{"schema_version":"ocme-question-v0.1","id":"q-20261014-advance-20261030-r06-cumulative-distribution-function-0001","batch_id":"batch-20261014-advance-20261030-r06-cumulative-distribution-function-foundations","language":"zh-Hant","source_mko_ids":["mko-cumulative-distribution-function"],"title_zh":"累積分布函數","stem_zh":"完整有限離散law與F(t)=P(X小於等於t)。操作=cdf-evaluate；資料={\"support\":[-12,-5,1],\"masses\":[[1,4],[1,4],[1,2]],\"t\":-12}。請依 [t,F_t,boundary] 欄序回答。","answer":{"kind":"expression","value":"(-12, 1/4, uses_X_less_than_or_equal_t)","explanation_zh":"Wave4第四層核對=(-12, 1/4, uses_X_less_than_or_equal_t)；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；保留小於等於單調右連續與端點；CDF不混同PMF或density且jump為點質量。"},"difficulty":{"band":"undergraduate_core","level":1,"skills":["累積分布函數"]},"variant":{"family_id":"qf-mod30-cdf-evaluate","seed":202610306001,"parameters":{"support":[-12,-5,1],"masses":[[1,4],[1,4],[1,2]],"t":-12,"domain":"Exact_finite_discrete_CDF","operation":"cdf-evaluate","semantic_template":"qf-mod30-cdf-evaluate/{\"masses\":[[1,4],[1,4],[1,2]],\"support\":[-12,-5,1],\"t\":-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-r06-cumulative-distribution-function-0002","batch_id":"batch-20261014-advance-20261030-r06-cumulative-distribution-function-foundations","language":"zh-Hant","source_mko_ids":["mko-cumulative-distribution-function"],"title_zh":"累積分布函數","stem_zh":"完整有限離散law與F(t)=P(X小於等於t)。操作=cdf-evaluate；資料={\"support\":[-11,-4,2],\"masses\":[[1,4],[1,4],[1,2]],\"t\":-4}。請依 [t,F_t,boundary] 欄序回答。","answer":{"kind":"expression","value":"(-4, 1/2, uses_X_less_than_or_equal_t)","explanation_zh":"Wave4第四層核對=(-4, 1/2, uses_X_less_than_or_equal_t)；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；保留小於等於單調右連續與端點；CDF不混同PMF或density且jump為點質量。"},"difficulty":{"band":"undergraduate_core","level":1,"skills":["累積分布函數"]},"variant":{"family_id":"qf-mod30-cdf-evaluate","seed":202610306002,"parameters":{"support":[-11,-4,2],"masses":[[1,4],[1,4],[1,2]],"t":-4,"domain":"Exact_finite_discrete_CDF","operation":"cdf-evaluate","semantic_template":"qf-mod30-cdf-evaluate/{\"masses\":[[1,4],[1,4],[1,2]],\"support\":[-11,-4,2],\"t\":-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-r06-cumulative-distribution-function-0003","batch_id":"batch-20261014-advance-20261030-r06-cumulative-distribution-function-foundations","language":"zh-Hant","source_mko_ids":["mko-cumulative-distribution-function"],"title_zh":"累積分布函數","stem_zh":"完整有限離散law與F(t)=P(X小於等於t)。操作=cdf-evaluate；資料={\"support\":[-10,-3,3],\"masses\":[[1,4],[1,4],[1,2]],\"t\":3}。請依 [t,F_t,boundary] 欄序回答。","answer":{"kind":"expression","value":"(3, 1, uses_X_less_than_or_equal_t)","explanation_zh":"Wave4第四層核對=(3, 1, uses_X_less_than_or_equal_t)；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；保留小於等於單調右連續與端點；CDF不混同PMF或density且jump為點質量。"},"difficulty":{"band":"undergraduate_core","level":1,"skills":["累積分布函數"]},"variant":{"family_id":"qf-mod30-cdf-evaluate","seed":202610306003,"parameters":{"support":[-10,-3,3],"masses":[[1,4],[1,4],[1,2]],"t":3,"domain":"Exact_finite_discrete_CDF","operation":"cdf-evaluate","semantic_template":"qf-mod30-cdf-evaluate/{\"masses\":[[1,4],[1,4],[1,2]],\"support\":[-10,-3,3],\"t\":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-r06-cumulative-distribution-function-0004","batch_id":"batch-20261014-advance-20261030-r06-cumulative-distribution-function-foundations","language":"zh-Hant","source_mko_ids":["mko-cumulative-distribution-function"],"title_zh":"累積分布函數","stem_zh":"完整有限離散law與F(t)=P(X小於等於t)。操作=cdf-evaluate；資料={\"support\":[-9,-2,4],\"masses\":[[1,4],[1,4],[1,2]],\"t\":-9}。請依 [t,F_t,boundary] 欄序回答。","answer":{"kind":"expression","value":"(-9, 1/4, uses_X_less_than_or_equal_t)","explanation_zh":"Wave4第四層核對=(-9, 1/4, uses_X_less_than_or_equal_t)；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；保留小於等於單調右連續與端點；CDF不混同PMF或density且jump為點質量。"},"difficulty":{"band":"undergraduate_core","level":1,"skills":["累積分布函數"]},"variant":{"family_id":"qf-mod30-cdf-evaluate","seed":202610306004,"parameters":{"support":[-9,-2,4],"masses":[[1,4],[1,4],[1,2]],"t":-9,"domain":"Exact_finite_discrete_CDF","operation":"cdf-evaluate","semantic_template":"qf-mod30-cdf-evaluate/{\"masses\":[[1,4],[1,4],[1,2]],\"support\":[-9,-2,4],\"t\":-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-r06-cumulative-distribution-function-0005","batch_id":"batch-20261014-advance-20261030-r06-cumulative-distribution-function-foundations","language":"zh-Hant","source_mko_ids":["mko-cumulative-distribution-function"],"title_zh":"累積分布函數","stem_zh":"完整有限離散law與F(t)=P(X小於等於t)。操作=cdf-evaluate；資料={\"support\":[-8,-1,5],\"masses\":[[1,4],[1,4],[1,2]],\"t\":-1}。請依 [t,F_t,boundary] 欄序回答。","answer":{"kind":"expression","value":"(-1, 1/2, uses_X_less_than_or_equal_t)","explanation_zh":"Wave4第四層核對=(-1, 1/2, uses_X_less_than_or_equal_t)；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；保留小於等於單調右連續與端點；CDF不混同PMF或density且jump為點質量。"},"difficulty":{"band":"undergraduate_core","level":1,"skills":["累積分布函數"]},"variant":{"family_id":"qf-mod30-cdf-evaluate","seed":202610306005,"parameters":{"support":[-8,-1,5],"masses":[[1,4],[1,4],[1,2]],"t":-1,"domain":"Exact_finite_discrete_CDF","operation":"cdf-evaluate","semantic_template":"qf-mod30-cdf-evaluate/{\"masses\":[[1,4],[1,4],[1,2]],\"support\":[-8,-1,5],\"t\":-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-r06-cumulative-distribution-function-0006","batch_id":"batch-20261014-advance-20261030-r06-cumulative-distribution-function-foundations","language":"zh-Hant","source_mko_ids":["mko-cumulative-distribution-function"],"title_zh":"累積分布函數","stem_zh":"完整有限離散law與F(t)=P(X小於等於t)。操作=cdf-evaluate；資料={\"support\":[-7,0,6],\"masses\":[[1,4],[1,4],[1,2]],\"t\":6}。請依 [t,F_t,boundary] 欄序回答。","answer":{"kind":"expression","value":"(6, 1, uses_X_less_than_or_equal_t)","explanation_zh":"Wave4第四層核對=(6, 1, uses_X_less_than_or_equal_t)；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；保留小於等於單調右連續與端點；CDF不混同PMF或density且jump為點質量。"},"difficulty":{"band":"undergraduate_core","level":1,"skills":["累積分布函數"]},"variant":{"family_id":"qf-mod30-cdf-evaluate","seed":202610306006,"parameters":{"support":[-7,0,6],"masses":[[1,4],[1,4],[1,2]],"t":6,"domain":"Exact_finite_discrete_CDF","operation":"cdf-evaluate","semantic_template":"qf-mod30-cdf-evaluate/{\"masses\":[[1,4],[1,4],[1,2]],\"support\":[-7,0,6],\"t\":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-r06-cumulative-distribution-function-0007","batch_id":"batch-20261014-advance-20261030-r06-cumulative-distribution-function-foundations","language":"zh-Hant","source_mko_ids":["mko-cumulative-distribution-function"],"title_zh":"累積分布函數","stem_zh":"完整有限離散law與F(t)=P(X小於等於t)。操作=cdf-evaluate；資料={\"support\":[-6,1,7],\"masses\":[[1,4],[1,4],[1,2]],\"t\":-6}。請依 [t,F_t,boundary] 欄序回答。","answer":{"kind":"expression","value":"(-6, 1/4, uses_X_less_than_or_equal_t)","explanation_zh":"Wave4第四層核對=(-6, 1/4, uses_X_less_than_or_equal_t)；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；保留小於等於單調右連續與端點；CDF不混同PMF或density且jump為點質量。"},"difficulty":{"band":"undergraduate_core","level":1,"skills":["累積分布函數"]},"variant":{"family_id":"qf-mod30-cdf-evaluate","seed":202610306007,"parameters":{"support":[-6,1,7],"masses":[[1,4],[1,4],[1,2]],"t":-6,"domain":"Exact_finite_discrete_CDF","operation":"cdf-evaluate","semantic_template":"qf-mod30-cdf-evaluate/{\"masses\":[[1,4],[1,4],[1,2]],\"support\":[-6,1,7],\"t\":-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-r06-cumulative-distribution-function-0008","batch_id":"batch-20261014-advance-20261030-r06-cumulative-distribution-function-foundations","language":"zh-Hant","source_mko_ids":["mko-cumulative-distribution-function"],"title_zh":"累積分布函數","stem_zh":"完整有限離散law與F(t)=P(X小於等於t)。操作=cdf-evaluate；資料={\"support\":[-5,2,8],\"masses\":[[1,4],[1,4],[1,2]],\"t\":2}。請依 [t,F_t,boundary] 欄序回答。","answer":{"kind":"expression","value":"(2, 1/2, uses_X_less_than_or_equal_t)","explanation_zh":"Wave4第四層核對=(2, 1/2, uses_X_less_than_or_equal_t)；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；保留小於等於單調右連續與端點；CDF不混同PMF或density且jump為點質量。"},"difficulty":{"band":"undergraduate_core","level":1,"skills":["累積分布函數"]},"variant":{"family_id":"qf-mod30-cdf-evaluate","seed":202610306008,"parameters":{"support":[-5,2,8],"masses":[[1,4],[1,4],[1,2]],"t":2,"domain":"Exact_finite_discrete_CDF","operation":"cdf-evaluate","semantic_template":"qf-mod30-cdf-evaluate/{\"masses\":[[1,4],[1,4],[1,2]],\"support\":[-5,2,8],\"t\":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-r06-cumulative-distribution-function-0009","batch_id":"batch-20261014-advance-20261030-r06-cumulative-distribution-function-foundations","language":"zh-Hant","source_mko_ids":["mko-cumulative-distribution-function"],"title_zh":"累積分布函數","stem_zh":"完整有限離散law與F(t)=P(X小於等於t)。操作=cdf-evaluate；資料={\"support\":[-4,3,9],\"masses\":[[1,4],[1,4],[1,2]],\"t\":9}。請依 [t,F_t,boundary] 欄序回答。","answer":{"kind":"expression","value":"(9, 1, uses_X_less_than_or_equal_t)","explanation_zh":"Wave4第四層核對=(9, 1, uses_X_less_than_or_equal_t)；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；保留小於等於單調右連續與端點；CDF不混同PMF或density且jump為點質量。"},"difficulty":{"band":"undergraduate_core","level":2,"skills":["累積分布函數"]},"variant":{"family_id":"qf-mod30-cdf-evaluate","seed":202610306009,"parameters":{"support":[-4,3,9],"masses":[[1,4],[1,4],[1,2]],"t":9,"domain":"Exact_finite_discrete_CDF","operation":"cdf-evaluate","semantic_template":"qf-mod30-cdf-evaluate/{\"masses\":[[1,4],[1,4],[1,2]],\"support\":[-4,3,9],\"t\":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-r06-cumulative-distribution-function-0010","batch_id":"batch-20261014-advance-20261030-r06-cumulative-distribution-function-foundations","language":"zh-Hant","source_mko_ids":["mko-cumulative-distribution-function"],"title_zh":"累積分布函數","stem_zh":"完整有限離散law與F(t)=P(X小於等於t)。操作=cdf-evaluate；資料={\"support\":[-3,4,10],\"masses\":[[1,4],[1,4],[1,2]],\"t\":-3}。請依 [t,F_t,boundary] 欄序回答。","answer":{"kind":"expression","value":"(-3, 1/4, uses_X_less_than_or_equal_t)","explanation_zh":"Wave4第四層核對=(-3, 1/4, uses_X_less_than_or_equal_t)；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；保留小於等於單調右連續與端點；CDF不混同PMF或density且jump為點質量。"},"difficulty":{"band":"undergraduate_core","level":2,"skills":["累積分布函數"]},"variant":{"family_id":"qf-mod30-cdf-evaluate","seed":202610306010,"parameters":{"support":[-3,4,10],"masses":[[1,4],[1,4],[1,2]],"t":-3,"domain":"Exact_finite_discrete_CDF","operation":"cdf-evaluate","semantic_template":"qf-mod30-cdf-evaluate/{\"masses\":[[1,4],[1,4],[1,2]],\"support\":[-3,4,10],\"t\":-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-r06-cumulative-distribution-function-0011","batch_id":"batch-20261014-advance-20261030-r06-cumulative-distribution-function-foundations","language":"zh-Hant","source_mko_ids":["mko-cumulative-distribution-function"],"title_zh":"累積分布函數","stem_zh":"完整有限離散law與F(t)=P(X小於等於t)。操作=cdf-evaluate；資料={\"support\":[-2,5,11],\"masses\":[[1,4],[1,4],[1,2]],\"t\":5}。請依 [t,F_t,boundary] 欄序回答。","answer":{"kind":"expression","value":"(5, 1/2, uses_X_less_than_or_equal_t)","explanation_zh":"Wave4第四層核對=(5, 1/2, uses_X_less_than_or_equal_t)；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；保留小於等於單調右連續與端點；CDF不混同PMF或density且jump為點質量。"},"difficulty":{"band":"undergraduate_core","level":2,"skills":["累積分布函數"]},"variant":{"family_id":"qf-mod30-cdf-evaluate","seed":202610306011,"parameters":{"support":[-2,5,11],"masses":[[1,4],[1,4],[1,2]],"t":5,"domain":"Exact_finite_discrete_CDF","operation":"cdf-evaluate","semantic_template":"qf-mod30-cdf-evaluate/{\"masses\":[[1,4],[1,4],[1,2]],\"support\":[-2,5,11],\"t\":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-r06-cumulative-distribution-function-0012","batch_id":"batch-20261014-advance-20261030-r06-cumulative-distribution-function-foundations","language":"zh-Hant","source_mko_ids":["mko-cumulative-distribution-function"],"title_zh":"累積分布函數","stem_zh":"完整有限離散law與F(t)=P(X小於等於t)。操作=cdf-evaluate；資料={\"support\":[-1,6,12],\"masses\":[[1,4],[1,4],[1,2]],\"t\":12}。請依 [t,F_t,boundary] 欄序回答。","answer":{"kind":"expression","value":"(12, 1, uses_X_less_than_or_equal_t)","explanation_zh":"Wave4第四層核對=(12, 1, uses_X_less_than_or_equal_t)；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；保留小於等於單調右連續與端點；CDF不混同PMF或density且jump為點質量。"},"difficulty":{"band":"undergraduate_core","level":2,"skills":["累積分布函數"]},"variant":{"family_id":"qf-mod30-cdf-evaluate","seed":202610306012,"parameters":{"support":[-1,6,12],"masses":[[1,4],[1,4],[1,2]],"t":12,"domain":"Exact_finite_discrete_CDF","operation":"cdf-evaluate","semantic_template":"qf-mod30-cdf-evaluate/{\"masses\":[[1,4],[1,4],[1,2]],\"support\":[-1,6,12],\"t\":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-r06-cumulative-distribution-function-0013","batch_id":"batch-20261014-advance-20261030-r06-cumulative-distribution-function-foundations","language":"zh-Hant","source_mko_ids":["mko-cumulative-distribution-function"],"title_zh":"累積分布函數","stem_zh":"完整有限離散law與F(t)=P(X小於等於t)。操作=cdf-evaluate；資料={\"support\":[0,7,13],\"masses\":[[1,4],[1,4],[1,2]],\"t\":0}。請依 [t,F_t,boundary] 欄序回答。","answer":{"kind":"expression","value":"(0, 1/4, uses_X_less_than_or_equal_t)","explanation_zh":"Wave4第四層核對=(0, 1/4, uses_X_less_than_or_equal_t)；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；保留小於等於單調右連續與端點；CDF不混同PMF或density且jump為點質量。"},"difficulty":{"band":"undergraduate_core","level":2,"skills":["累積分布函數"]},"variant":{"family_id":"qf-mod30-cdf-evaluate","seed":202610306013,"parameters":{"support":[0,7,13],"masses":[[1,4],[1,4],[1,2]],"t":0,"domain":"Exact_finite_discrete_CDF","operation":"cdf-evaluate","semantic_template":"qf-mod30-cdf-evaluate/{\"masses\":[[1,4],[1,4],[1,2]],\"support\":[0,7,13],\"t\":0}"}},"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-r06-cumulative-distribution-function-0014","batch_id":"batch-20261014-advance-20261030-r06-cumulative-distribution-function-foundations","language":"zh-Hant","source_mko_ids":["mko-cumulative-distribution-function"],"title_zh":"累積分布函數","stem_zh":"完整有限離散law與F(t)=P(X小於等於t)。操作=cdf-evaluate；資料={\"support\":[1,8,14],\"masses\":[[1,4],[1,4],[1,2]],\"t\":8}。請依 [t,F_t,boundary] 欄序回答。","answer":{"kind":"expression","value":"(8, 1/2, uses_X_less_than_or_equal_t)","explanation_zh":"Wave4第四層核對=(8, 1/2, uses_X_less_than_or_equal_t)；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；保留小於等於單調右連續與端點；CDF不混同PMF或density且jump為點質量。"},"difficulty":{"band":"undergraduate_core","level":2,"skills":["累積分布函數"]},"variant":{"family_id":"qf-mod30-cdf-evaluate","seed":202610306014,"parameters":{"support":[1,8,14],"masses":[[1,4],[1,4],[1,2]],"t":8,"domain":"Exact_finite_discrete_CDF","operation":"cdf-evaluate","semantic_template":"qf-mod30-cdf-evaluate/{\"masses\":[[1,4],[1,4],[1,2]],\"support\":[1,8,14],\"t\":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-r06-cumulative-distribution-function-0015","batch_id":"batch-20261014-advance-20261030-r06-cumulative-distribution-function-foundations","language":"zh-Hant","source_mko_ids":["mko-cumulative-distribution-function"],"title_zh":"累積分布函數","stem_zh":"完整有限離散law與F(t)=P(X小於等於t)。操作=cdf-evaluate；資料={\"support\":[2,9,15],\"masses\":[[1,4],[1,4],[1,2]],\"t\":15}。請依 [t,F_t,boundary] 欄序回答。","answer":{"kind":"expression","value":"(15, 1, uses_X_less_than_or_equal_t)","explanation_zh":"Wave4第四層核對=(15, 1, uses_X_less_than_or_equal_t)；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；保留小於等於單調右連續與端點；CDF不混同PMF或density且jump為點質量。"},"difficulty":{"band":"undergraduate_core","level":2,"skills":["累積分布函數"]},"variant":{"family_id":"qf-mod30-cdf-evaluate","seed":202610306015,"parameters":{"support":[2,9,15],"masses":[[1,4],[1,4],[1,2]],"t":15,"domain":"Exact_finite_discrete_CDF","operation":"cdf-evaluate","semantic_template":"qf-mod30-cdf-evaluate/{\"masses\":[[1,4],[1,4],[1,2]],\"support\":[2,9,15],\"t\":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-r06-cumulative-distribution-function-0016","batch_id":"batch-20261014-advance-20261030-r06-cumulative-distribution-function-foundations","language":"zh-Hant","source_mko_ids":["mko-cumulative-distribution-function"],"title_zh":"累積分布函數","stem_zh":"完整有限離散law與F(t)=P(X小於等於t)。操作=cdf-evaluate；資料={\"support\":[3,10,16],\"masses\":[[1,4],[1,4],[1,2]],\"t\":3}。請依 [t,F_t,boundary] 欄序回答。","answer":{"kind":"expression","value":"(3, 1/4, uses_X_less_than_or_equal_t)","explanation_zh":"Wave4第四層核對=(3, 1/4, uses_X_less_than_or_equal_t)；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；保留小於等於單調右連續與端點；CDF不混同PMF或density且jump為點質量。"},"difficulty":{"band":"undergraduate_core","level":2,"skills":["累積分布函數"]},"variant":{"family_id":"qf-mod30-cdf-evaluate","seed":202610306016,"parameters":{"support":[3,10,16],"masses":[[1,4],[1,4],[1,2]],"t":3,"domain":"Exact_finite_discrete_CDF","operation":"cdf-evaluate","semantic_template":"qf-mod30-cdf-evaluate/{\"masses\":[[1,4],[1,4],[1,2]],\"support\":[3,10,16],\"t\":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-r06-cumulative-distribution-function-0017","batch_id":"batch-20261014-advance-20261030-r06-cumulative-distribution-function-foundations","language":"zh-Hant","source_mko_ids":["mko-cumulative-distribution-function"],"title_zh":"累積分布函數","stem_zh":"完整有限離散law與F(t)=P(X小於等於t)。操作=cdf-evaluate；資料={\"support\":[4,11,17],\"masses\":[[1,4],[1,4],[1,2]],\"t\":11}。請依 [t,F_t,boundary] 欄序回答。","answer":{"kind":"expression","value":"(11, 1/2, uses_X_less_than_or_equal_t)","explanation_zh":"Wave4第四層核對=(11, 1/2, uses_X_less_than_or_equal_t)；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；保留小於等於單調右連續與端點；CDF不混同PMF或density且jump為點質量。"},"difficulty":{"band":"undergraduate_core","level":2,"skills":["累積分布函數"]},"variant":{"family_id":"qf-mod30-cdf-evaluate","seed":202610306017,"parameters":{"support":[4,11,17],"masses":[[1,4],[1,4],[1,2]],"t":11,"domain":"Exact_finite_discrete_CDF","operation":"cdf-evaluate","semantic_template":"qf-mod30-cdf-evaluate/{\"masses\":[[1,4],[1,4],[1,2]],\"support\":[4,11,17],\"t\":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-r06-cumulative-distribution-function-0018","batch_id":"batch-20261014-advance-20261030-r06-cumulative-distribution-function-foundations","language":"zh-Hant","source_mko_ids":["mko-cumulative-distribution-function"],"title_zh":"累積分布函數","stem_zh":"完整有限離散law與F(t)=P(X小於等於t)。操作=cdf-evaluate；資料={\"support\":[5,12,18],\"masses\":[[1,4],[1,4],[1,2]],\"t\":18}。請依 [t,F_t,boundary] 欄序回答。","answer":{"kind":"expression","value":"(18, 1, uses_X_less_than_or_equal_t)","explanation_zh":"Wave4第四層核對=(18, 1, uses_X_less_than_or_equal_t)；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；保留小於等於單調右連續與端點；CDF不混同PMF或density且jump為點質量。"},"difficulty":{"band":"undergraduate_core","level":3,"skills":["累積分布函數"]},"variant":{"family_id":"qf-mod30-cdf-evaluate","seed":202610306018,"parameters":{"support":[5,12,18],"masses":[[1,4],[1,4],[1,2]],"t":18,"domain":"Exact_finite_discrete_CDF","operation":"cdf-evaluate","semantic_template":"qf-mod30-cdf-evaluate/{\"masses\":[[1,4],[1,4],[1,2]],\"support\":[5,12,18],\"t\":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-r06-cumulative-distribution-function-0019","batch_id":"batch-20261014-advance-20261030-r06-cumulative-distribution-function-foundations","language":"zh-Hant","source_mko_ids":["mko-cumulative-distribution-function"],"title_zh":"累積分布函數","stem_zh":"完整有限離散law與F(t)=P(X小於等於t)。操作=cdf-evaluate；資料={\"support\":[6,13,19],\"masses\":[[1,4],[1,4],[1,2]],\"t\":6}。請依 [t,F_t,boundary] 欄序回答。","answer":{"kind":"expression","value":"(6, 1/4, uses_X_less_than_or_equal_t)","explanation_zh":"Wave4第四層核對=(6, 1/4, uses_X_less_than_or_equal_t)；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；保留小於等於單調右連續與端點；CDF不混同PMF或density且jump為點質量。"},"difficulty":{"band":"undergraduate_core","level":3,"skills":["累積分布函數"]},"variant":{"family_id":"qf-mod30-cdf-evaluate","seed":202610306019,"parameters":{"support":[6,13,19],"masses":[[1,4],[1,4],[1,2]],"t":6,"domain":"Exact_finite_discrete_CDF","operation":"cdf-evaluate","semantic_template":"qf-mod30-cdf-evaluate/{\"masses\":[[1,4],[1,4],[1,2]],\"support\":[6,13,19],\"t\":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-r06-cumulative-distribution-function-0020","batch_id":"batch-20261014-advance-20261030-r06-cumulative-distribution-function-foundations","language":"zh-Hant","source_mko_ids":["mko-cumulative-distribution-function"],"title_zh":"累積分布函數","stem_zh":"完整有限離散law與F(t)=P(X小於等於t)。操作=cdf-evaluate；資料={\"support\":[7,14,20],\"masses\":[[1,4],[1,4],[1,2]],\"t\":14}。請依 [t,F_t,boundary] 欄序回答。","answer":{"kind":"expression","value":"(14, 1/2, uses_X_less_than_or_equal_t)","explanation_zh":"Wave4第四層核對=(14, 1/2, uses_X_less_than_or_equal_t)；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；保留小於等於單調右連續與端點；CDF不混同PMF或density且jump為點質量。"},"difficulty":{"band":"undergraduate_core","level":3,"skills":["累積分布函數"]},"variant":{"family_id":"qf-mod30-cdf-evaluate","seed":202610306020,"parameters":{"support":[7,14,20],"masses":[[1,4],[1,4],[1,2]],"t":14,"domain":"Exact_finite_discrete_CDF","operation":"cdf-evaluate","semantic_template":"qf-mod30-cdf-evaluate/{\"masses\":[[1,4],[1,4],[1,2]],\"support\":[7,14,20],\"t\":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-r06-cumulative-distribution-function-0021","batch_id":"batch-20261014-advance-20261030-r06-cumulative-distribution-function-foundations","language":"zh-Hant","source_mko_ids":["mko-cumulative-distribution-function"],"title_zh":"累積分布函數","stem_zh":"完整有限離散law與F(t)=P(X小於等於t)。操作=cdf-evaluate；資料={\"support\":[8,15,21],\"masses\":[[1,4],[1,4],[1,2]],\"t\":21}。請依 [t,F_t,boundary] 欄序回答。","answer":{"kind":"expression","value":"(21, 1, uses_X_less_than_or_equal_t)","explanation_zh":"Wave4第四層核對=(21, 1, uses_X_less_than_or_equal_t)；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；保留小於等於單調右連續與端點；CDF不混同PMF或density且jump為點質量。"},"difficulty":{"band":"undergraduate_core","level":3,"skills":["累積分布函數"]},"variant":{"family_id":"qf-mod30-cdf-evaluate","seed":202610306021,"parameters":{"support":[8,15,21],"masses":[[1,4],[1,4],[1,2]],"t":21,"domain":"Exact_finite_discrete_CDF","operation":"cdf-evaluate","semantic_template":"qf-mod30-cdf-evaluate/{\"masses\":[[1,4],[1,4],[1,2]],\"support\":[8,15,21],\"t\":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-r06-cumulative-distribution-function-0022","batch_id":"batch-20261014-advance-20261030-r06-cumulative-distribution-function-foundations","language":"zh-Hant","source_mko_ids":["mko-cumulative-distribution-function"],"title_zh":"累積分布函數","stem_zh":"完整有限離散law與F(t)=P(X小於等於t)。操作=cdf-evaluate；資料={\"support\":[9,16,22],\"masses\":[[1,4],[1,4],[1,2]],\"t\":9}。請依 [t,F_t,boundary] 欄序回答。","answer":{"kind":"expression","value":"(9, 1/4, uses_X_less_than_or_equal_t)","explanation_zh":"Wave4第四層核對=(9, 1/4, uses_X_less_than_or_equal_t)；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；保留小於等於單調右連續與端點；CDF不混同PMF或density且jump為點質量。"},"difficulty":{"band":"undergraduate_core","level":3,"skills":["累積分布函數"]},"variant":{"family_id":"qf-mod30-cdf-evaluate","seed":202610306022,"parameters":{"support":[9,16,22],"masses":[[1,4],[1,4],[1,2]],"t":9,"domain":"Exact_finite_discrete_CDF","operation":"cdf-evaluate","semantic_template":"qf-mod30-cdf-evaluate/{\"masses\":[[1,4],[1,4],[1,2]],\"support\":[9,16,22],\"t\":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-r06-cumulative-distribution-function-0023","batch_id":"batch-20261014-advance-20261030-r06-cumulative-distribution-function-foundations","language":"zh-Hant","source_mko_ids":["mko-cumulative-distribution-function"],"title_zh":"累積分布函數","stem_zh":"完整有限離散law與F(t)=P(X小於等於t)。操作=cdf-evaluate；資料={\"support\":[10,17,23],\"masses\":[[1,4],[1,4],[1,2]],\"t\":17}。請依 [t,F_t,boundary] 欄序回答。","answer":{"kind":"expression","value":"(17, 1/2, uses_X_less_than_or_equal_t)","explanation_zh":"Wave4第四層核對=(17, 1/2, uses_X_less_than_or_equal_t)；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；保留小於等於單調右連續與端點；CDF不混同PMF或density且jump為點質量。"},"difficulty":{"band":"undergraduate_core","level":3,"skills":["累積分布函數"]},"variant":{"family_id":"qf-mod30-cdf-evaluate","seed":202610306023,"parameters":{"support":[10,17,23],"masses":[[1,4],[1,4],[1,2]],"t":17,"domain":"Exact_finite_discrete_CDF","operation":"cdf-evaluate","semantic_template":"qf-mod30-cdf-evaluate/{\"masses\":[[1,4],[1,4],[1,2]],\"support\":[10,17,23],\"t\":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-r06-cumulative-distribution-function-0024","batch_id":"batch-20261014-advance-20261030-r06-cumulative-distribution-function-foundations","language":"zh-Hant","source_mko_ids":["mko-cumulative-distribution-function"],"title_zh":"累積分布函數","stem_zh":"完整有限離散law與F(t)=P(X小於等於t)。操作=cdf-evaluate；資料={\"support\":[11,18,24],\"masses\":[[1,4],[1,4],[1,2]],\"t\":24}。請依 [t,F_t,boundary] 欄序回答。","answer":{"kind":"expression","value":"(24, 1, uses_X_less_than_or_equal_t)","explanation_zh":"Wave4第四層核對=(24, 1, uses_X_less_than_or_equal_t)；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；保留小於等於單調右連續與端點；CDF不混同PMF或density且jump為點質量。"},"difficulty":{"band":"undergraduate_core","level":3,"skills":["累積分布函數"]},"variant":{"family_id":"qf-mod30-cdf-evaluate","seed":202610306024,"parameters":{"support":[11,18,24],"masses":[[1,4],[1,4],[1,2]],"t":24,"domain":"Exact_finite_discrete_CDF","operation":"cdf-evaluate","semantic_template":"qf-mod30-cdf-evaluate/{\"masses\":[[1,4],[1,4],[1,2]],\"support\":[11,18,24],\"t\":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-r06-cumulative-distribution-function-0025","batch_id":"batch-20261014-advance-20261030-r06-cumulative-distribution-function-foundations","language":"zh-Hant","source_mko_ids":["mko-cumulative-distribution-function"],"title_zh":"累積分布函數","stem_zh":"完整有限離散law與F(t)=P(X小於等於t)。操作=cdf-evaluate；資料={\"support\":[12,19,25],\"masses\":[[1,4],[1,4],[1,2]],\"t\":12}。請依 [t,F_t,boundary] 欄序回答。","answer":{"kind":"expression","value":"(12, 1/4, uses_X_less_than_or_equal_t)","explanation_zh":"Wave4第四層核對=(12, 1/4, uses_X_less_than_or_equal_t)；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；保留小於等於單調右連續與端點；CDF不混同PMF或density且jump為點質量。"},"difficulty":{"band":"undergraduate_core","level":3,"skills":["累積分布函數"]},"variant":{"family_id":"qf-mod30-cdf-evaluate","seed":202610306025,"parameters":{"support":[12,19,25],"masses":[[1,4],[1,4],[1,2]],"t":12,"domain":"Exact_finite_discrete_CDF","operation":"cdf-evaluate","semantic_template":"qf-mod30-cdf-evaluate/{\"masses\":[[1,4],[1,4],[1,2]],\"support\":[12,19,25],\"t\":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-r06-cumulative-distribution-function-0026","batch_id":"batch-20261014-advance-20261030-r06-cumulative-distribution-function-foundations","language":"zh-Hant","source_mko_ids":["mko-cumulative-distribution-function"],"title_zh":"累積分布函數","stem_zh":"完整有限離散law與F(t)=P(X小於等於t)。操作=cdf-jump；資料={\"support\":[-12,-5,1],\"masses\":[[1,4],[1,4],[1,2]],\"t\":-12}。請依 [t,left_limit,F_t,point_mass,jump_identity] 欄序回答。","answer":{"kind":"expression","value":"(-12, 0, 1/4, 1/4, 是)","explanation_zh":"Wave4第四層核對=(-12, 0, 1/4, 1/4, 是)；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；保留小於等於單調右連續與端點；CDF不混同PMF或density且jump為點質量。"},"difficulty":{"band":"undergraduate_core","level":1,"skills":["累積分布函數"]},"variant":{"family_id":"qf-mod30-cdf-jump","seed":202610306026,"parameters":{"support":[-12,-5,1],"masses":[[1,4],[1,4],[1,2]],"t":-12,"domain":"Exact_finite_discrete_CDF","operation":"cdf-jump","semantic_template":"qf-mod30-cdf-jump/{\"masses\":[[1,4],[1,4],[1,2]],\"support\":[-12,-5,1],\"t\":-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-r06-cumulative-distribution-function-0027","batch_id":"batch-20261014-advance-20261030-r06-cumulative-distribution-function-foundations","language":"zh-Hant","source_mko_ids":["mko-cumulative-distribution-function"],"title_zh":"累積分布函數","stem_zh":"完整有限離散law與F(t)=P(X小於等於t)。操作=cdf-jump；資料={\"support\":[-11,-4,2],\"masses\":[[1,4],[1,4],[1,2]],\"t\":-4}。請依 [t,left_limit,F_t,point_mass,jump_identity] 欄序回答。","answer":{"kind":"expression","value":"(-4, 1/4, 1/2, 1/4, 是)","explanation_zh":"Wave4第四層核對=(-4, 1/4, 1/2, 1/4, 是)；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；保留小於等於單調右連續與端點；CDF不混同PMF或density且jump為點質量。"},"difficulty":{"band":"undergraduate_core","level":1,"skills":["累積分布函數"]},"variant":{"family_id":"qf-mod30-cdf-jump","seed":202610306027,"parameters":{"support":[-11,-4,2],"masses":[[1,4],[1,4],[1,2]],"t":-4,"domain":"Exact_finite_discrete_CDF","operation":"cdf-jump","semantic_template":"qf-mod30-cdf-jump/{\"masses\":[[1,4],[1,4],[1,2]],\"support\":[-11,-4,2],\"t\":-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-r06-cumulative-distribution-function-0028","batch_id":"batch-20261014-advance-20261030-r06-cumulative-distribution-function-foundations","language":"zh-Hant","source_mko_ids":["mko-cumulative-distribution-function"],"title_zh":"累積分布函數","stem_zh":"完整有限離散law與F(t)=P(X小於等於t)。操作=cdf-jump；資料={\"support\":[-10,-3,3],\"masses\":[[1,4],[1,4],[1,2]],\"t\":3}。請依 [t,left_limit,F_t,point_mass,jump_identity] 欄序回答。","answer":{"kind":"expression","value":"(3, 1/2, 1, 1/2, 是)","explanation_zh":"Wave4第四層核對=(3, 1/2, 1, 1/2, 是)；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；保留小於等於單調右連續與端點；CDF不混同PMF或density且jump為點質量。"},"difficulty":{"band":"undergraduate_core","level":1,"skills":["累積分布函數"]},"variant":{"family_id":"qf-mod30-cdf-jump","seed":202610306028,"parameters":{"support":[-10,-3,3],"masses":[[1,4],[1,4],[1,2]],"t":3,"domain":"Exact_finite_discrete_CDF","operation":"cdf-jump","semantic_template":"qf-mod30-cdf-jump/{\"masses\":[[1,4],[1,4],[1,2]],\"support\":[-10,-3,3],\"t\":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-r06-cumulative-distribution-function-0029","batch_id":"batch-20261014-advance-20261030-r06-cumulative-distribution-function-foundations","language":"zh-Hant","source_mko_ids":["mko-cumulative-distribution-function"],"title_zh":"累積分布函數","stem_zh":"完整有限離散law與F(t)=P(X小於等於t)。操作=cdf-jump；資料={\"support\":[-9,-2,4],\"masses\":[[1,4],[1,4],[1,2]],\"t\":-9}。請依 [t,left_limit,F_t,point_mass,jump_identity] 欄序回答。","answer":{"kind":"expression","value":"(-9, 0, 1/4, 1/4, 是)","explanation_zh":"Wave4第四層核對=(-9, 0, 1/4, 1/4, 是)；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；保留小於等於單調右連續與端點；CDF不混同PMF或density且jump為點質量。"},"difficulty":{"band":"undergraduate_core","level":1,"skills":["累積分布函數"]},"variant":{"family_id":"qf-mod30-cdf-jump","seed":202610306029,"parameters":{"support":[-9,-2,4],"masses":[[1,4],[1,4],[1,2]],"t":-9,"domain":"Exact_finite_discrete_CDF","operation":"cdf-jump","semantic_template":"qf-mod30-cdf-jump/{\"masses\":[[1,4],[1,4],[1,2]],\"support\":[-9,-2,4],\"t\":-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-r06-cumulative-distribution-function-0030","batch_id":"batch-20261014-advance-20261030-r06-cumulative-distribution-function-foundations","language":"zh-Hant","source_mko_ids":["mko-cumulative-distribution-function"],"title_zh":"累積分布函數","stem_zh":"完整有限離散law與F(t)=P(X小於等於t)。操作=cdf-jump；資料={\"support\":[-8,-1,5],\"masses\":[[1,4],[1,4],[1,2]],\"t\":-1}。請依 [t,left_limit,F_t,point_mass,jump_identity] 欄序回答。","answer":{"kind":"expression","value":"(-1, 1/4, 1/2, 1/4, 是)","explanation_zh":"Wave4第四層核對=(-1, 1/4, 1/2, 1/4, 是)；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；保留小於等於單調右連續與端點；CDF不混同PMF或density且jump為點質量。"},"difficulty":{"band":"undergraduate_core","level":1,"skills":["累積分布函數"]},"variant":{"family_id":"qf-mod30-cdf-jump","seed":202610306030,"parameters":{"support":[-8,-1,5],"masses":[[1,4],[1,4],[1,2]],"t":-1,"domain":"Exact_finite_discrete_CDF","operation":"cdf-jump","semantic_template":"qf-mod30-cdf-jump/{\"masses\":[[1,4],[1,4],[1,2]],\"support\":[-8,-1,5],\"t\":-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-r06-cumulative-distribution-function-0031","batch_id":"batch-20261014-advance-20261030-r06-cumulative-distribution-function-foundations","language":"zh-Hant","source_mko_ids":["mko-cumulative-distribution-function"],"title_zh":"累積分布函數","stem_zh":"完整有限離散law與F(t)=P(X小於等於t)。操作=cdf-jump；資料={\"support\":[-7,0,6],\"masses\":[[1,4],[1,4],[1,2]],\"t\":6}。請依 [t,left_limit,F_t,point_mass,jump_identity] 欄序回答。","answer":{"kind":"expression","value":"(6, 1/2, 1, 1/2, 是)","explanation_zh":"Wave4第四層核對=(6, 1/2, 1, 1/2, 是)；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；保留小於等於單調右連續與端點；CDF不混同PMF或density且jump為點質量。"},"difficulty":{"band":"undergraduate_core","level":1,"skills":["累積分布函數"]},"variant":{"family_id":"qf-mod30-cdf-jump","seed":202610306031,"parameters":{"support":[-7,0,6],"masses":[[1,4],[1,4],[1,2]],"t":6,"domain":"Exact_finite_discrete_CDF","operation":"cdf-jump","semantic_template":"qf-mod30-cdf-jump/{\"masses\":[[1,4],[1,4],[1,2]],\"support\":[-7,0,6],\"t\":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-r06-cumulative-distribution-function-0032","batch_id":"batch-20261014-advance-20261030-r06-cumulative-distribution-function-foundations","language":"zh-Hant","source_mko_ids":["mko-cumulative-distribution-function"],"title_zh":"累積分布函數","stem_zh":"完整有限離散law與F(t)=P(X小於等於t)。操作=cdf-jump；資料={\"support\":[-6,1,7],\"masses\":[[1,4],[1,4],[1,2]],\"t\":-6}。請依 [t,left_limit,F_t,point_mass,jump_identity] 欄序回答。","answer":{"kind":"expression","value":"(-6, 0, 1/4, 1/4, 是)","explanation_zh":"Wave4第四層核對=(-6, 0, 1/4, 1/4, 是)；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；保留小於等於單調右連續與端點；CDF不混同PMF或density且jump為點質量。"},"difficulty":{"band":"undergraduate_core","level":1,"skills":["累積分布函數"]},"variant":{"family_id":"qf-mod30-cdf-jump","seed":202610306032,"parameters":{"support":[-6,1,7],"masses":[[1,4],[1,4],[1,2]],"t":-6,"domain":"Exact_finite_discrete_CDF","operation":"cdf-jump","semantic_template":"qf-mod30-cdf-jump/{\"masses\":[[1,4],[1,4],[1,2]],\"support\":[-6,1,7],\"t\":-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-r06-cumulative-distribution-function-0033","batch_id":"batch-20261014-advance-20261030-r06-cumulative-distribution-function-foundations","language":"zh-Hant","source_mko_ids":["mko-cumulative-distribution-function"],"title_zh":"累積分布函數","stem_zh":"完整有限離散law與F(t)=P(X小於等於t)。操作=cdf-jump；資料={\"support\":[-5,2,8],\"masses\":[[1,4],[1,4],[1,2]],\"t\":2}。請依 [t,left_limit,F_t,point_mass,jump_identity] 欄序回答。","answer":{"kind":"expression","value":"(2, 1/4, 1/2, 1/4, 是)","explanation_zh":"Wave4第四層核對=(2, 1/4, 1/2, 1/4, 是)；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；保留小於等於單調右連續與端點；CDF不混同PMF或density且jump為點質量。"},"difficulty":{"band":"undergraduate_core","level":1,"skills":["累積分布函數"]},"variant":{"family_id":"qf-mod30-cdf-jump","seed":202610306033,"parameters":{"support":[-5,2,8],"masses":[[1,4],[1,4],[1,2]],"t":2,"domain":"Exact_finite_discrete_CDF","operation":"cdf-jump","semantic_template":"qf-mod30-cdf-jump/{\"masses\":[[1,4],[1,4],[1,2]],\"support\":[-5,2,8],\"t\":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-r06-cumulative-distribution-function-0034","batch_id":"batch-20261014-advance-20261030-r06-cumulative-distribution-function-foundations","language":"zh-Hant","source_mko_ids":["mko-cumulative-distribution-function"],"title_zh":"累積分布函數","stem_zh":"完整有限離散law與F(t)=P(X小於等於t)。操作=cdf-jump；資料={\"support\":[-4,3,9],\"masses\":[[1,4],[1,4],[1,2]],\"t\":9}。請依 [t,left_limit,F_t,point_mass,jump_identity] 欄序回答。","answer":{"kind":"expression","value":"(9, 1/2, 1, 1/2, 是)","explanation_zh":"Wave4第四層核對=(9, 1/2, 1, 1/2, 是)；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；保留小於等於單調右連續與端點；CDF不混同PMF或density且jump為點質量。"},"difficulty":{"band":"undergraduate_core","level":2,"skills":["累積分布函數"]},"variant":{"family_id":"qf-mod30-cdf-jump","seed":202610306034,"parameters":{"support":[-4,3,9],"masses":[[1,4],[1,4],[1,2]],"t":9,"domain":"Exact_finite_discrete_CDF","operation":"cdf-jump","semantic_template":"qf-mod30-cdf-jump/{\"masses\":[[1,4],[1,4],[1,2]],\"support\":[-4,3,9],\"t\":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-r06-cumulative-distribution-function-0035","batch_id":"batch-20261014-advance-20261030-r06-cumulative-distribution-function-foundations","language":"zh-Hant","source_mko_ids":["mko-cumulative-distribution-function"],"title_zh":"累積分布函數","stem_zh":"完整有限離散law與F(t)=P(X小於等於t)。操作=cdf-jump；資料={\"support\":[-3,4,10],\"masses\":[[1,4],[1,4],[1,2]],\"t\":-3}。請依 [t,left_limit,F_t,point_mass,jump_identity] 欄序回答。","answer":{"kind":"expression","value":"(-3, 0, 1/4, 1/4, 是)","explanation_zh":"Wave4第四層核對=(-3, 0, 1/4, 1/4, 是)；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；保留小於等於單調右連續與端點；CDF不混同PMF或density且jump為點質量。"},"difficulty":{"band":"undergraduate_core","level":2,"skills":["累積分布函數"]},"variant":{"family_id":"qf-mod30-cdf-jump","seed":202610306035,"parameters":{"support":[-3,4,10],"masses":[[1,4],[1,4],[1,2]],"t":-3,"domain":"Exact_finite_discrete_CDF","operation":"cdf-jump","semantic_template":"qf-mod30-cdf-jump/{\"masses\":[[1,4],[1,4],[1,2]],\"support\":[-3,4,10],\"t\":-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-r06-cumulative-distribution-function-0036","batch_id":"batch-20261014-advance-20261030-r06-cumulative-distribution-function-foundations","language":"zh-Hant","source_mko_ids":["mko-cumulative-distribution-function"],"title_zh":"累積分布函數","stem_zh":"完整有限離散law與F(t)=P(X小於等於t)。操作=cdf-jump；資料={\"support\":[-2,5,11],\"masses\":[[1,4],[1,4],[1,2]],\"t\":5}。請依 [t,left_limit,F_t,point_mass,jump_identity] 欄序回答。","answer":{"kind":"expression","value":"(5, 1/4, 1/2, 1/4, 是)","explanation_zh":"Wave4第四層核對=(5, 1/4, 1/2, 1/4, 是)；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；保留小於等於單調右連續與端點；CDF不混同PMF或density且jump為點質量。"},"difficulty":{"band":"undergraduate_core","level":2,"skills":["累積分布函數"]},"variant":{"family_id":"qf-mod30-cdf-jump","seed":202610306036,"parameters":{"support":[-2,5,11],"masses":[[1,4],[1,4],[1,2]],"t":5,"domain":"Exact_finite_discrete_CDF","operation":"cdf-jump","semantic_template":"qf-mod30-cdf-jump/{\"masses\":[[1,4],[1,4],[1,2]],\"support\":[-2,5,11],\"t\":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-r06-cumulative-distribution-function-0037","batch_id":"batch-20261014-advance-20261030-r06-cumulative-distribution-function-foundations","language":"zh-Hant","source_mko_ids":["mko-cumulative-distribution-function"],"title_zh":"累積分布函數","stem_zh":"完整有限離散law與F(t)=P(X小於等於t)。操作=cdf-jump；資料={\"support\":[-1,6,12],\"masses\":[[1,4],[1,4],[1,2]],\"t\":12}。請依 [t,left_limit,F_t,point_mass,jump_identity] 欄序回答。","answer":{"kind":"expression","value":"(12, 1/2, 1, 1/2, 是)","explanation_zh":"Wave4第四層核對=(12, 1/2, 1, 1/2, 是)；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；保留小於等於單調右連續與端點；CDF不混同PMF或density且jump為點質量。"},"difficulty":{"band":"undergraduate_core","level":2,"skills":["累積分布函數"]},"variant":{"family_id":"qf-mod30-cdf-jump","seed":202610306037,"parameters":{"support":[-1,6,12],"masses":[[1,4],[1,4],[1,2]],"t":12,"domain":"Exact_finite_discrete_CDF","operation":"cdf-jump","semantic_template":"qf-mod30-cdf-jump/{\"masses\":[[1,4],[1,4],[1,2]],\"support\":[-1,6,12],\"t\":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-r06-cumulative-distribution-function-0038","batch_id":"batch-20261014-advance-20261030-r06-cumulative-distribution-function-foundations","language":"zh-Hant","source_mko_ids":["mko-cumulative-distribution-function"],"title_zh":"累積分布函數","stem_zh":"完整有限離散law與F(t)=P(X小於等於t)。操作=cdf-jump；資料={\"support\":[0,7,13],\"masses\":[[1,4],[1,4],[1,2]],\"t\":0}。請依 [t,left_limit,F_t,point_mass,jump_identity] 欄序回答。","answer":{"kind":"expression","value":"(0, 0, 1/4, 1/4, 是)","explanation_zh":"Wave4第四層核對=(0, 0, 1/4, 1/4, 是)；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；保留小於等於單調右連續與端點；CDF不混同PMF或density且jump為點質量。"},"difficulty":{"band":"undergraduate_core","level":2,"skills":["累積分布函數"]},"variant":{"family_id":"qf-mod30-cdf-jump","seed":202610306038,"parameters":{"support":[0,7,13],"masses":[[1,4],[1,4],[1,2]],"t":0,"domain":"Exact_finite_discrete_CDF","operation":"cdf-jump","semantic_template":"qf-mod30-cdf-jump/{\"masses\":[[1,4],[1,4],[1,2]],\"support\":[0,7,13],\"t\":0}"}},"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-r06-cumulative-distribution-function-0039","batch_id":"batch-20261014-advance-20261030-r06-cumulative-distribution-function-foundations","language":"zh-Hant","source_mko_ids":["mko-cumulative-distribution-function"],"title_zh":"累積分布函數","stem_zh":"完整有限離散law與F(t)=P(X小於等於t)。操作=cdf-jump；資料={\"support\":[1,8,14],\"masses\":[[1,4],[1,4],[1,2]],\"t\":8}。請依 [t,left_limit,F_t,point_mass,jump_identity] 欄序回答。","answer":{"kind":"expression","value":"(8, 1/4, 1/2, 1/4, 是)","explanation_zh":"Wave4第四層核對=(8, 1/4, 1/2, 1/4, 是)；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；保留小於等於單調右連續與端點；CDF不混同PMF或density且jump為點質量。"},"difficulty":{"band":"undergraduate_core","level":2,"skills":["累積分布函數"]},"variant":{"family_id":"qf-mod30-cdf-jump","seed":202610306039,"parameters":{"support":[1,8,14],"masses":[[1,4],[1,4],[1,2]],"t":8,"domain":"Exact_finite_discrete_CDF","operation":"cdf-jump","semantic_template":"qf-mod30-cdf-jump/{\"masses\":[[1,4],[1,4],[1,2]],\"support\":[1,8,14],\"t\":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-r06-cumulative-distribution-function-0040","batch_id":"batch-20261014-advance-20261030-r06-cumulative-distribution-function-foundations","language":"zh-Hant","source_mko_ids":["mko-cumulative-distribution-function"],"title_zh":"累積分布函數","stem_zh":"完整有限離散law與F(t)=P(X小於等於t)。操作=cdf-jump；資料={\"support\":[2,9,15],\"masses\":[[1,4],[1,4],[1,2]],\"t\":15}。請依 [t,left_limit,F_t,point_mass,jump_identity] 欄序回答。","answer":{"kind":"expression","value":"(15, 1/2, 1, 1/2, 是)","explanation_zh":"Wave4第四層核對=(15, 1/2, 1, 1/2, 是)；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；保留小於等於單調右連續與端點；CDF不混同PMF或density且jump為點質量。"},"difficulty":{"band":"undergraduate_core","level":2,"skills":["累積分布函數"]},"variant":{"family_id":"qf-mod30-cdf-jump","seed":202610306040,"parameters":{"support":[2,9,15],"masses":[[1,4],[1,4],[1,2]],"t":15,"domain":"Exact_finite_discrete_CDF","operation":"cdf-jump","semantic_template":"qf-mod30-cdf-jump/{\"masses\":[[1,4],[1,4],[1,2]],\"support\":[2,9,15],\"t\":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-r06-cumulative-distribution-function-0041","batch_id":"batch-20261014-advance-20261030-r06-cumulative-distribution-function-foundations","language":"zh-Hant","source_mko_ids":["mko-cumulative-distribution-function"],"title_zh":"累積分布函數","stem_zh":"完整有限離散law與F(t)=P(X小於等於t)。操作=cdf-jump；資料={\"support\":[3,10,16],\"masses\":[[1,4],[1,4],[1,2]],\"t\":3}。請依 [t,left_limit,F_t,point_mass,jump_identity] 欄序回答。","answer":{"kind":"expression","value":"(3, 0, 1/4, 1/4, 是)","explanation_zh":"Wave4第四層核對=(3, 0, 1/4, 1/4, 是)；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；保留小於等於單調右連續與端點；CDF不混同PMF或density且jump為點質量。"},"difficulty":{"band":"undergraduate_core","level":2,"skills":["累積分布函數"]},"variant":{"family_id":"qf-mod30-cdf-jump","seed":202610306041,"parameters":{"support":[3,10,16],"masses":[[1,4],[1,4],[1,2]],"t":3,"domain":"Exact_finite_discrete_CDF","operation":"cdf-jump","semantic_template":"qf-mod30-cdf-jump/{\"masses\":[[1,4],[1,4],[1,2]],\"support\":[3,10,16],\"t\":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-r06-cumulative-distribution-function-0042","batch_id":"batch-20261014-advance-20261030-r06-cumulative-distribution-function-foundations","language":"zh-Hant","source_mko_ids":["mko-cumulative-distribution-function"],"title_zh":"累積分布函數","stem_zh":"完整有限離散law與F(t)=P(X小於等於t)。操作=cdf-jump；資料={\"support\":[4,11,17],\"masses\":[[1,4],[1,4],[1,2]],\"t\":11}。請依 [t,left_limit,F_t,point_mass,jump_identity] 欄序回答。","answer":{"kind":"expression","value":"(11, 1/4, 1/2, 1/4, 是)","explanation_zh":"Wave4第四層核對=(11, 1/4, 1/2, 1/4, 是)；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；保留小於等於單調右連續與端點；CDF不混同PMF或density且jump為點質量。"},"difficulty":{"band":"undergraduate_core","level":2,"skills":["累積分布函數"]},"variant":{"family_id":"qf-mod30-cdf-jump","seed":202610306042,"parameters":{"support":[4,11,17],"masses":[[1,4],[1,4],[1,2]],"t":11,"domain":"Exact_finite_discrete_CDF","operation":"cdf-jump","semantic_template":"qf-mod30-cdf-jump/{\"masses\":[[1,4],[1,4],[1,2]],\"support\":[4,11,17],\"t\":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-r06-cumulative-distribution-function-0043","batch_id":"batch-20261014-advance-20261030-r06-cumulative-distribution-function-foundations","language":"zh-Hant","source_mko_ids":["mko-cumulative-distribution-function"],"title_zh":"累積分布函數","stem_zh":"完整有限離散law與F(t)=P(X小於等於t)。操作=cdf-jump；資料={\"support\":[5,12,18],\"masses\":[[1,4],[1,4],[1,2]],\"t\":18}。請依 [t,left_limit,F_t,point_mass,jump_identity] 欄序回答。","answer":{"kind":"expression","value":"(18, 1/2, 1, 1/2, 是)","explanation_zh":"Wave4第四層核對=(18, 1/2, 1, 1/2, 是)；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；保留小於等於單調右連續與端點；CDF不混同PMF或density且jump為點質量。"},"difficulty":{"band":"undergraduate_core","level":3,"skills":["累積分布函數"]},"variant":{"family_id":"qf-mod30-cdf-jump","seed":202610306043,"parameters":{"support":[5,12,18],"masses":[[1,4],[1,4],[1,2]],"t":18,"domain":"Exact_finite_discrete_CDF","operation":"cdf-jump","semantic_template":"qf-mod30-cdf-jump/{\"masses\":[[1,4],[1,4],[1,2]],\"support\":[5,12,18],\"t\":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-r06-cumulative-distribution-function-0044","batch_id":"batch-20261014-advance-20261030-r06-cumulative-distribution-function-foundations","language":"zh-Hant","source_mko_ids":["mko-cumulative-distribution-function"],"title_zh":"累積分布函數","stem_zh":"完整有限離散law與F(t)=P(X小於等於t)。操作=cdf-jump；資料={\"support\":[6,13,19],\"masses\":[[1,4],[1,4],[1,2]],\"t\":6}。請依 [t,left_limit,F_t,point_mass,jump_identity] 欄序回答。","answer":{"kind":"expression","value":"(6, 0, 1/4, 1/4, 是)","explanation_zh":"Wave4第四層核對=(6, 0, 1/4, 1/4, 是)；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；保留小於等於單調右連續與端點；CDF不混同PMF或density且jump為點質量。"},"difficulty":{"band":"undergraduate_core","level":3,"skills":["累積分布函數"]},"variant":{"family_id":"qf-mod30-cdf-jump","seed":202610306044,"parameters":{"support":[6,13,19],"masses":[[1,4],[1,4],[1,2]],"t":6,"domain":"Exact_finite_discrete_CDF","operation":"cdf-jump","semantic_template":"qf-mod30-cdf-jump/{\"masses\":[[1,4],[1,4],[1,2]],\"support\":[6,13,19],\"t\":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-r06-cumulative-distribution-function-0045","batch_id":"batch-20261014-advance-20261030-r06-cumulative-distribution-function-foundations","language":"zh-Hant","source_mko_ids":["mko-cumulative-distribution-function"],"title_zh":"累積分布函數","stem_zh":"完整有限離散law與F(t)=P(X小於等於t)。操作=cdf-jump；資料={\"support\":[7,14,20],\"masses\":[[1,4],[1,4],[1,2]],\"t\":14}。請依 [t,left_limit,F_t,point_mass,jump_identity] 欄序回答。","answer":{"kind":"expression","value":"(14, 1/4, 1/2, 1/4, 是)","explanation_zh":"Wave4第四層核對=(14, 1/4, 1/2, 1/4, 是)；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；保留小於等於單調右連續與端點；CDF不混同PMF或density且jump為點質量。"},"difficulty":{"band":"undergraduate_core","level":3,"skills":["累積分布函數"]},"variant":{"family_id":"qf-mod30-cdf-jump","seed":202610306045,"parameters":{"support":[7,14,20],"masses":[[1,4],[1,4],[1,2]],"t":14,"domain":"Exact_finite_discrete_CDF","operation":"cdf-jump","semantic_template":"qf-mod30-cdf-jump/{\"masses\":[[1,4],[1,4],[1,2]],\"support\":[7,14,20],\"t\":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-r06-cumulative-distribution-function-0046","batch_id":"batch-20261014-advance-20261030-r06-cumulative-distribution-function-foundations","language":"zh-Hant","source_mko_ids":["mko-cumulative-distribution-function"],"title_zh":"累積分布函數","stem_zh":"完整有限離散law與F(t)=P(X小於等於t)。操作=cdf-jump；資料={\"support\":[8,15,21],\"masses\":[[1,4],[1,4],[1,2]],\"t\":21}。請依 [t,left_limit,F_t,point_mass,jump_identity] 欄序回答。","answer":{"kind":"expression","value":"(21, 1/2, 1, 1/2, 是)","explanation_zh":"Wave4第四層核對=(21, 1/2, 1, 1/2, 是)；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；保留小於等於單調右連續與端點；CDF不混同PMF或density且jump為點質量。"},"difficulty":{"band":"undergraduate_core","level":3,"skills":["累積分布函數"]},"variant":{"family_id":"qf-mod30-cdf-jump","seed":202610306046,"parameters":{"support":[8,15,21],"masses":[[1,4],[1,4],[1,2]],"t":21,"domain":"Exact_finite_discrete_CDF","operation":"cdf-jump","semantic_template":"qf-mod30-cdf-jump/{\"masses\":[[1,4],[1,4],[1,2]],\"support\":[8,15,21],\"t\":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-r06-cumulative-distribution-function-0047","batch_id":"batch-20261014-advance-20261030-r06-cumulative-distribution-function-foundations","language":"zh-Hant","source_mko_ids":["mko-cumulative-distribution-function"],"title_zh":"累積分布函數","stem_zh":"完整有限離散law與F(t)=P(X小於等於t)。操作=cdf-jump；資料={\"support\":[9,16,22],\"masses\":[[1,4],[1,4],[1,2]],\"t\":9}。請依 [t,left_limit,F_t,point_mass,jump_identity] 欄序回答。","answer":{"kind":"expression","value":"(9, 0, 1/4, 1/4, 是)","explanation_zh":"Wave4第四層核對=(9, 0, 1/4, 1/4, 是)；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；保留小於等於單調右連續與端點；CDF不混同PMF或density且jump為點質量。"},"difficulty":{"band":"undergraduate_core","level":3,"skills":["累積分布函數"]},"variant":{"family_id":"qf-mod30-cdf-jump","seed":202610306047,"parameters":{"support":[9,16,22],"masses":[[1,4],[1,4],[1,2]],"t":9,"domain":"Exact_finite_discrete_CDF","operation":"cdf-jump","semantic_template":"qf-mod30-cdf-jump/{\"masses\":[[1,4],[1,4],[1,2]],\"support\":[9,16,22],\"t\":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-r06-cumulative-distribution-function-0048","batch_id":"batch-20261014-advance-20261030-r06-cumulative-distribution-function-foundations","language":"zh-Hant","source_mko_ids":["mko-cumulative-distribution-function"],"title_zh":"累積分布函數","stem_zh":"完整有限離散law與F(t)=P(X小於等於t)。操作=cdf-jump；資料={\"support\":[10,17,23],\"masses\":[[1,4],[1,4],[1,2]],\"t\":17}。請依 [t,left_limit,F_t,point_mass,jump_identity] 欄序回答。","answer":{"kind":"expression","value":"(17, 1/4, 1/2, 1/4, 是)","explanation_zh":"Wave4第四層核對=(17, 1/4, 1/2, 1/4, 是)；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；保留小於等於單調右連續與端點；CDF不混同PMF或density且jump為點質量。"},"difficulty":{"band":"undergraduate_core","level":3,"skills":["累積分布函數"]},"variant":{"family_id":"qf-mod30-cdf-jump","seed":202610306048,"parameters":{"support":[10,17,23],"masses":[[1,4],[1,4],[1,2]],"t":17,"domain":"Exact_finite_discrete_CDF","operation":"cdf-jump","semantic_template":"qf-mod30-cdf-jump/{\"masses\":[[1,4],[1,4],[1,2]],\"support\":[10,17,23],\"t\":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-r06-cumulative-distribution-function-0049","batch_id":"batch-20261014-advance-20261030-r06-cumulative-distribution-function-foundations","language":"zh-Hant","source_mko_ids":["mko-cumulative-distribution-function"],"title_zh":"累積分布函數","stem_zh":"完整有限離散law與F(t)=P(X小於等於t)。操作=cdf-jump；資料={\"support\":[11,18,24],\"masses\":[[1,4],[1,4],[1,2]],\"t\":24}。請依 [t,left_limit,F_t,point_mass,jump_identity] 欄序回答。","answer":{"kind":"expression","value":"(24, 1/2, 1, 1/2, 是)","explanation_zh":"Wave4第四層核對=(24, 1/2, 1, 1/2, 是)；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；保留小於等於單調右連續與端點；CDF不混同PMF或density且jump為點質量。"},"difficulty":{"band":"undergraduate_core","level":3,"skills":["累積分布函數"]},"variant":{"family_id":"qf-mod30-cdf-jump","seed":202610306049,"parameters":{"support":[11,18,24],"masses":[[1,4],[1,4],[1,2]],"t":24,"domain":"Exact_finite_discrete_CDF","operation":"cdf-jump","semantic_template":"qf-mod30-cdf-jump/{\"masses\":[[1,4],[1,4],[1,2]],\"support\":[11,18,24],\"t\":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-r06-cumulative-distribution-function-0050","batch_id":"batch-20261014-advance-20261030-r06-cumulative-distribution-function-foundations","language":"zh-Hant","source_mko_ids":["mko-cumulative-distribution-function"],"title_zh":"累積分布函數","stem_zh":"完整有限離散law與F(t)=P(X小於等於t)。操作=cdf-jump；資料={\"support\":[12,19,25],\"masses\":[[1,4],[1,4],[1,2]],\"t\":12}。請依 [t,left_limit,F_t,point_mass,jump_identity] 欄序回答。","answer":{"kind":"expression","value":"(12, 0, 1/4, 1/4, 是)","explanation_zh":"Wave4第四層核對=(12, 0, 1/4, 1/4, 是)；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；保留小於等於單調右連續與端點；CDF不混同PMF或density且jump為點質量。"},"difficulty":{"band":"undergraduate_core","level":3,"skills":["累積分布函數"]},"variant":{"family_id":"qf-mod30-cdf-jump","seed":202610306050,"parameters":{"support":[12,19,25],"masses":[[1,4],[1,4],[1,2]],"t":12,"domain":"Exact_finite_discrete_CDF","operation":"cdf-jump","semantic_template":"qf-mod30-cdf-jump/{\"masses\":[[1,4],[1,4],[1,2]],\"support\":[12,19,25],\"t\":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-r06-cumulative-distribution-function-0051","batch_id":"batch-20261014-advance-20261030-r06-cumulative-distribution-function-foundations","language":"zh-Hant","source_mko_ids":["mko-cumulative-distribution-function"],"title_zh":"累積分布函數","stem_zh":"完整有限離散law與F(t)=P(X小於等於t)。操作=cdf-monotonicity；資料={\"support\":[-12,-5,1],\"masses\":[[1,4],[1,4],[1,2]],\"left\":-12,\"right\":1}。請依 [left,right,F_left,F_right,monotone] 欄序回答。","answer":{"kind":"expression","value":"(-12, 1, 1/4, 1, 是)","explanation_zh":"Wave4第四層核對=(-12, 1, 1/4, 1, 是)；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；保留小於等於單調右連續與端點；CDF不混同PMF或density且jump為點質量。"},"difficulty":{"band":"undergraduate_core","level":1,"skills":["累積分布函數"]},"variant":{"family_id":"qf-mod30-cdf-monotonicity","seed":202610306051,"parameters":{"support":[-12,-5,1],"masses":[[1,4],[1,4],[1,2]],"left":-12,"right":1,"domain":"Exact_finite_discrete_CDF","operation":"cdf-monotonicity","semantic_template":"qf-mod30-cdf-monotonicity/{\"left\":-12,\"masses\":[[1,4],[1,4],[1,2]],\"right\":1,\"support\":[-12,-5,1]}"}},"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-r06-cumulative-distribution-function-0052","batch_id":"batch-20261014-advance-20261030-r06-cumulative-distribution-function-foundations","language":"zh-Hant","source_mko_ids":["mko-cumulative-distribution-function"],"title_zh":"累積分布函數","stem_zh":"完整有限離散law與F(t)=P(X小於等於t)。操作=cdf-monotonicity；資料={\"support\":[-11,-4,2],\"masses\":[[1,4],[1,4],[1,2]],\"left\":-11,\"right\":2}。請依 [left,right,F_left,F_right,monotone] 欄序回答。","answer":{"kind":"expression","value":"(-11, 2, 1/4, 1, 是)","explanation_zh":"Wave4第四層核對=(-11, 2, 1/4, 1, 是)；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；保留小於等於單調右連續與端點；CDF不混同PMF或density且jump為點質量。"},"difficulty":{"band":"undergraduate_core","level":1,"skills":["累積分布函數"]},"variant":{"family_id":"qf-mod30-cdf-monotonicity","seed":202610306052,"parameters":{"support":[-11,-4,2],"masses":[[1,4],[1,4],[1,2]],"left":-11,"right":2,"domain":"Exact_finite_discrete_CDF","operation":"cdf-monotonicity","semantic_template":"qf-mod30-cdf-monotonicity/{\"left\":-11,\"masses\":[[1,4],[1,4],[1,2]],\"right\":2,\"support\":[-11,-4,2]}"}},"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-r06-cumulative-distribution-function-0053","batch_id":"batch-20261014-advance-20261030-r06-cumulative-distribution-function-foundations","language":"zh-Hant","source_mko_ids":["mko-cumulative-distribution-function"],"title_zh":"累積分布函數","stem_zh":"完整有限離散law與F(t)=P(X小於等於t)。操作=cdf-monotonicity；資料={\"support\":[-10,-3,3],\"masses\":[[1,4],[1,4],[1,2]],\"left\":-10,\"right\":3}。請依 [left,right,F_left,F_right,monotone] 欄序回答。","answer":{"kind":"expression","value":"(-10, 3, 1/4, 1, 是)","explanation_zh":"Wave4第四層核對=(-10, 3, 1/4, 1, 是)；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；保留小於等於單調右連續與端點；CDF不混同PMF或density且jump為點質量。"},"difficulty":{"band":"undergraduate_core","level":1,"skills":["累積分布函數"]},"variant":{"family_id":"qf-mod30-cdf-monotonicity","seed":202610306053,"parameters":{"support":[-10,-3,3],"masses":[[1,4],[1,4],[1,2]],"left":-10,"right":3,"domain":"Exact_finite_discrete_CDF","operation":"cdf-monotonicity","semantic_template":"qf-mod30-cdf-monotonicity/{\"left\":-10,\"masses\":[[1,4],[1,4],[1,2]],\"right\":3,\"support\":[-10,-3,3]}"}},"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-r06-cumulative-distribution-function-0054","batch_id":"batch-20261014-advance-20261030-r06-cumulative-distribution-function-foundations","language":"zh-Hant","source_mko_ids":["mko-cumulative-distribution-function"],"title_zh":"累積分布函數","stem_zh":"完整有限離散law與F(t)=P(X小於等於t)。操作=cdf-monotonicity；資料={\"support\":[-9,-2,4],\"masses\":[[1,4],[1,4],[1,2]],\"left\":-9,\"right\":4}。請依 [left,right,F_left,F_right,monotone] 欄序回答。","answer":{"kind":"expression","value":"(-9, 4, 1/4, 1, 是)","explanation_zh":"Wave4第四層核對=(-9, 4, 1/4, 1, 是)；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；保留小於等於單調右連續與端點；CDF不混同PMF或density且jump為點質量。"},"difficulty":{"band":"undergraduate_core","level":1,"skills":["累積分布函數"]},"variant":{"family_id":"qf-mod30-cdf-monotonicity","seed":202610306054,"parameters":{"support":[-9,-2,4],"masses":[[1,4],[1,4],[1,2]],"left":-9,"right":4,"domain":"Exact_finite_discrete_CDF","operation":"cdf-monotonicity","semantic_template":"qf-mod30-cdf-monotonicity/{\"left\":-9,\"masses\":[[1,4],[1,4],[1,2]],\"right\":4,\"support\":[-9,-2,4]}"}},"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-r06-cumulative-distribution-function-0055","batch_id":"batch-20261014-advance-20261030-r06-cumulative-distribution-function-foundations","language":"zh-Hant","source_mko_ids":["mko-cumulative-distribution-function"],"title_zh":"累積分布函數","stem_zh":"完整有限離散law與F(t)=P(X小於等於t)。操作=cdf-monotonicity；資料={\"support\":[-8,-1,5],\"masses\":[[1,4],[1,4],[1,2]],\"left\":-8,\"right\":5}。請依 [left,right,F_left,F_right,monotone] 欄序回答。","answer":{"kind":"expression","value":"(-8, 5, 1/4, 1, 是)","explanation_zh":"Wave4第四層核對=(-8, 5, 1/4, 1, 是)；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；保留小於等於單調右連續與端點；CDF不混同PMF或density且jump為點質量。"},"difficulty":{"band":"undergraduate_core","level":1,"skills":["累積分布函數"]},"variant":{"family_id":"qf-mod30-cdf-monotonicity","seed":202610306055,"parameters":{"support":[-8,-1,5],"masses":[[1,4],[1,4],[1,2]],"left":-8,"right":5,"domain":"Exact_finite_discrete_CDF","operation":"cdf-monotonicity","semantic_template":"qf-mod30-cdf-monotonicity/{\"left\":-8,\"masses\":[[1,4],[1,4],[1,2]],\"right\":5,\"support\":[-8,-1,5]}"}},"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-r06-cumulative-distribution-function-0056","batch_id":"batch-20261014-advance-20261030-r06-cumulative-distribution-function-foundations","language":"zh-Hant","source_mko_ids":["mko-cumulative-distribution-function"],"title_zh":"累積分布函數","stem_zh":"完整有限離散law與F(t)=P(X小於等於t)。操作=cdf-monotonicity；資料={\"support\":[-7,0,6],\"masses\":[[1,4],[1,4],[1,2]],\"left\":-7,\"right\":6}。請依 [left,right,F_left,F_right,monotone] 欄序回答。","answer":{"kind":"expression","value":"(-7, 6, 1/4, 1, 是)","explanation_zh":"Wave4第四層核對=(-7, 6, 1/4, 1, 是)；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；保留小於等於單調右連續與端點；CDF不混同PMF或density且jump為點質量。"},"difficulty":{"band":"undergraduate_core","level":1,"skills":["累積分布函數"]},"variant":{"family_id":"qf-mod30-cdf-monotonicity","seed":202610306056,"parameters":{"support":[-7,0,6],"masses":[[1,4],[1,4],[1,2]],"left":-7,"right":6,"domain":"Exact_finite_discrete_CDF","operation":"cdf-monotonicity","semantic_template":"qf-mod30-cdf-monotonicity/{\"left\":-7,\"masses\":[[1,4],[1,4],[1,2]],\"right\":6,\"support\":[-7,0,6]}"}},"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-r06-cumulative-distribution-function-0057","batch_id":"batch-20261014-advance-20261030-r06-cumulative-distribution-function-foundations","language":"zh-Hant","source_mko_ids":["mko-cumulative-distribution-function"],"title_zh":"累積分布函數","stem_zh":"完整有限離散law與F(t)=P(X小於等於t)。操作=cdf-monotonicity；資料={\"support\":[-6,1,7],\"masses\":[[1,4],[1,4],[1,2]],\"left\":-6,\"right\":7}。請依 [left,right,F_left,F_right,monotone] 欄序回答。","answer":{"kind":"expression","value":"(-6, 7, 1/4, 1, 是)","explanation_zh":"Wave4第四層核對=(-6, 7, 1/4, 1, 是)；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；保留小於等於單調右連續與端點；CDF不混同PMF或density且jump為點質量。"},"difficulty":{"band":"undergraduate_core","level":1,"skills":["累積分布函數"]},"variant":{"family_id":"qf-mod30-cdf-monotonicity","seed":202610306057,"parameters":{"support":[-6,1,7],"masses":[[1,4],[1,4],[1,2]],"left":-6,"right":7,"domain":"Exact_finite_discrete_CDF","operation":"cdf-monotonicity","semantic_template":"qf-mod30-cdf-monotonicity/{\"left\":-6,\"masses\":[[1,4],[1,4],[1,2]],\"right\":7,\"support\":[-6,1,7]}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_model","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"候選須主端重算；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-r06-cumulative-distribution-function-0058","batch_id":"batch-20261014-advance-20261030-r06-cumulative-distribution-function-foundations","language":"zh-Hant","source_mko_ids":["mko-cumulative-distribution-function"],"title_zh":"累積分布函數","stem_zh":"完整有限離散law與F(t)=P(X小於等於t)。操作=cdf-monotonicity；資料={\"support\":[-5,2,8],\"masses\":[[1,4],[1,4],[1,2]],\"left\":-5,\"right\":8}。請依 [left,right,F_left,F_right,monotone] 欄序回答。","answer":{"kind":"expression","value":"(-5, 8, 1/4, 1, 是)","explanation_zh":"Wave4第四層核對=(-5, 8, 1/4, 1, 是)；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；保留小於等於單調右連續與端點；CDF不混同PMF或density且jump為點質量。"},"difficulty":{"band":"undergraduate_core","level":1,"skills":["累積分布函數"]},"variant":{"family_id":"qf-mod30-cdf-monotonicity","seed":202610306058,"parameters":{"support":[-5,2,8],"masses":[[1,4],[1,4],[1,2]],"left":-5,"right":8,"domain":"Exact_finite_discrete_CDF","operation":"cdf-monotonicity","semantic_template":"qf-mod30-cdf-monotonicity/{\"left\":-5,\"masses\":[[1,4],[1,4],[1,2]],\"right\":8,\"support\":[-5,2,8]}"}},"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-r06-cumulative-distribution-function-0059","batch_id":"batch-20261014-advance-20261030-r06-cumulative-distribution-function-foundations","language":"zh-Hant","source_mko_ids":["mko-cumulative-distribution-function"],"title_zh":"累積分布函數","stem_zh":"完整有限離散law與F(t)=P(X小於等於t)。操作=cdf-monotonicity；資料={\"support\":[-4,3,9],\"masses\":[[1,4],[1,4],[1,2]],\"left\":-4,\"right\":9}。請依 [left,right,F_left,F_right,monotone] 欄序回答。","answer":{"kind":"expression","value":"(-4, 9, 1/4, 1, 是)","explanation_zh":"Wave4第四層核對=(-4, 9, 1/4, 1, 是)；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；保留小於等於單調右連續與端點；CDF不混同PMF或density且jump為點質量。"},"difficulty":{"band":"undergraduate_core","level":2,"skills":["累積分布函數"]},"variant":{"family_id":"qf-mod30-cdf-monotonicity","seed":202610306059,"parameters":{"support":[-4,3,9],"masses":[[1,4],[1,4],[1,2]],"left":-4,"right":9,"domain":"Exact_finite_discrete_CDF","operation":"cdf-monotonicity","semantic_template":"qf-mod30-cdf-monotonicity/{\"left\":-4,\"masses\":[[1,4],[1,4],[1,2]],\"right\":9,\"support\":[-4,3,9]}"}},"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-r06-cumulative-distribution-function-0060","batch_id":"batch-20261014-advance-20261030-r06-cumulative-distribution-function-foundations","language":"zh-Hant","source_mko_ids":["mko-cumulative-distribution-function"],"title_zh":"累積分布函數","stem_zh":"完整有限離散law與F(t)=P(X小於等於t)。操作=cdf-monotonicity；資料={\"support\":[-3,4,10],\"masses\":[[1,4],[1,4],[1,2]],\"left\":-3,\"right\":10}。請依 [left,right,F_left,F_right,monotone] 欄序回答。","answer":{"kind":"expression","value":"(-3, 10, 1/4, 1, 是)","explanation_zh":"Wave4第四層核對=(-3, 10, 1/4, 1, 是)；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；保留小於等於單調右連續與端點；CDF不混同PMF或density且jump為點質量。"},"difficulty":{"band":"undergraduate_core","level":2,"skills":["累積分布函數"]},"variant":{"family_id":"qf-mod30-cdf-monotonicity","seed":202610306060,"parameters":{"support":[-3,4,10],"masses":[[1,4],[1,4],[1,2]],"left":-3,"right":10,"domain":"Exact_finite_discrete_CDF","operation":"cdf-monotonicity","semantic_template":"qf-mod30-cdf-monotonicity/{\"left\":-3,\"masses\":[[1,4],[1,4],[1,2]],\"right\":10,\"support\":[-3,4,10]}"}},"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-r06-cumulative-distribution-function-0061","batch_id":"batch-20261014-advance-20261030-r06-cumulative-distribution-function-foundations","language":"zh-Hant","source_mko_ids":["mko-cumulative-distribution-function"],"title_zh":"累積分布函數","stem_zh":"完整有限離散law與F(t)=P(X小於等於t)。操作=cdf-monotonicity；資料={\"support\":[-2,5,11],\"masses\":[[1,4],[1,4],[1,2]],\"left\":-2,\"right\":11}。請依 [left,right,F_left,F_right,monotone] 欄序回答。","answer":{"kind":"expression","value":"(-2, 11, 1/4, 1, 是)","explanation_zh":"Wave4第四層核對=(-2, 11, 1/4, 1, 是)；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；保留小於等於單調右連續與端點；CDF不混同PMF或density且jump為點質量。"},"difficulty":{"band":"undergraduate_core","level":2,"skills":["累積分布函數"]},"variant":{"family_id":"qf-mod30-cdf-monotonicity","seed":202610306061,"parameters":{"support":[-2,5,11],"masses":[[1,4],[1,4],[1,2]],"left":-2,"right":11,"domain":"Exact_finite_discrete_CDF","operation":"cdf-monotonicity","semantic_template":"qf-mod30-cdf-monotonicity/{\"left\":-2,\"masses\":[[1,4],[1,4],[1,2]],\"right\":11,\"support\":[-2,5,11]}"}},"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-r06-cumulative-distribution-function-0062","batch_id":"batch-20261014-advance-20261030-r06-cumulative-distribution-function-foundations","language":"zh-Hant","source_mko_ids":["mko-cumulative-distribution-function"],"title_zh":"累積分布函數","stem_zh":"完整有限離散law與F(t)=P(X小於等於t)。操作=cdf-monotonicity；資料={\"support\":[-1,6,12],\"masses\":[[1,4],[1,4],[1,2]],\"left\":-1,\"right\":12}。請依 [left,right,F_left,F_right,monotone] 欄序回答。","answer":{"kind":"expression","value":"(-1, 12, 1/4, 1, 是)","explanation_zh":"Wave4第四層核對=(-1, 12, 1/4, 1, 是)；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；保留小於等於單調右連續與端點；CDF不混同PMF或density且jump為點質量。"},"difficulty":{"band":"undergraduate_core","level":2,"skills":["累積分布函數"]},"variant":{"family_id":"qf-mod30-cdf-monotonicity","seed":202610306062,"parameters":{"support":[-1,6,12],"masses":[[1,4],[1,4],[1,2]],"left":-1,"right":12,"domain":"Exact_finite_discrete_CDF","operation":"cdf-monotonicity","semantic_template":"qf-mod30-cdf-monotonicity/{\"left\":-1,\"masses\":[[1,4],[1,4],[1,2]],\"right\":12,\"support\":[-1,6,12]}"}},"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-r06-cumulative-distribution-function-0063","batch_id":"batch-20261014-advance-20261030-r06-cumulative-distribution-function-foundations","language":"zh-Hant","source_mko_ids":["mko-cumulative-distribution-function"],"title_zh":"累積分布函數","stem_zh":"完整有限離散law與F(t)=P(X小於等於t)。操作=cdf-monotonicity；資料={\"support\":[0,7,13],\"masses\":[[1,4],[1,4],[1,2]],\"left\":0,\"right\":13}。請依 [left,right,F_left,F_right,monotone] 欄序回答。","answer":{"kind":"expression","value":"(0, 13, 1/4, 1, 是)","explanation_zh":"Wave4第四層核對=(0, 13, 1/4, 1, 是)；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；保留小於等於單調右連續與端點；CDF不混同PMF或density且jump為點質量。"},"difficulty":{"band":"undergraduate_core","level":2,"skills":["累積分布函數"]},"variant":{"family_id":"qf-mod30-cdf-monotonicity","seed":202610306063,"parameters":{"support":[0,7,13],"masses":[[1,4],[1,4],[1,2]],"left":0,"right":13,"domain":"Exact_finite_discrete_CDF","operation":"cdf-monotonicity","semantic_template":"qf-mod30-cdf-monotonicity/{\"left\":0,\"masses\":[[1,4],[1,4],[1,2]],\"right\":13,\"support\":[0,7,13]}"}},"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-r06-cumulative-distribution-function-0064","batch_id":"batch-20261014-advance-20261030-r06-cumulative-distribution-function-foundations","language":"zh-Hant","source_mko_ids":["mko-cumulative-distribution-function"],"title_zh":"累積分布函數","stem_zh":"完整有限離散law與F(t)=P(X小於等於t)。操作=cdf-monotonicity；資料={\"support\":[1,8,14],\"masses\":[[1,4],[1,4],[1,2]],\"left\":1,\"right\":14}。請依 [left,right,F_left,F_right,monotone] 欄序回答。","answer":{"kind":"expression","value":"(1, 14, 1/4, 1, 是)","explanation_zh":"Wave4第四層核對=(1, 14, 1/4, 1, 是)；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；保留小於等於單調右連續與端點；CDF不混同PMF或density且jump為點質量。"},"difficulty":{"band":"undergraduate_core","level":2,"skills":["累積分布函數"]},"variant":{"family_id":"qf-mod30-cdf-monotonicity","seed":202610306064,"parameters":{"support":[1,8,14],"masses":[[1,4],[1,4],[1,2]],"left":1,"right":14,"domain":"Exact_finite_discrete_CDF","operation":"cdf-monotonicity","semantic_template":"qf-mod30-cdf-monotonicity/{\"left\":1,\"masses\":[[1,4],[1,4],[1,2]],\"right\":14,\"support\":[1,8,14]}"}},"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-r06-cumulative-distribution-function-0065","batch_id":"batch-20261014-advance-20261030-r06-cumulative-distribution-function-foundations","language":"zh-Hant","source_mko_ids":["mko-cumulative-distribution-function"],"title_zh":"累積分布函數","stem_zh":"完整有限離散law與F(t)=P(X小於等於t)。操作=cdf-monotonicity；資料={\"support\":[2,9,15],\"masses\":[[1,4],[1,4],[1,2]],\"left\":2,\"right\":15}。請依 [left,right,F_left,F_right,monotone] 欄序回答。","answer":{"kind":"expression","value":"(2, 15, 1/4, 1, 是)","explanation_zh":"Wave4第四層核對=(2, 15, 1/4, 1, 是)；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；保留小於等於單調右連續與端點；CDF不混同PMF或density且jump為點質量。"},"difficulty":{"band":"undergraduate_core","level":2,"skills":["累積分布函數"]},"variant":{"family_id":"qf-mod30-cdf-monotonicity","seed":202610306065,"parameters":{"support":[2,9,15],"masses":[[1,4],[1,4],[1,2]],"left":2,"right":15,"domain":"Exact_finite_discrete_CDF","operation":"cdf-monotonicity","semantic_template":"qf-mod30-cdf-monotonicity/{\"left\":2,\"masses\":[[1,4],[1,4],[1,2]],\"right\":15,\"support\":[2,9,15]}"}},"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-r06-cumulative-distribution-function-0066","batch_id":"batch-20261014-advance-20261030-r06-cumulative-distribution-function-foundations","language":"zh-Hant","source_mko_ids":["mko-cumulative-distribution-function"],"title_zh":"累積分布函數","stem_zh":"完整有限離散law與F(t)=P(X小於等於t)。操作=cdf-monotonicity；資料={\"support\":[3,10,16],\"masses\":[[1,4],[1,4],[1,2]],\"left\":3,\"right\":16}。請依 [left,right,F_left,F_right,monotone] 欄序回答。","answer":{"kind":"expression","value":"(3, 16, 1/4, 1, 是)","explanation_zh":"Wave4第四層核對=(3, 16, 1/4, 1, 是)；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；保留小於等於單調右連續與端點；CDF不混同PMF或density且jump為點質量。"},"difficulty":{"band":"undergraduate_core","level":2,"skills":["累積分布函數"]},"variant":{"family_id":"qf-mod30-cdf-monotonicity","seed":202610306066,"parameters":{"support":[3,10,16],"masses":[[1,4],[1,4],[1,2]],"left":3,"right":16,"domain":"Exact_finite_discrete_CDF","operation":"cdf-monotonicity","semantic_template":"qf-mod30-cdf-monotonicity/{\"left\":3,\"masses\":[[1,4],[1,4],[1,2]],\"right\":16,\"support\":[3,10,16]}"}},"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-r06-cumulative-distribution-function-0067","batch_id":"batch-20261014-advance-20261030-r06-cumulative-distribution-function-foundations","language":"zh-Hant","source_mko_ids":["mko-cumulative-distribution-function"],"title_zh":"累積分布函數","stem_zh":"完整有限離散law與F(t)=P(X小於等於t)。操作=cdf-monotonicity；資料={\"support\":[4,11,17],\"masses\":[[1,4],[1,4],[1,2]],\"left\":4,\"right\":17}。請依 [left,right,F_left,F_right,monotone] 欄序回答。","answer":{"kind":"expression","value":"(4, 17, 1/4, 1, 是)","explanation_zh":"Wave4第四層核對=(4, 17, 1/4, 1, 是)；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；保留小於等於單調右連續與端點；CDF不混同PMF或density且jump為點質量。"},"difficulty":{"band":"undergraduate_core","level":2,"skills":["累積分布函數"]},"variant":{"family_id":"qf-mod30-cdf-monotonicity","seed":202610306067,"parameters":{"support":[4,11,17],"masses":[[1,4],[1,4],[1,2]],"left":4,"right":17,"domain":"Exact_finite_discrete_CDF","operation":"cdf-monotonicity","semantic_template":"qf-mod30-cdf-monotonicity/{\"left\":4,\"masses\":[[1,4],[1,4],[1,2]],\"right\":17,\"support\":[4,11,17]}"}},"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-r06-cumulative-distribution-function-0068","batch_id":"batch-20261014-advance-20261030-r06-cumulative-distribution-function-foundations","language":"zh-Hant","source_mko_ids":["mko-cumulative-distribution-function"],"title_zh":"累積分布函數","stem_zh":"完整有限離散law與F(t)=P(X小於等於t)。操作=cdf-monotonicity；資料={\"support\":[5,12,18],\"masses\":[[1,4],[1,4],[1,2]],\"left\":5,\"right\":18}。請依 [left,right,F_left,F_right,monotone] 欄序回答。","answer":{"kind":"expression","value":"(5, 18, 1/4, 1, 是)","explanation_zh":"Wave4第四層核對=(5, 18, 1/4, 1, 是)；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；保留小於等於單調右連續與端點；CDF不混同PMF或density且jump為點質量。"},"difficulty":{"band":"undergraduate_core","level":3,"skills":["累積分布函數"]},"variant":{"family_id":"qf-mod30-cdf-monotonicity","seed":202610306068,"parameters":{"support":[5,12,18],"masses":[[1,4],[1,4],[1,2]],"left":5,"right":18,"domain":"Exact_finite_discrete_CDF","operation":"cdf-monotonicity","semantic_template":"qf-mod30-cdf-monotonicity/{\"left\":5,\"masses\":[[1,4],[1,4],[1,2]],\"right\":18,\"support\":[5,12,18]}"}},"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-r06-cumulative-distribution-function-0069","batch_id":"batch-20261014-advance-20261030-r06-cumulative-distribution-function-foundations","language":"zh-Hant","source_mko_ids":["mko-cumulative-distribution-function"],"title_zh":"累積分布函數","stem_zh":"完整有限離散law與F(t)=P(X小於等於t)。操作=cdf-monotonicity；資料={\"support\":[6,13,19],\"masses\":[[1,4],[1,4],[1,2]],\"left\":6,\"right\":19}。請依 [left,right,F_left,F_right,monotone] 欄序回答。","answer":{"kind":"expression","value":"(6, 19, 1/4, 1, 是)","explanation_zh":"Wave4第四層核對=(6, 19, 1/4, 1, 是)；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；保留小於等於單調右連續與端點；CDF不混同PMF或density且jump為點質量。"},"difficulty":{"band":"undergraduate_core","level":3,"skills":["累積分布函數"]},"variant":{"family_id":"qf-mod30-cdf-monotonicity","seed":202610306069,"parameters":{"support":[6,13,19],"masses":[[1,4],[1,4],[1,2]],"left":6,"right":19,"domain":"Exact_finite_discrete_CDF","operation":"cdf-monotonicity","semantic_template":"qf-mod30-cdf-monotonicity/{\"left\":6,\"masses\":[[1,4],[1,4],[1,2]],\"right\":19,\"support\":[6,13,19]}"}},"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-r06-cumulative-distribution-function-0070","batch_id":"batch-20261014-advance-20261030-r06-cumulative-distribution-function-foundations","language":"zh-Hant","source_mko_ids":["mko-cumulative-distribution-function"],"title_zh":"累積分布函數","stem_zh":"完整有限離散law與F(t)=P(X小於等於t)。操作=cdf-monotonicity；資料={\"support\":[7,14,20],\"masses\":[[1,4],[1,4],[1,2]],\"left\":7,\"right\":20}。請依 [left,right,F_left,F_right,monotone] 欄序回答。","answer":{"kind":"expression","value":"(7, 20, 1/4, 1, 是)","explanation_zh":"Wave4第四層核對=(7, 20, 1/4, 1, 是)；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；保留小於等於單調右連續與端點；CDF不混同PMF或density且jump為點質量。"},"difficulty":{"band":"undergraduate_core","level":3,"skills":["累積分布函數"]},"variant":{"family_id":"qf-mod30-cdf-monotonicity","seed":202610306070,"parameters":{"support":[7,14,20],"masses":[[1,4],[1,4],[1,2]],"left":7,"right":20,"domain":"Exact_finite_discrete_CDF","operation":"cdf-monotonicity","semantic_template":"qf-mod30-cdf-monotonicity/{\"left\":7,\"masses\":[[1,4],[1,4],[1,2]],\"right\":20,\"support\":[7,14,20]}"}},"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-r06-cumulative-distribution-function-0071","batch_id":"batch-20261014-advance-20261030-r06-cumulative-distribution-function-foundations","language":"zh-Hant","source_mko_ids":["mko-cumulative-distribution-function"],"title_zh":"累積分布函數","stem_zh":"完整有限離散law與F(t)=P(X小於等於t)。操作=cdf-monotonicity；資料={\"support\":[8,15,21],\"masses\":[[1,4],[1,4],[1,2]],\"left\":8,\"right\":21}。請依 [left,right,F_left,F_right,monotone] 欄序回答。","answer":{"kind":"expression","value":"(8, 21, 1/4, 1, 是)","explanation_zh":"Wave4第四層核對=(8, 21, 1/4, 1, 是)；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；保留小於等於單調右連續與端點；CDF不混同PMF或density且jump為點質量。"},"difficulty":{"band":"undergraduate_core","level":3,"skills":["累積分布函數"]},"variant":{"family_id":"qf-mod30-cdf-monotonicity","seed":202610306071,"parameters":{"support":[8,15,21],"masses":[[1,4],[1,4],[1,2]],"left":8,"right":21,"domain":"Exact_finite_discrete_CDF","operation":"cdf-monotonicity","semantic_template":"qf-mod30-cdf-monotonicity/{\"left\":8,\"masses\":[[1,4],[1,4],[1,2]],\"right\":21,\"support\":[8,15,21]}"}},"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-r06-cumulative-distribution-function-0072","batch_id":"batch-20261014-advance-20261030-r06-cumulative-distribution-function-foundations","language":"zh-Hant","source_mko_ids":["mko-cumulative-distribution-function"],"title_zh":"累積分布函數","stem_zh":"完整有限離散law與F(t)=P(X小於等於t)。操作=cdf-monotonicity；資料={\"support\":[9,16,22],\"masses\":[[1,4],[1,4],[1,2]],\"left\":9,\"right\":22}。請依 [left,right,F_left,F_right,monotone] 欄序回答。","answer":{"kind":"expression","value":"(9, 22, 1/4, 1, 是)","explanation_zh":"Wave4第四層核對=(9, 22, 1/4, 1, 是)；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；保留小於等於單調右連續與端點；CDF不混同PMF或density且jump為點質量。"},"difficulty":{"band":"undergraduate_core","level":3,"skills":["累積分布函數"]},"variant":{"family_id":"qf-mod30-cdf-monotonicity","seed":202610306072,"parameters":{"support":[9,16,22],"masses":[[1,4],[1,4],[1,2]],"left":9,"right":22,"domain":"Exact_finite_discrete_CDF","operation":"cdf-monotonicity","semantic_template":"qf-mod30-cdf-monotonicity/{\"left\":9,\"masses\":[[1,4],[1,4],[1,2]],\"right\":22,\"support\":[9,16,22]}"}},"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-r06-cumulative-distribution-function-0073","batch_id":"batch-20261014-advance-20261030-r06-cumulative-distribution-function-foundations","language":"zh-Hant","source_mko_ids":["mko-cumulative-distribution-function"],"title_zh":"累積分布函數","stem_zh":"完整有限離散law與F(t)=P(X小於等於t)。操作=cdf-monotonicity；資料={\"support\":[10,17,23],\"masses\":[[1,4],[1,4],[1,2]],\"left\":10,\"right\":23}。請依 [left,right,F_left,F_right,monotone] 欄序回答。","answer":{"kind":"expression","value":"(10, 23, 1/4, 1, 是)","explanation_zh":"Wave4第四層核對=(10, 23, 1/4, 1, 是)；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；保留小於等於單調右連續與端點；CDF不混同PMF或density且jump為點質量。"},"difficulty":{"band":"undergraduate_core","level":3,"skills":["累積分布函數"]},"variant":{"family_id":"qf-mod30-cdf-monotonicity","seed":202610306073,"parameters":{"support":[10,17,23],"masses":[[1,4],[1,4],[1,2]],"left":10,"right":23,"domain":"Exact_finite_discrete_CDF","operation":"cdf-monotonicity","semantic_template":"qf-mod30-cdf-monotonicity/{\"left\":10,\"masses\":[[1,4],[1,4],[1,2]],\"right\":23,\"support\":[10,17,23]}"}},"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-r06-cumulative-distribution-function-0074","batch_id":"batch-20261014-advance-20261030-r06-cumulative-distribution-function-foundations","language":"zh-Hant","source_mko_ids":["mko-cumulative-distribution-function"],"title_zh":"累積分布函數","stem_zh":"完整有限離散law與F(t)=P(X小於等於t)。操作=cdf-monotonicity；資料={\"support\":[11,18,24],\"masses\":[[1,4],[1,4],[1,2]],\"left\":11,\"right\":24}。請依 [left,right,F_left,F_right,monotone] 欄序回答。","answer":{"kind":"expression","value":"(11, 24, 1/4, 1, 是)","explanation_zh":"Wave4第四層核對=(11, 24, 1/4, 1, 是)；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；保留小於等於單調右連續與端點；CDF不混同PMF或density且jump為點質量。"},"difficulty":{"band":"undergraduate_core","level":3,"skills":["累積分布函數"]},"variant":{"family_id":"qf-mod30-cdf-monotonicity","seed":202610306074,"parameters":{"support":[11,18,24],"masses":[[1,4],[1,4],[1,2]],"left":11,"right":24,"domain":"Exact_finite_discrete_CDF","operation":"cdf-monotonicity","semantic_template":"qf-mod30-cdf-monotonicity/{\"left\":11,\"masses\":[[1,4],[1,4],[1,2]],\"right\":24,\"support\":[11,18,24]}"}},"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-r06-cumulative-distribution-function-0075","batch_id":"batch-20261014-advance-20261030-r06-cumulative-distribution-function-foundations","language":"zh-Hant","source_mko_ids":["mko-cumulative-distribution-function"],"title_zh":"累積分布函數","stem_zh":"完整有限離散law與F(t)=P(X小於等於t)。操作=cdf-monotonicity；資料={\"support\":[12,19,25],\"masses\":[[1,4],[1,4],[1,2]],\"left\":12,\"right\":25}。請依 [left,right,F_left,F_right,monotone] 欄序回答。","answer":{"kind":"expression","value":"(12, 25, 1/4, 1, 是)","explanation_zh":"Wave4第四層核對=(12, 25, 1/4, 1, 是)；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；保留小於等於單調右連續與端點；CDF不混同PMF或density且jump為點質量。"},"difficulty":{"band":"undergraduate_core","level":3,"skills":["累積分布函數"]},"variant":{"family_id":"qf-mod30-cdf-monotonicity","seed":202610306075,"parameters":{"support":[12,19,25],"masses":[[1,4],[1,4],[1,2]],"left":12,"right":25,"domain":"Exact_finite_discrete_CDF","operation":"cdf-monotonicity","semantic_template":"qf-mod30-cdf-monotonicity/{\"left\":12,\"masses\":[[1,4],[1,4],[1,2]],\"right\":25,\"support\":[12,19,25]}"}},"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"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261014-advance-20261030-r06-cumulative-distribution-function-0076","batch_id":"batch-20261014-advance-20261030-r06-cumulative-distribution-function-foundations","language":"zh-Hant","source_mko_ids":["mko-cumulative-distribution-function"],"title_zh":"累積分布函數","stem_zh":"完整有限離散law與F(t)=P(X小於等於t)。操作=cdf-right-continuity；資料={\"support\":[-12,-5,1],\"masses\":[[1,4],[1,4],[1,2]],\"t\":-12}。請依 [t,F_t,next_support,certificate,right_continuous] 欄序回答。","answer":{"kind":"expression","value":"(-12, 1/4, -5, constant_on_right_neighborhood_before_next_support, 是)","explanation_zh":"Wave4第四層核對=(-12, 1/4, -5, constant_on_right_neighborhood_before_next_support, 是)；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；保留小於等於單調右連續與端點；CDF不混同PMF或density且jump為點質量。"},"difficulty":{"band":"undergraduate_core","level":1,"skills":["累積分布函數"]},"variant":{"family_id":"qf-mod30-cdf-right-continuity","seed":202610306076,"parameters":{"support":[-12,-5,1],"masses":[[1,4],[1,4],[1,2]],"t":-12,"domain":"Exact_finite_discrete_CDF","operation":"cdf-right-continuity","semantic_template":"qf-mod30-cdf-right-continuity/{\"masses\":[[1,4],[1,4],[1,2]],\"support\":[-12,-5,1],\"t\":-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-r06-cumulative-distribution-function-0077","batch_id":"batch-20261014-advance-20261030-r06-cumulative-distribution-function-foundations","language":"zh-Hant","source_mko_ids":["mko-cumulative-distribution-function"],"title_zh":"累積分布函數","stem_zh":"完整有限離散law與F(t)=P(X小於等於t)。操作=cdf-right-continuity；資料={\"support\":[-11,-4,2],\"masses\":[[1,4],[1,4],[1,2]],\"t\":-4}。請依 [t,F_t,next_support,certificate,right_continuous] 欄序回答。","answer":{"kind":"expression","value":"(-4, 1/2, 2, constant_on_right_neighborhood_before_next_support, 是)","explanation_zh":"Wave4第四層核對=(-4, 1/2, 2, constant_on_right_neighborhood_before_next_support, 是)；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；保留小於等於單調右連續與端點；CDF不混同PMF或density且jump為點質量。"},"difficulty":{"band":"undergraduate_core","level":1,"skills":["累積分布函數"]},"variant":{"family_id":"qf-mod30-cdf-right-continuity","seed":202610306077,"parameters":{"support":[-11,-4,2],"masses":[[1,4],[1,4],[1,2]],"t":-4,"domain":"Exact_finite_discrete_CDF","operation":"cdf-right-continuity","semantic_template":"qf-mod30-cdf-right-continuity/{\"masses\":[[1,4],[1,4],[1,2]],\"support\":[-11,-4,2],\"t\":-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-r06-cumulative-distribution-function-0078","batch_id":"batch-20261014-advance-20261030-r06-cumulative-distribution-function-foundations","language":"zh-Hant","source_mko_ids":["mko-cumulative-distribution-function"],"title_zh":"累積分布函數","stem_zh":"完整有限離散law與F(t)=P(X小於等於t)。操作=cdf-right-continuity；資料={\"support\":[-10,-3,3],\"masses\":[[1,4],[1,4],[1,2]],\"t\":3}。請依 [t,F_t,next_support,certificate,right_continuous] 欄序回答。","answer":{"kind":"expression","value":"(3, 1, null, constant_on_right_neighborhood_before_next_support, 是)","explanation_zh":"Wave4第四層核對=(3, 1, null, constant_on_right_neighborhood_before_next_support, 是)；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；保留小於等於單調右連續與端點；CDF不混同PMF或density且jump為點質量。"},"difficulty":{"band":"undergraduate_core","level":1,"skills":["累積分布函數"]},"variant":{"family_id":"qf-mod30-cdf-right-continuity","seed":202610306078,"parameters":{"support":[-10,-3,3],"masses":[[1,4],[1,4],[1,2]],"t":3,"domain":"Exact_finite_discrete_CDF","operation":"cdf-right-continuity","semantic_template":"qf-mod30-cdf-right-continuity/{\"masses\":[[1,4],[1,4],[1,2]],\"support\":[-10,-3,3],\"t\":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-r06-cumulative-distribution-function-0079","batch_id":"batch-20261014-advance-20261030-r06-cumulative-distribution-function-foundations","language":"zh-Hant","source_mko_ids":["mko-cumulative-distribution-function"],"title_zh":"累積分布函數","stem_zh":"完整有限離散law與F(t)=P(X小於等於t)。操作=cdf-right-continuity；資料={\"support\":[-9,-2,4],\"masses\":[[1,4],[1,4],[1,2]],\"t\":-9}。請依 [t,F_t,next_support,certificate,right_continuous] 欄序回答。","answer":{"kind":"expression","value":"(-9, 1/4, -2, constant_on_right_neighborhood_before_next_support, 是)","explanation_zh":"Wave4第四層核對=(-9, 1/4, -2, constant_on_right_neighborhood_before_next_support, 是)；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；保留小於等於單調右連續與端點；CDF不混同PMF或density且jump為點質量。"},"difficulty":{"band":"undergraduate_core","level":1,"skills":["累積分布函數"]},"variant":{"family_id":"qf-mod30-cdf-right-continuity","seed":202610306079,"parameters":{"support":[-9,-2,4],"masses":[[1,4],[1,4],[1,2]],"t":-9,"domain":"Exact_finite_discrete_CDF","operation":"cdf-right-continuity","semantic_template":"qf-mod30-cdf-right-continuity/{\"masses\":[[1,4],[1,4],[1,2]],\"support\":[-9,-2,4],\"t\":-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-r06-cumulative-distribution-function-0080","batch_id":"batch-20261014-advance-20261030-r06-cumulative-distribution-function-foundations","language":"zh-Hant","source_mko_ids":["mko-cumulative-distribution-function"],"title_zh":"累積分布函數","stem_zh":"完整有限離散law與F(t)=P(X小於等於t)。操作=cdf-right-continuity；資料={\"support\":[-8,-1,5],\"masses\":[[1,4],[1,4],[1,2]],\"t\":-1}。請依 [t,F_t,next_support,certificate,right_continuous] 欄序回答。","answer":{"kind":"expression","value":"(-1, 1/2, 5, constant_on_right_neighborhood_before_next_support, 是)","explanation_zh":"Wave4第四層核對=(-1, 1/2, 5, constant_on_right_neighborhood_before_next_support, 是)；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；保留小於等於單調右連續與端點；CDF不混同PMF或density且jump為點質量。"},"difficulty":{"band":"undergraduate_core","level":1,"skills":["累積分布函數"]},"variant":{"family_id":"qf-mod30-cdf-right-continuity","seed":202610306080,"parameters":{"support":[-8,-1,5],"masses":[[1,4],[1,4],[1,2]],"t":-1,"domain":"Exact_finite_discrete_CDF","operation":"cdf-right-continuity","semantic_template":"qf-mod30-cdf-right-continuity/{\"masses\":[[1,4],[1,4],[1,2]],\"support\":[-8,-1,5],\"t\":-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-r06-cumulative-distribution-function-0081","batch_id":"batch-20261014-advance-20261030-r06-cumulative-distribution-function-foundations","language":"zh-Hant","source_mko_ids":["mko-cumulative-distribution-function"],"title_zh":"累積分布函數","stem_zh":"完整有限離散law與F(t)=P(X小於等於t)。操作=cdf-right-continuity；資料={\"support\":[-7,0,6],\"masses\":[[1,4],[1,4],[1,2]],\"t\":6}。請依 [t,F_t,next_support,certificate,right_continuous] 欄序回答。","answer":{"kind":"expression","value":"(6, 1, null, constant_on_right_neighborhood_before_next_support, 是)","explanation_zh":"Wave4第四層核對=(6, 1, null, constant_on_right_neighborhood_before_next_support, 是)；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；保留小於等於單調右連續與端點；CDF不混同PMF或density且jump為點質量。"},"difficulty":{"band":"undergraduate_core","level":1,"skills":["累積分布函數"]},"variant":{"family_id":"qf-mod30-cdf-right-continuity","seed":202610306081,"parameters":{"support":[-7,0,6],"masses":[[1,4],[1,4],[1,2]],"t":6,"domain":"Exact_finite_discrete_CDF","operation":"cdf-right-continuity","semantic_template":"qf-mod30-cdf-right-continuity/{\"masses\":[[1,4],[1,4],[1,2]],\"support\":[-7,0,6],\"t\":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-r06-cumulative-distribution-function-0082","batch_id":"batch-20261014-advance-20261030-r06-cumulative-distribution-function-foundations","language":"zh-Hant","source_mko_ids":["mko-cumulative-distribution-function"],"title_zh":"累積分布函數","stem_zh":"完整有限離散law與F(t)=P(X小於等於t)。操作=cdf-right-continuity；資料={\"support\":[-6,1,7],\"masses\":[[1,4],[1,4],[1,2]],\"t\":-6}。請依 [t,F_t,next_support,certificate,right_continuous] 欄序回答。","answer":{"kind":"expression","value":"(-6, 1/4, 1, constant_on_right_neighborhood_before_next_support, 是)","explanation_zh":"Wave4第四層核對=(-6, 1/4, 1, constant_on_right_neighborhood_before_next_support, 是)；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；保留小於等於單調右連續與端點；CDF不混同PMF或density且jump為點質量。"},"difficulty":{"band":"undergraduate_core","level":1,"skills":["累積分布函數"]},"variant":{"family_id":"qf-mod30-cdf-right-continuity","seed":202610306082,"parameters":{"support":[-6,1,7],"masses":[[1,4],[1,4],[1,2]],"t":-6,"domain":"Exact_finite_discrete_CDF","operation":"cdf-right-continuity","semantic_template":"qf-mod30-cdf-right-continuity/{\"masses\":[[1,4],[1,4],[1,2]],\"support\":[-6,1,7],\"t\":-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-r06-cumulative-distribution-function-0083","batch_id":"batch-20261014-advance-20261030-r06-cumulative-distribution-function-foundations","language":"zh-Hant","source_mko_ids":["mko-cumulative-distribution-function"],"title_zh":"累積分布函數","stem_zh":"完整有限離散law與F(t)=P(X小於等於t)。操作=cdf-right-continuity；資料={\"support\":[-5,2,8],\"masses\":[[1,4],[1,4],[1,2]],\"t\":2}。請依 [t,F_t,next_support,certificate,right_continuous] 欄序回答。","answer":{"kind":"expression","value":"(2, 1/2, 8, constant_on_right_neighborhood_before_next_support, 是)","explanation_zh":"Wave4第四層核對=(2, 1/2, 8, constant_on_right_neighborhood_before_next_support, 是)；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；保留小於等於單調右連續與端點；CDF不混同PMF或density且jump為點質量。"},"difficulty":{"band":"undergraduate_core","level":1,"skills":["累積分布函數"]},"variant":{"family_id":"qf-mod30-cdf-right-continuity","seed":202610306083,"parameters":{"support":[-5,2,8],"masses":[[1,4],[1,4],[1,2]],"t":2,"domain":"Exact_finite_discrete_CDF","operation":"cdf-right-continuity","semantic_template":"qf-mod30-cdf-right-continuity/{\"masses\":[[1,4],[1,4],[1,2]],\"support\":[-5,2,8],\"t\":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-r06-cumulative-distribution-function-0084","batch_id":"batch-20261014-advance-20261030-r06-cumulative-distribution-function-foundations","language":"zh-Hant","source_mko_ids":["mko-cumulative-distribution-function"],"title_zh":"累積分布函數","stem_zh":"完整有限離散law與F(t)=P(X小於等於t)。操作=cdf-right-continuity；資料={\"support\":[-4,3,9],\"masses\":[[1,4],[1,4],[1,2]],\"t\":9}。請依 [t,F_t,next_support,certificate,right_continuous] 欄序回答。","answer":{"kind":"expression","value":"(9, 1, null, constant_on_right_neighborhood_before_next_support, 是)","explanation_zh":"Wave4第四層核對=(9, 1, null, constant_on_right_neighborhood_before_next_support, 是)；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；保留小於等於單調右連續與端點；CDF不混同PMF或density且jump為點質量。"},"difficulty":{"band":"undergraduate_core","level":2,"skills":["累積分布函數"]},"variant":{"family_id":"qf-mod30-cdf-right-continuity","seed":202610306084,"parameters":{"support":[-4,3,9],"masses":[[1,4],[1,4],[1,2]],"t":9,"domain":"Exact_finite_discrete_CDF","operation":"cdf-right-continuity","semantic_template":"qf-mod30-cdf-right-continuity/{\"masses\":[[1,4],[1,4],[1,2]],\"support\":[-4,3,9],\"t\":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-r06-cumulative-distribution-function-0085","batch_id":"batch-20261014-advance-20261030-r06-cumulative-distribution-function-foundations","language":"zh-Hant","source_mko_ids":["mko-cumulative-distribution-function"],"title_zh":"累積分布函數","stem_zh":"完整有限離散law與F(t)=P(X小於等於t)。操作=cdf-right-continuity；資料={\"support\":[-3,4,10],\"masses\":[[1,4],[1,4],[1,2]],\"t\":-3}。請依 [t,F_t,next_support,certificate,right_continuous] 欄序回答。","answer":{"kind":"expression","value":"(-3, 1/4, 4, constant_on_right_neighborhood_before_next_support, 是)","explanation_zh":"Wave4第四層核對=(-3, 1/4, 4, constant_on_right_neighborhood_before_next_support, 是)；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；保留小於等於單調右連續與端點；CDF不混同PMF或density且jump為點質量。"},"difficulty":{"band":"undergraduate_core","level":2,"skills":["累積分布函數"]},"variant":{"family_id":"qf-mod30-cdf-right-continuity","seed":202610306085,"parameters":{"support":[-3,4,10],"masses":[[1,4],[1,4],[1,2]],"t":-3,"domain":"Exact_finite_discrete_CDF","operation":"cdf-right-continuity","semantic_template":"qf-mod30-cdf-right-continuity/{\"masses\":[[1,4],[1,4],[1,2]],\"support\":[-3,4,10],\"t\":-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-r06-cumulative-distribution-function-0086","batch_id":"batch-20261014-advance-20261030-r06-cumulative-distribution-function-foundations","language":"zh-Hant","source_mko_ids":["mko-cumulative-distribution-function"],"title_zh":"累積分布函數","stem_zh":"完整有限離散law與F(t)=P(X小於等於t)。操作=cdf-right-continuity；資料={\"support\":[-2,5,11],\"masses\":[[1,4],[1,4],[1,2]],\"t\":5}。請依 [t,F_t,next_support,certificate,right_continuous] 欄序回答。","answer":{"kind":"expression","value":"(5, 1/2, 11, constant_on_right_neighborhood_before_next_support, 是)","explanation_zh":"Wave4第四層核對=(5, 1/2, 11, constant_on_right_neighborhood_before_next_support, 是)；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；保留小於等於單調右連續與端點；CDF不混同PMF或density且jump為點質量。"},"difficulty":{"band":"undergraduate_core","level":2,"skills":["累積分布函數"]},"variant":{"family_id":"qf-mod30-cdf-right-continuity","seed":202610306086,"parameters":{"support":[-2,5,11],"masses":[[1,4],[1,4],[1,2]],"t":5,"domain":"Exact_finite_discrete_CDF","operation":"cdf-right-continuity","semantic_template":"qf-mod30-cdf-right-continuity/{\"masses\":[[1,4],[1,4],[1,2]],\"support\":[-2,5,11],\"t\":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-r06-cumulative-distribution-function-0087","batch_id":"batch-20261014-advance-20261030-r06-cumulative-distribution-function-foundations","language":"zh-Hant","source_mko_ids":["mko-cumulative-distribution-function"],"title_zh":"累積分布函數","stem_zh":"完整有限離散law與F(t)=P(X小於等於t)。操作=cdf-right-continuity；資料={\"support\":[-1,6,12],\"masses\":[[1,4],[1,4],[1,2]],\"t\":12}。請依 [t,F_t,next_support,certificate,right_continuous] 欄序回答。","answer":{"kind":"expression","value":"(12, 1, null, constant_on_right_neighborhood_before_next_support, 是)","explanation_zh":"Wave4第四層核對=(12, 1, null, constant_on_right_neighborhood_before_next_support, 是)；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；保留小於等於單調右連續與端點；CDF不混同PMF或density且jump為點質量。"},"difficulty":{"band":"undergraduate_core","level":2,"skills":["累積分布函數"]},"variant":{"family_id":"qf-mod30-cdf-right-continuity","seed":202610306087,"parameters":{"support":[-1,6,12],"masses":[[1,4],[1,4],[1,2]],"t":12,"domain":"Exact_finite_discrete_CDF","operation":"cdf-right-continuity","semantic_template":"qf-mod30-cdf-right-continuity/{\"masses\":[[1,4],[1,4],[1,2]],\"support\":[-1,6,12],\"t\":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-r06-cumulative-distribution-function-0088","batch_id":"batch-20261014-advance-20261030-r06-cumulative-distribution-function-foundations","language":"zh-Hant","source_mko_ids":["mko-cumulative-distribution-function"],"title_zh":"累積分布函數","stem_zh":"完整有限離散law與F(t)=P(X小於等於t)。操作=cdf-right-continuity；資料={\"support\":[0,7,13],\"masses\":[[1,4],[1,4],[1,2]],\"t\":0}。請依 [t,F_t,next_support,certificate,right_continuous] 欄序回答。","answer":{"kind":"expression","value":"(0, 1/4, 7, constant_on_right_neighborhood_before_next_support, 是)","explanation_zh":"Wave4第四層核對=(0, 1/4, 7, constant_on_right_neighborhood_before_next_support, 是)；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；保留小於等於單調右連續與端點；CDF不混同PMF或density且jump為點質量。"},"difficulty":{"band":"undergraduate_core","level":2,"skills":["累積分布函數"]},"variant":{"family_id":"qf-mod30-cdf-right-continuity","seed":202610306088,"parameters":{"support":[0,7,13],"masses":[[1,4],[1,4],[1,2]],"t":0,"domain":"Exact_finite_discrete_CDF","operation":"cdf-right-continuity","semantic_template":"qf-mod30-cdf-right-continuity/{\"masses\":[[1,4],[1,4],[1,2]],\"support\":[0,7,13],\"t\":0}"}},"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-r06-cumulative-distribution-function-0089","batch_id":"batch-20261014-advance-20261030-r06-cumulative-distribution-function-foundations","language":"zh-Hant","source_mko_ids":["mko-cumulative-distribution-function"],"title_zh":"累積分布函數","stem_zh":"完整有限離散law與F(t)=P(X小於等於t)。操作=cdf-right-continuity；資料={\"support\":[1,8,14],\"masses\":[[1,4],[1,4],[1,2]],\"t\":8}。請依 [t,F_t,next_support,certificate,right_continuous] 欄序回答。","answer":{"kind":"expression","value":"(8, 1/2, 14, constant_on_right_neighborhood_before_next_support, 是)","explanation_zh":"Wave4第四層核對=(8, 1/2, 14, constant_on_right_neighborhood_before_next_support, 是)；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；保留小於等於單調右連續與端點；CDF不混同PMF或density且jump為點質量。"},"difficulty":{"band":"undergraduate_core","level":2,"skills":["累積分布函數"]},"variant":{"family_id":"qf-mod30-cdf-right-continuity","seed":202610306089,"parameters":{"support":[1,8,14],"masses":[[1,4],[1,4],[1,2]],"t":8,"domain":"Exact_finite_discrete_CDF","operation":"cdf-right-continuity","semantic_template":"qf-mod30-cdf-right-continuity/{\"masses\":[[1,4],[1,4],[1,2]],\"support\":[1,8,14],\"t\":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-r06-cumulative-distribution-function-0090","batch_id":"batch-20261014-advance-20261030-r06-cumulative-distribution-function-foundations","language":"zh-Hant","source_mko_ids":["mko-cumulative-distribution-function"],"title_zh":"累積分布函數","stem_zh":"完整有限離散law與F(t)=P(X小於等於t)。操作=cdf-right-continuity；資料={\"support\":[2,9,15],\"masses\":[[1,4],[1,4],[1,2]],\"t\":15}。請依 [t,F_t,next_support,certificate,right_continuous] 欄序回答。","answer":{"kind":"expression","value":"(15, 1, null, constant_on_right_neighborhood_before_next_support, 是)","explanation_zh":"Wave4第四層核對=(15, 1, null, constant_on_right_neighborhood_before_next_support, 是)；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；保留小於等於單調右連續與端點；CDF不混同PMF或density且jump為點質量。"},"difficulty":{"band":"undergraduate_core","level":2,"skills":["累積分布函數"]},"variant":{"family_id":"qf-mod30-cdf-right-continuity","seed":202610306090,"parameters":{"support":[2,9,15],"masses":[[1,4],[1,4],[1,2]],"t":15,"domain":"Exact_finite_discrete_CDF","operation":"cdf-right-continuity","semantic_template":"qf-mod30-cdf-right-continuity/{\"masses\":[[1,4],[1,4],[1,2]],\"support\":[2,9,15],\"t\":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-r06-cumulative-distribution-function-0091","batch_id":"batch-20261014-advance-20261030-r06-cumulative-distribution-function-foundations","language":"zh-Hant","source_mko_ids":["mko-cumulative-distribution-function"],"title_zh":"累積分布函數","stem_zh":"完整有限離散law與F(t)=P(X小於等於t)。操作=cdf-right-continuity；資料={\"support\":[3,10,16],\"masses\":[[1,4],[1,4],[1,2]],\"t\":3}。請依 [t,F_t,next_support,certificate,right_continuous] 欄序回答。","answer":{"kind":"expression","value":"(3, 1/4, 10, constant_on_right_neighborhood_before_next_support, 是)","explanation_zh":"Wave4第四層核對=(3, 1/4, 10, constant_on_right_neighborhood_before_next_support, 是)；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；保留小於等於單調右連續與端點；CDF不混同PMF或density且jump為點質量。"},"difficulty":{"band":"undergraduate_core","level":2,"skills":["累積分布函數"]},"variant":{"family_id":"qf-mod30-cdf-right-continuity","seed":202610306091,"parameters":{"support":[3,10,16],"masses":[[1,4],[1,4],[1,2]],"t":3,"domain":"Exact_finite_discrete_CDF","operation":"cdf-right-continuity","semantic_template":"qf-mod30-cdf-right-continuity/{\"masses\":[[1,4],[1,4],[1,2]],\"support\":[3,10,16],\"t\":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-r06-cumulative-distribution-function-0092","batch_id":"batch-20261014-advance-20261030-r06-cumulative-distribution-function-foundations","language":"zh-Hant","source_mko_ids":["mko-cumulative-distribution-function"],"title_zh":"累積分布函數","stem_zh":"完整有限離散law與F(t)=P(X小於等於t)。操作=cdf-right-continuity；資料={\"support\":[4,11,17],\"masses\":[[1,4],[1,4],[1,2]],\"t\":11}。請依 [t,F_t,next_support,certificate,right_continuous] 欄序回答。","answer":{"kind":"expression","value":"(11, 1/2, 17, constant_on_right_neighborhood_before_next_support, 是)","explanation_zh":"Wave4第四層核對=(11, 1/2, 17, constant_on_right_neighborhood_before_next_support, 是)；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；保留小於等於單調右連續與端點；CDF不混同PMF或density且jump為點質量。"},"difficulty":{"band":"undergraduate_core","level":2,"skills":["累積分布函數"]},"variant":{"family_id":"qf-mod30-cdf-right-continuity","seed":202610306092,"parameters":{"support":[4,11,17],"masses":[[1,4],[1,4],[1,2]],"t":11,"domain":"Exact_finite_discrete_CDF","operation":"cdf-right-continuity","semantic_template":"qf-mod30-cdf-right-continuity/{\"masses\":[[1,4],[1,4],[1,2]],\"support\":[4,11,17],\"t\":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-r06-cumulative-distribution-function-0093","batch_id":"batch-20261014-advance-20261030-r06-cumulative-distribution-function-foundations","language":"zh-Hant","source_mko_ids":["mko-cumulative-distribution-function"],"title_zh":"累積分布函數","stem_zh":"完整有限離散law與F(t)=P(X小於等於t)。操作=cdf-right-continuity；資料={\"support\":[5,12,18],\"masses\":[[1,4],[1,4],[1,2]],\"t\":18}。請依 [t,F_t,next_support,certificate,right_continuous] 欄序回答。","answer":{"kind":"expression","value":"(18, 1, null, constant_on_right_neighborhood_before_next_support, 是)","explanation_zh":"Wave4第四層核對=(18, 1, null, constant_on_right_neighborhood_before_next_support, 是)；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；保留小於等於單調右連續與端點；CDF不混同PMF或density且jump為點質量。"},"difficulty":{"band":"undergraduate_core","level":3,"skills":["累積分布函數"]},"variant":{"family_id":"qf-mod30-cdf-right-continuity","seed":202610306093,"parameters":{"support":[5,12,18],"masses":[[1,4],[1,4],[1,2]],"t":18,"domain":"Exact_finite_discrete_CDF","operation":"cdf-right-continuity","semantic_template":"qf-mod30-cdf-right-continuity/{\"masses\":[[1,4],[1,4],[1,2]],\"support\":[5,12,18],\"t\":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-r06-cumulative-distribution-function-0094","batch_id":"batch-20261014-advance-20261030-r06-cumulative-distribution-function-foundations","language":"zh-Hant","source_mko_ids":["mko-cumulative-distribution-function"],"title_zh":"累積分布函數","stem_zh":"完整有限離散law與F(t)=P(X小於等於t)。操作=cdf-right-continuity；資料={\"support\":[6,13,19],\"masses\":[[1,4],[1,4],[1,2]],\"t\":6}。請依 [t,F_t,next_support,certificate,right_continuous] 欄序回答。","answer":{"kind":"expression","value":"(6, 1/4, 13, constant_on_right_neighborhood_before_next_support, 是)","explanation_zh":"Wave4第四層核對=(6, 1/4, 13, constant_on_right_neighborhood_before_next_support, 是)；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；保留小於等於單調右連續與端點；CDF不混同PMF或density且jump為點質量。"},"difficulty":{"band":"undergraduate_core","level":3,"skills":["累積分布函數"]},"variant":{"family_id":"qf-mod30-cdf-right-continuity","seed":202610306094,"parameters":{"support":[6,13,19],"masses":[[1,4],[1,4],[1,2]],"t":6,"domain":"Exact_finite_discrete_CDF","operation":"cdf-right-continuity","semantic_template":"qf-mod30-cdf-right-continuity/{\"masses\":[[1,4],[1,4],[1,2]],\"support\":[6,13,19],\"t\":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-r06-cumulative-distribution-function-0095","batch_id":"batch-20261014-advance-20261030-r06-cumulative-distribution-function-foundations","language":"zh-Hant","source_mko_ids":["mko-cumulative-distribution-function"],"title_zh":"累積分布函數","stem_zh":"完整有限離散law與F(t)=P(X小於等於t)。操作=cdf-right-continuity；資料={\"support\":[7,14,20],\"masses\":[[1,4],[1,4],[1,2]],\"t\":14}。請依 [t,F_t,next_support,certificate,right_continuous] 欄序回答。","answer":{"kind":"expression","value":"(14, 1/2, 20, constant_on_right_neighborhood_before_next_support, 是)","explanation_zh":"Wave4第四層核對=(14, 1/2, 20, constant_on_right_neighborhood_before_next_support, 是)；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；保留小於等於單調右連續與端點；CDF不混同PMF或density且jump為點質量。"},"difficulty":{"band":"undergraduate_core","level":3,"skills":["累積分布函數"]},"variant":{"family_id":"qf-mod30-cdf-right-continuity","seed":202610306095,"parameters":{"support":[7,14,20],"masses":[[1,4],[1,4],[1,2]],"t":14,"domain":"Exact_finite_discrete_CDF","operation":"cdf-right-continuity","semantic_template":"qf-mod30-cdf-right-continuity/{\"masses\":[[1,4],[1,4],[1,2]],\"support\":[7,14,20],\"t\":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-r06-cumulative-distribution-function-0096","batch_id":"batch-20261014-advance-20261030-r06-cumulative-distribution-function-foundations","language":"zh-Hant","source_mko_ids":["mko-cumulative-distribution-function"],"title_zh":"累積分布函數","stem_zh":"完整有限離散law與F(t)=P(X小於等於t)。操作=cdf-right-continuity；資料={\"support\":[8,15,21],\"masses\":[[1,4],[1,4],[1,2]],\"t\":21}。請依 [t,F_t,next_support,certificate,right_continuous] 欄序回答。","answer":{"kind":"expression","value":"(21, 1, null, constant_on_right_neighborhood_before_next_support, 是)","explanation_zh":"Wave4第四層核對=(21, 1, null, constant_on_right_neighborhood_before_next_support, 是)；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；保留小於等於單調右連續與端點；CDF不混同PMF或density且jump為點質量。"},"difficulty":{"band":"undergraduate_core","level":3,"skills":["累積分布函數"]},"variant":{"family_id":"qf-mod30-cdf-right-continuity","seed":202610306096,"parameters":{"support":[8,15,21],"masses":[[1,4],[1,4],[1,2]],"t":21,"domain":"Exact_finite_discrete_CDF","operation":"cdf-right-continuity","semantic_template":"qf-mod30-cdf-right-continuity/{\"masses\":[[1,4],[1,4],[1,2]],\"support\":[8,15,21],\"t\":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-r06-cumulative-distribution-function-0097","batch_id":"batch-20261014-advance-20261030-r06-cumulative-distribution-function-foundations","language":"zh-Hant","source_mko_ids":["mko-cumulative-distribution-function"],"title_zh":"累積分布函數","stem_zh":"完整有限離散law與F(t)=P(X小於等於t)。操作=cdf-right-continuity；資料={\"support\":[9,16,22],\"masses\":[[1,4],[1,4],[1,2]],\"t\":9}。請依 [t,F_t,next_support,certificate,right_continuous] 欄序回答。","answer":{"kind":"expression","value":"(9, 1/4, 16, constant_on_right_neighborhood_before_next_support, 是)","explanation_zh":"Wave4第四層核對=(9, 1/4, 16, constant_on_right_neighborhood_before_next_support, 是)；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；保留小於等於單調右連續與端點；CDF不混同PMF或density且jump為點質量。"},"difficulty":{"band":"undergraduate_core","level":3,"skills":["累積分布函數"]},"variant":{"family_id":"qf-mod30-cdf-right-continuity","seed":202610306097,"parameters":{"support":[9,16,22],"masses":[[1,4],[1,4],[1,2]],"t":9,"domain":"Exact_finite_discrete_CDF","operation":"cdf-right-continuity","semantic_template":"qf-mod30-cdf-right-continuity/{\"masses\":[[1,4],[1,4],[1,2]],\"support\":[9,16,22],\"t\":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-r06-cumulative-distribution-function-0098","batch_id":"batch-20261014-advance-20261030-r06-cumulative-distribution-function-foundations","language":"zh-Hant","source_mko_ids":["mko-cumulative-distribution-function"],"title_zh":"累積分布函數","stem_zh":"完整有限離散law與F(t)=P(X小於等於t)。操作=cdf-right-continuity；資料={\"support\":[10,17,23],\"masses\":[[1,4],[1,4],[1,2]],\"t\":17}。請依 [t,F_t,next_support,certificate,right_continuous] 欄序回答。","answer":{"kind":"expression","value":"(17, 1/2, 23, constant_on_right_neighborhood_before_next_support, 是)","explanation_zh":"Wave4第四層核對=(17, 1/2, 23, constant_on_right_neighborhood_before_next_support, 是)；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；保留小於等於單調右連續與端點；CDF不混同PMF或density且jump為點質量。"},"difficulty":{"band":"undergraduate_core","level":3,"skills":["累積分布函數"]},"variant":{"family_id":"qf-mod30-cdf-right-continuity","seed":202610306098,"parameters":{"support":[10,17,23],"masses":[[1,4],[1,4],[1,2]],"t":17,"domain":"Exact_finite_discrete_CDF","operation":"cdf-right-continuity","semantic_template":"qf-mod30-cdf-right-continuity/{\"masses\":[[1,4],[1,4],[1,2]],\"support\":[10,17,23],\"t\":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-r06-cumulative-distribution-function-0099","batch_id":"batch-20261014-advance-20261030-r06-cumulative-distribution-function-foundations","language":"zh-Hant","source_mko_ids":["mko-cumulative-distribution-function"],"title_zh":"累積分布函數","stem_zh":"完整有限離散law與F(t)=P(X小於等於t)。操作=cdf-right-continuity；資料={\"support\":[11,18,24],\"masses\":[[1,4],[1,4],[1,2]],\"t\":24}。請依 [t,F_t,next_support,certificate,right_continuous] 欄序回答。","answer":{"kind":"expression","value":"(24, 1, null, constant_on_right_neighborhood_before_next_support, 是)","explanation_zh":"Wave4第四層核對=(24, 1, null, constant_on_right_neighborhood_before_next_support, 是)；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；保留小於等於單調右連續與端點；CDF不混同PMF或density且jump為點質量。"},"difficulty":{"band":"undergraduate_core","level":3,"skills":["累積分布函數"]},"variant":{"family_id":"qf-mod30-cdf-right-continuity","seed":202610306099,"parameters":{"support":[11,18,24],"masses":[[1,4],[1,4],[1,2]],"t":24,"domain":"Exact_finite_discrete_CDF","operation":"cdf-right-continuity","semantic_template":"qf-mod30-cdf-right-continuity/{\"masses\":[[1,4],[1,4],[1,2]],\"support\":[11,18,24],\"t\":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-r06-cumulative-distribution-function-0100","batch_id":"batch-20261014-advance-20261030-r06-cumulative-distribution-function-foundations","language":"zh-Hant","source_mko_ids":["mko-cumulative-distribution-function"],"title_zh":"累積分布函數","stem_zh":"完整有限離散law與F(t)=P(X小於等於t)。操作=cdf-right-continuity；資料={\"support\":[12,19,25],\"masses\":[[1,4],[1,4],[1,2]],\"t\":12}。請依 [t,F_t,next_support,certificate,right_continuous] 欄序回答。","answer":{"kind":"expression","value":"(12, 1/4, 19, constant_on_right_neighborhood_before_next_support, 是)","explanation_zh":"Wave4第四層核對=(12, 1/4, 19, constant_on_right_neighborhood_before_next_support, 是)；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；保留小於等於單調右連續與端點；CDF不混同PMF或density且jump為點質量。"},"difficulty":{"band":"undergraduate_core","level":3,"skills":["累積分布函數"]},"variant":{"family_id":"qf-mod30-cdf-right-continuity","seed":202610306100,"parameters":{"support":[12,19,25],"masses":[[1,4],[1,4],[1,2]],"t":12,"domain":"Exact_finite_discrete_CDF","operation":"cdf-right-continuity","semantic_template":"qf-mod30-cdf-right-continuity/{\"masses\":[[1,4],[1,4],[1,2]],\"support\":[12,19,25],\"t\":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"}}