{"schema_version":"ocme-question-v0.1","id":"q-20261014-advance-20261111-r04-continuous-real-distribution-function-0001","batch_id":"batch-20261014-advance-20261111-r04-continuous-real-distribution-function-foundations","language":"zh-Hant","source_mko_ids":["mko-continuous-real-distribution-function"],"title_zh":"連續實值分布函數","stem_zh":"CDF本身continuous、nondecreasing、right-continuous且audit query_points嚴格遞增。操作=contcdf-piecewise-linear-qualification；資料={\"knots\":[-2,0,2],\"values\":[0,[1,2],1]}。請依 exact_ordered_tuple_declared_by_interface 欄序回答。","answer":{"kind":"expression","value":"([-2, 0, 2], [0, 1/2, 1], 是, 是, 是, 是, linear_interpolation_is_continuous_and_flat_intervals_are_allowed)","explanation_zh":"Wave6第五層核對=([-2, 0, 2], [0, 1/2, 1], 是, 是, 是, 是, linear_interpolation_is_continuous_and_flat_intervals_are_allowed)；依完整明示資料獨立重算；continuous CDF無jumps所以singletons質量0，flat intervals仍允許且兩端limits為0與1；continuous或atomless不推出density或absolute continuity；singular Cantor law是boundary。"},"difficulty":{"band":"undergraduate_core","level":1,"skills":["連續實值分布函數"]},"variant":{"family_id":"qf-mod42-contcdf-piecewise-linear-qualification","seed":202611114001,"parameters":{"knots":[-2,0,2],"values":[0,[1,2],1],"domain":"Exact_continuous_piecewise_linear_CDF","operation":"contcdf-piecewise-linear-qualification","semantic_template":"qf-mod42-contcdf-piecewise-linear-qualification/{\"knots\":[-2,0,2],\"values\":[0,[1,2],1]}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_or_symbolic_model","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"候選須主端重算；不構成人工審定、Lagrange converse existence、higher-order analyticity、sampled Hausdorff、CDF density、unchecked Catalan division、Euler criterion、bounded NFA rejection、Lean或Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-14","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261014-advance-20261111-r04-continuous-real-distribution-function-0002","batch_id":"batch-20261014-advance-20261111-r04-continuous-real-distribution-function-foundations","language":"zh-Hant","source_mko_ids":["mko-continuous-real-distribution-function"],"title_zh":"連續實值分布函數","stem_zh":"CDF本身continuous、nondecreasing、right-continuous且audit query_points嚴格遞增。操作=contcdf-piecewise-linear-qualification；資料={\"knots\":[-3,0,3],\"values\":[0,[2,3],1]}。請依 exact_ordered_tuple_declared_by_interface 欄序回答。","answer":{"kind":"expression","value":"([-3, 0, 3], [0, 2/3, 1], 是, 是, 是, 是, linear_interpolation_is_continuous_and_flat_intervals_are_allowed)","explanation_zh":"Wave6第五層核對=([-3, 0, 3], [0, 2/3, 1], 是, 是, 是, 是, linear_interpolation_is_continuous_and_flat_intervals_are_allowed)；依完整明示資料獨立重算；continuous CDF無jumps所以singletons質量0，flat intervals仍允許且兩端limits為0與1；continuous或atomless不推出density或absolute continuity；singular Cantor law是boundary。"},"difficulty":{"band":"undergraduate_core","level":1,"skills":["連續實值分布函數"]},"variant":{"family_id":"qf-mod42-contcdf-piecewise-linear-qualification","seed":202611114002,"parameters":{"knots":[-3,0,3],"values":[0,[2,3],1],"domain":"Exact_continuous_piecewise_linear_CDF","operation":"contcdf-piecewise-linear-qualification","semantic_template":"qf-mod42-contcdf-piecewise-linear-qualification/{\"knots\":[-3,0,3],\"values\":[0,[2,3],1]}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_or_symbolic_model","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"候選須主端重算；不構成人工審定、Lagrange converse existence、higher-order analyticity、sampled Hausdorff、CDF density、unchecked Catalan division、Euler criterion、bounded NFA rejection、Lean或Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-14","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261014-advance-20261111-r04-continuous-real-distribution-function-0003","batch_id":"batch-20261014-advance-20261111-r04-continuous-real-distribution-function-foundations","language":"zh-Hant","source_mko_ids":["mko-continuous-real-distribution-function"],"title_zh":"連續實值分布函數","stem_zh":"CDF本身continuous、nondecreasing、right-continuous且audit query_points嚴格遞增。操作=contcdf-piecewise-linear-qualification；資料={\"knots\":[-4,0,4],\"values\":[0,[3,4],1]}。請依 exact_ordered_tuple_declared_by_interface 欄序回答。","answer":{"kind":"expression","value":"([-4, 0, 4], [0, 3/4, 1], 是, 是, 是, 是, linear_interpolation_is_continuous_and_flat_intervals_are_allowed)","explanation_zh":"Wave6第五層核對=([-4, 0, 4], [0, 3/4, 1], 是, 是, 是, 是, linear_interpolation_is_continuous_and_flat_intervals_are_allowed)；依完整明示資料獨立重算；continuous CDF無jumps所以singletons質量0，flat intervals仍允許且兩端limits為0與1；continuous或atomless不推出density或absolute continuity；singular Cantor law是boundary。"},"difficulty":{"band":"undergraduate_core","level":1,"skills":["連續實值分布函數"]},"variant":{"family_id":"qf-mod42-contcdf-piecewise-linear-qualification","seed":202611114003,"parameters":{"knots":[-4,0,4],"values":[0,[3,4],1],"domain":"Exact_continuous_piecewise_linear_CDF","operation":"contcdf-piecewise-linear-qualification","semantic_template":"qf-mod42-contcdf-piecewise-linear-qualification/{\"knots\":[-4,0,4],\"values\":[0,[3,4],1]}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_or_symbolic_model","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"候選須主端重算；不構成人工審定、Lagrange converse existence、higher-order analyticity、sampled Hausdorff、CDF density、unchecked Catalan division、Euler criterion、bounded NFA rejection、Lean或Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-14","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261014-advance-20261111-r04-continuous-real-distribution-function-0004","batch_id":"batch-20261014-advance-20261111-r04-continuous-real-distribution-function-foundations","language":"zh-Hant","source_mko_ids":["mko-continuous-real-distribution-function"],"title_zh":"連續實值分布函數","stem_zh":"CDF本身continuous、nondecreasing、right-continuous且audit query_points嚴格遞增。操作=contcdf-piecewise-linear-qualification；資料={\"knots\":[-5,0,5],\"values\":[0,[4,5],1]}。請依 exact_ordered_tuple_declared_by_interface 欄序回答。","answer":{"kind":"expression","value":"([-5, 0, 5], [0, 4/5, 1], 是, 是, 是, 是, linear_interpolation_is_continuous_and_flat_intervals_are_allowed)","explanation_zh":"Wave6第五層核對=([-5, 0, 5], [0, 4/5, 1], 是, 是, 是, 是, linear_interpolation_is_continuous_and_flat_intervals_are_allowed)；依完整明示資料獨立重算；continuous CDF無jumps所以singletons質量0，flat intervals仍允許且兩端limits為0與1；continuous或atomless不推出density或absolute continuity；singular Cantor law是boundary。"},"difficulty":{"band":"undergraduate_core","level":1,"skills":["連續實值分布函數"]},"variant":{"family_id":"qf-mod42-contcdf-piecewise-linear-qualification","seed":202611114004,"parameters":{"knots":[-5,0,5],"values":[0,[4,5],1],"domain":"Exact_continuous_piecewise_linear_CDF","operation":"contcdf-piecewise-linear-qualification","semantic_template":"qf-mod42-contcdf-piecewise-linear-qualification/{\"knots\":[-5,0,5],\"values\":[0,[4,5],1]}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_or_symbolic_model","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"候選須主端重算；不構成人工審定、Lagrange converse existence、higher-order analyticity、sampled Hausdorff、CDF density、unchecked Catalan division、Euler criterion、bounded NFA rejection、Lean或Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-14","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261014-advance-20261111-r04-continuous-real-distribution-function-0005","batch_id":"batch-20261014-advance-20261111-r04-continuous-real-distribution-function-foundations","language":"zh-Hant","source_mko_ids":["mko-continuous-real-distribution-function"],"title_zh":"連續實值分布函數","stem_zh":"CDF本身continuous、nondecreasing、right-continuous且audit query_points嚴格遞增。操作=contcdf-piecewise-linear-qualification；資料={\"knots\":[-6,0,6],\"values\":[0,[5,6],1]}。請依 exact_ordered_tuple_declared_by_interface 欄序回答。","answer":{"kind":"expression","value":"([-6, 0, 6], [0, 5/6, 1], 是, 是, 是, 是, linear_interpolation_is_continuous_and_flat_intervals_are_allowed)","explanation_zh":"Wave6第五層核對=([-6, 0, 6], [0, 5/6, 1], 是, 是, 是, 是, linear_interpolation_is_continuous_and_flat_intervals_are_allowed)；依完整明示資料獨立重算；continuous CDF無jumps所以singletons質量0，flat intervals仍允許且兩端limits為0與1；continuous或atomless不推出density或absolute continuity；singular Cantor law是boundary。"},"difficulty":{"band":"undergraduate_core","level":1,"skills":["連續實值分布函數"]},"variant":{"family_id":"qf-mod42-contcdf-piecewise-linear-qualification","seed":202611114005,"parameters":{"knots":[-6,0,6],"values":[0,[5,6],1],"domain":"Exact_continuous_piecewise_linear_CDF","operation":"contcdf-piecewise-linear-qualification","semantic_template":"qf-mod42-contcdf-piecewise-linear-qualification/{\"knots\":[-6,0,6],\"values\":[0,[5,6],1]}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_or_symbolic_model","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"候選須主端重算；不構成人工審定、Lagrange converse existence、higher-order analyticity、sampled Hausdorff、CDF density、unchecked Catalan division、Euler criterion、bounded NFA rejection、Lean或Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-14","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261014-advance-20261111-r04-continuous-real-distribution-function-0006","batch_id":"batch-20261014-advance-20261111-r04-continuous-real-distribution-function-foundations","language":"zh-Hant","source_mko_ids":["mko-continuous-real-distribution-function"],"title_zh":"連續實值分布函數","stem_zh":"CDF本身continuous、nondecreasing、right-continuous且audit query_points嚴格遞增。操作=contcdf-piecewise-linear-qualification；資料={\"knots\":[-7,0,7],\"values\":[0,[6,7],1]}。請依 exact_ordered_tuple_declared_by_interface 欄序回答。","answer":{"kind":"expression","value":"([-7, 0, 7], [0, 6/7, 1], 是, 是, 是, 是, linear_interpolation_is_continuous_and_flat_intervals_are_allowed)","explanation_zh":"Wave6第五層核對=([-7, 0, 7], [0, 6/7, 1], 是, 是, 是, 是, linear_interpolation_is_continuous_and_flat_intervals_are_allowed)；依完整明示資料獨立重算；continuous CDF無jumps所以singletons質量0，flat intervals仍允許且兩端limits為0與1；continuous或atomless不推出density或absolute continuity；singular Cantor law是boundary。"},"difficulty":{"band":"undergraduate_core","level":1,"skills":["連續實值分布函數"]},"variant":{"family_id":"qf-mod42-contcdf-piecewise-linear-qualification","seed":202611114006,"parameters":{"knots":[-7,0,7],"values":[0,[6,7],1],"domain":"Exact_continuous_piecewise_linear_CDF","operation":"contcdf-piecewise-linear-qualification","semantic_template":"qf-mod42-contcdf-piecewise-linear-qualification/{\"knots\":[-7,0,7],\"values\":[0,[6,7],1]}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_or_symbolic_model","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"候選須主端重算；不構成人工審定、Lagrange converse existence、higher-order analyticity、sampled Hausdorff、CDF density、unchecked Catalan division、Euler criterion、bounded NFA rejection、Lean或Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-14","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261014-advance-20261111-r04-continuous-real-distribution-function-0007","batch_id":"batch-20261014-advance-20261111-r04-continuous-real-distribution-function-foundations","language":"zh-Hant","source_mko_ids":["mko-continuous-real-distribution-function"],"title_zh":"連續實值分布函數","stem_zh":"CDF本身continuous、nondecreasing、right-continuous且audit query_points嚴格遞增。操作=contcdf-piecewise-linear-qualification；資料={\"knots\":[-8,0,8],\"values\":[0,[7,8],1]}。請依 exact_ordered_tuple_declared_by_interface 欄序回答。","answer":{"kind":"expression","value":"([-8, 0, 8], [0, 7/8, 1], 是, 是, 是, 是, linear_interpolation_is_continuous_and_flat_intervals_are_allowed)","explanation_zh":"Wave6第五層核對=([-8, 0, 8], [0, 7/8, 1], 是, 是, 是, 是, linear_interpolation_is_continuous_and_flat_intervals_are_allowed)；依完整明示資料獨立重算；continuous CDF無jumps所以singletons質量0，flat intervals仍允許且兩端limits為0與1；continuous或atomless不推出density或absolute continuity；singular Cantor law是boundary。"},"difficulty":{"band":"undergraduate_core","level":1,"skills":["連續實值分布函數"]},"variant":{"family_id":"qf-mod42-contcdf-piecewise-linear-qualification","seed":202611114007,"parameters":{"knots":[-8,0,8],"values":[0,[7,8],1],"domain":"Exact_continuous_piecewise_linear_CDF","operation":"contcdf-piecewise-linear-qualification","semantic_template":"qf-mod42-contcdf-piecewise-linear-qualification/{\"knots\":[-8,0,8],\"values\":[0,[7,8],1]}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_or_symbolic_model","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"候選須主端重算；不構成人工審定、Lagrange converse existence、higher-order analyticity、sampled Hausdorff、CDF density、unchecked Catalan division、Euler criterion、bounded NFA rejection、Lean或Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-14","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261014-advance-20261111-r04-continuous-real-distribution-function-0008","batch_id":"batch-20261014-advance-20261111-r04-continuous-real-distribution-function-foundations","language":"zh-Hant","source_mko_ids":["mko-continuous-real-distribution-function"],"title_zh":"連續實值分布函數","stem_zh":"CDF本身continuous、nondecreasing、right-continuous且audit query_points嚴格遞增。操作=contcdf-piecewise-linear-qualification；資料={\"knots\":[-9,0,9],\"values\":[0,[8,9],1]}。請依 exact_ordered_tuple_declared_by_interface 欄序回答。","answer":{"kind":"expression","value":"([-9, 0, 9], [0, 8/9, 1], 是, 是, 是, 是, linear_interpolation_is_continuous_and_flat_intervals_are_allowed)","explanation_zh":"Wave6第五層核對=([-9, 0, 9], [0, 8/9, 1], 是, 是, 是, 是, linear_interpolation_is_continuous_and_flat_intervals_are_allowed)；依完整明示資料獨立重算；continuous CDF無jumps所以singletons質量0，flat intervals仍允許且兩端limits為0與1；continuous或atomless不推出density或absolute continuity；singular Cantor law是boundary。"},"difficulty":{"band":"undergraduate_core","level":1,"skills":["連續實值分布函數"]},"variant":{"family_id":"qf-mod42-contcdf-piecewise-linear-qualification","seed":202611114008,"parameters":{"knots":[-9,0,9],"values":[0,[8,9],1],"domain":"Exact_continuous_piecewise_linear_CDF","operation":"contcdf-piecewise-linear-qualification","semantic_template":"qf-mod42-contcdf-piecewise-linear-qualification/{\"knots\":[-9,0,9],\"values\":[0,[8,9],1]}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_or_symbolic_model","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"候選須主端重算；不構成人工審定、Lagrange converse existence、higher-order analyticity、sampled Hausdorff、CDF density、unchecked Catalan division、Euler criterion、bounded NFA rejection、Lean或Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-14","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261014-advance-20261111-r04-continuous-real-distribution-function-0009","batch_id":"batch-20261014-advance-20261111-r04-continuous-real-distribution-function-foundations","language":"zh-Hant","source_mko_ids":["mko-continuous-real-distribution-function"],"title_zh":"連續實值分布函數","stem_zh":"CDF本身continuous、nondecreasing、right-continuous且audit query_points嚴格遞增。操作=contcdf-piecewise-linear-qualification；資料={\"knots\":[-10,0,10],\"values\":[0,[9,10],1]}。請依 exact_ordered_tuple_declared_by_interface 欄序回答。","answer":{"kind":"expression","value":"([-10, 0, 10], [0, 9/10, 1], 是, 是, 是, 是, linear_interpolation_is_continuous_and_flat_intervals_are_allowed)","explanation_zh":"Wave6第五層核對=([-10, 0, 10], [0, 9/10, 1], 是, 是, 是, 是, linear_interpolation_is_continuous_and_flat_intervals_are_allowed)；依完整明示資料獨立重算；continuous CDF無jumps所以singletons質量0，flat intervals仍允許且兩端limits為0與1；continuous或atomless不推出density或absolute continuity；singular Cantor law是boundary。"},"difficulty":{"band":"undergraduate_core","level":2,"skills":["連續實值分布函數"]},"variant":{"family_id":"qf-mod42-contcdf-piecewise-linear-qualification","seed":202611114009,"parameters":{"knots":[-10,0,10],"values":[0,[9,10],1],"domain":"Exact_continuous_piecewise_linear_CDF","operation":"contcdf-piecewise-linear-qualification","semantic_template":"qf-mod42-contcdf-piecewise-linear-qualification/{\"knots\":[-10,0,10],\"values\":[0,[9,10],1]}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_or_symbolic_model","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"候選須主端重算；不構成人工審定、Lagrange converse existence、higher-order analyticity、sampled Hausdorff、CDF density、unchecked Catalan division、Euler criterion、bounded NFA rejection、Lean或Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-14","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261014-advance-20261111-r04-continuous-real-distribution-function-0010","batch_id":"batch-20261014-advance-20261111-r04-continuous-real-distribution-function-foundations","language":"zh-Hant","source_mko_ids":["mko-continuous-real-distribution-function"],"title_zh":"連續實值分布函數","stem_zh":"CDF本身continuous、nondecreasing、right-continuous且audit query_points嚴格遞增。操作=contcdf-piecewise-linear-qualification；資料={\"knots\":[-11,0,11],\"values\":[0,[10,11],1]}。請依 exact_ordered_tuple_declared_by_interface 欄序回答。","answer":{"kind":"expression","value":"([-11, 0, 11], [0, 10/11, 1], 是, 是, 是, 是, linear_interpolation_is_continuous_and_flat_intervals_are_allowed)","explanation_zh":"Wave6第五層核對=([-11, 0, 11], [0, 10/11, 1], 是, 是, 是, 是, linear_interpolation_is_continuous_and_flat_intervals_are_allowed)；依完整明示資料獨立重算；continuous CDF無jumps所以singletons質量0，flat intervals仍允許且兩端limits為0與1；continuous或atomless不推出density或absolute continuity；singular Cantor law是boundary。"},"difficulty":{"band":"undergraduate_core","level":2,"skills":["連續實值分布函數"]},"variant":{"family_id":"qf-mod42-contcdf-piecewise-linear-qualification","seed":202611114010,"parameters":{"knots":[-11,0,11],"values":[0,[10,11],1],"domain":"Exact_continuous_piecewise_linear_CDF","operation":"contcdf-piecewise-linear-qualification","semantic_template":"qf-mod42-contcdf-piecewise-linear-qualification/{\"knots\":[-11,0,11],\"values\":[0,[10,11],1]}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_or_symbolic_model","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"候選須主端重算；不構成人工審定、Lagrange converse existence、higher-order analyticity、sampled Hausdorff、CDF density、unchecked Catalan division、Euler criterion、bounded NFA rejection、Lean或Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-14","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261014-advance-20261111-r04-continuous-real-distribution-function-0011","batch_id":"batch-20261014-advance-20261111-r04-continuous-real-distribution-function-foundations","language":"zh-Hant","source_mko_ids":["mko-continuous-real-distribution-function"],"title_zh":"連續實值分布函數","stem_zh":"CDF本身continuous、nondecreasing、right-continuous且audit query_points嚴格遞增。操作=contcdf-piecewise-linear-qualification；資料={\"knots\":[-12,0,12],\"values\":[0,[11,12],1]}。請依 exact_ordered_tuple_declared_by_interface 欄序回答。","answer":{"kind":"expression","value":"([-12, 0, 12], [0, 11/12, 1], 是, 是, 是, 是, linear_interpolation_is_continuous_and_flat_intervals_are_allowed)","explanation_zh":"Wave6第五層核對=([-12, 0, 12], [0, 11/12, 1], 是, 是, 是, 是, linear_interpolation_is_continuous_and_flat_intervals_are_allowed)；依完整明示資料獨立重算；continuous CDF無jumps所以singletons質量0，flat intervals仍允許且兩端limits為0與1；continuous或atomless不推出density或absolute continuity；singular Cantor law是boundary。"},"difficulty":{"band":"undergraduate_core","level":2,"skills":["連續實值分布函數"]},"variant":{"family_id":"qf-mod42-contcdf-piecewise-linear-qualification","seed":202611114011,"parameters":{"knots":[-12,0,12],"values":[0,[11,12],1],"domain":"Exact_continuous_piecewise_linear_CDF","operation":"contcdf-piecewise-linear-qualification","semantic_template":"qf-mod42-contcdf-piecewise-linear-qualification/{\"knots\":[-12,0,12],\"values\":[0,[11,12],1]}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_or_symbolic_model","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"候選須主端重算；不構成人工審定、Lagrange converse existence、higher-order analyticity、sampled Hausdorff、CDF density、unchecked Catalan division、Euler criterion、bounded NFA rejection、Lean或Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-14","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261014-advance-20261111-r04-continuous-real-distribution-function-0012","batch_id":"batch-20261014-advance-20261111-r04-continuous-real-distribution-function-foundations","language":"zh-Hant","source_mko_ids":["mko-continuous-real-distribution-function"],"title_zh":"連續實值分布函數","stem_zh":"CDF本身continuous、nondecreasing、right-continuous且audit query_points嚴格遞增。操作=contcdf-piecewise-linear-qualification；資料={\"knots\":[-13,0,13],\"values\":[0,[12,13],1]}。請依 exact_ordered_tuple_declared_by_interface 欄序回答。","answer":{"kind":"expression","value":"([-13, 0, 13], [0, 12/13, 1], 是, 是, 是, 是, linear_interpolation_is_continuous_and_flat_intervals_are_allowed)","explanation_zh":"Wave6第五層核對=([-13, 0, 13], [0, 12/13, 1], 是, 是, 是, 是, linear_interpolation_is_continuous_and_flat_intervals_are_allowed)；依完整明示資料獨立重算；continuous CDF無jumps所以singletons質量0，flat intervals仍允許且兩端limits為0與1；continuous或atomless不推出density或absolute continuity；singular Cantor law是boundary。"},"difficulty":{"band":"undergraduate_core","level":2,"skills":["連續實值分布函數"]},"variant":{"family_id":"qf-mod42-contcdf-piecewise-linear-qualification","seed":202611114012,"parameters":{"knots":[-13,0,13],"values":[0,[12,13],1],"domain":"Exact_continuous_piecewise_linear_CDF","operation":"contcdf-piecewise-linear-qualification","semantic_template":"qf-mod42-contcdf-piecewise-linear-qualification/{\"knots\":[-13,0,13],\"values\":[0,[12,13],1]}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_or_symbolic_model","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"候選須主端重算；不構成人工審定、Lagrange converse existence、higher-order analyticity、sampled Hausdorff、CDF density、unchecked Catalan division、Euler criterion、bounded NFA rejection、Lean或Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-14","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261014-advance-20261111-r04-continuous-real-distribution-function-0013","batch_id":"batch-20261014-advance-20261111-r04-continuous-real-distribution-function-foundations","language":"zh-Hant","source_mko_ids":["mko-continuous-real-distribution-function"],"title_zh":"連續實值分布函數","stem_zh":"CDF本身continuous、nondecreasing、right-continuous且audit query_points嚴格遞增。操作=contcdf-piecewise-linear-qualification；資料={\"knots\":[-14,0,14],\"values\":[0,[13,14],1]}。請依 exact_ordered_tuple_declared_by_interface 欄序回答。","answer":{"kind":"expression","value":"([-14, 0, 14], [0, 13/14, 1], 是, 是, 是, 是, linear_interpolation_is_continuous_and_flat_intervals_are_allowed)","explanation_zh":"Wave6第五層核對=([-14, 0, 14], [0, 13/14, 1], 是, 是, 是, 是, linear_interpolation_is_continuous_and_flat_intervals_are_allowed)；依完整明示資料獨立重算；continuous CDF無jumps所以singletons質量0，flat intervals仍允許且兩端limits為0與1；continuous或atomless不推出density或absolute continuity；singular Cantor law是boundary。"},"difficulty":{"band":"undergraduate_core","level":2,"skills":["連續實值分布函數"]},"variant":{"family_id":"qf-mod42-contcdf-piecewise-linear-qualification","seed":202611114013,"parameters":{"knots":[-14,0,14],"values":[0,[13,14],1],"domain":"Exact_continuous_piecewise_linear_CDF","operation":"contcdf-piecewise-linear-qualification","semantic_template":"qf-mod42-contcdf-piecewise-linear-qualification/{\"knots\":[-14,0,14],\"values\":[0,[13,14],1]}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_or_symbolic_model","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"候選須主端重算；不構成人工審定、Lagrange converse existence、higher-order analyticity、sampled Hausdorff、CDF density、unchecked Catalan division、Euler criterion、bounded NFA rejection、Lean或Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-14","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261014-advance-20261111-r04-continuous-real-distribution-function-0014","batch_id":"batch-20261014-advance-20261111-r04-continuous-real-distribution-function-foundations","language":"zh-Hant","source_mko_ids":["mko-continuous-real-distribution-function"],"title_zh":"連續實值分布函數","stem_zh":"CDF本身continuous、nondecreasing、right-continuous且audit query_points嚴格遞增。操作=contcdf-piecewise-linear-qualification；資料={\"knots\":[-15,0,15],\"values\":[0,[14,15],1]}。請依 exact_ordered_tuple_declared_by_interface 欄序回答。","answer":{"kind":"expression","value":"([-15, 0, 15], [0, 14/15, 1], 是, 是, 是, 是, linear_interpolation_is_continuous_and_flat_intervals_are_allowed)","explanation_zh":"Wave6第五層核對=([-15, 0, 15], [0, 14/15, 1], 是, 是, 是, 是, linear_interpolation_is_continuous_and_flat_intervals_are_allowed)；依完整明示資料獨立重算；continuous CDF無jumps所以singletons質量0，flat intervals仍允許且兩端limits為0與1；continuous或atomless不推出density或absolute continuity；singular Cantor law是boundary。"},"difficulty":{"band":"undergraduate_core","level":2,"skills":["連續實值分布函數"]},"variant":{"family_id":"qf-mod42-contcdf-piecewise-linear-qualification","seed":202611114014,"parameters":{"knots":[-15,0,15],"values":[0,[14,15],1],"domain":"Exact_continuous_piecewise_linear_CDF","operation":"contcdf-piecewise-linear-qualification","semantic_template":"qf-mod42-contcdf-piecewise-linear-qualification/{\"knots\":[-15,0,15],\"values\":[0,[14,15],1]}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_or_symbolic_model","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"候選須主端重算；不構成人工審定、Lagrange converse existence、higher-order analyticity、sampled Hausdorff、CDF density、unchecked Catalan division、Euler criterion、bounded NFA rejection、Lean或Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-14","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261014-advance-20261111-r04-continuous-real-distribution-function-0015","batch_id":"batch-20261014-advance-20261111-r04-continuous-real-distribution-function-foundations","language":"zh-Hant","source_mko_ids":["mko-continuous-real-distribution-function"],"title_zh":"連續實值分布函數","stem_zh":"CDF本身continuous、nondecreasing、right-continuous且audit query_points嚴格遞增。操作=contcdf-piecewise-linear-qualification；資料={\"knots\":[-16,0,16],\"values\":[0,[15,16],1]}。請依 exact_ordered_tuple_declared_by_interface 欄序回答。","answer":{"kind":"expression","value":"([-16, 0, 16], [0, 15/16, 1], 是, 是, 是, 是, linear_interpolation_is_continuous_and_flat_intervals_are_allowed)","explanation_zh":"Wave6第五層核對=([-16, 0, 16], [0, 15/16, 1], 是, 是, 是, 是, linear_interpolation_is_continuous_and_flat_intervals_are_allowed)；依完整明示資料獨立重算；continuous CDF無jumps所以singletons質量0，flat intervals仍允許且兩端limits為0與1；continuous或atomless不推出density或absolute continuity；singular Cantor law是boundary。"},"difficulty":{"band":"undergraduate_core","level":2,"skills":["連續實值分布函數"]},"variant":{"family_id":"qf-mod42-contcdf-piecewise-linear-qualification","seed":202611114015,"parameters":{"knots":[-16,0,16],"values":[0,[15,16],1],"domain":"Exact_continuous_piecewise_linear_CDF","operation":"contcdf-piecewise-linear-qualification","semantic_template":"qf-mod42-contcdf-piecewise-linear-qualification/{\"knots\":[-16,0,16],\"values\":[0,[15,16],1]}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_or_symbolic_model","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"候選須主端重算；不構成人工審定、Lagrange converse existence、higher-order analyticity、sampled Hausdorff、CDF density、unchecked Catalan division、Euler criterion、bounded NFA rejection、Lean或Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-14","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261014-advance-20261111-r04-continuous-real-distribution-function-0016","batch_id":"batch-20261014-advance-20261111-r04-continuous-real-distribution-function-foundations","language":"zh-Hant","source_mko_ids":["mko-continuous-real-distribution-function"],"title_zh":"連續實值分布函數","stem_zh":"CDF本身continuous、nondecreasing、right-continuous且audit query_points嚴格遞增。操作=contcdf-piecewise-linear-qualification；資料={\"knots\":[-17,0,17],\"values\":[0,[16,17],1]}。請依 exact_ordered_tuple_declared_by_interface 欄序回答。","answer":{"kind":"expression","value":"([-17, 0, 17], [0, 16/17, 1], 是, 是, 是, 是, linear_interpolation_is_continuous_and_flat_intervals_are_allowed)","explanation_zh":"Wave6第五層核對=([-17, 0, 17], [0, 16/17, 1], 是, 是, 是, 是, linear_interpolation_is_continuous_and_flat_intervals_are_allowed)；依完整明示資料獨立重算；continuous CDF無jumps所以singletons質量0，flat intervals仍允許且兩端limits為0與1；continuous或atomless不推出density或absolute continuity；singular Cantor law是boundary。"},"difficulty":{"band":"undergraduate_core","level":2,"skills":["連續實值分布函數"]},"variant":{"family_id":"qf-mod42-contcdf-piecewise-linear-qualification","seed":202611114016,"parameters":{"knots":[-17,0,17],"values":[0,[16,17],1],"domain":"Exact_continuous_piecewise_linear_CDF","operation":"contcdf-piecewise-linear-qualification","semantic_template":"qf-mod42-contcdf-piecewise-linear-qualification/{\"knots\":[-17,0,17],\"values\":[0,[16,17],1]}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_or_symbolic_model","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"候選須主端重算；不構成人工審定、Lagrange converse existence、higher-order analyticity、sampled Hausdorff、CDF density、unchecked Catalan division、Euler criterion、bounded NFA rejection、Lean或Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-14","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261014-advance-20261111-r04-continuous-real-distribution-function-0017","batch_id":"batch-20261014-advance-20261111-r04-continuous-real-distribution-function-foundations","language":"zh-Hant","source_mko_ids":["mko-continuous-real-distribution-function"],"title_zh":"連續實值分布函數","stem_zh":"CDF本身continuous、nondecreasing、right-continuous且audit query_points嚴格遞增。操作=contcdf-piecewise-linear-qualification；資料={\"knots\":[-18,0,18],\"values\":[0,[17,18],1]}。請依 exact_ordered_tuple_declared_by_interface 欄序回答。","answer":{"kind":"expression","value":"([-18, 0, 18], [0, 17/18, 1], 是, 是, 是, 是, linear_interpolation_is_continuous_and_flat_intervals_are_allowed)","explanation_zh":"Wave6第五層核對=([-18, 0, 18], [0, 17/18, 1], 是, 是, 是, 是, linear_interpolation_is_continuous_and_flat_intervals_are_allowed)；依完整明示資料獨立重算；continuous CDF無jumps所以singletons質量0，flat intervals仍允許且兩端limits為0與1；continuous或atomless不推出density或absolute continuity；singular Cantor law是boundary。"},"difficulty":{"band":"undergraduate_core","level":2,"skills":["連續實值分布函數"]},"variant":{"family_id":"qf-mod42-contcdf-piecewise-linear-qualification","seed":202611114017,"parameters":{"knots":[-18,0,18],"values":[0,[17,18],1],"domain":"Exact_continuous_piecewise_linear_CDF","operation":"contcdf-piecewise-linear-qualification","semantic_template":"qf-mod42-contcdf-piecewise-linear-qualification/{\"knots\":[-18,0,18],\"values\":[0,[17,18],1]}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_or_symbolic_model","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"候選須主端重算；不構成人工審定、Lagrange converse existence、higher-order analyticity、sampled Hausdorff、CDF density、unchecked Catalan division、Euler criterion、bounded NFA rejection、Lean或Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-14","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261014-advance-20261111-r04-continuous-real-distribution-function-0018","batch_id":"batch-20261014-advance-20261111-r04-continuous-real-distribution-function-foundations","language":"zh-Hant","source_mko_ids":["mko-continuous-real-distribution-function"],"title_zh":"連續實值分布函數","stem_zh":"CDF本身continuous、nondecreasing、right-continuous且audit query_points嚴格遞增。操作=contcdf-piecewise-linear-qualification；資料={\"knots\":[-19,0,19],\"values\":[0,[18,19],1]}。請依 exact_ordered_tuple_declared_by_interface 欄序回答。","answer":{"kind":"expression","value":"([-19, 0, 19], [0, 18/19, 1], 是, 是, 是, 是, linear_interpolation_is_continuous_and_flat_intervals_are_allowed)","explanation_zh":"Wave6第五層核對=([-19, 0, 19], [0, 18/19, 1], 是, 是, 是, 是, linear_interpolation_is_continuous_and_flat_intervals_are_allowed)；依完整明示資料獨立重算；continuous CDF無jumps所以singletons質量0，flat intervals仍允許且兩端limits為0與1；continuous或atomless不推出density或absolute continuity；singular Cantor law是boundary。"},"difficulty":{"band":"undergraduate_core","level":3,"skills":["連續實值分布函數"]},"variant":{"family_id":"qf-mod42-contcdf-piecewise-linear-qualification","seed":202611114018,"parameters":{"knots":[-19,0,19],"values":[0,[18,19],1],"domain":"Exact_continuous_piecewise_linear_CDF","operation":"contcdf-piecewise-linear-qualification","semantic_template":"qf-mod42-contcdf-piecewise-linear-qualification/{\"knots\":[-19,0,19],\"values\":[0,[18,19],1]}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_or_symbolic_model","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"候選須主端重算；不構成人工審定、Lagrange converse existence、higher-order analyticity、sampled Hausdorff、CDF density、unchecked Catalan division、Euler criterion、bounded NFA rejection、Lean或Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-14","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261014-advance-20261111-r04-continuous-real-distribution-function-0019","batch_id":"batch-20261014-advance-20261111-r04-continuous-real-distribution-function-foundations","language":"zh-Hant","source_mko_ids":["mko-continuous-real-distribution-function"],"title_zh":"連續實值分布函數","stem_zh":"CDF本身continuous、nondecreasing、right-continuous且audit query_points嚴格遞增。操作=contcdf-piecewise-linear-qualification；資料={\"knots\":[-20,0,20],\"values\":[0,[19,20],1]}。請依 exact_ordered_tuple_declared_by_interface 欄序回答。","answer":{"kind":"expression","value":"([-20, 0, 20], [0, 19/20, 1], 是, 是, 是, 是, linear_interpolation_is_continuous_and_flat_intervals_are_allowed)","explanation_zh":"Wave6第五層核對=([-20, 0, 20], [0, 19/20, 1], 是, 是, 是, 是, linear_interpolation_is_continuous_and_flat_intervals_are_allowed)；依完整明示資料獨立重算；continuous CDF無jumps所以singletons質量0，flat intervals仍允許且兩端limits為0與1；continuous或atomless不推出density或absolute continuity；singular Cantor law是boundary。"},"difficulty":{"band":"undergraduate_core","level":3,"skills":["連續實值分布函數"]},"variant":{"family_id":"qf-mod42-contcdf-piecewise-linear-qualification","seed":202611114019,"parameters":{"knots":[-20,0,20],"values":[0,[19,20],1],"domain":"Exact_continuous_piecewise_linear_CDF","operation":"contcdf-piecewise-linear-qualification","semantic_template":"qf-mod42-contcdf-piecewise-linear-qualification/{\"knots\":[-20,0,20],\"values\":[0,[19,20],1]}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_or_symbolic_model","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"候選須主端重算；不構成人工審定、Lagrange converse existence、higher-order analyticity、sampled Hausdorff、CDF density、unchecked Catalan division、Euler criterion、bounded NFA rejection、Lean或Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-14","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261014-advance-20261111-r04-continuous-real-distribution-function-0020","batch_id":"batch-20261014-advance-20261111-r04-continuous-real-distribution-function-foundations","language":"zh-Hant","source_mko_ids":["mko-continuous-real-distribution-function"],"title_zh":"連續實值分布函數","stem_zh":"CDF本身continuous、nondecreasing、right-continuous且audit query_points嚴格遞增。操作=contcdf-piecewise-linear-qualification；資料={\"knots\":[-21,0,21],\"values\":[0,[20,21],1]}。請依 exact_ordered_tuple_declared_by_interface 欄序回答。","answer":{"kind":"expression","value":"([-21, 0, 21], [0, 20/21, 1], 是, 是, 是, 是, linear_interpolation_is_continuous_and_flat_intervals_are_allowed)","explanation_zh":"Wave6第五層核對=([-21, 0, 21], [0, 20/21, 1], 是, 是, 是, 是, linear_interpolation_is_continuous_and_flat_intervals_are_allowed)；依完整明示資料獨立重算；continuous CDF無jumps所以singletons質量0，flat intervals仍允許且兩端limits為0與1；continuous或atomless不推出density或absolute continuity；singular Cantor law是boundary。"},"difficulty":{"band":"undergraduate_core","level":3,"skills":["連續實值分布函數"]},"variant":{"family_id":"qf-mod42-contcdf-piecewise-linear-qualification","seed":202611114020,"parameters":{"knots":[-21,0,21],"values":[0,[20,21],1],"domain":"Exact_continuous_piecewise_linear_CDF","operation":"contcdf-piecewise-linear-qualification","semantic_template":"qf-mod42-contcdf-piecewise-linear-qualification/{\"knots\":[-21,0,21],\"values\":[0,[20,21],1]}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_or_symbolic_model","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"候選須主端重算；不構成人工審定、Lagrange converse existence、higher-order analyticity、sampled Hausdorff、CDF density、unchecked Catalan division、Euler criterion、bounded NFA rejection、Lean或Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-14","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261014-advance-20261111-r04-continuous-real-distribution-function-0021","batch_id":"batch-20261014-advance-20261111-r04-continuous-real-distribution-function-foundations","language":"zh-Hant","source_mko_ids":["mko-continuous-real-distribution-function"],"title_zh":"連續實值分布函數","stem_zh":"CDF本身continuous、nondecreasing、right-continuous且audit query_points嚴格遞增。操作=contcdf-piecewise-linear-qualification；資料={\"knots\":[-22,0,22],\"values\":[0,[21,22],1]}。請依 exact_ordered_tuple_declared_by_interface 欄序回答。","answer":{"kind":"expression","value":"([-22, 0, 22], [0, 21/22, 1], 是, 是, 是, 是, linear_interpolation_is_continuous_and_flat_intervals_are_allowed)","explanation_zh":"Wave6第五層核對=([-22, 0, 22], [0, 21/22, 1], 是, 是, 是, 是, linear_interpolation_is_continuous_and_flat_intervals_are_allowed)；依完整明示資料獨立重算；continuous CDF無jumps所以singletons質量0，flat intervals仍允許且兩端limits為0與1；continuous或atomless不推出density或absolute continuity；singular Cantor law是boundary。"},"difficulty":{"band":"undergraduate_core","level":3,"skills":["連續實值分布函數"]},"variant":{"family_id":"qf-mod42-contcdf-piecewise-linear-qualification","seed":202611114021,"parameters":{"knots":[-22,0,22],"values":[0,[21,22],1],"domain":"Exact_continuous_piecewise_linear_CDF","operation":"contcdf-piecewise-linear-qualification","semantic_template":"qf-mod42-contcdf-piecewise-linear-qualification/{\"knots\":[-22,0,22],\"values\":[0,[21,22],1]}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_or_symbolic_model","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"候選須主端重算；不構成人工審定、Lagrange converse existence、higher-order analyticity、sampled Hausdorff、CDF density、unchecked Catalan division、Euler criterion、bounded NFA rejection、Lean或Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-14","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261014-advance-20261111-r04-continuous-real-distribution-function-0022","batch_id":"batch-20261014-advance-20261111-r04-continuous-real-distribution-function-foundations","language":"zh-Hant","source_mko_ids":["mko-continuous-real-distribution-function"],"title_zh":"連續實值分布函數","stem_zh":"CDF本身continuous、nondecreasing、right-continuous且audit query_points嚴格遞增。操作=contcdf-piecewise-linear-qualification；資料={\"knots\":[-23,0,23],\"values\":[0,[22,23],1]}。請依 exact_ordered_tuple_declared_by_interface 欄序回答。","answer":{"kind":"expression","value":"([-23, 0, 23], [0, 22/23, 1], 是, 是, 是, 是, linear_interpolation_is_continuous_and_flat_intervals_are_allowed)","explanation_zh":"Wave6第五層核對=([-23, 0, 23], [0, 22/23, 1], 是, 是, 是, 是, linear_interpolation_is_continuous_and_flat_intervals_are_allowed)；依完整明示資料獨立重算；continuous CDF無jumps所以singletons質量0，flat intervals仍允許且兩端limits為0與1；continuous或atomless不推出density或absolute continuity；singular Cantor law是boundary。"},"difficulty":{"band":"undergraduate_core","level":3,"skills":["連續實值分布函數"]},"variant":{"family_id":"qf-mod42-contcdf-piecewise-linear-qualification","seed":202611114022,"parameters":{"knots":[-23,0,23],"values":[0,[22,23],1],"domain":"Exact_continuous_piecewise_linear_CDF","operation":"contcdf-piecewise-linear-qualification","semantic_template":"qf-mod42-contcdf-piecewise-linear-qualification/{\"knots\":[-23,0,23],\"values\":[0,[22,23],1]}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_or_symbolic_model","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"候選須主端重算；不構成人工審定、Lagrange converse existence、higher-order analyticity、sampled Hausdorff、CDF density、unchecked Catalan division、Euler criterion、bounded NFA rejection、Lean或Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-14","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261014-advance-20261111-r04-continuous-real-distribution-function-0023","batch_id":"batch-20261014-advance-20261111-r04-continuous-real-distribution-function-foundations","language":"zh-Hant","source_mko_ids":["mko-continuous-real-distribution-function"],"title_zh":"連續實值分布函數","stem_zh":"CDF本身continuous、nondecreasing、right-continuous且audit query_points嚴格遞增。操作=contcdf-piecewise-linear-qualification；資料={\"knots\":[-24,0,24],\"values\":[0,[23,24],1]}。請依 exact_ordered_tuple_declared_by_interface 欄序回答。","answer":{"kind":"expression","value":"([-24, 0, 24], [0, 23/24, 1], 是, 是, 是, 是, linear_interpolation_is_continuous_and_flat_intervals_are_allowed)","explanation_zh":"Wave6第五層核對=([-24, 0, 24], [0, 23/24, 1], 是, 是, 是, 是, linear_interpolation_is_continuous_and_flat_intervals_are_allowed)；依完整明示資料獨立重算；continuous CDF無jumps所以singletons質量0，flat intervals仍允許且兩端limits為0與1；continuous或atomless不推出density或absolute continuity；singular Cantor law是boundary。"},"difficulty":{"band":"undergraduate_core","level":3,"skills":["連續實值分布函數"]},"variant":{"family_id":"qf-mod42-contcdf-piecewise-linear-qualification","seed":202611114023,"parameters":{"knots":[-24,0,24],"values":[0,[23,24],1],"domain":"Exact_continuous_piecewise_linear_CDF","operation":"contcdf-piecewise-linear-qualification","semantic_template":"qf-mod42-contcdf-piecewise-linear-qualification/{\"knots\":[-24,0,24],\"values\":[0,[23,24],1]}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_or_symbolic_model","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"候選須主端重算；不構成人工審定、Lagrange converse existence、higher-order analyticity、sampled Hausdorff、CDF density、unchecked Catalan division、Euler criterion、bounded NFA rejection、Lean或Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-14","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261014-advance-20261111-r04-continuous-real-distribution-function-0024","batch_id":"batch-20261014-advance-20261111-r04-continuous-real-distribution-function-foundations","language":"zh-Hant","source_mko_ids":["mko-continuous-real-distribution-function"],"title_zh":"連續實值分布函數","stem_zh":"CDF本身continuous、nondecreasing、right-continuous且audit query_points嚴格遞增。操作=contcdf-piecewise-linear-qualification；資料={\"knots\":[-25,0,25],\"values\":[0,[24,25],1]}。請依 exact_ordered_tuple_declared_by_interface 欄序回答。","answer":{"kind":"expression","value":"([-25, 0, 25], [0, 24/25, 1], 是, 是, 是, 是, linear_interpolation_is_continuous_and_flat_intervals_are_allowed)","explanation_zh":"Wave6第五層核對=([-25, 0, 25], [0, 24/25, 1], 是, 是, 是, 是, linear_interpolation_is_continuous_and_flat_intervals_are_allowed)；依完整明示資料獨立重算；continuous CDF無jumps所以singletons質量0，flat intervals仍允許且兩端limits為0與1；continuous或atomless不推出density或absolute continuity；singular Cantor law是boundary。"},"difficulty":{"band":"undergraduate_core","level":3,"skills":["連續實值分布函數"]},"variant":{"family_id":"qf-mod42-contcdf-piecewise-linear-qualification","seed":202611114024,"parameters":{"knots":[-25,0,25],"values":[0,[24,25],1],"domain":"Exact_continuous_piecewise_linear_CDF","operation":"contcdf-piecewise-linear-qualification","semantic_template":"qf-mod42-contcdf-piecewise-linear-qualification/{\"knots\":[-25,0,25],\"values\":[0,[24,25],1]}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_or_symbolic_model","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"候選須主端重算；不構成人工審定、Lagrange converse existence、higher-order analyticity、sampled Hausdorff、CDF density、unchecked Catalan division、Euler criterion、bounded NFA rejection、Lean或Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-14","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261014-advance-20261111-r04-continuous-real-distribution-function-0025","batch_id":"batch-20261014-advance-20261111-r04-continuous-real-distribution-function-foundations","language":"zh-Hant","source_mko_ids":["mko-continuous-real-distribution-function"],"title_zh":"連續實值分布函數","stem_zh":"CDF本身continuous、nondecreasing、right-continuous且audit query_points嚴格遞增。操作=contcdf-piecewise-linear-qualification；資料={\"knots\":[-26,0,26],\"values\":[0,[25,26],1]}。請依 exact_ordered_tuple_declared_by_interface 欄序回答。","answer":{"kind":"expression","value":"([-26, 0, 26], [0, 25/26, 1], 是, 是, 是, 是, linear_interpolation_is_continuous_and_flat_intervals_are_allowed)","explanation_zh":"Wave6第五層核對=([-26, 0, 26], [0, 25/26, 1], 是, 是, 是, 是, linear_interpolation_is_continuous_and_flat_intervals_are_allowed)；依完整明示資料獨立重算；continuous CDF無jumps所以singletons質量0，flat intervals仍允許且兩端limits為0與1；continuous或atomless不推出density或absolute continuity；singular Cantor law是boundary。"},"difficulty":{"band":"undergraduate_core","level":3,"skills":["連續實值分布函數"]},"variant":{"family_id":"qf-mod42-contcdf-piecewise-linear-qualification","seed":202611114025,"parameters":{"knots":[-26,0,26],"values":[0,[25,26],1],"domain":"Exact_continuous_piecewise_linear_CDF","operation":"contcdf-piecewise-linear-qualification","semantic_template":"qf-mod42-contcdf-piecewise-linear-qualification/{\"knots\":[-26,0,26],\"values\":[0,[25,26],1]}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_or_symbolic_model","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"候選須主端重算；不構成人工審定、Lagrange converse existence、higher-order analyticity、sampled Hausdorff、CDF density、unchecked Catalan division、Euler criterion、bounded NFA rejection、Lean或Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-14","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261014-advance-20261111-r04-continuous-real-distribution-function-0026","batch_id":"batch-20261014-advance-20261111-r04-continuous-real-distribution-function-foundations","language":"zh-Hant","source_mko_ids":["mko-continuous-real-distribution-function"],"title_zh":"連續實值分布函數","stem_zh":"CDF本身continuous、nondecreasing、right-continuous且audit query_points嚴格遞增。操作=contcdf-monotone-endpoint-audit；資料={\"knots\":[-2,0,2],\"values\":[0,[1,2],1],\"query_points\":[-3,0,3]}。請依 exact_ordered_tuple_declared_by_interface 欄序回答。","answer":{"kind":"expression","value":"([[-3, 0], [0, 1/2], [3, 1]], 是, 0, 1, nondecreasing_with_left_zero_and_right_one_limits)","explanation_zh":"Wave6第五層核對=([[-3, 0], [0, 1/2], [3, 1]], 是, 0, 1, nondecreasing_with_left_zero_and_right_one_limits)；依完整明示資料獨立重算；continuous CDF無jumps所以singletons質量0，flat intervals仍允許且兩端limits為0與1；continuous或atomless不推出density或absolute continuity；singular Cantor law是boundary。"},"difficulty":{"band":"undergraduate_core","level":1,"skills":["連續實值分布函數"]},"variant":{"family_id":"qf-mod42-contcdf-monotone-endpoint-audit","seed":202611114026,"parameters":{"knots":[-2,0,2],"values":[0,[1,2],1],"query_points":[-3,0,3],"domain":"Exact_continuous_piecewise_linear_CDF","operation":"contcdf-monotone-endpoint-audit","semantic_template":"qf-mod42-contcdf-monotone-endpoint-audit/{\"knots\":[-2,0,2],\"query_points\":[-3,0,3],\"values\":[0,[1,2],1]}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_or_symbolic_model","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"候選須主端重算；不構成人工審定、Lagrange converse existence、higher-order analyticity、sampled Hausdorff、CDF density、unchecked Catalan division、Euler criterion、bounded NFA rejection、Lean或Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-14","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261014-advance-20261111-r04-continuous-real-distribution-function-0027","batch_id":"batch-20261014-advance-20261111-r04-continuous-real-distribution-function-foundations","language":"zh-Hant","source_mko_ids":["mko-continuous-real-distribution-function"],"title_zh":"連續實值分布函數","stem_zh":"CDF本身continuous、nondecreasing、right-continuous且audit query_points嚴格遞增。操作=contcdf-monotone-endpoint-audit；資料={\"knots\":[-3,0,3],\"values\":[0,[2,3],1],\"query_points\":[-4,0,4]}。請依 exact_ordered_tuple_declared_by_interface 欄序回答。","answer":{"kind":"expression","value":"([[-4, 0], [0, 2/3], [4, 1]], 是, 0, 1, nondecreasing_with_left_zero_and_right_one_limits)","explanation_zh":"Wave6第五層核對=([[-4, 0], [0, 2/3], [4, 1]], 是, 0, 1, nondecreasing_with_left_zero_and_right_one_limits)；依完整明示資料獨立重算；continuous CDF無jumps所以singletons質量0，flat intervals仍允許且兩端limits為0與1；continuous或atomless不推出density或absolute continuity；singular Cantor law是boundary。"},"difficulty":{"band":"undergraduate_core","level":1,"skills":["連續實值分布函數"]},"variant":{"family_id":"qf-mod42-contcdf-monotone-endpoint-audit","seed":202611114027,"parameters":{"knots":[-3,0,3],"values":[0,[2,3],1],"query_points":[-4,0,4],"domain":"Exact_continuous_piecewise_linear_CDF","operation":"contcdf-monotone-endpoint-audit","semantic_template":"qf-mod42-contcdf-monotone-endpoint-audit/{\"knots\":[-3,0,3],\"query_points\":[-4,0,4],\"values\":[0,[2,3],1]}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_or_symbolic_model","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"候選須主端重算；不構成人工審定、Lagrange converse existence、higher-order analyticity、sampled Hausdorff、CDF density、unchecked Catalan division、Euler criterion、bounded NFA rejection、Lean或Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-14","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261014-advance-20261111-r04-continuous-real-distribution-function-0028","batch_id":"batch-20261014-advance-20261111-r04-continuous-real-distribution-function-foundations","language":"zh-Hant","source_mko_ids":["mko-continuous-real-distribution-function"],"title_zh":"連續實值分布函數","stem_zh":"CDF本身continuous、nondecreasing、right-continuous且audit query_points嚴格遞增。操作=contcdf-monotone-endpoint-audit；資料={\"knots\":[-4,0,4],\"values\":[0,[3,4],1],\"query_points\":[-5,0,5]}。請依 exact_ordered_tuple_declared_by_interface 欄序回答。","answer":{"kind":"expression","value":"([[-5, 0], [0, 3/4], [5, 1]], 是, 0, 1, nondecreasing_with_left_zero_and_right_one_limits)","explanation_zh":"Wave6第五層核對=([[-5, 0], [0, 3/4], [5, 1]], 是, 0, 1, nondecreasing_with_left_zero_and_right_one_limits)；依完整明示資料獨立重算；continuous CDF無jumps所以singletons質量0，flat intervals仍允許且兩端limits為0與1；continuous或atomless不推出density或absolute continuity；singular Cantor law是boundary。"},"difficulty":{"band":"undergraduate_core","level":1,"skills":["連續實值分布函數"]},"variant":{"family_id":"qf-mod42-contcdf-monotone-endpoint-audit","seed":202611114028,"parameters":{"knots":[-4,0,4],"values":[0,[3,4],1],"query_points":[-5,0,5],"domain":"Exact_continuous_piecewise_linear_CDF","operation":"contcdf-monotone-endpoint-audit","semantic_template":"qf-mod42-contcdf-monotone-endpoint-audit/{\"knots\":[-4,0,4],\"query_points\":[-5,0,5],\"values\":[0,[3,4],1]}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_or_symbolic_model","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"候選須主端重算；不構成人工審定、Lagrange converse existence、higher-order analyticity、sampled Hausdorff、CDF density、unchecked Catalan division、Euler criterion、bounded NFA rejection、Lean或Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-14","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261014-advance-20261111-r04-continuous-real-distribution-function-0029","batch_id":"batch-20261014-advance-20261111-r04-continuous-real-distribution-function-foundations","language":"zh-Hant","source_mko_ids":["mko-continuous-real-distribution-function"],"title_zh":"連續實值分布函數","stem_zh":"CDF本身continuous、nondecreasing、right-continuous且audit query_points嚴格遞增。操作=contcdf-monotone-endpoint-audit；資料={\"knots\":[-5,0,5],\"values\":[0,[4,5],1],\"query_points\":[-6,0,6]}。請依 exact_ordered_tuple_declared_by_interface 欄序回答。","answer":{"kind":"expression","value":"([[-6, 0], [0, 4/5], [6, 1]], 是, 0, 1, nondecreasing_with_left_zero_and_right_one_limits)","explanation_zh":"Wave6第五層核對=([[-6, 0], [0, 4/5], [6, 1]], 是, 0, 1, nondecreasing_with_left_zero_and_right_one_limits)；依完整明示資料獨立重算；continuous CDF無jumps所以singletons質量0，flat intervals仍允許且兩端limits為0與1；continuous或atomless不推出density或absolute continuity；singular Cantor law是boundary。"},"difficulty":{"band":"undergraduate_core","level":1,"skills":["連續實值分布函數"]},"variant":{"family_id":"qf-mod42-contcdf-monotone-endpoint-audit","seed":202611114029,"parameters":{"knots":[-5,0,5],"values":[0,[4,5],1],"query_points":[-6,0,6],"domain":"Exact_continuous_piecewise_linear_CDF","operation":"contcdf-monotone-endpoint-audit","semantic_template":"qf-mod42-contcdf-monotone-endpoint-audit/{\"knots\":[-5,0,5],\"query_points\":[-6,0,6],\"values\":[0,[4,5],1]}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_or_symbolic_model","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"候選須主端重算；不構成人工審定、Lagrange converse existence、higher-order analyticity、sampled Hausdorff、CDF density、unchecked Catalan division、Euler criterion、bounded NFA rejection、Lean或Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-14","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261014-advance-20261111-r04-continuous-real-distribution-function-0030","batch_id":"batch-20261014-advance-20261111-r04-continuous-real-distribution-function-foundations","language":"zh-Hant","source_mko_ids":["mko-continuous-real-distribution-function"],"title_zh":"連續實值分布函數","stem_zh":"CDF本身continuous、nondecreasing、right-continuous且audit query_points嚴格遞增。操作=contcdf-monotone-endpoint-audit；資料={\"knots\":[-6,0,6],\"values\":[0,[5,6],1],\"query_points\":[-7,0,7]}。請依 exact_ordered_tuple_declared_by_interface 欄序回答。","answer":{"kind":"expression","value":"([[-7, 0], [0, 5/6], [7, 1]], 是, 0, 1, nondecreasing_with_left_zero_and_right_one_limits)","explanation_zh":"Wave6第五層核對=([[-7, 0], [0, 5/6], [7, 1]], 是, 0, 1, nondecreasing_with_left_zero_and_right_one_limits)；依完整明示資料獨立重算；continuous CDF無jumps所以singletons質量0，flat intervals仍允許且兩端limits為0與1；continuous或atomless不推出density或absolute continuity；singular Cantor law是boundary。"},"difficulty":{"band":"undergraduate_core","level":1,"skills":["連續實值分布函數"]},"variant":{"family_id":"qf-mod42-contcdf-monotone-endpoint-audit","seed":202611114030,"parameters":{"knots":[-6,0,6],"values":[0,[5,6],1],"query_points":[-7,0,7],"domain":"Exact_continuous_piecewise_linear_CDF","operation":"contcdf-monotone-endpoint-audit","semantic_template":"qf-mod42-contcdf-monotone-endpoint-audit/{\"knots\":[-6,0,6],\"query_points\":[-7,0,7],\"values\":[0,[5,6],1]}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_or_symbolic_model","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"候選須主端重算；不構成人工審定、Lagrange converse existence、higher-order analyticity、sampled Hausdorff、CDF density、unchecked Catalan division、Euler criterion、bounded NFA rejection、Lean或Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-14","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261014-advance-20261111-r04-continuous-real-distribution-function-0031","batch_id":"batch-20261014-advance-20261111-r04-continuous-real-distribution-function-foundations","language":"zh-Hant","source_mko_ids":["mko-continuous-real-distribution-function"],"title_zh":"連續實值分布函數","stem_zh":"CDF本身continuous、nondecreasing、right-continuous且audit query_points嚴格遞增。操作=contcdf-monotone-endpoint-audit；資料={\"knots\":[-7,0,7],\"values\":[0,[6,7],1],\"query_points\":[-8,0,8]}。請依 exact_ordered_tuple_declared_by_interface 欄序回答。","answer":{"kind":"expression","value":"([[-8, 0], [0, 6/7], [8, 1]], 是, 0, 1, nondecreasing_with_left_zero_and_right_one_limits)","explanation_zh":"Wave6第五層核對=([[-8, 0], [0, 6/7], [8, 1]], 是, 0, 1, nondecreasing_with_left_zero_and_right_one_limits)；依完整明示資料獨立重算；continuous CDF無jumps所以singletons質量0，flat intervals仍允許且兩端limits為0與1；continuous或atomless不推出density或absolute continuity；singular Cantor law是boundary。"},"difficulty":{"band":"undergraduate_core","level":1,"skills":["連續實值分布函數"]},"variant":{"family_id":"qf-mod42-contcdf-monotone-endpoint-audit","seed":202611114031,"parameters":{"knots":[-7,0,7],"values":[0,[6,7],1],"query_points":[-8,0,8],"domain":"Exact_continuous_piecewise_linear_CDF","operation":"contcdf-monotone-endpoint-audit","semantic_template":"qf-mod42-contcdf-monotone-endpoint-audit/{\"knots\":[-7,0,7],\"query_points\":[-8,0,8],\"values\":[0,[6,7],1]}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_or_symbolic_model","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"候選須主端重算；不構成人工審定、Lagrange converse existence、higher-order analyticity、sampled Hausdorff、CDF density、unchecked Catalan division、Euler criterion、bounded NFA rejection、Lean或Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-14","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261014-advance-20261111-r04-continuous-real-distribution-function-0032","batch_id":"batch-20261014-advance-20261111-r04-continuous-real-distribution-function-foundations","language":"zh-Hant","source_mko_ids":["mko-continuous-real-distribution-function"],"title_zh":"連續實值分布函數","stem_zh":"CDF本身continuous、nondecreasing、right-continuous且audit query_points嚴格遞增。操作=contcdf-monotone-endpoint-audit；資料={\"knots\":[-8,0,8],\"values\":[0,[7,8],1],\"query_points\":[-9,0,9]}。請依 exact_ordered_tuple_declared_by_interface 欄序回答。","answer":{"kind":"expression","value":"([[-9, 0], [0, 7/8], [9, 1]], 是, 0, 1, nondecreasing_with_left_zero_and_right_one_limits)","explanation_zh":"Wave6第五層核對=([[-9, 0], [0, 7/8], [9, 1]], 是, 0, 1, nondecreasing_with_left_zero_and_right_one_limits)；依完整明示資料獨立重算；continuous CDF無jumps所以singletons質量0，flat intervals仍允許且兩端limits為0與1；continuous或atomless不推出density或absolute continuity；singular Cantor law是boundary。"},"difficulty":{"band":"undergraduate_core","level":1,"skills":["連續實值分布函數"]},"variant":{"family_id":"qf-mod42-contcdf-monotone-endpoint-audit","seed":202611114032,"parameters":{"knots":[-8,0,8],"values":[0,[7,8],1],"query_points":[-9,0,9],"domain":"Exact_continuous_piecewise_linear_CDF","operation":"contcdf-monotone-endpoint-audit","semantic_template":"qf-mod42-contcdf-monotone-endpoint-audit/{\"knots\":[-8,0,8],\"query_points\":[-9,0,9],\"values\":[0,[7,8],1]}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_or_symbolic_model","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"候選須主端重算；不構成人工審定、Lagrange converse existence、higher-order analyticity、sampled Hausdorff、CDF density、unchecked Catalan division、Euler criterion、bounded NFA rejection、Lean或Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-14","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261014-advance-20261111-r04-continuous-real-distribution-function-0033","batch_id":"batch-20261014-advance-20261111-r04-continuous-real-distribution-function-foundations","language":"zh-Hant","source_mko_ids":["mko-continuous-real-distribution-function"],"title_zh":"連續實值分布函數","stem_zh":"CDF本身continuous、nondecreasing、right-continuous且audit query_points嚴格遞增。操作=contcdf-monotone-endpoint-audit；資料={\"knots\":[-9,0,9],\"values\":[0,[8,9],1],\"query_points\":[-10,0,10]}。請依 exact_ordered_tuple_declared_by_interface 欄序回答。","answer":{"kind":"expression","value":"([[-10, 0], [0, 8/9], [10, 1]], 是, 0, 1, nondecreasing_with_left_zero_and_right_one_limits)","explanation_zh":"Wave6第五層核對=([[-10, 0], [0, 8/9], [10, 1]], 是, 0, 1, nondecreasing_with_left_zero_and_right_one_limits)；依完整明示資料獨立重算；continuous CDF無jumps所以singletons質量0，flat intervals仍允許且兩端limits為0與1；continuous或atomless不推出density或absolute continuity；singular Cantor law是boundary。"},"difficulty":{"band":"undergraduate_core","level":1,"skills":["連續實值分布函數"]},"variant":{"family_id":"qf-mod42-contcdf-monotone-endpoint-audit","seed":202611114033,"parameters":{"knots":[-9,0,9],"values":[0,[8,9],1],"query_points":[-10,0,10],"domain":"Exact_continuous_piecewise_linear_CDF","operation":"contcdf-monotone-endpoint-audit","semantic_template":"qf-mod42-contcdf-monotone-endpoint-audit/{\"knots\":[-9,0,9],\"query_points\":[-10,0,10],\"values\":[0,[8,9],1]}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_or_symbolic_model","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"候選須主端重算；不構成人工審定、Lagrange converse existence、higher-order analyticity、sampled Hausdorff、CDF density、unchecked Catalan division、Euler criterion、bounded NFA rejection、Lean或Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-14","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261014-advance-20261111-r04-continuous-real-distribution-function-0034","batch_id":"batch-20261014-advance-20261111-r04-continuous-real-distribution-function-foundations","language":"zh-Hant","source_mko_ids":["mko-continuous-real-distribution-function"],"title_zh":"連續實值分布函數","stem_zh":"CDF本身continuous、nondecreasing、right-continuous且audit query_points嚴格遞增。操作=contcdf-monotone-endpoint-audit；資料={\"knots\":[-10,0,10],\"values\":[0,[9,10],1],\"query_points\":[-11,0,11]}。請依 exact_ordered_tuple_declared_by_interface 欄序回答。","answer":{"kind":"expression","value":"([[-11, 0], [0, 9/10], [11, 1]], 是, 0, 1, nondecreasing_with_left_zero_and_right_one_limits)","explanation_zh":"Wave6第五層核對=([[-11, 0], [0, 9/10], [11, 1]], 是, 0, 1, nondecreasing_with_left_zero_and_right_one_limits)；依完整明示資料獨立重算；continuous CDF無jumps所以singletons質量0，flat intervals仍允許且兩端limits為0與1；continuous或atomless不推出density或absolute continuity；singular Cantor law是boundary。"},"difficulty":{"band":"undergraduate_core","level":2,"skills":["連續實值分布函數"]},"variant":{"family_id":"qf-mod42-contcdf-monotone-endpoint-audit","seed":202611114034,"parameters":{"knots":[-10,0,10],"values":[0,[9,10],1],"query_points":[-11,0,11],"domain":"Exact_continuous_piecewise_linear_CDF","operation":"contcdf-monotone-endpoint-audit","semantic_template":"qf-mod42-contcdf-monotone-endpoint-audit/{\"knots\":[-10,0,10],\"query_points\":[-11,0,11],\"values\":[0,[9,10],1]}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_or_symbolic_model","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"候選須主端重算；不構成人工審定、Lagrange converse existence、higher-order analyticity、sampled Hausdorff、CDF density、unchecked Catalan division、Euler criterion、bounded NFA rejection、Lean或Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-14","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261014-advance-20261111-r04-continuous-real-distribution-function-0035","batch_id":"batch-20261014-advance-20261111-r04-continuous-real-distribution-function-foundations","language":"zh-Hant","source_mko_ids":["mko-continuous-real-distribution-function"],"title_zh":"連續實值分布函數","stem_zh":"CDF本身continuous、nondecreasing、right-continuous且audit query_points嚴格遞增。操作=contcdf-monotone-endpoint-audit；資料={\"knots\":[-11,0,11],\"values\":[0,[10,11],1],\"query_points\":[-12,0,12]}。請依 exact_ordered_tuple_declared_by_interface 欄序回答。","answer":{"kind":"expression","value":"([[-12, 0], [0, 10/11], [12, 1]], 是, 0, 1, nondecreasing_with_left_zero_and_right_one_limits)","explanation_zh":"Wave6第五層核對=([[-12, 0], [0, 10/11], [12, 1]], 是, 0, 1, nondecreasing_with_left_zero_and_right_one_limits)；依完整明示資料獨立重算；continuous CDF無jumps所以singletons質量0，flat intervals仍允許且兩端limits為0與1；continuous或atomless不推出density或absolute continuity；singular Cantor law是boundary。"},"difficulty":{"band":"undergraduate_core","level":2,"skills":["連續實值分布函數"]},"variant":{"family_id":"qf-mod42-contcdf-monotone-endpoint-audit","seed":202611114035,"parameters":{"knots":[-11,0,11],"values":[0,[10,11],1],"query_points":[-12,0,12],"domain":"Exact_continuous_piecewise_linear_CDF","operation":"contcdf-monotone-endpoint-audit","semantic_template":"qf-mod42-contcdf-monotone-endpoint-audit/{\"knots\":[-11,0,11],\"query_points\":[-12,0,12],\"values\":[0,[10,11],1]}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_or_symbolic_model","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"候選須主端重算；不構成人工審定、Lagrange converse existence、higher-order analyticity、sampled Hausdorff、CDF density、unchecked Catalan division、Euler criterion、bounded NFA rejection、Lean或Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-14","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261014-advance-20261111-r04-continuous-real-distribution-function-0036","batch_id":"batch-20261014-advance-20261111-r04-continuous-real-distribution-function-foundations","language":"zh-Hant","source_mko_ids":["mko-continuous-real-distribution-function"],"title_zh":"連續實值分布函數","stem_zh":"CDF本身continuous、nondecreasing、right-continuous且audit query_points嚴格遞增。操作=contcdf-monotone-endpoint-audit；資料={\"knots\":[-12,0,12],\"values\":[0,[11,12],1],\"query_points\":[-13,0,13]}。請依 exact_ordered_tuple_declared_by_interface 欄序回答。","answer":{"kind":"expression","value":"([[-13, 0], [0, 11/12], [13, 1]], 是, 0, 1, nondecreasing_with_left_zero_and_right_one_limits)","explanation_zh":"Wave6第五層核對=([[-13, 0], [0, 11/12], [13, 1]], 是, 0, 1, nondecreasing_with_left_zero_and_right_one_limits)；依完整明示資料獨立重算；continuous CDF無jumps所以singletons質量0，flat intervals仍允許且兩端limits為0與1；continuous或atomless不推出density或absolute continuity；singular Cantor law是boundary。"},"difficulty":{"band":"undergraduate_core","level":2,"skills":["連續實值分布函數"]},"variant":{"family_id":"qf-mod42-contcdf-monotone-endpoint-audit","seed":202611114036,"parameters":{"knots":[-12,0,12],"values":[0,[11,12],1],"query_points":[-13,0,13],"domain":"Exact_continuous_piecewise_linear_CDF","operation":"contcdf-monotone-endpoint-audit","semantic_template":"qf-mod42-contcdf-monotone-endpoint-audit/{\"knots\":[-12,0,12],\"query_points\":[-13,0,13],\"values\":[0,[11,12],1]}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_or_symbolic_model","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"候選須主端重算；不構成人工審定、Lagrange converse existence、higher-order analyticity、sampled Hausdorff、CDF density、unchecked Catalan division、Euler criterion、bounded NFA rejection、Lean或Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-14","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261014-advance-20261111-r04-continuous-real-distribution-function-0037","batch_id":"batch-20261014-advance-20261111-r04-continuous-real-distribution-function-foundations","language":"zh-Hant","source_mko_ids":["mko-continuous-real-distribution-function"],"title_zh":"連續實值分布函數","stem_zh":"CDF本身continuous、nondecreasing、right-continuous且audit query_points嚴格遞增。操作=contcdf-monotone-endpoint-audit；資料={\"knots\":[-13,0,13],\"values\":[0,[12,13],1],\"query_points\":[-14,0,14]}。請依 exact_ordered_tuple_declared_by_interface 欄序回答。","answer":{"kind":"expression","value":"([[-14, 0], [0, 12/13], [14, 1]], 是, 0, 1, nondecreasing_with_left_zero_and_right_one_limits)","explanation_zh":"Wave6第五層核對=([[-14, 0], [0, 12/13], [14, 1]], 是, 0, 1, nondecreasing_with_left_zero_and_right_one_limits)；依完整明示資料獨立重算；continuous CDF無jumps所以singletons質量0，flat intervals仍允許且兩端limits為0與1；continuous或atomless不推出density或absolute continuity；singular Cantor law是boundary。"},"difficulty":{"band":"undergraduate_core","level":2,"skills":["連續實值分布函數"]},"variant":{"family_id":"qf-mod42-contcdf-monotone-endpoint-audit","seed":202611114037,"parameters":{"knots":[-13,0,13],"values":[0,[12,13],1],"query_points":[-14,0,14],"domain":"Exact_continuous_piecewise_linear_CDF","operation":"contcdf-monotone-endpoint-audit","semantic_template":"qf-mod42-contcdf-monotone-endpoint-audit/{\"knots\":[-13,0,13],\"query_points\":[-14,0,14],\"values\":[0,[12,13],1]}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_or_symbolic_model","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"候選須主端重算；不構成人工審定、Lagrange converse existence、higher-order analyticity、sampled Hausdorff、CDF density、unchecked Catalan division、Euler criterion、bounded NFA rejection、Lean或Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-14","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261014-advance-20261111-r04-continuous-real-distribution-function-0038","batch_id":"batch-20261014-advance-20261111-r04-continuous-real-distribution-function-foundations","language":"zh-Hant","source_mko_ids":["mko-continuous-real-distribution-function"],"title_zh":"連續實值分布函數","stem_zh":"CDF本身continuous、nondecreasing、right-continuous且audit query_points嚴格遞增。操作=contcdf-monotone-endpoint-audit；資料={\"knots\":[-14,0,14],\"values\":[0,[13,14],1],\"query_points\":[-15,0,15]}。請依 exact_ordered_tuple_declared_by_interface 欄序回答。","answer":{"kind":"expression","value":"([[-15, 0], [0, 13/14], [15, 1]], 是, 0, 1, nondecreasing_with_left_zero_and_right_one_limits)","explanation_zh":"Wave6第五層核對=([[-15, 0], [0, 13/14], [15, 1]], 是, 0, 1, nondecreasing_with_left_zero_and_right_one_limits)；依完整明示資料獨立重算；continuous CDF無jumps所以singletons質量0，flat intervals仍允許且兩端limits為0與1；continuous或atomless不推出density或absolute continuity；singular Cantor law是boundary。"},"difficulty":{"band":"undergraduate_core","level":2,"skills":["連續實值分布函數"]},"variant":{"family_id":"qf-mod42-contcdf-monotone-endpoint-audit","seed":202611114038,"parameters":{"knots":[-14,0,14],"values":[0,[13,14],1],"query_points":[-15,0,15],"domain":"Exact_continuous_piecewise_linear_CDF","operation":"contcdf-monotone-endpoint-audit","semantic_template":"qf-mod42-contcdf-monotone-endpoint-audit/{\"knots\":[-14,0,14],\"query_points\":[-15,0,15],\"values\":[0,[13,14],1]}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_or_symbolic_model","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"候選須主端重算；不構成人工審定、Lagrange converse existence、higher-order analyticity、sampled Hausdorff、CDF density、unchecked Catalan division、Euler criterion、bounded NFA rejection、Lean或Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-14","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261014-advance-20261111-r04-continuous-real-distribution-function-0039","batch_id":"batch-20261014-advance-20261111-r04-continuous-real-distribution-function-foundations","language":"zh-Hant","source_mko_ids":["mko-continuous-real-distribution-function"],"title_zh":"連續實值分布函數","stem_zh":"CDF本身continuous、nondecreasing、right-continuous且audit query_points嚴格遞增。操作=contcdf-monotone-endpoint-audit；資料={\"knots\":[-15,0,15],\"values\":[0,[14,15],1],\"query_points\":[-16,0,16]}。請依 exact_ordered_tuple_declared_by_interface 欄序回答。","answer":{"kind":"expression","value":"([[-16, 0], [0, 14/15], [16, 1]], 是, 0, 1, nondecreasing_with_left_zero_and_right_one_limits)","explanation_zh":"Wave6第五層核對=([[-16, 0], [0, 14/15], [16, 1]], 是, 0, 1, nondecreasing_with_left_zero_and_right_one_limits)；依完整明示資料獨立重算；continuous CDF無jumps所以singletons質量0，flat intervals仍允許且兩端limits為0與1；continuous或atomless不推出density或absolute continuity；singular Cantor law是boundary。"},"difficulty":{"band":"undergraduate_core","level":2,"skills":["連續實值分布函數"]},"variant":{"family_id":"qf-mod42-contcdf-monotone-endpoint-audit","seed":202611114039,"parameters":{"knots":[-15,0,15],"values":[0,[14,15],1],"query_points":[-16,0,16],"domain":"Exact_continuous_piecewise_linear_CDF","operation":"contcdf-monotone-endpoint-audit","semantic_template":"qf-mod42-contcdf-monotone-endpoint-audit/{\"knots\":[-15,0,15],\"query_points\":[-16,0,16],\"values\":[0,[14,15],1]}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_or_symbolic_model","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"候選須主端重算；不構成人工審定、Lagrange converse existence、higher-order analyticity、sampled Hausdorff、CDF density、unchecked Catalan division、Euler criterion、bounded NFA rejection、Lean或Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-14","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261014-advance-20261111-r04-continuous-real-distribution-function-0040","batch_id":"batch-20261014-advance-20261111-r04-continuous-real-distribution-function-foundations","language":"zh-Hant","source_mko_ids":["mko-continuous-real-distribution-function"],"title_zh":"連續實值分布函數","stem_zh":"CDF本身continuous、nondecreasing、right-continuous且audit query_points嚴格遞增。操作=contcdf-monotone-endpoint-audit；資料={\"knots\":[-16,0,16],\"values\":[0,[15,16],1],\"query_points\":[-17,0,17]}。請依 exact_ordered_tuple_declared_by_interface 欄序回答。","answer":{"kind":"expression","value":"([[-17, 0], [0, 15/16], [17, 1]], 是, 0, 1, nondecreasing_with_left_zero_and_right_one_limits)","explanation_zh":"Wave6第五層核對=([[-17, 0], [0, 15/16], [17, 1]], 是, 0, 1, nondecreasing_with_left_zero_and_right_one_limits)；依完整明示資料獨立重算；continuous CDF無jumps所以singletons質量0，flat intervals仍允許且兩端limits為0與1；continuous或atomless不推出density或absolute continuity；singular Cantor law是boundary。"},"difficulty":{"band":"undergraduate_core","level":2,"skills":["連續實值分布函數"]},"variant":{"family_id":"qf-mod42-contcdf-monotone-endpoint-audit","seed":202611114040,"parameters":{"knots":[-16,0,16],"values":[0,[15,16],1],"query_points":[-17,0,17],"domain":"Exact_continuous_piecewise_linear_CDF","operation":"contcdf-monotone-endpoint-audit","semantic_template":"qf-mod42-contcdf-monotone-endpoint-audit/{\"knots\":[-16,0,16],\"query_points\":[-17,0,17],\"values\":[0,[15,16],1]}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_or_symbolic_model","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"候選須主端重算；不構成人工審定、Lagrange converse existence、higher-order analyticity、sampled Hausdorff、CDF density、unchecked Catalan division、Euler criterion、bounded NFA rejection、Lean或Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-14","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261014-advance-20261111-r04-continuous-real-distribution-function-0041","batch_id":"batch-20261014-advance-20261111-r04-continuous-real-distribution-function-foundations","language":"zh-Hant","source_mko_ids":["mko-continuous-real-distribution-function"],"title_zh":"連續實值分布函數","stem_zh":"CDF本身continuous、nondecreasing、right-continuous且audit query_points嚴格遞增。操作=contcdf-monotone-endpoint-audit；資料={\"knots\":[-17,0,17],\"values\":[0,[16,17],1],\"query_points\":[-18,0,18]}。請依 exact_ordered_tuple_declared_by_interface 欄序回答。","answer":{"kind":"expression","value":"([[-18, 0], [0, 16/17], [18, 1]], 是, 0, 1, nondecreasing_with_left_zero_and_right_one_limits)","explanation_zh":"Wave6第五層核對=([[-18, 0], [0, 16/17], [18, 1]], 是, 0, 1, nondecreasing_with_left_zero_and_right_one_limits)；依完整明示資料獨立重算；continuous CDF無jumps所以singletons質量0，flat intervals仍允許且兩端limits為0與1；continuous或atomless不推出density或absolute continuity；singular Cantor law是boundary。"},"difficulty":{"band":"undergraduate_core","level":2,"skills":["連續實值分布函數"]},"variant":{"family_id":"qf-mod42-contcdf-monotone-endpoint-audit","seed":202611114041,"parameters":{"knots":[-17,0,17],"values":[0,[16,17],1],"query_points":[-18,0,18],"domain":"Exact_continuous_piecewise_linear_CDF","operation":"contcdf-monotone-endpoint-audit","semantic_template":"qf-mod42-contcdf-monotone-endpoint-audit/{\"knots\":[-17,0,17],\"query_points\":[-18,0,18],\"values\":[0,[16,17],1]}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_or_symbolic_model","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"候選須主端重算；不構成人工審定、Lagrange converse existence、higher-order analyticity、sampled Hausdorff、CDF density、unchecked Catalan division、Euler criterion、bounded NFA rejection、Lean或Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-14","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261014-advance-20261111-r04-continuous-real-distribution-function-0042","batch_id":"batch-20261014-advance-20261111-r04-continuous-real-distribution-function-foundations","language":"zh-Hant","source_mko_ids":["mko-continuous-real-distribution-function"],"title_zh":"連續實值分布函數","stem_zh":"CDF本身continuous、nondecreasing、right-continuous且audit query_points嚴格遞增。操作=contcdf-monotone-endpoint-audit；資料={\"knots\":[-18,0,18],\"values\":[0,[17,18],1],\"query_points\":[-19,0,19]}。請依 exact_ordered_tuple_declared_by_interface 欄序回答。","answer":{"kind":"expression","value":"([[-19, 0], [0, 17/18], [19, 1]], 是, 0, 1, nondecreasing_with_left_zero_and_right_one_limits)","explanation_zh":"Wave6第五層核對=([[-19, 0], [0, 17/18], [19, 1]], 是, 0, 1, nondecreasing_with_left_zero_and_right_one_limits)；依完整明示資料獨立重算；continuous CDF無jumps所以singletons質量0，flat intervals仍允許且兩端limits為0與1；continuous或atomless不推出density或absolute continuity；singular Cantor law是boundary。"},"difficulty":{"band":"undergraduate_core","level":2,"skills":["連續實值分布函數"]},"variant":{"family_id":"qf-mod42-contcdf-monotone-endpoint-audit","seed":202611114042,"parameters":{"knots":[-18,0,18],"values":[0,[17,18],1],"query_points":[-19,0,19],"domain":"Exact_continuous_piecewise_linear_CDF","operation":"contcdf-monotone-endpoint-audit","semantic_template":"qf-mod42-contcdf-monotone-endpoint-audit/{\"knots\":[-18,0,18],\"query_points\":[-19,0,19],\"values\":[0,[17,18],1]}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_or_symbolic_model","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"候選須主端重算；不構成人工審定、Lagrange converse existence、higher-order analyticity、sampled Hausdorff、CDF density、unchecked Catalan division、Euler criterion、bounded NFA rejection、Lean或Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-14","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261014-advance-20261111-r04-continuous-real-distribution-function-0043","batch_id":"batch-20261014-advance-20261111-r04-continuous-real-distribution-function-foundations","language":"zh-Hant","source_mko_ids":["mko-continuous-real-distribution-function"],"title_zh":"連續實值分布函數","stem_zh":"CDF本身continuous、nondecreasing、right-continuous且audit query_points嚴格遞增。操作=contcdf-monotone-endpoint-audit；資料={\"knots\":[-19,0,19],\"values\":[0,[18,19],1],\"query_points\":[-20,0,20]}。請依 exact_ordered_tuple_declared_by_interface 欄序回答。","answer":{"kind":"expression","value":"([[-20, 0], [0, 18/19], [20, 1]], 是, 0, 1, nondecreasing_with_left_zero_and_right_one_limits)","explanation_zh":"Wave6第五層核對=([[-20, 0], [0, 18/19], [20, 1]], 是, 0, 1, nondecreasing_with_left_zero_and_right_one_limits)；依完整明示資料獨立重算；continuous CDF無jumps所以singletons質量0，flat intervals仍允許且兩端limits為0與1；continuous或atomless不推出density或absolute continuity；singular Cantor law是boundary。"},"difficulty":{"band":"undergraduate_core","level":3,"skills":["連續實值分布函數"]},"variant":{"family_id":"qf-mod42-contcdf-monotone-endpoint-audit","seed":202611114043,"parameters":{"knots":[-19,0,19],"values":[0,[18,19],1],"query_points":[-20,0,20],"domain":"Exact_continuous_piecewise_linear_CDF","operation":"contcdf-monotone-endpoint-audit","semantic_template":"qf-mod42-contcdf-monotone-endpoint-audit/{\"knots\":[-19,0,19],\"query_points\":[-20,0,20],\"values\":[0,[18,19],1]}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_or_symbolic_model","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"候選須主端重算；不構成人工審定、Lagrange converse existence、higher-order analyticity、sampled Hausdorff、CDF density、unchecked Catalan division、Euler criterion、bounded NFA rejection、Lean或Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-14","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261014-advance-20261111-r04-continuous-real-distribution-function-0044","batch_id":"batch-20261014-advance-20261111-r04-continuous-real-distribution-function-foundations","language":"zh-Hant","source_mko_ids":["mko-continuous-real-distribution-function"],"title_zh":"連續實值分布函數","stem_zh":"CDF本身continuous、nondecreasing、right-continuous且audit query_points嚴格遞增。操作=contcdf-monotone-endpoint-audit；資料={\"knots\":[-20,0,20],\"values\":[0,[19,20],1],\"query_points\":[-21,0,21]}。請依 exact_ordered_tuple_declared_by_interface 欄序回答。","answer":{"kind":"expression","value":"([[-21, 0], [0, 19/20], [21, 1]], 是, 0, 1, nondecreasing_with_left_zero_and_right_one_limits)","explanation_zh":"Wave6第五層核對=([[-21, 0], [0, 19/20], [21, 1]], 是, 0, 1, nondecreasing_with_left_zero_and_right_one_limits)；依完整明示資料獨立重算；continuous CDF無jumps所以singletons質量0，flat intervals仍允許且兩端limits為0與1；continuous或atomless不推出density或absolute continuity；singular Cantor law是boundary。"},"difficulty":{"band":"undergraduate_core","level":3,"skills":["連續實值分布函數"]},"variant":{"family_id":"qf-mod42-contcdf-monotone-endpoint-audit","seed":202611114044,"parameters":{"knots":[-20,0,20],"values":[0,[19,20],1],"query_points":[-21,0,21],"domain":"Exact_continuous_piecewise_linear_CDF","operation":"contcdf-monotone-endpoint-audit","semantic_template":"qf-mod42-contcdf-monotone-endpoint-audit/{\"knots\":[-20,0,20],\"query_points\":[-21,0,21],\"values\":[0,[19,20],1]}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_or_symbolic_model","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"候選須主端重算；不構成人工審定、Lagrange converse existence、higher-order analyticity、sampled Hausdorff、CDF density、unchecked Catalan division、Euler criterion、bounded NFA rejection、Lean或Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-14","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261014-advance-20261111-r04-continuous-real-distribution-function-0045","batch_id":"batch-20261014-advance-20261111-r04-continuous-real-distribution-function-foundations","language":"zh-Hant","source_mko_ids":["mko-continuous-real-distribution-function"],"title_zh":"連續實值分布函數","stem_zh":"CDF本身continuous、nondecreasing、right-continuous且audit query_points嚴格遞增。操作=contcdf-monotone-endpoint-audit；資料={\"knots\":[-21,0,21],\"values\":[0,[20,21],1],\"query_points\":[-22,0,22]}。請依 exact_ordered_tuple_declared_by_interface 欄序回答。","answer":{"kind":"expression","value":"([[-22, 0], [0, 20/21], [22, 1]], 是, 0, 1, nondecreasing_with_left_zero_and_right_one_limits)","explanation_zh":"Wave6第五層核對=([[-22, 0], [0, 20/21], [22, 1]], 是, 0, 1, nondecreasing_with_left_zero_and_right_one_limits)；依完整明示資料獨立重算；continuous CDF無jumps所以singletons質量0，flat intervals仍允許且兩端limits為0與1；continuous或atomless不推出density或absolute continuity；singular Cantor law是boundary。"},"difficulty":{"band":"undergraduate_core","level":3,"skills":["連續實值分布函數"]},"variant":{"family_id":"qf-mod42-contcdf-monotone-endpoint-audit","seed":202611114045,"parameters":{"knots":[-21,0,21],"values":[0,[20,21],1],"query_points":[-22,0,22],"domain":"Exact_continuous_piecewise_linear_CDF","operation":"contcdf-monotone-endpoint-audit","semantic_template":"qf-mod42-contcdf-monotone-endpoint-audit/{\"knots\":[-21,0,21],\"query_points\":[-22,0,22],\"values\":[0,[20,21],1]}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_or_symbolic_model","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"候選須主端重算；不構成人工審定、Lagrange converse existence、higher-order analyticity、sampled Hausdorff、CDF density、unchecked Catalan division、Euler criterion、bounded NFA rejection、Lean或Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-14","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261014-advance-20261111-r04-continuous-real-distribution-function-0046","batch_id":"batch-20261014-advance-20261111-r04-continuous-real-distribution-function-foundations","language":"zh-Hant","source_mko_ids":["mko-continuous-real-distribution-function"],"title_zh":"連續實值分布函數","stem_zh":"CDF本身continuous、nondecreasing、right-continuous且audit query_points嚴格遞增。操作=contcdf-monotone-endpoint-audit；資料={\"knots\":[-22,0,22],\"values\":[0,[21,22],1],\"query_points\":[-23,0,23]}。請依 exact_ordered_tuple_declared_by_interface 欄序回答。","answer":{"kind":"expression","value":"([[-23, 0], [0, 21/22], [23, 1]], 是, 0, 1, nondecreasing_with_left_zero_and_right_one_limits)","explanation_zh":"Wave6第五層核對=([[-23, 0], [0, 21/22], [23, 1]], 是, 0, 1, nondecreasing_with_left_zero_and_right_one_limits)；依完整明示資料獨立重算；continuous CDF無jumps所以singletons質量0，flat intervals仍允許且兩端limits為0與1；continuous或atomless不推出density或absolute continuity；singular Cantor law是boundary。"},"difficulty":{"band":"undergraduate_core","level":3,"skills":["連續實值分布函數"]},"variant":{"family_id":"qf-mod42-contcdf-monotone-endpoint-audit","seed":202611114046,"parameters":{"knots":[-22,0,22],"values":[0,[21,22],1],"query_points":[-23,0,23],"domain":"Exact_continuous_piecewise_linear_CDF","operation":"contcdf-monotone-endpoint-audit","semantic_template":"qf-mod42-contcdf-monotone-endpoint-audit/{\"knots\":[-22,0,22],\"query_points\":[-23,0,23],\"values\":[0,[21,22],1]}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_or_symbolic_model","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"候選須主端重算；不構成人工審定、Lagrange converse existence、higher-order analyticity、sampled Hausdorff、CDF density、unchecked Catalan division、Euler criterion、bounded NFA rejection、Lean或Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-14","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261014-advance-20261111-r04-continuous-real-distribution-function-0047","batch_id":"batch-20261014-advance-20261111-r04-continuous-real-distribution-function-foundations","language":"zh-Hant","source_mko_ids":["mko-continuous-real-distribution-function"],"title_zh":"連續實值分布函數","stem_zh":"CDF本身continuous、nondecreasing、right-continuous且audit query_points嚴格遞增。操作=contcdf-monotone-endpoint-audit；資料={\"knots\":[-23,0,23],\"values\":[0,[22,23],1],\"query_points\":[-24,0,24]}。請依 exact_ordered_tuple_declared_by_interface 欄序回答。","answer":{"kind":"expression","value":"([[-24, 0], [0, 22/23], [24, 1]], 是, 0, 1, nondecreasing_with_left_zero_and_right_one_limits)","explanation_zh":"Wave6第五層核對=([[-24, 0], [0, 22/23], [24, 1]], 是, 0, 1, nondecreasing_with_left_zero_and_right_one_limits)；依完整明示資料獨立重算；continuous CDF無jumps所以singletons質量0，flat intervals仍允許且兩端limits為0與1；continuous或atomless不推出density或absolute continuity；singular Cantor law是boundary。"},"difficulty":{"band":"undergraduate_core","level":3,"skills":["連續實值分布函數"]},"variant":{"family_id":"qf-mod42-contcdf-monotone-endpoint-audit","seed":202611114047,"parameters":{"knots":[-23,0,23],"values":[0,[22,23],1],"query_points":[-24,0,24],"domain":"Exact_continuous_piecewise_linear_CDF","operation":"contcdf-monotone-endpoint-audit","semantic_template":"qf-mod42-contcdf-monotone-endpoint-audit/{\"knots\":[-23,0,23],\"query_points\":[-24,0,24],\"values\":[0,[22,23],1]}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_or_symbolic_model","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"候選須主端重算；不構成人工審定、Lagrange converse existence、higher-order analyticity、sampled Hausdorff、CDF density、unchecked Catalan division、Euler criterion、bounded NFA rejection、Lean或Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-14","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261014-advance-20261111-r04-continuous-real-distribution-function-0048","batch_id":"batch-20261014-advance-20261111-r04-continuous-real-distribution-function-foundations","language":"zh-Hant","source_mko_ids":["mko-continuous-real-distribution-function"],"title_zh":"連續實值分布函數","stem_zh":"CDF本身continuous、nondecreasing、right-continuous且audit query_points嚴格遞增。操作=contcdf-monotone-endpoint-audit；資料={\"knots\":[-24,0,24],\"values\":[0,[23,24],1],\"query_points\":[-25,0,25]}。請依 exact_ordered_tuple_declared_by_interface 欄序回答。","answer":{"kind":"expression","value":"([[-25, 0], [0, 23/24], [25, 1]], 是, 0, 1, nondecreasing_with_left_zero_and_right_one_limits)","explanation_zh":"Wave6第五層核對=([[-25, 0], [0, 23/24], [25, 1]], 是, 0, 1, nondecreasing_with_left_zero_and_right_one_limits)；依完整明示資料獨立重算；continuous CDF無jumps所以singletons質量0，flat intervals仍允許且兩端limits為0與1；continuous或atomless不推出density或absolute continuity；singular Cantor law是boundary。"},"difficulty":{"band":"undergraduate_core","level":3,"skills":["連續實值分布函數"]},"variant":{"family_id":"qf-mod42-contcdf-monotone-endpoint-audit","seed":202611114048,"parameters":{"knots":[-24,0,24],"values":[0,[23,24],1],"query_points":[-25,0,25],"domain":"Exact_continuous_piecewise_linear_CDF","operation":"contcdf-monotone-endpoint-audit","semantic_template":"qf-mod42-contcdf-monotone-endpoint-audit/{\"knots\":[-24,0,24],\"query_points\":[-25,0,25],\"values\":[0,[23,24],1]}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_or_symbolic_model","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"候選須主端重算；不構成人工審定、Lagrange converse existence、higher-order analyticity、sampled Hausdorff、CDF density、unchecked Catalan division、Euler criterion、bounded NFA rejection、Lean或Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-14","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261014-advance-20261111-r04-continuous-real-distribution-function-0049","batch_id":"batch-20261014-advance-20261111-r04-continuous-real-distribution-function-foundations","language":"zh-Hant","source_mko_ids":["mko-continuous-real-distribution-function"],"title_zh":"連續實值分布函數","stem_zh":"CDF本身continuous、nondecreasing、right-continuous且audit query_points嚴格遞增。操作=contcdf-monotone-endpoint-audit；資料={\"knots\":[-25,0,25],\"values\":[0,[24,25],1],\"query_points\":[-26,0,26]}。請依 exact_ordered_tuple_declared_by_interface 欄序回答。","answer":{"kind":"expression","value":"([[-26, 0], [0, 24/25], [26, 1]], 是, 0, 1, nondecreasing_with_left_zero_and_right_one_limits)","explanation_zh":"Wave6第五層核對=([[-26, 0], [0, 24/25], [26, 1]], 是, 0, 1, nondecreasing_with_left_zero_and_right_one_limits)；依完整明示資料獨立重算；continuous CDF無jumps所以singletons質量0，flat intervals仍允許且兩端limits為0與1；continuous或atomless不推出density或absolute continuity；singular Cantor law是boundary。"},"difficulty":{"band":"undergraduate_core","level":3,"skills":["連續實值分布函數"]},"variant":{"family_id":"qf-mod42-contcdf-monotone-endpoint-audit","seed":202611114049,"parameters":{"knots":[-25,0,25],"values":[0,[24,25],1],"query_points":[-26,0,26],"domain":"Exact_continuous_piecewise_linear_CDF","operation":"contcdf-monotone-endpoint-audit","semantic_template":"qf-mod42-contcdf-monotone-endpoint-audit/{\"knots\":[-25,0,25],\"query_points\":[-26,0,26],\"values\":[0,[24,25],1]}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_or_symbolic_model","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"候選須主端重算；不構成人工審定、Lagrange converse existence、higher-order analyticity、sampled Hausdorff、CDF density、unchecked Catalan division、Euler criterion、bounded NFA rejection、Lean或Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-14","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261014-advance-20261111-r04-continuous-real-distribution-function-0050","batch_id":"batch-20261014-advance-20261111-r04-continuous-real-distribution-function-foundations","language":"zh-Hant","source_mko_ids":["mko-continuous-real-distribution-function"],"title_zh":"連續實值分布函數","stem_zh":"CDF本身continuous、nondecreasing、right-continuous且audit query_points嚴格遞增。操作=contcdf-monotone-endpoint-audit；資料={\"knots\":[-26,0,26],\"values\":[0,[25,26],1],\"query_points\":[-27,0,27]}。請依 exact_ordered_tuple_declared_by_interface 欄序回答。","answer":{"kind":"expression","value":"([[-27, 0], [0, 25/26], [27, 1]], 是, 0, 1, nondecreasing_with_left_zero_and_right_one_limits)","explanation_zh":"Wave6第五層核對=([[-27, 0], [0, 25/26], [27, 1]], 是, 0, 1, nondecreasing_with_left_zero_and_right_one_limits)；依完整明示資料獨立重算；continuous CDF無jumps所以singletons質量0，flat intervals仍允許且兩端limits為0與1；continuous或atomless不推出density或absolute continuity；singular Cantor law是boundary。"},"difficulty":{"band":"undergraduate_core","level":3,"skills":["連續實值分布函數"]},"variant":{"family_id":"qf-mod42-contcdf-monotone-endpoint-audit","seed":202611114050,"parameters":{"knots":[-26,0,26],"values":[0,[25,26],1],"query_points":[-27,0,27],"domain":"Exact_continuous_piecewise_linear_CDF","operation":"contcdf-monotone-endpoint-audit","semantic_template":"qf-mod42-contcdf-monotone-endpoint-audit/{\"knots\":[-26,0,26],\"query_points\":[-27,0,27],\"values\":[0,[25,26],1]}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_or_symbolic_model","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"候選須主端重算；不構成人工審定、Lagrange converse existence、higher-order analyticity、sampled Hausdorff、CDF density、unchecked Catalan division、Euler criterion、bounded NFA rejection、Lean或Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-14","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261014-advance-20261111-r04-continuous-real-distribution-function-0051","batch_id":"batch-20261014-advance-20261111-r04-continuous-real-distribution-function-foundations","language":"zh-Hant","source_mko_ids":["mko-continuous-real-distribution-function"],"title_zh":"連續實值分布函數","stem_zh":"CDF本身continuous、nondecreasing、right-continuous且audit query_points嚴格遞增。操作=contcdf-zero-jump-atomlessness；資料={\"knots\":[-2,0,2],\"values\":[0,[1,2],1],\"point\":0}。請依 exact_ordered_tuple_declared_by_interface 欄序回答。","answer":{"kind":"expression","value":"(0, 1/2, 1/2, 0, 是, continuous_CDF_has_zero_singleton_mass_but_need_not_have_density)","explanation_zh":"Wave6第五層核對=(0, 1/2, 1/2, 0, 是, continuous_CDF_has_zero_singleton_mass_but_need_not_have_density)；依完整明示資料獨立重算；continuous CDF無jumps所以singletons質量0，flat intervals仍允許且兩端limits為0與1；continuous或atomless不推出density或absolute continuity；singular Cantor law是boundary。"},"difficulty":{"band":"undergraduate_core","level":1,"skills":["連續實值分布函數"]},"variant":{"family_id":"qf-mod42-contcdf-zero-jump-atomlessness","seed":202611114051,"parameters":{"knots":[-2,0,2],"values":[0,[1,2],1],"point":0,"domain":"Exact_continuous_piecewise_linear_CDF","operation":"contcdf-zero-jump-atomlessness","semantic_template":"qf-mod42-contcdf-zero-jump-atomlessness/{\"knots\":[-2,0,2],\"point\":0,\"values\":[0,[1,2],1]}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_or_symbolic_model","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"候選須主端重算；不構成人工審定、Lagrange converse existence、higher-order analyticity、sampled Hausdorff、CDF density、unchecked Catalan division、Euler criterion、bounded NFA rejection、Lean或Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-14","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261014-advance-20261111-r04-continuous-real-distribution-function-0052","batch_id":"batch-20261014-advance-20261111-r04-continuous-real-distribution-function-foundations","language":"zh-Hant","source_mko_ids":["mko-continuous-real-distribution-function"],"title_zh":"連續實值分布函數","stem_zh":"CDF本身continuous、nondecreasing、right-continuous且audit query_points嚴格遞增。操作=contcdf-zero-jump-atomlessness；資料={\"knots\":[-3,0,3],\"values\":[0,[2,3],1],\"point\":0}。請依 exact_ordered_tuple_declared_by_interface 欄序回答。","answer":{"kind":"expression","value":"(0, 2/3, 2/3, 0, 是, continuous_CDF_has_zero_singleton_mass_but_need_not_have_density)","explanation_zh":"Wave6第五層核對=(0, 2/3, 2/3, 0, 是, continuous_CDF_has_zero_singleton_mass_but_need_not_have_density)；依完整明示資料獨立重算；continuous CDF無jumps所以singletons質量0，flat intervals仍允許且兩端limits為0與1；continuous或atomless不推出density或absolute continuity；singular Cantor law是boundary。"},"difficulty":{"band":"undergraduate_core","level":1,"skills":["連續實值分布函數"]},"variant":{"family_id":"qf-mod42-contcdf-zero-jump-atomlessness","seed":202611114052,"parameters":{"knots":[-3,0,3],"values":[0,[2,3],1],"point":0,"domain":"Exact_continuous_piecewise_linear_CDF","operation":"contcdf-zero-jump-atomlessness","semantic_template":"qf-mod42-contcdf-zero-jump-atomlessness/{\"knots\":[-3,0,3],\"point\":0,\"values\":[0,[2,3],1]}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_or_symbolic_model","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"候選須主端重算；不構成人工審定、Lagrange converse existence、higher-order analyticity、sampled Hausdorff、CDF density、unchecked Catalan division、Euler criterion、bounded NFA rejection、Lean或Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-14","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261014-advance-20261111-r04-continuous-real-distribution-function-0053","batch_id":"batch-20261014-advance-20261111-r04-continuous-real-distribution-function-foundations","language":"zh-Hant","source_mko_ids":["mko-continuous-real-distribution-function"],"title_zh":"連續實值分布函數","stem_zh":"CDF本身continuous、nondecreasing、right-continuous且audit query_points嚴格遞增。操作=contcdf-zero-jump-atomlessness；資料={\"knots\":[-4,0,4],\"values\":[0,[3,4],1],\"point\":0}。請依 exact_ordered_tuple_declared_by_interface 欄序回答。","answer":{"kind":"expression","value":"(0, 3/4, 3/4, 0, 是, continuous_CDF_has_zero_singleton_mass_but_need_not_have_density)","explanation_zh":"Wave6第五層核對=(0, 3/4, 3/4, 0, 是, continuous_CDF_has_zero_singleton_mass_but_need_not_have_density)；依完整明示資料獨立重算；continuous CDF無jumps所以singletons質量0，flat intervals仍允許且兩端limits為0與1；continuous或atomless不推出density或absolute continuity；singular Cantor law是boundary。"},"difficulty":{"band":"undergraduate_core","level":1,"skills":["連續實值分布函數"]},"variant":{"family_id":"qf-mod42-contcdf-zero-jump-atomlessness","seed":202611114053,"parameters":{"knots":[-4,0,4],"values":[0,[3,4],1],"point":0,"domain":"Exact_continuous_piecewise_linear_CDF","operation":"contcdf-zero-jump-atomlessness","semantic_template":"qf-mod42-contcdf-zero-jump-atomlessness/{\"knots\":[-4,0,4],\"point\":0,\"values\":[0,[3,4],1]}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_or_symbolic_model","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"候選須主端重算；不構成人工審定、Lagrange converse existence、higher-order analyticity、sampled Hausdorff、CDF density、unchecked Catalan division、Euler criterion、bounded NFA rejection、Lean或Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-14","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261014-advance-20261111-r04-continuous-real-distribution-function-0054","batch_id":"batch-20261014-advance-20261111-r04-continuous-real-distribution-function-foundations","language":"zh-Hant","source_mko_ids":["mko-continuous-real-distribution-function"],"title_zh":"連續實值分布函數","stem_zh":"CDF本身continuous、nondecreasing、right-continuous且audit query_points嚴格遞增。操作=contcdf-zero-jump-atomlessness；資料={\"knots\":[-5,0,5],\"values\":[0,[4,5],1],\"point\":0}。請依 exact_ordered_tuple_declared_by_interface 欄序回答。","answer":{"kind":"expression","value":"(0, 4/5, 4/5, 0, 是, continuous_CDF_has_zero_singleton_mass_but_need_not_have_density)","explanation_zh":"Wave6第五層核對=(0, 4/5, 4/5, 0, 是, continuous_CDF_has_zero_singleton_mass_but_need_not_have_density)；依完整明示資料獨立重算；continuous CDF無jumps所以singletons質量0，flat intervals仍允許且兩端limits為0與1；continuous或atomless不推出density或absolute continuity；singular Cantor law是boundary。"},"difficulty":{"band":"undergraduate_core","level":1,"skills":["連續實值分布函數"]},"variant":{"family_id":"qf-mod42-contcdf-zero-jump-atomlessness","seed":202611114054,"parameters":{"knots":[-5,0,5],"values":[0,[4,5],1],"point":0,"domain":"Exact_continuous_piecewise_linear_CDF","operation":"contcdf-zero-jump-atomlessness","semantic_template":"qf-mod42-contcdf-zero-jump-atomlessness/{\"knots\":[-5,0,5],\"point\":0,\"values\":[0,[4,5],1]}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_or_symbolic_model","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"候選須主端重算；不構成人工審定、Lagrange converse existence、higher-order analyticity、sampled Hausdorff、CDF density、unchecked Catalan division、Euler criterion、bounded NFA rejection、Lean或Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-14","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261014-advance-20261111-r04-continuous-real-distribution-function-0055","batch_id":"batch-20261014-advance-20261111-r04-continuous-real-distribution-function-foundations","language":"zh-Hant","source_mko_ids":["mko-continuous-real-distribution-function"],"title_zh":"連續實值分布函數","stem_zh":"CDF本身continuous、nondecreasing、right-continuous且audit query_points嚴格遞增。操作=contcdf-zero-jump-atomlessness；資料={\"knots\":[-6,0,6],\"values\":[0,[5,6],1],\"point\":0}。請依 exact_ordered_tuple_declared_by_interface 欄序回答。","answer":{"kind":"expression","value":"(0, 5/6, 5/6, 0, 是, continuous_CDF_has_zero_singleton_mass_but_need_not_have_density)","explanation_zh":"Wave6第五層核對=(0, 5/6, 5/6, 0, 是, continuous_CDF_has_zero_singleton_mass_but_need_not_have_density)；依完整明示資料獨立重算；continuous CDF無jumps所以singletons質量0，flat intervals仍允許且兩端limits為0與1；continuous或atomless不推出density或absolute continuity；singular Cantor law是boundary。"},"difficulty":{"band":"undergraduate_core","level":1,"skills":["連續實值分布函數"]},"variant":{"family_id":"qf-mod42-contcdf-zero-jump-atomlessness","seed":202611114055,"parameters":{"knots":[-6,0,6],"values":[0,[5,6],1],"point":0,"domain":"Exact_continuous_piecewise_linear_CDF","operation":"contcdf-zero-jump-atomlessness","semantic_template":"qf-mod42-contcdf-zero-jump-atomlessness/{\"knots\":[-6,0,6],\"point\":0,\"values\":[0,[5,6],1]}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_or_symbolic_model","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"候選須主端重算；不構成人工審定、Lagrange converse existence、higher-order analyticity、sampled Hausdorff、CDF density、unchecked Catalan division、Euler criterion、bounded NFA rejection、Lean或Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-14","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261014-advance-20261111-r04-continuous-real-distribution-function-0056","batch_id":"batch-20261014-advance-20261111-r04-continuous-real-distribution-function-foundations","language":"zh-Hant","source_mko_ids":["mko-continuous-real-distribution-function"],"title_zh":"連續實值分布函數","stem_zh":"CDF本身continuous、nondecreasing、right-continuous且audit query_points嚴格遞增。操作=contcdf-zero-jump-atomlessness；資料={\"knots\":[-7,0,7],\"values\":[0,[6,7],1],\"point\":0}。請依 exact_ordered_tuple_declared_by_interface 欄序回答。","answer":{"kind":"expression","value":"(0, 6/7, 6/7, 0, 是, continuous_CDF_has_zero_singleton_mass_but_need_not_have_density)","explanation_zh":"Wave6第五層核對=(0, 6/7, 6/7, 0, 是, continuous_CDF_has_zero_singleton_mass_but_need_not_have_density)；依完整明示資料獨立重算；continuous CDF無jumps所以singletons質量0，flat intervals仍允許且兩端limits為0與1；continuous或atomless不推出density或absolute continuity；singular Cantor law是boundary。"},"difficulty":{"band":"undergraduate_core","level":1,"skills":["連續實值分布函數"]},"variant":{"family_id":"qf-mod42-contcdf-zero-jump-atomlessness","seed":202611114056,"parameters":{"knots":[-7,0,7],"values":[0,[6,7],1],"point":0,"domain":"Exact_continuous_piecewise_linear_CDF","operation":"contcdf-zero-jump-atomlessness","semantic_template":"qf-mod42-contcdf-zero-jump-atomlessness/{\"knots\":[-7,0,7],\"point\":0,\"values\":[0,[6,7],1]}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_or_symbolic_model","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"候選須主端重算；不構成人工審定、Lagrange converse existence、higher-order analyticity、sampled Hausdorff、CDF density、unchecked Catalan division、Euler criterion、bounded NFA rejection、Lean或Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-14","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261014-advance-20261111-r04-continuous-real-distribution-function-0057","batch_id":"batch-20261014-advance-20261111-r04-continuous-real-distribution-function-foundations","language":"zh-Hant","source_mko_ids":["mko-continuous-real-distribution-function"],"title_zh":"連續實值分布函數","stem_zh":"CDF本身continuous、nondecreasing、right-continuous且audit query_points嚴格遞增。操作=contcdf-zero-jump-atomlessness；資料={\"knots\":[-8,0,8],\"values\":[0,[7,8],1],\"point\":0}。請依 exact_ordered_tuple_declared_by_interface 欄序回答。","answer":{"kind":"expression","value":"(0, 7/8, 7/8, 0, 是, continuous_CDF_has_zero_singleton_mass_but_need_not_have_density)","explanation_zh":"Wave6第五層核對=(0, 7/8, 7/8, 0, 是, continuous_CDF_has_zero_singleton_mass_but_need_not_have_density)；依完整明示資料獨立重算；continuous CDF無jumps所以singletons質量0，flat intervals仍允許且兩端limits為0與1；continuous或atomless不推出density或absolute continuity；singular Cantor law是boundary。"},"difficulty":{"band":"undergraduate_core","level":1,"skills":["連續實值分布函數"]},"variant":{"family_id":"qf-mod42-contcdf-zero-jump-atomlessness","seed":202611114057,"parameters":{"knots":[-8,0,8],"values":[0,[7,8],1],"point":0,"domain":"Exact_continuous_piecewise_linear_CDF","operation":"contcdf-zero-jump-atomlessness","semantic_template":"qf-mod42-contcdf-zero-jump-atomlessness/{\"knots\":[-8,0,8],\"point\":0,\"values\":[0,[7,8],1]}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_or_symbolic_model","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"候選須主端重算；不構成人工審定、Lagrange converse existence、higher-order analyticity、sampled Hausdorff、CDF density、unchecked Catalan division、Euler criterion、bounded NFA rejection、Lean或Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-14","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261014-advance-20261111-r04-continuous-real-distribution-function-0058","batch_id":"batch-20261014-advance-20261111-r04-continuous-real-distribution-function-foundations","language":"zh-Hant","source_mko_ids":["mko-continuous-real-distribution-function"],"title_zh":"連續實值分布函數","stem_zh":"CDF本身continuous、nondecreasing、right-continuous且audit query_points嚴格遞增。操作=contcdf-zero-jump-atomlessness；資料={\"knots\":[-9,0,9],\"values\":[0,[8,9],1],\"point\":0}。請依 exact_ordered_tuple_declared_by_interface 欄序回答。","answer":{"kind":"expression","value":"(0, 8/9, 8/9, 0, 是, continuous_CDF_has_zero_singleton_mass_but_need_not_have_density)","explanation_zh":"Wave6第五層核對=(0, 8/9, 8/9, 0, 是, continuous_CDF_has_zero_singleton_mass_but_need_not_have_density)；依完整明示資料獨立重算；continuous CDF無jumps所以singletons質量0，flat intervals仍允許且兩端limits為0與1；continuous或atomless不推出density或absolute continuity；singular Cantor law是boundary。"},"difficulty":{"band":"undergraduate_core","level":1,"skills":["連續實值分布函數"]},"variant":{"family_id":"qf-mod42-contcdf-zero-jump-atomlessness","seed":202611114058,"parameters":{"knots":[-9,0,9],"values":[0,[8,9],1],"point":0,"domain":"Exact_continuous_piecewise_linear_CDF","operation":"contcdf-zero-jump-atomlessness","semantic_template":"qf-mod42-contcdf-zero-jump-atomlessness/{\"knots\":[-9,0,9],\"point\":0,\"values\":[0,[8,9],1]}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_or_symbolic_model","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"候選須主端重算；不構成人工審定、Lagrange converse existence、higher-order analyticity、sampled Hausdorff、CDF density、unchecked Catalan division、Euler criterion、bounded NFA rejection、Lean或Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-14","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261014-advance-20261111-r04-continuous-real-distribution-function-0059","batch_id":"batch-20261014-advance-20261111-r04-continuous-real-distribution-function-foundations","language":"zh-Hant","source_mko_ids":["mko-continuous-real-distribution-function"],"title_zh":"連續實值分布函數","stem_zh":"CDF本身continuous、nondecreasing、right-continuous且audit query_points嚴格遞增。操作=contcdf-zero-jump-atomlessness；資料={\"knots\":[-10,0,10],\"values\":[0,[9,10],1],\"point\":0}。請依 exact_ordered_tuple_declared_by_interface 欄序回答。","answer":{"kind":"expression","value":"(0, 9/10, 9/10, 0, 是, continuous_CDF_has_zero_singleton_mass_but_need_not_have_density)","explanation_zh":"Wave6第五層核對=(0, 9/10, 9/10, 0, 是, continuous_CDF_has_zero_singleton_mass_but_need_not_have_density)；依完整明示資料獨立重算；continuous CDF無jumps所以singletons質量0，flat intervals仍允許且兩端limits為0與1；continuous或atomless不推出density或absolute continuity；singular Cantor law是boundary。"},"difficulty":{"band":"undergraduate_core","level":2,"skills":["連續實值分布函數"]},"variant":{"family_id":"qf-mod42-contcdf-zero-jump-atomlessness","seed":202611114059,"parameters":{"knots":[-10,0,10],"values":[0,[9,10],1],"point":0,"domain":"Exact_continuous_piecewise_linear_CDF","operation":"contcdf-zero-jump-atomlessness","semantic_template":"qf-mod42-contcdf-zero-jump-atomlessness/{\"knots\":[-10,0,10],\"point\":0,\"values\":[0,[9,10],1]}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_or_symbolic_model","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"候選須主端重算；不構成人工審定、Lagrange converse existence、higher-order analyticity、sampled Hausdorff、CDF density、unchecked Catalan division、Euler criterion、bounded NFA rejection、Lean或Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-14","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261014-advance-20261111-r04-continuous-real-distribution-function-0060","batch_id":"batch-20261014-advance-20261111-r04-continuous-real-distribution-function-foundations","language":"zh-Hant","source_mko_ids":["mko-continuous-real-distribution-function"],"title_zh":"連續實值分布函數","stem_zh":"CDF本身continuous、nondecreasing、right-continuous且audit query_points嚴格遞增。操作=contcdf-zero-jump-atomlessness；資料={\"knots\":[-11,0,11],\"values\":[0,[10,11],1],\"point\":0}。請依 exact_ordered_tuple_declared_by_interface 欄序回答。","answer":{"kind":"expression","value":"(0, 10/11, 10/11, 0, 是, continuous_CDF_has_zero_singleton_mass_but_need_not_have_density)","explanation_zh":"Wave6第五層核對=(0, 10/11, 10/11, 0, 是, continuous_CDF_has_zero_singleton_mass_but_need_not_have_density)；依完整明示資料獨立重算；continuous CDF無jumps所以singletons質量0，flat intervals仍允許且兩端limits為0與1；continuous或atomless不推出density或absolute continuity；singular Cantor law是boundary。"},"difficulty":{"band":"undergraduate_core","level":2,"skills":["連續實值分布函數"]},"variant":{"family_id":"qf-mod42-contcdf-zero-jump-atomlessness","seed":202611114060,"parameters":{"knots":[-11,0,11],"values":[0,[10,11],1],"point":0,"domain":"Exact_continuous_piecewise_linear_CDF","operation":"contcdf-zero-jump-atomlessness","semantic_template":"qf-mod42-contcdf-zero-jump-atomlessness/{\"knots\":[-11,0,11],\"point\":0,\"values\":[0,[10,11],1]}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_or_symbolic_model","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"候選須主端重算；不構成人工審定、Lagrange converse existence、higher-order analyticity、sampled Hausdorff、CDF density、unchecked Catalan division、Euler criterion、bounded NFA rejection、Lean或Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-14","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261014-advance-20261111-r04-continuous-real-distribution-function-0061","batch_id":"batch-20261014-advance-20261111-r04-continuous-real-distribution-function-foundations","language":"zh-Hant","source_mko_ids":["mko-continuous-real-distribution-function"],"title_zh":"連續實值分布函數","stem_zh":"CDF本身continuous、nondecreasing、right-continuous且audit query_points嚴格遞增。操作=contcdf-zero-jump-atomlessness；資料={\"knots\":[-12,0,12],\"values\":[0,[11,12],1],\"point\":0}。請依 exact_ordered_tuple_declared_by_interface 欄序回答。","answer":{"kind":"expression","value":"(0, 11/12, 11/12, 0, 是, continuous_CDF_has_zero_singleton_mass_but_need_not_have_density)","explanation_zh":"Wave6第五層核對=(0, 11/12, 11/12, 0, 是, continuous_CDF_has_zero_singleton_mass_but_need_not_have_density)；依完整明示資料獨立重算；continuous CDF無jumps所以singletons質量0，flat intervals仍允許且兩端limits為0與1；continuous或atomless不推出density或absolute continuity；singular Cantor law是boundary。"},"difficulty":{"band":"undergraduate_core","level":2,"skills":["連續實值分布函數"]},"variant":{"family_id":"qf-mod42-contcdf-zero-jump-atomlessness","seed":202611114061,"parameters":{"knots":[-12,0,12],"values":[0,[11,12],1],"point":0,"domain":"Exact_continuous_piecewise_linear_CDF","operation":"contcdf-zero-jump-atomlessness","semantic_template":"qf-mod42-contcdf-zero-jump-atomlessness/{\"knots\":[-12,0,12],\"point\":0,\"values\":[0,[11,12],1]}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_or_symbolic_model","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"候選須主端重算；不構成人工審定、Lagrange converse existence、higher-order analyticity、sampled Hausdorff、CDF density、unchecked Catalan division、Euler criterion、bounded NFA rejection、Lean或Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-14","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261014-advance-20261111-r04-continuous-real-distribution-function-0062","batch_id":"batch-20261014-advance-20261111-r04-continuous-real-distribution-function-foundations","language":"zh-Hant","source_mko_ids":["mko-continuous-real-distribution-function"],"title_zh":"連續實值分布函數","stem_zh":"CDF本身continuous、nondecreasing、right-continuous且audit query_points嚴格遞增。操作=contcdf-zero-jump-atomlessness；資料={\"knots\":[-13,0,13],\"values\":[0,[12,13],1],\"point\":0}。請依 exact_ordered_tuple_declared_by_interface 欄序回答。","answer":{"kind":"expression","value":"(0, 12/13, 12/13, 0, 是, continuous_CDF_has_zero_singleton_mass_but_need_not_have_density)","explanation_zh":"Wave6第五層核對=(0, 12/13, 12/13, 0, 是, continuous_CDF_has_zero_singleton_mass_but_need_not_have_density)；依完整明示資料獨立重算；continuous CDF無jumps所以singletons質量0，flat intervals仍允許且兩端limits為0與1；continuous或atomless不推出density或absolute continuity；singular Cantor law是boundary。"},"difficulty":{"band":"undergraduate_core","level":2,"skills":["連續實值分布函數"]},"variant":{"family_id":"qf-mod42-contcdf-zero-jump-atomlessness","seed":202611114062,"parameters":{"knots":[-13,0,13],"values":[0,[12,13],1],"point":0,"domain":"Exact_continuous_piecewise_linear_CDF","operation":"contcdf-zero-jump-atomlessness","semantic_template":"qf-mod42-contcdf-zero-jump-atomlessness/{\"knots\":[-13,0,13],\"point\":0,\"values\":[0,[12,13],1]}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_or_symbolic_model","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"候選須主端重算；不構成人工審定、Lagrange converse existence、higher-order analyticity、sampled Hausdorff、CDF density、unchecked Catalan division、Euler criterion、bounded NFA rejection、Lean或Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-14","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261014-advance-20261111-r04-continuous-real-distribution-function-0063","batch_id":"batch-20261014-advance-20261111-r04-continuous-real-distribution-function-foundations","language":"zh-Hant","source_mko_ids":["mko-continuous-real-distribution-function"],"title_zh":"連續實值分布函數","stem_zh":"CDF本身continuous、nondecreasing、right-continuous且audit query_points嚴格遞增。操作=contcdf-zero-jump-atomlessness；資料={\"knots\":[-14,0,14],\"values\":[0,[13,14],1],\"point\":0}。請依 exact_ordered_tuple_declared_by_interface 欄序回答。","answer":{"kind":"expression","value":"(0, 13/14, 13/14, 0, 是, continuous_CDF_has_zero_singleton_mass_but_need_not_have_density)","explanation_zh":"Wave6第五層核對=(0, 13/14, 13/14, 0, 是, continuous_CDF_has_zero_singleton_mass_but_need_not_have_density)；依完整明示資料獨立重算；continuous CDF無jumps所以singletons質量0，flat intervals仍允許且兩端limits為0與1；continuous或atomless不推出density或absolute continuity；singular Cantor law是boundary。"},"difficulty":{"band":"undergraduate_core","level":2,"skills":["連續實值分布函數"]},"variant":{"family_id":"qf-mod42-contcdf-zero-jump-atomlessness","seed":202611114063,"parameters":{"knots":[-14,0,14],"values":[0,[13,14],1],"point":0,"domain":"Exact_continuous_piecewise_linear_CDF","operation":"contcdf-zero-jump-atomlessness","semantic_template":"qf-mod42-contcdf-zero-jump-atomlessness/{\"knots\":[-14,0,14],\"point\":0,\"values\":[0,[13,14],1]}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_or_symbolic_model","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"候選須主端重算；不構成人工審定、Lagrange converse existence、higher-order analyticity、sampled Hausdorff、CDF density、unchecked Catalan division、Euler criterion、bounded NFA rejection、Lean或Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-14","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261014-advance-20261111-r04-continuous-real-distribution-function-0064","batch_id":"batch-20261014-advance-20261111-r04-continuous-real-distribution-function-foundations","language":"zh-Hant","source_mko_ids":["mko-continuous-real-distribution-function"],"title_zh":"連續實值分布函數","stem_zh":"CDF本身continuous、nondecreasing、right-continuous且audit query_points嚴格遞增。操作=contcdf-zero-jump-atomlessness；資料={\"knots\":[-15,0,15],\"values\":[0,[14,15],1],\"point\":0}。請依 exact_ordered_tuple_declared_by_interface 欄序回答。","answer":{"kind":"expression","value":"(0, 14/15, 14/15, 0, 是, continuous_CDF_has_zero_singleton_mass_but_need_not_have_density)","explanation_zh":"Wave6第五層核對=(0, 14/15, 14/15, 0, 是, continuous_CDF_has_zero_singleton_mass_but_need_not_have_density)；依完整明示資料獨立重算；continuous CDF無jumps所以singletons質量0，flat intervals仍允許且兩端limits為0與1；continuous或atomless不推出density或absolute continuity；singular Cantor law是boundary。"},"difficulty":{"band":"undergraduate_core","level":2,"skills":["連續實值分布函數"]},"variant":{"family_id":"qf-mod42-contcdf-zero-jump-atomlessness","seed":202611114064,"parameters":{"knots":[-15,0,15],"values":[0,[14,15],1],"point":0,"domain":"Exact_continuous_piecewise_linear_CDF","operation":"contcdf-zero-jump-atomlessness","semantic_template":"qf-mod42-contcdf-zero-jump-atomlessness/{\"knots\":[-15,0,15],\"point\":0,\"values\":[0,[14,15],1]}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_or_symbolic_model","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"候選須主端重算；不構成人工審定、Lagrange converse existence、higher-order analyticity、sampled Hausdorff、CDF density、unchecked Catalan division、Euler criterion、bounded NFA rejection、Lean或Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-14","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261014-advance-20261111-r04-continuous-real-distribution-function-0065","batch_id":"batch-20261014-advance-20261111-r04-continuous-real-distribution-function-foundations","language":"zh-Hant","source_mko_ids":["mko-continuous-real-distribution-function"],"title_zh":"連續實值分布函數","stem_zh":"CDF本身continuous、nondecreasing、right-continuous且audit query_points嚴格遞增。操作=contcdf-zero-jump-atomlessness；資料={\"knots\":[-16,0,16],\"values\":[0,[15,16],1],\"point\":0}。請依 exact_ordered_tuple_declared_by_interface 欄序回答。","answer":{"kind":"expression","value":"(0, 15/16, 15/16, 0, 是, continuous_CDF_has_zero_singleton_mass_but_need_not_have_density)","explanation_zh":"Wave6第五層核對=(0, 15/16, 15/16, 0, 是, continuous_CDF_has_zero_singleton_mass_but_need_not_have_density)；依完整明示資料獨立重算；continuous CDF無jumps所以singletons質量0，flat intervals仍允許且兩端limits為0與1；continuous或atomless不推出density或absolute continuity；singular Cantor law是boundary。"},"difficulty":{"band":"undergraduate_core","level":2,"skills":["連續實值分布函數"]},"variant":{"family_id":"qf-mod42-contcdf-zero-jump-atomlessness","seed":202611114065,"parameters":{"knots":[-16,0,16],"values":[0,[15,16],1],"point":0,"domain":"Exact_continuous_piecewise_linear_CDF","operation":"contcdf-zero-jump-atomlessness","semantic_template":"qf-mod42-contcdf-zero-jump-atomlessness/{\"knots\":[-16,0,16],\"point\":0,\"values\":[0,[15,16],1]}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_or_symbolic_model","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"候選須主端重算；不構成人工審定、Lagrange converse existence、higher-order analyticity、sampled Hausdorff、CDF density、unchecked Catalan division、Euler criterion、bounded NFA rejection、Lean或Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-14","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261014-advance-20261111-r04-continuous-real-distribution-function-0066","batch_id":"batch-20261014-advance-20261111-r04-continuous-real-distribution-function-foundations","language":"zh-Hant","source_mko_ids":["mko-continuous-real-distribution-function"],"title_zh":"連續實值分布函數","stem_zh":"CDF本身continuous、nondecreasing、right-continuous且audit query_points嚴格遞增。操作=contcdf-zero-jump-atomlessness；資料={\"knots\":[-17,0,17],\"values\":[0,[16,17],1],\"point\":0}。請依 exact_ordered_tuple_declared_by_interface 欄序回答。","answer":{"kind":"expression","value":"(0, 16/17, 16/17, 0, 是, continuous_CDF_has_zero_singleton_mass_but_need_not_have_density)","explanation_zh":"Wave6第五層核對=(0, 16/17, 16/17, 0, 是, continuous_CDF_has_zero_singleton_mass_but_need_not_have_density)；依完整明示資料獨立重算；continuous CDF無jumps所以singletons質量0，flat intervals仍允許且兩端limits為0與1；continuous或atomless不推出density或absolute continuity；singular Cantor law是boundary。"},"difficulty":{"band":"undergraduate_core","level":2,"skills":["連續實值分布函數"]},"variant":{"family_id":"qf-mod42-contcdf-zero-jump-atomlessness","seed":202611114066,"parameters":{"knots":[-17,0,17],"values":[0,[16,17],1],"point":0,"domain":"Exact_continuous_piecewise_linear_CDF","operation":"contcdf-zero-jump-atomlessness","semantic_template":"qf-mod42-contcdf-zero-jump-atomlessness/{\"knots\":[-17,0,17],\"point\":0,\"values\":[0,[16,17],1]}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_or_symbolic_model","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"候選須主端重算；不構成人工審定、Lagrange converse existence、higher-order analyticity、sampled Hausdorff、CDF density、unchecked Catalan division、Euler criterion、bounded NFA rejection、Lean或Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-14","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261014-advance-20261111-r04-continuous-real-distribution-function-0067","batch_id":"batch-20261014-advance-20261111-r04-continuous-real-distribution-function-foundations","language":"zh-Hant","source_mko_ids":["mko-continuous-real-distribution-function"],"title_zh":"連續實值分布函數","stem_zh":"CDF本身continuous、nondecreasing、right-continuous且audit query_points嚴格遞增。操作=contcdf-zero-jump-atomlessness；資料={\"knots\":[-18,0,18],\"values\":[0,[17,18],1],\"point\":0}。請依 exact_ordered_tuple_declared_by_interface 欄序回答。","answer":{"kind":"expression","value":"(0, 17/18, 17/18, 0, 是, continuous_CDF_has_zero_singleton_mass_but_need_not_have_density)","explanation_zh":"Wave6第五層核對=(0, 17/18, 17/18, 0, 是, continuous_CDF_has_zero_singleton_mass_but_need_not_have_density)；依完整明示資料獨立重算；continuous CDF無jumps所以singletons質量0，flat intervals仍允許且兩端limits為0與1；continuous或atomless不推出density或absolute continuity；singular Cantor law是boundary。"},"difficulty":{"band":"undergraduate_core","level":2,"skills":["連續實值分布函數"]},"variant":{"family_id":"qf-mod42-contcdf-zero-jump-atomlessness","seed":202611114067,"parameters":{"knots":[-18,0,18],"values":[0,[17,18],1],"point":0,"domain":"Exact_continuous_piecewise_linear_CDF","operation":"contcdf-zero-jump-atomlessness","semantic_template":"qf-mod42-contcdf-zero-jump-atomlessness/{\"knots\":[-18,0,18],\"point\":0,\"values\":[0,[17,18],1]}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_or_symbolic_model","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"候選須主端重算；不構成人工審定、Lagrange converse existence、higher-order analyticity、sampled Hausdorff、CDF density、unchecked Catalan division、Euler criterion、bounded NFA rejection、Lean或Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-14","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261014-advance-20261111-r04-continuous-real-distribution-function-0068","batch_id":"batch-20261014-advance-20261111-r04-continuous-real-distribution-function-foundations","language":"zh-Hant","source_mko_ids":["mko-continuous-real-distribution-function"],"title_zh":"連續實值分布函數","stem_zh":"CDF本身continuous、nondecreasing、right-continuous且audit query_points嚴格遞增。操作=contcdf-zero-jump-atomlessness；資料={\"knots\":[-19,0,19],\"values\":[0,[18,19],1],\"point\":0}。請依 exact_ordered_tuple_declared_by_interface 欄序回答。","answer":{"kind":"expression","value":"(0, 18/19, 18/19, 0, 是, continuous_CDF_has_zero_singleton_mass_but_need_not_have_density)","explanation_zh":"Wave6第五層核對=(0, 18/19, 18/19, 0, 是, continuous_CDF_has_zero_singleton_mass_but_need_not_have_density)；依完整明示資料獨立重算；continuous CDF無jumps所以singletons質量0，flat intervals仍允許且兩端limits為0與1；continuous或atomless不推出density或absolute continuity；singular Cantor law是boundary。"},"difficulty":{"band":"undergraduate_core","level":3,"skills":["連續實值分布函數"]},"variant":{"family_id":"qf-mod42-contcdf-zero-jump-atomlessness","seed":202611114068,"parameters":{"knots":[-19,0,19],"values":[0,[18,19],1],"point":0,"domain":"Exact_continuous_piecewise_linear_CDF","operation":"contcdf-zero-jump-atomlessness","semantic_template":"qf-mod42-contcdf-zero-jump-atomlessness/{\"knots\":[-19,0,19],\"point\":0,\"values\":[0,[18,19],1]}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_or_symbolic_model","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"候選須主端重算；不構成人工審定、Lagrange converse existence、higher-order analyticity、sampled Hausdorff、CDF density、unchecked Catalan division、Euler criterion、bounded NFA rejection、Lean或Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-14","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261014-advance-20261111-r04-continuous-real-distribution-function-0069","batch_id":"batch-20261014-advance-20261111-r04-continuous-real-distribution-function-foundations","language":"zh-Hant","source_mko_ids":["mko-continuous-real-distribution-function"],"title_zh":"連續實值分布函數","stem_zh":"CDF本身continuous、nondecreasing、right-continuous且audit query_points嚴格遞增。操作=contcdf-zero-jump-atomlessness；資料={\"knots\":[-20,0,20],\"values\":[0,[19,20],1],\"point\":0}。請依 exact_ordered_tuple_declared_by_interface 欄序回答。","answer":{"kind":"expression","value":"(0, 19/20, 19/20, 0, 是, continuous_CDF_has_zero_singleton_mass_but_need_not_have_density)","explanation_zh":"Wave6第五層核對=(0, 19/20, 19/20, 0, 是, continuous_CDF_has_zero_singleton_mass_but_need_not_have_density)；依完整明示資料獨立重算；continuous CDF無jumps所以singletons質量0，flat intervals仍允許且兩端limits為0與1；continuous或atomless不推出density或absolute continuity；singular Cantor law是boundary。"},"difficulty":{"band":"undergraduate_core","level":3,"skills":["連續實值分布函數"]},"variant":{"family_id":"qf-mod42-contcdf-zero-jump-atomlessness","seed":202611114069,"parameters":{"knots":[-20,0,20],"values":[0,[19,20],1],"point":0,"domain":"Exact_continuous_piecewise_linear_CDF","operation":"contcdf-zero-jump-atomlessness","semantic_template":"qf-mod42-contcdf-zero-jump-atomlessness/{\"knots\":[-20,0,20],\"point\":0,\"values\":[0,[19,20],1]}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_or_symbolic_model","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"候選須主端重算；不構成人工審定、Lagrange converse existence、higher-order analyticity、sampled Hausdorff、CDF density、unchecked Catalan division、Euler criterion、bounded NFA rejection、Lean或Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-14","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261014-advance-20261111-r04-continuous-real-distribution-function-0070","batch_id":"batch-20261014-advance-20261111-r04-continuous-real-distribution-function-foundations","language":"zh-Hant","source_mko_ids":["mko-continuous-real-distribution-function"],"title_zh":"連續實值分布函數","stem_zh":"CDF本身continuous、nondecreasing、right-continuous且audit query_points嚴格遞增。操作=contcdf-zero-jump-atomlessness；資料={\"knots\":[-21,0,21],\"values\":[0,[20,21],1],\"point\":0}。請依 exact_ordered_tuple_declared_by_interface 欄序回答。","answer":{"kind":"expression","value":"(0, 20/21, 20/21, 0, 是, continuous_CDF_has_zero_singleton_mass_but_need_not_have_density)","explanation_zh":"Wave6第五層核對=(0, 20/21, 20/21, 0, 是, continuous_CDF_has_zero_singleton_mass_but_need_not_have_density)；依完整明示資料獨立重算；continuous CDF無jumps所以singletons質量0，flat intervals仍允許且兩端limits為0與1；continuous或atomless不推出density或absolute continuity；singular Cantor law是boundary。"},"difficulty":{"band":"undergraduate_core","level":3,"skills":["連續實值分布函數"]},"variant":{"family_id":"qf-mod42-contcdf-zero-jump-atomlessness","seed":202611114070,"parameters":{"knots":[-21,0,21],"values":[0,[20,21],1],"point":0,"domain":"Exact_continuous_piecewise_linear_CDF","operation":"contcdf-zero-jump-atomlessness","semantic_template":"qf-mod42-contcdf-zero-jump-atomlessness/{\"knots\":[-21,0,21],\"point\":0,\"values\":[0,[20,21],1]}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_or_symbolic_model","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"候選須主端重算；不構成人工審定、Lagrange converse existence、higher-order analyticity、sampled Hausdorff、CDF density、unchecked Catalan division、Euler criterion、bounded NFA rejection、Lean或Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-14","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261014-advance-20261111-r04-continuous-real-distribution-function-0071","batch_id":"batch-20261014-advance-20261111-r04-continuous-real-distribution-function-foundations","language":"zh-Hant","source_mko_ids":["mko-continuous-real-distribution-function"],"title_zh":"連續實值分布函數","stem_zh":"CDF本身continuous、nondecreasing、right-continuous且audit query_points嚴格遞增。操作=contcdf-zero-jump-atomlessness；資料={\"knots\":[-22,0,22],\"values\":[0,[21,22],1],\"point\":0}。請依 exact_ordered_tuple_declared_by_interface 欄序回答。","answer":{"kind":"expression","value":"(0, 21/22, 21/22, 0, 是, continuous_CDF_has_zero_singleton_mass_but_need_not_have_density)","explanation_zh":"Wave6第五層核對=(0, 21/22, 21/22, 0, 是, continuous_CDF_has_zero_singleton_mass_but_need_not_have_density)；依完整明示資料獨立重算；continuous CDF無jumps所以singletons質量0，flat intervals仍允許且兩端limits為0與1；continuous或atomless不推出density或absolute continuity；singular Cantor law是boundary。"},"difficulty":{"band":"undergraduate_core","level":3,"skills":["連續實值分布函數"]},"variant":{"family_id":"qf-mod42-contcdf-zero-jump-atomlessness","seed":202611114071,"parameters":{"knots":[-22,0,22],"values":[0,[21,22],1],"point":0,"domain":"Exact_continuous_piecewise_linear_CDF","operation":"contcdf-zero-jump-atomlessness","semantic_template":"qf-mod42-contcdf-zero-jump-atomlessness/{\"knots\":[-22,0,22],\"point\":0,\"values\":[0,[21,22],1]}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_or_symbolic_model","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"候選須主端重算；不構成人工審定、Lagrange converse existence、higher-order analyticity、sampled Hausdorff、CDF density、unchecked Catalan division、Euler criterion、bounded NFA rejection、Lean或Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-14","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261014-advance-20261111-r04-continuous-real-distribution-function-0072","batch_id":"batch-20261014-advance-20261111-r04-continuous-real-distribution-function-foundations","language":"zh-Hant","source_mko_ids":["mko-continuous-real-distribution-function"],"title_zh":"連續實值分布函數","stem_zh":"CDF本身continuous、nondecreasing、right-continuous且audit query_points嚴格遞增。操作=contcdf-zero-jump-atomlessness；資料={\"knots\":[-23,0,23],\"values\":[0,[22,23],1],\"point\":0}。請依 exact_ordered_tuple_declared_by_interface 欄序回答。","answer":{"kind":"expression","value":"(0, 22/23, 22/23, 0, 是, continuous_CDF_has_zero_singleton_mass_but_need_not_have_density)","explanation_zh":"Wave6第五層核對=(0, 22/23, 22/23, 0, 是, continuous_CDF_has_zero_singleton_mass_but_need_not_have_density)；依完整明示資料獨立重算；continuous CDF無jumps所以singletons質量0，flat intervals仍允許且兩端limits為0與1；continuous或atomless不推出density或absolute continuity；singular Cantor law是boundary。"},"difficulty":{"band":"undergraduate_core","level":3,"skills":["連續實值分布函數"]},"variant":{"family_id":"qf-mod42-contcdf-zero-jump-atomlessness","seed":202611114072,"parameters":{"knots":[-23,0,23],"values":[0,[22,23],1],"point":0,"domain":"Exact_continuous_piecewise_linear_CDF","operation":"contcdf-zero-jump-atomlessness","semantic_template":"qf-mod42-contcdf-zero-jump-atomlessness/{\"knots\":[-23,0,23],\"point\":0,\"values\":[0,[22,23],1]}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_or_symbolic_model","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"候選須主端重算；不構成人工審定、Lagrange converse existence、higher-order analyticity、sampled Hausdorff、CDF density、unchecked Catalan division、Euler criterion、bounded NFA rejection、Lean或Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-14","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261014-advance-20261111-r04-continuous-real-distribution-function-0073","batch_id":"batch-20261014-advance-20261111-r04-continuous-real-distribution-function-foundations","language":"zh-Hant","source_mko_ids":["mko-continuous-real-distribution-function"],"title_zh":"連續實值分布函數","stem_zh":"CDF本身continuous、nondecreasing、right-continuous且audit query_points嚴格遞增。操作=contcdf-zero-jump-atomlessness；資料={\"knots\":[-24,0,24],\"values\":[0,[23,24],1],\"point\":0}。請依 exact_ordered_tuple_declared_by_interface 欄序回答。","answer":{"kind":"expression","value":"(0, 23/24, 23/24, 0, 是, continuous_CDF_has_zero_singleton_mass_but_need_not_have_density)","explanation_zh":"Wave6第五層核對=(0, 23/24, 23/24, 0, 是, continuous_CDF_has_zero_singleton_mass_but_need_not_have_density)；依完整明示資料獨立重算；continuous CDF無jumps所以singletons質量0，flat intervals仍允許且兩端limits為0與1；continuous或atomless不推出density或absolute continuity；singular Cantor law是boundary。"},"difficulty":{"band":"undergraduate_core","level":3,"skills":["連續實值分布函數"]},"variant":{"family_id":"qf-mod42-contcdf-zero-jump-atomlessness","seed":202611114073,"parameters":{"knots":[-24,0,24],"values":[0,[23,24],1],"point":0,"domain":"Exact_continuous_piecewise_linear_CDF","operation":"contcdf-zero-jump-atomlessness","semantic_template":"qf-mod42-contcdf-zero-jump-atomlessness/{\"knots\":[-24,0,24],\"point\":0,\"values\":[0,[23,24],1]}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_or_symbolic_model","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"候選須主端重算；不構成人工審定、Lagrange converse existence、higher-order analyticity、sampled Hausdorff、CDF density、unchecked Catalan division、Euler criterion、bounded NFA rejection、Lean或Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-14","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261014-advance-20261111-r04-continuous-real-distribution-function-0074","batch_id":"batch-20261014-advance-20261111-r04-continuous-real-distribution-function-foundations","language":"zh-Hant","source_mko_ids":["mko-continuous-real-distribution-function"],"title_zh":"連續實值分布函數","stem_zh":"CDF本身continuous、nondecreasing、right-continuous且audit query_points嚴格遞增。操作=contcdf-zero-jump-atomlessness；資料={\"knots\":[-25,0,25],\"values\":[0,[24,25],1],\"point\":0}。請依 exact_ordered_tuple_declared_by_interface 欄序回答。","answer":{"kind":"expression","value":"(0, 24/25, 24/25, 0, 是, continuous_CDF_has_zero_singleton_mass_but_need_not_have_density)","explanation_zh":"Wave6第五層核對=(0, 24/25, 24/25, 0, 是, continuous_CDF_has_zero_singleton_mass_but_need_not_have_density)；依完整明示資料獨立重算；continuous CDF無jumps所以singletons質量0，flat intervals仍允許且兩端limits為0與1；continuous或atomless不推出density或absolute continuity；singular Cantor law是boundary。"},"difficulty":{"band":"undergraduate_core","level":3,"skills":["連續實值分布函數"]},"variant":{"family_id":"qf-mod42-contcdf-zero-jump-atomlessness","seed":202611114074,"parameters":{"knots":[-25,0,25],"values":[0,[24,25],1],"point":0,"domain":"Exact_continuous_piecewise_linear_CDF","operation":"contcdf-zero-jump-atomlessness","semantic_template":"qf-mod42-contcdf-zero-jump-atomlessness/{\"knots\":[-25,0,25],\"point\":0,\"values\":[0,[24,25],1]}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_or_symbolic_model","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"候選須主端重算；不構成人工審定、Lagrange converse existence、higher-order analyticity、sampled Hausdorff、CDF density、unchecked Catalan division、Euler criterion、bounded NFA rejection、Lean或Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-14","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261014-advance-20261111-r04-continuous-real-distribution-function-0075","batch_id":"batch-20261014-advance-20261111-r04-continuous-real-distribution-function-foundations","language":"zh-Hant","source_mko_ids":["mko-continuous-real-distribution-function"],"title_zh":"連續實值分布函數","stem_zh":"CDF本身continuous、nondecreasing、right-continuous且audit query_points嚴格遞增。操作=contcdf-zero-jump-atomlessness；資料={\"knots\":[-26,0,26],\"values\":[0,[25,26],1],\"point\":0}。請依 exact_ordered_tuple_declared_by_interface 欄序回答。","answer":{"kind":"expression","value":"(0, 25/26, 25/26, 0, 是, continuous_CDF_has_zero_singleton_mass_but_need_not_have_density)","explanation_zh":"Wave6第五層核對=(0, 25/26, 25/26, 0, 是, continuous_CDF_has_zero_singleton_mass_but_need_not_have_density)；依完整明示資料獨立重算；continuous CDF無jumps所以singletons質量0，flat intervals仍允許且兩端limits為0與1；continuous或atomless不推出density或absolute continuity；singular Cantor law是boundary。"},"difficulty":{"band":"undergraduate_core","level":3,"skills":["連續實值分布函數"]},"variant":{"family_id":"qf-mod42-contcdf-zero-jump-atomlessness","seed":202611114075,"parameters":{"knots":[-26,0,26],"values":[0,[25,26],1],"point":0,"domain":"Exact_continuous_piecewise_linear_CDF","operation":"contcdf-zero-jump-atomlessness","semantic_template":"qf-mod42-contcdf-zero-jump-atomlessness/{\"knots\":[-26,0,26],\"point\":0,\"values\":[0,[25,26],1]}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_or_symbolic_model","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"候選須主端重算；不構成人工審定、Lagrange converse existence、higher-order analyticity、sampled Hausdorff、CDF density、unchecked Catalan division、Euler criterion、bounded NFA rejection、Lean或Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-14","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261014-advance-20261111-r04-continuous-real-distribution-function-0076","batch_id":"batch-20261014-advance-20261111-r04-continuous-real-distribution-function-foundations","language":"zh-Hant","source_mko_ids":["mko-continuous-real-distribution-function"],"title_zh":"連續實值分布函數","stem_zh":"CDF本身continuous、nondecreasing、right-continuous且audit query_points嚴格遞增。操作=contcdf-singular-no-density-boundary；資料={\"left\":-1,\"right\":2}。請依 exact_ordered_tuple_declared_by_interface 欄序回答。","answer":{"kind":"expression","value":"(-1, 2, 是, 是, 否, 是, affine_Cantor_distribution_is_continuous_atomless_and_singular_without_a_density)","explanation_zh":"Wave6第五層核對=(-1, 2, 是, 是, 否, 是, affine_Cantor_distribution_is_continuous_atomless_and_singular_without_a_density)；依完整明示資料獨立重算；continuous CDF無jumps所以singletons質量0，flat intervals仍允許且兩端limits為0與1；continuous或atomless不推出density或absolute continuity；singular Cantor law是boundary。"},"difficulty":{"band":"undergraduate_core","level":1,"skills":["連續實值分布函數"]},"variant":{"family_id":"qf-mod42-contcdf-singular-no-density-boundary","seed":202611114076,"parameters":{"left":-1,"right":2,"domain":"Exact_continuous_piecewise_linear_CDF","operation":"contcdf-singular-no-density-boundary","semantic_template":"qf-mod42-contcdf-singular-no-density-boundary/{\"left\":-1,\"right\":2}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_or_symbolic_model","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"候選須主端重算；不構成人工審定、Lagrange converse existence、higher-order analyticity、sampled Hausdorff、CDF density、unchecked Catalan division、Euler criterion、bounded NFA rejection、Lean或Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-14","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261014-advance-20261111-r04-continuous-real-distribution-function-0077","batch_id":"batch-20261014-advance-20261111-r04-continuous-real-distribution-function-foundations","language":"zh-Hant","source_mko_ids":["mko-continuous-real-distribution-function"],"title_zh":"連續實值分布函數","stem_zh":"CDF本身continuous、nondecreasing、right-continuous且audit query_points嚴格遞增。操作=contcdf-singular-no-density-boundary；資料={\"left\":-2,\"right\":3}。請依 exact_ordered_tuple_declared_by_interface 欄序回答。","answer":{"kind":"expression","value":"(-2, 3, 是, 是, 否, 是, affine_Cantor_distribution_is_continuous_atomless_and_singular_without_a_density)","explanation_zh":"Wave6第五層核對=(-2, 3, 是, 是, 否, 是, affine_Cantor_distribution_is_continuous_atomless_and_singular_without_a_density)；依完整明示資料獨立重算；continuous CDF無jumps所以singletons質量0，flat intervals仍允許且兩端limits為0與1；continuous或atomless不推出density或absolute continuity；singular Cantor law是boundary。"},"difficulty":{"band":"undergraduate_core","level":1,"skills":["連續實值分布函數"]},"variant":{"family_id":"qf-mod42-contcdf-singular-no-density-boundary","seed":202611114077,"parameters":{"left":-2,"right":3,"domain":"Exact_continuous_piecewise_linear_CDF","operation":"contcdf-singular-no-density-boundary","semantic_template":"qf-mod42-contcdf-singular-no-density-boundary/{\"left\":-2,\"right\":3}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_or_symbolic_model","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"候選須主端重算；不構成人工審定、Lagrange converse existence、higher-order analyticity、sampled Hausdorff、CDF density、unchecked Catalan division、Euler criterion、bounded NFA rejection、Lean或Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-14","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261014-advance-20261111-r04-continuous-real-distribution-function-0078","batch_id":"batch-20261014-advance-20261111-r04-continuous-real-distribution-function-foundations","language":"zh-Hant","source_mko_ids":["mko-continuous-real-distribution-function"],"title_zh":"連續實值分布函數","stem_zh":"CDF本身continuous、nondecreasing、right-continuous且audit query_points嚴格遞增。操作=contcdf-singular-no-density-boundary；資料={\"left\":-3,\"right\":4}。請依 exact_ordered_tuple_declared_by_interface 欄序回答。","answer":{"kind":"expression","value":"(-3, 4, 是, 是, 否, 是, affine_Cantor_distribution_is_continuous_atomless_and_singular_without_a_density)","explanation_zh":"Wave6第五層核對=(-3, 4, 是, 是, 否, 是, affine_Cantor_distribution_is_continuous_atomless_and_singular_without_a_density)；依完整明示資料獨立重算；continuous CDF無jumps所以singletons質量0，flat intervals仍允許且兩端limits為0與1；continuous或atomless不推出density或absolute continuity；singular Cantor law是boundary。"},"difficulty":{"band":"undergraduate_core","level":1,"skills":["連續實值分布函數"]},"variant":{"family_id":"qf-mod42-contcdf-singular-no-density-boundary","seed":202611114078,"parameters":{"left":-3,"right":4,"domain":"Exact_continuous_piecewise_linear_CDF","operation":"contcdf-singular-no-density-boundary","semantic_template":"qf-mod42-contcdf-singular-no-density-boundary/{\"left\":-3,\"right\":4}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_or_symbolic_model","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"候選須主端重算；不構成人工審定、Lagrange converse existence、higher-order analyticity、sampled Hausdorff、CDF density、unchecked Catalan division、Euler criterion、bounded NFA rejection、Lean或Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-14","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261014-advance-20261111-r04-continuous-real-distribution-function-0079","batch_id":"batch-20261014-advance-20261111-r04-continuous-real-distribution-function-foundations","language":"zh-Hant","source_mko_ids":["mko-continuous-real-distribution-function"],"title_zh":"連續實值分布函數","stem_zh":"CDF本身continuous、nondecreasing、right-continuous且audit query_points嚴格遞增。操作=contcdf-singular-no-density-boundary；資料={\"left\":-4,\"right\":5}。請依 exact_ordered_tuple_declared_by_interface 欄序回答。","answer":{"kind":"expression","value":"(-4, 5, 是, 是, 否, 是, affine_Cantor_distribution_is_continuous_atomless_and_singular_without_a_density)","explanation_zh":"Wave6第五層核對=(-4, 5, 是, 是, 否, 是, affine_Cantor_distribution_is_continuous_atomless_and_singular_without_a_density)；依完整明示資料獨立重算；continuous CDF無jumps所以singletons質量0，flat intervals仍允許且兩端limits為0與1；continuous或atomless不推出density或absolute continuity；singular Cantor law是boundary。"},"difficulty":{"band":"undergraduate_core","level":1,"skills":["連續實值分布函數"]},"variant":{"family_id":"qf-mod42-contcdf-singular-no-density-boundary","seed":202611114079,"parameters":{"left":-4,"right":5,"domain":"Exact_continuous_piecewise_linear_CDF","operation":"contcdf-singular-no-density-boundary","semantic_template":"qf-mod42-contcdf-singular-no-density-boundary/{\"left\":-4,\"right\":5}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_or_symbolic_model","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"候選須主端重算；不構成人工審定、Lagrange converse existence、higher-order analyticity、sampled Hausdorff、CDF density、unchecked Catalan division、Euler criterion、bounded NFA rejection、Lean或Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-14","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261014-advance-20261111-r04-continuous-real-distribution-function-0080","batch_id":"batch-20261014-advance-20261111-r04-continuous-real-distribution-function-foundations","language":"zh-Hant","source_mko_ids":["mko-continuous-real-distribution-function"],"title_zh":"連續實值分布函數","stem_zh":"CDF本身continuous、nondecreasing、right-continuous且audit query_points嚴格遞增。操作=contcdf-singular-no-density-boundary；資料={\"left\":-5,\"right\":6}。請依 exact_ordered_tuple_declared_by_interface 欄序回答。","answer":{"kind":"expression","value":"(-5, 6, 是, 是, 否, 是, affine_Cantor_distribution_is_continuous_atomless_and_singular_without_a_density)","explanation_zh":"Wave6第五層核對=(-5, 6, 是, 是, 否, 是, affine_Cantor_distribution_is_continuous_atomless_and_singular_without_a_density)；依完整明示資料獨立重算；continuous CDF無jumps所以singletons質量0，flat intervals仍允許且兩端limits為0與1；continuous或atomless不推出density或absolute continuity；singular Cantor law是boundary。"},"difficulty":{"band":"undergraduate_core","level":1,"skills":["連續實值分布函數"]},"variant":{"family_id":"qf-mod42-contcdf-singular-no-density-boundary","seed":202611114080,"parameters":{"left":-5,"right":6,"domain":"Exact_continuous_piecewise_linear_CDF","operation":"contcdf-singular-no-density-boundary","semantic_template":"qf-mod42-contcdf-singular-no-density-boundary/{\"left\":-5,\"right\":6}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_or_symbolic_model","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"候選須主端重算；不構成人工審定、Lagrange converse existence、higher-order analyticity、sampled Hausdorff、CDF density、unchecked Catalan division、Euler criterion、bounded NFA rejection、Lean或Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-14","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261014-advance-20261111-r04-continuous-real-distribution-function-0081","batch_id":"batch-20261014-advance-20261111-r04-continuous-real-distribution-function-foundations","language":"zh-Hant","source_mko_ids":["mko-continuous-real-distribution-function"],"title_zh":"連續實值分布函數","stem_zh":"CDF本身continuous、nondecreasing、right-continuous且audit query_points嚴格遞增。操作=contcdf-singular-no-density-boundary；資料={\"left\":-6,\"right\":7}。請依 exact_ordered_tuple_declared_by_interface 欄序回答。","answer":{"kind":"expression","value":"(-6, 7, 是, 是, 否, 是, affine_Cantor_distribution_is_continuous_atomless_and_singular_without_a_density)","explanation_zh":"Wave6第五層核對=(-6, 7, 是, 是, 否, 是, affine_Cantor_distribution_is_continuous_atomless_and_singular_without_a_density)；依完整明示資料獨立重算；continuous CDF無jumps所以singletons質量0，flat intervals仍允許且兩端limits為0與1；continuous或atomless不推出density或absolute continuity；singular Cantor law是boundary。"},"difficulty":{"band":"undergraduate_core","level":1,"skills":["連續實值分布函數"]},"variant":{"family_id":"qf-mod42-contcdf-singular-no-density-boundary","seed":202611114081,"parameters":{"left":-6,"right":7,"domain":"Exact_continuous_piecewise_linear_CDF","operation":"contcdf-singular-no-density-boundary","semantic_template":"qf-mod42-contcdf-singular-no-density-boundary/{\"left\":-6,\"right\":7}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_or_symbolic_model","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"候選須主端重算；不構成人工審定、Lagrange converse existence、higher-order analyticity、sampled Hausdorff、CDF density、unchecked Catalan division、Euler criterion、bounded NFA rejection、Lean或Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-14","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261014-advance-20261111-r04-continuous-real-distribution-function-0082","batch_id":"batch-20261014-advance-20261111-r04-continuous-real-distribution-function-foundations","language":"zh-Hant","source_mko_ids":["mko-continuous-real-distribution-function"],"title_zh":"連續實值分布函數","stem_zh":"CDF本身continuous、nondecreasing、right-continuous且audit query_points嚴格遞增。操作=contcdf-singular-no-density-boundary；資料={\"left\":-7,\"right\":8}。請依 exact_ordered_tuple_declared_by_interface 欄序回答。","answer":{"kind":"expression","value":"(-7, 8, 是, 是, 否, 是, affine_Cantor_distribution_is_continuous_atomless_and_singular_without_a_density)","explanation_zh":"Wave6第五層核對=(-7, 8, 是, 是, 否, 是, affine_Cantor_distribution_is_continuous_atomless_and_singular_without_a_density)；依完整明示資料獨立重算；continuous CDF無jumps所以singletons質量0，flat intervals仍允許且兩端limits為0與1；continuous或atomless不推出density或absolute continuity；singular Cantor law是boundary。"},"difficulty":{"band":"undergraduate_core","level":1,"skills":["連續實值分布函數"]},"variant":{"family_id":"qf-mod42-contcdf-singular-no-density-boundary","seed":202611114082,"parameters":{"left":-7,"right":8,"domain":"Exact_continuous_piecewise_linear_CDF","operation":"contcdf-singular-no-density-boundary","semantic_template":"qf-mod42-contcdf-singular-no-density-boundary/{\"left\":-7,\"right\":8}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_or_symbolic_model","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"候選須主端重算；不構成人工審定、Lagrange converse existence、higher-order analyticity、sampled Hausdorff、CDF density、unchecked Catalan division、Euler criterion、bounded NFA rejection、Lean或Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-14","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261014-advance-20261111-r04-continuous-real-distribution-function-0083","batch_id":"batch-20261014-advance-20261111-r04-continuous-real-distribution-function-foundations","language":"zh-Hant","source_mko_ids":["mko-continuous-real-distribution-function"],"title_zh":"連續實值分布函數","stem_zh":"CDF本身continuous、nondecreasing、right-continuous且audit query_points嚴格遞增。操作=contcdf-singular-no-density-boundary；資料={\"left\":-8,\"right\":9}。請依 exact_ordered_tuple_declared_by_interface 欄序回答。","answer":{"kind":"expression","value":"(-8, 9, 是, 是, 否, 是, affine_Cantor_distribution_is_continuous_atomless_and_singular_without_a_density)","explanation_zh":"Wave6第五層核對=(-8, 9, 是, 是, 否, 是, affine_Cantor_distribution_is_continuous_atomless_and_singular_without_a_density)；依完整明示資料獨立重算；continuous CDF無jumps所以singletons質量0，flat intervals仍允許且兩端limits為0與1；continuous或atomless不推出density或absolute continuity；singular Cantor law是boundary。"},"difficulty":{"band":"undergraduate_core","level":1,"skills":["連續實值分布函數"]},"variant":{"family_id":"qf-mod42-contcdf-singular-no-density-boundary","seed":202611114083,"parameters":{"left":-8,"right":9,"domain":"Exact_continuous_piecewise_linear_CDF","operation":"contcdf-singular-no-density-boundary","semantic_template":"qf-mod42-contcdf-singular-no-density-boundary/{\"left\":-8,\"right\":9}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_or_symbolic_model","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"候選須主端重算；不構成人工審定、Lagrange converse existence、higher-order analyticity、sampled Hausdorff、CDF density、unchecked Catalan division、Euler criterion、bounded NFA rejection、Lean或Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-14","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261014-advance-20261111-r04-continuous-real-distribution-function-0084","batch_id":"batch-20261014-advance-20261111-r04-continuous-real-distribution-function-foundations","language":"zh-Hant","source_mko_ids":["mko-continuous-real-distribution-function"],"title_zh":"連續實值分布函數","stem_zh":"CDF本身continuous、nondecreasing、right-continuous且audit query_points嚴格遞增。操作=contcdf-singular-no-density-boundary；資料={\"left\":-9,\"right\":10}。請依 exact_ordered_tuple_declared_by_interface 欄序回答。","answer":{"kind":"expression","value":"(-9, 10, 是, 是, 否, 是, affine_Cantor_distribution_is_continuous_atomless_and_singular_without_a_density)","explanation_zh":"Wave6第五層核對=(-9, 10, 是, 是, 否, 是, affine_Cantor_distribution_is_continuous_atomless_and_singular_without_a_density)；依完整明示資料獨立重算；continuous CDF無jumps所以singletons質量0，flat intervals仍允許且兩端limits為0與1；continuous或atomless不推出density或absolute continuity；singular Cantor law是boundary。"},"difficulty":{"band":"undergraduate_core","level":2,"skills":["連續實值分布函數"]},"variant":{"family_id":"qf-mod42-contcdf-singular-no-density-boundary","seed":202611114084,"parameters":{"left":-9,"right":10,"domain":"Exact_continuous_piecewise_linear_CDF","operation":"contcdf-singular-no-density-boundary","semantic_template":"qf-mod42-contcdf-singular-no-density-boundary/{\"left\":-9,\"right\":10}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_or_symbolic_model","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"候選須主端重算；不構成人工審定、Lagrange converse existence、higher-order analyticity、sampled Hausdorff、CDF density、unchecked Catalan division、Euler criterion、bounded NFA rejection、Lean或Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-14","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261014-advance-20261111-r04-continuous-real-distribution-function-0085","batch_id":"batch-20261014-advance-20261111-r04-continuous-real-distribution-function-foundations","language":"zh-Hant","source_mko_ids":["mko-continuous-real-distribution-function"],"title_zh":"連續實值分布函數","stem_zh":"CDF本身continuous、nondecreasing、right-continuous且audit query_points嚴格遞增。操作=contcdf-singular-no-density-boundary；資料={\"left\":-10,\"right\":11}。請依 exact_ordered_tuple_declared_by_interface 欄序回答。","answer":{"kind":"expression","value":"(-10, 11, 是, 是, 否, 是, affine_Cantor_distribution_is_continuous_atomless_and_singular_without_a_density)","explanation_zh":"Wave6第五層核對=(-10, 11, 是, 是, 否, 是, affine_Cantor_distribution_is_continuous_atomless_and_singular_without_a_density)；依完整明示資料獨立重算；continuous CDF無jumps所以singletons質量0，flat intervals仍允許且兩端limits為0與1；continuous或atomless不推出density或absolute continuity；singular Cantor law是boundary。"},"difficulty":{"band":"undergraduate_core","level":2,"skills":["連續實值分布函數"]},"variant":{"family_id":"qf-mod42-contcdf-singular-no-density-boundary","seed":202611114085,"parameters":{"left":-10,"right":11,"domain":"Exact_continuous_piecewise_linear_CDF","operation":"contcdf-singular-no-density-boundary","semantic_template":"qf-mod42-contcdf-singular-no-density-boundary/{\"left\":-10,\"right\":11}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_or_symbolic_model","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"候選須主端重算；不構成人工審定、Lagrange converse existence、higher-order analyticity、sampled Hausdorff、CDF density、unchecked Catalan division、Euler criterion、bounded NFA rejection、Lean或Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-14","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261014-advance-20261111-r04-continuous-real-distribution-function-0086","batch_id":"batch-20261014-advance-20261111-r04-continuous-real-distribution-function-foundations","language":"zh-Hant","source_mko_ids":["mko-continuous-real-distribution-function"],"title_zh":"連續實值分布函數","stem_zh":"CDF本身continuous、nondecreasing、right-continuous且audit query_points嚴格遞增。操作=contcdf-singular-no-density-boundary；資料={\"left\":-11,\"right\":12}。請依 exact_ordered_tuple_declared_by_interface 欄序回答。","answer":{"kind":"expression","value":"(-11, 12, 是, 是, 否, 是, affine_Cantor_distribution_is_continuous_atomless_and_singular_without_a_density)","explanation_zh":"Wave6第五層核對=(-11, 12, 是, 是, 否, 是, affine_Cantor_distribution_is_continuous_atomless_and_singular_without_a_density)；依完整明示資料獨立重算；continuous CDF無jumps所以singletons質量0，flat intervals仍允許且兩端limits為0與1；continuous或atomless不推出density或absolute continuity；singular Cantor law是boundary。"},"difficulty":{"band":"undergraduate_core","level":2,"skills":["連續實值分布函數"]},"variant":{"family_id":"qf-mod42-contcdf-singular-no-density-boundary","seed":202611114086,"parameters":{"left":-11,"right":12,"domain":"Exact_continuous_piecewise_linear_CDF","operation":"contcdf-singular-no-density-boundary","semantic_template":"qf-mod42-contcdf-singular-no-density-boundary/{\"left\":-11,\"right\":12}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_or_symbolic_model","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"候選須主端重算；不構成人工審定、Lagrange converse existence、higher-order analyticity、sampled Hausdorff、CDF density、unchecked Catalan division、Euler criterion、bounded NFA rejection、Lean或Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-14","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261014-advance-20261111-r04-continuous-real-distribution-function-0087","batch_id":"batch-20261014-advance-20261111-r04-continuous-real-distribution-function-foundations","language":"zh-Hant","source_mko_ids":["mko-continuous-real-distribution-function"],"title_zh":"連續實值分布函數","stem_zh":"CDF本身continuous、nondecreasing、right-continuous且audit query_points嚴格遞增。操作=contcdf-singular-no-density-boundary；資料={\"left\":-12,\"right\":13}。請依 exact_ordered_tuple_declared_by_interface 欄序回答。","answer":{"kind":"expression","value":"(-12, 13, 是, 是, 否, 是, affine_Cantor_distribution_is_continuous_atomless_and_singular_without_a_density)","explanation_zh":"Wave6第五層核對=(-12, 13, 是, 是, 否, 是, affine_Cantor_distribution_is_continuous_atomless_and_singular_without_a_density)；依完整明示資料獨立重算；continuous CDF無jumps所以singletons質量0，flat intervals仍允許且兩端limits為0與1；continuous或atomless不推出density或absolute continuity；singular Cantor law是boundary。"},"difficulty":{"band":"undergraduate_core","level":2,"skills":["連續實值分布函數"]},"variant":{"family_id":"qf-mod42-contcdf-singular-no-density-boundary","seed":202611114087,"parameters":{"left":-12,"right":13,"domain":"Exact_continuous_piecewise_linear_CDF","operation":"contcdf-singular-no-density-boundary","semantic_template":"qf-mod42-contcdf-singular-no-density-boundary/{\"left\":-12,\"right\":13}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_or_symbolic_model","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"候選須主端重算；不構成人工審定、Lagrange converse existence、higher-order analyticity、sampled Hausdorff、CDF density、unchecked Catalan division、Euler criterion、bounded NFA rejection、Lean或Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-14","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261014-advance-20261111-r04-continuous-real-distribution-function-0088","batch_id":"batch-20261014-advance-20261111-r04-continuous-real-distribution-function-foundations","language":"zh-Hant","source_mko_ids":["mko-continuous-real-distribution-function"],"title_zh":"連續實值分布函數","stem_zh":"CDF本身continuous、nondecreasing、right-continuous且audit query_points嚴格遞增。操作=contcdf-singular-no-density-boundary；資料={\"left\":-13,\"right\":14}。請依 exact_ordered_tuple_declared_by_interface 欄序回答。","answer":{"kind":"expression","value":"(-13, 14, 是, 是, 否, 是, affine_Cantor_distribution_is_continuous_atomless_and_singular_without_a_density)","explanation_zh":"Wave6第五層核對=(-13, 14, 是, 是, 否, 是, affine_Cantor_distribution_is_continuous_atomless_and_singular_without_a_density)；依完整明示資料獨立重算；continuous CDF無jumps所以singletons質量0，flat intervals仍允許且兩端limits為0與1；continuous或atomless不推出density或absolute continuity；singular Cantor law是boundary。"},"difficulty":{"band":"undergraduate_core","level":2,"skills":["連續實值分布函數"]},"variant":{"family_id":"qf-mod42-contcdf-singular-no-density-boundary","seed":202611114088,"parameters":{"left":-13,"right":14,"domain":"Exact_continuous_piecewise_linear_CDF","operation":"contcdf-singular-no-density-boundary","semantic_template":"qf-mod42-contcdf-singular-no-density-boundary/{\"left\":-13,\"right\":14}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_or_symbolic_model","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"候選須主端重算；不構成人工審定、Lagrange converse existence、higher-order analyticity、sampled Hausdorff、CDF density、unchecked Catalan division、Euler criterion、bounded NFA rejection、Lean或Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-14","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261014-advance-20261111-r04-continuous-real-distribution-function-0089","batch_id":"batch-20261014-advance-20261111-r04-continuous-real-distribution-function-foundations","language":"zh-Hant","source_mko_ids":["mko-continuous-real-distribution-function"],"title_zh":"連續實值分布函數","stem_zh":"CDF本身continuous、nondecreasing、right-continuous且audit query_points嚴格遞增。操作=contcdf-singular-no-density-boundary；資料={\"left\":-14,\"right\":15}。請依 exact_ordered_tuple_declared_by_interface 欄序回答。","answer":{"kind":"expression","value":"(-14, 15, 是, 是, 否, 是, affine_Cantor_distribution_is_continuous_atomless_and_singular_without_a_density)","explanation_zh":"Wave6第五層核對=(-14, 15, 是, 是, 否, 是, affine_Cantor_distribution_is_continuous_atomless_and_singular_without_a_density)；依完整明示資料獨立重算；continuous CDF無jumps所以singletons質量0，flat intervals仍允許且兩端limits為0與1；continuous或atomless不推出density或absolute continuity；singular Cantor law是boundary。"},"difficulty":{"band":"undergraduate_core","level":2,"skills":["連續實值分布函數"]},"variant":{"family_id":"qf-mod42-contcdf-singular-no-density-boundary","seed":202611114089,"parameters":{"left":-14,"right":15,"domain":"Exact_continuous_piecewise_linear_CDF","operation":"contcdf-singular-no-density-boundary","semantic_template":"qf-mod42-contcdf-singular-no-density-boundary/{\"left\":-14,\"right\":15}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_or_symbolic_model","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"候選須主端重算；不構成人工審定、Lagrange converse existence、higher-order analyticity、sampled Hausdorff、CDF density、unchecked Catalan division、Euler criterion、bounded NFA rejection、Lean或Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-14","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261014-advance-20261111-r04-continuous-real-distribution-function-0090","batch_id":"batch-20261014-advance-20261111-r04-continuous-real-distribution-function-foundations","language":"zh-Hant","source_mko_ids":["mko-continuous-real-distribution-function"],"title_zh":"連續實值分布函數","stem_zh":"CDF本身continuous、nondecreasing、right-continuous且audit query_points嚴格遞增。操作=contcdf-singular-no-density-boundary；資料={\"left\":-15,\"right\":16}。請依 exact_ordered_tuple_declared_by_interface 欄序回答。","answer":{"kind":"expression","value":"(-15, 16, 是, 是, 否, 是, affine_Cantor_distribution_is_continuous_atomless_and_singular_without_a_density)","explanation_zh":"Wave6第五層核對=(-15, 16, 是, 是, 否, 是, affine_Cantor_distribution_is_continuous_atomless_and_singular_without_a_density)；依完整明示資料獨立重算；continuous CDF無jumps所以singletons質量0，flat intervals仍允許且兩端limits為0與1；continuous或atomless不推出density或absolute continuity；singular Cantor law是boundary。"},"difficulty":{"band":"undergraduate_core","level":2,"skills":["連續實值分布函數"]},"variant":{"family_id":"qf-mod42-contcdf-singular-no-density-boundary","seed":202611114090,"parameters":{"left":-15,"right":16,"domain":"Exact_continuous_piecewise_linear_CDF","operation":"contcdf-singular-no-density-boundary","semantic_template":"qf-mod42-contcdf-singular-no-density-boundary/{\"left\":-15,\"right\":16}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_or_symbolic_model","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"候選須主端重算；不構成人工審定、Lagrange converse existence、higher-order analyticity、sampled Hausdorff、CDF density、unchecked Catalan division、Euler criterion、bounded NFA rejection、Lean或Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-14","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261014-advance-20261111-r04-continuous-real-distribution-function-0091","batch_id":"batch-20261014-advance-20261111-r04-continuous-real-distribution-function-foundations","language":"zh-Hant","source_mko_ids":["mko-continuous-real-distribution-function"],"title_zh":"連續實值分布函數","stem_zh":"CDF本身continuous、nondecreasing、right-continuous且audit query_points嚴格遞增。操作=contcdf-singular-no-density-boundary；資料={\"left\":-16,\"right\":17}。請依 exact_ordered_tuple_declared_by_interface 欄序回答。","answer":{"kind":"expression","value":"(-16, 17, 是, 是, 否, 是, affine_Cantor_distribution_is_continuous_atomless_and_singular_without_a_density)","explanation_zh":"Wave6第五層核對=(-16, 17, 是, 是, 否, 是, affine_Cantor_distribution_is_continuous_atomless_and_singular_without_a_density)；依完整明示資料獨立重算；continuous CDF無jumps所以singletons質量0，flat intervals仍允許且兩端limits為0與1；continuous或atomless不推出density或absolute continuity；singular Cantor law是boundary。"},"difficulty":{"band":"undergraduate_core","level":2,"skills":["連續實值分布函數"]},"variant":{"family_id":"qf-mod42-contcdf-singular-no-density-boundary","seed":202611114091,"parameters":{"left":-16,"right":17,"domain":"Exact_continuous_piecewise_linear_CDF","operation":"contcdf-singular-no-density-boundary","semantic_template":"qf-mod42-contcdf-singular-no-density-boundary/{\"left\":-16,\"right\":17}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_or_symbolic_model","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"候選須主端重算；不構成人工審定、Lagrange converse existence、higher-order analyticity、sampled Hausdorff、CDF density、unchecked Catalan division、Euler criterion、bounded NFA rejection、Lean或Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-14","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261014-advance-20261111-r04-continuous-real-distribution-function-0092","batch_id":"batch-20261014-advance-20261111-r04-continuous-real-distribution-function-foundations","language":"zh-Hant","source_mko_ids":["mko-continuous-real-distribution-function"],"title_zh":"連續實值分布函數","stem_zh":"CDF本身continuous、nondecreasing、right-continuous且audit query_points嚴格遞增。操作=contcdf-singular-no-density-boundary；資料={\"left\":-17,\"right\":18}。請依 exact_ordered_tuple_declared_by_interface 欄序回答。","answer":{"kind":"expression","value":"(-17, 18, 是, 是, 否, 是, affine_Cantor_distribution_is_continuous_atomless_and_singular_without_a_density)","explanation_zh":"Wave6第五層核對=(-17, 18, 是, 是, 否, 是, affine_Cantor_distribution_is_continuous_atomless_and_singular_without_a_density)；依完整明示資料獨立重算；continuous CDF無jumps所以singletons質量0，flat intervals仍允許且兩端limits為0與1；continuous或atomless不推出density或absolute continuity；singular Cantor law是boundary。"},"difficulty":{"band":"undergraduate_core","level":2,"skills":["連續實值分布函數"]},"variant":{"family_id":"qf-mod42-contcdf-singular-no-density-boundary","seed":202611114092,"parameters":{"left":-17,"right":18,"domain":"Exact_continuous_piecewise_linear_CDF","operation":"contcdf-singular-no-density-boundary","semantic_template":"qf-mod42-contcdf-singular-no-density-boundary/{\"left\":-17,\"right\":18}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_or_symbolic_model","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"候選須主端重算；不構成人工審定、Lagrange converse existence、higher-order analyticity、sampled Hausdorff、CDF density、unchecked Catalan division、Euler criterion、bounded NFA rejection、Lean或Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-14","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261014-advance-20261111-r04-continuous-real-distribution-function-0093","batch_id":"batch-20261014-advance-20261111-r04-continuous-real-distribution-function-foundations","language":"zh-Hant","source_mko_ids":["mko-continuous-real-distribution-function"],"title_zh":"連續實值分布函數","stem_zh":"CDF本身continuous、nondecreasing、right-continuous且audit query_points嚴格遞增。操作=contcdf-singular-no-density-boundary；資料={\"left\":-18,\"right\":19}。請依 exact_ordered_tuple_declared_by_interface 欄序回答。","answer":{"kind":"expression","value":"(-18, 19, 是, 是, 否, 是, affine_Cantor_distribution_is_continuous_atomless_and_singular_without_a_density)","explanation_zh":"Wave6第五層核對=(-18, 19, 是, 是, 否, 是, affine_Cantor_distribution_is_continuous_atomless_and_singular_without_a_density)；依完整明示資料獨立重算；continuous CDF無jumps所以singletons質量0，flat intervals仍允許且兩端limits為0與1；continuous或atomless不推出density或absolute continuity；singular Cantor law是boundary。"},"difficulty":{"band":"undergraduate_core","level":3,"skills":["連續實值分布函數"]},"variant":{"family_id":"qf-mod42-contcdf-singular-no-density-boundary","seed":202611114093,"parameters":{"left":-18,"right":19,"domain":"Exact_continuous_piecewise_linear_CDF","operation":"contcdf-singular-no-density-boundary","semantic_template":"qf-mod42-contcdf-singular-no-density-boundary/{\"left\":-18,\"right\":19}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_or_symbolic_model","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"候選須主端重算；不構成人工審定、Lagrange converse existence、higher-order analyticity、sampled Hausdorff、CDF density、unchecked Catalan division、Euler criterion、bounded NFA rejection、Lean或Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-14","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261014-advance-20261111-r04-continuous-real-distribution-function-0094","batch_id":"batch-20261014-advance-20261111-r04-continuous-real-distribution-function-foundations","language":"zh-Hant","source_mko_ids":["mko-continuous-real-distribution-function"],"title_zh":"連續實值分布函數","stem_zh":"CDF本身continuous、nondecreasing、right-continuous且audit query_points嚴格遞增。操作=contcdf-singular-no-density-boundary；資料={\"left\":-19,\"right\":20}。請依 exact_ordered_tuple_declared_by_interface 欄序回答。","answer":{"kind":"expression","value":"(-19, 20, 是, 是, 否, 是, affine_Cantor_distribution_is_continuous_atomless_and_singular_without_a_density)","explanation_zh":"Wave6第五層核對=(-19, 20, 是, 是, 否, 是, affine_Cantor_distribution_is_continuous_atomless_and_singular_without_a_density)；依完整明示資料獨立重算；continuous CDF無jumps所以singletons質量0，flat intervals仍允許且兩端limits為0與1；continuous或atomless不推出density或absolute continuity；singular Cantor law是boundary。"},"difficulty":{"band":"undergraduate_core","level":3,"skills":["連續實值分布函數"]},"variant":{"family_id":"qf-mod42-contcdf-singular-no-density-boundary","seed":202611114094,"parameters":{"left":-19,"right":20,"domain":"Exact_continuous_piecewise_linear_CDF","operation":"contcdf-singular-no-density-boundary","semantic_template":"qf-mod42-contcdf-singular-no-density-boundary/{\"left\":-19,\"right\":20}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_or_symbolic_model","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"候選須主端重算；不構成人工審定、Lagrange converse existence、higher-order analyticity、sampled Hausdorff、CDF density、unchecked Catalan division、Euler criterion、bounded NFA rejection、Lean或Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-14","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261014-advance-20261111-r04-continuous-real-distribution-function-0095","batch_id":"batch-20261014-advance-20261111-r04-continuous-real-distribution-function-foundations","language":"zh-Hant","source_mko_ids":["mko-continuous-real-distribution-function"],"title_zh":"連續實值分布函數","stem_zh":"CDF本身continuous、nondecreasing、right-continuous且audit query_points嚴格遞增。操作=contcdf-singular-no-density-boundary；資料={\"left\":-20,\"right\":21}。請依 exact_ordered_tuple_declared_by_interface 欄序回答。","answer":{"kind":"expression","value":"(-20, 21, 是, 是, 否, 是, affine_Cantor_distribution_is_continuous_atomless_and_singular_without_a_density)","explanation_zh":"Wave6第五層核對=(-20, 21, 是, 是, 否, 是, affine_Cantor_distribution_is_continuous_atomless_and_singular_without_a_density)；依完整明示資料獨立重算；continuous CDF無jumps所以singletons質量0，flat intervals仍允許且兩端limits為0與1；continuous或atomless不推出density或absolute continuity；singular Cantor law是boundary。"},"difficulty":{"band":"undergraduate_core","level":3,"skills":["連續實值分布函數"]},"variant":{"family_id":"qf-mod42-contcdf-singular-no-density-boundary","seed":202611114095,"parameters":{"left":-20,"right":21,"domain":"Exact_continuous_piecewise_linear_CDF","operation":"contcdf-singular-no-density-boundary","semantic_template":"qf-mod42-contcdf-singular-no-density-boundary/{\"left\":-20,\"right\":21}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_or_symbolic_model","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"候選須主端重算；不構成人工審定、Lagrange converse existence、higher-order analyticity、sampled Hausdorff、CDF density、unchecked Catalan division、Euler criterion、bounded NFA rejection、Lean或Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-14","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261014-advance-20261111-r04-continuous-real-distribution-function-0096","batch_id":"batch-20261014-advance-20261111-r04-continuous-real-distribution-function-foundations","language":"zh-Hant","source_mko_ids":["mko-continuous-real-distribution-function"],"title_zh":"連續實值分布函數","stem_zh":"CDF本身continuous、nondecreasing、right-continuous且audit query_points嚴格遞增。操作=contcdf-singular-no-density-boundary；資料={\"left\":-21,\"right\":22}。請依 exact_ordered_tuple_declared_by_interface 欄序回答。","answer":{"kind":"expression","value":"(-21, 22, 是, 是, 否, 是, affine_Cantor_distribution_is_continuous_atomless_and_singular_without_a_density)","explanation_zh":"Wave6第五層核對=(-21, 22, 是, 是, 否, 是, affine_Cantor_distribution_is_continuous_atomless_and_singular_without_a_density)；依完整明示資料獨立重算；continuous CDF無jumps所以singletons質量0，flat intervals仍允許且兩端limits為0與1；continuous或atomless不推出density或absolute continuity；singular Cantor law是boundary。"},"difficulty":{"band":"undergraduate_core","level":3,"skills":["連續實值分布函數"]},"variant":{"family_id":"qf-mod42-contcdf-singular-no-density-boundary","seed":202611114096,"parameters":{"left":-21,"right":22,"domain":"Exact_continuous_piecewise_linear_CDF","operation":"contcdf-singular-no-density-boundary","semantic_template":"qf-mod42-contcdf-singular-no-density-boundary/{\"left\":-21,\"right\":22}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_or_symbolic_model","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"候選須主端重算；不構成人工審定、Lagrange converse existence、higher-order analyticity、sampled Hausdorff、CDF density、unchecked Catalan division、Euler criterion、bounded NFA rejection、Lean或Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-14","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261014-advance-20261111-r04-continuous-real-distribution-function-0097","batch_id":"batch-20261014-advance-20261111-r04-continuous-real-distribution-function-foundations","language":"zh-Hant","source_mko_ids":["mko-continuous-real-distribution-function"],"title_zh":"連續實值分布函數","stem_zh":"CDF本身continuous、nondecreasing、right-continuous且audit query_points嚴格遞增。操作=contcdf-singular-no-density-boundary；資料={\"left\":-22,\"right\":23}。請依 exact_ordered_tuple_declared_by_interface 欄序回答。","answer":{"kind":"expression","value":"(-22, 23, 是, 是, 否, 是, affine_Cantor_distribution_is_continuous_atomless_and_singular_without_a_density)","explanation_zh":"Wave6第五層核對=(-22, 23, 是, 是, 否, 是, affine_Cantor_distribution_is_continuous_atomless_and_singular_without_a_density)；依完整明示資料獨立重算；continuous CDF無jumps所以singletons質量0，flat intervals仍允許且兩端limits為0與1；continuous或atomless不推出density或absolute continuity；singular Cantor law是boundary。"},"difficulty":{"band":"undergraduate_core","level":3,"skills":["連續實值分布函數"]},"variant":{"family_id":"qf-mod42-contcdf-singular-no-density-boundary","seed":202611114097,"parameters":{"left":-22,"right":23,"domain":"Exact_continuous_piecewise_linear_CDF","operation":"contcdf-singular-no-density-boundary","semantic_template":"qf-mod42-contcdf-singular-no-density-boundary/{\"left\":-22,\"right\":23}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_or_symbolic_model","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"候選須主端重算；不構成人工審定、Lagrange converse existence、higher-order analyticity、sampled Hausdorff、CDF density、unchecked Catalan division、Euler criterion、bounded NFA rejection、Lean或Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-14","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261014-advance-20261111-r04-continuous-real-distribution-function-0098","batch_id":"batch-20261014-advance-20261111-r04-continuous-real-distribution-function-foundations","language":"zh-Hant","source_mko_ids":["mko-continuous-real-distribution-function"],"title_zh":"連續實值分布函數","stem_zh":"CDF本身continuous、nondecreasing、right-continuous且audit query_points嚴格遞增。操作=contcdf-singular-no-density-boundary；資料={\"left\":-23,\"right\":24}。請依 exact_ordered_tuple_declared_by_interface 欄序回答。","answer":{"kind":"expression","value":"(-23, 24, 是, 是, 否, 是, affine_Cantor_distribution_is_continuous_atomless_and_singular_without_a_density)","explanation_zh":"Wave6第五層核對=(-23, 24, 是, 是, 否, 是, affine_Cantor_distribution_is_continuous_atomless_and_singular_without_a_density)；依完整明示資料獨立重算；continuous CDF無jumps所以singletons質量0，flat intervals仍允許且兩端limits為0與1；continuous或atomless不推出density或absolute continuity；singular Cantor law是boundary。"},"difficulty":{"band":"undergraduate_core","level":3,"skills":["連續實值分布函數"]},"variant":{"family_id":"qf-mod42-contcdf-singular-no-density-boundary","seed":202611114098,"parameters":{"left":-23,"right":24,"domain":"Exact_continuous_piecewise_linear_CDF","operation":"contcdf-singular-no-density-boundary","semantic_template":"qf-mod42-contcdf-singular-no-density-boundary/{\"left\":-23,\"right\":24}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_or_symbolic_model","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"候選須主端重算；不構成人工審定、Lagrange converse existence、higher-order analyticity、sampled Hausdorff、CDF density、unchecked Catalan division、Euler criterion、bounded NFA rejection、Lean或Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-14","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261014-advance-20261111-r04-continuous-real-distribution-function-0099","batch_id":"batch-20261014-advance-20261111-r04-continuous-real-distribution-function-foundations","language":"zh-Hant","source_mko_ids":["mko-continuous-real-distribution-function"],"title_zh":"連續實值分布函數","stem_zh":"CDF本身continuous、nondecreasing、right-continuous且audit query_points嚴格遞增。操作=contcdf-singular-no-density-boundary；資料={\"left\":-24,\"right\":25}。請依 exact_ordered_tuple_declared_by_interface 欄序回答。","answer":{"kind":"expression","value":"(-24, 25, 是, 是, 否, 是, affine_Cantor_distribution_is_continuous_atomless_and_singular_without_a_density)","explanation_zh":"Wave6第五層核對=(-24, 25, 是, 是, 否, 是, affine_Cantor_distribution_is_continuous_atomless_and_singular_without_a_density)；依完整明示資料獨立重算；continuous CDF無jumps所以singletons質量0，flat intervals仍允許且兩端limits為0與1；continuous或atomless不推出density或absolute continuity；singular Cantor law是boundary。"},"difficulty":{"band":"undergraduate_core","level":3,"skills":["連續實值分布函數"]},"variant":{"family_id":"qf-mod42-contcdf-singular-no-density-boundary","seed":202611114099,"parameters":{"left":-24,"right":25,"domain":"Exact_continuous_piecewise_linear_CDF","operation":"contcdf-singular-no-density-boundary","semantic_template":"qf-mod42-contcdf-singular-no-density-boundary/{\"left\":-24,\"right\":25}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_or_symbolic_model","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"候選須主端重算；不構成人工審定、Lagrange converse existence、higher-order analyticity、sampled Hausdorff、CDF density、unchecked Catalan division、Euler criterion、bounded NFA rejection、Lean或Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-14","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261014-advance-20261111-r04-continuous-real-distribution-function-0100","batch_id":"batch-20261014-advance-20261111-r04-continuous-real-distribution-function-foundations","language":"zh-Hant","source_mko_ids":["mko-continuous-real-distribution-function"],"title_zh":"連續實值分布函數","stem_zh":"CDF本身continuous、nondecreasing、right-continuous且audit query_points嚴格遞增。操作=contcdf-singular-no-density-boundary；資料={\"left\":-25,\"right\":26}。請依 exact_ordered_tuple_declared_by_interface 欄序回答。","answer":{"kind":"expression","value":"(-25, 26, 是, 是, 否, 是, affine_Cantor_distribution_is_continuous_atomless_and_singular_without_a_density)","explanation_zh":"Wave6第五層核對=(-25, 26, 是, 是, 否, 是, affine_Cantor_distribution_is_continuous_atomless_and_singular_without_a_density)；依完整明示資料獨立重算；continuous CDF無jumps所以singletons質量0，flat intervals仍允許且兩端limits為0與1；continuous或atomless不推出density或absolute continuity；singular Cantor law是boundary。"},"difficulty":{"band":"undergraduate_core","level":3,"skills":["連續實值分布函數"]},"variant":{"family_id":"qf-mod42-contcdf-singular-no-density-boundary","seed":202611114100,"parameters":{"left":-25,"right":26,"domain":"Exact_continuous_piecewise_linear_CDF","operation":"contcdf-singular-no-density-boundary","semantic_template":"qf-mod42-contcdf-singular-no-density-boundary/{\"left\":-25,\"right\":26}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_or_symbolic_model","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"候選須主端重算；不構成人工審定、Lagrange converse existence、higher-order analyticity、sampled Hausdorff、CDF density、unchecked Catalan division、Euler criterion、bounded NFA rejection、Lean或Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-14","contract_version":"ocme-question-factory-v0.1"}}