{"schema_version":"ocme-question-v0.1","id":"q-20261015-pulse-20261119-r02-0001","batch_id":"batch-20261015-advance-20261119-r02-trapezoidal-quadrature-foundations","language":"zh-Hant","source_mko_ids":["mko-trapezoidal-quadrature"],"title_zh":"複合梯形法","stem_zh":"嚴格遞增partition、n+1 nodes與逐subinterval寬度。操作=trap-partition-qualification；明示資料={\"nodes\":[0,1,3],\"values\":[0,1,3]}；請依 exact_ordered_tuple_declared_by_interface 回答。","answer":{"kind":"expression","value":"([0, 1, 3], [0, 1, 3], 2, 3, [1, 2], 是, n_subintervals_have_n_plus_one_nodes)","explanation_zh":"Wave6第十三層核對=([0, 1, 3], [0, 1, 3], 2, 3, [1, 2], 是, n_subintervals_have_n_plus_one_nodes)；依完整明示資料精確重算；複合梯形逐段使用endpoint average與自己的width；signed error固定為I-T；affine exact或指定quadratic reference不推出一般誤差界、收斂階或唯一integrand。"},"difficulty":{"band":"undergraduate_core","level":1,"skills":["複合梯形法"]},"variant":{"family_id":"qf-mod50-trap-partition-qualification","seed":202611192001,"parameters":{"nodes":[0,1,3],"values":[0,1,3],"domain":"Exact_composite_trapezoidal_quadrature","operation":"trap-partition-qualification","semantic_template":"trap-partition-qualification|{\"nodes\":[[0,1],[1,1],[3,1]],\"values\":[[0,1],[1,1],[3,1]]}"}},"verification":{"status":"candidate","checks":["producer_contract_recomputation","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"candidate 僅對明示有限或符號模型重算；不構成一般定理、人工審定、Lean 或 Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"GPT-5.6 Terra","generated_at":"2026-10-15","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261015-pulse-20261119-r02-0002","batch_id":"batch-20261015-advance-20261119-r02-trapezoidal-quadrature-foundations","language":"zh-Hant","source_mko_ids":["mko-trapezoidal-quadrature"],"title_zh":"複合梯形法","stem_zh":"嚴格遞增partition、n+1 nodes與逐subinterval寬度。操作=trap-partition-qualification；明示資料={\"nodes\":[0,1,4],\"values\":[1,2,4]}；請依 exact_ordered_tuple_declared_by_interface 回答。","answer":{"kind":"expression","value":"([0, 1, 4], [1, 2, 4], 2, 3, [1, 3], 是, n_subintervals_have_n_plus_one_nodes)","explanation_zh":"Wave6第十三層核對=([0, 1, 4], [1, 2, 4], 2, 3, [1, 3], 是, n_subintervals_have_n_plus_one_nodes)；依完整明示資料精確重算；複合梯形逐段使用endpoint average與自己的width；signed error固定為I-T；affine exact或指定quadratic reference不推出一般誤差界、收斂階或唯一integrand。"},"difficulty":{"band":"undergraduate_core","level":1,"skills":["複合梯形法"]},"variant":{"family_id":"qf-mod50-trap-partition-qualification","seed":202611192002,"parameters":{"nodes":[0,1,4],"values":[1,2,4],"domain":"Exact_composite_trapezoidal_quadrature","operation":"trap-partition-qualification","semantic_template":"trap-partition-qualification|{\"nodes\":[[0,1],[1,1],[4,1]],\"values\":[[1,1],[2,1],[4,1]]}"}},"verification":{"status":"candidate","checks":["producer_contract_recomputation","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"candidate 僅對明示有限或符號模型重算；不構成一般定理、人工審定、Lean 或 Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"GPT-5.6 Terra","generated_at":"2026-10-15","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261015-pulse-20261119-r02-0003","batch_id":"batch-20261015-advance-20261119-r02-trapezoidal-quadrature-foundations","language":"zh-Hant","source_mko_ids":["mko-trapezoidal-quadrature"],"title_zh":"複合梯形法","stem_zh":"嚴格遞增partition、n+1 nodes與逐subinterval寬度。操作=trap-partition-qualification；明示資料={\"nodes\":[0,1,5],\"values\":[2,3,5]}；請依 exact_ordered_tuple_declared_by_interface 回答。","answer":{"kind":"expression","value":"([0, 1, 5], [2, 3, 5], 2, 3, [1, 4], 是, n_subintervals_have_n_plus_one_nodes)","explanation_zh":"Wave6第十三層核對=([0, 1, 5], [2, 3, 5], 2, 3, [1, 4], 是, n_subintervals_have_n_plus_one_nodes)；依完整明示資料精確重算；複合梯形逐段使用endpoint average與自己的width；signed error固定為I-T；affine exact或指定quadratic reference不推出一般誤差界、收斂階或唯一integrand。"},"difficulty":{"band":"undergraduate_core","level":1,"skills":["複合梯形法"]},"variant":{"family_id":"qf-mod50-trap-partition-qualification","seed":202611192003,"parameters":{"nodes":[0,1,5],"values":[2,3,5],"domain":"Exact_composite_trapezoidal_quadrature","operation":"trap-partition-qualification","semantic_template":"trap-partition-qualification|{\"nodes\":[[0,1],[1,1],[5,1]],\"values\":[[2,1],[3,1],[5,1]]}"}},"verification":{"status":"candidate","checks":["producer_contract_recomputation","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"candidate 僅對明示有限或符號模型重算；不構成一般定理、人工審定、Lean 或 Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"GPT-5.6 Terra","generated_at":"2026-10-15","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261015-pulse-20261119-r02-0004","batch_id":"batch-20261015-advance-20261119-r02-trapezoidal-quadrature-foundations","language":"zh-Hant","source_mko_ids":["mko-trapezoidal-quadrature"],"title_zh":"複合梯形法","stem_zh":"嚴格遞增partition、n+1 nodes與逐subinterval寬度。操作=trap-partition-qualification；明示資料={\"nodes\":[0,1,6],\"values\":[3,4,6]}；請依 exact_ordered_tuple_declared_by_interface 回答。","answer":{"kind":"expression","value":"([0, 1, 6], [3, 4, 6], 2, 3, [1, 5], 是, n_subintervals_have_n_plus_one_nodes)","explanation_zh":"Wave6第十三層核對=([0, 1, 6], [3, 4, 6], 2, 3, [1, 5], 是, n_subintervals_have_n_plus_one_nodes)；依完整明示資料精確重算；複合梯形逐段使用endpoint average與自己的width；signed error固定為I-T；affine exact或指定quadratic reference不推出一般誤差界、收斂階或唯一integrand。"},"difficulty":{"band":"undergraduate_core","level":1,"skills":["複合梯形法"]},"variant":{"family_id":"qf-mod50-trap-partition-qualification","seed":202611192004,"parameters":{"nodes":[0,1,6],"values":[3,4,6],"domain":"Exact_composite_trapezoidal_quadrature","operation":"trap-partition-qualification","semantic_template":"trap-partition-qualification|{\"nodes\":[[0,1],[1,1],[6,1]],\"values\":[[3,1],[4,1],[6,1]]}"}},"verification":{"status":"candidate","checks":["producer_contract_recomputation","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"candidate 僅對明示有限或符號模型重算；不構成一般定理、人工審定、Lean 或 Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"GPT-5.6 Terra","generated_at":"2026-10-15","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261015-pulse-20261119-r02-0005","batch_id":"batch-20261015-advance-20261119-r02-trapezoidal-quadrature-foundations","language":"zh-Hant","source_mko_ids":["mko-trapezoidal-quadrature"],"title_zh":"複合梯形法","stem_zh":"嚴格遞增partition、n+1 nodes與逐subinterval寬度。操作=trap-partition-qualification；明示資料={\"nodes\":[0,1,7],\"values\":[4,5,7]}；請依 exact_ordered_tuple_declared_by_interface 回答。","answer":{"kind":"expression","value":"([0, 1, 7], [4, 5, 7], 2, 3, [1, 6], 是, n_subintervals_have_n_plus_one_nodes)","explanation_zh":"Wave6第十三層核對=([0, 1, 7], [4, 5, 7], 2, 3, [1, 6], 是, n_subintervals_have_n_plus_one_nodes)；依完整明示資料精確重算；複合梯形逐段使用endpoint average與自己的width；signed error固定為I-T；affine exact或指定quadratic reference不推出一般誤差界、收斂階或唯一integrand。"},"difficulty":{"band":"undergraduate_core","level":1,"skills":["複合梯形法"]},"variant":{"family_id":"qf-mod50-trap-partition-qualification","seed":202611192005,"parameters":{"nodes":[0,1,7],"values":[4,5,7],"domain":"Exact_composite_trapezoidal_quadrature","operation":"trap-partition-qualification","semantic_template":"trap-partition-qualification|{\"nodes\":[[0,1],[1,1],[7,1]],\"values\":[[4,1],[5,1],[7,1]]}"}},"verification":{"status":"candidate","checks":["producer_contract_recomputation","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"candidate 僅對明示有限或符號模型重算；不構成一般定理、人工審定、Lean 或 Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"GPT-5.6 Terra","generated_at":"2026-10-15","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261015-pulse-20261119-r02-0006","batch_id":"batch-20261015-advance-20261119-r02-trapezoidal-quadrature-foundations","language":"zh-Hant","source_mko_ids":["mko-trapezoidal-quadrature"],"title_zh":"複合梯形法","stem_zh":"嚴格遞增partition、n+1 nodes與逐subinterval寬度。操作=trap-partition-qualification；明示資料={\"nodes\":[0,1,8],\"values\":[5,6,8]}；請依 exact_ordered_tuple_declared_by_interface 回答。","answer":{"kind":"expression","value":"([0, 1, 8], [5, 6, 8], 2, 3, [1, 7], 是, n_subintervals_have_n_plus_one_nodes)","explanation_zh":"Wave6第十三層核對=([0, 1, 8], [5, 6, 8], 2, 3, [1, 7], 是, n_subintervals_have_n_plus_one_nodes)；依完整明示資料精確重算；複合梯形逐段使用endpoint average與自己的width；signed error固定為I-T；affine exact或指定quadratic reference不推出一般誤差界、收斂階或唯一integrand。"},"difficulty":{"band":"undergraduate_core","level":1,"skills":["複合梯形法"]},"variant":{"family_id":"qf-mod50-trap-partition-qualification","seed":202611192006,"parameters":{"nodes":[0,1,8],"values":[5,6,8],"domain":"Exact_composite_trapezoidal_quadrature","operation":"trap-partition-qualification","semantic_template":"trap-partition-qualification|{\"nodes\":[[0,1],[1,1],[8,1]],\"values\":[[5,1],[6,1],[8,1]]}"}},"verification":{"status":"candidate","checks":["producer_contract_recomputation","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"candidate 僅對明示有限或符號模型重算；不構成一般定理、人工審定、Lean 或 Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"GPT-5.6 Terra","generated_at":"2026-10-15","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261015-pulse-20261119-r02-0007","batch_id":"batch-20261015-advance-20261119-r02-trapezoidal-quadrature-foundations","language":"zh-Hant","source_mko_ids":["mko-trapezoidal-quadrature"],"title_zh":"複合梯形法","stem_zh":"嚴格遞增partition、n+1 nodes與逐subinterval寬度。操作=trap-partition-qualification；明示資料={\"nodes\":[0,1,9],\"values\":[6,7,9]}；請依 exact_ordered_tuple_declared_by_interface 回答。","answer":{"kind":"expression","value":"([0, 1, 9], [6, 7, 9], 2, 3, [1, 8], 是, n_subintervals_have_n_plus_one_nodes)","explanation_zh":"Wave6第十三層核對=([0, 1, 9], [6, 7, 9], 2, 3, [1, 8], 是, n_subintervals_have_n_plus_one_nodes)；依完整明示資料精確重算；複合梯形逐段使用endpoint average與自己的width；signed error固定為I-T；affine exact或指定quadratic reference不推出一般誤差界、收斂階或唯一integrand。"},"difficulty":{"band":"undergraduate_core","level":1,"skills":["複合梯形法"]},"variant":{"family_id":"qf-mod50-trap-partition-qualification","seed":202611192007,"parameters":{"nodes":[0,1,9],"values":[6,7,9],"domain":"Exact_composite_trapezoidal_quadrature","operation":"trap-partition-qualification","semantic_template":"trap-partition-qualification|{\"nodes\":[[0,1],[1,1],[9,1]],\"values\":[[6,1],[7,1],[9,1]]}"}},"verification":{"status":"candidate","checks":["producer_contract_recomputation","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"candidate 僅對明示有限或符號模型重算；不構成一般定理、人工審定、Lean 或 Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"GPT-5.6 Terra","generated_at":"2026-10-15","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261015-pulse-20261119-r02-0008","batch_id":"batch-20261015-advance-20261119-r02-trapezoidal-quadrature-foundations","language":"zh-Hant","source_mko_ids":["mko-trapezoidal-quadrature"],"title_zh":"複合梯形法","stem_zh":"嚴格遞增partition、n+1 nodes與逐subinterval寬度。操作=trap-partition-qualification；明示資料={\"nodes\":[0,1,10],\"values\":[7,8,10]}；請依 exact_ordered_tuple_declared_by_interface 回答。","answer":{"kind":"expression","value":"([0, 1, 10], [7, 8, 10], 2, 3, [1, 9], 是, n_subintervals_have_n_plus_one_nodes)","explanation_zh":"Wave6第十三層核對=([0, 1, 10], [7, 8, 10], 2, 3, [1, 9], 是, n_subintervals_have_n_plus_one_nodes)；依完整明示資料精確重算；複合梯形逐段使用endpoint average與自己的width；signed error固定為I-T；affine exact或指定quadratic reference不推出一般誤差界、收斂階或唯一integrand。"},"difficulty":{"band":"undergraduate_core","level":1,"skills":["複合梯形法"]},"variant":{"family_id":"qf-mod50-trap-partition-qualification","seed":202611192008,"parameters":{"nodes":[0,1,10],"values":[7,8,10],"domain":"Exact_composite_trapezoidal_quadrature","operation":"trap-partition-qualification","semantic_template":"trap-partition-qualification|{\"nodes\":[[0,1],[1,1],[10,1]],\"values\":[[7,1],[8,1],[10,1]]}"}},"verification":{"status":"candidate","checks":["producer_contract_recomputation","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"candidate 僅對明示有限或符號模型重算；不構成一般定理、人工審定、Lean 或 Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"GPT-5.6 Terra","generated_at":"2026-10-15","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261015-pulse-20261119-r02-0009","batch_id":"batch-20261015-advance-20261119-r02-trapezoidal-quadrature-foundations","language":"zh-Hant","source_mko_ids":["mko-trapezoidal-quadrature"],"title_zh":"複合梯形法","stem_zh":"嚴格遞增partition、n+1 nodes與逐subinterval寬度。操作=trap-partition-qualification；明示資料={\"nodes\":[0,1,11],\"values\":[8,9,11]}；請依 exact_ordered_tuple_declared_by_interface 回答。","answer":{"kind":"expression","value":"([0, 1, 11], [8, 9, 11], 2, 3, [1, 10], 是, n_subintervals_have_n_plus_one_nodes)","explanation_zh":"Wave6第十三層核對=([0, 1, 11], [8, 9, 11], 2, 3, [1, 10], 是, n_subintervals_have_n_plus_one_nodes)；依完整明示資料精確重算；複合梯形逐段使用endpoint average與自己的width；signed error固定為I-T；affine exact或指定quadratic reference不推出一般誤差界、收斂階或唯一integrand。"},"difficulty":{"band":"undergraduate_core","level":2,"skills":["複合梯形法"]},"variant":{"family_id":"qf-mod50-trap-partition-qualification","seed":202611192009,"parameters":{"nodes":[0,1,11],"values":[8,9,11],"domain":"Exact_composite_trapezoidal_quadrature","operation":"trap-partition-qualification","semantic_template":"trap-partition-qualification|{\"nodes\":[[0,1],[1,1],[11,1]],\"values\":[[8,1],[9,1],[11,1]]}"}},"verification":{"status":"candidate","checks":["producer_contract_recomputation","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"candidate 僅對明示有限或符號模型重算；不構成一般定理、人工審定、Lean 或 Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"GPT-5.6 Terra","generated_at":"2026-10-15","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261015-pulse-20261119-r02-0010","batch_id":"batch-20261015-advance-20261119-r02-trapezoidal-quadrature-foundations","language":"zh-Hant","source_mko_ids":["mko-trapezoidal-quadrature"],"title_zh":"複合梯形法","stem_zh":"嚴格遞增partition、n+1 nodes與逐subinterval寬度。操作=trap-partition-qualification；明示資料={\"nodes\":[0,1,12],\"values\":[9,10,12]}；請依 exact_ordered_tuple_declared_by_interface 回答。","answer":{"kind":"expression","value":"([0, 1, 12], [9, 10, 12], 2, 3, [1, 11], 是, n_subintervals_have_n_plus_one_nodes)","explanation_zh":"Wave6第十三層核對=([0, 1, 12], [9, 10, 12], 2, 3, [1, 11], 是, n_subintervals_have_n_plus_one_nodes)；依完整明示資料精確重算；複合梯形逐段使用endpoint average與自己的width；signed error固定為I-T；affine exact或指定quadratic reference不推出一般誤差界、收斂階或唯一integrand。"},"difficulty":{"band":"undergraduate_core","level":2,"skills":["複合梯形法"]},"variant":{"family_id":"qf-mod50-trap-partition-qualification","seed":202611192010,"parameters":{"nodes":[0,1,12],"values":[9,10,12],"domain":"Exact_composite_trapezoidal_quadrature","operation":"trap-partition-qualification","semantic_template":"trap-partition-qualification|{\"nodes\":[[0,1],[1,1],[12,1]],\"values\":[[9,1],[10,1],[12,1]]}"}},"verification":{"status":"candidate","checks":["producer_contract_recomputation","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"candidate 僅對明示有限或符號模型重算；不構成一般定理、人工審定、Lean 或 Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"GPT-5.6 Terra","generated_at":"2026-10-15","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261015-pulse-20261119-r02-0011","batch_id":"batch-20261015-advance-20261119-r02-trapezoidal-quadrature-foundations","language":"zh-Hant","source_mko_ids":["mko-trapezoidal-quadrature"],"title_zh":"複合梯形法","stem_zh":"嚴格遞增partition、n+1 nodes與逐subinterval寬度。操作=trap-partition-qualification；明示資料={\"nodes\":[0,1,13],\"values\":[10,11,13]}；請依 exact_ordered_tuple_declared_by_interface 回答。","answer":{"kind":"expression","value":"([0, 1, 13], [10, 11, 13], 2, 3, [1, 12], 是, n_subintervals_have_n_plus_one_nodes)","explanation_zh":"Wave6第十三層核對=([0, 1, 13], [10, 11, 13], 2, 3, [1, 12], 是, n_subintervals_have_n_plus_one_nodes)；依完整明示資料精確重算；複合梯形逐段使用endpoint average與自己的width；signed error固定為I-T；affine exact或指定quadratic reference不推出一般誤差界、收斂階或唯一integrand。"},"difficulty":{"band":"undergraduate_core","level":2,"skills":["複合梯形法"]},"variant":{"family_id":"qf-mod50-trap-partition-qualification","seed":202611192011,"parameters":{"nodes":[0,1,13],"values":[10,11,13],"domain":"Exact_composite_trapezoidal_quadrature","operation":"trap-partition-qualification","semantic_template":"trap-partition-qualification|{\"nodes\":[[0,1],[1,1],[13,1]],\"values\":[[10,1],[11,1],[13,1]]}"}},"verification":{"status":"candidate","checks":["producer_contract_recomputation","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"candidate 僅對明示有限或符號模型重算；不構成一般定理、人工審定、Lean 或 Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"GPT-5.6 Terra","generated_at":"2026-10-15","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261015-pulse-20261119-r02-0012","batch_id":"batch-20261015-advance-20261119-r02-trapezoidal-quadrature-foundations","language":"zh-Hant","source_mko_ids":["mko-trapezoidal-quadrature"],"title_zh":"複合梯形法","stem_zh":"嚴格遞增partition、n+1 nodes與逐subinterval寬度。操作=trap-partition-qualification；明示資料={\"nodes\":[0,1,14],\"values\":[11,12,14]}；請依 exact_ordered_tuple_declared_by_interface 回答。","answer":{"kind":"expression","value":"([0, 1, 14], [11, 12, 14], 2, 3, [1, 13], 是, n_subintervals_have_n_plus_one_nodes)","explanation_zh":"Wave6第十三層核對=([0, 1, 14], [11, 12, 14], 2, 3, [1, 13], 是, n_subintervals_have_n_plus_one_nodes)；依完整明示資料精確重算；複合梯形逐段使用endpoint average與自己的width；signed error固定為I-T；affine exact或指定quadratic reference不推出一般誤差界、收斂階或唯一integrand。"},"difficulty":{"band":"undergraduate_core","level":2,"skills":["複合梯形法"]},"variant":{"family_id":"qf-mod50-trap-partition-qualification","seed":202611192012,"parameters":{"nodes":[0,1,14],"values":[11,12,14],"domain":"Exact_composite_trapezoidal_quadrature","operation":"trap-partition-qualification","semantic_template":"trap-partition-qualification|{\"nodes\":[[0,1],[1,1],[14,1]],\"values\":[[11,1],[12,1],[14,1]]}"}},"verification":{"status":"candidate","checks":["producer_contract_recomputation","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"candidate 僅對明示有限或符號模型重算；不構成一般定理、人工審定、Lean 或 Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"GPT-5.6 Terra","generated_at":"2026-10-15","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261015-pulse-20261119-r02-0013","batch_id":"batch-20261015-advance-20261119-r02-trapezoidal-quadrature-foundations","language":"zh-Hant","source_mko_ids":["mko-trapezoidal-quadrature"],"title_zh":"複合梯形法","stem_zh":"嚴格遞增partition、n+1 nodes與逐subinterval寬度。操作=trap-partition-qualification；明示資料={\"nodes\":[0,1,15],\"values\":[12,13,15]}；請依 exact_ordered_tuple_declared_by_interface 回答。","answer":{"kind":"expression","value":"([0, 1, 15], [12, 13, 15], 2, 3, [1, 14], 是, n_subintervals_have_n_plus_one_nodes)","explanation_zh":"Wave6第十三層核對=([0, 1, 15], [12, 13, 15], 2, 3, [1, 14], 是, n_subintervals_have_n_plus_one_nodes)；依完整明示資料精確重算；複合梯形逐段使用endpoint average與自己的width；signed error固定為I-T；affine exact或指定quadratic reference不推出一般誤差界、收斂階或唯一integrand。"},"difficulty":{"band":"undergraduate_core","level":2,"skills":["複合梯形法"]},"variant":{"family_id":"qf-mod50-trap-partition-qualification","seed":202611192013,"parameters":{"nodes":[0,1,15],"values":[12,13,15],"domain":"Exact_composite_trapezoidal_quadrature","operation":"trap-partition-qualification","semantic_template":"trap-partition-qualification|{\"nodes\":[[0,1],[1,1],[15,1]],\"values\":[[12,1],[13,1],[15,1]]}"}},"verification":{"status":"candidate","checks":["producer_contract_recomputation","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"candidate 僅對明示有限或符號模型重算；不構成一般定理、人工審定、Lean 或 Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"GPT-5.6 Terra","generated_at":"2026-10-15","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261015-pulse-20261119-r02-0014","batch_id":"batch-20261015-advance-20261119-r02-trapezoidal-quadrature-foundations","language":"zh-Hant","source_mko_ids":["mko-trapezoidal-quadrature"],"title_zh":"複合梯形法","stem_zh":"嚴格遞增partition、n+1 nodes與逐subinterval寬度。操作=trap-partition-qualification；明示資料={\"nodes\":[0,1,16],\"values\":[13,14,16]}；請依 exact_ordered_tuple_declared_by_interface 回答。","answer":{"kind":"expression","value":"([0, 1, 16], [13, 14, 16], 2, 3, [1, 15], 是, n_subintervals_have_n_plus_one_nodes)","explanation_zh":"Wave6第十三層核對=([0, 1, 16], [13, 14, 16], 2, 3, [1, 15], 是, n_subintervals_have_n_plus_one_nodes)；依完整明示資料精確重算；複合梯形逐段使用endpoint average與自己的width；signed error固定為I-T；affine exact或指定quadratic reference不推出一般誤差界、收斂階或唯一integrand。"},"difficulty":{"band":"undergraduate_core","level":2,"skills":["複合梯形法"]},"variant":{"family_id":"qf-mod50-trap-partition-qualification","seed":202611192014,"parameters":{"nodes":[0,1,16],"values":[13,14,16],"domain":"Exact_composite_trapezoidal_quadrature","operation":"trap-partition-qualification","semantic_template":"trap-partition-qualification|{\"nodes\":[[0,1],[1,1],[16,1]],\"values\":[[13,1],[14,1],[16,1]]}"}},"verification":{"status":"candidate","checks":["producer_contract_recomputation","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"candidate 僅對明示有限或符號模型重算；不構成一般定理、人工審定、Lean 或 Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"GPT-5.6 Terra","generated_at":"2026-10-15","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261015-pulse-20261119-r02-0015","batch_id":"batch-20261015-advance-20261119-r02-trapezoidal-quadrature-foundations","language":"zh-Hant","source_mko_ids":["mko-trapezoidal-quadrature"],"title_zh":"複合梯形法","stem_zh":"嚴格遞增partition、n+1 nodes與逐subinterval寬度。操作=trap-partition-qualification；明示資料={\"nodes\":[0,1,17],\"values\":[14,15,17]}；請依 exact_ordered_tuple_declared_by_interface 回答。","answer":{"kind":"expression","value":"([0, 1, 17], [14, 15, 17], 2, 3, [1, 16], 是, n_subintervals_have_n_plus_one_nodes)","explanation_zh":"Wave6第十三層核對=([0, 1, 17], [14, 15, 17], 2, 3, [1, 16], 是, n_subintervals_have_n_plus_one_nodes)；依完整明示資料精確重算；複合梯形逐段使用endpoint average與自己的width；signed error固定為I-T；affine exact或指定quadratic reference不推出一般誤差界、收斂階或唯一integrand。"},"difficulty":{"band":"undergraduate_core","level":2,"skills":["複合梯形法"]},"variant":{"family_id":"qf-mod50-trap-partition-qualification","seed":202611192015,"parameters":{"nodes":[0,1,17],"values":[14,15,17],"domain":"Exact_composite_trapezoidal_quadrature","operation":"trap-partition-qualification","semantic_template":"trap-partition-qualification|{\"nodes\":[[0,1],[1,1],[17,1]],\"values\":[[14,1],[15,1],[17,1]]}"}},"verification":{"status":"candidate","checks":["producer_contract_recomputation","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"candidate 僅對明示有限或符號模型重算；不構成一般定理、人工審定、Lean 或 Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"GPT-5.6 Terra","generated_at":"2026-10-15","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261015-pulse-20261119-r02-0016","batch_id":"batch-20261015-advance-20261119-r02-trapezoidal-quadrature-foundations","language":"zh-Hant","source_mko_ids":["mko-trapezoidal-quadrature"],"title_zh":"複合梯形法","stem_zh":"嚴格遞增partition、n+1 nodes與逐subinterval寬度。操作=trap-partition-qualification；明示資料={\"nodes\":[0,1,18],\"values\":[15,16,18]}；請依 exact_ordered_tuple_declared_by_interface 回答。","answer":{"kind":"expression","value":"([0, 1, 18], [15, 16, 18], 2, 3, [1, 17], 是, n_subintervals_have_n_plus_one_nodes)","explanation_zh":"Wave6第十三層核對=([0, 1, 18], [15, 16, 18], 2, 3, [1, 17], 是, n_subintervals_have_n_plus_one_nodes)；依完整明示資料精確重算；複合梯形逐段使用endpoint average與自己的width；signed error固定為I-T；affine exact或指定quadratic reference不推出一般誤差界、收斂階或唯一integrand。"},"difficulty":{"band":"undergraduate_core","level":2,"skills":["複合梯形法"]},"variant":{"family_id":"qf-mod50-trap-partition-qualification","seed":202611192016,"parameters":{"nodes":[0,1,18],"values":[15,16,18],"domain":"Exact_composite_trapezoidal_quadrature","operation":"trap-partition-qualification","semantic_template":"trap-partition-qualification|{\"nodes\":[[0,1],[1,1],[18,1]],\"values\":[[15,1],[16,1],[18,1]]}"}},"verification":{"status":"candidate","checks":["producer_contract_recomputation","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"candidate 僅對明示有限或符號模型重算；不構成一般定理、人工審定、Lean 或 Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"GPT-5.6 Terra","generated_at":"2026-10-15","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261015-pulse-20261119-r02-0017","batch_id":"batch-20261015-advance-20261119-r02-trapezoidal-quadrature-foundations","language":"zh-Hant","source_mko_ids":["mko-trapezoidal-quadrature"],"title_zh":"複合梯形法","stem_zh":"嚴格遞增partition、n+1 nodes與逐subinterval寬度。操作=trap-partition-qualification；明示資料={\"nodes\":[0,1,19],\"values\":[16,17,19]}；請依 exact_ordered_tuple_declared_by_interface 回答。","answer":{"kind":"expression","value":"([0, 1, 19], [16, 17, 19], 2, 3, [1, 18], 是, n_subintervals_have_n_plus_one_nodes)","explanation_zh":"Wave6第十三層核對=([0, 1, 19], [16, 17, 19], 2, 3, [1, 18], 是, n_subintervals_have_n_plus_one_nodes)；依完整明示資料精確重算；複合梯形逐段使用endpoint average與自己的width；signed error固定為I-T；affine exact或指定quadratic reference不推出一般誤差界、收斂階或唯一integrand。"},"difficulty":{"band":"undergraduate_core","level":2,"skills":["複合梯形法"]},"variant":{"family_id":"qf-mod50-trap-partition-qualification","seed":202611192017,"parameters":{"nodes":[0,1,19],"values":[16,17,19],"domain":"Exact_composite_trapezoidal_quadrature","operation":"trap-partition-qualification","semantic_template":"trap-partition-qualification|{\"nodes\":[[0,1],[1,1],[19,1]],\"values\":[[16,1],[17,1],[19,1]]}"}},"verification":{"status":"candidate","checks":["producer_contract_recomputation","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"candidate 僅對明示有限或符號模型重算；不構成一般定理、人工審定、Lean 或 Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"GPT-5.6 Terra","generated_at":"2026-10-15","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261015-pulse-20261119-r02-0018","batch_id":"batch-20261015-advance-20261119-r02-trapezoidal-quadrature-foundations","language":"zh-Hant","source_mko_ids":["mko-trapezoidal-quadrature"],"title_zh":"複合梯形法","stem_zh":"嚴格遞增partition、n+1 nodes與逐subinterval寬度。操作=trap-partition-qualification；明示資料={\"nodes\":[0,1,20],\"values\":[17,18,20]}；請依 exact_ordered_tuple_declared_by_interface 回答。","answer":{"kind":"expression","value":"([0, 1, 20], [17, 18, 20], 2, 3, [1, 19], 是, n_subintervals_have_n_plus_one_nodes)","explanation_zh":"Wave6第十三層核對=([0, 1, 20], [17, 18, 20], 2, 3, [1, 19], 是, n_subintervals_have_n_plus_one_nodes)；依完整明示資料精確重算；複合梯形逐段使用endpoint average與自己的width；signed error固定為I-T；affine exact或指定quadratic reference不推出一般誤差界、收斂階或唯一integrand。"},"difficulty":{"band":"undergraduate_core","level":3,"skills":["複合梯形法"]},"variant":{"family_id":"qf-mod50-trap-partition-qualification","seed":202611192018,"parameters":{"nodes":[0,1,20],"values":[17,18,20],"domain":"Exact_composite_trapezoidal_quadrature","operation":"trap-partition-qualification","semantic_template":"trap-partition-qualification|{\"nodes\":[[0,1],[1,1],[20,1]],\"values\":[[17,1],[18,1],[20,1]]}"}},"verification":{"status":"candidate","checks":["producer_contract_recomputation","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"candidate 僅對明示有限或符號模型重算；不構成一般定理、人工審定、Lean 或 Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"GPT-5.6 Terra","generated_at":"2026-10-15","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261015-pulse-20261119-r02-0019","batch_id":"batch-20261015-advance-20261119-r02-trapezoidal-quadrature-foundations","language":"zh-Hant","source_mko_ids":["mko-trapezoidal-quadrature"],"title_zh":"複合梯形法","stem_zh":"嚴格遞增partition、n+1 nodes與逐subinterval寬度。操作=trap-partition-qualification；明示資料={\"nodes\":[0,1,21],\"values\":[18,19,21]}；請依 exact_ordered_tuple_declared_by_interface 回答。","answer":{"kind":"expression","value":"([0, 1, 21], [18, 19, 21], 2, 3, [1, 20], 是, n_subintervals_have_n_plus_one_nodes)","explanation_zh":"Wave6第十三層核對=([0, 1, 21], [18, 19, 21], 2, 3, [1, 20], 是, n_subintervals_have_n_plus_one_nodes)；依完整明示資料精確重算；複合梯形逐段使用endpoint average與自己的width；signed error固定為I-T；affine exact或指定quadratic reference不推出一般誤差界、收斂階或唯一integrand。"},"difficulty":{"band":"undergraduate_core","level":3,"skills":["複合梯形法"]},"variant":{"family_id":"qf-mod50-trap-partition-qualification","seed":202611192019,"parameters":{"nodes":[0,1,21],"values":[18,19,21],"domain":"Exact_composite_trapezoidal_quadrature","operation":"trap-partition-qualification","semantic_template":"trap-partition-qualification|{\"nodes\":[[0,1],[1,1],[21,1]],\"values\":[[18,1],[19,1],[21,1]]}"}},"verification":{"status":"candidate","checks":["producer_contract_recomputation","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"candidate 僅對明示有限或符號模型重算；不構成一般定理、人工審定、Lean 或 Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"GPT-5.6 Terra","generated_at":"2026-10-15","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261015-pulse-20261119-r02-0020","batch_id":"batch-20261015-advance-20261119-r02-trapezoidal-quadrature-foundations","language":"zh-Hant","source_mko_ids":["mko-trapezoidal-quadrature"],"title_zh":"複合梯形法","stem_zh":"嚴格遞增partition、n+1 nodes與逐subinterval寬度。操作=trap-partition-qualification；明示資料={\"nodes\":[0,1,22],\"values\":[19,20,22]}；請依 exact_ordered_tuple_declared_by_interface 回答。","answer":{"kind":"expression","value":"([0, 1, 22], [19, 20, 22], 2, 3, [1, 21], 是, n_subintervals_have_n_plus_one_nodes)","explanation_zh":"Wave6第十三層核對=([0, 1, 22], [19, 20, 22], 2, 3, [1, 21], 是, n_subintervals_have_n_plus_one_nodes)；依完整明示資料精確重算；複合梯形逐段使用endpoint average與自己的width；signed error固定為I-T；affine exact或指定quadratic reference不推出一般誤差界、收斂階或唯一integrand。"},"difficulty":{"band":"undergraduate_core","level":3,"skills":["複合梯形法"]},"variant":{"family_id":"qf-mod50-trap-partition-qualification","seed":202611192020,"parameters":{"nodes":[0,1,22],"values":[19,20,22],"domain":"Exact_composite_trapezoidal_quadrature","operation":"trap-partition-qualification","semantic_template":"trap-partition-qualification|{\"nodes\":[[0,1],[1,1],[22,1]],\"values\":[[19,1],[20,1],[22,1]]}"}},"verification":{"status":"candidate","checks":["producer_contract_recomputation","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"candidate 僅對明示有限或符號模型重算；不構成一般定理、人工審定、Lean 或 Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"GPT-5.6 Terra","generated_at":"2026-10-15","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261015-pulse-20261119-r02-0021","batch_id":"batch-20261015-advance-20261119-r02-trapezoidal-quadrature-foundations","language":"zh-Hant","source_mko_ids":["mko-trapezoidal-quadrature"],"title_zh":"複合梯形法","stem_zh":"嚴格遞增partition、n+1 nodes與逐subinterval寬度。操作=trap-partition-qualification；明示資料={\"nodes\":[0,1,23],\"values\":[20,21,23]}；請依 exact_ordered_tuple_declared_by_interface 回答。","answer":{"kind":"expression","value":"([0, 1, 23], [20, 21, 23], 2, 3, [1, 22], 是, n_subintervals_have_n_plus_one_nodes)","explanation_zh":"Wave6第十三層核對=([0, 1, 23], [20, 21, 23], 2, 3, [1, 22], 是, n_subintervals_have_n_plus_one_nodes)；依完整明示資料精確重算；複合梯形逐段使用endpoint average與自己的width；signed error固定為I-T；affine exact或指定quadratic reference不推出一般誤差界、收斂階或唯一integrand。"},"difficulty":{"band":"undergraduate_core","level":3,"skills":["複合梯形法"]},"variant":{"family_id":"qf-mod50-trap-partition-qualification","seed":202611192021,"parameters":{"nodes":[0,1,23],"values":[20,21,23],"domain":"Exact_composite_trapezoidal_quadrature","operation":"trap-partition-qualification","semantic_template":"trap-partition-qualification|{\"nodes\":[[0,1],[1,1],[23,1]],\"values\":[[20,1],[21,1],[23,1]]}"}},"verification":{"status":"candidate","checks":["producer_contract_recomputation","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"candidate 僅對明示有限或符號模型重算；不構成一般定理、人工審定、Lean 或 Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"GPT-5.6 Terra","generated_at":"2026-10-15","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261015-pulse-20261119-r02-0022","batch_id":"batch-20261015-advance-20261119-r02-trapezoidal-quadrature-foundations","language":"zh-Hant","source_mko_ids":["mko-trapezoidal-quadrature"],"title_zh":"複合梯形法","stem_zh":"嚴格遞增partition、n+1 nodes與逐subinterval寬度。操作=trap-partition-qualification；明示資料={\"nodes\":[0,1,24],\"values\":[21,22,24]}；請依 exact_ordered_tuple_declared_by_interface 回答。","answer":{"kind":"expression","value":"([0, 1, 24], [21, 22, 24], 2, 3, [1, 23], 是, n_subintervals_have_n_plus_one_nodes)","explanation_zh":"Wave6第十三層核對=([0, 1, 24], [21, 22, 24], 2, 3, [1, 23], 是, n_subintervals_have_n_plus_one_nodes)；依完整明示資料精確重算；複合梯形逐段使用endpoint average與自己的width；signed error固定為I-T；affine exact或指定quadratic reference不推出一般誤差界、收斂階或唯一integrand。"},"difficulty":{"band":"undergraduate_core","level":3,"skills":["複合梯形法"]},"variant":{"family_id":"qf-mod50-trap-partition-qualification","seed":202611192022,"parameters":{"nodes":[0,1,24],"values":[21,22,24],"domain":"Exact_composite_trapezoidal_quadrature","operation":"trap-partition-qualification","semantic_template":"trap-partition-qualification|{\"nodes\":[[0,1],[1,1],[24,1]],\"values\":[[21,1],[22,1],[24,1]]}"}},"verification":{"status":"candidate","checks":["producer_contract_recomputation","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"candidate 僅對明示有限或符號模型重算；不構成一般定理、人工審定、Lean 或 Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"GPT-5.6 Terra","generated_at":"2026-10-15","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261015-pulse-20261119-r02-0023","batch_id":"batch-20261015-advance-20261119-r02-trapezoidal-quadrature-foundations","language":"zh-Hant","source_mko_ids":["mko-trapezoidal-quadrature"],"title_zh":"複合梯形法","stem_zh":"嚴格遞增partition、n+1 nodes與逐subinterval寬度。操作=trap-partition-qualification；明示資料={\"nodes\":[0,1,25],\"values\":[22,23,25]}；請依 exact_ordered_tuple_declared_by_interface 回答。","answer":{"kind":"expression","value":"([0, 1, 25], [22, 23, 25], 2, 3, [1, 24], 是, n_subintervals_have_n_plus_one_nodes)","explanation_zh":"Wave6第十三層核對=([0, 1, 25], [22, 23, 25], 2, 3, [1, 24], 是, n_subintervals_have_n_plus_one_nodes)；依完整明示資料精確重算；複合梯形逐段使用endpoint average與自己的width；signed error固定為I-T；affine exact或指定quadratic reference不推出一般誤差界、收斂階或唯一integrand。"},"difficulty":{"band":"undergraduate_core","level":3,"skills":["複合梯形法"]},"variant":{"family_id":"qf-mod50-trap-partition-qualification","seed":202611192023,"parameters":{"nodes":[0,1,25],"values":[22,23,25],"domain":"Exact_composite_trapezoidal_quadrature","operation":"trap-partition-qualification","semantic_template":"trap-partition-qualification|{\"nodes\":[[0,1],[1,1],[25,1]],\"values\":[[22,1],[23,1],[25,1]]}"}},"verification":{"status":"candidate","checks":["producer_contract_recomputation","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"candidate 僅對明示有限或符號模型重算；不構成一般定理、人工審定、Lean 或 Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"GPT-5.6 Terra","generated_at":"2026-10-15","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261015-pulse-20261119-r02-0024","batch_id":"batch-20261015-advance-20261119-r02-trapezoidal-quadrature-foundations","language":"zh-Hant","source_mko_ids":["mko-trapezoidal-quadrature"],"title_zh":"複合梯形法","stem_zh":"嚴格遞增partition、n+1 nodes與逐subinterval寬度。操作=trap-partition-qualification；明示資料={\"nodes\":[0,1,26],\"values\":[23,24,26]}；請依 exact_ordered_tuple_declared_by_interface 回答。","answer":{"kind":"expression","value":"([0, 1, 26], [23, 24, 26], 2, 3, [1, 25], 是, n_subintervals_have_n_plus_one_nodes)","explanation_zh":"Wave6第十三層核對=([0, 1, 26], [23, 24, 26], 2, 3, [1, 25], 是, n_subintervals_have_n_plus_one_nodes)；依完整明示資料精確重算；複合梯形逐段使用endpoint average與自己的width；signed error固定為I-T；affine exact或指定quadratic reference不推出一般誤差界、收斂階或唯一integrand。"},"difficulty":{"band":"undergraduate_core","level":3,"skills":["複合梯形法"]},"variant":{"family_id":"qf-mod50-trap-partition-qualification","seed":202611192024,"parameters":{"nodes":[0,1,26],"values":[23,24,26],"domain":"Exact_composite_trapezoidal_quadrature","operation":"trap-partition-qualification","semantic_template":"trap-partition-qualification|{\"nodes\":[[0,1],[1,1],[26,1]],\"values\":[[23,1],[24,1],[26,1]]}"}},"verification":{"status":"candidate","checks":["producer_contract_recomputation","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"candidate 僅對明示有限或符號模型重算；不構成一般定理、人工審定、Lean 或 Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"GPT-5.6 Terra","generated_at":"2026-10-15","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261015-pulse-20261119-r02-0025","batch_id":"batch-20261015-advance-20261119-r02-trapezoidal-quadrature-foundations","language":"zh-Hant","source_mko_ids":["mko-trapezoidal-quadrature"],"title_zh":"複合梯形法","stem_zh":"嚴格遞增partition、n+1 nodes與逐subinterval寬度。操作=trap-partition-qualification；明示資料={\"nodes\":[0,1,27],\"values\":[24,25,27]}；請依 exact_ordered_tuple_declared_by_interface 回答。","answer":{"kind":"expression","value":"([0, 1, 27], [24, 25, 27], 2, 3, [1, 26], 是, n_subintervals_have_n_plus_one_nodes)","explanation_zh":"Wave6第十三層核對=([0, 1, 27], [24, 25, 27], 2, 3, [1, 26], 是, n_subintervals_have_n_plus_one_nodes)；依完整明示資料精確重算；複合梯形逐段使用endpoint average與自己的width；signed error固定為I-T；affine exact或指定quadratic reference不推出一般誤差界、收斂階或唯一integrand。"},"difficulty":{"band":"undergraduate_core","level":3,"skills":["複合梯形法"]},"variant":{"family_id":"qf-mod50-trap-partition-qualification","seed":202611192025,"parameters":{"nodes":[0,1,27],"values":[24,25,27],"domain":"Exact_composite_trapezoidal_quadrature","operation":"trap-partition-qualification","semantic_template":"trap-partition-qualification|{\"nodes\":[[0,1],[1,1],[27,1]],\"values\":[[24,1],[25,1],[27,1]]}"}},"verification":{"status":"candidate","checks":["producer_contract_recomputation","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"candidate 僅對明示有限或符號模型重算；不構成一般定理、人工審定、Lean 或 Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"GPT-5.6 Terra","generated_at":"2026-10-15","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261015-pulse-20261119-r02-0026","batch_id":"batch-20261015-advance-20261119-r02-trapezoidal-quadrature-foundations","language":"zh-Hant","source_mko_ids":["mko-trapezoidal-quadrature"],"title_zh":"複合梯形法","stem_zh":"嚴格遞增partition、n+1 nodes與逐subinterval寬度。操作=trap-composite-value；明示資料={\"nodes\":[0,1,3],\"values\":[0,1,3]}；請依 exact_ordered_tuple_declared_by_interface 回答。","answer":{"kind":"expression","value":"([0, 1, 3], [0, 1, 3], [1/2, 4], 9/2, each_subinterval_uses_its_own_width)","explanation_zh":"Wave6第十三層核對=([0, 1, 3], [0, 1, 3], [1/2, 4], 9/2, each_subinterval_uses_its_own_width)；依完整明示資料精確重算；複合梯形逐段使用endpoint average與自己的width；signed error固定為I-T；affine exact或指定quadratic reference不推出一般誤差界、收斂階或唯一integrand。"},"difficulty":{"band":"undergraduate_core","level":1,"skills":["複合梯形法"]},"variant":{"family_id":"qf-mod50-trap-composite-value","seed":202611192026,"parameters":{"nodes":[0,1,3],"values":[0,1,3],"domain":"Exact_composite_trapezoidal_quadrature","operation":"trap-composite-value","semantic_template":"trap-composite-value|{\"nodes\":[[0,1],[1,1],[3,1]],\"values\":[[0,1],[1,1],[3,1]]}"}},"verification":{"status":"candidate","checks":["producer_contract_recomputation","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"candidate 僅對明示有限或符號模型重算；不構成一般定理、人工審定、Lean 或 Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"GPT-5.6 Terra","generated_at":"2026-10-15","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261015-pulse-20261119-r02-0027","batch_id":"batch-20261015-advance-20261119-r02-trapezoidal-quadrature-foundations","language":"zh-Hant","source_mko_ids":["mko-trapezoidal-quadrature"],"title_zh":"複合梯形法","stem_zh":"嚴格遞增partition、n+1 nodes與逐subinterval寬度。操作=trap-composite-value；明示資料={\"nodes\":[0,1,4],\"values\":[1,2,4]}；請依 exact_ordered_tuple_declared_by_interface 回答。","answer":{"kind":"expression","value":"([0, 1, 4], [1, 2, 4], [3/2, 9], 21/2, each_subinterval_uses_its_own_width)","explanation_zh":"Wave6第十三層核對=([0, 1, 4], [1, 2, 4], [3/2, 9], 21/2, each_subinterval_uses_its_own_width)；依完整明示資料精確重算；複合梯形逐段使用endpoint average與自己的width；signed error固定為I-T；affine exact或指定quadratic reference不推出一般誤差界、收斂階或唯一integrand。"},"difficulty":{"band":"undergraduate_core","level":1,"skills":["複合梯形法"]},"variant":{"family_id":"qf-mod50-trap-composite-value","seed":202611192027,"parameters":{"nodes":[0,1,4],"values":[1,2,4],"domain":"Exact_composite_trapezoidal_quadrature","operation":"trap-composite-value","semantic_template":"trap-composite-value|{\"nodes\":[[0,1],[1,1],[4,1]],\"values\":[[1,1],[2,1],[4,1]]}"}},"verification":{"status":"candidate","checks":["producer_contract_recomputation","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"candidate 僅對明示有限或符號模型重算；不構成一般定理、人工審定、Lean 或 Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"GPT-5.6 Terra","generated_at":"2026-10-15","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261015-pulse-20261119-r02-0028","batch_id":"batch-20261015-advance-20261119-r02-trapezoidal-quadrature-foundations","language":"zh-Hant","source_mko_ids":["mko-trapezoidal-quadrature"],"title_zh":"複合梯形法","stem_zh":"嚴格遞增partition、n+1 nodes與逐subinterval寬度。操作=trap-composite-value；明示資料={\"nodes\":[0,1,5],\"values\":[2,3,5]}；請依 exact_ordered_tuple_declared_by_interface 回答。","answer":{"kind":"expression","value":"([0, 1, 5], [2, 3, 5], [5/2, 16], 37/2, each_subinterval_uses_its_own_width)","explanation_zh":"Wave6第十三層核對=([0, 1, 5], [2, 3, 5], [5/2, 16], 37/2, each_subinterval_uses_its_own_width)；依完整明示資料精確重算；複合梯形逐段使用endpoint average與自己的width；signed error固定為I-T；affine exact或指定quadratic reference不推出一般誤差界、收斂階或唯一integrand。"},"difficulty":{"band":"undergraduate_core","level":1,"skills":["複合梯形法"]},"variant":{"family_id":"qf-mod50-trap-composite-value","seed":202611192028,"parameters":{"nodes":[0,1,5],"values":[2,3,5],"domain":"Exact_composite_trapezoidal_quadrature","operation":"trap-composite-value","semantic_template":"trap-composite-value|{\"nodes\":[[0,1],[1,1],[5,1]],\"values\":[[2,1],[3,1],[5,1]]}"}},"verification":{"status":"candidate","checks":["producer_contract_recomputation","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"candidate 僅對明示有限或符號模型重算；不構成一般定理、人工審定、Lean 或 Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"GPT-5.6 Terra","generated_at":"2026-10-15","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261015-pulse-20261119-r02-0029","batch_id":"batch-20261015-advance-20261119-r02-trapezoidal-quadrature-foundations","language":"zh-Hant","source_mko_ids":["mko-trapezoidal-quadrature"],"title_zh":"複合梯形法","stem_zh":"嚴格遞增partition、n+1 nodes與逐subinterval寬度。操作=trap-composite-value；明示資料={\"nodes\":[0,1,6],\"values\":[3,4,6]}；請依 exact_ordered_tuple_declared_by_interface 回答。","answer":{"kind":"expression","value":"([0, 1, 6], [3, 4, 6], [7/2, 25], 57/2, each_subinterval_uses_its_own_width)","explanation_zh":"Wave6第十三層核對=([0, 1, 6], [3, 4, 6], [7/2, 25], 57/2, each_subinterval_uses_its_own_width)；依完整明示資料精確重算；複合梯形逐段使用endpoint average與自己的width；signed error固定為I-T；affine exact或指定quadratic reference不推出一般誤差界、收斂階或唯一integrand。"},"difficulty":{"band":"undergraduate_core","level":1,"skills":["複合梯形法"]},"variant":{"family_id":"qf-mod50-trap-composite-value","seed":202611192029,"parameters":{"nodes":[0,1,6],"values":[3,4,6],"domain":"Exact_composite_trapezoidal_quadrature","operation":"trap-composite-value","semantic_template":"trap-composite-value|{\"nodes\":[[0,1],[1,1],[6,1]],\"values\":[[3,1],[4,1],[6,1]]}"}},"verification":{"status":"candidate","checks":["producer_contract_recomputation","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"candidate 僅對明示有限或符號模型重算；不構成一般定理、人工審定、Lean 或 Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"GPT-5.6 Terra","generated_at":"2026-10-15","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261015-pulse-20261119-r02-0030","batch_id":"batch-20261015-advance-20261119-r02-trapezoidal-quadrature-foundations","language":"zh-Hant","source_mko_ids":["mko-trapezoidal-quadrature"],"title_zh":"複合梯形法","stem_zh":"嚴格遞增partition、n+1 nodes與逐subinterval寬度。操作=trap-composite-value；明示資料={\"nodes\":[0,1,7],\"values\":[4,5,7]}；請依 exact_ordered_tuple_declared_by_interface 回答。","answer":{"kind":"expression","value":"([0, 1, 7], [4, 5, 7], [9/2, 36], 81/2, each_subinterval_uses_its_own_width)","explanation_zh":"Wave6第十三層核對=([0, 1, 7], [4, 5, 7], [9/2, 36], 81/2, each_subinterval_uses_its_own_width)；依完整明示資料精確重算；複合梯形逐段使用endpoint average與自己的width；signed error固定為I-T；affine exact或指定quadratic reference不推出一般誤差界、收斂階或唯一integrand。"},"difficulty":{"band":"undergraduate_core","level":1,"skills":["複合梯形法"]},"variant":{"family_id":"qf-mod50-trap-composite-value","seed":202611192030,"parameters":{"nodes":[0,1,7],"values":[4,5,7],"domain":"Exact_composite_trapezoidal_quadrature","operation":"trap-composite-value","semantic_template":"trap-composite-value|{\"nodes\":[[0,1],[1,1],[7,1]],\"values\":[[4,1],[5,1],[7,1]]}"}},"verification":{"status":"candidate","checks":["producer_contract_recomputation","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"candidate 僅對明示有限或符號模型重算；不構成一般定理、人工審定、Lean 或 Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"GPT-5.6 Terra","generated_at":"2026-10-15","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261015-pulse-20261119-r02-0031","batch_id":"batch-20261015-advance-20261119-r02-trapezoidal-quadrature-foundations","language":"zh-Hant","source_mko_ids":["mko-trapezoidal-quadrature"],"title_zh":"複合梯形法","stem_zh":"嚴格遞增partition、n+1 nodes與逐subinterval寬度。操作=trap-composite-value；明示資料={\"nodes\":[0,1,8],\"values\":[5,6,8]}；請依 exact_ordered_tuple_declared_by_interface 回答。","answer":{"kind":"expression","value":"([0, 1, 8], [5, 6, 8], [11/2, 49], 109/2, each_subinterval_uses_its_own_width)","explanation_zh":"Wave6第十三層核對=([0, 1, 8], [5, 6, 8], [11/2, 49], 109/2, each_subinterval_uses_its_own_width)；依完整明示資料精確重算；複合梯形逐段使用endpoint average與自己的width；signed error固定為I-T；affine exact或指定quadratic reference不推出一般誤差界、收斂階或唯一integrand。"},"difficulty":{"band":"undergraduate_core","level":1,"skills":["複合梯形法"]},"variant":{"family_id":"qf-mod50-trap-composite-value","seed":202611192031,"parameters":{"nodes":[0,1,8],"values":[5,6,8],"domain":"Exact_composite_trapezoidal_quadrature","operation":"trap-composite-value","semantic_template":"trap-composite-value|{\"nodes\":[[0,1],[1,1],[8,1]],\"values\":[[5,1],[6,1],[8,1]]}"}},"verification":{"status":"candidate","checks":["producer_contract_recomputation","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"candidate 僅對明示有限或符號模型重算；不構成一般定理、人工審定、Lean 或 Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"GPT-5.6 Terra","generated_at":"2026-10-15","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261015-pulse-20261119-r02-0032","batch_id":"batch-20261015-advance-20261119-r02-trapezoidal-quadrature-foundations","language":"zh-Hant","source_mko_ids":["mko-trapezoidal-quadrature"],"title_zh":"複合梯形法","stem_zh":"嚴格遞增partition、n+1 nodes與逐subinterval寬度。操作=trap-composite-value；明示資料={\"nodes\":[0,1,9],\"values\":[6,7,9]}；請依 exact_ordered_tuple_declared_by_interface 回答。","answer":{"kind":"expression","value":"([0, 1, 9], [6, 7, 9], [13/2, 64], 141/2, each_subinterval_uses_its_own_width)","explanation_zh":"Wave6第十三層核對=([0, 1, 9], [6, 7, 9], [13/2, 64], 141/2, each_subinterval_uses_its_own_width)；依完整明示資料精確重算；複合梯形逐段使用endpoint average與自己的width；signed error固定為I-T；affine exact或指定quadratic reference不推出一般誤差界、收斂階或唯一integrand。"},"difficulty":{"band":"undergraduate_core","level":1,"skills":["複合梯形法"]},"variant":{"family_id":"qf-mod50-trap-composite-value","seed":202611192032,"parameters":{"nodes":[0,1,9],"values":[6,7,9],"domain":"Exact_composite_trapezoidal_quadrature","operation":"trap-composite-value","semantic_template":"trap-composite-value|{\"nodes\":[[0,1],[1,1],[9,1]],\"values\":[[6,1],[7,1],[9,1]]}"}},"verification":{"status":"candidate","checks":["producer_contract_recomputation","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"candidate 僅對明示有限或符號模型重算；不構成一般定理、人工審定、Lean 或 Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"GPT-5.6 Terra","generated_at":"2026-10-15","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261015-pulse-20261119-r02-0033","batch_id":"batch-20261015-advance-20261119-r02-trapezoidal-quadrature-foundations","language":"zh-Hant","source_mko_ids":["mko-trapezoidal-quadrature"],"title_zh":"複合梯形法","stem_zh":"嚴格遞增partition、n+1 nodes與逐subinterval寬度。操作=trap-composite-value；明示資料={\"nodes\":[0,1,10],\"values\":[7,8,10]}；請依 exact_ordered_tuple_declared_by_interface 回答。","answer":{"kind":"expression","value":"([0, 1, 10], [7, 8, 10], [15/2, 81], 177/2, each_subinterval_uses_its_own_width)","explanation_zh":"Wave6第十三層核對=([0, 1, 10], [7, 8, 10], [15/2, 81], 177/2, each_subinterval_uses_its_own_width)；依完整明示資料精確重算；複合梯形逐段使用endpoint average與自己的width；signed error固定為I-T；affine exact或指定quadratic reference不推出一般誤差界、收斂階或唯一integrand。"},"difficulty":{"band":"undergraduate_core","level":1,"skills":["複合梯形法"]},"variant":{"family_id":"qf-mod50-trap-composite-value","seed":202611192033,"parameters":{"nodes":[0,1,10],"values":[7,8,10],"domain":"Exact_composite_trapezoidal_quadrature","operation":"trap-composite-value","semantic_template":"trap-composite-value|{\"nodes\":[[0,1],[1,1],[10,1]],\"values\":[[7,1],[8,1],[10,1]]}"}},"verification":{"status":"candidate","checks":["producer_contract_recomputation","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"candidate 僅對明示有限或符號模型重算；不構成一般定理、人工審定、Lean 或 Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"GPT-5.6 Terra","generated_at":"2026-10-15","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261015-pulse-20261119-r02-0034","batch_id":"batch-20261015-advance-20261119-r02-trapezoidal-quadrature-foundations","language":"zh-Hant","source_mko_ids":["mko-trapezoidal-quadrature"],"title_zh":"複合梯形法","stem_zh":"嚴格遞增partition、n+1 nodes與逐subinterval寬度。操作=trap-composite-value；明示資料={\"nodes\":[0,1,11],\"values\":[8,9,11]}；請依 exact_ordered_tuple_declared_by_interface 回答。","answer":{"kind":"expression","value":"([0, 1, 11], [8, 9, 11], [17/2, 100], 217/2, each_subinterval_uses_its_own_width)","explanation_zh":"Wave6第十三層核對=([0, 1, 11], [8, 9, 11], [17/2, 100], 217/2, each_subinterval_uses_its_own_width)；依完整明示資料精確重算；複合梯形逐段使用endpoint average與自己的width；signed error固定為I-T；affine exact或指定quadratic reference不推出一般誤差界、收斂階或唯一integrand。"},"difficulty":{"band":"undergraduate_core","level":2,"skills":["複合梯形法"]},"variant":{"family_id":"qf-mod50-trap-composite-value","seed":202611192034,"parameters":{"nodes":[0,1,11],"values":[8,9,11],"domain":"Exact_composite_trapezoidal_quadrature","operation":"trap-composite-value","semantic_template":"trap-composite-value|{\"nodes\":[[0,1],[1,1],[11,1]],\"values\":[[8,1],[9,1],[11,1]]}"}},"verification":{"status":"candidate","checks":["producer_contract_recomputation","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"candidate 僅對明示有限或符號模型重算；不構成一般定理、人工審定、Lean 或 Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"GPT-5.6 Terra","generated_at":"2026-10-15","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261015-pulse-20261119-r02-0035","batch_id":"batch-20261015-advance-20261119-r02-trapezoidal-quadrature-foundations","language":"zh-Hant","source_mko_ids":["mko-trapezoidal-quadrature"],"title_zh":"複合梯形法","stem_zh":"嚴格遞增partition、n+1 nodes與逐subinterval寬度。操作=trap-composite-value；明示資料={\"nodes\":[0,1,12],\"values\":[9,10,12]}；請依 exact_ordered_tuple_declared_by_interface 回答。","answer":{"kind":"expression","value":"([0, 1, 12], [9, 10, 12], [19/2, 121], 261/2, each_subinterval_uses_its_own_width)","explanation_zh":"Wave6第十三層核對=([0, 1, 12], [9, 10, 12], [19/2, 121], 261/2, each_subinterval_uses_its_own_width)；依完整明示資料精確重算；複合梯形逐段使用endpoint average與自己的width；signed error固定為I-T；affine exact或指定quadratic reference不推出一般誤差界、收斂階或唯一integrand。"},"difficulty":{"band":"undergraduate_core","level":2,"skills":["複合梯形法"]},"variant":{"family_id":"qf-mod50-trap-composite-value","seed":202611192035,"parameters":{"nodes":[0,1,12],"values":[9,10,12],"domain":"Exact_composite_trapezoidal_quadrature","operation":"trap-composite-value","semantic_template":"trap-composite-value|{\"nodes\":[[0,1],[1,1],[12,1]],\"values\":[[9,1],[10,1],[12,1]]}"}},"verification":{"status":"candidate","checks":["producer_contract_recomputation","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"candidate 僅對明示有限或符號模型重算；不構成一般定理、人工審定、Lean 或 Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"GPT-5.6 Terra","generated_at":"2026-10-15","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261015-pulse-20261119-r02-0036","batch_id":"batch-20261015-advance-20261119-r02-trapezoidal-quadrature-foundations","language":"zh-Hant","source_mko_ids":["mko-trapezoidal-quadrature"],"title_zh":"複合梯形法","stem_zh":"嚴格遞增partition、n+1 nodes與逐subinterval寬度。操作=trap-composite-value；明示資料={\"nodes\":[0,1,13],\"values\":[10,11,13]}；請依 exact_ordered_tuple_declared_by_interface 回答。","answer":{"kind":"expression","value":"([0, 1, 13], [10, 11, 13], [21/2, 144], 309/2, each_subinterval_uses_its_own_width)","explanation_zh":"Wave6第十三層核對=([0, 1, 13], [10, 11, 13], [21/2, 144], 309/2, each_subinterval_uses_its_own_width)；依完整明示資料精確重算；複合梯形逐段使用endpoint average與自己的width；signed error固定為I-T；affine exact或指定quadratic reference不推出一般誤差界、收斂階或唯一integrand。"},"difficulty":{"band":"undergraduate_core","level":2,"skills":["複合梯形法"]},"variant":{"family_id":"qf-mod50-trap-composite-value","seed":202611192036,"parameters":{"nodes":[0,1,13],"values":[10,11,13],"domain":"Exact_composite_trapezoidal_quadrature","operation":"trap-composite-value","semantic_template":"trap-composite-value|{\"nodes\":[[0,1],[1,1],[13,1]],\"values\":[[10,1],[11,1],[13,1]]}"}},"verification":{"status":"candidate","checks":["producer_contract_recomputation","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"candidate 僅對明示有限或符號模型重算；不構成一般定理、人工審定、Lean 或 Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"GPT-5.6 Terra","generated_at":"2026-10-15","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261015-pulse-20261119-r02-0037","batch_id":"batch-20261015-advance-20261119-r02-trapezoidal-quadrature-foundations","language":"zh-Hant","source_mko_ids":["mko-trapezoidal-quadrature"],"title_zh":"複合梯形法","stem_zh":"嚴格遞增partition、n+1 nodes與逐subinterval寬度。操作=trap-composite-value；明示資料={\"nodes\":[0,1,14],\"values\":[11,12,14]}；請依 exact_ordered_tuple_declared_by_interface 回答。","answer":{"kind":"expression","value":"([0, 1, 14], [11, 12, 14], [23/2, 169], 361/2, each_subinterval_uses_its_own_width)","explanation_zh":"Wave6第十三層核對=([0, 1, 14], [11, 12, 14], [23/2, 169], 361/2, each_subinterval_uses_its_own_width)；依完整明示資料精確重算；複合梯形逐段使用endpoint average與自己的width；signed error固定為I-T；affine exact或指定quadratic reference不推出一般誤差界、收斂階或唯一integrand。"},"difficulty":{"band":"undergraduate_core","level":2,"skills":["複合梯形法"]},"variant":{"family_id":"qf-mod50-trap-composite-value","seed":202611192037,"parameters":{"nodes":[0,1,14],"values":[11,12,14],"domain":"Exact_composite_trapezoidal_quadrature","operation":"trap-composite-value","semantic_template":"trap-composite-value|{\"nodes\":[[0,1],[1,1],[14,1]],\"values\":[[11,1],[12,1],[14,1]]}"}},"verification":{"status":"candidate","checks":["producer_contract_recomputation","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"candidate 僅對明示有限或符號模型重算；不構成一般定理、人工審定、Lean 或 Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"GPT-5.6 Terra","generated_at":"2026-10-15","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261015-pulse-20261119-r02-0038","batch_id":"batch-20261015-advance-20261119-r02-trapezoidal-quadrature-foundations","language":"zh-Hant","source_mko_ids":["mko-trapezoidal-quadrature"],"title_zh":"複合梯形法","stem_zh":"嚴格遞增partition、n+1 nodes與逐subinterval寬度。操作=trap-composite-value；明示資料={\"nodes\":[0,1,15],\"values\":[12,13,15]}；請依 exact_ordered_tuple_declared_by_interface 回答。","answer":{"kind":"expression","value":"([0, 1, 15], [12, 13, 15], [25/2, 196], 417/2, each_subinterval_uses_its_own_width)","explanation_zh":"Wave6第十三層核對=([0, 1, 15], [12, 13, 15], [25/2, 196], 417/2, each_subinterval_uses_its_own_width)；依完整明示資料精確重算；複合梯形逐段使用endpoint average與自己的width；signed error固定為I-T；affine exact或指定quadratic reference不推出一般誤差界、收斂階或唯一integrand。"},"difficulty":{"band":"undergraduate_core","level":2,"skills":["複合梯形法"]},"variant":{"family_id":"qf-mod50-trap-composite-value","seed":202611192038,"parameters":{"nodes":[0,1,15],"values":[12,13,15],"domain":"Exact_composite_trapezoidal_quadrature","operation":"trap-composite-value","semantic_template":"trap-composite-value|{\"nodes\":[[0,1],[1,1],[15,1]],\"values\":[[12,1],[13,1],[15,1]]}"}},"verification":{"status":"candidate","checks":["producer_contract_recomputation","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"candidate 僅對明示有限或符號模型重算；不構成一般定理、人工審定、Lean 或 Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"GPT-5.6 Terra","generated_at":"2026-10-15","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261015-pulse-20261119-r02-0039","batch_id":"batch-20261015-advance-20261119-r02-trapezoidal-quadrature-foundations","language":"zh-Hant","source_mko_ids":["mko-trapezoidal-quadrature"],"title_zh":"複合梯形法","stem_zh":"嚴格遞增partition、n+1 nodes與逐subinterval寬度。操作=trap-composite-value；明示資料={\"nodes\":[0,1,16],\"values\":[13,14,16]}；請依 exact_ordered_tuple_declared_by_interface 回答。","answer":{"kind":"expression","value":"([0, 1, 16], [13, 14, 16], [27/2, 225], 477/2, each_subinterval_uses_its_own_width)","explanation_zh":"Wave6第十三層核對=([0, 1, 16], [13, 14, 16], [27/2, 225], 477/2, each_subinterval_uses_its_own_width)；依完整明示資料精確重算；複合梯形逐段使用endpoint average與自己的width；signed error固定為I-T；affine exact或指定quadratic reference不推出一般誤差界、收斂階或唯一integrand。"},"difficulty":{"band":"undergraduate_core","level":2,"skills":["複合梯形法"]},"variant":{"family_id":"qf-mod50-trap-composite-value","seed":202611192039,"parameters":{"nodes":[0,1,16],"values":[13,14,16],"domain":"Exact_composite_trapezoidal_quadrature","operation":"trap-composite-value","semantic_template":"trap-composite-value|{\"nodes\":[[0,1],[1,1],[16,1]],\"values\":[[13,1],[14,1],[16,1]]}"}},"verification":{"status":"candidate","checks":["producer_contract_recomputation","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"candidate 僅對明示有限或符號模型重算；不構成一般定理、人工審定、Lean 或 Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"GPT-5.6 Terra","generated_at":"2026-10-15","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261015-pulse-20261119-r02-0040","batch_id":"batch-20261015-advance-20261119-r02-trapezoidal-quadrature-foundations","language":"zh-Hant","source_mko_ids":["mko-trapezoidal-quadrature"],"title_zh":"複合梯形法","stem_zh":"嚴格遞增partition、n+1 nodes與逐subinterval寬度。操作=trap-composite-value；明示資料={\"nodes\":[0,1,17],\"values\":[14,15,17]}；請依 exact_ordered_tuple_declared_by_interface 回答。","answer":{"kind":"expression","value":"([0, 1, 17], [14, 15, 17], [29/2, 256], 541/2, each_subinterval_uses_its_own_width)","explanation_zh":"Wave6第十三層核對=([0, 1, 17], [14, 15, 17], [29/2, 256], 541/2, each_subinterval_uses_its_own_width)；依完整明示資料精確重算；複合梯形逐段使用endpoint average與自己的width；signed error固定為I-T；affine exact或指定quadratic reference不推出一般誤差界、收斂階或唯一integrand。"},"difficulty":{"band":"undergraduate_core","level":2,"skills":["複合梯形法"]},"variant":{"family_id":"qf-mod50-trap-composite-value","seed":202611192040,"parameters":{"nodes":[0,1,17],"values":[14,15,17],"domain":"Exact_composite_trapezoidal_quadrature","operation":"trap-composite-value","semantic_template":"trap-composite-value|{\"nodes\":[[0,1],[1,1],[17,1]],\"values\":[[14,1],[15,1],[17,1]]}"}},"verification":{"status":"candidate","checks":["producer_contract_recomputation","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"candidate 僅對明示有限或符號模型重算；不構成一般定理、人工審定、Lean 或 Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"GPT-5.6 Terra","generated_at":"2026-10-15","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261015-pulse-20261119-r02-0041","batch_id":"batch-20261015-advance-20261119-r02-trapezoidal-quadrature-foundations","language":"zh-Hant","source_mko_ids":["mko-trapezoidal-quadrature"],"title_zh":"複合梯形法","stem_zh":"嚴格遞增partition、n+1 nodes與逐subinterval寬度。操作=trap-composite-value；明示資料={\"nodes\":[0,1,18],\"values\":[15,16,18]}；請依 exact_ordered_tuple_declared_by_interface 回答。","answer":{"kind":"expression","value":"([0, 1, 18], [15, 16, 18], [31/2, 289], 609/2, each_subinterval_uses_its_own_width)","explanation_zh":"Wave6第十三層核對=([0, 1, 18], [15, 16, 18], [31/2, 289], 609/2, each_subinterval_uses_its_own_width)；依完整明示資料精確重算；複合梯形逐段使用endpoint average與自己的width；signed error固定為I-T；affine exact或指定quadratic reference不推出一般誤差界、收斂階或唯一integrand。"},"difficulty":{"band":"undergraduate_core","level":2,"skills":["複合梯形法"]},"variant":{"family_id":"qf-mod50-trap-composite-value","seed":202611192041,"parameters":{"nodes":[0,1,18],"values":[15,16,18],"domain":"Exact_composite_trapezoidal_quadrature","operation":"trap-composite-value","semantic_template":"trap-composite-value|{\"nodes\":[[0,1],[1,1],[18,1]],\"values\":[[15,1],[16,1],[18,1]]}"}},"verification":{"status":"candidate","checks":["producer_contract_recomputation","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"candidate 僅對明示有限或符號模型重算；不構成一般定理、人工審定、Lean 或 Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"GPT-5.6 Terra","generated_at":"2026-10-15","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261015-pulse-20261119-r02-0042","batch_id":"batch-20261015-advance-20261119-r02-trapezoidal-quadrature-foundations","language":"zh-Hant","source_mko_ids":["mko-trapezoidal-quadrature"],"title_zh":"複合梯形法","stem_zh":"嚴格遞增partition、n+1 nodes與逐subinterval寬度。操作=trap-composite-value；明示資料={\"nodes\":[0,1,19],\"values\":[16,17,19]}；請依 exact_ordered_tuple_declared_by_interface 回答。","answer":{"kind":"expression","value":"([0, 1, 19], [16, 17, 19], [33/2, 324], 681/2, each_subinterval_uses_its_own_width)","explanation_zh":"Wave6第十三層核對=([0, 1, 19], [16, 17, 19], [33/2, 324], 681/2, each_subinterval_uses_its_own_width)；依完整明示資料精確重算；複合梯形逐段使用endpoint average與自己的width；signed error固定為I-T；affine exact或指定quadratic reference不推出一般誤差界、收斂階或唯一integrand。"},"difficulty":{"band":"undergraduate_core","level":2,"skills":["複合梯形法"]},"variant":{"family_id":"qf-mod50-trap-composite-value","seed":202611192042,"parameters":{"nodes":[0,1,19],"values":[16,17,19],"domain":"Exact_composite_trapezoidal_quadrature","operation":"trap-composite-value","semantic_template":"trap-composite-value|{\"nodes\":[[0,1],[1,1],[19,1]],\"values\":[[16,1],[17,1],[19,1]]}"}},"verification":{"status":"candidate","checks":["producer_contract_recomputation","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"candidate 僅對明示有限或符號模型重算；不構成一般定理、人工審定、Lean 或 Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"GPT-5.6 Terra","generated_at":"2026-10-15","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261015-pulse-20261119-r02-0043","batch_id":"batch-20261015-advance-20261119-r02-trapezoidal-quadrature-foundations","language":"zh-Hant","source_mko_ids":["mko-trapezoidal-quadrature"],"title_zh":"複合梯形法","stem_zh":"嚴格遞增partition、n+1 nodes與逐subinterval寬度。操作=trap-composite-value；明示資料={\"nodes\":[0,1,20],\"values\":[17,18,20]}；請依 exact_ordered_tuple_declared_by_interface 回答。","answer":{"kind":"expression","value":"([0, 1, 20], [17, 18, 20], [35/2, 361], 757/2, each_subinterval_uses_its_own_width)","explanation_zh":"Wave6第十三層核對=([0, 1, 20], [17, 18, 20], [35/2, 361], 757/2, each_subinterval_uses_its_own_width)；依完整明示資料精確重算；複合梯形逐段使用endpoint average與自己的width；signed error固定為I-T；affine exact或指定quadratic reference不推出一般誤差界、收斂階或唯一integrand。"},"difficulty":{"band":"undergraduate_core","level":3,"skills":["複合梯形法"]},"variant":{"family_id":"qf-mod50-trap-composite-value","seed":202611192043,"parameters":{"nodes":[0,1,20],"values":[17,18,20],"domain":"Exact_composite_trapezoidal_quadrature","operation":"trap-composite-value","semantic_template":"trap-composite-value|{\"nodes\":[[0,1],[1,1],[20,1]],\"values\":[[17,1],[18,1],[20,1]]}"}},"verification":{"status":"candidate","checks":["producer_contract_recomputation","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"candidate 僅對明示有限或符號模型重算；不構成一般定理、人工審定、Lean 或 Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"GPT-5.6 Terra","generated_at":"2026-10-15","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261015-pulse-20261119-r02-0044","batch_id":"batch-20261015-advance-20261119-r02-trapezoidal-quadrature-foundations","language":"zh-Hant","source_mko_ids":["mko-trapezoidal-quadrature"],"title_zh":"複合梯形法","stem_zh":"嚴格遞增partition、n+1 nodes與逐subinterval寬度。操作=trap-composite-value；明示資料={\"nodes\":[0,1,21],\"values\":[18,19,21]}；請依 exact_ordered_tuple_declared_by_interface 回答。","answer":{"kind":"expression","value":"([0, 1, 21], [18, 19, 21], [37/2, 400], 837/2, each_subinterval_uses_its_own_width)","explanation_zh":"Wave6第十三層核對=([0, 1, 21], [18, 19, 21], [37/2, 400], 837/2, each_subinterval_uses_its_own_width)；依完整明示資料精確重算；複合梯形逐段使用endpoint average與自己的width；signed error固定為I-T；affine exact或指定quadratic reference不推出一般誤差界、收斂階或唯一integrand。"},"difficulty":{"band":"undergraduate_core","level":3,"skills":["複合梯形法"]},"variant":{"family_id":"qf-mod50-trap-composite-value","seed":202611192044,"parameters":{"nodes":[0,1,21],"values":[18,19,21],"domain":"Exact_composite_trapezoidal_quadrature","operation":"trap-composite-value","semantic_template":"trap-composite-value|{\"nodes\":[[0,1],[1,1],[21,1]],\"values\":[[18,1],[19,1],[21,1]]}"}},"verification":{"status":"candidate","checks":["producer_contract_recomputation","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"candidate 僅對明示有限或符號模型重算；不構成一般定理、人工審定、Lean 或 Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"GPT-5.6 Terra","generated_at":"2026-10-15","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261015-pulse-20261119-r02-0045","batch_id":"batch-20261015-advance-20261119-r02-trapezoidal-quadrature-foundations","language":"zh-Hant","source_mko_ids":["mko-trapezoidal-quadrature"],"title_zh":"複合梯形法","stem_zh":"嚴格遞增partition、n+1 nodes與逐subinterval寬度。操作=trap-composite-value；明示資料={\"nodes\":[0,1,22],\"values\":[19,20,22]}；請依 exact_ordered_tuple_declared_by_interface 回答。","answer":{"kind":"expression","value":"([0, 1, 22], [19, 20, 22], [39/2, 441], 921/2, each_subinterval_uses_its_own_width)","explanation_zh":"Wave6第十三層核對=([0, 1, 22], [19, 20, 22], [39/2, 441], 921/2, each_subinterval_uses_its_own_width)；依完整明示資料精確重算；複合梯形逐段使用endpoint average與自己的width；signed error固定為I-T；affine exact或指定quadratic reference不推出一般誤差界、收斂階或唯一integrand。"},"difficulty":{"band":"undergraduate_core","level":3,"skills":["複合梯形法"]},"variant":{"family_id":"qf-mod50-trap-composite-value","seed":202611192045,"parameters":{"nodes":[0,1,22],"values":[19,20,22],"domain":"Exact_composite_trapezoidal_quadrature","operation":"trap-composite-value","semantic_template":"trap-composite-value|{\"nodes\":[[0,1],[1,1],[22,1]],\"values\":[[19,1],[20,1],[22,1]]}"}},"verification":{"status":"candidate","checks":["producer_contract_recomputation","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"candidate 僅對明示有限或符號模型重算；不構成一般定理、人工審定、Lean 或 Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"GPT-5.6 Terra","generated_at":"2026-10-15","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261015-pulse-20261119-r02-0046","batch_id":"batch-20261015-advance-20261119-r02-trapezoidal-quadrature-foundations","language":"zh-Hant","source_mko_ids":["mko-trapezoidal-quadrature"],"title_zh":"複合梯形法","stem_zh":"嚴格遞增partition、n+1 nodes與逐subinterval寬度。操作=trap-composite-value；明示資料={\"nodes\":[0,1,23],\"values\":[20,21,23]}；請依 exact_ordered_tuple_declared_by_interface 回答。","answer":{"kind":"expression","value":"([0, 1, 23], [20, 21, 23], [41/2, 484], 1009/2, each_subinterval_uses_its_own_width)","explanation_zh":"Wave6第十三層核對=([0, 1, 23], [20, 21, 23], [41/2, 484], 1009/2, each_subinterval_uses_its_own_width)；依完整明示資料精確重算；複合梯形逐段使用endpoint average與自己的width；signed error固定為I-T；affine exact或指定quadratic reference不推出一般誤差界、收斂階或唯一integrand。"},"difficulty":{"band":"undergraduate_core","level":3,"skills":["複合梯形法"]},"variant":{"family_id":"qf-mod50-trap-composite-value","seed":202611192046,"parameters":{"nodes":[0,1,23],"values":[20,21,23],"domain":"Exact_composite_trapezoidal_quadrature","operation":"trap-composite-value","semantic_template":"trap-composite-value|{\"nodes\":[[0,1],[1,1],[23,1]],\"values\":[[20,1],[21,1],[23,1]]}"}},"verification":{"status":"candidate","checks":["producer_contract_recomputation","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"candidate 僅對明示有限或符號模型重算；不構成一般定理、人工審定、Lean 或 Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"GPT-5.6 Terra","generated_at":"2026-10-15","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261015-pulse-20261119-r02-0047","batch_id":"batch-20261015-advance-20261119-r02-trapezoidal-quadrature-foundations","language":"zh-Hant","source_mko_ids":["mko-trapezoidal-quadrature"],"title_zh":"複合梯形法","stem_zh":"嚴格遞增partition、n+1 nodes與逐subinterval寬度。操作=trap-composite-value；明示資料={\"nodes\":[0,1,24],\"values\":[21,22,24]}；請依 exact_ordered_tuple_declared_by_interface 回答。","answer":{"kind":"expression","value":"([0, 1, 24], [21, 22, 24], [43/2, 529], 1101/2, each_subinterval_uses_its_own_width)","explanation_zh":"Wave6第十三層核對=([0, 1, 24], [21, 22, 24], [43/2, 529], 1101/2, each_subinterval_uses_its_own_width)；依完整明示資料精確重算；複合梯形逐段使用endpoint average與自己的width；signed error固定為I-T；affine exact或指定quadratic reference不推出一般誤差界、收斂階或唯一integrand。"},"difficulty":{"band":"undergraduate_core","level":3,"skills":["複合梯形法"]},"variant":{"family_id":"qf-mod50-trap-composite-value","seed":202611192047,"parameters":{"nodes":[0,1,24],"values":[21,22,24],"domain":"Exact_composite_trapezoidal_quadrature","operation":"trap-composite-value","semantic_template":"trap-composite-value|{\"nodes\":[[0,1],[1,1],[24,1]],\"values\":[[21,1],[22,1],[24,1]]}"}},"verification":{"status":"candidate","checks":["producer_contract_recomputation","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"candidate 僅對明示有限或符號模型重算；不構成一般定理、人工審定、Lean 或 Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"GPT-5.6 Terra","generated_at":"2026-10-15","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261015-pulse-20261119-r02-0048","batch_id":"batch-20261015-advance-20261119-r02-trapezoidal-quadrature-foundations","language":"zh-Hant","source_mko_ids":["mko-trapezoidal-quadrature"],"title_zh":"複合梯形法","stem_zh":"嚴格遞增partition、n+1 nodes與逐subinterval寬度。操作=trap-composite-value；明示資料={\"nodes\":[0,1,25],\"values\":[22,23,25]}；請依 exact_ordered_tuple_declared_by_interface 回答。","answer":{"kind":"expression","value":"([0, 1, 25], [22, 23, 25], [45/2, 576], 1197/2, each_subinterval_uses_its_own_width)","explanation_zh":"Wave6第十三層核對=([0, 1, 25], [22, 23, 25], [45/2, 576], 1197/2, each_subinterval_uses_its_own_width)；依完整明示資料精確重算；複合梯形逐段使用endpoint average與自己的width；signed error固定為I-T；affine exact或指定quadratic reference不推出一般誤差界、收斂階或唯一integrand。"},"difficulty":{"band":"undergraduate_core","level":3,"skills":["複合梯形法"]},"variant":{"family_id":"qf-mod50-trap-composite-value","seed":202611192048,"parameters":{"nodes":[0,1,25],"values":[22,23,25],"domain":"Exact_composite_trapezoidal_quadrature","operation":"trap-composite-value","semantic_template":"trap-composite-value|{\"nodes\":[[0,1],[1,1],[25,1]],\"values\":[[22,1],[23,1],[25,1]]}"}},"verification":{"status":"candidate","checks":["producer_contract_recomputation","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"candidate 僅對明示有限或符號模型重算；不構成一般定理、人工審定、Lean 或 Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"GPT-5.6 Terra","generated_at":"2026-10-15","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261015-pulse-20261119-r02-0049","batch_id":"batch-20261015-advance-20261119-r02-trapezoidal-quadrature-foundations","language":"zh-Hant","source_mko_ids":["mko-trapezoidal-quadrature"],"title_zh":"複合梯形法","stem_zh":"嚴格遞增partition、n+1 nodes與逐subinterval寬度。操作=trap-composite-value；明示資料={\"nodes\":[0,1,26],\"values\":[23,24,26]}；請依 exact_ordered_tuple_declared_by_interface 回答。","answer":{"kind":"expression","value":"([0, 1, 26], [23, 24, 26], [47/2, 625], 1297/2, each_subinterval_uses_its_own_width)","explanation_zh":"Wave6第十三層核對=([0, 1, 26], [23, 24, 26], [47/2, 625], 1297/2, each_subinterval_uses_its_own_width)；依完整明示資料精確重算；複合梯形逐段使用endpoint average與自己的width；signed error固定為I-T；affine exact或指定quadratic reference不推出一般誤差界、收斂階或唯一integrand。"},"difficulty":{"band":"undergraduate_core","level":3,"skills":["複合梯形法"]},"variant":{"family_id":"qf-mod50-trap-composite-value","seed":202611192049,"parameters":{"nodes":[0,1,26],"values":[23,24,26],"domain":"Exact_composite_trapezoidal_quadrature","operation":"trap-composite-value","semantic_template":"trap-composite-value|{\"nodes\":[[0,1],[1,1],[26,1]],\"values\":[[23,1],[24,1],[26,1]]}"}},"verification":{"status":"candidate","checks":["producer_contract_recomputation","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"candidate 僅對明示有限或符號模型重算；不構成一般定理、人工審定、Lean 或 Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"GPT-5.6 Terra","generated_at":"2026-10-15","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261015-pulse-20261119-r02-0050","batch_id":"batch-20261015-advance-20261119-r02-trapezoidal-quadrature-foundations","language":"zh-Hant","source_mko_ids":["mko-trapezoidal-quadrature"],"title_zh":"複合梯形法","stem_zh":"嚴格遞增partition、n+1 nodes與逐subinterval寬度。操作=trap-composite-value；明示資料={\"nodes\":[0,1,27],\"values\":[24,25,27]}；請依 exact_ordered_tuple_declared_by_interface 回答。","answer":{"kind":"expression","value":"([0, 1, 27], [24, 25, 27], [49/2, 676], 1401/2, each_subinterval_uses_its_own_width)","explanation_zh":"Wave6第十三層核對=([0, 1, 27], [24, 25, 27], [49/2, 676], 1401/2, each_subinterval_uses_its_own_width)；依完整明示資料精確重算；複合梯形逐段使用endpoint average與自己的width；signed error固定為I-T；affine exact或指定quadratic reference不推出一般誤差界、收斂階或唯一integrand。"},"difficulty":{"band":"undergraduate_core","level":3,"skills":["複合梯形法"]},"variant":{"family_id":"qf-mod50-trap-composite-value","seed":202611192050,"parameters":{"nodes":[0,1,27],"values":[24,25,27],"domain":"Exact_composite_trapezoidal_quadrature","operation":"trap-composite-value","semantic_template":"trap-composite-value|{\"nodes\":[[0,1],[1,1],[27,1]],\"values\":[[24,1],[25,1],[27,1]]}"}},"verification":{"status":"candidate","checks":["producer_contract_recomputation","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"candidate 僅對明示有限或符號模型重算；不構成一般定理、人工審定、Lean 或 Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"GPT-5.6 Terra","generated_at":"2026-10-15","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261015-pulse-20261119-r02-0051","batch_id":"batch-20261015-advance-20261119-r02-trapezoidal-quadrature-foundations","language":"zh-Hant","source_mko_ids":["mko-trapezoidal-quadrature"],"title_zh":"複合梯形法","stem_zh":"嚴格遞增partition、n+1 nodes與逐subinterval寬度。操作=trap-affine-exactness；明示資料={\"intercept\":1,\"nodes\":[0,1,3],\"slope\":-3}；請依 exact_ordered_tuple_declared_by_interface 回答。","answer":{"kind":"expression","value":"(-3, 1, [0, 1, 3], [1, -2, -8], -21/2, -21/2, 是, affine_exactness_on_this_partition_does_not_imply_all_functions_are_exact)","explanation_zh":"Wave6第十三層核對=(-3, 1, [0, 1, 3], [1, -2, -8], -21/2, -21/2, 是, affine_exactness_on_this_partition_does_not_imply_all_functions_are_exact)；依完整明示資料精確重算；複合梯形逐段使用endpoint average與自己的width；signed error固定為I-T；affine exact或指定quadratic reference不推出一般誤差界、收斂階或唯一integrand。"},"difficulty":{"band":"undergraduate_core","level":1,"skills":["複合梯形法"]},"variant":{"family_id":"qf-mod50-trap-affine-exactness","seed":202611192051,"parameters":{"slope":-3,"intercept":1,"nodes":[0,1,3],"domain":"Exact_composite_trapezoidal_quadrature","operation":"trap-affine-exactness","semantic_template":"trap-affine-exactness|{\"intercept\":[1,1],\"nodes\":[[0,1],[1,1],[3,1]],\"slope\":[-3,1]}"}},"verification":{"status":"candidate","checks":["producer_contract_recomputation","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"candidate 僅對明示有限或符號模型重算；不構成一般定理、人工審定、Lean 或 Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"GPT-5.6 Terra","generated_at":"2026-10-15","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261015-pulse-20261119-r02-0052","batch_id":"batch-20261015-advance-20261119-r02-trapezoidal-quadrature-foundations","language":"zh-Hant","source_mko_ids":["mko-trapezoidal-quadrature"],"title_zh":"複合梯形法","stem_zh":"嚴格遞增partition、n+1 nodes與逐subinterval寬度。操作=trap-affine-exactness；明示資料={\"intercept\":2,\"nodes\":[0,1,4],\"slope\":-2}；請依 exact_ordered_tuple_declared_by_interface 回答。","answer":{"kind":"expression","value":"(-2, 2, [0, 1, 4], [2, 0, -6], -8, -8, 是, affine_exactness_on_this_partition_does_not_imply_all_functions_are_exact)","explanation_zh":"Wave6第十三層核對=(-2, 2, [0, 1, 4], [2, 0, -6], -8, -8, 是, affine_exactness_on_this_partition_does_not_imply_all_functions_are_exact)；依完整明示資料精確重算；複合梯形逐段使用endpoint average與自己的width；signed error固定為I-T；affine exact或指定quadratic reference不推出一般誤差界、收斂階或唯一integrand。"},"difficulty":{"band":"undergraduate_core","level":1,"skills":["複合梯形法"]},"variant":{"family_id":"qf-mod50-trap-affine-exactness","seed":202611192052,"parameters":{"slope":-2,"intercept":2,"nodes":[0,1,4],"domain":"Exact_composite_trapezoidal_quadrature","operation":"trap-affine-exactness","semantic_template":"trap-affine-exactness|{\"intercept\":[2,1],\"nodes\":[[0,1],[1,1],[4,1]],\"slope\":[-2,1]}"}},"verification":{"status":"candidate","checks":["producer_contract_recomputation","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"candidate 僅對明示有限或符號模型重算；不構成一般定理、人工審定、Lean 或 Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"GPT-5.6 Terra","generated_at":"2026-10-15","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261015-pulse-20261119-r02-0053","batch_id":"batch-20261015-advance-20261119-r02-trapezoidal-quadrature-foundations","language":"zh-Hant","source_mko_ids":["mko-trapezoidal-quadrature"],"title_zh":"複合梯形法","stem_zh":"嚴格遞增partition、n+1 nodes與逐subinterval寬度。操作=trap-affine-exactness；明示資料={\"intercept\":3,\"nodes\":[0,1,5],\"slope\":-1}；請依 exact_ordered_tuple_declared_by_interface 回答。","answer":{"kind":"expression","value":"(-1, 3, [0, 1, 5], [3, 2, -2], 5/2, 5/2, 是, affine_exactness_on_this_partition_does_not_imply_all_functions_are_exact)","explanation_zh":"Wave6第十三層核對=(-1, 3, [0, 1, 5], [3, 2, -2], 5/2, 5/2, 是, affine_exactness_on_this_partition_does_not_imply_all_functions_are_exact)；依完整明示資料精確重算；複合梯形逐段使用endpoint average與自己的width；signed error固定為I-T；affine exact或指定quadratic reference不推出一般誤差界、收斂階或唯一integrand。"},"difficulty":{"band":"undergraduate_core","level":1,"skills":["複合梯形法"]},"variant":{"family_id":"qf-mod50-trap-affine-exactness","seed":202611192053,"parameters":{"slope":-1,"intercept":3,"nodes":[0,1,5],"domain":"Exact_composite_trapezoidal_quadrature","operation":"trap-affine-exactness","semantic_template":"trap-affine-exactness|{\"intercept\":[3,1],\"nodes\":[[0,1],[1,1],[5,1]],\"slope\":[-1,1]}"}},"verification":{"status":"candidate","checks":["producer_contract_recomputation","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"candidate 僅對明示有限或符號模型重算；不構成一般定理、人工審定、Lean 或 Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"GPT-5.6 Terra","generated_at":"2026-10-15","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261015-pulse-20261119-r02-0054","batch_id":"batch-20261015-advance-20261119-r02-trapezoidal-quadrature-foundations","language":"zh-Hant","source_mko_ids":["mko-trapezoidal-quadrature"],"title_zh":"複合梯形法","stem_zh":"嚴格遞增partition、n+1 nodes與逐subinterval寬度。操作=trap-affine-exactness；明示資料={\"intercept\":4,\"nodes\":[0,1,6],\"slope\":2}；請依 exact_ordered_tuple_declared_by_interface 回答。","answer":{"kind":"expression","value":"(2, 4, [0, 1, 6], [4, 6, 16], 60, 60, 是, affine_exactness_on_this_partition_does_not_imply_all_functions_are_exact)","explanation_zh":"Wave6第十三層核對=(2, 4, [0, 1, 6], [4, 6, 16], 60, 60, 是, affine_exactness_on_this_partition_does_not_imply_all_functions_are_exact)；依完整明示資料精確重算；複合梯形逐段使用endpoint average與自己的width；signed error固定為I-T；affine exact或指定quadratic reference不推出一般誤差界、收斂階或唯一integrand。"},"difficulty":{"band":"undergraduate_core","level":1,"skills":["複合梯形法"]},"variant":{"family_id":"qf-mod50-trap-affine-exactness","seed":202611192054,"parameters":{"slope":2,"intercept":4,"nodes":[0,1,6],"domain":"Exact_composite_trapezoidal_quadrature","operation":"trap-affine-exactness","semantic_template":"trap-affine-exactness|{\"intercept\":[4,1],\"nodes\":[[0,1],[1,1],[6,1]],\"slope\":[2,1]}"}},"verification":{"status":"candidate","checks":["producer_contract_recomputation","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"candidate 僅對明示有限或符號模型重算；不構成一般定理、人工審定、Lean 或 Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"GPT-5.6 Terra","generated_at":"2026-10-15","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261015-pulse-20261119-r02-0055","batch_id":"batch-20261015-advance-20261119-r02-trapezoidal-quadrature-foundations","language":"zh-Hant","source_mko_ids":["mko-trapezoidal-quadrature"],"title_zh":"複合梯形法","stem_zh":"嚴格遞增partition、n+1 nodes與逐subinterval寬度。操作=trap-affine-exactness；明示資料={\"intercept\":5,\"nodes\":[0,1,7],\"slope\":1}；請依 exact_ordered_tuple_declared_by_interface 回答。","answer":{"kind":"expression","value":"(1, 5, [0, 1, 7], [5, 6, 12], 119/2, 119/2, 是, affine_exactness_on_this_partition_does_not_imply_all_functions_are_exact)","explanation_zh":"Wave6第十三層核對=(1, 5, [0, 1, 7], [5, 6, 12], 119/2, 119/2, 是, affine_exactness_on_this_partition_does_not_imply_all_functions_are_exact)；依完整明示資料精確重算；複合梯形逐段使用endpoint average與自己的width；signed error固定為I-T；affine exact或指定quadratic reference不推出一般誤差界、收斂階或唯一integrand。"},"difficulty":{"band":"undergraduate_core","level":1,"skills":["複合梯形法"]},"variant":{"family_id":"qf-mod50-trap-affine-exactness","seed":202611192055,"parameters":{"slope":1,"intercept":5,"nodes":[0,1,7],"domain":"Exact_composite_trapezoidal_quadrature","operation":"trap-affine-exactness","semantic_template":"trap-affine-exactness|{\"intercept\":[5,1],\"nodes\":[[0,1],[1,1],[7,1]],\"slope\":[1,1]}"}},"verification":{"status":"candidate","checks":["producer_contract_recomputation","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"candidate 僅對明示有限或符號模型重算；不構成一般定理、人工審定、Lean 或 Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"GPT-5.6 Terra","generated_at":"2026-10-15","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261015-pulse-20261119-r02-0056","batch_id":"batch-20261015-advance-20261119-r02-trapezoidal-quadrature-foundations","language":"zh-Hant","source_mko_ids":["mko-trapezoidal-quadrature"],"title_zh":"複合梯形法","stem_zh":"嚴格遞增partition、n+1 nodes與逐subinterval寬度。操作=trap-affine-exactness；明示資料={\"intercept\":6,\"nodes\":[0,1,8],\"slope\":2}；請依 exact_ordered_tuple_declared_by_interface 回答。","answer":{"kind":"expression","value":"(2, 6, [0, 1, 8], [6, 8, 22], 112, 112, 是, affine_exactness_on_this_partition_does_not_imply_all_functions_are_exact)","explanation_zh":"Wave6第十三層核對=(2, 6, [0, 1, 8], [6, 8, 22], 112, 112, 是, affine_exactness_on_this_partition_does_not_imply_all_functions_are_exact)；依完整明示資料精確重算；複合梯形逐段使用endpoint average與自己的width；signed error固定為I-T；affine exact或指定quadratic reference不推出一般誤差界、收斂階或唯一integrand。"},"difficulty":{"band":"undergraduate_core","level":1,"skills":["複合梯形法"]},"variant":{"family_id":"qf-mod50-trap-affine-exactness","seed":202611192056,"parameters":{"slope":2,"intercept":6,"nodes":[0,1,8],"domain":"Exact_composite_trapezoidal_quadrature","operation":"trap-affine-exactness","semantic_template":"trap-affine-exactness|{\"intercept\":[6,1],\"nodes\":[[0,1],[1,1],[8,1]],\"slope\":[2,1]}"}},"verification":{"status":"candidate","checks":["producer_contract_recomputation","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"candidate 僅對明示有限或符號模型重算；不構成一般定理、人工審定、Lean 或 Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"GPT-5.6 Terra","generated_at":"2026-10-15","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261015-pulse-20261119-r02-0057","batch_id":"batch-20261015-advance-20261119-r02-trapezoidal-quadrature-foundations","language":"zh-Hant","source_mko_ids":["mko-trapezoidal-quadrature"],"title_zh":"複合梯形法","stem_zh":"嚴格遞增partition、n+1 nodes與逐subinterval寬度。操作=trap-affine-exactness；明示資料={\"intercept\":7,\"nodes\":[0,1,9],\"slope\":3}；請依 exact_ordered_tuple_declared_by_interface 回答。","answer":{"kind":"expression","value":"(3, 7, [0, 1, 9], [7, 10, 34], 369/2, 369/2, 是, affine_exactness_on_this_partition_does_not_imply_all_functions_are_exact)","explanation_zh":"Wave6第十三層核對=(3, 7, [0, 1, 9], [7, 10, 34], 369/2, 369/2, 是, affine_exactness_on_this_partition_does_not_imply_all_functions_are_exact)；依完整明示資料精確重算；複合梯形逐段使用endpoint average與自己的width；signed error固定為I-T；affine exact或指定quadratic reference不推出一般誤差界、收斂階或唯一integrand。"},"difficulty":{"band":"undergraduate_core","level":1,"skills":["複合梯形法"]},"variant":{"family_id":"qf-mod50-trap-affine-exactness","seed":202611192057,"parameters":{"slope":3,"intercept":7,"nodes":[0,1,9],"domain":"Exact_composite_trapezoidal_quadrature","operation":"trap-affine-exactness","semantic_template":"trap-affine-exactness|{\"intercept\":[7,1],\"nodes\":[[0,1],[1,1],[9,1]],\"slope\":[3,1]}"}},"verification":{"status":"candidate","checks":["producer_contract_recomputation","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"candidate 僅對明示有限或符號模型重算；不構成一般定理、人工審定、Lean 或 Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"GPT-5.6 Terra","generated_at":"2026-10-15","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261015-pulse-20261119-r02-0058","batch_id":"batch-20261015-advance-20261119-r02-trapezoidal-quadrature-foundations","language":"zh-Hant","source_mko_ids":["mko-trapezoidal-quadrature"],"title_zh":"複合梯形法","stem_zh":"嚴格遞增partition、n+1 nodes與逐subinterval寬度。操作=trap-affine-exactness；明示資料={\"intercept\":8,\"nodes\":[0,1,10],\"slope\":-3}；請依 exact_ordered_tuple_declared_by_interface 回答。","answer":{"kind":"expression","value":"(-3, 8, [0, 1, 10], [8, 5, -22], -70, -70, 是, affine_exactness_on_this_partition_does_not_imply_all_functions_are_exact)","explanation_zh":"Wave6第十三層核對=(-3, 8, [0, 1, 10], [8, 5, -22], -70, -70, 是, affine_exactness_on_this_partition_does_not_imply_all_functions_are_exact)；依完整明示資料精確重算；複合梯形逐段使用endpoint average與自己的width；signed error固定為I-T；affine exact或指定quadratic reference不推出一般誤差界、收斂階或唯一integrand。"},"difficulty":{"band":"undergraduate_core","level":1,"skills":["複合梯形法"]},"variant":{"family_id":"qf-mod50-trap-affine-exactness","seed":202611192058,"parameters":{"slope":-3,"intercept":8,"nodes":[0,1,10],"domain":"Exact_composite_trapezoidal_quadrature","operation":"trap-affine-exactness","semantic_template":"trap-affine-exactness|{\"intercept\":[8,1],\"nodes\":[[0,1],[1,1],[10,1]],\"slope\":[-3,1]}"}},"verification":{"status":"candidate","checks":["producer_contract_recomputation","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"candidate 僅對明示有限或符號模型重算；不構成一般定理、人工審定、Lean 或 Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"GPT-5.6 Terra","generated_at":"2026-10-15","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261015-pulse-20261119-r02-0059","batch_id":"batch-20261015-advance-20261119-r02-trapezoidal-quadrature-foundations","language":"zh-Hant","source_mko_ids":["mko-trapezoidal-quadrature"],"title_zh":"複合梯形法","stem_zh":"嚴格遞增partition、n+1 nodes與逐subinterval寬度。操作=trap-affine-exactness；明示資料={\"intercept\":9,\"nodes\":[0,1,11],\"slope\":-2}；請依 exact_ordered_tuple_declared_by_interface 回答。","answer":{"kind":"expression","value":"(-2, 9, [0, 1, 11], [9, 7, -13], -22, -22, 是, affine_exactness_on_this_partition_does_not_imply_all_functions_are_exact)","explanation_zh":"Wave6第十三層核對=(-2, 9, [0, 1, 11], [9, 7, -13], -22, -22, 是, affine_exactness_on_this_partition_does_not_imply_all_functions_are_exact)；依完整明示資料精確重算；複合梯形逐段使用endpoint average與自己的width；signed error固定為I-T；affine exact或指定quadratic reference不推出一般誤差界、收斂階或唯一integrand。"},"difficulty":{"band":"undergraduate_core","level":2,"skills":["複合梯形法"]},"variant":{"family_id":"qf-mod50-trap-affine-exactness","seed":202611192059,"parameters":{"slope":-2,"intercept":9,"nodes":[0,1,11],"domain":"Exact_composite_trapezoidal_quadrature","operation":"trap-affine-exactness","semantic_template":"trap-affine-exactness|{\"intercept\":[9,1],\"nodes\":[[0,1],[1,1],[11,1]],\"slope\":[-2,1]}"}},"verification":{"status":"candidate","checks":["producer_contract_recomputation","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"candidate 僅對明示有限或符號模型重算；不構成一般定理、人工審定、Lean 或 Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"GPT-5.6 Terra","generated_at":"2026-10-15","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261015-pulse-20261119-r02-0060","batch_id":"batch-20261015-advance-20261119-r02-trapezoidal-quadrature-foundations","language":"zh-Hant","source_mko_ids":["mko-trapezoidal-quadrature"],"title_zh":"複合梯形法","stem_zh":"嚴格遞增partition、n+1 nodes與逐subinterval寬度。操作=trap-affine-exactness；明示資料={\"intercept\":10,\"nodes\":[0,1,12],\"slope\":-1}；請依 exact_ordered_tuple_declared_by_interface 回答。","answer":{"kind":"expression","value":"(-1, 10, [0, 1, 12], [10, 9, -2], 48, 48, 是, affine_exactness_on_this_partition_does_not_imply_all_functions_are_exact)","explanation_zh":"Wave6第十三層核對=(-1, 10, [0, 1, 12], [10, 9, -2], 48, 48, 是, affine_exactness_on_this_partition_does_not_imply_all_functions_are_exact)；依完整明示資料精確重算；複合梯形逐段使用endpoint average與自己的width；signed error固定為I-T；affine exact或指定quadratic reference不推出一般誤差界、收斂階或唯一integrand。"},"difficulty":{"band":"undergraduate_core","level":2,"skills":["複合梯形法"]},"variant":{"family_id":"qf-mod50-trap-affine-exactness","seed":202611192060,"parameters":{"slope":-1,"intercept":10,"nodes":[0,1,12],"domain":"Exact_composite_trapezoidal_quadrature","operation":"trap-affine-exactness","semantic_template":"trap-affine-exactness|{\"intercept\":[10,1],\"nodes\":[[0,1],[1,1],[12,1]],\"slope\":[-1,1]}"}},"verification":{"status":"candidate","checks":["producer_contract_recomputation","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"candidate 僅對明示有限或符號模型重算；不構成一般定理、人工審定、Lean 或 Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"GPT-5.6 Terra","generated_at":"2026-10-15","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261015-pulse-20261119-r02-0061","batch_id":"batch-20261015-advance-20261119-r02-trapezoidal-quadrature-foundations","language":"zh-Hant","source_mko_ids":["mko-trapezoidal-quadrature"],"title_zh":"複合梯形法","stem_zh":"嚴格遞增partition、n+1 nodes與逐subinterval寬度。操作=trap-affine-exactness；明示資料={\"intercept\":11,\"nodes\":[0,1,13],\"slope\":2}；請依 exact_ordered_tuple_declared_by_interface 回答。","answer":{"kind":"expression","value":"(2, 11, [0, 1, 13], [11, 13, 37], 312, 312, 是, affine_exactness_on_this_partition_does_not_imply_all_functions_are_exact)","explanation_zh":"Wave6第十三層核對=(2, 11, [0, 1, 13], [11, 13, 37], 312, 312, 是, affine_exactness_on_this_partition_does_not_imply_all_functions_are_exact)；依完整明示資料精確重算；複合梯形逐段使用endpoint average與自己的width；signed error固定為I-T；affine exact或指定quadratic reference不推出一般誤差界、收斂階或唯一integrand。"},"difficulty":{"band":"undergraduate_core","level":2,"skills":["複合梯形法"]},"variant":{"family_id":"qf-mod50-trap-affine-exactness","seed":202611192061,"parameters":{"slope":2,"intercept":11,"nodes":[0,1,13],"domain":"Exact_composite_trapezoidal_quadrature","operation":"trap-affine-exactness","semantic_template":"trap-affine-exactness|{\"intercept\":[11,1],\"nodes\":[[0,1],[1,1],[13,1]],\"slope\":[2,1]}"}},"verification":{"status":"candidate","checks":["producer_contract_recomputation","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"candidate 僅對明示有限或符號模型重算；不構成一般定理、人工審定、Lean 或 Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"GPT-5.6 Terra","generated_at":"2026-10-15","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261015-pulse-20261119-r02-0062","batch_id":"batch-20261015-advance-20261119-r02-trapezoidal-quadrature-foundations","language":"zh-Hant","source_mko_ids":["mko-trapezoidal-quadrature"],"title_zh":"複合梯形法","stem_zh":"嚴格遞增partition、n+1 nodes與逐subinterval寬度。操作=trap-affine-exactness；明示資料={\"intercept\":12,\"nodes\":[0,1,14],\"slope\":1}；請依 exact_ordered_tuple_declared_by_interface 回答。","answer":{"kind":"expression","value":"(1, 12, [0, 1, 14], [12, 13, 26], 266, 266, 是, affine_exactness_on_this_partition_does_not_imply_all_functions_are_exact)","explanation_zh":"Wave6第十三層核對=(1, 12, [0, 1, 14], [12, 13, 26], 266, 266, 是, affine_exactness_on_this_partition_does_not_imply_all_functions_are_exact)；依完整明示資料精確重算；複合梯形逐段使用endpoint average與自己的width；signed error固定為I-T；affine exact或指定quadratic reference不推出一般誤差界、收斂階或唯一integrand。"},"difficulty":{"band":"undergraduate_core","level":2,"skills":["複合梯形法"]},"variant":{"family_id":"qf-mod50-trap-affine-exactness","seed":202611192062,"parameters":{"slope":1,"intercept":12,"nodes":[0,1,14],"domain":"Exact_composite_trapezoidal_quadrature","operation":"trap-affine-exactness","semantic_template":"trap-affine-exactness|{\"intercept\":[12,1],\"nodes\":[[0,1],[1,1],[14,1]],\"slope\":[1,1]}"}},"verification":{"status":"candidate","checks":["producer_contract_recomputation","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"candidate 僅對明示有限或符號模型重算；不構成一般定理、人工審定、Lean 或 Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"GPT-5.6 Terra","generated_at":"2026-10-15","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261015-pulse-20261119-r02-0063","batch_id":"batch-20261015-advance-20261119-r02-trapezoidal-quadrature-foundations","language":"zh-Hant","source_mko_ids":["mko-trapezoidal-quadrature"],"title_zh":"複合梯形法","stem_zh":"嚴格遞增partition、n+1 nodes與逐subinterval寬度。操作=trap-affine-exactness；明示資料={\"intercept\":13,\"nodes\":[0,1,15],\"slope\":2}；請依 exact_ordered_tuple_declared_by_interface 回答。","answer":{"kind":"expression","value":"(2, 13, [0, 1, 15], [13, 15, 43], 420, 420, 是, affine_exactness_on_this_partition_does_not_imply_all_functions_are_exact)","explanation_zh":"Wave6第十三層核對=(2, 13, [0, 1, 15], [13, 15, 43], 420, 420, 是, affine_exactness_on_this_partition_does_not_imply_all_functions_are_exact)；依完整明示資料精確重算；複合梯形逐段使用endpoint average與自己的width；signed error固定為I-T；affine exact或指定quadratic reference不推出一般誤差界、收斂階或唯一integrand。"},"difficulty":{"band":"undergraduate_core","level":2,"skills":["複合梯形法"]},"variant":{"family_id":"qf-mod50-trap-affine-exactness","seed":202611192063,"parameters":{"slope":2,"intercept":13,"nodes":[0,1,15],"domain":"Exact_composite_trapezoidal_quadrature","operation":"trap-affine-exactness","semantic_template":"trap-affine-exactness|{\"intercept\":[13,1],\"nodes\":[[0,1],[1,1],[15,1]],\"slope\":[2,1]}"}},"verification":{"status":"candidate","checks":["producer_contract_recomputation","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"candidate 僅對明示有限或符號模型重算；不構成一般定理、人工審定、Lean 或 Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"GPT-5.6 Terra","generated_at":"2026-10-15","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261015-pulse-20261119-r02-0064","batch_id":"batch-20261015-advance-20261119-r02-trapezoidal-quadrature-foundations","language":"zh-Hant","source_mko_ids":["mko-trapezoidal-quadrature"],"title_zh":"複合梯形法","stem_zh":"嚴格遞增partition、n+1 nodes與逐subinterval寬度。操作=trap-affine-exactness；明示資料={\"intercept\":14,\"nodes\":[0,1,16],\"slope\":3}；請依 exact_ordered_tuple_declared_by_interface 回答。","answer":{"kind":"expression","value":"(3, 14, [0, 1, 16], [14, 17, 62], 608, 608, 是, affine_exactness_on_this_partition_does_not_imply_all_functions_are_exact)","explanation_zh":"Wave6第十三層核對=(3, 14, [0, 1, 16], [14, 17, 62], 608, 608, 是, affine_exactness_on_this_partition_does_not_imply_all_functions_are_exact)；依完整明示資料精確重算；複合梯形逐段使用endpoint average與自己的width；signed error固定為I-T；affine exact或指定quadratic reference不推出一般誤差界、收斂階或唯一integrand。"},"difficulty":{"band":"undergraduate_core","level":2,"skills":["複合梯形法"]},"variant":{"family_id":"qf-mod50-trap-affine-exactness","seed":202611192064,"parameters":{"slope":3,"intercept":14,"nodes":[0,1,16],"domain":"Exact_composite_trapezoidal_quadrature","operation":"trap-affine-exactness","semantic_template":"trap-affine-exactness|{\"intercept\":[14,1],\"nodes\":[[0,1],[1,1],[16,1]],\"slope\":[3,1]}"}},"verification":{"status":"candidate","checks":["producer_contract_recomputation","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"candidate 僅對明示有限或符號模型重算；不構成一般定理、人工審定、Lean 或 Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"GPT-5.6 Terra","generated_at":"2026-10-15","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261015-pulse-20261119-r02-0065","batch_id":"batch-20261015-advance-20261119-r02-trapezoidal-quadrature-foundations","language":"zh-Hant","source_mko_ids":["mko-trapezoidal-quadrature"],"title_zh":"複合梯形法","stem_zh":"嚴格遞增partition、n+1 nodes與逐subinterval寬度。操作=trap-affine-exactness；明示資料={\"intercept\":15,\"nodes\":[0,1,17],\"slope\":-3}；請依 exact_ordered_tuple_declared_by_interface 回答。","answer":{"kind":"expression","value":"(-3, 15, [0, 1, 17], [15, 12, -36], -357/2, -357/2, 是, affine_exactness_on_this_partition_does_not_imply_all_functions_are_exact)","explanation_zh":"Wave6第十三層核對=(-3, 15, [0, 1, 17], [15, 12, -36], -357/2, -357/2, 是, affine_exactness_on_this_partition_does_not_imply_all_functions_are_exact)；依完整明示資料精確重算；複合梯形逐段使用endpoint average與自己的width；signed error固定為I-T；affine exact或指定quadratic reference不推出一般誤差界、收斂階或唯一integrand。"},"difficulty":{"band":"undergraduate_core","level":2,"skills":["複合梯形法"]},"variant":{"family_id":"qf-mod50-trap-affine-exactness","seed":202611192065,"parameters":{"slope":-3,"intercept":15,"nodes":[0,1,17],"domain":"Exact_composite_trapezoidal_quadrature","operation":"trap-affine-exactness","semantic_template":"trap-affine-exactness|{\"intercept\":[15,1],\"nodes\":[[0,1],[1,1],[17,1]],\"slope\":[-3,1]}"}},"verification":{"status":"candidate","checks":["producer_contract_recomputation","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"candidate 僅對明示有限或符號模型重算；不構成一般定理、人工審定、Lean 或 Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"GPT-5.6 Terra","generated_at":"2026-10-15","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261015-pulse-20261119-r02-0066","batch_id":"batch-20261015-advance-20261119-r02-trapezoidal-quadrature-foundations","language":"zh-Hant","source_mko_ids":["mko-trapezoidal-quadrature"],"title_zh":"複合梯形法","stem_zh":"嚴格遞增partition、n+1 nodes與逐subinterval寬度。操作=trap-affine-exactness；明示資料={\"intercept\":16,\"nodes\":[0,1,18],\"slope\":-2}；請依 exact_ordered_tuple_declared_by_interface 回答。","answer":{"kind":"expression","value":"(-2, 16, [0, 1, 18], [16, 14, -20], -36, -36, 是, affine_exactness_on_this_partition_does_not_imply_all_functions_are_exact)","explanation_zh":"Wave6第十三層核對=(-2, 16, [0, 1, 18], [16, 14, -20], -36, -36, 是, affine_exactness_on_this_partition_does_not_imply_all_functions_are_exact)；依完整明示資料精確重算；複合梯形逐段使用endpoint average與自己的width；signed error固定為I-T；affine exact或指定quadratic reference不推出一般誤差界、收斂階或唯一integrand。"},"difficulty":{"band":"undergraduate_core","level":2,"skills":["複合梯形法"]},"variant":{"family_id":"qf-mod50-trap-affine-exactness","seed":202611192066,"parameters":{"slope":-2,"intercept":16,"nodes":[0,1,18],"domain":"Exact_composite_trapezoidal_quadrature","operation":"trap-affine-exactness","semantic_template":"trap-affine-exactness|{\"intercept\":[16,1],\"nodes\":[[0,1],[1,1],[18,1]],\"slope\":[-2,1]}"}},"verification":{"status":"candidate","checks":["producer_contract_recomputation","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"candidate 僅對明示有限或符號模型重算；不構成一般定理、人工審定、Lean 或 Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"GPT-5.6 Terra","generated_at":"2026-10-15","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261015-pulse-20261119-r02-0067","batch_id":"batch-20261015-advance-20261119-r02-trapezoidal-quadrature-foundations","language":"zh-Hant","source_mko_ids":["mko-trapezoidal-quadrature"],"title_zh":"複合梯形法","stem_zh":"嚴格遞增partition、n+1 nodes與逐subinterval寬度。操作=trap-affine-exactness；明示資料={\"intercept\":17,\"nodes\":[0,1,19],\"slope\":-1}；請依 exact_ordered_tuple_declared_by_interface 回答。","answer":{"kind":"expression","value":"(-1, 17, [0, 1, 19], [17, 16, -2], 285/2, 285/2, 是, affine_exactness_on_this_partition_does_not_imply_all_functions_are_exact)","explanation_zh":"Wave6第十三層核對=(-1, 17, [0, 1, 19], [17, 16, -2], 285/2, 285/2, 是, affine_exactness_on_this_partition_does_not_imply_all_functions_are_exact)；依完整明示資料精確重算；複合梯形逐段使用endpoint average與自己的width；signed error固定為I-T；affine exact或指定quadratic reference不推出一般誤差界、收斂階或唯一integrand。"},"difficulty":{"band":"undergraduate_core","level":2,"skills":["複合梯形法"]},"variant":{"family_id":"qf-mod50-trap-affine-exactness","seed":202611192067,"parameters":{"slope":-1,"intercept":17,"nodes":[0,1,19],"domain":"Exact_composite_trapezoidal_quadrature","operation":"trap-affine-exactness","semantic_template":"trap-affine-exactness|{\"intercept\":[17,1],\"nodes\":[[0,1],[1,1],[19,1]],\"slope\":[-1,1]}"}},"verification":{"status":"candidate","checks":["producer_contract_recomputation","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"candidate 僅對明示有限或符號模型重算；不構成一般定理、人工審定、Lean 或 Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"GPT-5.6 Terra","generated_at":"2026-10-15","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261015-pulse-20261119-r02-0068","batch_id":"batch-20261015-advance-20261119-r02-trapezoidal-quadrature-foundations","language":"zh-Hant","source_mko_ids":["mko-trapezoidal-quadrature"],"title_zh":"複合梯形法","stem_zh":"嚴格遞增partition、n+1 nodes與逐subinterval寬度。操作=trap-affine-exactness；明示資料={\"intercept\":18,\"nodes\":[0,1,20],\"slope\":2}；請依 exact_ordered_tuple_declared_by_interface 回答。","answer":{"kind":"expression","value":"(2, 18, [0, 1, 20], [18, 20, 58], 760, 760, 是, affine_exactness_on_this_partition_does_not_imply_all_functions_are_exact)","explanation_zh":"Wave6第十三層核對=(2, 18, [0, 1, 20], [18, 20, 58], 760, 760, 是, affine_exactness_on_this_partition_does_not_imply_all_functions_are_exact)；依完整明示資料精確重算；複合梯形逐段使用endpoint average與自己的width；signed error固定為I-T；affine exact或指定quadratic reference不推出一般誤差界、收斂階或唯一integrand。"},"difficulty":{"band":"undergraduate_core","level":3,"skills":["複合梯形法"]},"variant":{"family_id":"qf-mod50-trap-affine-exactness","seed":202611192068,"parameters":{"slope":2,"intercept":18,"nodes":[0,1,20],"domain":"Exact_composite_trapezoidal_quadrature","operation":"trap-affine-exactness","semantic_template":"trap-affine-exactness|{\"intercept\":[18,1],\"nodes\":[[0,1],[1,1],[20,1]],\"slope\":[2,1]}"}},"verification":{"status":"candidate","checks":["producer_contract_recomputation","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"candidate 僅對明示有限或符號模型重算；不構成一般定理、人工審定、Lean 或 Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"GPT-5.6 Terra","generated_at":"2026-10-15","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261015-pulse-20261119-r02-0069","batch_id":"batch-20261015-advance-20261119-r02-trapezoidal-quadrature-foundations","language":"zh-Hant","source_mko_ids":["mko-trapezoidal-quadrature"],"title_zh":"複合梯形法","stem_zh":"嚴格遞增partition、n+1 nodes與逐subinterval寬度。操作=trap-affine-exactness；明示資料={\"intercept\":19,\"nodes\":[0,1,21],\"slope\":1}；請依 exact_ordered_tuple_declared_by_interface 回答。","answer":{"kind":"expression","value":"(1, 19, [0, 1, 21], [19, 20, 40], 1239/2, 1239/2, 是, affine_exactness_on_this_partition_does_not_imply_all_functions_are_exact)","explanation_zh":"Wave6第十三層核對=(1, 19, [0, 1, 21], [19, 20, 40], 1239/2, 1239/2, 是, affine_exactness_on_this_partition_does_not_imply_all_functions_are_exact)；依完整明示資料精確重算；複合梯形逐段使用endpoint average與自己的width；signed error固定為I-T；affine exact或指定quadratic reference不推出一般誤差界、收斂階或唯一integrand。"},"difficulty":{"band":"undergraduate_core","level":3,"skills":["複合梯形法"]},"variant":{"family_id":"qf-mod50-trap-affine-exactness","seed":202611192069,"parameters":{"slope":1,"intercept":19,"nodes":[0,1,21],"domain":"Exact_composite_trapezoidal_quadrature","operation":"trap-affine-exactness","semantic_template":"trap-affine-exactness|{\"intercept\":[19,1],\"nodes\":[[0,1],[1,1],[21,1]],\"slope\":[1,1]}"}},"verification":{"status":"candidate","checks":["producer_contract_recomputation","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"candidate 僅對明示有限或符號模型重算；不構成一般定理、人工審定、Lean 或 Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"GPT-5.6 Terra","generated_at":"2026-10-15","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261015-pulse-20261119-r02-0070","batch_id":"batch-20261015-advance-20261119-r02-trapezoidal-quadrature-foundations","language":"zh-Hant","source_mko_ids":["mko-trapezoidal-quadrature"],"title_zh":"複合梯形法","stem_zh":"嚴格遞增partition、n+1 nodes與逐subinterval寬度。操作=trap-affine-exactness；明示資料={\"intercept\":20,\"nodes\":[0,1,22],\"slope\":2}；請依 exact_ordered_tuple_declared_by_interface 回答。","answer":{"kind":"expression","value":"(2, 20, [0, 1, 22], [20, 22, 64], 924, 924, 是, affine_exactness_on_this_partition_does_not_imply_all_functions_are_exact)","explanation_zh":"Wave6第十三層核對=(2, 20, [0, 1, 22], [20, 22, 64], 924, 924, 是, affine_exactness_on_this_partition_does_not_imply_all_functions_are_exact)；依完整明示資料精確重算；複合梯形逐段使用endpoint average與自己的width；signed error固定為I-T；affine exact或指定quadratic reference不推出一般誤差界、收斂階或唯一integrand。"},"difficulty":{"band":"undergraduate_core","level":3,"skills":["複合梯形法"]},"variant":{"family_id":"qf-mod50-trap-affine-exactness","seed":202611192070,"parameters":{"slope":2,"intercept":20,"nodes":[0,1,22],"domain":"Exact_composite_trapezoidal_quadrature","operation":"trap-affine-exactness","semantic_template":"trap-affine-exactness|{\"intercept\":[20,1],\"nodes\":[[0,1],[1,1],[22,1]],\"slope\":[2,1]}"}},"verification":{"status":"candidate","checks":["producer_contract_recomputation","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"candidate 僅對明示有限或符號模型重算；不構成一般定理、人工審定、Lean 或 Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"GPT-5.6 Terra","generated_at":"2026-10-15","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261015-pulse-20261119-r02-0071","batch_id":"batch-20261015-advance-20261119-r02-trapezoidal-quadrature-foundations","language":"zh-Hant","source_mko_ids":["mko-trapezoidal-quadrature"],"title_zh":"複合梯形法","stem_zh":"嚴格遞增partition、n+1 nodes與逐subinterval寬度。操作=trap-affine-exactness；明示資料={\"intercept\":21,\"nodes\":[0,1,23],\"slope\":3}；請依 exact_ordered_tuple_declared_by_interface 回答。","answer":{"kind":"expression","value":"(3, 21, [0, 1, 23], [21, 24, 90], 2553/2, 2553/2, 是, affine_exactness_on_this_partition_does_not_imply_all_functions_are_exact)","explanation_zh":"Wave6第十三層核對=(3, 21, [0, 1, 23], [21, 24, 90], 2553/2, 2553/2, 是, affine_exactness_on_this_partition_does_not_imply_all_functions_are_exact)；依完整明示資料精確重算；複合梯形逐段使用endpoint average與自己的width；signed error固定為I-T；affine exact或指定quadratic reference不推出一般誤差界、收斂階或唯一integrand。"},"difficulty":{"band":"undergraduate_core","level":3,"skills":["複合梯形法"]},"variant":{"family_id":"qf-mod50-trap-affine-exactness","seed":202611192071,"parameters":{"slope":3,"intercept":21,"nodes":[0,1,23],"domain":"Exact_composite_trapezoidal_quadrature","operation":"trap-affine-exactness","semantic_template":"trap-affine-exactness|{\"intercept\":[21,1],\"nodes\":[[0,1],[1,1],[23,1]],\"slope\":[3,1]}"}},"verification":{"status":"candidate","checks":["producer_contract_recomputation","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"candidate 僅對明示有限或符號模型重算；不構成一般定理、人工審定、Lean 或 Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"GPT-5.6 Terra","generated_at":"2026-10-15","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261015-pulse-20261119-r02-0072","batch_id":"batch-20261015-advance-20261119-r02-trapezoidal-quadrature-foundations","language":"zh-Hant","source_mko_ids":["mko-trapezoidal-quadrature"],"title_zh":"複合梯形法","stem_zh":"嚴格遞增partition、n+1 nodes與逐subinterval寬度。操作=trap-affine-exactness；明示資料={\"intercept\":22,\"nodes\":[0,1,24],\"slope\":-3}；請依 exact_ordered_tuple_declared_by_interface 回答。","answer":{"kind":"expression","value":"(-3, 22, [0, 1, 24], [22, 19, -50], -336, -336, 是, affine_exactness_on_this_partition_does_not_imply_all_functions_are_exact)","explanation_zh":"Wave6第十三層核對=(-3, 22, [0, 1, 24], [22, 19, -50], -336, -336, 是, affine_exactness_on_this_partition_does_not_imply_all_functions_are_exact)；依完整明示資料精確重算；複合梯形逐段使用endpoint average與自己的width；signed error固定為I-T；affine exact或指定quadratic reference不推出一般誤差界、收斂階或唯一integrand。"},"difficulty":{"band":"undergraduate_core","level":3,"skills":["複合梯形法"]},"variant":{"family_id":"qf-mod50-trap-affine-exactness","seed":202611192072,"parameters":{"slope":-3,"intercept":22,"nodes":[0,1,24],"domain":"Exact_composite_trapezoidal_quadrature","operation":"trap-affine-exactness","semantic_template":"trap-affine-exactness|{\"intercept\":[22,1],\"nodes\":[[0,1],[1,1],[24,1]],\"slope\":[-3,1]}"}},"verification":{"status":"candidate","checks":["producer_contract_recomputation","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"candidate 僅對明示有限或符號模型重算；不構成一般定理、人工審定、Lean 或 Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"GPT-5.6 Terra","generated_at":"2026-10-15","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261015-pulse-20261119-r02-0073","batch_id":"batch-20261015-advance-20261119-r02-trapezoidal-quadrature-foundations","language":"zh-Hant","source_mko_ids":["mko-trapezoidal-quadrature"],"title_zh":"複合梯形法","stem_zh":"嚴格遞增partition、n+1 nodes與逐subinterval寬度。操作=trap-affine-exactness；明示資料={\"intercept\":23,\"nodes\":[0,1,25],\"slope\":-2}；請依 exact_ordered_tuple_declared_by_interface 回答。","answer":{"kind":"expression","value":"(-2, 23, [0, 1, 25], [23, 21, -27], -50, -50, 是, affine_exactness_on_this_partition_does_not_imply_all_functions_are_exact)","explanation_zh":"Wave6第十三層核對=(-2, 23, [0, 1, 25], [23, 21, -27], -50, -50, 是, affine_exactness_on_this_partition_does_not_imply_all_functions_are_exact)；依完整明示資料精確重算；複合梯形逐段使用endpoint average與自己的width；signed error固定為I-T；affine exact或指定quadratic reference不推出一般誤差界、收斂階或唯一integrand。"},"difficulty":{"band":"undergraduate_core","level":3,"skills":["複合梯形法"]},"variant":{"family_id":"qf-mod50-trap-affine-exactness","seed":202611192073,"parameters":{"slope":-2,"intercept":23,"nodes":[0,1,25],"domain":"Exact_composite_trapezoidal_quadrature","operation":"trap-affine-exactness","semantic_template":"trap-affine-exactness|{\"intercept\":[23,1],\"nodes\":[[0,1],[1,1],[25,1]],\"slope\":[-2,1]}"}},"verification":{"status":"candidate","checks":["producer_contract_recomputation","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"candidate 僅對明示有限或符號模型重算；不構成一般定理、人工審定、Lean 或 Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"GPT-5.6 Terra","generated_at":"2026-10-15","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261015-pulse-20261119-r02-0074","batch_id":"batch-20261015-advance-20261119-r02-trapezoidal-quadrature-foundations","language":"zh-Hant","source_mko_ids":["mko-trapezoidal-quadrature"],"title_zh":"複合梯形法","stem_zh":"嚴格遞增partition、n+1 nodes與逐subinterval寬度。操作=trap-affine-exactness；明示資料={\"intercept\":24,\"nodes\":[0,1,26],\"slope\":-1}；請依 exact_ordered_tuple_declared_by_interface 回答。","answer":{"kind":"expression","value":"(-1, 24, [0, 1, 26], [24, 23, -2], 286, 286, 是, affine_exactness_on_this_partition_does_not_imply_all_functions_are_exact)","explanation_zh":"Wave6第十三層核對=(-1, 24, [0, 1, 26], [24, 23, -2], 286, 286, 是, affine_exactness_on_this_partition_does_not_imply_all_functions_are_exact)；依完整明示資料精確重算；複合梯形逐段使用endpoint average與自己的width；signed error固定為I-T；affine exact或指定quadratic reference不推出一般誤差界、收斂階或唯一integrand。"},"difficulty":{"band":"undergraduate_core","level":3,"skills":["複合梯形法"]},"variant":{"family_id":"qf-mod50-trap-affine-exactness","seed":202611192074,"parameters":{"slope":-1,"intercept":24,"nodes":[0,1,26],"domain":"Exact_composite_trapezoidal_quadrature","operation":"trap-affine-exactness","semantic_template":"trap-affine-exactness|{\"intercept\":[24,1],\"nodes\":[[0,1],[1,1],[26,1]],\"slope\":[-1,1]}"}},"verification":{"status":"candidate","checks":["producer_contract_recomputation","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"candidate 僅對明示有限或符號模型重算；不構成一般定理、人工審定、Lean 或 Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"GPT-5.6 Terra","generated_at":"2026-10-15","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261015-pulse-20261119-r02-0075","batch_id":"batch-20261015-advance-20261119-r02-trapezoidal-quadrature-foundations","language":"zh-Hant","source_mko_ids":["mko-trapezoidal-quadrature"],"title_zh":"複合梯形法","stem_zh":"嚴格遞增partition、n+1 nodes與逐subinterval寬度。操作=trap-affine-exactness；明示資料={\"intercept\":25,\"nodes\":[0,1,27],\"slope\":2}；請依 exact_ordered_tuple_declared_by_interface 回答。","answer":{"kind":"expression","value":"(2, 25, [0, 1, 27], [25, 27, 79], 1404, 1404, 是, affine_exactness_on_this_partition_does_not_imply_all_functions_are_exact)","explanation_zh":"Wave6第十三層核對=(2, 25, [0, 1, 27], [25, 27, 79], 1404, 1404, 是, affine_exactness_on_this_partition_does_not_imply_all_functions_are_exact)；依完整明示資料精確重算；複合梯形逐段使用endpoint average與自己的width；signed error固定為I-T；affine exact或指定quadratic reference不推出一般誤差界、收斂階或唯一integrand。"},"difficulty":{"band":"undergraduate_core","level":3,"skills":["複合梯形法"]},"variant":{"family_id":"qf-mod50-trap-affine-exactness","seed":202611192075,"parameters":{"slope":2,"intercept":25,"nodes":[0,1,27],"domain":"Exact_composite_trapezoidal_quadrature","operation":"trap-affine-exactness","semantic_template":"trap-affine-exactness|{\"intercept\":[25,1],\"nodes\":[[0,1],[1,1],[27,1]],\"slope\":[2,1]}"}},"verification":{"status":"candidate","checks":["producer_contract_recomputation","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"candidate 僅對明示有限或符號模型重算；不構成一般定理、人工審定、Lean 或 Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"GPT-5.6 Terra","generated_at":"2026-10-15","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261015-pulse-20261119-r02-0076","batch_id":"batch-20261015-advance-20261119-r02-trapezoidal-quadrature-foundations","language":"zh-Hant","source_mko_ids":["mko-trapezoidal-quadrature"],"title_zh":"複合梯形法","stem_zh":"嚴格遞增partition、n+1 nodes與逐subinterval寬度。操作=trap-error-boundary；明示資料={\"mode\":\"quadratic_reference\",\"model\":{\"coefficients\":[1,1,1],\"nodes\":[0,1,3]}}；請依 exact_ordered_tuple_declared_by_interface 回答。","answer":{"kind":"expression","value":"(quadratic_reference, [1, 1, 1], [0, 1, 3], 18, 33/2, -3/2, 3/2, 否, exact_polynomial_reference_error_is_not_a_general_second_derivative_error_bound)","explanation_zh":"Wave6第十三層核對=(quadratic_reference, [1, 1, 1], [0, 1, 3], 18, 33/2, -3/2, 3/2, 否, exact_polynomial_reference_error_is_not_a_general_second_derivative_error_bound)；依完整明示資料精確重算；複合梯形逐段使用endpoint average與自己的width；signed error固定為I-T；affine exact或指定quadratic reference不推出一般誤差界、收斂階或唯一integrand。"},"difficulty":{"band":"undergraduate_core","level":1,"skills":["複合梯形法"]},"variant":{"family_id":"qf-mod50-trap-error-boundary","seed":202611192076,"parameters":{"mode":"quadratic_reference","model":{"coefficients":[1,1,1],"nodes":[0,1,3]},"domain":"Exact_composite_trapezoidal_quadrature","operation":"trap-error-boundary","semantic_template":"trap-error-boundary|{\"mode\":\"quadratic_reference\",\"model\":{\"coefficients\":[[1,1],[1,1],[1,1]],\"nodes\":[[0,1],[1,1],[3,1]]}}"}},"verification":{"status":"candidate","checks":["producer_contract_recomputation","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"candidate 僅對明示有限或符號模型重算；不構成一般定理、人工審定、Lean 或 Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"GPT-5.6 Terra","generated_at":"2026-10-15","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261015-pulse-20261119-r02-0077","batch_id":"batch-20261015-advance-20261119-r02-trapezoidal-quadrature-foundations","language":"zh-Hant","source_mko_ids":["mko-trapezoidal-quadrature"],"title_zh":"複合梯形法","stem_zh":"嚴格遞增partition、n+1 nodes與逐subinterval寬度。操作=trap-error-boundary；明示資料={\"mode\":\"nonincreasing_partition\",\"model\":{\"nodes\":[0,0,2],\"values\":[1,2,3]}}；請依 exact_ordered_tuple_declared_by_interface 回答。","answer":{"kind":"expression","value":"(nonincreasing_partition, [0, 0, 2], [1, 2, 3], 是, 否, 否, partition_must_be_strictly_increasing)","explanation_zh":"Wave6第十三層核對=(nonincreasing_partition, [0, 0, 2], [1, 2, 3], 是, 否, 否, partition_must_be_strictly_increasing)；依完整明示資料精確重算；複合梯形逐段使用endpoint average與自己的width；signed error固定為I-T；affine exact或指定quadratic reference不推出一般誤差界、收斂階或唯一integrand。"},"difficulty":{"band":"undergraduate_core","level":1,"skills":["複合梯形法"]},"variant":{"family_id":"qf-mod50-trap-error-boundary","seed":202611192077,"parameters":{"mode":"nonincreasing_partition","model":{"nodes":[0,0,2],"values":[1,2,3]},"domain":"Exact_composite_trapezoidal_quadrature","operation":"trap-error-boundary","semantic_template":"trap-error-boundary|{\"mode\":\"nonincreasing_partition\",\"model\":{\"nodes\":[[0,1],[0,1],[2,1]],\"values\":[[1,1],[2,1],[3,1]]}}"}},"verification":{"status":"candidate","checks":["producer_contract_recomputation","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"candidate 僅對明示有限或符號模型重算；不構成一般定理、人工審定、Lean 或 Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"GPT-5.6 Terra","generated_at":"2026-10-15","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261015-pulse-20261119-r02-0078","batch_id":"batch-20261015-advance-20261119-r02-trapezoidal-quadrature-foundations","language":"zh-Hant","source_mko_ids":["mko-trapezoidal-quadrature"],"title_zh":"複合梯形法","stem_zh":"嚴格遞增partition、n+1 nodes與逐subinterval寬度。操作=trap-error-boundary；明示資料={\"mode\":\"sample_table_scope\",\"model\":{\"nodes\":[0,1,5],\"values\":[2,3,5]}}；請依 exact_ordered_tuple_declared_by_interface 回答。","answer":{"kind":"expression","value":"(sample_table_scope, [0, 1, 5], [2, 3, 5], 37/2, 是, 否, endpoint_table_determines_this_quadrature_sum_not_a_unique_integrand_or_integral)","explanation_zh":"Wave6第十三層核對=(sample_table_scope, [0, 1, 5], [2, 3, 5], 37/2, 是, 否, endpoint_table_determines_this_quadrature_sum_not_a_unique_integrand_or_integral)；依完整明示資料精確重算；複合梯形逐段使用endpoint average與自己的width；signed error固定為I-T；affine exact或指定quadratic reference不推出一般誤差界、收斂階或唯一integrand。"},"difficulty":{"band":"undergraduate_core","level":1,"skills":["複合梯形法"]},"variant":{"family_id":"qf-mod50-trap-error-boundary","seed":202611192078,"parameters":{"mode":"sample_table_scope","model":{"nodes":[0,1,5],"values":[2,3,5]},"domain":"Exact_composite_trapezoidal_quadrature","operation":"trap-error-boundary","semantic_template":"trap-error-boundary|{\"mode\":\"sample_table_scope\",\"model\":{\"nodes\":[[0,1],[1,1],[5,1]],\"values\":[[2,1],[3,1],[5,1]]}}"}},"verification":{"status":"candidate","checks":["producer_contract_recomputation","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"candidate 僅對明示有限或符號模型重算；不構成一般定理、人工審定、Lean 或 Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"GPT-5.6 Terra","generated_at":"2026-10-15","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261015-pulse-20261119-r02-0079","batch_id":"batch-20261015-advance-20261119-r02-trapezoidal-quadrature-foundations","language":"zh-Hant","source_mko_ids":["mko-trapezoidal-quadrature"],"title_zh":"複合梯形法","stem_zh":"嚴格遞增partition、n+1 nodes與逐subinterval寬度。操作=trap-error-boundary；明示資料={\"mode\":\"single_width_confusion\",\"model\":{\"nodes\":[0,1,6],\"values\":[3,7,13]}}；請依 exact_ordered_tuple_declared_by_interface 回答。","answer":{"kind":"expression","value":"(single_width_confusion, [1, 5], 55, 15, 否, nonuniform_partition_cannot_use_one_global_width)","explanation_zh":"Wave6第十三層核對=(single_width_confusion, [1, 5], 55, 15, 否, nonuniform_partition_cannot_use_one_global_width)；依完整明示資料精確重算；複合梯形逐段使用endpoint average與自己的width；signed error固定為I-T；affine exact或指定quadratic reference不推出一般誤差界、收斂階或唯一integrand。"},"difficulty":{"band":"undergraduate_core","level":1,"skills":["複合梯形法"]},"variant":{"family_id":"qf-mod50-trap-error-boundary","seed":202611192079,"parameters":{"mode":"single_width_confusion","model":{"nodes":[0,1,6],"values":[3,7,13]},"domain":"Exact_composite_trapezoidal_quadrature","operation":"trap-error-boundary","semantic_template":"trap-error-boundary|{\"mode\":\"single_width_confusion\",\"model\":{\"nodes\":[[0,1],[1,1],[6,1]],\"values\":[[3,1],[7,1],[13,1]]}}"}},"verification":{"status":"candidate","checks":["producer_contract_recomputation","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"candidate 僅對明示有限或符號模型重算；不構成一般定理、人工審定、Lean 或 Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"GPT-5.6 Terra","generated_at":"2026-10-15","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261015-pulse-20261119-r02-0080","batch_id":"batch-20261015-advance-20261119-r02-trapezoidal-quadrature-foundations","language":"zh-Hant","source_mko_ids":["mko-trapezoidal-quadrature"],"title_zh":"複合梯形法","stem_zh":"嚴格遞增partition、n+1 nodes與逐subinterval寬度。操作=trap-error-boundary；明示資料={\"mode\":\"quadratic_reference\",\"model\":{\"coefficients\":[5,1,1],\"nodes\":[0,1,7]}}；請依 exact_ordered_tuple_declared_by_interface 回答。","answer":{"kind":"expression","value":"(quadratic_reference, [5, 1, 1], [0, 1, 7], 210, 1043/6, -217/6, 217/6, 否, exact_polynomial_reference_error_is_not_a_general_second_derivative_error_bound)","explanation_zh":"Wave6第十三層核對=(quadratic_reference, [5, 1, 1], [0, 1, 7], 210, 1043/6, -217/6, 217/6, 否, exact_polynomial_reference_error_is_not_a_general_second_derivative_error_bound)；依完整明示資料精確重算；複合梯形逐段使用endpoint average與自己的width；signed error固定為I-T；affine exact或指定quadratic reference不推出一般誤差界、收斂階或唯一integrand。"},"difficulty":{"band":"undergraduate_core","level":1,"skills":["複合梯形法"]},"variant":{"family_id":"qf-mod50-trap-error-boundary","seed":202611192080,"parameters":{"mode":"quadratic_reference","model":{"coefficients":[5,1,1],"nodes":[0,1,7]},"domain":"Exact_composite_trapezoidal_quadrature","operation":"trap-error-boundary","semantic_template":"trap-error-boundary|{\"mode\":\"quadratic_reference\",\"model\":{\"coefficients\":[[5,1],[1,1],[1,1]],\"nodes\":[[0,1],[1,1],[7,1]]}}"}},"verification":{"status":"candidate","checks":["producer_contract_recomputation","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"candidate 僅對明示有限或符號模型重算；不構成一般定理、人工審定、Lean 或 Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"GPT-5.6 Terra","generated_at":"2026-10-15","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261015-pulse-20261119-r02-0081","batch_id":"batch-20261015-advance-20261119-r02-trapezoidal-quadrature-foundations","language":"zh-Hant","source_mko_ids":["mko-trapezoidal-quadrature"],"title_zh":"複合梯形法","stem_zh":"嚴格遞增partition、n+1 nodes與逐subinterval寬度。操作=trap-error-boundary；明示資料={\"mode\":\"nonincreasing_partition\",\"model\":{\"nodes\":[0,0,6],\"values\":[5,6,7]}}；請依 exact_ordered_tuple_declared_by_interface 回答。","answer":{"kind":"expression","value":"(nonincreasing_partition, [0, 0, 6], [5, 6, 7], 是, 否, 否, partition_must_be_strictly_increasing)","explanation_zh":"Wave6第十三層核對=(nonincreasing_partition, [0, 0, 6], [5, 6, 7], 是, 否, 否, partition_must_be_strictly_increasing)；依完整明示資料精確重算；複合梯形逐段使用endpoint average與自己的width；signed error固定為I-T；affine exact或指定quadratic reference不推出一般誤差界、收斂階或唯一integrand。"},"difficulty":{"band":"undergraduate_core","level":1,"skills":["複合梯形法"]},"variant":{"family_id":"qf-mod50-trap-error-boundary","seed":202611192081,"parameters":{"mode":"nonincreasing_partition","model":{"nodes":[0,0,6],"values":[5,6,7]},"domain":"Exact_composite_trapezoidal_quadrature","operation":"trap-error-boundary","semantic_template":"trap-error-boundary|{\"mode\":\"nonincreasing_partition\",\"model\":{\"nodes\":[[0,1],[0,1],[6,1]],\"values\":[[5,1],[6,1],[7,1]]}}"}},"verification":{"status":"candidate","checks":["producer_contract_recomputation","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"candidate 僅對明示有限或符號模型重算；不構成一般定理、人工審定、Lean 或 Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"GPT-5.6 Terra","generated_at":"2026-10-15","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261015-pulse-20261119-r02-0082","batch_id":"batch-20261015-advance-20261119-r02-trapezoidal-quadrature-foundations","language":"zh-Hant","source_mko_ids":["mko-trapezoidal-quadrature"],"title_zh":"複合梯形法","stem_zh":"嚴格遞增partition、n+1 nodes與逐subinterval寬度。操作=trap-error-boundary；明示資料={\"mode\":\"sample_table_scope\",\"model\":{\"nodes\":[0,1,9],\"values\":[6,7,9]}}；請依 exact_ordered_tuple_declared_by_interface 回答。","answer":{"kind":"expression","value":"(sample_table_scope, [0, 1, 9], [6, 7, 9], 141/2, 是, 否, endpoint_table_determines_this_quadrature_sum_not_a_unique_integrand_or_integral)","explanation_zh":"Wave6第十三層核對=(sample_table_scope, [0, 1, 9], [6, 7, 9], 141/2, 是, 否, endpoint_table_determines_this_quadrature_sum_not_a_unique_integrand_or_integral)；依完整明示資料精確重算；複合梯形逐段使用endpoint average與自己的width；signed error固定為I-T；affine exact或指定quadratic reference不推出一般誤差界、收斂階或唯一integrand。"},"difficulty":{"band":"undergraduate_core","level":1,"skills":["複合梯形法"]},"variant":{"family_id":"qf-mod50-trap-error-boundary","seed":202611192082,"parameters":{"mode":"sample_table_scope","model":{"nodes":[0,1,9],"values":[6,7,9]},"domain":"Exact_composite_trapezoidal_quadrature","operation":"trap-error-boundary","semantic_template":"trap-error-boundary|{\"mode\":\"sample_table_scope\",\"model\":{\"nodes\":[[0,1],[1,1],[9,1]],\"values\":[[6,1],[7,1],[9,1]]}}"}},"verification":{"status":"candidate","checks":["producer_contract_recomputation","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"candidate 僅對明示有限或符號模型重算；不構成一般定理、人工審定、Lean 或 Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"GPT-5.6 Terra","generated_at":"2026-10-15","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261015-pulse-20261119-r02-0083","batch_id":"batch-20261015-advance-20261119-r02-trapezoidal-quadrature-foundations","language":"zh-Hant","source_mko_ids":["mko-trapezoidal-quadrature"],"title_zh":"複合梯形法","stem_zh":"嚴格遞增partition、n+1 nodes與逐subinterval寬度。操作=trap-error-boundary；明示資料={\"mode\":\"single_width_confusion\",\"model\":{\"nodes\":[0,1,10],\"values\":[7,15,25]}}；請依 exact_ordered_tuple_declared_by_interface 回答。","answer":{"kind":"expression","value":"(single_width_confusion, [1, 9], 191, 31, 否, nonuniform_partition_cannot_use_one_global_width)","explanation_zh":"Wave6第十三層核對=(single_width_confusion, [1, 9], 191, 31, 否, nonuniform_partition_cannot_use_one_global_width)；依完整明示資料精確重算；複合梯形逐段使用endpoint average與自己的width；signed error固定為I-T；affine exact或指定quadratic reference不推出一般誤差界、收斂階或唯一integrand。"},"difficulty":{"band":"undergraduate_core","level":1,"skills":["複合梯形法"]},"variant":{"family_id":"qf-mod50-trap-error-boundary","seed":202611192083,"parameters":{"mode":"single_width_confusion","model":{"nodes":[0,1,10],"values":[7,15,25]},"domain":"Exact_composite_trapezoidal_quadrature","operation":"trap-error-boundary","semantic_template":"trap-error-boundary|{\"mode\":\"single_width_confusion\",\"model\":{\"nodes\":[[0,1],[1,1],[10,1]],\"values\":[[7,1],[15,1],[25,1]]}}"}},"verification":{"status":"candidate","checks":["producer_contract_recomputation","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"candidate 僅對明示有限或符號模型重算；不構成一般定理、人工審定、Lean 或 Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"GPT-5.6 Terra","generated_at":"2026-10-15","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261015-pulse-20261119-r02-0084","batch_id":"batch-20261015-advance-20261119-r02-trapezoidal-quadrature-foundations","language":"zh-Hant","source_mko_ids":["mko-trapezoidal-quadrature"],"title_zh":"複合梯形法","stem_zh":"嚴格遞增partition、n+1 nodes與逐subinterval寬度。操作=trap-error-boundary；明示資料={\"mode\":\"quadratic_reference\",\"model\":{\"coefficients\":[9,1,1],\"nodes\":[0,1,11]}}；請依 exact_ordered_tuple_declared_by_interface 回答。","answer":{"kind":"expression","value":"(quadratic_reference, [9, 1, 1], [0, 1, 11], 770, 3619/6, -1001/6, 1001/6, 否, exact_polynomial_reference_error_is_not_a_general_second_derivative_error_bound)","explanation_zh":"Wave6第十三層核對=(quadratic_reference, [9, 1, 1], [0, 1, 11], 770, 3619/6, -1001/6, 1001/6, 否, exact_polynomial_reference_error_is_not_a_general_second_derivative_error_bound)；依完整明示資料精確重算；複合梯形逐段使用endpoint average與自己的width；signed error固定為I-T；affine exact或指定quadratic reference不推出一般誤差界、收斂階或唯一integrand。"},"difficulty":{"band":"undergraduate_core","level":2,"skills":["複合梯形法"]},"variant":{"family_id":"qf-mod50-trap-error-boundary","seed":202611192084,"parameters":{"mode":"quadratic_reference","model":{"coefficients":[9,1,1],"nodes":[0,1,11]},"domain":"Exact_composite_trapezoidal_quadrature","operation":"trap-error-boundary","semantic_template":"trap-error-boundary|{\"mode\":\"quadratic_reference\",\"model\":{\"coefficients\":[[9,1],[1,1],[1,1]],\"nodes\":[[0,1],[1,1],[11,1]]}}"}},"verification":{"status":"candidate","checks":["producer_contract_recomputation","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"candidate 僅對明示有限或符號模型重算；不構成一般定理、人工審定、Lean 或 Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"GPT-5.6 Terra","generated_at":"2026-10-15","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261015-pulse-20261119-r02-0085","batch_id":"batch-20261015-advance-20261119-r02-trapezoidal-quadrature-foundations","language":"zh-Hant","source_mko_ids":["mko-trapezoidal-quadrature"],"title_zh":"複合梯形法","stem_zh":"嚴格遞增partition、n+1 nodes與逐subinterval寬度。操作=trap-error-boundary；明示資料={\"mode\":\"nonincreasing_partition\",\"model\":{\"nodes\":[0,0,10],\"values\":[9,10,11]}}；請依 exact_ordered_tuple_declared_by_interface 回答。","answer":{"kind":"expression","value":"(nonincreasing_partition, [0, 0, 10], [9, 10, 11], 是, 否, 否, partition_must_be_strictly_increasing)","explanation_zh":"Wave6第十三層核對=(nonincreasing_partition, [0, 0, 10], [9, 10, 11], 是, 否, 否, partition_must_be_strictly_increasing)；依完整明示資料精確重算；複合梯形逐段使用endpoint average與自己的width；signed error固定為I-T；affine exact或指定quadratic reference不推出一般誤差界、收斂階或唯一integrand。"},"difficulty":{"band":"undergraduate_core","level":2,"skills":["複合梯形法"]},"variant":{"family_id":"qf-mod50-trap-error-boundary","seed":202611192085,"parameters":{"mode":"nonincreasing_partition","model":{"nodes":[0,0,10],"values":[9,10,11]},"domain":"Exact_composite_trapezoidal_quadrature","operation":"trap-error-boundary","semantic_template":"trap-error-boundary|{\"mode\":\"nonincreasing_partition\",\"model\":{\"nodes\":[[0,1],[0,1],[10,1]],\"values\":[[9,1],[10,1],[11,1]]}}"}},"verification":{"status":"candidate","checks":["producer_contract_recomputation","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"candidate 僅對明示有限或符號模型重算；不構成一般定理、人工審定、Lean 或 Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"GPT-5.6 Terra","generated_at":"2026-10-15","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261015-pulse-20261119-r02-0086","batch_id":"batch-20261015-advance-20261119-r02-trapezoidal-quadrature-foundations","language":"zh-Hant","source_mko_ids":["mko-trapezoidal-quadrature"],"title_zh":"複合梯形法","stem_zh":"嚴格遞增partition、n+1 nodes與逐subinterval寬度。操作=trap-error-boundary；明示資料={\"mode\":\"sample_table_scope\",\"model\":{\"nodes\":[0,1,13],\"values\":[10,11,13]}}；請依 exact_ordered_tuple_declared_by_interface 回答。","answer":{"kind":"expression","value":"(sample_table_scope, [0, 1, 13], [10, 11, 13], 309/2, 是, 否, endpoint_table_determines_this_quadrature_sum_not_a_unique_integrand_or_integral)","explanation_zh":"Wave6第十三層核對=(sample_table_scope, [0, 1, 13], [10, 11, 13], 309/2, 是, 否, endpoint_table_determines_this_quadrature_sum_not_a_unique_integrand_or_integral)；依完整明示資料精確重算；複合梯形逐段使用endpoint average與自己的width；signed error固定為I-T；affine exact或指定quadratic reference不推出一般誤差界、收斂階或唯一integrand。"},"difficulty":{"band":"undergraduate_core","level":2,"skills":["複合梯形法"]},"variant":{"family_id":"qf-mod50-trap-error-boundary","seed":202611192086,"parameters":{"mode":"sample_table_scope","model":{"nodes":[0,1,13],"values":[10,11,13]},"domain":"Exact_composite_trapezoidal_quadrature","operation":"trap-error-boundary","semantic_template":"trap-error-boundary|{\"mode\":\"sample_table_scope\",\"model\":{\"nodes\":[[0,1],[1,1],[13,1]],\"values\":[[10,1],[11,1],[13,1]]}}"}},"verification":{"status":"candidate","checks":["producer_contract_recomputation","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"candidate 僅對明示有限或符號模型重算；不構成一般定理、人工審定、Lean 或 Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"GPT-5.6 Terra","generated_at":"2026-10-15","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261015-pulse-20261119-r02-0087","batch_id":"batch-20261015-advance-20261119-r02-trapezoidal-quadrature-foundations","language":"zh-Hant","source_mko_ids":["mko-trapezoidal-quadrature"],"title_zh":"複合梯形法","stem_zh":"嚴格遞增partition、n+1 nodes與逐subinterval寬度。操作=trap-error-boundary；明示資料={\"mode\":\"single_width_confusion\",\"model\":{\"nodes\":[0,1,14],\"values\":[11,23,37]}}；請依 exact_ordered_tuple_declared_by_interface 回答。","answer":{"kind":"expression","value":"(single_width_confusion, [1, 13], 407, 47, 否, nonuniform_partition_cannot_use_one_global_width)","explanation_zh":"Wave6第十三層核對=(single_width_confusion, [1, 13], 407, 47, 否, nonuniform_partition_cannot_use_one_global_width)；依完整明示資料精確重算；複合梯形逐段使用endpoint average與自己的width；signed error固定為I-T；affine exact或指定quadratic reference不推出一般誤差界、收斂階或唯一integrand。"},"difficulty":{"band":"undergraduate_core","level":2,"skills":["複合梯形法"]},"variant":{"family_id":"qf-mod50-trap-error-boundary","seed":202611192087,"parameters":{"mode":"single_width_confusion","model":{"nodes":[0,1,14],"values":[11,23,37]},"domain":"Exact_composite_trapezoidal_quadrature","operation":"trap-error-boundary","semantic_template":"trap-error-boundary|{\"mode\":\"single_width_confusion\",\"model\":{\"nodes\":[[0,1],[1,1],[14,1]],\"values\":[[11,1],[23,1],[37,1]]}}"}},"verification":{"status":"candidate","checks":["producer_contract_recomputation","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"candidate 僅對明示有限或符號模型重算；不構成一般定理、人工審定、Lean 或 Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"GPT-5.6 Terra","generated_at":"2026-10-15","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261015-pulse-20261119-r02-0088","batch_id":"batch-20261015-advance-20261119-r02-trapezoidal-quadrature-foundations","language":"zh-Hant","source_mko_ids":["mko-trapezoidal-quadrature"],"title_zh":"複合梯形法","stem_zh":"嚴格遞增partition、n+1 nodes與逐subinterval寬度。操作=trap-error-boundary；明示資料={\"mode\":\"quadratic_reference\",\"model\":{\"coefficients\":[13,1,1],\"nodes\":[0,1,15]}}；請依 exact_ordered_tuple_declared_by_interface 回答。","answer":{"kind":"expression","value":"(quadratic_reference, [13, 1, 1], [0, 1, 15], 1890, 2865/2, -915/2, 915/2, 否, exact_polynomial_reference_error_is_not_a_general_second_derivative_error_bound)","explanation_zh":"Wave6第十三層核對=(quadratic_reference, [13, 1, 1], [0, 1, 15], 1890, 2865/2, -915/2, 915/2, 否, exact_polynomial_reference_error_is_not_a_general_second_derivative_error_bound)；依完整明示資料精確重算；複合梯形逐段使用endpoint average與自己的width；signed error固定為I-T；affine exact或指定quadratic reference不推出一般誤差界、收斂階或唯一integrand。"},"difficulty":{"band":"undergraduate_core","level":2,"skills":["複合梯形法"]},"variant":{"family_id":"qf-mod50-trap-error-boundary","seed":202611192088,"parameters":{"mode":"quadratic_reference","model":{"coefficients":[13,1,1],"nodes":[0,1,15]},"domain":"Exact_composite_trapezoidal_quadrature","operation":"trap-error-boundary","semantic_template":"trap-error-boundary|{\"mode\":\"quadratic_reference\",\"model\":{\"coefficients\":[[13,1],[1,1],[1,1]],\"nodes\":[[0,1],[1,1],[15,1]]}}"}},"verification":{"status":"candidate","checks":["producer_contract_recomputation","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"candidate 僅對明示有限或符號模型重算；不構成一般定理、人工審定、Lean 或 Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"GPT-5.6 Terra","generated_at":"2026-10-15","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261015-pulse-20261119-r02-0089","batch_id":"batch-20261015-advance-20261119-r02-trapezoidal-quadrature-foundations","language":"zh-Hant","source_mko_ids":["mko-trapezoidal-quadrature"],"title_zh":"複合梯形法","stem_zh":"嚴格遞增partition、n+1 nodes與逐subinterval寬度。操作=trap-error-boundary；明示資料={\"mode\":\"nonincreasing_partition\",\"model\":{\"nodes\":[0,0,14],\"values\":[13,14,15]}}；請依 exact_ordered_tuple_declared_by_interface 回答。","answer":{"kind":"expression","value":"(nonincreasing_partition, [0, 0, 14], [13, 14, 15], 是, 否, 否, partition_must_be_strictly_increasing)","explanation_zh":"Wave6第十三層核對=(nonincreasing_partition, [0, 0, 14], [13, 14, 15], 是, 否, 否, partition_must_be_strictly_increasing)；依完整明示資料精確重算；複合梯形逐段使用endpoint average與自己的width；signed error固定為I-T；affine exact或指定quadratic reference不推出一般誤差界、收斂階或唯一integrand。"},"difficulty":{"band":"undergraduate_core","level":2,"skills":["複合梯形法"]},"variant":{"family_id":"qf-mod50-trap-error-boundary","seed":202611192089,"parameters":{"mode":"nonincreasing_partition","model":{"nodes":[0,0,14],"values":[13,14,15]},"domain":"Exact_composite_trapezoidal_quadrature","operation":"trap-error-boundary","semantic_template":"trap-error-boundary|{\"mode\":\"nonincreasing_partition\",\"model\":{\"nodes\":[[0,1],[0,1],[14,1]],\"values\":[[13,1],[14,1],[15,1]]}}"}},"verification":{"status":"candidate","checks":["producer_contract_recomputation","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"candidate 僅對明示有限或符號模型重算；不構成一般定理、人工審定、Lean 或 Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"GPT-5.6 Terra","generated_at":"2026-10-15","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261015-pulse-20261119-r02-0090","batch_id":"batch-20261015-advance-20261119-r02-trapezoidal-quadrature-foundations","language":"zh-Hant","source_mko_ids":["mko-trapezoidal-quadrature"],"title_zh":"複合梯形法","stem_zh":"嚴格遞增partition、n+1 nodes與逐subinterval寬度。操作=trap-error-boundary；明示資料={\"mode\":\"sample_table_scope\",\"model\":{\"nodes\":[0,1,17],\"values\":[14,15,17]}}；請依 exact_ordered_tuple_declared_by_interface 回答。","answer":{"kind":"expression","value":"(sample_table_scope, [0, 1, 17], [14, 15, 17], 541/2, 是, 否, endpoint_table_determines_this_quadrature_sum_not_a_unique_integrand_or_integral)","explanation_zh":"Wave6第十三層核對=(sample_table_scope, [0, 1, 17], [14, 15, 17], 541/2, 是, 否, endpoint_table_determines_this_quadrature_sum_not_a_unique_integrand_or_integral)；依完整明示資料精確重算；複合梯形逐段使用endpoint average與自己的width；signed error固定為I-T；affine exact或指定quadratic reference不推出一般誤差界、收斂階或唯一integrand。"},"difficulty":{"band":"undergraduate_core","level":2,"skills":["複合梯形法"]},"variant":{"family_id":"qf-mod50-trap-error-boundary","seed":202611192090,"parameters":{"mode":"sample_table_scope","model":{"nodes":[0,1,17],"values":[14,15,17]},"domain":"Exact_composite_trapezoidal_quadrature","operation":"trap-error-boundary","semantic_template":"trap-error-boundary|{\"mode\":\"sample_table_scope\",\"model\":{\"nodes\":[[0,1],[1,1],[17,1]],\"values\":[[14,1],[15,1],[17,1]]}}"}},"verification":{"status":"candidate","checks":["producer_contract_recomputation","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"candidate 僅對明示有限或符號模型重算；不構成一般定理、人工審定、Lean 或 Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"GPT-5.6 Terra","generated_at":"2026-10-15","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261015-pulse-20261119-r02-0091","batch_id":"batch-20261015-advance-20261119-r02-trapezoidal-quadrature-foundations","language":"zh-Hant","source_mko_ids":["mko-trapezoidal-quadrature"],"title_zh":"複合梯形法","stem_zh":"嚴格遞增partition、n+1 nodes與逐subinterval寬度。操作=trap-error-boundary；明示資料={\"mode\":\"single_width_confusion\",\"model\":{\"nodes\":[0,1,18],\"values\":[15,31,49]}}；請依 exact_ordered_tuple_declared_by_interface 回答。","answer":{"kind":"expression","value":"(single_width_confusion, [1, 17], 703, 63, 否, nonuniform_partition_cannot_use_one_global_width)","explanation_zh":"Wave6第十三層核對=(single_width_confusion, [1, 17], 703, 63, 否, nonuniform_partition_cannot_use_one_global_width)；依完整明示資料精確重算；複合梯形逐段使用endpoint average與自己的width；signed error固定為I-T；affine exact或指定quadratic reference不推出一般誤差界、收斂階或唯一integrand。"},"difficulty":{"band":"undergraduate_core","level":2,"skills":["複合梯形法"]},"variant":{"family_id":"qf-mod50-trap-error-boundary","seed":202611192091,"parameters":{"mode":"single_width_confusion","model":{"nodes":[0,1,18],"values":[15,31,49]},"domain":"Exact_composite_trapezoidal_quadrature","operation":"trap-error-boundary","semantic_template":"trap-error-boundary|{\"mode\":\"single_width_confusion\",\"model\":{\"nodes\":[[0,1],[1,1],[18,1]],\"values\":[[15,1],[31,1],[49,1]]}}"}},"verification":{"status":"candidate","checks":["producer_contract_recomputation","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"candidate 僅對明示有限或符號模型重算；不構成一般定理、人工審定、Lean 或 Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"GPT-5.6 Terra","generated_at":"2026-10-15","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261015-pulse-20261119-r02-0092","batch_id":"batch-20261015-advance-20261119-r02-trapezoidal-quadrature-foundations","language":"zh-Hant","source_mko_ids":["mko-trapezoidal-quadrature"],"title_zh":"複合梯形法","stem_zh":"嚴格遞增partition、n+1 nodes與逐subinterval寬度。操作=trap-error-boundary；明示資料={\"mode\":\"quadratic_reference\",\"model\":{\"coefficients\":[17,1,1],\"nodes\":[0,1,19]}}；請依 exact_ordered_tuple_declared_by_interface 回答。","answer":{"kind":"expression","value":"(quadratic_reference, [17, 1, 1], [0, 1, 19], 3762, 16739/6, -5833/6, 5833/6, 否, exact_polynomial_reference_error_is_not_a_general_second_derivative_error_bound)","explanation_zh":"Wave6第十三層核對=(quadratic_reference, [17, 1, 1], [0, 1, 19], 3762, 16739/6, -5833/6, 5833/6, 否, exact_polynomial_reference_error_is_not_a_general_second_derivative_error_bound)；依完整明示資料精確重算；複合梯形逐段使用endpoint average與自己的width；signed error固定為I-T；affine exact或指定quadratic reference不推出一般誤差界、收斂階或唯一integrand。"},"difficulty":{"band":"undergraduate_core","level":2,"skills":["複合梯形法"]},"variant":{"family_id":"qf-mod50-trap-error-boundary","seed":202611192092,"parameters":{"mode":"quadratic_reference","model":{"coefficients":[17,1,1],"nodes":[0,1,19]},"domain":"Exact_composite_trapezoidal_quadrature","operation":"trap-error-boundary","semantic_template":"trap-error-boundary|{\"mode\":\"quadratic_reference\",\"model\":{\"coefficients\":[[17,1],[1,1],[1,1]],\"nodes\":[[0,1],[1,1],[19,1]]}}"}},"verification":{"status":"candidate","checks":["producer_contract_recomputation","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"candidate 僅對明示有限或符號模型重算；不構成一般定理、人工審定、Lean 或 Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"GPT-5.6 Terra","generated_at":"2026-10-15","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261015-pulse-20261119-r02-0093","batch_id":"batch-20261015-advance-20261119-r02-trapezoidal-quadrature-foundations","language":"zh-Hant","source_mko_ids":["mko-trapezoidal-quadrature"],"title_zh":"複合梯形法","stem_zh":"嚴格遞增partition、n+1 nodes與逐subinterval寬度。操作=trap-error-boundary；明示資料={\"mode\":\"nonincreasing_partition\",\"model\":{\"nodes\":[0,0,18],\"values\":[17,18,19]}}；請依 exact_ordered_tuple_declared_by_interface 回答。","answer":{"kind":"expression","value":"(nonincreasing_partition, [0, 0, 18], [17, 18, 19], 是, 否, 否, partition_must_be_strictly_increasing)","explanation_zh":"Wave6第十三層核對=(nonincreasing_partition, [0, 0, 18], [17, 18, 19], 是, 否, 否, partition_must_be_strictly_increasing)；依完整明示資料精確重算；複合梯形逐段使用endpoint average與自己的width；signed error固定為I-T；affine exact或指定quadratic reference不推出一般誤差界、收斂階或唯一integrand。"},"difficulty":{"band":"undergraduate_core","level":3,"skills":["複合梯形法"]},"variant":{"family_id":"qf-mod50-trap-error-boundary","seed":202611192093,"parameters":{"mode":"nonincreasing_partition","model":{"nodes":[0,0,18],"values":[17,18,19]},"domain":"Exact_composite_trapezoidal_quadrature","operation":"trap-error-boundary","semantic_template":"trap-error-boundary|{\"mode\":\"nonincreasing_partition\",\"model\":{\"nodes\":[[0,1],[0,1],[18,1]],\"values\":[[17,1],[18,1],[19,1]]}}"}},"verification":{"status":"candidate","checks":["producer_contract_recomputation","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"candidate 僅對明示有限或符號模型重算；不構成一般定理、人工審定、Lean 或 Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"GPT-5.6 Terra","generated_at":"2026-10-15","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261015-pulse-20261119-r02-0094","batch_id":"batch-20261015-advance-20261119-r02-trapezoidal-quadrature-foundations","language":"zh-Hant","source_mko_ids":["mko-trapezoidal-quadrature"],"title_zh":"複合梯形法","stem_zh":"嚴格遞增partition、n+1 nodes與逐subinterval寬度。操作=trap-error-boundary；明示資料={\"mode\":\"sample_table_scope\",\"model\":{\"nodes\":[0,1,21],\"values\":[18,19,21]}}；請依 exact_ordered_tuple_declared_by_interface 回答。","answer":{"kind":"expression","value":"(sample_table_scope, [0, 1, 21], [18, 19, 21], 837/2, 是, 否, endpoint_table_determines_this_quadrature_sum_not_a_unique_integrand_or_integral)","explanation_zh":"Wave6第十三層核對=(sample_table_scope, [0, 1, 21], [18, 19, 21], 837/2, 是, 否, endpoint_table_determines_this_quadrature_sum_not_a_unique_integrand_or_integral)；依完整明示資料精確重算；複合梯形逐段使用endpoint average與自己的width；signed error固定為I-T；affine exact或指定quadratic reference不推出一般誤差界、收斂階或唯一integrand。"},"difficulty":{"band":"undergraduate_core","level":3,"skills":["複合梯形法"]},"variant":{"family_id":"qf-mod50-trap-error-boundary","seed":202611192094,"parameters":{"mode":"sample_table_scope","model":{"nodes":[0,1,21],"values":[18,19,21]},"domain":"Exact_composite_trapezoidal_quadrature","operation":"trap-error-boundary","semantic_template":"trap-error-boundary|{\"mode\":\"sample_table_scope\",\"model\":{\"nodes\":[[0,1],[1,1],[21,1]],\"values\":[[18,1],[19,1],[21,1]]}}"}},"verification":{"status":"candidate","checks":["producer_contract_recomputation","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"candidate 僅對明示有限或符號模型重算；不構成一般定理、人工審定、Lean 或 Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"GPT-5.6 Terra","generated_at":"2026-10-15","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261015-pulse-20261119-r02-0095","batch_id":"batch-20261015-advance-20261119-r02-trapezoidal-quadrature-foundations","language":"zh-Hant","source_mko_ids":["mko-trapezoidal-quadrature"],"title_zh":"複合梯形法","stem_zh":"嚴格遞增partition、n+1 nodes與逐subinterval寬度。操作=trap-error-boundary；明示資料={\"mode\":\"single_width_confusion\",\"model\":{\"nodes\":[0,1,22],\"values\":[19,39,61]}}；請依 exact_ordered_tuple_declared_by_interface 回答。","answer":{"kind":"expression","value":"(single_width_confusion, [1, 21], 1079, 79, 否, nonuniform_partition_cannot_use_one_global_width)","explanation_zh":"Wave6第十三層核對=(single_width_confusion, [1, 21], 1079, 79, 否, nonuniform_partition_cannot_use_one_global_width)；依完整明示資料精確重算；複合梯形逐段使用endpoint average與自己的width；signed error固定為I-T；affine exact或指定quadratic reference不推出一般誤差界、收斂階或唯一integrand。"},"difficulty":{"band":"undergraduate_core","level":3,"skills":["複合梯形法"]},"variant":{"family_id":"qf-mod50-trap-error-boundary","seed":202611192095,"parameters":{"mode":"single_width_confusion","model":{"nodes":[0,1,22],"values":[19,39,61]},"domain":"Exact_composite_trapezoidal_quadrature","operation":"trap-error-boundary","semantic_template":"trap-error-boundary|{\"mode\":\"single_width_confusion\",\"model\":{\"nodes\":[[0,1],[1,1],[22,1]],\"values\":[[19,1],[39,1],[61,1]]}}"}},"verification":{"status":"candidate","checks":["producer_contract_recomputation","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"candidate 僅對明示有限或符號模型重算；不構成一般定理、人工審定、Lean 或 Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"GPT-5.6 Terra","generated_at":"2026-10-15","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261015-pulse-20261119-r02-0096","batch_id":"batch-20261015-advance-20261119-r02-trapezoidal-quadrature-foundations","language":"zh-Hant","source_mko_ids":["mko-trapezoidal-quadrature"],"title_zh":"複合梯形法","stem_zh":"嚴格遞增partition、n+1 nodes與逐subinterval寬度。操作=trap-error-boundary；明示資料={\"mode\":\"quadratic_reference\",\"model\":{\"coefficients\":[21,1,1],\"nodes\":[0,1,23]}}；請依 exact_ordered_tuple_declared_by_interface 回答。","answer":{"kind":"expression","value":"(quadratic_reference, [21, 1, 1], [0, 1, 23], 6578, 28819/6, -10649/6, 10649/6, 否, exact_polynomial_reference_error_is_not_a_general_second_derivative_error_bound)","explanation_zh":"Wave6第十三層核對=(quadratic_reference, [21, 1, 1], [0, 1, 23], 6578, 28819/6, -10649/6, 10649/6, 否, exact_polynomial_reference_error_is_not_a_general_second_derivative_error_bound)；依完整明示資料精確重算；複合梯形逐段使用endpoint average與自己的width；signed error固定為I-T；affine exact或指定quadratic reference不推出一般誤差界、收斂階或唯一integrand。"},"difficulty":{"band":"undergraduate_core","level":3,"skills":["複合梯形法"]},"variant":{"family_id":"qf-mod50-trap-error-boundary","seed":202611192096,"parameters":{"mode":"quadratic_reference","model":{"coefficients":[21,1,1],"nodes":[0,1,23]},"domain":"Exact_composite_trapezoidal_quadrature","operation":"trap-error-boundary","semantic_template":"trap-error-boundary|{\"mode\":\"quadratic_reference\",\"model\":{\"coefficients\":[[21,1],[1,1],[1,1]],\"nodes\":[[0,1],[1,1],[23,1]]}}"}},"verification":{"status":"candidate","checks":["producer_contract_recomputation","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"candidate 僅對明示有限或符號模型重算；不構成一般定理、人工審定、Lean 或 Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"GPT-5.6 Terra","generated_at":"2026-10-15","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261015-pulse-20261119-r02-0097","batch_id":"batch-20261015-advance-20261119-r02-trapezoidal-quadrature-foundations","language":"zh-Hant","source_mko_ids":["mko-trapezoidal-quadrature"],"title_zh":"複合梯形法","stem_zh":"嚴格遞增partition、n+1 nodes與逐subinterval寬度。操作=trap-error-boundary；明示資料={\"mode\":\"nonincreasing_partition\",\"model\":{\"nodes\":[0,0,22],\"values\":[21,22,23]}}；請依 exact_ordered_tuple_declared_by_interface 回答。","answer":{"kind":"expression","value":"(nonincreasing_partition, [0, 0, 22], [21, 22, 23], 是, 否, 否, partition_must_be_strictly_increasing)","explanation_zh":"Wave6第十三層核對=(nonincreasing_partition, [0, 0, 22], [21, 22, 23], 是, 否, 否, partition_must_be_strictly_increasing)；依完整明示資料精確重算；複合梯形逐段使用endpoint average與自己的width；signed error固定為I-T；affine exact或指定quadratic reference不推出一般誤差界、收斂階或唯一integrand。"},"difficulty":{"band":"undergraduate_core","level":3,"skills":["複合梯形法"]},"variant":{"family_id":"qf-mod50-trap-error-boundary","seed":202611192097,"parameters":{"mode":"nonincreasing_partition","model":{"nodes":[0,0,22],"values":[21,22,23]},"domain":"Exact_composite_trapezoidal_quadrature","operation":"trap-error-boundary","semantic_template":"trap-error-boundary|{\"mode\":\"nonincreasing_partition\",\"model\":{\"nodes\":[[0,1],[0,1],[22,1]],\"values\":[[21,1],[22,1],[23,1]]}}"}},"verification":{"status":"candidate","checks":["producer_contract_recomputation","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"candidate 僅對明示有限或符號模型重算；不構成一般定理、人工審定、Lean 或 Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"GPT-5.6 Terra","generated_at":"2026-10-15","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261015-pulse-20261119-r02-0098","batch_id":"batch-20261015-advance-20261119-r02-trapezoidal-quadrature-foundations","language":"zh-Hant","source_mko_ids":["mko-trapezoidal-quadrature"],"title_zh":"複合梯形法","stem_zh":"嚴格遞增partition、n+1 nodes與逐subinterval寬度。操作=trap-error-boundary；明示資料={\"mode\":\"sample_table_scope\",\"model\":{\"nodes\":[0,1,25],\"values\":[22,23,25]}}；請依 exact_ordered_tuple_declared_by_interface 回答。","answer":{"kind":"expression","value":"(sample_table_scope, [0, 1, 25], [22, 23, 25], 1197/2, 是, 否, endpoint_table_determines_this_quadrature_sum_not_a_unique_integrand_or_integral)","explanation_zh":"Wave6第十三層核對=(sample_table_scope, [0, 1, 25], [22, 23, 25], 1197/2, 是, 否, endpoint_table_determines_this_quadrature_sum_not_a_unique_integrand_or_integral)；依完整明示資料精確重算；複合梯形逐段使用endpoint average與自己的width；signed error固定為I-T；affine exact或指定quadratic reference不推出一般誤差界、收斂階或唯一integrand。"},"difficulty":{"band":"undergraduate_core","level":3,"skills":["複合梯形法"]},"variant":{"family_id":"qf-mod50-trap-error-boundary","seed":202611192098,"parameters":{"mode":"sample_table_scope","model":{"nodes":[0,1,25],"values":[22,23,25]},"domain":"Exact_composite_trapezoidal_quadrature","operation":"trap-error-boundary","semantic_template":"trap-error-boundary|{\"mode\":\"sample_table_scope\",\"model\":{\"nodes\":[[0,1],[1,1],[25,1]],\"values\":[[22,1],[23,1],[25,1]]}}"}},"verification":{"status":"candidate","checks":["producer_contract_recomputation","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"candidate 僅對明示有限或符號模型重算；不構成一般定理、人工審定、Lean 或 Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"GPT-5.6 Terra","generated_at":"2026-10-15","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261015-pulse-20261119-r02-0099","batch_id":"batch-20261015-advance-20261119-r02-trapezoidal-quadrature-foundations","language":"zh-Hant","source_mko_ids":["mko-trapezoidal-quadrature"],"title_zh":"複合梯形法","stem_zh":"嚴格遞增partition、n+1 nodes與逐subinterval寬度。操作=trap-error-boundary；明示資料={\"mode\":\"single_width_confusion\",\"model\":{\"nodes\":[0,1,26],\"values\":[23,47,73]}}；請依 exact_ordered_tuple_declared_by_interface 回答。","answer":{"kind":"expression","value":"(single_width_confusion, [1, 25], 1535, 95, 否, nonuniform_partition_cannot_use_one_global_width)","explanation_zh":"Wave6第十三層核對=(single_width_confusion, [1, 25], 1535, 95, 否, nonuniform_partition_cannot_use_one_global_width)；依完整明示資料精確重算；複合梯形逐段使用endpoint average與自己的width；signed error固定為I-T；affine exact或指定quadratic reference不推出一般誤差界、收斂階或唯一integrand。"},"difficulty":{"band":"undergraduate_core","level":3,"skills":["複合梯形法"]},"variant":{"family_id":"qf-mod50-trap-error-boundary","seed":202611192099,"parameters":{"mode":"single_width_confusion","model":{"nodes":[0,1,26],"values":[23,47,73]},"domain":"Exact_composite_trapezoidal_quadrature","operation":"trap-error-boundary","semantic_template":"trap-error-boundary|{\"mode\":\"single_width_confusion\",\"model\":{\"nodes\":[[0,1],[1,1],[26,1]],\"values\":[[23,1],[47,1],[73,1]]}}"}},"verification":{"status":"candidate","checks":["producer_contract_recomputation","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"candidate 僅對明示有限或符號模型重算；不構成一般定理、人工審定、Lean 或 Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"GPT-5.6 Terra","generated_at":"2026-10-15","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261015-pulse-20261119-r02-0100","batch_id":"batch-20261015-advance-20261119-r02-trapezoidal-quadrature-foundations","language":"zh-Hant","source_mko_ids":["mko-trapezoidal-quadrature"],"title_zh":"複合梯形法","stem_zh":"嚴格遞增partition、n+1 nodes與逐subinterval寬度。操作=trap-error-boundary；明示資料={\"mode\":\"quadratic_reference\",\"model\":{\"coefficients\":[25,1,1],\"nodes\":[0,1,27]}}；請依 exact_ordered_tuple_declared_by_interface 回答。","answer":{"kind":"expression","value":"(quadratic_reference, [25, 1, 1], [0, 1, 27], 10530, 15201/2, -5859/2, 5859/2, 否, exact_polynomial_reference_error_is_not_a_general_second_derivative_error_bound)","explanation_zh":"Wave6第十三層核對=(quadratic_reference, [25, 1, 1], [0, 1, 27], 10530, 15201/2, -5859/2, 5859/2, 否, exact_polynomial_reference_error_is_not_a_general_second_derivative_error_bound)；依完整明示資料精確重算；複合梯形逐段使用endpoint average與自己的width；signed error固定為I-T；affine exact或指定quadratic reference不推出一般誤差界、收斂階或唯一integrand。"},"difficulty":{"band":"undergraduate_core","level":3,"skills":["複合梯形法"]},"variant":{"family_id":"qf-mod50-trap-error-boundary","seed":202611192100,"parameters":{"mode":"quadratic_reference","model":{"coefficients":[25,1,1],"nodes":[0,1,27]},"domain":"Exact_composite_trapezoidal_quadrature","operation":"trap-error-boundary","semantic_template":"trap-error-boundary|{\"mode\":\"quadratic_reference\",\"model\":{\"coefficients\":[[25,1],[1,1],[1,1]],\"nodes\":[[0,1],[1,1],[27,1]]}}"}},"verification":{"status":"candidate","checks":["producer_contract_recomputation","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"candidate 僅對明示有限或符號模型重算；不構成一般定理、人工審定、Lean 或 Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"GPT-5.6 Terra","generated_at":"2026-10-15","contract_version":"ocme-question-factory-v0.1"}}