certificate] 欄序回答。","answer":{"kind":"expression","value":"(11, 13, 0, 是, eventual_equality_universal_tail_certificate)","explanation_zh":"Wave4第四層核對=(11, 13, 0, 是, eventual_equality_universal_tail_certificate)；依完整明示資料重算；完整有限／symbolic tail證書不自動升格為未聲明的一般定理；finite prefix不足且只接受symbolic tail或eventual equality；不混同almost sure Lp或distribution convergence。"},"difficulty":{"band":"undergraduate_core","level":2,"skills":["依機率收斂"]},"variant":{"family_id":"qf-mod30-convprob-eventual-equality","seed":202610307086,"parameters":{"settling_index":11,"n":13,"domain":"Symbolic_deviation_probability_tail","operation":"convprob-eventual-equality","semantic_template":"qf-mod30-convprob-eventual-equality/{\"n\":13,\"settling_index\":11}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_model","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"候選須主端重算；不構成人工審定、一般域／Hilbert／martingale／無限基數／一般收斂、Lean或Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-14","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261014-advance-20261030-r07-convergence-in-probability-0087","batch_id":"batch-20261014-advance-20261030-r07-convergence-in-probability-foundations","language":"zh-Hant","source_mko_ids":["mko-convergence-in-probability"],"title_zh":"依機率收斂","stem_zh":"共同機率空間與forall epsilon tail責任。操作=convprob-eventual-equality；資料={\"settling_index\":12,\"n\":14}。請依 [settling_index,n,deviation_probability,converges,certificate] 欄序回答。","answer":{"kind":"expression","value":"(12, 14, 0, 是, eventual_equality_universal_tail_certificate)","explanation_zh":"Wave4第四層核對=(12, 14, 0, 是, eventual_equality_universal_tail_certificate)；依完整明示資料重算；完整有限／symbolic tail證書不自動升格為未聲明的一般定理；finite prefix不足且只接受symbolic tail或eventual equality；不混同almost sure Lp或distribution convergence。"},"difficulty":{"band":"undergraduate_core","level":2,"skills":["依機率收斂"]},"variant":{"family_id":"qf-mod30-convprob-eventual-equality","seed":202610307087,"parameters":{"settling_index":12,"n":14,"domain":"Symbolic_deviation_probability_tail","operation":"convprob-eventual-equality","semantic_template":"qf-mod30-convprob-eventual-equality/{\"n\":14,\"settling_index\":12}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_model","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"候選須主端重算；不構成人工審定、一般域／Hilbert／martingale／無限基數／一般收斂、Lean或Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-14","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261014-advance-20261030-r07-convergence-in-probability-0088","batch_id":"batch-20261014-advance-20261030-r07-convergence-in-probability-foundations","language":"zh-Hant","source_mko_ids":["mko-convergence-in-probability"],"title_zh":"依機率收斂","stem_zh":"共同機率空間與forall epsilon tail責任。操作=convprob-eventual-equality；資料={\"settling_index\":13,\"n\":16}。請依 [settling_index,n,deviation_probability,converges,certificate] 欄序回答。","answer":{"kind":"expression","value":"(13, 16, 0, 是, eventual_equality_universal_tail_certificate)","explanation_zh":"Wave4第四層核對=(13, 16, 0, 是, eventual_equality_universal_tail_certificate)；依完整明示資料重算；完整有限／symbolic tail證書不自動升格為未聲明的一般定理；finite prefix不足且只接受symbolic tail或eventual equality；不混同almost sure Lp或distribution convergence。"},"difficulty":{"band":"undergraduate_core","level":2,"skills":["依機率收斂"]},"variant":{"family_id":"qf-mod30-convprob-eventual-equality","seed":202610307088,"parameters":{"settling_index":13,"n":16,"domain":"Symbolic_deviation_probability_tail","operation":"convprob-eventual-equality","semantic_template":"qf-mod30-convprob-eventual-equality/{\"n\":16,\"settling_index\":13}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_model","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"候選須主端重算；不構成人工審定、一般域／Hilbert／martingale／無限基數／一般收斂、Lean或Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-14","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261014-advance-20261030-r07-convergence-in-probability-0089","batch_id":"batch-20261014-advance-20261030-r07-convergence-in-probability-foundations","language":"zh-Hant","source_mko_ids":["mko-convergence-in-probability"],"title_zh":"依機率收斂","stem_zh":"共同機率空間與forall epsilon tail責任。操作=convprob-eventual-equality；資料={\"settling_index\":14,\"n\":17}。請依 [settling_index,n,deviation_probability,converges,certificate] 欄序回答。","answer":{"kind":"expression","value":"(14, 17, 0, 是, eventual_equality_universal_tail_certificate)","explanation_zh":"Wave4第四層核對=(14, 17, 0, 是, eventual_equality_universal_tail_certificate)；依完整明示資料重算；完整有限／symbolic tail證書不自動升格為未聲明的一般定理；finite prefix不足且只接受symbolic tail或eventual equality；不混同almost sure Lp或distribution convergence。"},"difficulty":{"band":"undergraduate_core","level":2,"skills":["依機率收斂"]},"variant":{"family_id":"qf-mod30-convprob-eventual-equality","seed":202610307089,"parameters":{"settling_index":14,"n":17,"domain":"Symbolic_deviation_probability_tail","operation":"convprob-eventual-equality","semantic_template":"qf-mod30-convprob-eventual-equality/{\"n\":17,\"settling_index\":14}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_model","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"候選須主端重算；不構成人工審定、一般域／Hilbert／martingale／無限基數／一般收斂、Lean或Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-14","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261014-advance-20261030-r07-convergence-in-probability-0090","batch_id":"batch-20261014-advance-20261030-r07-convergence-in-probability-foundations","language":"zh-Hant","source_mko_ids":["mko-convergence-in-probability"],"title_zh":"依機率收斂","stem_zh":"共同機率空間與forall epsilon tail責任。操作=convprob-eventual-equality；資料={\"settling_index\":15,\"n\":18}。請依 [settling_index,n,deviation_probability,converges,certificate] 欄序回答。","answer":{"kind":"expression","value":"(15, 18, 0, 是, eventual_equality_universal_tail_certificate)","explanation_zh":"Wave4第四層核對=(15, 18, 0, 是, eventual_equality_universal_tail_certificate)；依完整明示資料重算；完整有限／symbolic tail證書不自動升格為未聲明的一般定理；finite prefix不足且只接受symbolic tail或eventual equality；不混同almost sure Lp或distribution convergence。"},"difficulty":{"band":"undergraduate_core","level":2,"skills":["依機率收斂"]},"variant":{"family_id":"qf-mod30-convprob-eventual-equality","seed":202610307090,"parameters":{"settling_index":15,"n":18,"domain":"Symbolic_deviation_probability_tail","operation":"convprob-eventual-equality","semantic_template":"qf-mod30-convprob-eventual-equality/{\"n\":18,\"settling_index\":15}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_model","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"候選須主端重算；不構成人工審定、一般域／Hilbert／martingale／無限基數／一般收斂、Lean或Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-14","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261014-advance-20261030-r07-convergence-in-probability-0091","batch_id":"batch-20261014-advance-20261030-r07-convergence-in-probability-foundations","language":"zh-Hant","source_mko_ids":["mko-convergence-in-probability"],"title_zh":"依機率收斂","stem_zh":"共同機率空間與forall epsilon tail責任。操作=convprob-eventual-equality；資料={\"settling_index\":16,\"n\":20}。請依 [settling_index,n,deviation_probability,converges,certificate] 欄序回答。","answer":{"kind":"expression","value":"(16, 20, 0, 是, eventual_equality_universal_tail_certificate)","explanation_zh":"Wave4第四層核對=(16, 20, 0, 是, eventual_equality_universal_tail_certificate)；依完整明示資料重算；完整有限／symbolic tail證書不自動升格為未聲明的一般定理；finite prefix不足且只接受symbolic tail或eventual equality；不混同almost sure Lp或distribution convergence。"},"difficulty":{"band":"undergraduate_core","level":2,"skills":["依機率收斂"]},"variant":{"family_id":"qf-mod30-convprob-eventual-equality","seed":202610307091,"parameters":{"settling_index":16,"n":20,"domain":"Symbolic_deviation_probability_tail","operation":"convprob-eventual-equality","semantic_template":"qf-mod30-convprob-eventual-equality/{\"n\":20,\"settling_index\":16}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_model","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"候選須主端重算；不構成人工審定、一般域／Hilbert／martingale／無限基數／一般收斂、Lean或Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-14","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261014-advance-20261030-r07-convergence-in-probability-0092","batch_id":"batch-20261014-advance-20261030-r07-convergence-in-probability-foundations","language":"zh-Hant","source_mko_ids":["mko-convergence-in-probability"],"title_zh":"依機率收斂","stem_zh":"共同機率空間與forall epsilon tail責任。操作=convprob-eventual-equality；資料={\"settling_index\":17,\"n\":21}。請依 [settling_index,n,deviation_probability,converges,certificate] 欄序回答。","answer":{"kind":"expression","value":"(17, 21, 0, 是, eventual_equality_universal_tail_certificate)","explanation_zh":"Wave4第四層核對=(17, 21, 0, 是, eventual_equality_universal_tail_certificate)；依完整明示資料重算；完整有限／symbolic tail證書不自動升格為未聲明的一般定理；finite prefix不足且只接受symbolic tail或eventual equality；不混同almost sure Lp或distribution convergence。"},"difficulty":{"band":"undergraduate_core","level":2,"skills":["依機率收斂"]},"variant":{"family_id":"qf-mod30-convprob-eventual-equality","seed":202610307092,"parameters":{"settling_index":17,"n":21,"domain":"Symbolic_deviation_probability_tail","operation":"convprob-eventual-equality","semantic_template":"qf-mod30-convprob-eventual-equality/{\"n\":21,\"settling_index\":17}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_model","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"候選須主端重算；不構成人工審定、一般域／Hilbert／martingale／無限基數／一般收斂、Lean或Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-14","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261014-advance-20261030-r07-convergence-in-probability-0093","batch_id":"batch-20261014-advance-20261030-r07-convergence-in-probability-foundations","language":"zh-Hant","source_mko_ids":["mko-convergence-in-probability"],"title_zh":"依機率收斂","stem_zh":"共同機率空間與forall epsilon tail責任。操作=convprob-eventual-equality；資料={\"settling_index\":18,\"n\":22}。請依 [settling_index,n,deviation_probability,converges,certificate] 欄序回答。","answer":{"kind":"expression","value":"(18, 22, 0, 是, eventual_equality_universal_tail_certificate)","explanation_zh":"Wave4第四層核對=(18, 22, 0, 是, eventual_equality_universal_tail_certificate)；依完整明示資料重算；完整有限／symbolic tail證書不自動升格為未聲明的一般定理；finite prefix不足且只接受symbolic tail或eventual equality；不混同almost sure Lp或distribution convergence。"},"difficulty":{"band":"undergraduate_core","level":3,"skills":["依機率收斂"]},"variant":{"family_id":"qf-mod30-convprob-eventual-equality","seed":202610307093,"parameters":{"settling_index":18,"n":22,"domain":"Symbolic_deviation_probability_tail","operation":"convprob-eventual-equality","semantic_template":"qf-mod30-convprob-eventual-equality/{\"n\":22,\"settling_index\":18}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_model","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"候選須主端重算；不構成人工審定、一般域／Hilbert／martingale／無限基數／一般收斂、Lean或Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-14","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261014-advance-20261030-r07-convergence-in-probability-0094","batch_id":"batch-20261014-advance-20261030-r07-convergence-in-probability-foundations","language":"zh-Hant","source_mko_ids":["mko-convergence-in-probability"],"title_zh":"依機率收斂","stem_zh":"共同機率空間與forall epsilon tail責任。操作=convprob-eventual-equality；資料={\"settling_index\":19,\"n\":24}。請依 [settling_index,n,deviation_probability,converges,certificate] 欄序回答。","answer":{"kind":"expression","value":"(19, 24, 0, 是, eventual_equality_universal_tail_certificate)","explanation_zh":"Wave4第四層核對=(19, 24, 0, 是, eventual_equality_universal_tail_certificate)；依完整明示資料重算；完整有限／symbolic tail證書不自動升格為未聲明的一般定理；finite prefix不足且只接受symbolic tail或eventual equality；不混同almost sure Lp或distribution convergence。"},"difficulty":{"band":"undergraduate_core","level":3,"skills":["依機率收斂"]},"variant":{"family_id":"qf-mod30-convprob-eventual-equality","seed":202610307094,"parameters":{"settling_index":19,"n":24,"domain":"Symbolic_deviation_probability_tail","operation":"convprob-eventual-equality","semantic_template":"qf-mod30-convprob-eventual-equality/{\"n\":24,\"settling_index\":19}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_model","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"候選須主端重算；不構成人工審定、一般域／Hilbert／martingale／無限基數／一般收斂、Lean或Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-14","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261014-advance-20261030-r07-convergence-in-probability-0095","batch_id":"batch-20261014-advance-20261030-r07-convergence-in-probability-foundations","language":"zh-Hant","source_mko_ids":["mko-convergence-in-probability"],"title_zh":"依機率收斂","stem_zh":"共同機率空間與forall epsilon tail責任。操作=convprob-eventual-equality；資料={\"settling_index\":20,\"n\":25}。請依 [settling_index,n,deviation_probability,converges,certificate] 欄序回答。","answer":{"kind":"expression","value":"(20, 25, 0, 是, eventual_equality_universal_tail_certificate)","explanation_zh":"Wave4第四層核對=(20, 25, 0, 是, eventual_equality_universal_tail_certificate)；依完整明示資料重算；完整有限／symbolic tail證書不自動升格為未聲明的一般定理；finite prefix不足且只接受symbolic tail或eventual equality；不混同almost sure Lp或distribution convergence。"},"difficulty":{"band":"undergraduate_core","level":3,"skills":["依機率收斂"]},"variant":{"family_id":"qf-mod30-convprob-eventual-equality","seed":202610307095,"parameters":{"settling_index":20,"n":25,"domain":"Symbolic_deviation_probability_tail","operation":"convprob-eventual-equality","semantic_template":"qf-mod30-convprob-eventual-equality/{\"n\":25,\"settling_index\":20}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_model","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"候選須主端重算；不構成人工審定、一般域／Hilbert／martingale／無限基數／一般收斂、Lean或Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-14","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261014-advance-20261030-r07-convergence-in-probability-0096","batch_id":"batch-20261014-advance-20261030-r07-convergence-in-probability-foundations","language":"zh-Hant","source_mko_ids":["mko-convergence-in-probability"],"title_zh":"依機率收斂","stem_zh":"共同機率空間與forall epsilon tail責任。操作=convprob-eventual-equality；資料={\"settling_index\":21,\"n\":26}。請依 [settling_index,n,deviation_probability,converges,certificate] 欄序回答。","answer":{"kind":"expression","value":"(21, 26, 0, 是, eventual_equality_universal_tail_certificate)","explanation_zh":"Wave4第四層核對=(21, 26, 0, 是, eventual_equality_universal_tail_certificate)；依完整明示資料重算；完整有限／symbolic tail證書不自動升格為未聲明的一般定理；finite prefix不足且只接受symbolic tail或eventual equality；不混同almost sure Lp或distribution convergence。"},"difficulty":{"band":"undergraduate_core","level":3,"skills":["依機率收斂"]},"variant":{"family_id":"qf-mod30-convprob-eventual-equality","seed":202610307096,"parameters":{"settling_index":21,"n":26,"domain":"Symbolic_deviation_probability_tail","operation":"convprob-eventual-equality","semantic_template":"qf-mod30-convprob-eventual-equality/{\"n\":26,\"settling_index\":21}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_model","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"候選須主端重算；不構成人工審定、一般域／Hilbert／martingale／無限基數／一般收斂、Lean或Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-14","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261014-advance-20261030-r07-convergence-in-probability-0097","batch_id":"batch-20261014-advance-20261030-r07-convergence-in-probability-foundations","language":"zh-Hant","source_mko_ids":["mko-convergence-in-probability"],"title_zh":"依機率收斂","stem_zh":"共同機率空間與forall epsilon tail責任。操作=convprob-eventual-equality；資料={\"settling_index\":22,\"n\":28}。請依 [settling_index,n,deviation_probability,converges,certificate] 欄序回答。","answer":{"kind":"expression","value":"(22, 28, 0, 是, eventual_equality_universal_tail_certificate)","explanation_zh":"Wave4第四層核對=(22, 28, 0, 是, eventual_equality_universal_tail_certificate)；依完整明示資料重算；完整有限／symbolic tail證書不自動升格為未聲明的一般定理；finite prefix不足且只接受symbolic tail或eventual equality；不混同almost sure Lp或distribution convergence。"},"difficulty":{"band":"undergraduate_core","level":3,"skills":["依機率收斂"]},"variant":{"family_id":"qf-mod30-convprob-eventual-equality","seed":202610307097,"parameters":{"settling_index":22,"n":28,"domain":"Symbolic_deviation_probability_tail","operation":"convprob-eventual-equality","semantic_template":"qf-mod30-convprob-eventual-equality/{\"n\":28,\"settling_index\":22}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_model","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"候選須主端重算；不構成人工審定、一般域／Hilbert／martingale／無限基數／一般收斂、Lean或Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-14","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261014-advance-20261030-r07-convergence-in-probability-0098","batch_id":"batch-20261014-advance-20261030-r07-convergence-in-probability-foundations","language":"zh-Hant","source_mko_ids":["mko-convergence-in-probability"],"title_zh":"依機率收斂","stem_zh":"共同機率空間與forall epsilon tail責任。操作=convprob-eventual-equality；資料={\"settling_index\":23,\"n\":29}。請依 [settling_index,n,deviation_probability,converges,certificate] 欄序回答。","answer":{"kind":"expression","value":"(23, 29, 0, 是, eventual_equality_universal_tail_certificate)","explanation_zh":"Wave4第四層核對=(23, 29, 0, 是, eventual_equality_universal_tail_certificate)；依完整明示資料重算；完整有限／symbolic tail證書不自動升格為未聲明的一般定理；finite prefix不足且只接受symbolic tail或eventual equality；不混同almost sure Lp或distribution convergence。"},"difficulty":{"band":"undergraduate_core","level":3,"skills":["依機率收斂"]},"variant":{"family_id":"qf-mod30-convprob-eventual-equality","seed":202610307098,"parameters":{"settling_index":23,"n":29,"domain":"Symbolic_deviation_probability_tail","operation":"convprob-eventual-equality","semantic_template":"qf-mod30-convprob-eventual-equality/{\"n\":29,\"settling_index\":23}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_model","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"候選須主端重算；不構成人工審定、一般域／Hilbert／martingale／無限基數／一般收斂、Lean或Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-14","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261014-advance-20261030-r07-convergence-in-probability-0099","batch_id":"batch-20261014-advance-20261030-r07-convergence-in-probability-foundations","language":"zh-Hant","source_mko_ids":["mko-convergence-in-probability"],"title_zh":"依機率收斂","stem_zh":"共同機率空間與forall epsilon tail責任。操作=convprob-eventual-equality；資料={\"settling_index\":24,\"n\":30}。請依 [settling_index,n,deviation_probability,converges,certificate] 欄序回答。","answer":{"kind":"expression","value":"(24, 30, 0, 是, eventual_equality_universal_tail_certificate)","explanation_zh":"Wave4第四層核對=(24, 30, 0, 是, eventual_equality_universal_tail_certificate)；依完整明示資料重算；完整有限／symbolic tail證書不自動升格為未聲明的一般定理；finite prefix不足且只接受symbolic tail或eventual equality；不混同almost sure Lp或distribution convergence。"},"difficulty":{"band":"undergraduate_core","level":3,"skills":["依機率收斂"]},"variant":{"family_id":"qf-mod30-convprob-eventual-equality","seed":202610307099,"parameters":{"settling_index":24,"n":30,"domain":"Symbolic_deviation_probability_tail","operation":"convprob-eventual-equality","semantic_template":"qf-mod30-convprob-eventual-equality/{\"n\":30,\"settling_index\":24}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_model","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"候選須主端重算；不構成人工審定、一般域／Hilbert／martingale／無限基數／一般收斂、Lean或Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-14","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261014-advance-20261030-r07-convergence-in-probability-0100","batch_id":"batch-20261014-advance-20261030-r07-convergence-in-probability-foundations","language":"zh-Hant","source_mko_ids":["mko-convergence-in-probability"],"title_zh":"依機率收斂","stem_zh":"共同機率空間與forall epsilon tail責任。操作=convprob-eventual-equality；資料={\"settling_index\":25,\"n\":32}。請依 [settling_index,n,deviation_probability,converges,certificate] 欄序回答。","answer":{"kind":"expression","value":"(25, 32, 0, 是, eventual_equality_universal_tail_certificate)","explanation_zh":"Wave4第四層核對=(25, 32, 0, 是, eventual_equality_universal_tail_certificate)；依完整明示資料重算；完整有限／symbolic tail證書不自動升格為未聲明的一般定理；finite prefix不足且只接受symbolic tail或eventual equality；不混同almost sure Lp或distribution convergence。"},"difficulty":{"band":"undergraduate_core","level":3,"skills":["依機率收斂"]},"variant":{"family_id":"qf-mod30-convprob-eventual-equality","seed":202610307100,"parameters":{"settling_index":25,"n":32,"domain":"Symbolic_deviation_probability_tail","operation":"convprob-eventual-equality","semantic_template":"qf-mod30-convprob-eventual-equality/{\"n\":32,\"settling_index\":25}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_model","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"候選須主端重算；不構成人工審定、一般域／Hilbert／martingale／無限基數／一般收斂、Lean或Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-14","contract_version":"ocme-question-factory-v0.1"}}