{"schema_version":"ocme-question-v0.1","id":"q-20261015-advance-20261118-r03-finite-confidence-interval-coverage-0001","batch_id":"batch-20261015-advance-20261118-r03-finite-confidence-interval-coverage-foundations","language":"zh-Hant","source_mko_ids":["mko-finite-confidence-interval-coverage"],"title_zh":"有限模型信賴區間覆蓋率","stem_zh":"完整finite laws與total precommitted theta-independent interval procedure責任。操作=ci-procedure-qualification；資料={\"theta_values\":[0,1],\"samples\":[\"a\",\"b\"],\"probability_rows\":[[[1,3],[2,3]],[[2,3],[1,3]]],\"intervals\":[[0,0],[1,1]]}。請依 exact_ordered_tuple_declared_by_interface 欄序回答。","answer":{"kind":"expression","value":"([0, 1], [a, b], [[0, 0], [1, 1]], [[1/3, 2/3], [2/3, 1/3]], 是, total_precommitted_theta_independent_interval_procedure)","explanation_zh":"Wave6第十二層核對=([0, 1], [a, b], [[0, 0], [1, 1]], [[1/3, 2/3], [2/3, 1/3]], 是, total_precommitted_theta_independent_interval_procedure)；依完整明示資料獨立重算；pointwise coverage與worst-case minimum逐theta重算；average不等於uniform，posterior不是coverage；selection納入procedure後須重新計算。"},"difficulty":{"band":"undergraduate_core","level":1,"skills":["有限模型信賴區間覆蓋率"]},"variant":{"family_id":"qf-mod49-ci-procedure-qualification","seed":202611183001,"parameters":{"theta_values":[0,1],"samples":["a","b"],"probability_rows":[[[1,3],[2,3]],[[2,3],[1,3]]],"intervals":[[0,0],[1,1]],"domain":"Exact_finite_confidence_coverage","operation":"ci-procedure-qualification","semantic_template":"ci-procedure-qualification|{intervals:[[[0,1],[0,1]],[[1,1],[1,1]]],probability_rows:[[[1,3],[2,3]],[[2,3],[1,3]]],samples:[\"a\",\"b\"],theta:[0,1]}"}},"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；不構成一般limit theorem、coverage、number-theory或language theorem證明、人工審定、Lean或Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-15","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261015-advance-20261118-r03-finite-confidence-interval-coverage-0002","batch_id":"batch-20261015-advance-20261118-r03-finite-confidence-interval-coverage-foundations","language":"zh-Hant","source_mko_ids":["mko-finite-confidence-interval-coverage"],"title_zh":"有限模型信賴區間覆蓋率","stem_zh":"完整finite laws與total precommitted theta-independent interval procedure責任。操作=ci-procedure-qualification；資料={\"theta_values\":[0,1],\"samples\":[\"a\",\"b\"],\"probability_rows\":[[[2,4],[2,4]],[[2,4],[2,4]]],\"intervals\":[[0,0],[1,1]]}。請依 exact_ordered_tuple_declared_by_interface 欄序回答。","answer":{"kind":"expression","value":"([0, 1], [a, b], [[0, 0], [1, 1]], [[1/2, 1/2], [1/2, 1/2]], 是, total_precommitted_theta_independent_interval_procedure)","explanation_zh":"Wave6第十二層核對=([0, 1], [a, b], [[0, 0], [1, 1]], [[1/2, 1/2], [1/2, 1/2]], 是, total_precommitted_theta_independent_interval_procedure)；依完整明示資料獨立重算；pointwise coverage與worst-case minimum逐theta重算；average不等於uniform，posterior不是coverage；selection納入procedure後須重新計算。"},"difficulty":{"band":"undergraduate_core","level":1,"skills":["有限模型信賴區間覆蓋率"]},"variant":{"family_id":"qf-mod49-ci-procedure-qualification","seed":202611183002,"parameters":{"theta_values":[0,1],"samples":["a","b"],"probability_rows":[[[2,4],[2,4]],[[2,4],[2,4]]],"intervals":[[0,0],[1,1]],"domain":"Exact_finite_confidence_coverage","operation":"ci-procedure-qualification","semantic_template":"ci-procedure-qualification|{intervals:[[[0,1],[0,1]],[[1,1],[1,1]]],probability_rows:[[[1,2],[1,2]],[[1,2],[1,2]]],samples:[\"a\",\"b\"],theta:[0,1]}"}},"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；不構成一般limit theorem、coverage、number-theory或language theorem證明、人工審定、Lean或Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-15","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261015-advance-20261118-r03-finite-confidence-interval-coverage-0003","batch_id":"batch-20261015-advance-20261118-r03-finite-confidence-interval-coverage-foundations","language":"zh-Hant","source_mko_ids":["mko-finite-confidence-interval-coverage"],"title_zh":"有限模型信賴區間覆蓋率","stem_zh":"完整finite laws與total precommitted theta-independent interval procedure責任。操作=ci-procedure-qualification；資料={\"theta_values\":[0,1],\"samples\":[\"a\",\"b\"],\"probability_rows\":[[[3,5],[2,5]],[[2,5],[3,5]]],\"intervals\":[[0,0],[1,1]]}。請依 exact_ordered_tuple_declared_by_interface 欄序回答。","answer":{"kind":"expression","value":"([0, 1], [a, b], [[0, 0], [1, 1]], [[3/5, 2/5], [2/5, 3/5]], 是, total_precommitted_theta_independent_interval_procedure)","explanation_zh":"Wave6第十二層核對=([0, 1], [a, b], [[0, 0], [1, 1]], [[3/5, 2/5], [2/5, 3/5]], 是, total_precommitted_theta_independent_interval_procedure)；依完整明示資料獨立重算；pointwise coverage與worst-case minimum逐theta重算；average不等於uniform，posterior不是coverage；selection納入procedure後須重新計算。"},"difficulty":{"band":"undergraduate_core","level":1,"skills":["有限模型信賴區間覆蓋率"]},"variant":{"family_id":"qf-mod49-ci-procedure-qualification","seed":202611183003,"parameters":{"theta_values":[0,1],"samples":["a","b"],"probability_rows":[[[3,5],[2,5]],[[2,5],[3,5]]],"intervals":[[0,0],[1,1]],"domain":"Exact_finite_confidence_coverage","operation":"ci-procedure-qualification","semantic_template":"ci-procedure-qualification|{intervals:[[[0,1],[0,1]],[[1,1],[1,1]]],probability_rows:[[[3,5],[2,5]],[[2,5],[3,5]]],samples:[\"a\",\"b\"],theta:[0,1]}"}},"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；不構成一般limit theorem、coverage、number-theory或language theorem證明、人工審定、Lean或Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-15","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261015-advance-20261118-r03-finite-confidence-interval-coverage-0004","batch_id":"batch-20261015-advance-20261118-r03-finite-confidence-interval-coverage-foundations","language":"zh-Hant","source_mko_ids":["mko-finite-confidence-interval-coverage"],"title_zh":"有限模型信賴區間覆蓋率","stem_zh":"完整finite laws與total precommitted theta-independent interval procedure責任。操作=ci-procedure-qualification；資料={\"theta_values\":[0,1],\"samples\":[\"a\",\"b\"],\"probability_rows\":[[[4,6],[2,6]],[[2,6],[4,6]]],\"intervals\":[[0,0],[1,1]]}。請依 exact_ordered_tuple_declared_by_interface 欄序回答。","answer":{"kind":"expression","value":"([0, 1], [a, b], [[0, 0], [1, 1]], [[2/3, 1/3], [1/3, 2/3]], 是, total_precommitted_theta_independent_interval_procedure)","explanation_zh":"Wave6第十二層核對=([0, 1], [a, b], [[0, 0], [1, 1]], [[2/3, 1/3], [1/3, 2/3]], 是, total_precommitted_theta_independent_interval_procedure)；依完整明示資料獨立重算；pointwise coverage與worst-case minimum逐theta重算；average不等於uniform，posterior不是coverage；selection納入procedure後須重新計算。"},"difficulty":{"band":"undergraduate_core","level":1,"skills":["有限模型信賴區間覆蓋率"]},"variant":{"family_id":"qf-mod49-ci-procedure-qualification","seed":202611183004,"parameters":{"theta_values":[0,1],"samples":["a","b"],"probability_rows":[[[4,6],[2,6]],[[2,6],[4,6]]],"intervals":[[0,0],[1,1]],"domain":"Exact_finite_confidence_coverage","operation":"ci-procedure-qualification","semantic_template":"ci-procedure-qualification|{intervals:[[[0,1],[0,1]],[[1,1],[1,1]]],probability_rows:[[[2,3],[1,3]],[[1,3],[2,3]]],samples:[\"a\",\"b\"],theta:[0,1]}"}},"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；不構成一般limit theorem、coverage、number-theory或language theorem證明、人工審定、Lean或Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-15","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261015-advance-20261118-r03-finite-confidence-interval-coverage-0005","batch_id":"batch-20261015-advance-20261118-r03-finite-confidence-interval-coverage-foundations","language":"zh-Hant","source_mko_ids":["mko-finite-confidence-interval-coverage"],"title_zh":"有限模型信賴區間覆蓋率","stem_zh":"完整finite laws與total precommitted theta-independent interval procedure責任。操作=ci-procedure-qualification；資料={\"theta_values\":[0,1],\"samples\":[\"a\",\"b\"],\"probability_rows\":[[[5,7],[2,7]],[[2,7],[5,7]]],\"intervals\":[[0,0],[1,1]]}。請依 exact_ordered_tuple_declared_by_interface 欄序回答。","answer":{"kind":"expression","value":"([0, 1], [a, b], [[0, 0], [1, 1]], [[5/7, 2/7], [2/7, 5/7]], 是, total_precommitted_theta_independent_interval_procedure)","explanation_zh":"Wave6第十二層核對=([0, 1], [a, b], [[0, 0], [1, 1]], [[5/7, 2/7], [2/7, 5/7]], 是, total_precommitted_theta_independent_interval_procedure)；依完整明示資料獨立重算；pointwise coverage與worst-case minimum逐theta重算；average不等於uniform，posterior不是coverage；selection納入procedure後須重新計算。"},"difficulty":{"band":"undergraduate_core","level":1,"skills":["有限模型信賴區間覆蓋率"]},"variant":{"family_id":"qf-mod49-ci-procedure-qualification","seed":202611183005,"parameters":{"theta_values":[0,1],"samples":["a","b"],"probability_rows":[[[5,7],[2,7]],[[2,7],[5,7]]],"intervals":[[0,0],[1,1]],"domain":"Exact_finite_confidence_coverage","operation":"ci-procedure-qualification","semantic_template":"ci-procedure-qualification|{intervals:[[[0,1],[0,1]],[[1,1],[1,1]]],probability_rows:[[[5,7],[2,7]],[[2,7],[5,7]]],samples:[\"a\",\"b\"],theta:[0,1]}"}},"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；不構成一般limit theorem、coverage、number-theory或language theorem證明、人工審定、Lean或Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-15","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261015-advance-20261118-r03-finite-confidence-interval-coverage-0006","batch_id":"batch-20261015-advance-20261118-r03-finite-confidence-interval-coverage-foundations","language":"zh-Hant","source_mko_ids":["mko-finite-confidence-interval-coverage"],"title_zh":"有限模型信賴區間覆蓋率","stem_zh":"完整finite laws與total precommitted theta-independent interval procedure責任。操作=ci-procedure-qualification；資料={\"theta_values\":[0,1],\"samples\":[\"a\",\"b\"],\"probability_rows\":[[[6,8],[2,8]],[[2,8],[6,8]]],\"intervals\":[[0,0],[1,1]]}。請依 exact_ordered_tuple_declared_by_interface 欄序回答。","answer":{"kind":"expression","value":"([0, 1], [a, b], [[0, 0], [1, 1]], [[3/4, 1/4], [1/4, 3/4]], 是, total_precommitted_theta_independent_interval_procedure)","explanation_zh":"Wave6第十二層核對=([0, 1], [a, b], [[0, 0], [1, 1]], [[3/4, 1/4], [1/4, 3/4]], 是, total_precommitted_theta_independent_interval_procedure)；依完整明示資料獨立重算；pointwise coverage與worst-case minimum逐theta重算；average不等於uniform，posterior不是coverage；selection納入procedure後須重新計算。"},"difficulty":{"band":"undergraduate_core","level":1,"skills":["有限模型信賴區間覆蓋率"]},"variant":{"family_id":"qf-mod49-ci-procedure-qualification","seed":202611183006,"parameters":{"theta_values":[0,1],"samples":["a","b"],"probability_rows":[[[6,8],[2,8]],[[2,8],[6,8]]],"intervals":[[0,0],[1,1]],"domain":"Exact_finite_confidence_coverage","operation":"ci-procedure-qualification","semantic_template":"ci-procedure-qualification|{intervals:[[[0,1],[0,1]],[[1,1],[1,1]]],probability_rows:[[[3,4],[1,4]],[[1,4],[3,4]]],samples:[\"a\",\"b\"],theta:[0,1]}"}},"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；不構成一般limit theorem、coverage、number-theory或language theorem證明、人工審定、Lean或Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-15","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261015-advance-20261118-r03-finite-confidence-interval-coverage-0007","batch_id":"batch-20261015-advance-20261118-r03-finite-confidence-interval-coverage-foundations","language":"zh-Hant","source_mko_ids":["mko-finite-confidence-interval-coverage"],"title_zh":"有限模型信賴區間覆蓋率","stem_zh":"完整finite laws與total precommitted theta-independent interval procedure責任。操作=ci-procedure-qualification；資料={\"theta_values\":[0,1],\"samples\":[\"a\",\"b\"],\"probability_rows\":[[[7,9],[2,9]],[[2,9],[7,9]]],\"intervals\":[[0,0],[1,1]]}。請依 exact_ordered_tuple_declared_by_interface 欄序回答。","answer":{"kind":"expression","value":"([0, 1], [a, b], [[0, 0], [1, 1]], [[7/9, 2/9], [2/9, 7/9]], 是, total_precommitted_theta_independent_interval_procedure)","explanation_zh":"Wave6第十二層核對=([0, 1], [a, b], [[0, 0], [1, 1]], [[7/9, 2/9], [2/9, 7/9]], 是, total_precommitted_theta_independent_interval_procedure)；依完整明示資料獨立重算；pointwise coverage與worst-case minimum逐theta重算；average不等於uniform，posterior不是coverage；selection納入procedure後須重新計算。"},"difficulty":{"band":"undergraduate_core","level":1,"skills":["有限模型信賴區間覆蓋率"]},"variant":{"family_id":"qf-mod49-ci-procedure-qualification","seed":202611183007,"parameters":{"theta_values":[0,1],"samples":["a","b"],"probability_rows":[[[7,9],[2,9]],[[2,9],[7,9]]],"intervals":[[0,0],[1,1]],"domain":"Exact_finite_confidence_coverage","operation":"ci-procedure-qualification","semantic_template":"ci-procedure-qualification|{intervals:[[[0,1],[0,1]],[[1,1],[1,1]]],probability_rows:[[[7,9],[2,9]],[[2,9],[7,9]]],samples:[\"a\",\"b\"],theta:[0,1]}"}},"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；不構成一般limit theorem、coverage、number-theory或language theorem證明、人工審定、Lean或Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-15","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261015-advance-20261118-r03-finite-confidence-interval-coverage-0008","batch_id":"batch-20261015-advance-20261118-r03-finite-confidence-interval-coverage-foundations","language":"zh-Hant","source_mko_ids":["mko-finite-confidence-interval-coverage"],"title_zh":"有限模型信賴區間覆蓋率","stem_zh":"完整finite laws與total precommitted theta-independent interval procedure責任。操作=ci-procedure-qualification；資料={\"theta_values\":[0,1],\"samples\":[\"a\",\"b\"],\"probability_rows\":[[[8,10],[2,10]],[[2,10],[8,10]]],\"intervals\":[[0,0],[1,1]]}。請依 exact_ordered_tuple_declared_by_interface 欄序回答。","answer":{"kind":"expression","value":"([0, 1], [a, b], [[0, 0], [1, 1]], [[4/5, 1/5], [1/5, 4/5]], 是, total_precommitted_theta_independent_interval_procedure)","explanation_zh":"Wave6第十二層核對=([0, 1], [a, b], [[0, 0], [1, 1]], [[4/5, 1/5], [1/5, 4/5]], 是, total_precommitted_theta_independent_interval_procedure)；依完整明示資料獨立重算；pointwise coverage與worst-case minimum逐theta重算；average不等於uniform，posterior不是coverage；selection納入procedure後須重新計算。"},"difficulty":{"band":"undergraduate_core","level":1,"skills":["有限模型信賴區間覆蓋率"]},"variant":{"family_id":"qf-mod49-ci-procedure-qualification","seed":202611183008,"parameters":{"theta_values":[0,1],"samples":["a","b"],"probability_rows":[[[8,10],[2,10]],[[2,10],[8,10]]],"intervals":[[0,0],[1,1]],"domain":"Exact_finite_confidence_coverage","operation":"ci-procedure-qualification","semantic_template":"ci-procedure-qualification|{intervals:[[[0,1],[0,1]],[[1,1],[1,1]]],probability_rows:[[[4,5],[1,5]],[[1,5],[4,5]]],samples:[\"a\",\"b\"],theta:[0,1]}"}},"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；不構成一般limit theorem、coverage、number-theory或language theorem證明、人工審定、Lean或Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-15","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261015-advance-20261118-r03-finite-confidence-interval-coverage-0009","batch_id":"batch-20261015-advance-20261118-r03-finite-confidence-interval-coverage-foundations","language":"zh-Hant","source_mko_ids":["mko-finite-confidence-interval-coverage"],"title_zh":"有限模型信賴區間覆蓋率","stem_zh":"完整finite laws與total precommitted theta-independent interval procedure責任。操作=ci-procedure-qualification；資料={\"theta_values\":[0,1],\"samples\":[\"a\",\"b\"],\"probability_rows\":[[[9,11],[2,11]],[[2,11],[9,11]]],\"intervals\":[[0,0],[1,1]]}。請依 exact_ordered_tuple_declared_by_interface 欄序回答。","answer":{"kind":"expression","value":"([0, 1], [a, b], [[0, 0], [1, 1]], [[9/11, 2/11], [2/11, 9/11]], 是, total_precommitted_theta_independent_interval_procedure)","explanation_zh":"Wave6第十二層核對=([0, 1], [a, b], [[0, 0], [1, 1]], [[9/11, 2/11], [2/11, 9/11]], 是, total_precommitted_theta_independent_interval_procedure)；依完整明示資料獨立重算；pointwise coverage與worst-case minimum逐theta重算；average不等於uniform，posterior不是coverage；selection納入procedure後須重新計算。"},"difficulty":{"band":"undergraduate_core","level":2,"skills":["有限模型信賴區間覆蓋率"]},"variant":{"family_id":"qf-mod49-ci-procedure-qualification","seed":202611183009,"parameters":{"theta_values":[0,1],"samples":["a","b"],"probability_rows":[[[9,11],[2,11]],[[2,11],[9,11]]],"intervals":[[0,0],[1,1]],"domain":"Exact_finite_confidence_coverage","operation":"ci-procedure-qualification","semantic_template":"ci-procedure-qualification|{intervals:[[[0,1],[0,1]],[[1,1],[1,1]]],probability_rows:[[[9,11],[2,11]],[[2,11],[9,11]]],samples:[\"a\",\"b\"],theta:[0,1]}"}},"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；不構成一般limit theorem、coverage、number-theory或language theorem證明、人工審定、Lean或Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-15","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261015-advance-20261118-r03-finite-confidence-interval-coverage-0010","batch_id":"batch-20261015-advance-20261118-r03-finite-confidence-interval-coverage-foundations","language":"zh-Hant","source_mko_ids":["mko-finite-confidence-interval-coverage"],"title_zh":"有限模型信賴區間覆蓋率","stem_zh":"完整finite laws與total precommitted theta-independent interval procedure責任。操作=ci-procedure-qualification；資料={\"theta_values\":[0,1],\"samples\":[\"a\",\"b\"],\"probability_rows\":[[[10,12],[2,12]],[[2,12],[10,12]]],\"intervals\":[[0,0],[1,1]]}。請依 exact_ordered_tuple_declared_by_interface 欄序回答。","answer":{"kind":"expression","value":"([0, 1], [a, b], [[0, 0], [1, 1]], [[5/6, 1/6], [1/6, 5/6]], 是, total_precommitted_theta_independent_interval_procedure)","explanation_zh":"Wave6第十二層核對=([0, 1], [a, b], [[0, 0], [1, 1]], [[5/6, 1/6], [1/6, 5/6]], 是, total_precommitted_theta_independent_interval_procedure)；依完整明示資料獨立重算；pointwise coverage與worst-case minimum逐theta重算；average不等於uniform，posterior不是coverage；selection納入procedure後須重新計算。"},"difficulty":{"band":"undergraduate_core","level":2,"skills":["有限模型信賴區間覆蓋率"]},"variant":{"family_id":"qf-mod49-ci-procedure-qualification","seed":202611183010,"parameters":{"theta_values":[0,1],"samples":["a","b"],"probability_rows":[[[10,12],[2,12]],[[2,12],[10,12]]],"intervals":[[0,0],[1,1]],"domain":"Exact_finite_confidence_coverage","operation":"ci-procedure-qualification","semantic_template":"ci-procedure-qualification|{intervals:[[[0,1],[0,1]],[[1,1],[1,1]]],probability_rows:[[[5,6],[1,6]],[[1,6],[5,6]]],samples:[\"a\",\"b\"],theta:[0,1]}"}},"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；不構成一般limit theorem、coverage、number-theory或language theorem證明、人工審定、Lean或Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-15","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261015-advance-20261118-r03-finite-confidence-interval-coverage-0011","batch_id":"batch-20261015-advance-20261118-r03-finite-confidence-interval-coverage-foundations","language":"zh-Hant","source_mko_ids":["mko-finite-confidence-interval-coverage"],"title_zh":"有限模型信賴區間覆蓋率","stem_zh":"完整finite laws與total precommitted theta-independent interval procedure責任。操作=ci-procedure-qualification；資料={\"theta_values\":[0,1],\"samples\":[\"a\",\"b\"],\"probability_rows\":[[[11,13],[2,13]],[[2,13],[11,13]]],\"intervals\":[[0,0],[1,1]]}。請依 exact_ordered_tuple_declared_by_interface 欄序回答。","answer":{"kind":"expression","value":"([0, 1], [a, b], [[0, 0], [1, 1]], [[11/13, 2/13], [2/13, 11/13]], 是, total_precommitted_theta_independent_interval_procedure)","explanation_zh":"Wave6第十二層核對=([0, 1], [a, b], [[0, 0], [1, 1]], [[11/13, 2/13], [2/13, 11/13]], 是, total_precommitted_theta_independent_interval_procedure)；依完整明示資料獨立重算；pointwise coverage與worst-case minimum逐theta重算；average不等於uniform，posterior不是coverage；selection納入procedure後須重新計算。"},"difficulty":{"band":"undergraduate_core","level":2,"skills":["有限模型信賴區間覆蓋率"]},"variant":{"family_id":"qf-mod49-ci-procedure-qualification","seed":202611183011,"parameters":{"theta_values":[0,1],"samples":["a","b"],"probability_rows":[[[11,13],[2,13]],[[2,13],[11,13]]],"intervals":[[0,0],[1,1]],"domain":"Exact_finite_confidence_coverage","operation":"ci-procedure-qualification","semantic_template":"ci-procedure-qualification|{intervals:[[[0,1],[0,1]],[[1,1],[1,1]]],probability_rows:[[[11,13],[2,13]],[[2,13],[11,13]]],samples:[\"a\",\"b\"],theta:[0,1]}"}},"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；不構成一般limit theorem、coverage、number-theory或language theorem證明、人工審定、Lean或Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-15","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261015-advance-20261118-r03-finite-confidence-interval-coverage-0012","batch_id":"batch-20261015-advance-20261118-r03-finite-confidence-interval-coverage-foundations","language":"zh-Hant","source_mko_ids":["mko-finite-confidence-interval-coverage"],"title_zh":"有限模型信賴區間覆蓋率","stem_zh":"完整finite laws與total precommitted theta-independent interval procedure責任。操作=ci-procedure-qualification；資料={\"theta_values\":[0,1],\"samples\":[\"a\",\"b\"],\"probability_rows\":[[[12,14],[2,14]],[[2,14],[12,14]]],\"intervals\":[[0,0],[1,1]]}。請依 exact_ordered_tuple_declared_by_interface 欄序回答。","answer":{"kind":"expression","value":"([0, 1], [a, b], [[0, 0], [1, 1]], [[6/7, 1/7], [1/7, 6/7]], 是, total_precommitted_theta_independent_interval_procedure)","explanation_zh":"Wave6第十二層核對=([0, 1], [a, b], [[0, 0], [1, 1]], [[6/7, 1/7], [1/7, 6/7]], 是, total_precommitted_theta_independent_interval_procedure)；依完整明示資料獨立重算；pointwise coverage與worst-case minimum逐theta重算；average不等於uniform，posterior不是coverage；selection納入procedure後須重新計算。"},"difficulty":{"band":"undergraduate_core","level":2,"skills":["有限模型信賴區間覆蓋率"]},"variant":{"family_id":"qf-mod49-ci-procedure-qualification","seed":202611183012,"parameters":{"theta_values":[0,1],"samples":["a","b"],"probability_rows":[[[12,14],[2,14]],[[2,14],[12,14]]],"intervals":[[0,0],[1,1]],"domain":"Exact_finite_confidence_coverage","operation":"ci-procedure-qualification","semantic_template":"ci-procedure-qualification|{intervals:[[[0,1],[0,1]],[[1,1],[1,1]]],probability_rows:[[[6,7],[1,7]],[[1,7],[6,7]]],samples:[\"a\",\"b\"],theta:[0,1]}"}},"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；不構成一般limit theorem、coverage、number-theory或language theorem證明、人工審定、Lean或Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-15","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261015-advance-20261118-r03-finite-confidence-interval-coverage-0013","batch_id":"batch-20261015-advance-20261118-r03-finite-confidence-interval-coverage-foundations","language":"zh-Hant","source_mko_ids":["mko-finite-confidence-interval-coverage"],"title_zh":"有限模型信賴區間覆蓋率","stem_zh":"完整finite laws與total precommitted theta-independent interval procedure責任。操作=ci-procedure-qualification；資料={\"theta_values\":[0,1],\"samples\":[\"a\",\"b\"],\"probability_rows\":[[[13,15],[2,15]],[[2,15],[13,15]]],\"intervals\":[[0,0],[1,1]]}。請依 exact_ordered_tuple_declared_by_interface 欄序回答。","answer":{"kind":"expression","value":"([0, 1], [a, b], [[0, 0], [1, 1]], [[13/15, 2/15], [2/15, 13/15]], 是, total_precommitted_theta_independent_interval_procedure)","explanation_zh":"Wave6第十二層核對=([0, 1], [a, b], [[0, 0], [1, 1]], [[13/15, 2/15], [2/15, 13/15]], 是, total_precommitted_theta_independent_interval_procedure)；依完整明示資料獨立重算；pointwise coverage與worst-case minimum逐theta重算；average不等於uniform，posterior不是coverage；selection納入procedure後須重新計算。"},"difficulty":{"band":"undergraduate_core","level":2,"skills":["有限模型信賴區間覆蓋率"]},"variant":{"family_id":"qf-mod49-ci-procedure-qualification","seed":202611183013,"parameters":{"theta_values":[0,1],"samples":["a","b"],"probability_rows":[[[13,15],[2,15]],[[2,15],[13,15]]],"intervals":[[0,0],[1,1]],"domain":"Exact_finite_confidence_coverage","operation":"ci-procedure-qualification","semantic_template":"ci-procedure-qualification|{intervals:[[[0,1],[0,1]],[[1,1],[1,1]]],probability_rows:[[[13,15],[2,15]],[[2,15],[13,15]]],samples:[\"a\",\"b\"],theta:[0,1]}"}},"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；不構成一般limit theorem、coverage、number-theory或language theorem證明、人工審定、Lean或Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-15","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261015-advance-20261118-r03-finite-confidence-interval-coverage-0014","batch_id":"batch-20261015-advance-20261118-r03-finite-confidence-interval-coverage-foundations","language":"zh-Hant","source_mko_ids":["mko-finite-confidence-interval-coverage"],"title_zh":"有限模型信賴區間覆蓋率","stem_zh":"完整finite laws與total precommitted theta-independent interval procedure責任。操作=ci-procedure-qualification；資料={\"theta_values\":[0,1],\"samples\":[\"a\",\"b\"],\"probability_rows\":[[[14,16],[2,16]],[[2,16],[14,16]]],\"intervals\":[[0,0],[1,1]]}。請依 exact_ordered_tuple_declared_by_interface 欄序回答。","answer":{"kind":"expression","value":"([0, 1], [a, b], [[0, 0], [1, 1]], [[7/8, 1/8], [1/8, 7/8]], 是, total_precommitted_theta_independent_interval_procedure)","explanation_zh":"Wave6第十二層核對=([0, 1], [a, b], [[0, 0], [1, 1]], [[7/8, 1/8], [1/8, 7/8]], 是, total_precommitted_theta_independent_interval_procedure)；依完整明示資料獨立重算；pointwise coverage與worst-case minimum逐theta重算；average不等於uniform，posterior不是coverage；selection納入procedure後須重新計算。"},"difficulty":{"band":"undergraduate_core","level":2,"skills":["有限模型信賴區間覆蓋率"]},"variant":{"family_id":"qf-mod49-ci-procedure-qualification","seed":202611183014,"parameters":{"theta_values":[0,1],"samples":["a","b"],"probability_rows":[[[14,16],[2,16]],[[2,16],[14,16]]],"intervals":[[0,0],[1,1]],"domain":"Exact_finite_confidence_coverage","operation":"ci-procedure-qualification","semantic_template":"ci-procedure-qualification|{intervals:[[[0,1],[0,1]],[[1,1],[1,1]]],probability_rows:[[[7,8],[1,8]],[[1,8],[7,8]]],samples:[\"a\",\"b\"],theta:[0,1]}"}},"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；不構成一般limit theorem、coverage、number-theory或language theorem證明、人工審定、Lean或Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-15","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261015-advance-20261118-r03-finite-confidence-interval-coverage-0015","batch_id":"batch-20261015-advance-20261118-r03-finite-confidence-interval-coverage-foundations","language":"zh-Hant","source_mko_ids":["mko-finite-confidence-interval-coverage"],"title_zh":"有限模型信賴區間覆蓋率","stem_zh":"完整finite laws與total precommitted theta-independent interval procedure責任。操作=ci-procedure-qualification；資料={\"theta_values\":[0,1],\"samples\":[\"a\",\"b\"],\"probability_rows\":[[[15,17],[2,17]],[[2,17],[15,17]]],\"intervals\":[[0,0],[1,1]]}。請依 exact_ordered_tuple_declared_by_interface 欄序回答。","answer":{"kind":"expression","value":"([0, 1], [a, b], [[0, 0], [1, 1]], [[15/17, 2/17], [2/17, 15/17]], 是, total_precommitted_theta_independent_interval_procedure)","explanation_zh":"Wave6第十二層核對=([0, 1], [a, b], [[0, 0], [1, 1]], [[15/17, 2/17], [2/17, 15/17]], 是, total_precommitted_theta_independent_interval_procedure)；依完整明示資料獨立重算；pointwise coverage與worst-case minimum逐theta重算；average不等於uniform，posterior不是coverage；selection納入procedure後須重新計算。"},"difficulty":{"band":"undergraduate_core","level":2,"skills":["有限模型信賴區間覆蓋率"]},"variant":{"family_id":"qf-mod49-ci-procedure-qualification","seed":202611183015,"parameters":{"theta_values":[0,1],"samples":["a","b"],"probability_rows":[[[15,17],[2,17]],[[2,17],[15,17]]],"intervals":[[0,0],[1,1]],"domain":"Exact_finite_confidence_coverage","operation":"ci-procedure-qualification","semantic_template":"ci-procedure-qualification|{intervals:[[[0,1],[0,1]],[[1,1],[1,1]]],probability_rows:[[[15,17],[2,17]],[[2,17],[15,17]]],samples:[\"a\",\"b\"],theta:[0,1]}"}},"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；不構成一般limit theorem、coverage、number-theory或language theorem證明、人工審定、Lean或Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-15","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261015-advance-20261118-r03-finite-confidence-interval-coverage-0016","batch_id":"batch-20261015-advance-20261118-r03-finite-confidence-interval-coverage-foundations","language":"zh-Hant","source_mko_ids":["mko-finite-confidence-interval-coverage"],"title_zh":"有限模型信賴區間覆蓋率","stem_zh":"完整finite laws與total precommitted theta-independent interval procedure責任。操作=ci-procedure-qualification；資料={\"theta_values\":[0,1],\"samples\":[\"a\",\"b\"],\"probability_rows\":[[[16,18],[2,18]],[[2,18],[16,18]]],\"intervals\":[[0,0],[1,1]]}。請依 exact_ordered_tuple_declared_by_interface 欄序回答。","answer":{"kind":"expression","value":"([0, 1], [a, b], [[0, 0], [1, 1]], [[8/9, 1/9], [1/9, 8/9]], 是, total_precommitted_theta_independent_interval_procedure)","explanation_zh":"Wave6第十二層核對=([0, 1], [a, b], [[0, 0], [1, 1]], [[8/9, 1/9], [1/9, 8/9]], 是, total_precommitted_theta_independent_interval_procedure)；依完整明示資料獨立重算；pointwise coverage與worst-case minimum逐theta重算；average不等於uniform，posterior不是coverage；selection納入procedure後須重新計算。"},"difficulty":{"band":"undergraduate_core","level":2,"skills":["有限模型信賴區間覆蓋率"]},"variant":{"family_id":"qf-mod49-ci-procedure-qualification","seed":202611183016,"parameters":{"theta_values":[0,1],"samples":["a","b"],"probability_rows":[[[16,18],[2,18]],[[2,18],[16,18]]],"intervals":[[0,0],[1,1]],"domain":"Exact_finite_confidence_coverage","operation":"ci-procedure-qualification","semantic_template":"ci-procedure-qualification|{intervals:[[[0,1],[0,1]],[[1,1],[1,1]]],probability_rows:[[[8,9],[1,9]],[[1,9],[8,9]]],samples:[\"a\",\"b\"],theta:[0,1]}"}},"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；不構成一般limit theorem、coverage、number-theory或language theorem證明、人工審定、Lean或Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-15","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261015-advance-20261118-r03-finite-confidence-interval-coverage-0017","batch_id":"batch-20261015-advance-20261118-r03-finite-confidence-interval-coverage-foundations","language":"zh-Hant","source_mko_ids":["mko-finite-confidence-interval-coverage"],"title_zh":"有限模型信賴區間覆蓋率","stem_zh":"完整finite laws與total precommitted theta-independent interval procedure責任。操作=ci-procedure-qualification；資料={\"theta_values\":[0,1],\"samples\":[\"a\",\"b\"],\"probability_rows\":[[[17,19],[2,19]],[[2,19],[17,19]]],\"intervals\":[[0,0],[1,1]]}。請依 exact_ordered_tuple_declared_by_interface 欄序回答。","answer":{"kind":"expression","value":"([0, 1], [a, b], [[0, 0], [1, 1]], [[17/19, 2/19], [2/19, 17/19]], 是, total_precommitted_theta_independent_interval_procedure)","explanation_zh":"Wave6第十二層核對=([0, 1], [a, b], [[0, 0], [1, 1]], [[17/19, 2/19], [2/19, 17/19]], 是, total_precommitted_theta_independent_interval_procedure)；依完整明示資料獨立重算；pointwise coverage與worst-case minimum逐theta重算；average不等於uniform，posterior不是coverage；selection納入procedure後須重新計算。"},"difficulty":{"band":"undergraduate_core","level":2,"skills":["有限模型信賴區間覆蓋率"]},"variant":{"family_id":"qf-mod49-ci-procedure-qualification","seed":202611183017,"parameters":{"theta_values":[0,1],"samples":["a","b"],"probability_rows":[[[17,19],[2,19]],[[2,19],[17,19]]],"intervals":[[0,0],[1,1]],"domain":"Exact_finite_confidence_coverage","operation":"ci-procedure-qualification","semantic_template":"ci-procedure-qualification|{intervals:[[[0,1],[0,1]],[[1,1],[1,1]]],probability_rows:[[[17,19],[2,19]],[[2,19],[17,19]]],samples:[\"a\",\"b\"],theta:[0,1]}"}},"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；不構成一般limit theorem、coverage、number-theory或language theorem證明、人工審定、Lean或Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-15","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261015-advance-20261118-r03-finite-confidence-interval-coverage-0018","batch_id":"batch-20261015-advance-20261118-r03-finite-confidence-interval-coverage-foundations","language":"zh-Hant","source_mko_ids":["mko-finite-confidence-interval-coverage"],"title_zh":"有限模型信賴區間覆蓋率","stem_zh":"完整finite laws與total precommitted theta-independent interval procedure責任。操作=ci-procedure-qualification；資料={\"theta_values\":[0,1],\"samples\":[\"a\",\"b\"],\"probability_rows\":[[[18,20],[2,20]],[[2,20],[18,20]]],\"intervals\":[[0,0],[1,1]]}。請依 exact_ordered_tuple_declared_by_interface 欄序回答。","answer":{"kind":"expression","value":"([0, 1], [a, b], [[0, 0], [1, 1]], [[9/10, 1/10], [1/10, 9/10]], 是, total_precommitted_theta_independent_interval_procedure)","explanation_zh":"Wave6第十二層核對=([0, 1], [a, b], [[0, 0], [1, 1]], [[9/10, 1/10], [1/10, 9/10]], 是, total_precommitted_theta_independent_interval_procedure)；依完整明示資料獨立重算；pointwise coverage與worst-case minimum逐theta重算；average不等於uniform，posterior不是coverage；selection納入procedure後須重新計算。"},"difficulty":{"band":"undergraduate_core","level":3,"skills":["有限模型信賴區間覆蓋率"]},"variant":{"family_id":"qf-mod49-ci-procedure-qualification","seed":202611183018,"parameters":{"theta_values":[0,1],"samples":["a","b"],"probability_rows":[[[18,20],[2,20]],[[2,20],[18,20]]],"intervals":[[0,0],[1,1]],"domain":"Exact_finite_confidence_coverage","operation":"ci-procedure-qualification","semantic_template":"ci-procedure-qualification|{intervals:[[[0,1],[0,1]],[[1,1],[1,1]]],probability_rows:[[[9,10],[1,10]],[[1,10],[9,10]]],samples:[\"a\",\"b\"],theta:[0,1]}"}},"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；不構成一般limit theorem、coverage、number-theory或language theorem證明、人工審定、Lean或Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-15","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261015-advance-20261118-r03-finite-confidence-interval-coverage-0019","batch_id":"batch-20261015-advance-20261118-r03-finite-confidence-interval-coverage-foundations","language":"zh-Hant","source_mko_ids":["mko-finite-confidence-interval-coverage"],"title_zh":"有限模型信賴區間覆蓋率","stem_zh":"完整finite laws與total precommitted theta-independent interval procedure責任。操作=ci-procedure-qualification；資料={\"theta_values\":[0,1],\"samples\":[\"a\",\"b\"],\"probability_rows\":[[[19,21],[2,21]],[[2,21],[19,21]]],\"intervals\":[[0,0],[1,1]]}。請依 exact_ordered_tuple_declared_by_interface 欄序回答。","answer":{"kind":"expression","value":"([0, 1], [a, b], [[0, 0], [1, 1]], [[19/21, 2/21], [2/21, 19/21]], 是, total_precommitted_theta_independent_interval_procedure)","explanation_zh":"Wave6第十二層核對=([0, 1], [a, b], [[0, 0], [1, 1]], [[19/21, 2/21], [2/21, 19/21]], 是, total_precommitted_theta_independent_interval_procedure)；依完整明示資料獨立重算；pointwise coverage與worst-case minimum逐theta重算；average不等於uniform，posterior不是coverage；selection納入procedure後須重新計算。"},"difficulty":{"band":"undergraduate_core","level":3,"skills":["有限模型信賴區間覆蓋率"]},"variant":{"family_id":"qf-mod49-ci-procedure-qualification","seed":202611183019,"parameters":{"theta_values":[0,1],"samples":["a","b"],"probability_rows":[[[19,21],[2,21]],[[2,21],[19,21]]],"intervals":[[0,0],[1,1]],"domain":"Exact_finite_confidence_coverage","operation":"ci-procedure-qualification","semantic_template":"ci-procedure-qualification|{intervals:[[[0,1],[0,1]],[[1,1],[1,1]]],probability_rows:[[[19,21],[2,21]],[[2,21],[19,21]]],samples:[\"a\",\"b\"],theta:[0,1]}"}},"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；不構成一般limit theorem、coverage、number-theory或language theorem證明、人工審定、Lean或Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-15","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261015-advance-20261118-r03-finite-confidence-interval-coverage-0020","batch_id":"batch-20261015-advance-20261118-r03-finite-confidence-interval-coverage-foundations","language":"zh-Hant","source_mko_ids":["mko-finite-confidence-interval-coverage"],"title_zh":"有限模型信賴區間覆蓋率","stem_zh":"完整finite laws與total precommitted theta-independent interval procedure責任。操作=ci-procedure-qualification；資料={\"theta_values\":[0,1],\"samples\":[\"a\",\"b\"],\"probability_rows\":[[[20,22],[2,22]],[[2,22],[20,22]]],\"intervals\":[[0,0],[1,1]]}。請依 exact_ordered_tuple_declared_by_interface 欄序回答。","answer":{"kind":"expression","value":"([0, 1], [a, b], [[0, 0], [1, 1]], [[10/11, 1/11], [1/11, 10/11]], 是, total_precommitted_theta_independent_interval_procedure)","explanation_zh":"Wave6第十二層核對=([0, 1], [a, b], [[0, 0], [1, 1]], [[10/11, 1/11], [1/11, 10/11]], 是, total_precommitted_theta_independent_interval_procedure)；依完整明示資料獨立重算；pointwise coverage與worst-case minimum逐theta重算；average不等於uniform，posterior不是coverage；selection納入procedure後須重新計算。"},"difficulty":{"band":"undergraduate_core","level":3,"skills":["有限模型信賴區間覆蓋率"]},"variant":{"family_id":"qf-mod49-ci-procedure-qualification","seed":202611183020,"parameters":{"theta_values":[0,1],"samples":["a","b"],"probability_rows":[[[20,22],[2,22]],[[2,22],[20,22]]],"intervals":[[0,0],[1,1]],"domain":"Exact_finite_confidence_coverage","operation":"ci-procedure-qualification","semantic_template":"ci-procedure-qualification|{intervals:[[[0,1],[0,1]],[[1,1],[1,1]]],probability_rows:[[[10,11],[1,11]],[[1,11],[10,11]]],samples:[\"a\",\"b\"],theta:[0,1]}"}},"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；不構成一般limit theorem、coverage、number-theory或language theorem證明、人工審定、Lean或Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-15","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261015-advance-20261118-r03-finite-confidence-interval-coverage-0021","batch_id":"batch-20261015-advance-20261118-r03-finite-confidence-interval-coverage-foundations","language":"zh-Hant","source_mko_ids":["mko-finite-confidence-interval-coverage"],"title_zh":"有限模型信賴區間覆蓋率","stem_zh":"完整finite laws與total precommitted theta-independent interval procedure責任。操作=ci-procedure-qualification；資料={\"theta_values\":[0,1],\"samples\":[\"a\",\"b\"],\"probability_rows\":[[[21,23],[2,23]],[[2,23],[21,23]]],\"intervals\":[[0,0],[1,1]]}。請依 exact_ordered_tuple_declared_by_interface 欄序回答。","answer":{"kind":"expression","value":"([0, 1], [a, b], [[0, 0], [1, 1]], [[21/23, 2/23], [2/23, 21/23]], 是, total_precommitted_theta_independent_interval_procedure)","explanation_zh":"Wave6第十二層核對=([0, 1], [a, b], [[0, 0], [1, 1]], [[21/23, 2/23], [2/23, 21/23]], 是, total_precommitted_theta_independent_interval_procedure)；依完整明示資料獨立重算；pointwise coverage與worst-case minimum逐theta重算；average不等於uniform，posterior不是coverage；selection納入procedure後須重新計算。"},"difficulty":{"band":"undergraduate_core","level":3,"skills":["有限模型信賴區間覆蓋率"]},"variant":{"family_id":"qf-mod49-ci-procedure-qualification","seed":202611183021,"parameters":{"theta_values":[0,1],"samples":["a","b"],"probability_rows":[[[21,23],[2,23]],[[2,23],[21,23]]],"intervals":[[0,0],[1,1]],"domain":"Exact_finite_confidence_coverage","operation":"ci-procedure-qualification","semantic_template":"ci-procedure-qualification|{intervals:[[[0,1],[0,1]],[[1,1],[1,1]]],probability_rows:[[[21,23],[2,23]],[[2,23],[21,23]]],samples:[\"a\",\"b\"],theta:[0,1]}"}},"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；不構成一般limit theorem、coverage、number-theory或language theorem證明、人工審定、Lean或Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-15","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261015-advance-20261118-r03-finite-confidence-interval-coverage-0022","batch_id":"batch-20261015-advance-20261118-r03-finite-confidence-interval-coverage-foundations","language":"zh-Hant","source_mko_ids":["mko-finite-confidence-interval-coverage"],"title_zh":"有限模型信賴區間覆蓋率","stem_zh":"完整finite laws與total precommitted theta-independent interval procedure責任。操作=ci-procedure-qualification；資料={\"theta_values\":[0,1],\"samples\":[\"a\",\"b\"],\"probability_rows\":[[[22,24],[2,24]],[[2,24],[22,24]]],\"intervals\":[[0,0],[1,1]]}。請依 exact_ordered_tuple_declared_by_interface 欄序回答。","answer":{"kind":"expression","value":"([0, 1], [a, b], [[0, 0], [1, 1]], [[11/12, 1/12], [1/12, 11/12]], 是, total_precommitted_theta_independent_interval_procedure)","explanation_zh":"Wave6第十二層核對=([0, 1], [a, b], [[0, 0], [1, 1]], [[11/12, 1/12], [1/12, 11/12]], 是, total_precommitted_theta_independent_interval_procedure)；依完整明示資料獨立重算；pointwise coverage與worst-case minimum逐theta重算；average不等於uniform，posterior不是coverage；selection納入procedure後須重新計算。"},"difficulty":{"band":"undergraduate_core","level":3,"skills":["有限模型信賴區間覆蓋率"]},"variant":{"family_id":"qf-mod49-ci-procedure-qualification","seed":202611183022,"parameters":{"theta_values":[0,1],"samples":["a","b"],"probability_rows":[[[22,24],[2,24]],[[2,24],[22,24]]],"intervals":[[0,0],[1,1]],"domain":"Exact_finite_confidence_coverage","operation":"ci-procedure-qualification","semantic_template":"ci-procedure-qualification|{intervals:[[[0,1],[0,1]],[[1,1],[1,1]]],probability_rows:[[[11,12],[1,12]],[[1,12],[11,12]]],samples:[\"a\",\"b\"],theta:[0,1]}"}},"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；不構成一般limit theorem、coverage、number-theory或language theorem證明、人工審定、Lean或Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-15","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261015-advance-20261118-r03-finite-confidence-interval-coverage-0023","batch_id":"batch-20261015-advance-20261118-r03-finite-confidence-interval-coverage-foundations","language":"zh-Hant","source_mko_ids":["mko-finite-confidence-interval-coverage"],"title_zh":"有限模型信賴區間覆蓋率","stem_zh":"完整finite laws與total precommitted theta-independent interval procedure責任。操作=ci-procedure-qualification；資料={\"theta_values\":[0,1],\"samples\":[\"a\",\"b\"],\"probability_rows\":[[[23,25],[2,25]],[[2,25],[23,25]]],\"intervals\":[[0,0],[1,1]]}。請依 exact_ordered_tuple_declared_by_interface 欄序回答。","answer":{"kind":"expression","value":"([0, 1], [a, b], [[0, 0], [1, 1]], [[23/25, 2/25], [2/25, 23/25]], 是, total_precommitted_theta_independent_interval_procedure)","explanation_zh":"Wave6第十二層核對=([0, 1], [a, b], [[0, 0], [1, 1]], [[23/25, 2/25], [2/25, 23/25]], 是, total_precommitted_theta_independent_interval_procedure)；依完整明示資料獨立重算；pointwise coverage與worst-case minimum逐theta重算；average不等於uniform，posterior不是coverage；selection納入procedure後須重新計算。"},"difficulty":{"band":"undergraduate_core","level":3,"skills":["有限模型信賴區間覆蓋率"]},"variant":{"family_id":"qf-mod49-ci-procedure-qualification","seed":202611183023,"parameters":{"theta_values":[0,1],"samples":["a","b"],"probability_rows":[[[23,25],[2,25]],[[2,25],[23,25]]],"intervals":[[0,0],[1,1]],"domain":"Exact_finite_confidence_coverage","operation":"ci-procedure-qualification","semantic_template":"ci-procedure-qualification|{intervals:[[[0,1],[0,1]],[[1,1],[1,1]]],probability_rows:[[[23,25],[2,25]],[[2,25],[23,25]]],samples:[\"a\",\"b\"],theta:[0,1]}"}},"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；不構成一般limit theorem、coverage、number-theory或language theorem證明、人工審定、Lean或Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-15","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261015-advance-20261118-r03-finite-confidence-interval-coverage-0024","batch_id":"batch-20261015-advance-20261118-r03-finite-confidence-interval-coverage-foundations","language":"zh-Hant","source_mko_ids":["mko-finite-confidence-interval-coverage"],"title_zh":"有限模型信賴區間覆蓋率","stem_zh":"完整finite laws與total precommitted theta-independent interval procedure責任。操作=ci-procedure-qualification；資料={\"theta_values\":[0,1],\"samples\":[\"a\",\"b\"],\"probability_rows\":[[[24,26],[2,26]],[[2,26],[24,26]]],\"intervals\":[[0,0],[1,1]]}。請依 exact_ordered_tuple_declared_by_interface 欄序回答。","answer":{"kind":"expression","value":"([0, 1], [a, b], [[0, 0], [1, 1]], [[12/13, 1/13], [1/13, 12/13]], 是, total_precommitted_theta_independent_interval_procedure)","explanation_zh":"Wave6第十二層核對=([0, 1], [a, b], [[0, 0], [1, 1]], [[12/13, 1/13], [1/13, 12/13]], 是, total_precommitted_theta_independent_interval_procedure)；依完整明示資料獨立重算；pointwise coverage與worst-case minimum逐theta重算；average不等於uniform，posterior不是coverage；selection納入procedure後須重新計算。"},"difficulty":{"band":"undergraduate_core","level":3,"skills":["有限模型信賴區間覆蓋率"]},"variant":{"family_id":"qf-mod49-ci-procedure-qualification","seed":202611183024,"parameters":{"theta_values":[0,1],"samples":["a","b"],"probability_rows":[[[24,26],[2,26]],[[2,26],[24,26]]],"intervals":[[0,0],[1,1]],"domain":"Exact_finite_confidence_coverage","operation":"ci-procedure-qualification","semantic_template":"ci-procedure-qualification|{intervals:[[[0,1],[0,1]],[[1,1],[1,1]]],probability_rows:[[[12,13],[1,13]],[[1,13],[12,13]]],samples:[\"a\",\"b\"],theta:[0,1]}"}},"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；不構成一般limit theorem、coverage、number-theory或language theorem證明、人工審定、Lean或Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-15","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261015-advance-20261118-r03-finite-confidence-interval-coverage-0025","batch_id":"batch-20261015-advance-20261118-r03-finite-confidence-interval-coverage-foundations","language":"zh-Hant","source_mko_ids":["mko-finite-confidence-interval-coverage"],"title_zh":"有限模型信賴區間覆蓋率","stem_zh":"完整finite laws與total precommitted theta-independent interval procedure責任。操作=ci-procedure-qualification；資料={\"theta_values\":[0,1],\"samples\":[\"a\",\"b\"],\"probability_rows\":[[[25,27],[2,27]],[[2,27],[25,27]]],\"intervals\":[[0,0],[1,1]]}。請依 exact_ordered_tuple_declared_by_interface 欄序回答。","answer":{"kind":"expression","value":"([0, 1], [a, b], [[0, 0], [1, 1]], [[25/27, 2/27], [2/27, 25/27]], 是, total_precommitted_theta_independent_interval_procedure)","explanation_zh":"Wave6第十二層核對=([0, 1], [a, b], [[0, 0], [1, 1]], [[25/27, 2/27], [2/27, 25/27]], 是, total_precommitted_theta_independent_interval_procedure)；依完整明示資料獨立重算；pointwise coverage與worst-case minimum逐theta重算；average不等於uniform，posterior不是coverage；selection納入procedure後須重新計算。"},"difficulty":{"band":"undergraduate_core","level":3,"skills":["有限模型信賴區間覆蓋率"]},"variant":{"family_id":"qf-mod49-ci-procedure-qualification","seed":202611183025,"parameters":{"theta_values":[0,1],"samples":["a","b"],"probability_rows":[[[25,27],[2,27]],[[2,27],[25,27]]],"intervals":[[0,0],[1,1]],"domain":"Exact_finite_confidence_coverage","operation":"ci-procedure-qualification","semantic_template":"ci-procedure-qualification|{intervals:[[[0,1],[0,1]],[[1,1],[1,1]]],probability_rows:[[[25,27],[2,27]],[[2,27],[25,27]]],samples:[\"a\",\"b\"],theta:[0,1]}"}},"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；不構成一般limit theorem、coverage、number-theory或language theorem證明、人工審定、Lean或Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-15","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261015-advance-20261118-r03-finite-confidence-interval-coverage-0026","batch_id":"batch-20261015-advance-20261118-r03-finite-confidence-interval-coverage-foundations","language":"zh-Hant","source_mko_ids":["mko-finite-confidence-interval-coverage"],"title_zh":"有限模型信賴區間覆蓋率","stem_zh":"完整finite laws與total precommitted theta-independent interval procedure責任。操作=ci-pointwise-coverage；資料={\"theta_values\":[0,1],\"samples\":[\"a\",\"b\"],\"probability_rows\":[[[1,3],[2,3]],[[2,3],[1,3]]],\"intervals\":[[0,0],[1,1]]}。請依 exact_ordered_tuple_declared_by_interface 欄序回答。","answer":{"kind":"expression","value":"([[0, 1/3], [1, 1/3]], coverage_theta=P_theta(theta_in_I(X)), not_a_posterior_probability)","explanation_zh":"Wave6第十二層核對=([[0, 1/3], [1, 1/3]], coverage_theta=P_theta(theta_in_I(X)), not_a_posterior_probability)；依完整明示資料獨立重算；pointwise coverage與worst-case minimum逐theta重算；average不等於uniform，posterior不是coverage；selection納入procedure後須重新計算。"},"difficulty":{"band":"undergraduate_core","level":1,"skills":["有限模型信賴區間覆蓋率"]},"variant":{"family_id":"qf-mod49-ci-pointwise-coverage","seed":202611183026,"parameters":{"theta_values":[0,1],"samples":["a","b"],"probability_rows":[[[1,3],[2,3]],[[2,3],[1,3]]],"intervals":[[0,0],[1,1]],"domain":"Exact_finite_confidence_coverage","operation":"ci-pointwise-coverage","semantic_template":"ci-pointwise-coverage|{intervals:[[[0,1],[0,1]],[[1,1],[1,1]]],probability_rows:[[[1,3],[2,3]],[[2,3],[1,3]]],samples:[\"a\",\"b\"],theta:[0,1]}"}},"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；不構成一般limit theorem、coverage、number-theory或language theorem證明、人工審定、Lean或Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-15","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261015-advance-20261118-r03-finite-confidence-interval-coverage-0027","batch_id":"batch-20261015-advance-20261118-r03-finite-confidence-interval-coverage-foundations","language":"zh-Hant","source_mko_ids":["mko-finite-confidence-interval-coverage"],"title_zh":"有限模型信賴區間覆蓋率","stem_zh":"完整finite laws與total precommitted theta-independent interval procedure責任。操作=ci-pointwise-coverage；資料={\"theta_values\":[0,1],\"samples\":[\"a\",\"b\"],\"probability_rows\":[[[2,4],[2,4]],[[2,4],[2,4]]],\"intervals\":[[0,0],[1,1]]}。請依 exact_ordered_tuple_declared_by_interface 欄序回答。","answer":{"kind":"expression","value":"([[0, 1/2], [1, 1/2]], coverage_theta=P_theta(theta_in_I(X)), not_a_posterior_probability)","explanation_zh":"Wave6第十二層核對=([[0, 1/2], [1, 1/2]], coverage_theta=P_theta(theta_in_I(X)), not_a_posterior_probability)；依完整明示資料獨立重算；pointwise coverage與worst-case minimum逐theta重算；average不等於uniform，posterior不是coverage；selection納入procedure後須重新計算。"},"difficulty":{"band":"undergraduate_core","level":1,"skills":["有限模型信賴區間覆蓋率"]},"variant":{"family_id":"qf-mod49-ci-pointwise-coverage","seed":202611183027,"parameters":{"theta_values":[0,1],"samples":["a","b"],"probability_rows":[[[2,4],[2,4]],[[2,4],[2,4]]],"intervals":[[0,0],[1,1]],"domain":"Exact_finite_confidence_coverage","operation":"ci-pointwise-coverage","semantic_template":"ci-pointwise-coverage|{intervals:[[[0,1],[0,1]],[[1,1],[1,1]]],probability_rows:[[[1,2],[1,2]],[[1,2],[1,2]]],samples:[\"a\",\"b\"],theta:[0,1]}"}},"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；不構成一般limit theorem、coverage、number-theory或language theorem證明、人工審定、Lean或Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-15","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261015-advance-20261118-r03-finite-confidence-interval-coverage-0028","batch_id":"batch-20261015-advance-20261118-r03-finite-confidence-interval-coverage-foundations","language":"zh-Hant","source_mko_ids":["mko-finite-confidence-interval-coverage"],"title_zh":"有限模型信賴區間覆蓋率","stem_zh":"完整finite laws與total precommitted theta-independent interval procedure責任。操作=ci-pointwise-coverage；資料={\"theta_values\":[0,1],\"samples\":[\"a\",\"b\"],\"probability_rows\":[[[3,5],[2,5]],[[2,5],[3,5]]],\"intervals\":[[0,0],[1,1]]}。請依 exact_ordered_tuple_declared_by_interface 欄序回答。","answer":{"kind":"expression","value":"([[0, 3/5], [1, 3/5]], coverage_theta=P_theta(theta_in_I(X)), not_a_posterior_probability)","explanation_zh":"Wave6第十二層核對=([[0, 3/5], [1, 3/5]], coverage_theta=P_theta(theta_in_I(X)), not_a_posterior_probability)；依完整明示資料獨立重算；pointwise coverage與worst-case minimum逐theta重算；average不等於uniform，posterior不是coverage；selection納入procedure後須重新計算。"},"difficulty":{"band":"undergraduate_core","level":1,"skills":["有限模型信賴區間覆蓋率"]},"variant":{"family_id":"qf-mod49-ci-pointwise-coverage","seed":202611183028,"parameters":{"theta_values":[0,1],"samples":["a","b"],"probability_rows":[[[3,5],[2,5]],[[2,5],[3,5]]],"intervals":[[0,0],[1,1]],"domain":"Exact_finite_confidence_coverage","operation":"ci-pointwise-coverage","semantic_template":"ci-pointwise-coverage|{intervals:[[[0,1],[0,1]],[[1,1],[1,1]]],probability_rows:[[[3,5],[2,5]],[[2,5],[3,5]]],samples:[\"a\",\"b\"],theta:[0,1]}"}},"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；不構成一般limit theorem、coverage、number-theory或language theorem證明、人工審定、Lean或Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-15","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261015-advance-20261118-r03-finite-confidence-interval-coverage-0029","batch_id":"batch-20261015-advance-20261118-r03-finite-confidence-interval-coverage-foundations","language":"zh-Hant","source_mko_ids":["mko-finite-confidence-interval-coverage"],"title_zh":"有限模型信賴區間覆蓋率","stem_zh":"完整finite laws與total precommitted theta-independent interval procedure責任。操作=ci-pointwise-coverage；資料={\"theta_values\":[0,1],\"samples\":[\"a\",\"b\"],\"probability_rows\":[[[4,6],[2,6]],[[2,6],[4,6]]],\"intervals\":[[0,0],[1,1]]}。請依 exact_ordered_tuple_declared_by_interface 欄序回答。","answer":{"kind":"expression","value":"([[0, 2/3], [1, 2/3]], coverage_theta=P_theta(theta_in_I(X)), not_a_posterior_probability)","explanation_zh":"Wave6第十二層核對=([[0, 2/3], [1, 2/3]], coverage_theta=P_theta(theta_in_I(X)), not_a_posterior_probability)；依完整明示資料獨立重算；pointwise coverage與worst-case minimum逐theta重算；average不等於uniform，posterior不是coverage；selection納入procedure後須重新計算。"},"difficulty":{"band":"undergraduate_core","level":1,"skills":["有限模型信賴區間覆蓋率"]},"variant":{"family_id":"qf-mod49-ci-pointwise-coverage","seed":202611183029,"parameters":{"theta_values":[0,1],"samples":["a","b"],"probability_rows":[[[4,6],[2,6]],[[2,6],[4,6]]],"intervals":[[0,0],[1,1]],"domain":"Exact_finite_confidence_coverage","operation":"ci-pointwise-coverage","semantic_template":"ci-pointwise-coverage|{intervals:[[[0,1],[0,1]],[[1,1],[1,1]]],probability_rows:[[[2,3],[1,3]],[[1,3],[2,3]]],samples:[\"a\",\"b\"],theta:[0,1]}"}},"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；不構成一般limit theorem、coverage、number-theory或language theorem證明、人工審定、Lean或Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-15","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261015-advance-20261118-r03-finite-confidence-interval-coverage-0030","batch_id":"batch-20261015-advance-20261118-r03-finite-confidence-interval-coverage-foundations","language":"zh-Hant","source_mko_ids":["mko-finite-confidence-interval-coverage"],"title_zh":"有限模型信賴區間覆蓋率","stem_zh":"完整finite laws與total precommitted theta-independent interval procedure責任。操作=ci-pointwise-coverage；資料={\"theta_values\":[0,1],\"samples\":[\"a\",\"b\"],\"probability_rows\":[[[5,7],[2,7]],[[2,7],[5,7]]],\"intervals\":[[0,0],[1,1]]}。請依 exact_ordered_tuple_declared_by_interface 欄序回答。","answer":{"kind":"expression","value":"([[0, 5/7], [1, 5/7]], coverage_theta=P_theta(theta_in_I(X)), not_a_posterior_probability)","explanation_zh":"Wave6第十二層核對=([[0, 5/7], [1, 5/7]], coverage_theta=P_theta(theta_in_I(X)), not_a_posterior_probability)；依完整明示資料獨立重算；pointwise coverage與worst-case minimum逐theta重算；average不等於uniform，posterior不是coverage；selection納入procedure後須重新計算。"},"difficulty":{"band":"undergraduate_core","level":1,"skills":["有限模型信賴區間覆蓋率"]},"variant":{"family_id":"qf-mod49-ci-pointwise-coverage","seed":202611183030,"parameters":{"theta_values":[0,1],"samples":["a","b"],"probability_rows":[[[5,7],[2,7]],[[2,7],[5,7]]],"intervals":[[0,0],[1,1]],"domain":"Exact_finite_confidence_coverage","operation":"ci-pointwise-coverage","semantic_template":"ci-pointwise-coverage|{intervals:[[[0,1],[0,1]],[[1,1],[1,1]]],probability_rows:[[[5,7],[2,7]],[[2,7],[5,7]]],samples:[\"a\",\"b\"],theta:[0,1]}"}},"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；不構成一般limit theorem、coverage、number-theory或language theorem證明、人工審定、Lean或Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-15","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261015-advance-20261118-r03-finite-confidence-interval-coverage-0031","batch_id":"batch-20261015-advance-20261118-r03-finite-confidence-interval-coverage-foundations","language":"zh-Hant","source_mko_ids":["mko-finite-confidence-interval-coverage"],"title_zh":"有限模型信賴區間覆蓋率","stem_zh":"完整finite laws與total precommitted theta-independent interval procedure責任。操作=ci-pointwise-coverage；資料={\"theta_values\":[0,1],\"samples\":[\"a\",\"b\"],\"probability_rows\":[[[6,8],[2,8]],[[2,8],[6,8]]],\"intervals\":[[0,0],[1,1]]}。請依 exact_ordered_tuple_declared_by_interface 欄序回答。","answer":{"kind":"expression","value":"([[0, 3/4], [1, 3/4]], coverage_theta=P_theta(theta_in_I(X)), not_a_posterior_probability)","explanation_zh":"Wave6第十二層核對=([[0, 3/4], [1, 3/4]], coverage_theta=P_theta(theta_in_I(X)), not_a_posterior_probability)；依完整明示資料獨立重算；pointwise coverage與worst-case minimum逐theta重算；average不等於uniform，posterior不是coverage；selection納入procedure後須重新計算。"},"difficulty":{"band":"undergraduate_core","level":1,"skills":["有限模型信賴區間覆蓋率"]},"variant":{"family_id":"qf-mod49-ci-pointwise-coverage","seed":202611183031,"parameters":{"theta_values":[0,1],"samples":["a","b"],"probability_rows":[[[6,8],[2,8]],[[2,8],[6,8]]],"intervals":[[0,0],[1,1]],"domain":"Exact_finite_confidence_coverage","operation":"ci-pointwise-coverage","semantic_template":"ci-pointwise-coverage|{intervals:[[[0,1],[0,1]],[[1,1],[1,1]]],probability_rows:[[[3,4],[1,4]],[[1,4],[3,4]]],samples:[\"a\",\"b\"],theta:[0,1]}"}},"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；不構成一般limit theorem、coverage、number-theory或language theorem證明、人工審定、Lean或Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-15","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261015-advance-20261118-r03-finite-confidence-interval-coverage-0032","batch_id":"batch-20261015-advance-20261118-r03-finite-confidence-interval-coverage-foundations","language":"zh-Hant","source_mko_ids":["mko-finite-confidence-interval-coverage"],"title_zh":"有限模型信賴區間覆蓋率","stem_zh":"完整finite laws與total precommitted theta-independent interval procedure責任。操作=ci-pointwise-coverage；資料={\"theta_values\":[0,1],\"samples\":[\"a\",\"b\"],\"probability_rows\":[[[7,9],[2,9]],[[2,9],[7,9]]],\"intervals\":[[0,0],[1,1]]}。請依 exact_ordered_tuple_declared_by_interface 欄序回答。","answer":{"kind":"expression","value":"([[0, 7/9], [1, 7/9]], coverage_theta=P_theta(theta_in_I(X)), not_a_posterior_probability)","explanation_zh":"Wave6第十二層核對=([[0, 7/9], [1, 7/9]], coverage_theta=P_theta(theta_in_I(X)), not_a_posterior_probability)；依完整明示資料獨立重算；pointwise coverage與worst-case minimum逐theta重算；average不等於uniform，posterior不是coverage；selection納入procedure後須重新計算。"},"difficulty":{"band":"undergraduate_core","level":1,"skills":["有限模型信賴區間覆蓋率"]},"variant":{"family_id":"qf-mod49-ci-pointwise-coverage","seed":202611183032,"parameters":{"theta_values":[0,1],"samples":["a","b"],"probability_rows":[[[7,9],[2,9]],[[2,9],[7,9]]],"intervals":[[0,0],[1,1]],"domain":"Exact_finite_confidence_coverage","operation":"ci-pointwise-coverage","semantic_template":"ci-pointwise-coverage|{intervals:[[[0,1],[0,1]],[[1,1],[1,1]]],probability_rows:[[[7,9],[2,9]],[[2,9],[7,9]]],samples:[\"a\",\"b\"],theta:[0,1]}"}},"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；不構成一般limit theorem、coverage、number-theory或language theorem證明、人工審定、Lean或Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-15","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261015-advance-20261118-r03-finite-confidence-interval-coverage-0033","batch_id":"batch-20261015-advance-20261118-r03-finite-confidence-interval-coverage-foundations","language":"zh-Hant","source_mko_ids":["mko-finite-confidence-interval-coverage"],"title_zh":"有限模型信賴區間覆蓋率","stem_zh":"完整finite laws與total precommitted theta-independent interval procedure責任。操作=ci-pointwise-coverage；資料={\"theta_values\":[0,1],\"samples\":[\"a\",\"b\"],\"probability_rows\":[[[8,10],[2,10]],[[2,10],[8,10]]],\"intervals\":[[0,0],[1,1]]}。請依 exact_ordered_tuple_declared_by_interface 欄序回答。","answer":{"kind":"expression","value":"([[0, 4/5], [1, 4/5]], coverage_theta=P_theta(theta_in_I(X)), not_a_posterior_probability)","explanation_zh":"Wave6第十二層核對=([[0, 4/5], [1, 4/5]], coverage_theta=P_theta(theta_in_I(X)), not_a_posterior_probability)；依完整明示資料獨立重算；pointwise coverage與worst-case minimum逐theta重算；average不等於uniform，posterior不是coverage；selection納入procedure後須重新計算。"},"difficulty":{"band":"undergraduate_core","level":1,"skills":["有限模型信賴區間覆蓋率"]},"variant":{"family_id":"qf-mod49-ci-pointwise-coverage","seed":202611183033,"parameters":{"theta_values":[0,1],"samples":["a","b"],"probability_rows":[[[8,10],[2,10]],[[2,10],[8,10]]],"intervals":[[0,0],[1,1]],"domain":"Exact_finite_confidence_coverage","operation":"ci-pointwise-coverage","semantic_template":"ci-pointwise-coverage|{intervals:[[[0,1],[0,1]],[[1,1],[1,1]]],probability_rows:[[[4,5],[1,5]],[[1,5],[4,5]]],samples:[\"a\",\"b\"],theta:[0,1]}"}},"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；不構成一般limit theorem、coverage、number-theory或language theorem證明、人工審定、Lean或Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-15","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261015-advance-20261118-r03-finite-confidence-interval-coverage-0034","batch_id":"batch-20261015-advance-20261118-r03-finite-confidence-interval-coverage-foundations","language":"zh-Hant","source_mko_ids":["mko-finite-confidence-interval-coverage"],"title_zh":"有限模型信賴區間覆蓋率","stem_zh":"完整finite laws與total precommitted theta-independent interval procedure責任。操作=ci-pointwise-coverage；資料={\"theta_values\":[0,1],\"samples\":[\"a\",\"b\"],\"probability_rows\":[[[9,11],[2,11]],[[2,11],[9,11]]],\"intervals\":[[0,0],[1,1]]}。請依 exact_ordered_tuple_declared_by_interface 欄序回答。","answer":{"kind":"expression","value":"([[0, 9/11], [1, 9/11]], coverage_theta=P_theta(theta_in_I(X)), not_a_posterior_probability)","explanation_zh":"Wave6第十二層核對=([[0, 9/11], [1, 9/11]], coverage_theta=P_theta(theta_in_I(X)), not_a_posterior_probability)；依完整明示資料獨立重算；pointwise coverage與worst-case minimum逐theta重算；average不等於uniform，posterior不是coverage；selection納入procedure後須重新計算。"},"difficulty":{"band":"undergraduate_core","level":2,"skills":["有限模型信賴區間覆蓋率"]},"variant":{"family_id":"qf-mod49-ci-pointwise-coverage","seed":202611183034,"parameters":{"theta_values":[0,1],"samples":["a","b"],"probability_rows":[[[9,11],[2,11]],[[2,11],[9,11]]],"intervals":[[0,0],[1,1]],"domain":"Exact_finite_confidence_coverage","operation":"ci-pointwise-coverage","semantic_template":"ci-pointwise-coverage|{intervals:[[[0,1],[0,1]],[[1,1],[1,1]]],probability_rows:[[[9,11],[2,11]],[[2,11],[9,11]]],samples:[\"a\",\"b\"],theta:[0,1]}"}},"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；不構成一般limit theorem、coverage、number-theory或language theorem證明、人工審定、Lean或Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-15","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261015-advance-20261118-r03-finite-confidence-interval-coverage-0035","batch_id":"batch-20261015-advance-20261118-r03-finite-confidence-interval-coverage-foundations","language":"zh-Hant","source_mko_ids":["mko-finite-confidence-interval-coverage"],"title_zh":"有限模型信賴區間覆蓋率","stem_zh":"完整finite laws與total precommitted theta-independent interval procedure責任。操作=ci-pointwise-coverage；資料={\"theta_values\":[0,1],\"samples\":[\"a\",\"b\"],\"probability_rows\":[[[10,12],[2,12]],[[2,12],[10,12]]],\"intervals\":[[0,0],[1,1]]}。請依 exact_ordered_tuple_declared_by_interface 欄序回答。","answer":{"kind":"expression","value":"([[0, 5/6], [1, 5/6]], coverage_theta=P_theta(theta_in_I(X)), not_a_posterior_probability)","explanation_zh":"Wave6第十二層核對=([[0, 5/6], [1, 5/6]], coverage_theta=P_theta(theta_in_I(X)), not_a_posterior_probability)；依完整明示資料獨立重算；pointwise coverage與worst-case minimum逐theta重算；average不等於uniform，posterior不是coverage；selection納入procedure後須重新計算。"},"difficulty":{"band":"undergraduate_core","level":2,"skills":["有限模型信賴區間覆蓋率"]},"variant":{"family_id":"qf-mod49-ci-pointwise-coverage","seed":202611183035,"parameters":{"theta_values":[0,1],"samples":["a","b"],"probability_rows":[[[10,12],[2,12]],[[2,12],[10,12]]],"intervals":[[0,0],[1,1]],"domain":"Exact_finite_confidence_coverage","operation":"ci-pointwise-coverage","semantic_template":"ci-pointwise-coverage|{intervals:[[[0,1],[0,1]],[[1,1],[1,1]]],probability_rows:[[[5,6],[1,6]],[[1,6],[5,6]]],samples:[\"a\",\"b\"],theta:[0,1]}"}},"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；不構成一般limit theorem、coverage、number-theory或language theorem證明、人工審定、Lean或Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-15","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261015-advance-20261118-r03-finite-confidence-interval-coverage-0036","batch_id":"batch-20261015-advance-20261118-r03-finite-confidence-interval-coverage-foundations","language":"zh-Hant","source_mko_ids":["mko-finite-confidence-interval-coverage"],"title_zh":"有限模型信賴區間覆蓋率","stem_zh":"完整finite laws與total precommitted theta-independent interval procedure責任。操作=ci-pointwise-coverage；資料={\"theta_values\":[0,1],\"samples\":[\"a\",\"b\"],\"probability_rows\":[[[11,13],[2,13]],[[2,13],[11,13]]],\"intervals\":[[0,0],[1,1]]}。請依 exact_ordered_tuple_declared_by_interface 欄序回答。","answer":{"kind":"expression","value":"([[0, 11/13], [1, 11/13]], coverage_theta=P_theta(theta_in_I(X)), not_a_posterior_probability)","explanation_zh":"Wave6第十二層核對=([[0, 11/13], [1, 11/13]], coverage_theta=P_theta(theta_in_I(X)), not_a_posterior_probability)；依完整明示資料獨立重算；pointwise coverage與worst-case minimum逐theta重算；average不等於uniform，posterior不是coverage；selection納入procedure後須重新計算。"},"difficulty":{"band":"undergraduate_core","level":2,"skills":["有限模型信賴區間覆蓋率"]},"variant":{"family_id":"qf-mod49-ci-pointwise-coverage","seed":202611183036,"parameters":{"theta_values":[0,1],"samples":["a","b"],"probability_rows":[[[11,13],[2,13]],[[2,13],[11,13]]],"intervals":[[0,0],[1,1]],"domain":"Exact_finite_confidence_coverage","operation":"ci-pointwise-coverage","semantic_template":"ci-pointwise-coverage|{intervals:[[[0,1],[0,1]],[[1,1],[1,1]]],probability_rows:[[[11,13],[2,13]],[[2,13],[11,13]]],samples:[\"a\",\"b\"],theta:[0,1]}"}},"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；不構成一般limit theorem、coverage、number-theory或language theorem證明、人工審定、Lean或Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-15","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261015-advance-20261118-r03-finite-confidence-interval-coverage-0037","batch_id":"batch-20261015-advance-20261118-r03-finite-confidence-interval-coverage-foundations","language":"zh-Hant","source_mko_ids":["mko-finite-confidence-interval-coverage"],"title_zh":"有限模型信賴區間覆蓋率","stem_zh":"完整finite laws與total precommitted theta-independent interval procedure責任。操作=ci-pointwise-coverage；資料={\"theta_values\":[0,1],\"samples\":[\"a\",\"b\"],\"probability_rows\":[[[12,14],[2,14]],[[2,14],[12,14]]],\"intervals\":[[0,0],[1,1]]}。請依 exact_ordered_tuple_declared_by_interface 欄序回答。","answer":{"kind":"expression","value":"([[0, 6/7], [1, 6/7]], coverage_theta=P_theta(theta_in_I(X)), not_a_posterior_probability)","explanation_zh":"Wave6第十二層核對=([[0, 6/7], [1, 6/7]], coverage_theta=P_theta(theta_in_I(X)), not_a_posterior_probability)；依完整明示資料獨立重算；pointwise coverage與worst-case minimum逐theta重算；average不等於uniform，posterior不是coverage；selection納入procedure後須重新計算。"},"difficulty":{"band":"undergraduate_core","level":2,"skills":["有限模型信賴區間覆蓋率"]},"variant":{"family_id":"qf-mod49-ci-pointwise-coverage","seed":202611183037,"parameters":{"theta_values":[0,1],"samples":["a","b"],"probability_rows":[[[12,14],[2,14]],[[2,14],[12,14]]],"intervals":[[0,0],[1,1]],"domain":"Exact_finite_confidence_coverage","operation":"ci-pointwise-coverage","semantic_template":"ci-pointwise-coverage|{intervals:[[[0,1],[0,1]],[[1,1],[1,1]]],probability_rows:[[[6,7],[1,7]],[[1,7],[6,7]]],samples:[\"a\",\"b\"],theta:[0,1]}"}},"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；不構成一般limit theorem、coverage、number-theory或language theorem證明、人工審定、Lean或Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-15","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261015-advance-20261118-r03-finite-confidence-interval-coverage-0038","batch_id":"batch-20261015-advance-20261118-r03-finite-confidence-interval-coverage-foundations","language":"zh-Hant","source_mko_ids":["mko-finite-confidence-interval-coverage"],"title_zh":"有限模型信賴區間覆蓋率","stem_zh":"完整finite laws與total precommitted theta-independent interval procedure責任。操作=ci-pointwise-coverage；資料={\"theta_values\":[0,1],\"samples\":[\"a\",\"b\"],\"probability_rows\":[[[13,15],[2,15]],[[2,15],[13,15]]],\"intervals\":[[0,0],[1,1]]}。請依 exact_ordered_tuple_declared_by_interface 欄序回答。","answer":{"kind":"expression","value":"([[0, 13/15], [1, 13/15]], coverage_theta=P_theta(theta_in_I(X)), not_a_posterior_probability)","explanation_zh":"Wave6第十二層核對=([[0, 13/15], [1, 13/15]], coverage_theta=P_theta(theta_in_I(X)), not_a_posterior_probability)；依完整明示資料獨立重算；pointwise coverage與worst-case minimum逐theta重算；average不等於uniform，posterior不是coverage；selection納入procedure後須重新計算。"},"difficulty":{"band":"undergraduate_core","level":2,"skills":["有限模型信賴區間覆蓋率"]},"variant":{"family_id":"qf-mod49-ci-pointwise-coverage","seed":202611183038,"parameters":{"theta_values":[0,1],"samples":["a","b"],"probability_rows":[[[13,15],[2,15]],[[2,15],[13,15]]],"intervals":[[0,0],[1,1]],"domain":"Exact_finite_confidence_coverage","operation":"ci-pointwise-coverage","semantic_template":"ci-pointwise-coverage|{intervals:[[[0,1],[0,1]],[[1,1],[1,1]]],probability_rows:[[[13,15],[2,15]],[[2,15],[13,15]]],samples:[\"a\",\"b\"],theta:[0,1]}"}},"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；不構成一般limit theorem、coverage、number-theory或language theorem證明、人工審定、Lean或Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-15","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261015-advance-20261118-r03-finite-confidence-interval-coverage-0039","batch_id":"batch-20261015-advance-20261118-r03-finite-confidence-interval-coverage-foundations","language":"zh-Hant","source_mko_ids":["mko-finite-confidence-interval-coverage"],"title_zh":"有限模型信賴區間覆蓋率","stem_zh":"完整finite laws與total precommitted theta-independent interval procedure責任。操作=ci-pointwise-coverage；資料={\"theta_values\":[0,1],\"samples\":[\"a\",\"b\"],\"probability_rows\":[[[14,16],[2,16]],[[2,16],[14,16]]],\"intervals\":[[0,0],[1,1]]}。請依 exact_ordered_tuple_declared_by_interface 欄序回答。","answer":{"kind":"expression","value":"([[0, 7/8], [1, 7/8]], coverage_theta=P_theta(theta_in_I(X)), not_a_posterior_probability)","explanation_zh":"Wave6第十二層核對=([[0, 7/8], [1, 7/8]], coverage_theta=P_theta(theta_in_I(X)), not_a_posterior_probability)；依完整明示資料獨立重算；pointwise coverage與worst-case minimum逐theta重算；average不等於uniform，posterior不是coverage；selection納入procedure後須重新計算。"},"difficulty":{"band":"undergraduate_core","level":2,"skills":["有限模型信賴區間覆蓋率"]},"variant":{"family_id":"qf-mod49-ci-pointwise-coverage","seed":202611183039,"parameters":{"theta_values":[0,1],"samples":["a","b"],"probability_rows":[[[14,16],[2,16]],[[2,16],[14,16]]],"intervals":[[0,0],[1,1]],"domain":"Exact_finite_confidence_coverage","operation":"ci-pointwise-coverage","semantic_template":"ci-pointwise-coverage|{intervals:[[[0,1],[0,1]],[[1,1],[1,1]]],probability_rows:[[[7,8],[1,8]],[[1,8],[7,8]]],samples:[\"a\",\"b\"],theta:[0,1]}"}},"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；不構成一般limit theorem、coverage、number-theory或language theorem證明、人工審定、Lean或Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-15","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261015-advance-20261118-r03-finite-confidence-interval-coverage-0040","batch_id":"batch-20261015-advance-20261118-r03-finite-confidence-interval-coverage-foundations","language":"zh-Hant","source_mko_ids":["mko-finite-confidence-interval-coverage"],"title_zh":"有限模型信賴區間覆蓋率","stem_zh":"完整finite laws與total precommitted theta-independent interval procedure責任。操作=ci-pointwise-coverage；資料={\"theta_values\":[0,1],\"samples\":[\"a\",\"b\"],\"probability_rows\":[[[15,17],[2,17]],[[2,17],[15,17]]],\"intervals\":[[0,0],[1,1]]}。請依 exact_ordered_tuple_declared_by_interface 欄序回答。","answer":{"kind":"expression","value":"([[0, 15/17], [1, 15/17]], coverage_theta=P_theta(theta_in_I(X)), not_a_posterior_probability)","explanation_zh":"Wave6第十二層核對=([[0, 15/17], [1, 15/17]], coverage_theta=P_theta(theta_in_I(X)), not_a_posterior_probability)；依完整明示資料獨立重算；pointwise coverage與worst-case minimum逐theta重算；average不等於uniform，posterior不是coverage；selection納入procedure後須重新計算。"},"difficulty":{"band":"undergraduate_core","level":2,"skills":["有限模型信賴區間覆蓋率"]},"variant":{"family_id":"qf-mod49-ci-pointwise-coverage","seed":202611183040,"parameters":{"theta_values":[0,1],"samples":["a","b"],"probability_rows":[[[15,17],[2,17]],[[2,17],[15,17]]],"intervals":[[0,0],[1,1]],"domain":"Exact_finite_confidence_coverage","operation":"ci-pointwise-coverage","semantic_template":"ci-pointwise-coverage|{intervals:[[[0,1],[0,1]],[[1,1],[1,1]]],probability_rows:[[[15,17],[2,17]],[[2,17],[15,17]]],samples:[\"a\",\"b\"],theta:[0,1]}"}},"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；不構成一般limit theorem、coverage、number-theory或language theorem證明、人工審定、Lean或Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-15","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261015-advance-20261118-r03-finite-confidence-interval-coverage-0041","batch_id":"batch-20261015-advance-20261118-r03-finite-confidence-interval-coverage-foundations","language":"zh-Hant","source_mko_ids":["mko-finite-confidence-interval-coverage"],"title_zh":"有限模型信賴區間覆蓋率","stem_zh":"完整finite laws與total precommitted theta-independent interval procedure責任。操作=ci-pointwise-coverage；資料={\"theta_values\":[0,1],\"samples\":[\"a\",\"b\"],\"probability_rows\":[[[16,18],[2,18]],[[2,18],[16,18]]],\"intervals\":[[0,0],[1,1]]}。請依 exact_ordered_tuple_declared_by_interface 欄序回答。","answer":{"kind":"expression","value":"([[0, 8/9], [1, 8/9]], coverage_theta=P_theta(theta_in_I(X)), not_a_posterior_probability)","explanation_zh":"Wave6第十二層核對=([[0, 8/9], [1, 8/9]], coverage_theta=P_theta(theta_in_I(X)), not_a_posterior_probability)；依完整明示資料獨立重算；pointwise coverage與worst-case minimum逐theta重算；average不等於uniform，posterior不是coverage；selection納入procedure後須重新計算。"},"difficulty":{"band":"undergraduate_core","level":2,"skills":["有限模型信賴區間覆蓋率"]},"variant":{"family_id":"qf-mod49-ci-pointwise-coverage","seed":202611183041,"parameters":{"theta_values":[0,1],"samples":["a","b"],"probability_rows":[[[16,18],[2,18]],[[2,18],[16,18]]],"intervals":[[0,0],[1,1]],"domain":"Exact_finite_confidence_coverage","operation":"ci-pointwise-coverage","semantic_template":"ci-pointwise-coverage|{intervals:[[[0,1],[0,1]],[[1,1],[1,1]]],probability_rows:[[[8,9],[1,9]],[[1,9],[8,9]]],samples:[\"a\",\"b\"],theta:[0,1]}"}},"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；不構成一般limit theorem、coverage、number-theory或language theorem證明、人工審定、Lean或Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-15","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261015-advance-20261118-r03-finite-confidence-interval-coverage-0042","batch_id":"batch-20261015-advance-20261118-r03-finite-confidence-interval-coverage-foundations","language":"zh-Hant","source_mko_ids":["mko-finite-confidence-interval-coverage"],"title_zh":"有限模型信賴區間覆蓋率","stem_zh":"完整finite laws與total precommitted theta-independent interval procedure責任。操作=ci-pointwise-coverage；資料={\"theta_values\":[0,1],\"samples\":[\"a\",\"b\"],\"probability_rows\":[[[17,19],[2,19]],[[2,19],[17,19]]],\"intervals\":[[0,0],[1,1]]}。請依 exact_ordered_tuple_declared_by_interface 欄序回答。","answer":{"kind":"expression","value":"([[0, 17/19], [1, 17/19]], coverage_theta=P_theta(theta_in_I(X)), not_a_posterior_probability)","explanation_zh":"Wave6第十二層核對=([[0, 17/19], [1, 17/19]], coverage_theta=P_theta(theta_in_I(X)), not_a_posterior_probability)；依完整明示資料獨立重算；pointwise coverage與worst-case minimum逐theta重算；average不等於uniform，posterior不是coverage；selection納入procedure後須重新計算。"},"difficulty":{"band":"undergraduate_core","level":2,"skills":["有限模型信賴區間覆蓋率"]},"variant":{"family_id":"qf-mod49-ci-pointwise-coverage","seed":202611183042,"parameters":{"theta_values":[0,1],"samples":["a","b"],"probability_rows":[[[17,19],[2,19]],[[2,19],[17,19]]],"intervals":[[0,0],[1,1]],"domain":"Exact_finite_confidence_coverage","operation":"ci-pointwise-coverage","semantic_template":"ci-pointwise-coverage|{intervals:[[[0,1],[0,1]],[[1,1],[1,1]]],probability_rows:[[[17,19],[2,19]],[[2,19],[17,19]]],samples:[\"a\",\"b\"],theta:[0,1]}"}},"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；不構成一般limit theorem、coverage、number-theory或language theorem證明、人工審定、Lean或Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-15","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261015-advance-20261118-r03-finite-confidence-interval-coverage-0043","batch_id":"batch-20261015-advance-20261118-r03-finite-confidence-interval-coverage-foundations","language":"zh-Hant","source_mko_ids":["mko-finite-confidence-interval-coverage"],"title_zh":"有限模型信賴區間覆蓋率","stem_zh":"完整finite laws與total precommitted theta-independent interval procedure責任。操作=ci-pointwise-coverage；資料={\"theta_values\":[0,1],\"samples\":[\"a\",\"b\"],\"probability_rows\":[[[18,20],[2,20]],[[2,20],[18,20]]],\"intervals\":[[0,0],[1,1]]}。請依 exact_ordered_tuple_declared_by_interface 欄序回答。","answer":{"kind":"expression","value":"([[0, 9/10], [1, 9/10]], coverage_theta=P_theta(theta_in_I(X)), not_a_posterior_probability)","explanation_zh":"Wave6第十二層核對=([[0, 9/10], [1, 9/10]], coverage_theta=P_theta(theta_in_I(X)), not_a_posterior_probability)；依完整明示資料獨立重算；pointwise coverage與worst-case minimum逐theta重算；average不等於uniform，posterior不是coverage；selection納入procedure後須重新計算。"},"difficulty":{"band":"undergraduate_core","level":3,"skills":["有限模型信賴區間覆蓋率"]},"variant":{"family_id":"qf-mod49-ci-pointwise-coverage","seed":202611183043,"parameters":{"theta_values":[0,1],"samples":["a","b"],"probability_rows":[[[18,20],[2,20]],[[2,20],[18,20]]],"intervals":[[0,0],[1,1]],"domain":"Exact_finite_confidence_coverage","operation":"ci-pointwise-coverage","semantic_template":"ci-pointwise-coverage|{intervals:[[[0,1],[0,1]],[[1,1],[1,1]]],probability_rows:[[[9,10],[1,10]],[[1,10],[9,10]]],samples:[\"a\",\"b\"],theta:[0,1]}"}},"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；不構成一般limit theorem、coverage、number-theory或language theorem證明、人工審定、Lean或Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-15","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261015-advance-20261118-r03-finite-confidence-interval-coverage-0044","batch_id":"batch-20261015-advance-20261118-r03-finite-confidence-interval-coverage-foundations","language":"zh-Hant","source_mko_ids":["mko-finite-confidence-interval-coverage"],"title_zh":"有限模型信賴區間覆蓋率","stem_zh":"完整finite laws與total precommitted theta-independent interval procedure責任。操作=ci-pointwise-coverage；資料={\"theta_values\":[0,1],\"samples\":[\"a\",\"b\"],\"probability_rows\":[[[19,21],[2,21]],[[2,21],[19,21]]],\"intervals\":[[0,0],[1,1]]}。請依 exact_ordered_tuple_declared_by_interface 欄序回答。","answer":{"kind":"expression","value":"([[0, 19/21], [1, 19/21]], coverage_theta=P_theta(theta_in_I(X)), not_a_posterior_probability)","explanation_zh":"Wave6第十二層核對=([[0, 19/21], [1, 19/21]], coverage_theta=P_theta(theta_in_I(X)), not_a_posterior_probability)；依完整明示資料獨立重算；pointwise coverage與worst-case minimum逐theta重算；average不等於uniform，posterior不是coverage；selection納入procedure後須重新計算。"},"difficulty":{"band":"undergraduate_core","level":3,"skills":["有限模型信賴區間覆蓋率"]},"variant":{"family_id":"qf-mod49-ci-pointwise-coverage","seed":202611183044,"parameters":{"theta_values":[0,1],"samples":["a","b"],"probability_rows":[[[19,21],[2,21]],[[2,21],[19,21]]],"intervals":[[0,0],[1,1]],"domain":"Exact_finite_confidence_coverage","operation":"ci-pointwise-coverage","semantic_template":"ci-pointwise-coverage|{intervals:[[[0,1],[0,1]],[[1,1],[1,1]]],probability_rows:[[[19,21],[2,21]],[[2,21],[19,21]]],samples:[\"a\",\"b\"],theta:[0,1]}"}},"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；不構成一般limit theorem、coverage、number-theory或language theorem證明、人工審定、Lean或Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-15","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261015-advance-20261118-r03-finite-confidence-interval-coverage-0045","batch_id":"batch-20261015-advance-20261118-r03-finite-confidence-interval-coverage-foundations","language":"zh-Hant","source_mko_ids":["mko-finite-confidence-interval-coverage"],"title_zh":"有限模型信賴區間覆蓋率","stem_zh":"完整finite laws與total precommitted theta-independent interval procedure責任。操作=ci-pointwise-coverage；資料={\"theta_values\":[0,1],\"samples\":[\"a\",\"b\"],\"probability_rows\":[[[20,22],[2,22]],[[2,22],[20,22]]],\"intervals\":[[0,0],[1,1]]}。請依 exact_ordered_tuple_declared_by_interface 欄序回答。","answer":{"kind":"expression","value":"([[0, 10/11], [1, 10/11]], coverage_theta=P_theta(theta_in_I(X)), not_a_posterior_probability)","explanation_zh":"Wave6第十二層核對=([[0, 10/11], [1, 10/11]], coverage_theta=P_theta(theta_in_I(X)), not_a_posterior_probability)；依完整明示資料獨立重算；pointwise coverage與worst-case minimum逐theta重算；average不等於uniform，posterior不是coverage；selection納入procedure後須重新計算。"},"difficulty":{"band":"undergraduate_core","level":3,"skills":["有限模型信賴區間覆蓋率"]},"variant":{"family_id":"qf-mod49-ci-pointwise-coverage","seed":202611183045,"parameters":{"theta_values":[0,1],"samples":["a","b"],"probability_rows":[[[20,22],[2,22]],[[2,22],[20,22]]],"intervals":[[0,0],[1,1]],"domain":"Exact_finite_confidence_coverage","operation":"ci-pointwise-coverage","semantic_template":"ci-pointwise-coverage|{intervals:[[[0,1],[0,1]],[[1,1],[1,1]]],probability_rows:[[[10,11],[1,11]],[[1,11],[10,11]]],samples:[\"a\",\"b\"],theta:[0,1]}"}},"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；不構成一般limit theorem、coverage、number-theory或language theorem證明、人工審定、Lean或Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-15","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261015-advance-20261118-r03-finite-confidence-interval-coverage-0046","batch_id":"batch-20261015-advance-20261118-r03-finite-confidence-interval-coverage-foundations","language":"zh-Hant","source_mko_ids":["mko-finite-confidence-interval-coverage"],"title_zh":"有限模型信賴區間覆蓋率","stem_zh":"完整finite laws與total precommitted theta-independent interval procedure責任。操作=ci-pointwise-coverage；資料={\"theta_values\":[0,1],\"samples\":[\"a\",\"b\"],\"probability_rows\":[[[21,23],[2,23]],[[2,23],[21,23]]],\"intervals\":[[0,0],[1,1]]}。請依 exact_ordered_tuple_declared_by_interface 欄序回答。","answer":{"kind":"expression","value":"([[0, 21/23], [1, 21/23]], coverage_theta=P_theta(theta_in_I(X)), not_a_posterior_probability)","explanation_zh":"Wave6第十二層核對=([[0, 21/23], [1, 21/23]], coverage_theta=P_theta(theta_in_I(X)), not_a_posterior_probability)；依完整明示資料獨立重算；pointwise coverage與worst-case minimum逐theta重算；average不等於uniform，posterior不是coverage；selection納入procedure後須重新計算。"},"difficulty":{"band":"undergraduate_core","level":3,"skills":["有限模型信賴區間覆蓋率"]},"variant":{"family_id":"qf-mod49-ci-pointwise-coverage","seed":202611183046,"parameters":{"theta_values":[0,1],"samples":["a","b"],"probability_rows":[[[21,23],[2,23]],[[2,23],[21,23]]],"intervals":[[0,0],[1,1]],"domain":"Exact_finite_confidence_coverage","operation":"ci-pointwise-coverage","semantic_template":"ci-pointwise-coverage|{intervals:[[[0,1],[0,1]],[[1,1],[1,1]]],probability_rows:[[[21,23],[2,23]],[[2,23],[21,23]]],samples:[\"a\",\"b\"],theta:[0,1]}"}},"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；不構成一般limit theorem、coverage、number-theory或language theorem證明、人工審定、Lean或Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-15","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261015-advance-20261118-r03-finite-confidence-interval-coverage-0047","batch_id":"batch-20261015-advance-20261118-r03-finite-confidence-interval-coverage-foundations","language":"zh-Hant","source_mko_ids":["mko-finite-confidence-interval-coverage"],"title_zh":"有限模型信賴區間覆蓋率","stem_zh":"完整finite laws與total precommitted theta-independent interval procedure責任。操作=ci-pointwise-coverage；資料={\"theta_values\":[0,1],\"samples\":[\"a\",\"b\"],\"probability_rows\":[[[22,24],[2,24]],[[2,24],[22,24]]],\"intervals\":[[0,0],[1,1]]}。請依 exact_ordered_tuple_declared_by_interface 欄序回答。","answer":{"kind":"expression","value":"([[0, 11/12], [1, 11/12]], coverage_theta=P_theta(theta_in_I(X)), not_a_posterior_probability)","explanation_zh":"Wave6第十二層核對=([[0, 11/12], [1, 11/12]], coverage_theta=P_theta(theta_in_I(X)), not_a_posterior_probability)；依完整明示資料獨立重算；pointwise coverage與worst-case minimum逐theta重算；average不等於uniform，posterior不是coverage；selection納入procedure後須重新計算。"},"difficulty":{"band":"undergraduate_core","level":3,"skills":["有限模型信賴區間覆蓋率"]},"variant":{"family_id":"qf-mod49-ci-pointwise-coverage","seed":202611183047,"parameters":{"theta_values":[0,1],"samples":["a","b"],"probability_rows":[[[22,24],[2,24]],[[2,24],[22,24]]],"intervals":[[0,0],[1,1]],"domain":"Exact_finite_confidence_coverage","operation":"ci-pointwise-coverage","semantic_template":"ci-pointwise-coverage|{intervals:[[[0,1],[0,1]],[[1,1],[1,1]]],probability_rows:[[[11,12],[1,12]],[[1,12],[11,12]]],samples:[\"a\",\"b\"],theta:[0,1]}"}},"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；不構成一般limit theorem、coverage、number-theory或language theorem證明、人工審定、Lean或Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-15","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261015-advance-20261118-r03-finite-confidence-interval-coverage-0048","batch_id":"batch-20261015-advance-20261118-r03-finite-confidence-interval-coverage-foundations","language":"zh-Hant","source_mko_ids":["mko-finite-confidence-interval-coverage"],"title_zh":"有限模型信賴區間覆蓋率","stem_zh":"完整finite laws與total precommitted theta-independent interval procedure責任。操作=ci-pointwise-coverage；資料={\"theta_values\":[0,1],\"samples\":[\"a\",\"b\"],\"probability_rows\":[[[23,25],[2,25]],[[2,25],[23,25]]],\"intervals\":[[0,0],[1,1]]}。請依 exact_ordered_tuple_declared_by_interface 欄序回答。","answer":{"kind":"expression","value":"([[0, 23/25], [1, 23/25]], coverage_theta=P_theta(theta_in_I(X)), not_a_posterior_probability)","explanation_zh":"Wave6第十二層核對=([[0, 23/25], [1, 23/25]], coverage_theta=P_theta(theta_in_I(X)), not_a_posterior_probability)；依完整明示資料獨立重算；pointwise coverage與worst-case minimum逐theta重算；average不等於uniform，posterior不是coverage；selection納入procedure後須重新計算。"},"difficulty":{"band":"undergraduate_core","level":3,"skills":["有限模型信賴區間覆蓋率"]},"variant":{"family_id":"qf-mod49-ci-pointwise-coverage","seed":202611183048,"parameters":{"theta_values":[0,1],"samples":["a","b"],"probability_rows":[[[23,25],[2,25]],[[2,25],[23,25]]],"intervals":[[0,0],[1,1]],"domain":"Exact_finite_confidence_coverage","operation":"ci-pointwise-coverage","semantic_template":"ci-pointwise-coverage|{intervals:[[[0,1],[0,1]],[[1,1],[1,1]]],probability_rows:[[[23,25],[2,25]],[[2,25],[23,25]]],samples:[\"a\",\"b\"],theta:[0,1]}"}},"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；不構成一般limit theorem、coverage、number-theory或language theorem證明、人工審定、Lean或Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-15","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261015-advance-20261118-r03-finite-confidence-interval-coverage-0049","batch_id":"batch-20261015-advance-20261118-r03-finite-confidence-interval-coverage-foundations","language":"zh-Hant","source_mko_ids":["mko-finite-confidence-interval-coverage"],"title_zh":"有限模型信賴區間覆蓋率","stem_zh":"完整finite laws與total precommitted theta-independent interval procedure責任。操作=ci-pointwise-coverage；資料={\"theta_values\":[0,1],\"samples\":[\"a\",\"b\"],\"probability_rows\":[[[24,26],[2,26]],[[2,26],[24,26]]],\"intervals\":[[0,0],[1,1]]}。請依 exact_ordered_tuple_declared_by_interface 欄序回答。","answer":{"kind":"expression","value":"([[0, 12/13], [1, 12/13]], coverage_theta=P_theta(theta_in_I(X)), not_a_posterior_probability)","explanation_zh":"Wave6第十二層核對=([[0, 12/13], [1, 12/13]], coverage_theta=P_theta(theta_in_I(X)), not_a_posterior_probability)；依完整明示資料獨立重算；pointwise coverage與worst-case minimum逐theta重算；average不等於uniform，posterior不是coverage；selection納入procedure後須重新計算。"},"difficulty":{"band":"undergraduate_core","level":3,"skills":["有限模型信賴區間覆蓋率"]},"variant":{"family_id":"qf-mod49-ci-pointwise-coverage","seed":202611183049,"parameters":{"theta_values":[0,1],"samples":["a","b"],"probability_rows":[[[24,26],[2,26]],[[2,26],[24,26]]],"intervals":[[0,0],[1,1]],"domain":"Exact_finite_confidence_coverage","operation":"ci-pointwise-coverage","semantic_template":"ci-pointwise-coverage|{intervals:[[[0,1],[0,1]],[[1,1],[1,1]]],probability_rows:[[[12,13],[1,13]],[[1,13],[12,13]]],samples:[\"a\",\"b\"],theta:[0,1]}"}},"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；不構成一般limit theorem、coverage、number-theory或language theorem證明、人工審定、Lean或Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-15","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261015-advance-20261118-r03-finite-confidence-interval-coverage-0050","batch_id":"batch-20261015-advance-20261118-r03-finite-confidence-interval-coverage-foundations","language":"zh-Hant","source_mko_ids":["mko-finite-confidence-interval-coverage"],"title_zh":"有限模型信賴區間覆蓋率","stem_zh":"完整finite laws與total precommitted theta-independent interval procedure責任。操作=ci-pointwise-coverage；資料={\"theta_values\":[0,1],\"samples\":[\"a\",\"b\"],\"probability_rows\":[[[25,27],[2,27]],[[2,27],[25,27]]],\"intervals\":[[0,0],[1,1]]}。請依 exact_ordered_tuple_declared_by_interface 欄序回答。","answer":{"kind":"expression","value":"([[0, 25/27], [1, 25/27]], coverage_theta=P_theta(theta_in_I(X)), not_a_posterior_probability)","explanation_zh":"Wave6第十二層核對=([[0, 25/27], [1, 25/27]], coverage_theta=P_theta(theta_in_I(X)), not_a_posterior_probability)；依完整明示資料獨立重算；pointwise coverage與worst-case minimum逐theta重算；average不等於uniform，posterior不是coverage；selection納入procedure後須重新計算。"},"difficulty":{"band":"undergraduate_core","level":3,"skills":["有限模型信賴區間覆蓋率"]},"variant":{"family_id":"qf-mod49-ci-pointwise-coverage","seed":202611183050,"parameters":{"theta_values":[0,1],"samples":["a","b"],"probability_rows":[[[25,27],[2,27]],[[2,27],[25,27]]],"intervals":[[0,0],[1,1]],"domain":"Exact_finite_confidence_coverage","operation":"ci-pointwise-coverage","semantic_template":"ci-pointwise-coverage|{intervals:[[[0,1],[0,1]],[[1,1],[1,1]]],probability_rows:[[[25,27],[2,27]],[[2,27],[25,27]]],samples:[\"a\",\"b\"],theta:[0,1]}"}},"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；不構成一般limit theorem、coverage、number-theory或language theorem證明、人工審定、Lean或Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-15","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261015-advance-20261118-r03-finite-confidence-interval-coverage-0051","batch_id":"batch-20261015-advance-20261118-r03-finite-confidence-interval-coverage-foundations","language":"zh-Hant","source_mko_ids":["mko-finite-confidence-interval-coverage"],"title_zh":"有限模型信賴區間覆蓋率","stem_zh":"完整finite laws與total precommitted theta-independent interval procedure責任。操作=ci-worst-case-coverage；資料={\"theta_values\":[0,1],\"samples\":[\"a\",\"b\"],\"probability_rows\":[[[1,3],[2,3]],[[2,3],[1,3]]],\"intervals\":[[0,0],[1,1]],\"target\":[1,3]}。請依 exact_ordered_tuple_declared_by_interface 欄序回答。","answer":{"kind":"expression","value":"([[0, 1/3], [1, 1/3]], 1/3, 1/3, 是, worst_case_is_minimum_over_finite_theta)","explanation_zh":"Wave6第十二層核對=([[0, 1/3], [1, 1/3]], 1/3, 1/3, 是, worst_case_is_minimum_over_finite_theta)；依完整明示資料獨立重算；pointwise coverage與worst-case minimum逐theta重算；average不等於uniform，posterior不是coverage；selection納入procedure後須重新計算。"},"difficulty":{"band":"undergraduate_core","level":1,"skills":["有限模型信賴區間覆蓋率"]},"variant":{"family_id":"qf-mod49-ci-worst-case-coverage","seed":202611183051,"parameters":{"theta_values":[0,1],"samples":["a","b"],"probability_rows":[[[1,3],[2,3]],[[2,3],[1,3]]],"intervals":[[0,0],[1,1]],"target":[1,3],"domain":"Exact_finite_confidence_coverage","operation":"ci-worst-case-coverage","semantic_template":"ci-worst-case-coverage|{intervals:[[[0,1],[0,1]],[[1,1],[1,1]]],probability_rows:[[[1,3],[2,3]],[[2,3],[1,3]]],samples:[\"a\",\"b\"],target:[1,3],theta:[0,1]}"}},"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；不構成一般limit theorem、coverage、number-theory或language theorem證明、人工審定、Lean或Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-15","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261015-advance-20261118-r03-finite-confidence-interval-coverage-0052","batch_id":"batch-20261015-advance-20261118-r03-finite-confidence-interval-coverage-foundations","language":"zh-Hant","source_mko_ids":["mko-finite-confidence-interval-coverage"],"title_zh":"有限模型信賴區間覆蓋率","stem_zh":"完整finite laws與total precommitted theta-independent interval procedure責任。操作=ci-worst-case-coverage；資料={\"theta_values\":[0,1],\"samples\":[\"a\",\"b\"],\"probability_rows\":[[[2,4],[2,4]],[[2,4],[2,4]]],\"intervals\":[[0,0],[1,1]],\"target\":[2,4]}。請依 exact_ordered_tuple_declared_by_interface 欄序回答。","answer":{"kind":"expression","value":"([[0, 1/2], [1, 1/2]], 1/2, 1/2, 是, worst_case_is_minimum_over_finite_theta)","explanation_zh":"Wave6第十二層核對=([[0, 1/2], [1, 1/2]], 1/2, 1/2, 是, worst_case_is_minimum_over_finite_theta)；依完整明示資料獨立重算；pointwise coverage與worst-case minimum逐theta重算；average不等於uniform，posterior不是coverage；selection納入procedure後須重新計算。"},"difficulty":{"band":"undergraduate_core","level":1,"skills":["有限模型信賴區間覆蓋率"]},"variant":{"family_id":"qf-mod49-ci-worst-case-coverage","seed":202611183052,"parameters":{"theta_values":[0,1],"samples":["a","b"],"probability_rows":[[[2,4],[2,4]],[[2,4],[2,4]]],"intervals":[[0,0],[1,1]],"target":[2,4],"domain":"Exact_finite_confidence_coverage","operation":"ci-worst-case-coverage","semantic_template":"ci-worst-case-coverage|{intervals:[[[0,1],[0,1]],[[1,1],[1,1]]],probability_rows:[[[1,2],[1,2]],[[1,2],[1,2]]],samples:[\"a\",\"b\"],target:[1,2],theta:[0,1]}"}},"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；不構成一般limit theorem、coverage、number-theory或language theorem證明、人工審定、Lean或Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-15","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261015-advance-20261118-r03-finite-confidence-interval-coverage-0053","batch_id":"batch-20261015-advance-20261118-r03-finite-confidence-interval-coverage-foundations","language":"zh-Hant","source_mko_ids":["mko-finite-confidence-interval-coverage"],"title_zh":"有限模型信賴區間覆蓋率","stem_zh":"完整finite laws與total precommitted theta-independent interval procedure責任。操作=ci-worst-case-coverage；資料={\"theta_values\":[0,1],\"samples\":[\"a\",\"b\"],\"probability_rows\":[[[3,5],[2,5]],[[2,5],[3,5]]],\"intervals\":[[0,0],[1,1]],\"target\":[3,5]}。請依 exact_ordered_tuple_declared_by_interface 欄序回答。","answer":{"kind":"expression","value":"([[0, 3/5], [1, 3/5]], 3/5, 3/5, 是, worst_case_is_minimum_over_finite_theta)","explanation_zh":"Wave6第十二層核對=([[0, 3/5], [1, 3/5]], 3/5, 3/5, 是, worst_case_is_minimum_over_finite_theta)；依完整明示資料獨立重算；pointwise coverage與worst-case minimum逐theta重算；average不等於uniform，posterior不是coverage；selection納入procedure後須重新計算。"},"difficulty":{"band":"undergraduate_core","level":1,"skills":["有限模型信賴區間覆蓋率"]},"variant":{"family_id":"qf-mod49-ci-worst-case-coverage","seed":202611183053,"parameters":{"theta_values":[0,1],"samples":["a","b"],"probability_rows":[[[3,5],[2,5]],[[2,5],[3,5]]],"intervals":[[0,0],[1,1]],"target":[3,5],"domain":"Exact_finite_confidence_coverage","operation":"ci-worst-case-coverage","semantic_template":"ci-worst-case-coverage|{intervals:[[[0,1],[0,1]],[[1,1],[1,1]]],probability_rows:[[[3,5],[2,5]],[[2,5],[3,5]]],samples:[\"a\",\"b\"],target:[3,5],theta:[0,1]}"}},"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；不構成一般limit theorem、coverage、number-theory或language theorem證明、人工審定、Lean或Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-15","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261015-advance-20261118-r03-finite-confidence-interval-coverage-0054","batch_id":"batch-20261015-advance-20261118-r03-finite-confidence-interval-coverage-foundations","language":"zh-Hant","source_mko_ids":["mko-finite-confidence-interval-coverage"],"title_zh":"有限模型信賴區間覆蓋率","stem_zh":"完整finite laws與total precommitted theta-independent interval procedure責任。操作=ci-worst-case-coverage；資料={\"theta_values\":[0,1],\"samples\":[\"a\",\"b\"],\"probability_rows\":[[[4,6],[2,6]],[[2,6],[4,6]]],\"intervals\":[[0,0],[1,1]],\"target\":[4,6]}。請依 exact_ordered_tuple_declared_by_interface 欄序回答。","answer":{"kind":"expression","value":"([[0, 2/3], [1, 2/3]], 2/3, 2/3, 是, worst_case_is_minimum_over_finite_theta)","explanation_zh":"Wave6第十二層核對=([[0, 2/3], [1, 2/3]], 2/3, 2/3, 是, worst_case_is_minimum_over_finite_theta)；依完整明示資料獨立重算；pointwise coverage與worst-case minimum逐theta重算；average不等於uniform，posterior不是coverage；selection納入procedure後須重新計算。"},"difficulty":{"band":"undergraduate_core","level":1,"skills":["有限模型信賴區間覆蓋率"]},"variant":{"family_id":"qf-mod49-ci-worst-case-coverage","seed":202611183054,"parameters":{"theta_values":[0,1],"samples":["a","b"],"probability_rows":[[[4,6],[2,6]],[[2,6],[4,6]]],"intervals":[[0,0],[1,1]],"target":[4,6],"domain":"Exact_finite_confidence_coverage","operation":"ci-worst-case-coverage","semantic_template":"ci-worst-case-coverage|{intervals:[[[0,1],[0,1]],[[1,1],[1,1]]],probability_rows:[[[2,3],[1,3]],[[1,3],[2,3]]],samples:[\"a\",\"b\"],target:[2,3],theta:[0,1]}"}},"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；不構成一般limit theorem、coverage、number-theory或language theorem證明、人工審定、Lean或Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-15","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261015-advance-20261118-r03-finite-confidence-interval-coverage-0055","batch_id":"batch-20261015-advance-20261118-r03-finite-confidence-interval-coverage-foundations","language":"zh-Hant","source_mko_ids":["mko-finite-confidence-interval-coverage"],"title_zh":"有限模型信賴區間覆蓋率","stem_zh":"完整finite laws與total precommitted theta-independent interval procedure責任。操作=ci-worst-case-coverage；資料={\"theta_values\":[0,1],\"samples\":[\"a\",\"b\"],\"probability_rows\":[[[5,7],[2,7]],[[2,7],[5,7]]],\"intervals\":[[0,0],[1,1]],\"target\":[5,7]}。請依 exact_ordered_tuple_declared_by_interface 欄序回答。","answer":{"kind":"expression","value":"([[0, 5/7], [1, 5/7]], 5/7, 5/7, 是, worst_case_is_minimum_over_finite_theta)","explanation_zh":"Wave6第十二層核對=([[0, 5/7], [1, 5/7]], 5/7, 5/7, 是, worst_case_is_minimum_over_finite_theta)；依完整明示資料獨立重算；pointwise coverage與worst-case minimum逐theta重算；average不等於uniform，posterior不是coverage；selection納入procedure後須重新計算。"},"difficulty":{"band":"undergraduate_core","level":1,"skills":["有限模型信賴區間覆蓋率"]},"variant":{"family_id":"qf-mod49-ci-worst-case-coverage","seed":202611183055,"parameters":{"theta_values":[0,1],"samples":["a","b"],"probability_rows":[[[5,7],[2,7]],[[2,7],[5,7]]],"intervals":[[0,0],[1,1]],"target":[5,7],"domain":"Exact_finite_confidence_coverage","operation":"ci-worst-case-coverage","semantic_template":"ci-worst-case-coverage|{intervals:[[[0,1],[0,1]],[[1,1],[1,1]]],probability_rows:[[[5,7],[2,7]],[[2,7],[5,7]]],samples:[\"a\",\"b\"],target:[5,7],theta:[0,1]}"}},"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；不構成一般limit theorem、coverage、number-theory或language theorem證明、人工審定、Lean或Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-15","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261015-advance-20261118-r03-finite-confidence-interval-coverage-0056","batch_id":"batch-20261015-advance-20261118-r03-finite-confidence-interval-coverage-foundations","language":"zh-Hant","source_mko_ids":["mko-finite-confidence-interval-coverage"],"title_zh":"有限模型信賴區間覆蓋率","stem_zh":"完整finite laws與total precommitted theta-independent interval procedure責任。操作=ci-worst-case-coverage；資料={\"theta_values\":[0,1],\"samples\":[\"a\",\"b\"],\"probability_rows\":[[[6,8],[2,8]],[[2,8],[6,8]]],\"intervals\":[[0,0],[1,1]],\"target\":[1,3]}。請依 exact_ordered_tuple_declared_by_interface 欄序回答。","answer":{"kind":"expression","value":"([[0, 3/4], [1, 3/4]], 3/4, 1/3, 是, worst_case_is_minimum_over_finite_theta)","explanation_zh":"Wave6第十二層核對=([[0, 3/4], [1, 3/4]], 3/4, 1/3, 是, worst_case_is_minimum_over_finite_theta)；依完整明示資料獨立重算；pointwise coverage與worst-case minimum逐theta重算；average不等於uniform，posterior不是coverage；selection納入procedure後須重新計算。"},"difficulty":{"band":"undergraduate_core","level":1,"skills":["有限模型信賴區間覆蓋率"]},"variant":{"family_id":"qf-mod49-ci-worst-case-coverage","seed":202611183056,"parameters":{"theta_values":[0,1],"samples":["a","b"],"probability_rows":[[[6,8],[2,8]],[[2,8],[6,8]]],"intervals":[[0,0],[1,1]],"target":[1,3],"domain":"Exact_finite_confidence_coverage","operation":"ci-worst-case-coverage","semantic_template":"ci-worst-case-coverage|{intervals:[[[0,1],[0,1]],[[1,1],[1,1]]],probability_rows:[[[3,4],[1,4]],[[1,4],[3,4]]],samples:[\"a\",\"b\"],target:[1,3],theta:[0,1]}"}},"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；不構成一般limit theorem、coverage、number-theory或language theorem證明、人工審定、Lean或Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-15","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261015-advance-20261118-r03-finite-confidence-interval-coverage-0057","batch_id":"batch-20261015-advance-20261118-r03-finite-confidence-interval-coverage-foundations","language":"zh-Hant","source_mko_ids":["mko-finite-confidence-interval-coverage"],"title_zh":"有限模型信賴區間覆蓋率","stem_zh":"完整finite laws與total precommitted theta-independent interval procedure責任。操作=ci-worst-case-coverage；資料={\"theta_values\":[0,1],\"samples\":[\"a\",\"b\"],\"probability_rows\":[[[7,9],[2,9]],[[2,9],[7,9]]],\"intervals\":[[0,0],[1,1]],\"target\":[2,4]}。請依 exact_ordered_tuple_declared_by_interface 欄序回答。","answer":{"kind":"expression","value":"([[0, 7/9], [1, 7/9]], 7/9, 1/2, 是, worst_case_is_minimum_over_finite_theta)","explanation_zh":"Wave6第十二層核對=([[0, 7/9], [1, 7/9]], 7/9, 1/2, 是, worst_case_is_minimum_over_finite_theta)；依完整明示資料獨立重算；pointwise coverage與worst-case minimum逐theta重算；average不等於uniform，posterior不是coverage；selection納入procedure後須重新計算。"},"difficulty":{"band":"undergraduate_core","level":1,"skills":["有限模型信賴區間覆蓋率"]},"variant":{"family_id":"qf-mod49-ci-worst-case-coverage","seed":202611183057,"parameters":{"theta_values":[0,1],"samples":["a","b"],"probability_rows":[[[7,9],[2,9]],[[2,9],[7,9]]],"intervals":[[0,0],[1,1]],"target":[2,4],"domain":"Exact_finite_confidence_coverage","operation":"ci-worst-case-coverage","semantic_template":"ci-worst-case-coverage|{intervals:[[[0,1],[0,1]],[[1,1],[1,1]]],probability_rows:[[[7,9],[2,9]],[[2,9],[7,9]]],samples:[\"a\",\"b\"],target:[1,2],theta:[0,1]}"}},"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；不構成一般limit theorem、coverage、number-theory或language theorem證明、人工審定、Lean或Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-15","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261015-advance-20261118-r03-finite-confidence-interval-coverage-0058","batch_id":"batch-20261015-advance-20261118-r03-finite-confidence-interval-coverage-foundations","language":"zh-Hant","source_mko_ids":["mko-finite-confidence-interval-coverage"],"title_zh":"有限模型信賴區間覆蓋率","stem_zh":"完整finite laws與total precommitted theta-independent interval procedure責任。操作=ci-worst-case-coverage；資料={\"theta_values\":[0,1],\"samples\":[\"a\",\"b\"],\"probability_rows\":[[[8,10],[2,10]],[[2,10],[8,10]]],\"intervals\":[[0,0],[1,1]],\"target\":[3,5]}。請依 exact_ordered_tuple_declared_by_interface 欄序回答。","answer":{"kind":"expression","value":"([[0, 4/5], [1, 4/5]], 4/5, 3/5, 是, worst_case_is_minimum_over_finite_theta)","explanation_zh":"Wave6第十二層核對=([[0, 4/5], [1, 4/5]], 4/5, 3/5, 是, worst_case_is_minimum_over_finite_theta)；依完整明示資料獨立重算；pointwise coverage與worst-case minimum逐theta重算；average不等於uniform，posterior不是coverage；selection納入procedure後須重新計算。"},"difficulty":{"band":"undergraduate_core","level":1,"skills":["有限模型信賴區間覆蓋率"]},"variant":{"family_id":"qf-mod49-ci-worst-case-coverage","seed":202611183058,"parameters":{"theta_values":[0,1],"samples":["a","b"],"probability_rows":[[[8,10],[2,10]],[[2,10],[8,10]]],"intervals":[[0,0],[1,1]],"target":[3,5],"domain":"Exact_finite_confidence_coverage","operation":"ci-worst-case-coverage","semantic_template":"ci-worst-case-coverage|{intervals:[[[0,1],[0,1]],[[1,1],[1,1]]],probability_rows:[[[4,5],[1,5]],[[1,5],[4,5]]],samples:[\"a\",\"b\"],target:[3,5],theta:[0,1]}"}},"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；不構成一般limit theorem、coverage、number-theory或language theorem證明、人工審定、Lean或Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-15","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261015-advance-20261118-r03-finite-confidence-interval-coverage-0059","batch_id":"batch-20261015-advance-20261118-r03-finite-confidence-interval-coverage-foundations","language":"zh-Hant","source_mko_ids":["mko-finite-confidence-interval-coverage"],"title_zh":"有限模型信賴區間覆蓋率","stem_zh":"完整finite laws與total precommitted theta-independent interval procedure責任。操作=ci-worst-case-coverage；資料={\"theta_values\":[0,1],\"samples\":[\"a\",\"b\"],\"probability_rows\":[[[9,11],[2,11]],[[2,11],[9,11]]],\"intervals\":[[0,0],[1,1]],\"target\":[4,6]}。請依 exact_ordered_tuple_declared_by_interface 欄序回答。","answer":{"kind":"expression","value":"([[0, 9/11], [1, 9/11]], 9/11, 2/3, 是, worst_case_is_minimum_over_finite_theta)","explanation_zh":"Wave6第十二層核對=([[0, 9/11], [1, 9/11]], 9/11, 2/3, 是, worst_case_is_minimum_over_finite_theta)；依完整明示資料獨立重算；pointwise coverage與worst-case minimum逐theta重算；average不等於uniform，posterior不是coverage；selection納入procedure後須重新計算。"},"difficulty":{"band":"undergraduate_core","level":2,"skills":["有限模型信賴區間覆蓋率"]},"variant":{"family_id":"qf-mod49-ci-worst-case-coverage","seed":202611183059,"parameters":{"theta_values":[0,1],"samples":["a","b"],"probability_rows":[[[9,11],[2,11]],[[2,11],[9,11]]],"intervals":[[0,0],[1,1]],"target":[4,6],"domain":"Exact_finite_confidence_coverage","operation":"ci-worst-case-coverage","semantic_template":"ci-worst-case-coverage|{intervals:[[[0,1],[0,1]],[[1,1],[1,1]]],probability_rows:[[[9,11],[2,11]],[[2,11],[9,11]]],samples:[\"a\",\"b\"],target:[2,3],theta:[0,1]}"}},"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；不構成一般limit theorem、coverage、number-theory或language theorem證明、人工審定、Lean或Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-15","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261015-advance-20261118-r03-finite-confidence-interval-coverage-0060","batch_id":"batch-20261015-advance-20261118-r03-finite-confidence-interval-coverage-foundations","language":"zh-Hant","source_mko_ids":["mko-finite-confidence-interval-coverage"],"title_zh":"有限模型信賴區間覆蓋率","stem_zh":"完整finite laws與total precommitted theta-independent interval procedure責任。操作=ci-worst-case-coverage；資料={\"theta_values\":[0,1],\"samples\":[\"a\",\"b\"],\"probability_rows\":[[[10,12],[2,12]],[[2,12],[10,12]]],\"intervals\":[[0,0],[1,1]],\"target\":[5,7]}。請依 exact_ordered_tuple_declared_by_interface 欄序回答。","answer":{"kind":"expression","value":"([[0, 5/6], [1, 5/6]], 5/6, 5/7, 是, worst_case_is_minimum_over_finite_theta)","explanation_zh":"Wave6第十二層核對=([[0, 5/6], [1, 5/6]], 5/6, 5/7, 是, worst_case_is_minimum_over_finite_theta)；依完整明示資料獨立重算；pointwise coverage與worst-case minimum逐theta重算；average不等於uniform，posterior不是coverage；selection納入procedure後須重新計算。"},"difficulty":{"band":"undergraduate_core","level":2,"skills":["有限模型信賴區間覆蓋率"]},"variant":{"family_id":"qf-mod49-ci-worst-case-coverage","seed":202611183060,"parameters":{"theta_values":[0,1],"samples":["a","b"],"probability_rows":[[[10,12],[2,12]],[[2,12],[10,12]]],"intervals":[[0,0],[1,1]],"target":[5,7],"domain":"Exact_finite_confidence_coverage","operation":"ci-worst-case-coverage","semantic_template":"ci-worst-case-coverage|{intervals:[[[0,1],[0,1]],[[1,1],[1,1]]],probability_rows:[[[5,6],[1,6]],[[1,6],[5,6]]],samples:[\"a\",\"b\"],target:[5,7],theta:[0,1]}"}},"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；不構成一般limit theorem、coverage、number-theory或language theorem證明、人工審定、Lean或Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-15","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261015-advance-20261118-r03-finite-confidence-interval-coverage-0061","batch_id":"batch-20261015-advance-20261118-r03-finite-confidence-interval-coverage-foundations","language":"zh-Hant","source_mko_ids":["mko-finite-confidence-interval-coverage"],"title_zh":"有限模型信賴區間覆蓋率","stem_zh":"完整finite laws與total precommitted theta-independent interval procedure責任。操作=ci-worst-case-coverage；資料={\"theta_values\":[0,1],\"samples\":[\"a\",\"b\"],\"probability_rows\":[[[11,13],[2,13]],[[2,13],[11,13]]],\"intervals\":[[0,0],[1,1]],\"target\":[1,3]}。請依 exact_ordered_tuple_declared_by_interface 欄序回答。","answer":{"kind":"expression","value":"([[0, 11/13], [1, 11/13]], 11/13, 1/3, 是, worst_case_is_minimum_over_finite_theta)","explanation_zh":"Wave6第十二層核對=([[0, 11/13], [1, 11/13]], 11/13, 1/3, 是, worst_case_is_minimum_over_finite_theta)；依完整明示資料獨立重算；pointwise coverage與worst-case minimum逐theta重算；average不等於uniform，posterior不是coverage；selection納入procedure後須重新計算。"},"difficulty":{"band":"undergraduate_core","level":2,"skills":["有限模型信賴區間覆蓋率"]},"variant":{"family_id":"qf-mod49-ci-worst-case-coverage","seed":202611183061,"parameters":{"theta_values":[0,1],"samples":["a","b"],"probability_rows":[[[11,13],[2,13]],[[2,13],[11,13]]],"intervals":[[0,0],[1,1]],"target":[1,3],"domain":"Exact_finite_confidence_coverage","operation":"ci-worst-case-coverage","semantic_template":"ci-worst-case-coverage|{intervals:[[[0,1],[0,1]],[[1,1],[1,1]]],probability_rows:[[[11,13],[2,13]],[[2,13],[11,13]]],samples:[\"a\",\"b\"],target:[1,3],theta:[0,1]}"}},"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；不構成一般limit theorem、coverage、number-theory或language theorem證明、人工審定、Lean或Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-15","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261015-advance-20261118-r03-finite-confidence-interval-coverage-0062","batch_id":"batch-20261015-advance-20261118-r03-finite-confidence-interval-coverage-foundations","language":"zh-Hant","source_mko_ids":["mko-finite-confidence-interval-coverage"],"title_zh":"有限模型信賴區間覆蓋率","stem_zh":"完整finite laws與total precommitted theta-independent interval procedure責任。操作=ci-worst-case-coverage；資料={\"theta_values\":[0,1],\"samples\":[\"a\",\"b\"],\"probability_rows\":[[[12,14],[2,14]],[[2,14],[12,14]]],\"intervals\":[[0,0],[1,1]],\"target\":[2,4]}。請依 exact_ordered_tuple_declared_by_interface 欄序回答。","answer":{"kind":"expression","value":"([[0, 6/7], [1, 6/7]], 6/7, 1/2, 是, worst_case_is_minimum_over_finite_theta)","explanation_zh":"Wave6第十二層核對=([[0, 6/7], [1, 6/7]], 6/7, 1/2, 是, worst_case_is_minimum_over_finite_theta)；依完整明示資料獨立重算；pointwise coverage與worst-case minimum逐theta重算；average不等於uniform，posterior不是coverage；selection納入procedure後須重新計算。"},"difficulty":{"band":"undergraduate_core","level":2,"skills":["有限模型信賴區間覆蓋率"]},"variant":{"family_id":"qf-mod49-ci-worst-case-coverage","seed":202611183062,"parameters":{"theta_values":[0,1],"samples":["a","b"],"probability_rows":[[[12,14],[2,14]],[[2,14],[12,14]]],"intervals":[[0,0],[1,1]],"target":[2,4],"domain":"Exact_finite_confidence_coverage","operation":"ci-worst-case-coverage","semantic_template":"ci-worst-case-coverage|{intervals:[[[0,1],[0,1]],[[1,1],[1,1]]],probability_rows:[[[6,7],[1,7]],[[1,7],[6,7]]],samples:[\"a\",\"b\"],target:[1,2],theta:[0,1]}"}},"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；不構成一般limit theorem、coverage、number-theory或language theorem證明、人工審定、Lean或Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-15","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261015-advance-20261118-r03-finite-confidence-interval-coverage-0063","batch_id":"batch-20261015-advance-20261118-r03-finite-confidence-interval-coverage-foundations","language":"zh-Hant","source_mko_ids":["mko-finite-confidence-interval-coverage"],"title_zh":"有限模型信賴區間覆蓋率","stem_zh":"完整finite laws與total precommitted theta-independent interval procedure責任。操作=ci-worst-case-coverage；資料={\"theta_values\":[0,1],\"samples\":[\"a\",\"b\"],\"probability_rows\":[[[13,15],[2,15]],[[2,15],[13,15]]],\"intervals\":[[0,0],[1,1]],\"target\":[3,5]}。請依 exact_ordered_tuple_declared_by_interface 欄序回答。","answer":{"kind":"expression","value":"([[0, 13/15], [1, 13/15]], 13/15, 3/5, 是, worst_case_is_minimum_over_finite_theta)","explanation_zh":"Wave6第十二層核對=([[0, 13/15], [1, 13/15]], 13/15, 3/5, 是, worst_case_is_minimum_over_finite_theta)；依完整明示資料獨立重算；pointwise coverage與worst-case minimum逐theta重算；average不等於uniform，posterior不是coverage；selection納入procedure後須重新計算。"},"difficulty":{"band":"undergraduate_core","level":2,"skills":["有限模型信賴區間覆蓋率"]},"variant":{"family_id":"qf-mod49-ci-worst-case-coverage","seed":202611183063,"parameters":{"theta_values":[0,1],"samples":["a","b"],"probability_rows":[[[13,15],[2,15]],[[2,15],[13,15]]],"intervals":[[0,0],[1,1]],"target":[3,5],"domain":"Exact_finite_confidence_coverage","operation":"ci-worst-case-coverage","semantic_template":"ci-worst-case-coverage|{intervals:[[[0,1],[0,1]],[[1,1],[1,1]]],probability_rows:[[[13,15],[2,15]],[[2,15],[13,15]]],samples:[\"a\",\"b\"],target:[3,5],theta:[0,1]}"}},"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；不構成一般limit theorem、coverage、number-theory或language theorem證明、人工審定、Lean或Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-15","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261015-advance-20261118-r03-finite-confidence-interval-coverage-0064","batch_id":"batch-20261015-advance-20261118-r03-finite-confidence-interval-coverage-foundations","language":"zh-Hant","source_mko_ids":["mko-finite-confidence-interval-coverage"],"title_zh":"有限模型信賴區間覆蓋率","stem_zh":"完整finite laws與total precommitted theta-independent interval procedure責任。操作=ci-worst-case-coverage；資料={\"theta_values\":[0,1],\"samples\":[\"a\",\"b\"],\"probability_rows\":[[[14,16],[2,16]],[[2,16],[14,16]]],\"intervals\":[[0,0],[1,1]],\"target\":[4,6]}。請依 exact_ordered_tuple_declared_by_interface 欄序回答。","answer":{"kind":"expression","value":"([[0, 7/8], [1, 7/8]], 7/8, 2/3, 是, worst_case_is_minimum_over_finite_theta)","explanation_zh":"Wave6第十二層核對=([[0, 7/8], [1, 7/8]], 7/8, 2/3, 是, worst_case_is_minimum_over_finite_theta)；依完整明示資料獨立重算；pointwise coverage與worst-case minimum逐theta重算；average不等於uniform，posterior不是coverage；selection納入procedure後須重新計算。"},"difficulty":{"band":"undergraduate_core","level":2,"skills":["有限模型信賴區間覆蓋率"]},"variant":{"family_id":"qf-mod49-ci-worst-case-coverage","seed":202611183064,"parameters":{"theta_values":[0,1],"samples":["a","b"],"probability_rows":[[[14,16],[2,16]],[[2,16],[14,16]]],"intervals":[[0,0],[1,1]],"target":[4,6],"domain":"Exact_finite_confidence_coverage","operation":"ci-worst-case-coverage","semantic_template":"ci-worst-case-coverage|{intervals:[[[0,1],[0,1]],[[1,1],[1,1]]],probability_rows:[[[7,8],[1,8]],[[1,8],[7,8]]],samples:[\"a\",\"b\"],target:[2,3],theta:[0,1]}"}},"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；不構成一般limit theorem、coverage、number-theory或language theorem證明、人工審定、Lean或Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-15","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261015-advance-20261118-r03-finite-confidence-interval-coverage-0065","batch_id":"batch-20261015-advance-20261118-r03-finite-confidence-interval-coverage-foundations","language":"zh-Hant","source_mko_ids":["mko-finite-confidence-interval-coverage"],"title_zh":"有限模型信賴區間覆蓋率","stem_zh":"完整finite laws與total precommitted theta-independent interval procedure責任。操作=ci-worst-case-coverage；資料={\"theta_values\":[0,1],\"samples\":[\"a\",\"b\"],\"probability_rows\":[[[15,17],[2,17]],[[2,17],[15,17]]],\"intervals\":[[0,0],[1,1]],\"target\":[5,7]}。請依 exact_ordered_tuple_declared_by_interface 欄序回答。","answer":{"kind":"expression","value":"([[0, 15/17], [1, 15/17]], 15/17, 5/7, 是, worst_case_is_minimum_over_finite_theta)","explanation_zh":"Wave6第十二層核對=([[0, 15/17], [1, 15/17]], 15/17, 5/7, 是, worst_case_is_minimum_over_finite_theta)；依完整明示資料獨立重算；pointwise coverage與worst-case minimum逐theta重算；average不等於uniform，posterior不是coverage；selection納入procedure後須重新計算。"},"difficulty":{"band":"undergraduate_core","level":2,"skills":["有限模型信賴區間覆蓋率"]},"variant":{"family_id":"qf-mod49-ci-worst-case-coverage","seed":202611183065,"parameters":{"theta_values":[0,1],"samples":["a","b"],"probability_rows":[[[15,17],[2,17]],[[2,17],[15,17]]],"intervals":[[0,0],[1,1]],"target":[5,7],"domain":"Exact_finite_confidence_coverage","operation":"ci-worst-case-coverage","semantic_template":"ci-worst-case-coverage|{intervals:[[[0,1],[0,1]],[[1,1],[1,1]]],probability_rows:[[[15,17],[2,17]],[[2,17],[15,17]]],samples:[\"a\",\"b\"],target:[5,7],theta:[0,1]}"}},"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；不構成一般limit theorem、coverage、number-theory或language theorem證明、人工審定、Lean或Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-15","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261015-advance-20261118-r03-finite-confidence-interval-coverage-0066","batch_id":"batch-20261015-advance-20261118-r03-finite-confidence-interval-coverage-foundations","language":"zh-Hant","source_mko_ids":["mko-finite-confidence-interval-coverage"],"title_zh":"有限模型信賴區間覆蓋率","stem_zh":"完整finite laws與total precommitted theta-independent interval procedure責任。操作=ci-worst-case-coverage；資料={\"theta_values\":[0,1],\"samples\":[\"a\",\"b\"],\"probability_rows\":[[[16,18],[2,18]],[[2,18],[16,18]]],\"intervals\":[[0,0],[1,1]],\"target\":[1,3]}。請依 exact_ordered_tuple_declared_by_interface 欄序回答。","answer":{"kind":"expression","value":"([[0, 8/9], [1, 8/9]], 8/9, 1/3, 是, worst_case_is_minimum_over_finite_theta)","explanation_zh":"Wave6第十二層核對=([[0, 8/9], [1, 8/9]], 8/9, 1/3, 是, worst_case_is_minimum_over_finite_theta)；依完整明示資料獨立重算；pointwise coverage與worst-case minimum逐theta重算；average不等於uniform，posterior不是coverage；selection納入procedure後須重新計算。"},"difficulty":{"band":"undergraduate_core","level":2,"skills":["有限模型信賴區間覆蓋率"]},"variant":{"family_id":"qf-mod49-ci-worst-case-coverage","seed":202611183066,"parameters":{"theta_values":[0,1],"samples":["a","b"],"probability_rows":[[[16,18],[2,18]],[[2,18],[16,18]]],"intervals":[[0,0],[1,1]],"target":[1,3],"domain":"Exact_finite_confidence_coverage","operation":"ci-worst-case-coverage","semantic_template":"ci-worst-case-coverage|{intervals:[[[0,1],[0,1]],[[1,1],[1,1]]],probability_rows:[[[8,9],[1,9]],[[1,9],[8,9]]],samples:[\"a\",\"b\"],target:[1,3],theta:[0,1]}"}},"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；不構成一般limit theorem、coverage、number-theory或language theorem證明、人工審定、Lean或Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-15","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261015-advance-20261118-r03-finite-confidence-interval-coverage-0067","batch_id":"batch-20261015-advance-20261118-r03-finite-confidence-interval-coverage-foundations","language":"zh-Hant","source_mko_ids":["mko-finite-confidence-interval-coverage"],"title_zh":"有限模型信賴區間覆蓋率","stem_zh":"完整finite laws與total precommitted theta-independent interval procedure責任。操作=ci-worst-case-coverage；資料={\"theta_values\":[0,1],\"samples\":[\"a\",\"b\"],\"probability_rows\":[[[17,19],[2,19]],[[2,19],[17,19]]],\"intervals\":[[0,0],[1,1]],\"target\":[2,4]}。請依 exact_ordered_tuple_declared_by_interface 欄序回答。","answer":{"kind":"expression","value":"([[0, 17/19], [1, 17/19]], 17/19, 1/2, 是, worst_case_is_minimum_over_finite_theta)","explanation_zh":"Wave6第十二層核對=([[0, 17/19], [1, 17/19]], 17/19, 1/2, 是, worst_case_is_minimum_over_finite_theta)；依完整明示資料獨立重算；pointwise coverage與worst-case minimum逐theta重算；average不等於uniform，posterior不是coverage；selection納入procedure後須重新計算。"},"difficulty":{"band":"undergraduate_core","level":2,"skills":["有限模型信賴區間覆蓋率"]},"variant":{"family_id":"qf-mod49-ci-worst-case-coverage","seed":202611183067,"parameters":{"theta_values":[0,1],"samples":["a","b"],"probability_rows":[[[17,19],[2,19]],[[2,19],[17,19]]],"intervals":[[0,0],[1,1]],"target":[2,4],"domain":"Exact_finite_confidence_coverage","operation":"ci-worst-case-coverage","semantic_template":"ci-worst-case-coverage|{intervals:[[[0,1],[0,1]],[[1,1],[1,1]]],probability_rows:[[[17,19],[2,19]],[[2,19],[17,19]]],samples:[\"a\",\"b\"],target:[1,2],theta:[0,1]}"}},"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；不構成一般limit theorem、coverage、number-theory或language theorem證明、人工審定、Lean或Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-15","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261015-advance-20261118-r03-finite-confidence-interval-coverage-0068","batch_id":"batch-20261015-advance-20261118-r03-finite-confidence-interval-coverage-foundations","language":"zh-Hant","source_mko_ids":["mko-finite-confidence-interval-coverage"],"title_zh":"有限模型信賴區間覆蓋率","stem_zh":"完整finite laws與total precommitted theta-independent interval procedure責任。操作=ci-worst-case-coverage；資料={\"theta_values\":[0,1],\"samples\":[\"a\",\"b\"],\"probability_rows\":[[[18,20],[2,20]],[[2,20],[18,20]]],\"intervals\":[[0,0],[1,1]],\"target\":[3,5]}。請依 exact_ordered_tuple_declared_by_interface 欄序回答。","answer":{"kind":"expression","value":"([[0, 9/10], [1, 9/10]], 9/10, 3/5, 是, worst_case_is_minimum_over_finite_theta)","explanation_zh":"Wave6第十二層核對=([[0, 9/10], [1, 9/10]], 9/10, 3/5, 是, worst_case_is_minimum_over_finite_theta)；依完整明示資料獨立重算；pointwise coverage與worst-case minimum逐theta重算；average不等於uniform，posterior不是coverage；selection納入procedure後須重新計算。"},"difficulty":{"band":"undergraduate_core","level":3,"skills":["有限模型信賴區間覆蓋率"]},"variant":{"family_id":"qf-mod49-ci-worst-case-coverage","seed":202611183068,"parameters":{"theta_values":[0,1],"samples":["a","b"],"probability_rows":[[[18,20],[2,20]],[[2,20],[18,20]]],"intervals":[[0,0],[1,1]],"target":[3,5],"domain":"Exact_finite_confidence_coverage","operation":"ci-worst-case-coverage","semantic_template":"ci-worst-case-coverage|{intervals:[[[0,1],[0,1]],[[1,1],[1,1]]],probability_rows:[[[9,10],[1,10]],[[1,10],[9,10]]],samples:[\"a\",\"b\"],target:[3,5],theta:[0,1]}"}},"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；不構成一般limit theorem、coverage、number-theory或language theorem證明、人工審定、Lean或Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-15","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261015-advance-20261118-r03-finite-confidence-interval-coverage-0069","batch_id":"batch-20261015-advance-20261118-r03-finite-confidence-interval-coverage-foundations","language":"zh-Hant","source_mko_ids":["mko-finite-confidence-interval-coverage"],"title_zh":"有限模型信賴區間覆蓋率","stem_zh":"完整finite laws與total precommitted theta-independent interval procedure責任。操作=ci-worst-case-coverage；資料={\"theta_values\":[0,1],\"samples\":[\"a\",\"b\"],\"probability_rows\":[[[19,21],[2,21]],[[2,21],[19,21]]],\"intervals\":[[0,0],[1,1]],\"target\":[4,6]}。請依 exact_ordered_tuple_declared_by_interface 欄序回答。","answer":{"kind":"expression","value":"([[0, 19/21], [1, 19/21]], 19/21, 2/3, 是, worst_case_is_minimum_over_finite_theta)","explanation_zh":"Wave6第十二層核對=([[0, 19/21], [1, 19/21]], 19/21, 2/3, 是, worst_case_is_minimum_over_finite_theta)；依完整明示資料獨立重算；pointwise coverage與worst-case minimum逐theta重算；average不等於uniform，posterior不是coverage；selection納入procedure後須重新計算。"},"difficulty":{"band":"undergraduate_core","level":3,"skills":["有限模型信賴區間覆蓋率"]},"variant":{"family_id":"qf-mod49-ci-worst-case-coverage","seed":202611183069,"parameters":{"theta_values":[0,1],"samples":["a","b"],"probability_rows":[[[19,21],[2,21]],[[2,21],[19,21]]],"intervals":[[0,0],[1,1]],"target":[4,6],"domain":"Exact_finite_confidence_coverage","operation":"ci-worst-case-coverage","semantic_template":"ci-worst-case-coverage|{intervals:[[[0,1],[0,1]],[[1,1],[1,1]]],probability_rows:[[[19,21],[2,21]],[[2,21],[19,21]]],samples:[\"a\",\"b\"],target:[2,3],theta:[0,1]}"}},"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；不構成一般limit theorem、coverage、number-theory或language theorem證明、人工審定、Lean或Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-15","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261015-advance-20261118-r03-finite-confidence-interval-coverage-0070","batch_id":"batch-20261015-advance-20261118-r03-finite-confidence-interval-coverage-foundations","language":"zh-Hant","source_mko_ids":["mko-finite-confidence-interval-coverage"],"title_zh":"有限模型信賴區間覆蓋率","stem_zh":"完整finite laws與total precommitted theta-independent interval procedure責任。操作=ci-worst-case-coverage；資料={\"theta_values\":[0,1],\"samples\":[\"a\",\"b\"],\"probability_rows\":[[[20,22],[2,22]],[[2,22],[20,22]]],\"intervals\":[[0,0],[1,1]],\"target\":[5,7]}。請依 exact_ordered_tuple_declared_by_interface 欄序回答。","answer":{"kind":"expression","value":"([[0, 10/11], [1, 10/11]], 10/11, 5/7, 是, worst_case_is_minimum_over_finite_theta)","explanation_zh":"Wave6第十二層核對=([[0, 10/11], [1, 10/11]], 10/11, 5/7, 是, worst_case_is_minimum_over_finite_theta)；依完整明示資料獨立重算；pointwise coverage與worst-case minimum逐theta重算；average不等於uniform，posterior不是coverage；selection納入procedure後須重新計算。"},"difficulty":{"band":"undergraduate_core","level":3,"skills":["有限模型信賴區間覆蓋率"]},"variant":{"family_id":"qf-mod49-ci-worst-case-coverage","seed":202611183070,"parameters":{"theta_values":[0,1],"samples":["a","b"],"probability_rows":[[[20,22],[2,22]],[[2,22],[20,22]]],"intervals":[[0,0],[1,1]],"target":[5,7],"domain":"Exact_finite_confidence_coverage","operation":"ci-worst-case-coverage","semantic_template":"ci-worst-case-coverage|{intervals:[[[0,1],[0,1]],[[1,1],[1,1]]],probability_rows:[[[10,11],[1,11]],[[1,11],[10,11]]],samples:[\"a\",\"b\"],target:[5,7],theta:[0,1]}"}},"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；不構成一般limit theorem、coverage、number-theory或language theorem證明、人工審定、Lean或Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-15","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261015-advance-20261118-r03-finite-confidence-interval-coverage-0071","batch_id":"batch-20261015-advance-20261118-r03-finite-confidence-interval-coverage-foundations","language":"zh-Hant","source_mko_ids":["mko-finite-confidence-interval-coverage"],"title_zh":"有限模型信賴區間覆蓋率","stem_zh":"完整finite laws與total precommitted theta-independent interval procedure責任。操作=ci-worst-case-coverage；資料={\"theta_values\":[0,1],\"samples\":[\"a\",\"b\"],\"probability_rows\":[[[21,23],[2,23]],[[2,23],[21,23]]],\"intervals\":[[0,0],[1,1]],\"target\":[1,3]}。請依 exact_ordered_tuple_declared_by_interface 欄序回答。","answer":{"kind":"expression","value":"([[0, 21/23], [1, 21/23]], 21/23, 1/3, 是, worst_case_is_minimum_over_finite_theta)","explanation_zh":"Wave6第十二層核對=([[0, 21/23], [1, 21/23]], 21/23, 1/3, 是, worst_case_is_minimum_over_finite_theta)；依完整明示資料獨立重算；pointwise coverage與worst-case minimum逐theta重算；average不等於uniform，posterior不是coverage；selection納入procedure後須重新計算。"},"difficulty":{"band":"undergraduate_core","level":3,"skills":["有限模型信賴區間覆蓋率"]},"variant":{"family_id":"qf-mod49-ci-worst-case-coverage","seed":202611183071,"parameters":{"theta_values":[0,1],"samples":["a","b"],"probability_rows":[[[21,23],[2,23]],[[2,23],[21,23]]],"intervals":[[0,0],[1,1]],"target":[1,3],"domain":"Exact_finite_confidence_coverage","operation":"ci-worst-case-coverage","semantic_template":"ci-worst-case-coverage|{intervals:[[[0,1],[0,1]],[[1,1],[1,1]]],probability_rows:[[[21,23],[2,23]],[[2,23],[21,23]]],samples:[\"a\",\"b\"],target:[1,3],theta:[0,1]}"}},"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；不構成一般limit theorem、coverage、number-theory或language theorem證明、人工審定、Lean或Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-15","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261015-advance-20261118-r03-finite-confidence-interval-coverage-0072","batch_id":"batch-20261015-advance-20261118-r03-finite-confidence-interval-coverage-foundations","language":"zh-Hant","source_mko_ids":["mko-finite-confidence-interval-coverage"],"title_zh":"有限模型信賴區間覆蓋率","stem_zh":"完整finite laws與total precommitted theta-independent interval procedure責任。操作=ci-worst-case-coverage；資料={\"theta_values\":[0,1],\"samples\":[\"a\",\"b\"],\"probability_rows\":[[[22,24],[2,24]],[[2,24],[22,24]]],\"intervals\":[[0,0],[1,1]],\"target\":[2,4]}。請依 exact_ordered_tuple_declared_by_interface 欄序回答。","answer":{"kind":"expression","value":"([[0, 11/12], [1, 11/12]], 11/12, 1/2, 是, worst_case_is_minimum_over_finite_theta)","explanation_zh":"Wave6第十二層核對=([[0, 11/12], [1, 11/12]], 11/12, 1/2, 是, worst_case_is_minimum_over_finite_theta)；依完整明示資料獨立重算；pointwise coverage與worst-case minimum逐theta重算；average不等於uniform，posterior不是coverage；selection納入procedure後須重新計算。"},"difficulty":{"band":"undergraduate_core","level":3,"skills":["有限模型信賴區間覆蓋率"]},"variant":{"family_id":"qf-mod49-ci-worst-case-coverage","seed":202611183072,"parameters":{"theta_values":[0,1],"samples":["a","b"],"probability_rows":[[[22,24],[2,24]],[[2,24],[22,24]]],"intervals":[[0,0],[1,1]],"target":[2,4],"domain":"Exact_finite_confidence_coverage","operation":"ci-worst-case-coverage","semantic_template":"ci-worst-case-coverage|{intervals:[[[0,1],[0,1]],[[1,1],[1,1]]],probability_rows:[[[11,12],[1,12]],[[1,12],[11,12]]],samples:[\"a\",\"b\"],target:[1,2],theta:[0,1]}"}},"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；不構成一般limit theorem、coverage、number-theory或language theorem證明、人工審定、Lean或Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-15","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261015-advance-20261118-r03-finite-confidence-interval-coverage-0073","batch_id":"batch-20261015-advance-20261118-r03-finite-confidence-interval-coverage-foundations","language":"zh-Hant","source_mko_ids":["mko-finite-confidence-interval-coverage"],"title_zh":"有限模型信賴區間覆蓋率","stem_zh":"完整finite laws與total precommitted theta-independent interval procedure責任。操作=ci-worst-case-coverage；資料={\"theta_values\":[0,1],\"samples\":[\"a\",\"b\"],\"probability_rows\":[[[23,25],[2,25]],[[2,25],[23,25]]],\"intervals\":[[0,0],[1,1]],\"target\":[3,5]}。請依 exact_ordered_tuple_declared_by_interface 欄序回答。","answer":{"kind":"expression","value":"([[0, 23/25], [1, 23/25]], 23/25, 3/5, 是, worst_case_is_minimum_over_finite_theta)","explanation_zh":"Wave6第十二層核對=([[0, 23/25], [1, 23/25]], 23/25, 3/5, 是, worst_case_is_minimum_over_finite_theta)；依完整明示資料獨立重算；pointwise coverage與worst-case minimum逐theta重算；average不等於uniform，posterior不是coverage；selection納入procedure後須重新計算。"},"difficulty":{"band":"undergraduate_core","level":3,"skills":["有限模型信賴區間覆蓋率"]},"variant":{"family_id":"qf-mod49-ci-worst-case-coverage","seed":202611183073,"parameters":{"theta_values":[0,1],"samples":["a","b"],"probability_rows":[[[23,25],[2,25]],[[2,25],[23,25]]],"intervals":[[0,0],[1,1]],"target":[3,5],"domain":"Exact_finite_confidence_coverage","operation":"ci-worst-case-coverage","semantic_template":"ci-worst-case-coverage|{intervals:[[[0,1],[0,1]],[[1,1],[1,1]]],probability_rows:[[[23,25],[2,25]],[[2,25],[23,25]]],samples:[\"a\",\"b\"],target:[3,5],theta:[0,1]}"}},"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；不構成一般limit theorem、coverage、number-theory或language theorem證明、人工審定、Lean或Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-15","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261015-advance-20261118-r03-finite-confidence-interval-coverage-0074","batch_id":"batch-20261015-advance-20261118-r03-finite-confidence-interval-coverage-foundations","language":"zh-Hant","source_mko_ids":["mko-finite-confidence-interval-coverage"],"title_zh":"有限模型信賴區間覆蓋率","stem_zh":"完整finite laws與total precommitted theta-independent interval procedure責任。操作=ci-worst-case-coverage；資料={\"theta_values\":[0,1],\"samples\":[\"a\",\"b\"],\"probability_rows\":[[[24,26],[2,26]],[[2,26],[24,26]]],\"intervals\":[[0,0],[1,1]],\"target\":[4,6]}。請依 exact_ordered_tuple_declared_by_interface 欄序回答。","answer":{"kind":"expression","value":"([[0, 12/13], [1, 12/13]], 12/13, 2/3, 是, worst_case_is_minimum_over_finite_theta)","explanation_zh":"Wave6第十二層核對=([[0, 12/13], [1, 12/13]], 12/13, 2/3, 是, worst_case_is_minimum_over_finite_theta)；依完整明示資料獨立重算；pointwise coverage與worst-case minimum逐theta重算；average不等於uniform，posterior不是coverage；selection納入procedure後須重新計算。"},"difficulty":{"band":"undergraduate_core","level":3,"skills":["有限模型信賴區間覆蓋率"]},"variant":{"family_id":"qf-mod49-ci-worst-case-coverage","seed":202611183074,"parameters":{"theta_values":[0,1],"samples":["a","b"],"probability_rows":[[[24,26],[2,26]],[[2,26],[24,26]]],"intervals":[[0,0],[1,1]],"target":[4,6],"domain":"Exact_finite_confidence_coverage","operation":"ci-worst-case-coverage","semantic_template":"ci-worst-case-coverage|{intervals:[[[0,1],[0,1]],[[1,1],[1,1]]],probability_rows:[[[12,13],[1,13]],[[1,13],[12,13]]],samples:[\"a\",\"b\"],target:[2,3],theta:[0,1]}"}},"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；不構成一般limit theorem、coverage、number-theory或language theorem證明、人工審定、Lean或Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-15","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261015-advance-20261118-r03-finite-confidence-interval-coverage-0075","batch_id":"batch-20261015-advance-20261118-r03-finite-confidence-interval-coverage-foundations","language":"zh-Hant","source_mko_ids":["mko-finite-confidence-interval-coverage"],"title_zh":"有限模型信賴區間覆蓋率","stem_zh":"完整finite laws與total precommitted theta-independent interval procedure責任。操作=ci-worst-case-coverage；資料={\"theta_values\":[0,1],\"samples\":[\"a\",\"b\"],\"probability_rows\":[[[25,27],[2,27]],[[2,27],[25,27]]],\"intervals\":[[0,0],[1,1]],\"target\":[5,7]}。請依 exact_ordered_tuple_declared_by_interface 欄序回答。","answer":{"kind":"expression","value":"([[0, 25/27], [1, 25/27]], 25/27, 5/7, 是, worst_case_is_minimum_over_finite_theta)","explanation_zh":"Wave6第十二層核對=([[0, 25/27], [1, 25/27]], 25/27, 5/7, 是, worst_case_is_minimum_over_finite_theta)；依完整明示資料獨立重算；pointwise coverage與worst-case minimum逐theta重算；average不等於uniform，posterior不是coverage；selection納入procedure後須重新計算。"},"difficulty":{"band":"undergraduate_core","level":3,"skills":["有限模型信賴區間覆蓋率"]},"variant":{"family_id":"qf-mod49-ci-worst-case-coverage","seed":202611183075,"parameters":{"theta_values":[0,1],"samples":["a","b"],"probability_rows":[[[25,27],[2,27]],[[2,27],[25,27]]],"intervals":[[0,0],[1,1]],"target":[5,7],"domain":"Exact_finite_confidence_coverage","operation":"ci-worst-case-coverage","semantic_template":"ci-worst-case-coverage|{intervals:[[[0,1],[0,1]],[[1,1],[1,1]]],probability_rows:[[[25,27],[2,27]],[[2,27],[25,27]]],samples:[\"a\",\"b\"],target:[5,7],theta:[0,1]}"}},"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；不構成一般limit theorem、coverage、number-theory或language theorem證明、人工審定、Lean或Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-15","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261015-advance-20261118-r03-finite-confidence-interval-coverage-0076","batch_id":"batch-20261015-advance-20261118-r03-finite-confidence-interval-coverage-foundations","language":"zh-Hant","source_mko_ids":["mko-finite-confidence-interval-coverage"],"title_zh":"有限模型信賴區間覆蓋率","stem_zh":"完整finite laws與total precommitted theta-independent interval procedure責任。操作=ci-interpretation-boundary；資料={\"mode\":\"average_only\",\"model\":{\"theta_values\":[0,1],\"samples\":[\"a\",\"b\"],\"probability_rows\":[[[1,3],[2,3]],[[2,3],[1,3]]],\"intervals\":[[0,0],[0,0]],\"theta_weights\":[[1,3],[2,3]],\"target\":[1,3]}}。請依 exact_ordered_tuple_declared_by_interface 欄序回答。","answer":{"kind":"expression","value":"(average_only, [[0, 1], [1, 0]], [1/3, 2/3], 1/3, 0, 1/3, 是, 是, 是, 否, average_coverage_can_mask_failure_of_uniform_target)","explanation_zh":"Wave6第十二層核對=(average_only, [[0, 1], [1, 0]], [1/3, 2/3], 1/3, 0, 1/3, 是, 是, 是, 否, average_coverage_can_mask_failure_of_uniform_target)；依完整明示資料獨立重算；pointwise coverage與worst-case minimum逐theta重算；average不等於uniform，posterior不是coverage；selection納入procedure後須重新計算。"},"difficulty":{"band":"undergraduate_core","level":1,"skills":["有限模型信賴區間覆蓋率"]},"variant":{"family_id":"qf-mod49-ci-interpretation-boundary","seed":202611183076,"parameters":{"mode":"average_only","model":{"theta_values":[0,1],"samples":["a","b"],"probability_rows":[[[1,3],[2,3]],[[2,3],[1,3]]],"intervals":[[0,0],[0,0]],"theta_weights":[[1,3],[2,3]],"target":[1,3]},"domain":"Exact_finite_confidence_coverage","operation":"ci-interpretation-boundary","semantic_template":"ci-interpretation-boundary|{mode:\"average_only\",model:{intervals:[[[0,1],[0,1]],[[0,1],[0,1]]],probability_rows:[[[1,3],[2,3]],[[2,3],[1,3]]],samples:[\"a\",\"b\"],target:[1,3],theta:[0,1],theta_weights:[[1,3],[2,3]]}}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_or_symbolic_model","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"候選須主端重算；不構成一般limit theorem、coverage、number-theory或language theorem證明、人工審定、Lean或Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-15","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261015-advance-20261118-r03-finite-confidence-interval-coverage-0077","batch_id":"batch-20261015-advance-20261118-r03-finite-confidence-interval-coverage-foundations","language":"zh-Hant","source_mko_ids":["mko-finite-confidence-interval-coverage"],"title_zh":"有限模型信賴區間覆蓋率","stem_zh":"完整finite laws與total precommitted theta-independent interval procedure責任。操作=ci-interpretation-boundary；資料={\"mode\":\"posterior_confusion\",\"model\":{\"theta_values\":[0,1],\"samples\":[\"a\",\"b\"],\"probability_rows\":[[[2,4],[2,4]],[[2,4],[2,4]]],\"intervals\":[[0,0],[1,1]],\"prior\":[[2,4],[2,4]],\"observed\":\"b\"}}。請依 exact_ordered_tuple_declared_by_interface 欄序回答。","answer":{"kind":"expression","value":"(posterior_confusion, b, [1/2, 1/2], [[0, 1/2], [1, 1/2]], 否, posterior_given_observed_data_is_not_frequentist_coverage)","explanation_zh":"Wave6第十二層核對=(posterior_confusion, b, [1/2, 1/2], [[0, 1/2], [1, 1/2]], 否, posterior_given_observed_data_is_not_frequentist_coverage)；依完整明示資料獨立重算；pointwise coverage與worst-case minimum逐theta重算；average不等於uniform，posterior不是coverage；selection納入procedure後須重新計算。"},"difficulty":{"band":"undergraduate_core","level":1,"skills":["有限模型信賴區間覆蓋率"]},"variant":{"family_id":"qf-mod49-ci-interpretation-boundary","seed":202611183077,"parameters":{"mode":"posterior_confusion","model":{"theta_values":[0,1],"samples":["a","b"],"probability_rows":[[[2,4],[2,4]],[[2,4],[2,4]]],"intervals":[[0,0],[1,1]],"prior":[[2,4],[2,4]],"observed":"b"},"domain":"Exact_finite_confidence_coverage","operation":"ci-interpretation-boundary","semantic_template":"ci-interpretation-boundary|{mode:\"posterior_confusion\",model:{intervals:[[[0,1],[0,1]],[[1,1],[1,1]]],observed:\"b\",prior:[[1,2],[1,2]],probability_rows:[[[1,2],[1,2]],[[1,2],[1,2]]],samples:[\"a\",\"b\"],theta:[0,1]}}"}},"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；不構成一般limit theorem、coverage、number-theory或language theorem證明、人工審定、Lean或Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-15","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261015-advance-20261118-r03-finite-confidence-interval-coverage-0078","batch_id":"batch-20261015-advance-20261118-r03-finite-confidence-interval-coverage-foundations","language":"zh-Hant","source_mko_ids":["mko-finite-confidence-interval-coverage"],"title_zh":"有限模型信賴區間覆蓋率","stem_zh":"完整finite laws與total precommitted theta-independent interval procedure責任。操作=ci-interpretation-boundary；資料={\"mode\":\"ignored_selection\",\"model\":{\"theta_values\":[0,1],\"samples\":[\"a\",\"b\"],\"probability_rows\":[[[3,5],[2,5]],[[2,5],[3,5]]],\"intervals\":[[0,0],[1,1]],\"selected_samples\":[\"a\"]}}。請依 exact_ordered_tuple_declared_by_interface 欄序回答。","answer":{"kind":"expression","value":"(ignored_selection, [a], [[0, 3/5], [1, 3/5]], [[0, 3/5, 1], [1, 2/5, 0]], 否, selection_must_be_included_and_coverage_recomputed_not_declared_automatically_invalid)","explanation_zh":"Wave6第十二層核對=(ignored_selection, [a], [[0, 3/5], [1, 3/5]], [[0, 3/5, 1], [1, 2/5, 0]], 否, selection_must_be_included_and_coverage_recomputed_not_declared_automatically_invalid)；依完整明示資料獨立重算；pointwise coverage與worst-case minimum逐theta重算；average不等於uniform，posterior不是coverage；selection納入procedure後須重新計算。"},"difficulty":{"band":"undergraduate_core","level":1,"skills":["有限模型信賴區間覆蓋率"]},"variant":{"family_id":"qf-mod49-ci-interpretation-boundary","seed":202611183078,"parameters":{"mode":"ignored_selection","model":{"theta_values":[0,1],"samples":["a","b"],"probability_rows":[[[3,5],[2,5]],[[2,5],[3,5]]],"intervals":[[0,0],[1,1]],"selected_samples":["a"]},"domain":"Exact_finite_confidence_coverage","operation":"ci-interpretation-boundary","semantic_template":"ci-interpretation-boundary|{mode:\"ignored_selection\",model:{intervals:[[[0,1],[0,1]],[[1,1],[1,1]]],probability_rows:[[[3,5],[2,5]],[[2,5],[3,5]]],samples:[\"a\",\"b\"],selected_samples:[\"a\"],theta:[0,1]}}"}},"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；不構成一般limit theorem、coverage、number-theory或language theorem證明、人工審定、Lean或Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-15","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261015-advance-20261118-r03-finite-confidence-interval-coverage-0079","batch_id":"batch-20261015-advance-20261118-r03-finite-confidence-interval-coverage-foundations","language":"zh-Hant","source_mko_ids":["mko-finite-confidence-interval-coverage"],"title_zh":"有限模型信賴區間覆蓋率","stem_zh":"完整finite laws與total precommitted theta-independent interval procedure責任。操作=ci-interpretation-boundary；資料={\"mode\":\"invalid_procedure\",\"model\":{\"theta_values\":[0,1],\"samples\":[\"a\",\"b\"],\"probability_rows\":[[[4,6],[2,6]],[[2,6],[4,6]]],\"intervals\":[[4,3],[4,4]]}}。請依 exact_ordered_tuple_declared_by_interface 欄序回答。","answer":{"kind":"expression","value":"(invalid_procedure, 否, interval lower endpoint exceeds upper endpoint, 否)","explanation_zh":"Wave6第十二層核對=(invalid_procedure, 否, interval lower endpoint exceeds upper endpoint, 否)；依完整明示資料獨立重算；pointwise coverage與worst-case minimum逐theta重算；average不等於uniform，posterior不是coverage；selection納入procedure後須重新計算。"},"difficulty":{"band":"undergraduate_core","level":1,"skills":["有限模型信賴區間覆蓋率"]},"variant":{"family_id":"qf-mod49-ci-interpretation-boundary","seed":202611183079,"parameters":{"mode":"invalid_procedure","model":{"theta_values":[0,1],"samples":["a","b"],"probability_rows":[[[4,6],[2,6]],[[2,6],[4,6]]],"intervals":[[4,3],[4,4]]},"domain":"Exact_finite_confidence_coverage","operation":"ci-interpretation-boundary","semantic_template":"ci-interpretation-boundary|{mode:\"invalid_procedure\",model:{intervals:[[[4,1],[3,1]],[[4,1],[4,1]]],probability_rows:[[[2,3],[1,3]],[[1,3],[2,3]]],samples:[\"a\",\"b\"],theta:[0,1]}}"}},"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；不構成一般limit theorem、coverage、number-theory或language theorem證明、人工審定、Lean或Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-15","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261015-advance-20261118-r03-finite-confidence-interval-coverage-0080","batch_id":"batch-20261015-advance-20261118-r03-finite-confidence-interval-coverage-foundations","language":"zh-Hant","source_mko_ids":["mko-finite-confidence-interval-coverage"],"title_zh":"有限模型信賴區間覆蓋率","stem_zh":"完整finite laws與total precommitted theta-independent interval procedure責任。操作=ci-interpretation-boundary；資料={\"mode\":\"average_only\",\"model\":{\"theta_values\":[0,1],\"samples\":[\"a\",\"b\"],\"probability_rows\":[[[5,7],[2,7]],[[2,7],[5,7]]],\"intervals\":[[0,0],[0,0]],\"theta_weights\":[[1,3],[2,3]],\"target\":[1,3]}}。請依 exact_ordered_tuple_declared_by_interface 欄序回答。","answer":{"kind":"expression","value":"(average_only, [[0, 1], [1, 0]], [1/3, 2/3], 1/3, 0, 1/3, 是, 是, 是, 否, average_coverage_can_mask_failure_of_uniform_target)","explanation_zh":"Wave6第十二層核對=(average_only, [[0, 1], [1, 0]], [1/3, 2/3], 1/3, 0, 1/3, 是, 是, 是, 否, average_coverage_can_mask_failure_of_uniform_target)；依完整明示資料獨立重算；pointwise coverage與worst-case minimum逐theta重算；average不等於uniform，posterior不是coverage；selection納入procedure後須重新計算。"},"difficulty":{"band":"undergraduate_core","level":1,"skills":["有限模型信賴區間覆蓋率"]},"variant":{"family_id":"qf-mod49-ci-interpretation-boundary","seed":202611183080,"parameters":{"mode":"average_only","model":{"theta_values":[0,1],"samples":["a","b"],"probability_rows":[[[5,7],[2,7]],[[2,7],[5,7]]],"intervals":[[0,0],[0,0]],"theta_weights":[[1,3],[2,3]],"target":[1,3]},"domain":"Exact_finite_confidence_coverage","operation":"ci-interpretation-boundary","semantic_template":"ci-interpretation-boundary|{mode:\"average_only\",model:{intervals:[[[0,1],[0,1]],[[0,1],[0,1]]],probability_rows:[[[5,7],[2,7]],[[2,7],[5,7]]],samples:[\"a\",\"b\"],target:[1,3],theta:[0,1],theta_weights:[[1,3],[2,3]]}}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_or_symbolic_model","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"候選須主端重算；不構成一般limit theorem、coverage、number-theory或language theorem證明、人工審定、Lean或Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-15","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261015-advance-20261118-r03-finite-confidence-interval-coverage-0081","batch_id":"batch-20261015-advance-20261118-r03-finite-confidence-interval-coverage-foundations","language":"zh-Hant","source_mko_ids":["mko-finite-confidence-interval-coverage"],"title_zh":"有限模型信賴區間覆蓋率","stem_zh":"完整finite laws與total precommitted theta-independent interval procedure責任。操作=ci-interpretation-boundary；資料={\"mode\":\"posterior_confusion\",\"model\":{\"theta_values\":[0,1],\"samples\":[\"a\",\"b\"],\"probability_rows\":[[[6,8],[2,8]],[[2,8],[6,8]]],\"intervals\":[[0,0],[1,1]],\"prior\":[[2,4],[2,4]],\"observed\":\"b\"}}。請依 exact_ordered_tuple_declared_by_interface 欄序回答。","answer":{"kind":"expression","value":"(posterior_confusion, b, [1/4, 3/4], [[0, 3/4], [1, 3/4]], 否, posterior_given_observed_data_is_not_frequentist_coverage)","explanation_zh":"Wave6第十二層核對=(posterior_confusion, b, [1/4, 3/4], [[0, 3/4], [1, 3/4]], 否, posterior_given_observed_data_is_not_frequentist_coverage)；依完整明示資料獨立重算；pointwise coverage與worst-case minimum逐theta重算；average不等於uniform，posterior不是coverage；selection納入procedure後須重新計算。"},"difficulty":{"band":"undergraduate_core","level":1,"skills":["有限模型信賴區間覆蓋率"]},"variant":{"family_id":"qf-mod49-ci-interpretation-boundary","seed":202611183081,"parameters":{"mode":"posterior_confusion","model":{"theta_values":[0,1],"samples":["a","b"],"probability_rows":[[[6,8],[2,8]],[[2,8],[6,8]]],"intervals":[[0,0],[1,1]],"prior":[[2,4],[2,4]],"observed":"b"},"domain":"Exact_finite_confidence_coverage","operation":"ci-interpretation-boundary","semantic_template":"ci-interpretation-boundary|{mode:\"posterior_confusion\",model:{intervals:[[[0,1],[0,1]],[[1,1],[1,1]]],observed:\"b\",prior:[[1,2],[1,2]],probability_rows:[[[3,4],[1,4]],[[1,4],[3,4]]],samples:[\"a\",\"b\"],theta:[0,1]}}"}},"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；不構成一般limit theorem、coverage、number-theory或language theorem證明、人工審定、Lean或Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-15","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261015-advance-20261118-r03-finite-confidence-interval-coverage-0082","batch_id":"batch-20261015-advance-20261118-r03-finite-confidence-interval-coverage-foundations","language":"zh-Hant","source_mko_ids":["mko-finite-confidence-interval-coverage"],"title_zh":"有限模型信賴區間覆蓋率","stem_zh":"完整finite laws與total precommitted theta-independent interval procedure責任。操作=ci-interpretation-boundary；資料={\"mode\":\"ignored_selection\",\"model\":{\"theta_values\":[0,1],\"samples\":[\"a\",\"b\"],\"probability_rows\":[[[7,9],[2,9]],[[2,9],[7,9]]],\"intervals\":[[0,0],[1,1]],\"selected_samples\":[\"a\"]}}。請依 exact_ordered_tuple_declared_by_interface 欄序回答。","answer":{"kind":"expression","value":"(ignored_selection, [a], [[0, 7/9], [1, 7/9]], [[0, 7/9, 1], [1, 2/9, 0]], 否, selection_must_be_included_and_coverage_recomputed_not_declared_automatically_invalid)","explanation_zh":"Wave6第十二層核對=(ignored_selection, [a], [[0, 7/9], [1, 7/9]], [[0, 7/9, 1], [1, 2/9, 0]], 否, selection_must_be_included_and_coverage_recomputed_not_declared_automatically_invalid)；依完整明示資料獨立重算；pointwise coverage與worst-case minimum逐theta重算；average不等於uniform，posterior不是coverage；selection納入procedure後須重新計算。"},"difficulty":{"band":"undergraduate_core","level":1,"skills":["有限模型信賴區間覆蓋率"]},"variant":{"family_id":"qf-mod49-ci-interpretation-boundary","seed":202611183082,"parameters":{"mode":"ignored_selection","model":{"theta_values":[0,1],"samples":["a","b"],"probability_rows":[[[7,9],[2,9]],[[2,9],[7,9]]],"intervals":[[0,0],[1,1]],"selected_samples":["a"]},"domain":"Exact_finite_confidence_coverage","operation":"ci-interpretation-boundary","semantic_template":"ci-interpretation-boundary|{mode:\"ignored_selection\",model:{intervals:[[[0,1],[0,1]],[[1,1],[1,1]]],probability_rows:[[[7,9],[2,9]],[[2,9],[7,9]]],samples:[\"a\",\"b\"],selected_samples:[\"a\"],theta:[0,1]}}"}},"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；不構成一般limit theorem、coverage、number-theory或language theorem證明、人工審定、Lean或Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-15","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261015-advance-20261118-r03-finite-confidence-interval-coverage-0083","batch_id":"batch-20261015-advance-20261118-r03-finite-confidence-interval-coverage-foundations","language":"zh-Hant","source_mko_ids":["mko-finite-confidence-interval-coverage"],"title_zh":"有限模型信賴區間覆蓋率","stem_zh":"完整finite laws與total precommitted theta-independent interval procedure責任。操作=ci-interpretation-boundary；資料={\"mode\":\"invalid_procedure\",\"model\":{\"theta_values\":[0,1],\"samples\":[\"a\",\"b\"],\"probability_rows\":[[[8,10],[2,10]],[[2,10],[8,10]]],\"intervals\":[[8,7],[8,8]]}}。請依 exact_ordered_tuple_declared_by_interface 欄序回答。","answer":{"kind":"expression","value":"(invalid_procedure, 否, interval lower endpoint exceeds upper endpoint, 否)","explanation_zh":"Wave6第十二層核對=(invalid_procedure, 否, interval lower endpoint exceeds upper endpoint, 否)；依完整明示資料獨立重算；pointwise coverage與worst-case minimum逐theta重算；average不等於uniform，posterior不是coverage；selection納入procedure後須重新計算。"},"difficulty":{"band":"undergraduate_core","level":1,"skills":["有限模型信賴區間覆蓋率"]},"variant":{"family_id":"qf-mod49-ci-interpretation-boundary","seed":202611183083,"parameters":{"mode":"invalid_procedure","model":{"theta_values":[0,1],"samples":["a","b"],"probability_rows":[[[8,10],[2,10]],[[2,10],[8,10]]],"intervals":[[8,7],[8,8]]},"domain":"Exact_finite_confidence_coverage","operation":"ci-interpretation-boundary","semantic_template":"ci-interpretation-boundary|{mode:\"invalid_procedure\",model:{intervals:[[[8,1],[7,1]],[[8,1],[8,1]]],probability_rows:[[[4,5],[1,5]],[[1,5],[4,5]]],samples:[\"a\",\"b\"],theta:[0,1]}}"}},"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；不構成一般limit theorem、coverage、number-theory或language theorem證明、人工審定、Lean或Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-15","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261015-advance-20261118-r03-finite-confidence-interval-coverage-0084","batch_id":"batch-20261015-advance-20261118-r03-finite-confidence-interval-coverage-foundations","language":"zh-Hant","source_mko_ids":["mko-finite-confidence-interval-coverage"],"title_zh":"有限模型信賴區間覆蓋率","stem_zh":"完整finite laws與total precommitted theta-independent interval procedure責任。操作=ci-interpretation-boundary；資料={\"mode\":\"average_only\",\"model\":{\"theta_values\":[0,1],\"samples\":[\"a\",\"b\"],\"probability_rows\":[[[9,11],[2,11]],[[2,11],[9,11]]],\"intervals\":[[0,0],[0,0]],\"theta_weights\":[[1,3],[2,3]],\"target\":[1,3]}}。請依 exact_ordered_tuple_declared_by_interface 欄序回答。","answer":{"kind":"expression","value":"(average_only, [[0, 1], [1, 0]], [1/3, 2/3], 1/3, 0, 1/3, 是, 是, 是, 否, average_coverage_can_mask_failure_of_uniform_target)","explanation_zh":"Wave6第十二層核對=(average_only, [[0, 1], [1, 0]], [1/3, 2/3], 1/3, 0, 1/3, 是, 是, 是, 否, average_coverage_can_mask_failure_of_uniform_target)；依完整明示資料獨立重算；pointwise coverage與worst-case minimum逐theta重算；average不等於uniform，posterior不是coverage；selection納入procedure後須重新計算。"},"difficulty":{"band":"undergraduate_core","level":2,"skills":["有限模型信賴區間覆蓋率"]},"variant":{"family_id":"qf-mod49-ci-interpretation-boundary","seed":202611183084,"parameters":{"mode":"average_only","model":{"theta_values":[0,1],"samples":["a","b"],"probability_rows":[[[9,11],[2,11]],[[2,11],[9,11]]],"intervals":[[0,0],[0,0]],"theta_weights":[[1,3],[2,3]],"target":[1,3]},"domain":"Exact_finite_confidence_coverage","operation":"ci-interpretation-boundary","semantic_template":"ci-interpretation-boundary|{mode:\"average_only\",model:{intervals:[[[0,1],[0,1]],[[0,1],[0,1]]],probability_rows:[[[9,11],[2,11]],[[2,11],[9,11]]],samples:[\"a\",\"b\"],target:[1,3],theta:[0,1],theta_weights:[[1,3],[2,3]]}}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_or_symbolic_model","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"候選須主端重算；不構成一般limit theorem、coverage、number-theory或language theorem證明、人工審定、Lean或Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-15","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261015-advance-20261118-r03-finite-confidence-interval-coverage-0085","batch_id":"batch-20261015-advance-20261118-r03-finite-confidence-interval-coverage-foundations","language":"zh-Hant","source_mko_ids":["mko-finite-confidence-interval-coverage"],"title_zh":"有限模型信賴區間覆蓋率","stem_zh":"完整finite laws與total precommitted theta-independent interval procedure責任。操作=ci-interpretation-boundary；資料={\"mode\":\"posterior_confusion\",\"model\":{\"theta_values\":[0,1],\"samples\":[\"a\",\"b\"],\"probability_rows\":[[[10,12],[2,12]],[[2,12],[10,12]]],\"intervals\":[[0,0],[1,1]],\"prior\":[[2,4],[2,4]],\"observed\":\"b\"}}。請依 exact_ordered_tuple_declared_by_interface 欄序回答。","answer":{"kind":"expression","value":"(posterior_confusion, b, [1/6, 5/6], [[0, 5/6], [1, 5/6]], 否, posterior_given_observed_data_is_not_frequentist_coverage)","explanation_zh":"Wave6第十二層核對=(posterior_confusion, b, [1/6, 5/6], [[0, 5/6], [1, 5/6]], 否, posterior_given_observed_data_is_not_frequentist_coverage)；依完整明示資料獨立重算；pointwise coverage與worst-case minimum逐theta重算；average不等於uniform，posterior不是coverage；selection納入procedure後須重新計算。"},"difficulty":{"band":"undergraduate_core","level":2,"skills":["有限模型信賴區間覆蓋率"]},"variant":{"family_id":"qf-mod49-ci-interpretation-boundary","seed":202611183085,"parameters":{"mode":"posterior_confusion","model":{"theta_values":[0,1],"samples":["a","b"],"probability_rows":[[[10,12],[2,12]],[[2,12],[10,12]]],"intervals":[[0,0],[1,1]],"prior":[[2,4],[2,4]],"observed":"b"},"domain":"Exact_finite_confidence_coverage","operation":"ci-interpretation-boundary","semantic_template":"ci-interpretation-boundary|{mode:\"posterior_confusion\",model:{intervals:[[[0,1],[0,1]],[[1,1],[1,1]]],observed:\"b\",prior:[[1,2],[1,2]],probability_rows:[[[5,6],[1,6]],[[1,6],[5,6]]],samples:[\"a\",\"b\"],theta:[0,1]}}"}},"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；不構成一般limit theorem、coverage、number-theory或language theorem證明、人工審定、Lean或Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-15","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261015-advance-20261118-r03-finite-confidence-interval-coverage-0086","batch_id":"batch-20261015-advance-20261118-r03-finite-confidence-interval-coverage-foundations","language":"zh-Hant","source_mko_ids":["mko-finite-confidence-interval-coverage"],"title_zh":"有限模型信賴區間覆蓋率","stem_zh":"完整finite laws與total precommitted theta-independent interval procedure責任。操作=ci-interpretation-boundary；資料={\"mode\":\"ignored_selection\",\"model\":{\"theta_values\":[0,1],\"samples\":[\"a\",\"b\"],\"probability_rows\":[[[11,13],[2,13]],[[2,13],[11,13]]],\"intervals\":[[0,0],[1,1]],\"selected_samples\":[\"a\"]}}。請依 exact_ordered_tuple_declared_by_interface 欄序回答。","answer":{"kind":"expression","value":"(ignored_selection, [a], [[0, 11/13], [1, 11/13]], [[0, 11/13, 1], [1, 2/13, 0]], 否, selection_must_be_included_and_coverage_recomputed_not_declared_automatically_invalid)","explanation_zh":"Wave6第十二層核對=(ignored_selection, [a], [[0, 11/13], [1, 11/13]], [[0, 11/13, 1], [1, 2/13, 0]], 否, selection_must_be_included_and_coverage_recomputed_not_declared_automatically_invalid)；依完整明示資料獨立重算；pointwise coverage與worst-case minimum逐theta重算；average不等於uniform，posterior不是coverage；selection納入procedure後須重新計算。"},"difficulty":{"band":"undergraduate_core","level":2,"skills":["有限模型信賴區間覆蓋率"]},"variant":{"family_id":"qf-mod49-ci-interpretation-boundary","seed":202611183086,"parameters":{"mode":"ignored_selection","model":{"theta_values":[0,1],"samples":["a","b"],"probability_rows":[[[11,13],[2,13]],[[2,13],[11,13]]],"intervals":[[0,0],[1,1]],"selected_samples":["a"]},"domain":"Exact_finite_confidence_coverage","operation":"ci-interpretation-boundary","semantic_template":"ci-interpretation-boundary|{mode:\"ignored_selection\",model:{intervals:[[[0,1],[0,1]],[[1,1],[1,1]]],probability_rows:[[[11,13],[2,13]],[[2,13],[11,13]]],samples:[\"a\",\"b\"],selected_samples:[\"a\"],theta:[0,1]}}"}},"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；不構成一般limit theorem、coverage、number-theory或language theorem證明、人工審定、Lean或Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-15","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261015-advance-20261118-r03-finite-confidence-interval-coverage-0087","batch_id":"batch-20261015-advance-20261118-r03-finite-confidence-interval-coverage-foundations","language":"zh-Hant","source_mko_ids":["mko-finite-confidence-interval-coverage"],"title_zh":"有限模型信賴區間覆蓋率","stem_zh":"完整finite laws與total precommitted theta-independent interval procedure責任。操作=ci-interpretation-boundary；資料={\"mode\":\"invalid_procedure\",\"model\":{\"theta_values\":[0,1],\"samples\":[\"a\",\"b\"],\"probability_rows\":[[[12,14],[2,14]],[[2,14],[12,14]]],\"intervals\":[[12,11],[12,12]]}}。請依 exact_ordered_tuple_declared_by_interface 欄序回答。","answer":{"kind":"expression","value":"(invalid_procedure, 否, interval lower endpoint exceeds upper endpoint, 否)","explanation_zh":"Wave6第十二層核對=(invalid_procedure, 否, interval lower endpoint exceeds upper endpoint, 否)；依完整明示資料獨立重算；pointwise coverage與worst-case minimum逐theta重算；average不等於uniform，posterior不是coverage；selection納入procedure後須重新計算。"},"difficulty":{"band":"undergraduate_core","level":2,"skills":["有限模型信賴區間覆蓋率"]},"variant":{"family_id":"qf-mod49-ci-interpretation-boundary","seed":202611183087,"parameters":{"mode":"invalid_procedure","model":{"theta_values":[0,1],"samples":["a","b"],"probability_rows":[[[12,14],[2,14]],[[2,14],[12,14]]],"intervals":[[12,11],[12,12]]},"domain":"Exact_finite_confidence_coverage","operation":"ci-interpretation-boundary","semantic_template":"ci-interpretation-boundary|{mode:\"invalid_procedure\",model:{intervals:[[[12,1],[11,1]],[[12,1],[12,1]]],probability_rows:[[[6,7],[1,7]],[[1,7],[6,7]]],samples:[\"a\",\"b\"],theta:[0,1]}}"}},"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；不構成一般limit theorem、coverage、number-theory或language theorem證明、人工審定、Lean或Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-15","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261015-advance-20261118-r03-finite-confidence-interval-coverage-0088","batch_id":"batch-20261015-advance-20261118-r03-finite-confidence-interval-coverage-foundations","language":"zh-Hant","source_mko_ids":["mko-finite-confidence-interval-coverage"],"title_zh":"有限模型信賴區間覆蓋率","stem_zh":"完整finite laws與total precommitted theta-independent interval procedure責任。操作=ci-interpretation-boundary；資料={\"mode\":\"average_only\",\"model\":{\"theta_values\":[0,1],\"samples\":[\"a\",\"b\"],\"probability_rows\":[[[13,15],[2,15]],[[2,15],[13,15]]],\"intervals\":[[0,0],[0,0]],\"theta_weights\":[[1,3],[2,3]],\"target\":[1,3]}}。請依 exact_ordered_tuple_declared_by_interface 欄序回答。","answer":{"kind":"expression","value":"(average_only, [[0, 1], [1, 0]], [1/3, 2/3], 1/3, 0, 1/3, 是, 是, 是, 否, average_coverage_can_mask_failure_of_uniform_target)","explanation_zh":"Wave6第十二層核對=(average_only, [[0, 1], [1, 0]], [1/3, 2/3], 1/3, 0, 1/3, 是, 是, 是, 否, average_coverage_can_mask_failure_of_uniform_target)；依完整明示資料獨立重算；pointwise coverage與worst-case minimum逐theta重算；average不等於uniform，posterior不是coverage；selection納入procedure後須重新計算。"},"difficulty":{"band":"undergraduate_core","level":2,"skills":["有限模型信賴區間覆蓋率"]},"variant":{"family_id":"qf-mod49-ci-interpretation-boundary","seed":202611183088,"parameters":{"mode":"average_only","model":{"theta_values":[0,1],"samples":["a","b"],"probability_rows":[[[13,15],[2,15]],[[2,15],[13,15]]],"intervals":[[0,0],[0,0]],"theta_weights":[[1,3],[2,3]],"target":[1,3]},"domain":"Exact_finite_confidence_coverage","operation":"ci-interpretation-boundary","semantic_template":"ci-interpretation-boundary|{mode:\"average_only\",model:{intervals:[[[0,1],[0,1]],[[0,1],[0,1]]],probability_rows:[[[13,15],[2,15]],[[2,15],[13,15]]],samples:[\"a\",\"b\"],target:[1,3],theta:[0,1],theta_weights:[[1,3],[2,3]]}}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_or_symbolic_model","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"候選須主端重算；不構成一般limit theorem、coverage、number-theory或language theorem證明、人工審定、Lean或Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-15","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261015-advance-20261118-r03-finite-confidence-interval-coverage-0089","batch_id":"batch-20261015-advance-20261118-r03-finite-confidence-interval-coverage-foundations","language":"zh-Hant","source_mko_ids":["mko-finite-confidence-interval-coverage"],"title_zh":"有限模型信賴區間覆蓋率","stem_zh":"完整finite laws與total precommitted theta-independent interval procedure責任。操作=ci-interpretation-boundary；資料={\"mode\":\"posterior_confusion\",\"model\":{\"theta_values\":[0,1],\"samples\":[\"a\",\"b\"],\"probability_rows\":[[[14,16],[2,16]],[[2,16],[14,16]]],\"intervals\":[[0,0],[1,1]],\"prior\":[[2,4],[2,4]],\"observed\":\"b\"}}。請依 exact_ordered_tuple_declared_by_interface 欄序回答。","answer":{"kind":"expression","value":"(posterior_confusion, b, [1/8, 7/8], [[0, 7/8], [1, 7/8]], 否, posterior_given_observed_data_is_not_frequentist_coverage)","explanation_zh":"Wave6第十二層核對=(posterior_confusion, b, [1/8, 7/8], [[0, 7/8], [1, 7/8]], 否, posterior_given_observed_data_is_not_frequentist_coverage)；依完整明示資料獨立重算；pointwise coverage與worst-case minimum逐theta重算；average不等於uniform，posterior不是coverage；selection納入procedure後須重新計算。"},"difficulty":{"band":"undergraduate_core","level":2,"skills":["有限模型信賴區間覆蓋率"]},"variant":{"family_id":"qf-mod49-ci-interpretation-boundary","seed":202611183089,"parameters":{"mode":"posterior_confusion","model":{"theta_values":[0,1],"samples":["a","b"],"probability_rows":[[[14,16],[2,16]],[[2,16],[14,16]]],"intervals":[[0,0],[1,1]],"prior":[[2,4],[2,4]],"observed":"b"},"domain":"Exact_finite_confidence_coverage","operation":"ci-interpretation-boundary","semantic_template":"ci-interpretation-boundary|{mode:\"posterior_confusion\",model:{intervals:[[[0,1],[0,1]],[[1,1],[1,1]]],observed:\"b\",prior:[[1,2],[1,2]],probability_rows:[[[7,8],[1,8]],[[1,8],[7,8]]],samples:[\"a\",\"b\"],theta:[0,1]}}"}},"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；不構成一般limit theorem、coverage、number-theory或language theorem證明、人工審定、Lean或Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-15","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261015-advance-20261118-r03-finite-confidence-interval-coverage-0090","batch_id":"batch-20261015-advance-20261118-r03-finite-confidence-interval-coverage-foundations","language":"zh-Hant","source_mko_ids":["mko-finite-confidence-interval-coverage"],"title_zh":"有限模型信賴區間覆蓋率","stem_zh":"完整finite laws與total precommitted theta-independent interval procedure責任。操作=ci-interpretation-boundary；資料={\"mode\":\"ignored_selection\",\"model\":{\"theta_values\":[0,1],\"samples\":[\"a\",\"b\"],\"probability_rows\":[[[15,17],[2,17]],[[2,17],[15,17]]],\"intervals\":[[0,0],[1,1]],\"selected_samples\":[\"a\"]}}。請依 exact_ordered_tuple_declared_by_interface 欄序回答。","answer":{"kind":"expression","value":"(ignored_selection, [a], [[0, 15/17], [1, 15/17]], [[0, 15/17, 1], [1, 2/17, 0]], 否, selection_must_be_included_and_coverage_recomputed_not_declared_automatically_invalid)","explanation_zh":"Wave6第十二層核對=(ignored_selection, [a], [[0, 15/17], [1, 15/17]], [[0, 15/17, 1], [1, 2/17, 0]], 否, selection_must_be_included_and_coverage_recomputed_not_declared_automatically_invalid)；依完整明示資料獨立重算；pointwise coverage與worst-case minimum逐theta重算；average不等於uniform，posterior不是coverage；selection納入procedure後須重新計算。"},"difficulty":{"band":"undergraduate_core","level":2,"skills":["有限模型信賴區間覆蓋率"]},"variant":{"family_id":"qf-mod49-ci-interpretation-boundary","seed":202611183090,"parameters":{"mode":"ignored_selection","model":{"theta_values":[0,1],"samples":["a","b"],"probability_rows":[[[15,17],[2,17]],[[2,17],[15,17]]],"intervals":[[0,0],[1,1]],"selected_samples":["a"]},"domain":"Exact_finite_confidence_coverage","operation":"ci-interpretation-boundary","semantic_template":"ci-interpretation-boundary|{mode:\"ignored_selection\",model:{intervals:[[[0,1],[0,1]],[[1,1],[1,1]]],probability_rows:[[[15,17],[2,17]],[[2,17],[15,17]]],samples:[\"a\",\"b\"],selected_samples:[\"a\"],theta:[0,1]}}"}},"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；不構成一般limit theorem、coverage、number-theory或language theorem證明、人工審定、Lean或Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-15","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261015-advance-20261118-r03-finite-confidence-interval-coverage-0091","batch_id":"batch-20261015-advance-20261118-r03-finite-confidence-interval-coverage-foundations","language":"zh-Hant","source_mko_ids":["mko-finite-confidence-interval-coverage"],"title_zh":"有限模型信賴區間覆蓋率","stem_zh":"完整finite laws與total precommitted theta-independent interval procedure責任。操作=ci-interpretation-boundary；資料={\"mode\":\"invalid_procedure\",\"model\":{\"theta_values\":[0,1],\"samples\":[\"a\",\"b\"],\"probability_rows\":[[[16,18],[2,18]],[[2,18],[16,18]]],\"intervals\":[[16,15],[16,16]]}}。請依 exact_ordered_tuple_declared_by_interface 欄序回答。","answer":{"kind":"expression","value":"(invalid_procedure, 否, interval lower endpoint exceeds upper endpoint, 否)","explanation_zh":"Wave6第十二層核對=(invalid_procedure, 否, interval lower endpoint exceeds upper endpoint, 否)；依完整明示資料獨立重算；pointwise coverage與worst-case minimum逐theta重算；average不等於uniform，posterior不是coverage；selection納入procedure後須重新計算。"},"difficulty":{"band":"undergraduate_core","level":2,"skills":["有限模型信賴區間覆蓋率"]},"variant":{"family_id":"qf-mod49-ci-interpretation-boundary","seed":202611183091,"parameters":{"mode":"invalid_procedure","model":{"theta_values":[0,1],"samples":["a","b"],"probability_rows":[[[16,18],[2,18]],[[2,18],[16,18]]],"intervals":[[16,15],[16,16]]},"domain":"Exact_finite_confidence_coverage","operation":"ci-interpretation-boundary","semantic_template":"ci-interpretation-boundary|{mode:\"invalid_procedure\",model:{intervals:[[[16,1],[15,1]],[[16,1],[16,1]]],probability_rows:[[[8,9],[1,9]],[[1,9],[8,9]]],samples:[\"a\",\"b\"],theta:[0,1]}}"}},"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；不構成一般limit theorem、coverage、number-theory或language theorem證明、人工審定、Lean或Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-15","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261015-advance-20261118-r03-finite-confidence-interval-coverage-0092","batch_id":"batch-20261015-advance-20261118-r03-finite-confidence-interval-coverage-foundations","language":"zh-Hant","source_mko_ids":["mko-finite-confidence-interval-coverage"],"title_zh":"有限模型信賴區間覆蓋率","stem_zh":"完整finite laws與total precommitted theta-independent interval procedure責任。操作=ci-interpretation-boundary；資料={\"mode\":\"average_only\",\"model\":{\"theta_values\":[0,1],\"samples\":[\"a\",\"b\"],\"probability_rows\":[[[17,19],[2,19]],[[2,19],[17,19]]],\"intervals\":[[0,0],[0,0]],\"theta_weights\":[[1,3],[2,3]],\"target\":[1,3]}}。請依 exact_ordered_tuple_declared_by_interface 欄序回答。","answer":{"kind":"expression","value":"(average_only, [[0, 1], [1, 0]], [1/3, 2/3], 1/3, 0, 1/3, 是, 是, 是, 否, average_coverage_can_mask_failure_of_uniform_target)","explanation_zh":"Wave6第十二層核對=(average_only, [[0, 1], [1, 0]], [1/3, 2/3], 1/3, 0, 1/3, 是, 是, 是, 否, average_coverage_can_mask_failure_of_uniform_target)；依完整明示資料獨立重算；pointwise coverage與worst-case minimum逐theta重算；average不等於uniform，posterior不是coverage；selection納入procedure後須重新計算。"},"difficulty":{"band":"undergraduate_core","level":2,"skills":["有限模型信賴區間覆蓋率"]},"variant":{"family_id":"qf-mod49-ci-interpretation-boundary","seed":202611183092,"parameters":{"mode":"average_only","model":{"theta_values":[0,1],"samples":["a","b"],"probability_rows":[[[17,19],[2,19]],[[2,19],[17,19]]],"intervals":[[0,0],[0,0]],"theta_weights":[[1,3],[2,3]],"target":[1,3]},"domain":"Exact_finite_confidence_coverage","operation":"ci-interpretation-boundary","semantic_template":"ci-interpretation-boundary|{mode:\"average_only\",model:{intervals:[[[0,1],[0,1]],[[0,1],[0,1]]],probability_rows:[[[17,19],[2,19]],[[2,19],[17,19]]],samples:[\"a\",\"b\"],target:[1,3],theta:[0,1],theta_weights:[[1,3],[2,3]]}}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_or_symbolic_model","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"候選須主端重算；不構成一般limit theorem、coverage、number-theory或language theorem證明、人工審定、Lean或Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-15","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261015-advance-20261118-r03-finite-confidence-interval-coverage-0093","batch_id":"batch-20261015-advance-20261118-r03-finite-confidence-interval-coverage-foundations","language":"zh-Hant","source_mko_ids":["mko-finite-confidence-interval-coverage"],"title_zh":"有限模型信賴區間覆蓋率","stem_zh":"完整finite laws與total precommitted theta-independent interval procedure責任。操作=ci-interpretation-boundary；資料={\"mode\":\"posterior_confusion\",\"model\":{\"theta_values\":[0,1],\"samples\":[\"a\",\"b\"],\"probability_rows\":[[[18,20],[2,20]],[[2,20],[18,20]]],\"intervals\":[[0,0],[1,1]],\"prior\":[[2,4],[2,4]],\"observed\":\"b\"}}。請依 exact_ordered_tuple_declared_by_interface 欄序回答。","answer":{"kind":"expression","value":"(posterior_confusion, b, [1/10, 9/10], [[0, 9/10], [1, 9/10]], 否, posterior_given_observed_data_is_not_frequentist_coverage)","explanation_zh":"Wave6第十二層核對=(posterior_confusion, b, [1/10, 9/10], [[0, 9/10], [1, 9/10]], 否, posterior_given_observed_data_is_not_frequentist_coverage)；依完整明示資料獨立重算；pointwise coverage與worst-case minimum逐theta重算；average不等於uniform，posterior不是coverage；selection納入procedure後須重新計算。"},"difficulty":{"band":"undergraduate_core","level":3,"skills":["有限模型信賴區間覆蓋率"]},"variant":{"family_id":"qf-mod49-ci-interpretation-boundary","seed":202611183093,"parameters":{"mode":"posterior_confusion","model":{"theta_values":[0,1],"samples":["a","b"],"probability_rows":[[[18,20],[2,20]],[[2,20],[18,20]]],"intervals":[[0,0],[1,1]],"prior":[[2,4],[2,4]],"observed":"b"},"domain":"Exact_finite_confidence_coverage","operation":"ci-interpretation-boundary","semantic_template":"ci-interpretation-boundary|{mode:\"posterior_confusion\",model:{intervals:[[[0,1],[0,1]],[[1,1],[1,1]]],observed:\"b\",prior:[[1,2],[1,2]],probability_rows:[[[9,10],[1,10]],[[1,10],[9,10]]],samples:[\"a\",\"b\"],theta:[0,1]}}"}},"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；不構成一般limit theorem、coverage、number-theory或language theorem證明、人工審定、Lean或Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-15","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261015-advance-20261118-r03-finite-confidence-interval-coverage-0094","batch_id":"batch-20261015-advance-20261118-r03-finite-confidence-interval-coverage-foundations","language":"zh-Hant","source_mko_ids":["mko-finite-confidence-interval-coverage"],"title_zh":"有限模型信賴區間覆蓋率","stem_zh":"完整finite laws與total precommitted theta-independent interval procedure責任。操作=ci-interpretation-boundary；資料={\"mode\":\"ignored_selection\",\"model\":{\"theta_values\":[0,1],\"samples\":[\"a\",\"b\"],\"probability_rows\":[[[19,21],[2,21]],[[2,21],[19,21]]],\"intervals\":[[0,0],[1,1]],\"selected_samples\":[\"a\"]}}。請依 exact_ordered_tuple_declared_by_interface 欄序回答。","answer":{"kind":"expression","value":"(ignored_selection, [a], [[0, 19/21], [1, 19/21]], [[0, 19/21, 1], [1, 2/21, 0]], 否, selection_must_be_included_and_coverage_recomputed_not_declared_automatically_invalid)","explanation_zh":"Wave6第十二層核對=(ignored_selection, [a], [[0, 19/21], [1, 19/21]], [[0, 19/21, 1], [1, 2/21, 0]], 否, selection_must_be_included_and_coverage_recomputed_not_declared_automatically_invalid)；依完整明示資料獨立重算；pointwise coverage與worst-case minimum逐theta重算；average不等於uniform，posterior不是coverage；selection納入procedure後須重新計算。"},"difficulty":{"band":"undergraduate_core","level":3,"skills":["有限模型信賴區間覆蓋率"]},"variant":{"family_id":"qf-mod49-ci-interpretation-boundary","seed":202611183094,"parameters":{"mode":"ignored_selection","model":{"theta_values":[0,1],"samples":["a","b"],"probability_rows":[[[19,21],[2,21]],[[2,21],[19,21]]],"intervals":[[0,0],[1,1]],"selected_samples":["a"]},"domain":"Exact_finite_confidence_coverage","operation":"ci-interpretation-boundary","semantic_template":"ci-interpretation-boundary|{mode:\"ignored_selection\",model:{intervals:[[[0,1],[0,1]],[[1,1],[1,1]]],probability_rows:[[[19,21],[2,21]],[[2,21],[19,21]]],samples:[\"a\",\"b\"],selected_samples:[\"a\"],theta:[0,1]}}"}},"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；不構成一般limit theorem、coverage、number-theory或language theorem證明、人工審定、Lean或Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-15","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261015-advance-20261118-r03-finite-confidence-interval-coverage-0095","batch_id":"batch-20261015-advance-20261118-r03-finite-confidence-interval-coverage-foundations","language":"zh-Hant","source_mko_ids":["mko-finite-confidence-interval-coverage"],"title_zh":"有限模型信賴區間覆蓋率","stem_zh":"完整finite laws與total precommitted theta-independent interval procedure責任。操作=ci-interpretation-boundary；資料={\"mode\":\"invalid_procedure\",\"model\":{\"theta_values\":[0,1],\"samples\":[\"a\",\"b\"],\"probability_rows\":[[[20,22],[2,22]],[[2,22],[20,22]]],\"intervals\":[[20,19],[20,20]]}}。請依 exact_ordered_tuple_declared_by_interface 欄序回答。","answer":{"kind":"expression","value":"(invalid_procedure, 否, interval lower endpoint exceeds upper endpoint, 否)","explanation_zh":"Wave6第十二層核對=(invalid_procedure, 否, interval lower endpoint exceeds upper endpoint, 否)；依完整明示資料獨立重算；pointwise coverage與worst-case minimum逐theta重算；average不等於uniform，posterior不是coverage；selection納入procedure後須重新計算。"},"difficulty":{"band":"undergraduate_core","level":3,"skills":["有限模型信賴區間覆蓋率"]},"variant":{"family_id":"qf-mod49-ci-interpretation-boundary","seed":202611183095,"parameters":{"mode":"invalid_procedure","model":{"theta_values":[0,1],"samples":["a","b"],"probability_rows":[[[20,22],[2,22]],[[2,22],[20,22]]],"intervals":[[20,19],[20,20]]},"domain":"Exact_finite_confidence_coverage","operation":"ci-interpretation-boundary","semantic_template":"ci-interpretation-boundary|{mode:\"invalid_procedure\",model:{intervals:[[[20,1],[19,1]],[[20,1],[20,1]]],probability_rows:[[[10,11],[1,11]],[[1,11],[10,11]]],samples:[\"a\",\"b\"],theta:[0,1]}}"}},"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；不構成一般limit theorem、coverage、number-theory或language theorem證明、人工審定、Lean或Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-15","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261015-advance-20261118-r03-finite-confidence-interval-coverage-0096","batch_id":"batch-20261015-advance-20261118-r03-finite-confidence-interval-coverage-foundations","language":"zh-Hant","source_mko_ids":["mko-finite-confidence-interval-coverage"],"title_zh":"有限模型信賴區間覆蓋率","stem_zh":"完整finite laws與total precommitted theta-independent interval procedure責任。操作=ci-interpretation-boundary；資料={\"mode\":\"average_only\",\"model\":{\"theta_values\":[0,1],\"samples\":[\"a\",\"b\"],\"probability_rows\":[[[21,23],[2,23]],[[2,23],[21,23]]],\"intervals\":[[0,0],[0,0]],\"theta_weights\":[[1,3],[2,3]],\"target\":[1,3]}}。請依 exact_ordered_tuple_declared_by_interface 欄序回答。","answer":{"kind":"expression","value":"(average_only, [[0, 1], [1, 0]], [1/3, 2/3], 1/3, 0, 1/3, 是, 是, 是, 否, average_coverage_can_mask_failure_of_uniform_target)","explanation_zh":"Wave6第十二層核對=(average_only, [[0, 1], [1, 0]], [1/3, 2/3], 1/3, 0, 1/3, 是, 是, 是, 否, average_coverage_can_mask_failure_of_uniform_target)；依完整明示資料獨立重算；pointwise coverage與worst-case minimum逐theta重算；average不等於uniform，posterior不是coverage；selection納入procedure後須重新計算。"},"difficulty":{"band":"undergraduate_core","level":3,"skills":["有限模型信賴區間覆蓋率"]},"variant":{"family_id":"qf-mod49-ci-interpretation-boundary","seed":202611183096,"parameters":{"mode":"average_only","model":{"theta_values":[0,1],"samples":["a","b"],"probability_rows":[[[21,23],[2,23]],[[2,23],[21,23]]],"intervals":[[0,0],[0,0]],"theta_weights":[[1,3],[2,3]],"target":[1,3]},"domain":"Exact_finite_confidence_coverage","operation":"ci-interpretation-boundary","semantic_template":"ci-interpretation-boundary|{mode:\"average_only\",model:{intervals:[[[0,1],[0,1]],[[0,1],[0,1]]],probability_rows:[[[21,23],[2,23]],[[2,23],[21,23]]],samples:[\"a\",\"b\"],target:[1,3],theta:[0,1],theta_weights:[[1,3],[2,3]]}}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_or_symbolic_model","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"候選須主端重算；不構成一般limit theorem、coverage、number-theory或language theorem證明、人工審定、Lean或Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-15","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261015-advance-20261118-r03-finite-confidence-interval-coverage-0097","batch_id":"batch-20261015-advance-20261118-r03-finite-confidence-interval-coverage-foundations","language":"zh-Hant","source_mko_ids":["mko-finite-confidence-interval-coverage"],"title_zh":"有限模型信賴區間覆蓋率","stem_zh":"完整finite laws與total precommitted theta-independent interval procedure責任。操作=ci-interpretation-boundary；資料={\"mode\":\"posterior_confusion\",\"model\":{\"theta_values\":[0,1],\"samples\":[\"a\",\"b\"],\"probability_rows\":[[[22,24],[2,24]],[[2,24],[22,24]]],\"intervals\":[[0,0],[1,1]],\"prior\":[[2,4],[2,4]],\"observed\":\"b\"}}。請依 exact_ordered_tuple_declared_by_interface 欄序回答。","answer":{"kind":"expression","value":"(posterior_confusion, b, [1/12, 11/12], [[0, 11/12], [1, 11/12]], 否, posterior_given_observed_data_is_not_frequentist_coverage)","explanation_zh":"Wave6第十二層核對=(posterior_confusion, b, [1/12, 11/12], [[0, 11/12], [1, 11/12]], 否, posterior_given_observed_data_is_not_frequentist_coverage)；依完整明示資料獨立重算；pointwise coverage與worst-case minimum逐theta重算；average不等於uniform，posterior不是coverage；selection納入procedure後須重新計算。"},"difficulty":{"band":"undergraduate_core","level":3,"skills":["有限模型信賴區間覆蓋率"]},"variant":{"family_id":"qf-mod49-ci-interpretation-boundary","seed":202611183097,"parameters":{"mode":"posterior_confusion","model":{"theta_values":[0,1],"samples":["a","b"],"probability_rows":[[[22,24],[2,24]],[[2,24],[22,24]]],"intervals":[[0,0],[1,1]],"prior":[[2,4],[2,4]],"observed":"b"},"domain":"Exact_finite_confidence_coverage","operation":"ci-interpretation-boundary","semantic_template":"ci-interpretation-boundary|{mode:\"posterior_confusion\",model:{intervals:[[[0,1],[0,1]],[[1,1],[1,1]]],observed:\"b\",prior:[[1,2],[1,2]],probability_rows:[[[11,12],[1,12]],[[1,12],[11,12]]],samples:[\"a\",\"b\"],theta:[0,1]}}"}},"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；不構成一般limit theorem、coverage、number-theory或language theorem證明、人工審定、Lean或Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-15","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261015-advance-20261118-r03-finite-confidence-interval-coverage-0098","batch_id":"batch-20261015-advance-20261118-r03-finite-confidence-interval-coverage-foundations","language":"zh-Hant","source_mko_ids":["mko-finite-confidence-interval-coverage"],"title_zh":"有限模型信賴區間覆蓋率","stem_zh":"完整finite laws與total precommitted theta-independent interval procedure責任。操作=ci-interpretation-boundary；資料={\"mode\":\"ignored_selection\",\"model\":{\"theta_values\":[0,1],\"samples\":[\"a\",\"b\"],\"probability_rows\":[[[23,25],[2,25]],[[2,25],[23,25]]],\"intervals\":[[0,0],[1,1]],\"selected_samples\":[\"a\"]}}。請依 exact_ordered_tuple_declared_by_interface 欄序回答。","answer":{"kind":"expression","value":"(ignored_selection, [a], [[0, 23/25], [1, 23/25]], [[0, 23/25, 1], [1, 2/25, 0]], 否, selection_must_be_included_and_coverage_recomputed_not_declared_automatically_invalid)","explanation_zh":"Wave6第十二層核對=(ignored_selection, [a], [[0, 23/25], [1, 23/25]], [[0, 23/25, 1], [1, 2/25, 0]], 否, selection_must_be_included_and_coverage_recomputed_not_declared_automatically_invalid)；依完整明示資料獨立重算；pointwise coverage與worst-case minimum逐theta重算；average不等於uniform，posterior不是coverage；selection納入procedure後須重新計算。"},"difficulty":{"band":"undergraduate_core","level":3,"skills":["有限模型信賴區間覆蓋率"]},"variant":{"family_id":"qf-mod49-ci-interpretation-boundary","seed":202611183098,"parameters":{"mode":"ignored_selection","model":{"theta_values":[0,1],"samples":["a","b"],"probability_rows":[[[23,25],[2,25]],[[2,25],[23,25]]],"intervals":[[0,0],[1,1]],"selected_samples":["a"]},"domain":"Exact_finite_confidence_coverage","operation":"ci-interpretation-boundary","semantic_template":"ci-interpretation-boundary|{mode:\"ignored_selection\",model:{intervals:[[[0,1],[0,1]],[[1,1],[1,1]]],probability_rows:[[[23,25],[2,25]],[[2,25],[23,25]]],samples:[\"a\",\"b\"],selected_samples:[\"a\"],theta:[0,1]}}"}},"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；不構成一般limit theorem、coverage、number-theory或language theorem證明、人工審定、Lean或Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-15","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261015-advance-20261118-r03-finite-confidence-interval-coverage-0099","batch_id":"batch-20261015-advance-20261118-r03-finite-confidence-interval-coverage-foundations","language":"zh-Hant","source_mko_ids":["mko-finite-confidence-interval-coverage"],"title_zh":"有限模型信賴區間覆蓋率","stem_zh":"完整finite laws與total precommitted theta-independent interval procedure責任。操作=ci-interpretation-boundary；資料={\"mode\":\"invalid_procedure\",\"model\":{\"theta_values\":[0,1],\"samples\":[\"a\",\"b\"],\"probability_rows\":[[[24,26],[2,26]],[[2,26],[24,26]]],\"intervals\":[[24,23],[24,24]]}}。請依 exact_ordered_tuple_declared_by_interface 欄序回答。","answer":{"kind":"expression","value":"(invalid_procedure, 否, interval lower endpoint exceeds upper endpoint, 否)","explanation_zh":"Wave6第十二層核對=(invalid_procedure, 否, interval lower endpoint exceeds upper endpoint, 否)；依完整明示資料獨立重算；pointwise coverage與worst-case minimum逐theta重算；average不等於uniform，posterior不是coverage；selection納入procedure後須重新計算。"},"difficulty":{"band":"undergraduate_core","level":3,"skills":["有限模型信賴區間覆蓋率"]},"variant":{"family_id":"qf-mod49-ci-interpretation-boundary","seed":202611183099,"parameters":{"mode":"invalid_procedure","model":{"theta_values":[0,1],"samples":["a","b"],"probability_rows":[[[24,26],[2,26]],[[2,26],[24,26]]],"intervals":[[24,23],[24,24]]},"domain":"Exact_finite_confidence_coverage","operation":"ci-interpretation-boundary","semantic_template":"ci-interpretation-boundary|{mode:\"invalid_procedure\",model:{intervals:[[[24,1],[23,1]],[[24,1],[24,1]]],probability_rows:[[[12,13],[1,13]],[[1,13],[12,13]]],samples:[\"a\",\"b\"],theta:[0,1]}}"}},"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；不構成一般limit theorem、coverage、number-theory或language theorem證明、人工審定、Lean或Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-15","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261015-advance-20261118-r03-finite-confidence-interval-coverage-0100","batch_id":"batch-20261015-advance-20261118-r03-finite-confidence-interval-coverage-foundations","language":"zh-Hant","source_mko_ids":["mko-finite-confidence-interval-coverage"],"title_zh":"有限模型信賴區間覆蓋率","stem_zh":"完整finite laws與total precommitted theta-independent interval procedure責任。操作=ci-interpretation-boundary；資料={\"mode\":\"average_only\",\"model\":{\"theta_values\":[0,1],\"samples\":[\"a\",\"b\"],\"probability_rows\":[[[25,27],[2,27]],[[2,27],[25,27]]],\"intervals\":[[0,0],[0,0]],\"theta_weights\":[[1,3],[2,3]],\"target\":[1,3]}}。請依 exact_ordered_tuple_declared_by_interface 欄序回答。","answer":{"kind":"expression","value":"(average_only, [[0, 1], [1, 0]], [1/3, 2/3], 1/3, 0, 1/3, 是, 是, 是, 否, average_coverage_can_mask_failure_of_uniform_target)","explanation_zh":"Wave6第十二層核對=(average_only, [[0, 1], [1, 0]], [1/3, 2/3], 1/3, 0, 1/3, 是, 是, 是, 否, average_coverage_can_mask_failure_of_uniform_target)；依完整明示資料獨立重算；pointwise coverage與worst-case minimum逐theta重算；average不等於uniform，posterior不是coverage；selection納入procedure後須重新計算。"},"difficulty":{"band":"undergraduate_core","level":3,"skills":["有限模型信賴區間覆蓋率"]},"variant":{"family_id":"qf-mod49-ci-interpretation-boundary","seed":202611183100,"parameters":{"mode":"average_only","model":{"theta_values":[0,1],"samples":["a","b"],"probability_rows":[[[25,27],[2,27]],[[2,27],[25,27]]],"intervals":[[0,0],[0,0]],"theta_weights":[[1,3],[2,3]],"target":[1,3]},"domain":"Exact_finite_confidence_coverage","operation":"ci-interpretation-boundary","semantic_template":"ci-interpretation-boundary|{mode:\"average_only\",model:{intervals:[[[0,1],[0,1]],[[0,1],[0,1]]],probability_rows:[[[25,27],[2,27]],[[2,27],[25,27]]],samples:[\"a\",\"b\"],target:[1,3],theta:[0,1],theta_weights:[[1,3],[2,3]]}}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_or_symbolic_model","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"候選須主端重算；不構成一般limit theorem、coverage、number-theory或language theorem證明、人工審定、Lean或Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-15","contract_version":"ocme-question-factory-v0.1"}}