{"schema_version":"ocme-question-v0.1","id":"q-20261014-advance-20261104-r02-uniform-convergence-of-functions-0001","batch_id":"batch-20261014-advance-20261104-r02-uniform-convergence-of-functions-foundations","language":"zh-Hant","source_mko_ids":["mko-uniform-convergence-of-functions"],"title_zh":"一致收斂","stem_zh":"共同有限domain的symbolic tail與同一N(epsilon)。操作=uniform-finite-domain-witness；資料={\"limit\":[0,1],\"coefficients\":[1,-2],\"shift\":2,\"epsilon\":[1,10]}。請依 exact_ordered_tuple_declared_by_interface 欄序回答。","answer":{"kind":"expression","value":"(1/10, [[0, 9], [1, 19]], 19, 是, same_N_for_all_finite_domain_points)","explanation_zh":"Wave5第四層核對=(1/10, [[0, 9], [1, 19]], 19, 是, same_N_for_all_finite_domain_points)；依完整明示資料重算；同一N控制所有x且有限domain可取pointwise witnesses最大值；不可外推無限domain且finite prefix不足。"},"difficulty":{"band":"undergraduate_core","level":1,"skills":["一致收斂"]},"variant":{"family_id":"qf-mod35-uniform-finite-domain-witness","seed":202611042001,"parameters":{"limit":[0,1],"coefficients":[1,-2],"shift":2,"epsilon":[1,10],"domain":"Finite_domain_symbolic_uniform_tail","operation":"uniform-finite-domain-witness","semantic_template":"qf-mod35-uniform-finite-domain-witness/{\"coefficients\":[1,-2],\"epsilon\":[1,10],\"limit\":[0,1],\"shift\":2}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_or_symbolic_model","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"候選須主端重算；不構成人工審定、sampled rank-nullity、infinite-domain uniformity、term-zero convergence、estimator properties、noncoprime CRT shortcut、MST、mode implication、Lean或Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-14","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261014-advance-20261104-r02-uniform-convergence-of-functions-0002","batch_id":"batch-20261014-advance-20261104-r02-uniform-convergence-of-functions-foundations","language":"zh-Hant","source_mko_ids":["mko-uniform-convergence-of-functions"],"title_zh":"一致收斂","stem_zh":"共同有限domain的symbolic tail與同一N(epsilon)。操作=uniform-finite-domain-witness；資料={\"limit\":[1,2],\"coefficients\":[2,-3],\"shift\":2,\"epsilon\":[1,11]}。請依 exact_ordered_tuple_declared_by_interface 欄序回答。","answer":{"kind":"expression","value":"(1/11, [[0, 21], [1, 32]], 32, 是, same_N_for_all_finite_domain_points)","explanation_zh":"Wave5第四層核對=(1/11, [[0, 21], [1, 32]], 32, 是, same_N_for_all_finite_domain_points)；依完整明示資料重算；同一N控制所有x且有限domain可取pointwise witnesses最大值；不可外推無限domain且finite prefix不足。"},"difficulty":{"band":"undergraduate_core","level":1,"skills":["一致收斂"]},"variant":{"family_id":"qf-mod35-uniform-finite-domain-witness","seed":202611042002,"parameters":{"limit":[1,2],"coefficients":[2,-3],"shift":2,"epsilon":[1,11],"domain":"Finite_domain_symbolic_uniform_tail","operation":"uniform-finite-domain-witness","semantic_template":"qf-mod35-uniform-finite-domain-witness/{\"coefficients\":[2,-3],\"epsilon\":[1,11],\"limit\":[1,2],\"shift\":2}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_or_symbolic_model","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"候選須主端重算；不構成人工審定、sampled rank-nullity、infinite-domain uniformity、term-zero convergence、estimator properties、noncoprime CRT shortcut、MST、mode implication、Lean或Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-14","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261014-advance-20261104-r02-uniform-convergence-of-functions-0003","batch_id":"batch-20261014-advance-20261104-r02-uniform-convergence-of-functions-foundations","language":"zh-Hant","source_mko_ids":["mko-uniform-convergence-of-functions"],"title_zh":"一致收斂","stem_zh":"共同有限domain的symbolic tail與同一N(epsilon)。操作=uniform-finite-domain-witness；資料={\"limit\":[2,3],\"coefficients\":[3,-4],\"shift\":2,\"epsilon\":[1,12]}。請依 exact_ordered_tuple_declared_by_interface 欄序回答。","answer":{"kind":"expression","value":"(1/12, [[0, 35], [1, 47]], 47, 是, same_N_for_all_finite_domain_points)","explanation_zh":"Wave5第四層核對=(1/12, [[0, 35], [1, 47]], 47, 是, same_N_for_all_finite_domain_points)；依完整明示資料重算；同一N控制所有x且有限domain可取pointwise witnesses最大值；不可外推無限domain且finite prefix不足。"},"difficulty":{"band":"undergraduate_core","level":1,"skills":["一致收斂"]},"variant":{"family_id":"qf-mod35-uniform-finite-domain-witness","seed":202611042003,"parameters":{"limit":[2,3],"coefficients":[3,-4],"shift":2,"epsilon":[1,12],"domain":"Finite_domain_symbolic_uniform_tail","operation":"uniform-finite-domain-witness","semantic_template":"qf-mod35-uniform-finite-domain-witness/{\"coefficients\":[3,-4],\"epsilon\":[1,12],\"limit\":[2,3],\"shift\":2}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_or_symbolic_model","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"候選須主端重算；不構成人工審定、sampled rank-nullity、infinite-domain uniformity、term-zero convergence、estimator properties、noncoprime CRT shortcut、MST、mode implication、Lean或Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-14","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261014-advance-20261104-r02-uniform-convergence-of-functions-0004","batch_id":"batch-20261014-advance-20261104-r02-uniform-convergence-of-functions-foundations","language":"zh-Hant","source_mko_ids":["mko-uniform-convergence-of-functions"],"title_zh":"一致收斂","stem_zh":"共同有限domain的symbolic tail與同一N(epsilon)。操作=uniform-finite-domain-witness；資料={\"limit\":[3,4],\"coefficients\":[4,-5],\"shift\":2,\"epsilon\":[1,13]}。請依 exact_ordered_tuple_declared_by_interface 欄序回答。","answer":{"kind":"expression","value":"(1/13, [[0, 51], [1, 64]], 64, 是, same_N_for_all_finite_domain_points)","explanation_zh":"Wave5第四層核對=(1/13, [[0, 51], [1, 64]], 64, 是, same_N_for_all_finite_domain_points)；依完整明示資料重算；同一N控制所有x且有限domain可取pointwise witnesses最大值；不可外推無限domain且finite prefix不足。"},"difficulty":{"band":"undergraduate_core","level":1,"skills":["一致收斂"]},"variant":{"family_id":"qf-mod35-uniform-finite-domain-witness","seed":202611042004,"parameters":{"limit":[3,4],"coefficients":[4,-5],"shift":2,"epsilon":[1,13],"domain":"Finite_domain_symbolic_uniform_tail","operation":"uniform-finite-domain-witness","semantic_template":"qf-mod35-uniform-finite-domain-witness/{\"coefficients\":[4,-5],\"epsilon\":[1,13],\"limit\":[3,4],\"shift\":2}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_or_symbolic_model","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"候選須主端重算；不構成人工審定、sampled rank-nullity、infinite-domain uniformity、term-zero convergence、estimator properties、noncoprime CRT shortcut、MST、mode implication、Lean或Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-14","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261014-advance-20261104-r02-uniform-convergence-of-functions-0005","batch_id":"batch-20261014-advance-20261104-r02-uniform-convergence-of-functions-foundations","language":"zh-Hant","source_mko_ids":["mko-uniform-convergence-of-functions"],"title_zh":"一致收斂","stem_zh":"共同有限domain的symbolic tail與同一N(epsilon)。操作=uniform-finite-domain-witness；資料={\"limit\":[4,5],\"coefficients\":[5,-6],\"shift\":2,\"epsilon\":[1,14]}。請依 exact_ordered_tuple_declared_by_interface 欄序回答。","answer":{"kind":"expression","value":"(1/14, [[0, 69], [1, 83]], 83, 是, same_N_for_all_finite_domain_points)","explanation_zh":"Wave5第四層核對=(1/14, [[0, 69], [1, 83]], 83, 是, same_N_for_all_finite_domain_points)；依完整明示資料重算；同一N控制所有x且有限domain可取pointwise witnesses最大值；不可外推無限domain且finite prefix不足。"},"difficulty":{"band":"undergraduate_core","level":1,"skills":["一致收斂"]},"variant":{"family_id":"qf-mod35-uniform-finite-domain-witness","seed":202611042005,"parameters":{"limit":[4,5],"coefficients":[5,-6],"shift":2,"epsilon":[1,14],"domain":"Finite_domain_symbolic_uniform_tail","operation":"uniform-finite-domain-witness","semantic_template":"qf-mod35-uniform-finite-domain-witness/{\"coefficients\":[5,-6],\"epsilon\":[1,14],\"limit\":[4,5],\"shift\":2}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_or_symbolic_model","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"候選須主端重算；不構成人工審定、sampled rank-nullity、infinite-domain uniformity、term-zero convergence、estimator properties、noncoprime CRT shortcut、MST、mode implication、Lean或Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-14","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261014-advance-20261104-r02-uniform-convergence-of-functions-0006","batch_id":"batch-20261014-advance-20261104-r02-uniform-convergence-of-functions-foundations","language":"zh-Hant","source_mko_ids":["mko-uniform-convergence-of-functions"],"title_zh":"一致收斂","stem_zh":"共同有限domain的symbolic tail與同一N(epsilon)。操作=uniform-finite-domain-witness；資料={\"limit\":[5,6],\"coefficients\":[6,-7],\"shift\":2,\"epsilon\":[1,15]}。請依 exact_ordered_tuple_declared_by_interface 欄序回答。","answer":{"kind":"expression","value":"(1/15, [[0, 89], [1, 104]], 104, 是, same_N_for_all_finite_domain_points)","explanation_zh":"Wave5第四層核對=(1/15, [[0, 89], [1, 104]], 104, 是, same_N_for_all_finite_domain_points)；依完整明示資料重算；同一N控制所有x且有限domain可取pointwise witnesses最大值；不可外推無限domain且finite prefix不足。"},"difficulty":{"band":"undergraduate_core","level":1,"skills":["一致收斂"]},"variant":{"family_id":"qf-mod35-uniform-finite-domain-witness","seed":202611042006,"parameters":{"limit":[5,6],"coefficients":[6,-7],"shift":2,"epsilon":[1,15],"domain":"Finite_domain_symbolic_uniform_tail","operation":"uniform-finite-domain-witness","semantic_template":"qf-mod35-uniform-finite-domain-witness/{\"coefficients\":[6,-7],\"epsilon\":[1,15],\"limit\":[5,6],\"shift\":2}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_or_symbolic_model","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"候選須主端重算；不構成人工審定、sampled rank-nullity、infinite-domain uniformity、term-zero convergence、estimator properties、noncoprime CRT shortcut、MST、mode implication、Lean或Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-14","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261014-advance-20261104-r02-uniform-convergence-of-functions-0007","batch_id":"batch-20261014-advance-20261104-r02-uniform-convergence-of-functions-foundations","language":"zh-Hant","source_mko_ids":["mko-uniform-convergence-of-functions"],"title_zh":"一致收斂","stem_zh":"共同有限domain的symbolic tail與同一N(epsilon)。操作=uniform-finite-domain-witness；資料={\"limit\":[6,7],\"coefficients\":[7,-8],\"shift\":2,\"epsilon\":[1,16]}。請依 exact_ordered_tuple_declared_by_interface 欄序回答。","answer":{"kind":"expression","value":"(1/16, [[0, 111], [1, 127]], 127, 是, same_N_for_all_finite_domain_points)","explanation_zh":"Wave5第四層核對=(1/16, [[0, 111], [1, 127]], 127, 是, same_N_for_all_finite_domain_points)；依完整明示資料重算；同一N控制所有x且有限domain可取pointwise witnesses最大值；不可外推無限domain且finite prefix不足。"},"difficulty":{"band":"undergraduate_core","level":1,"skills":["一致收斂"]},"variant":{"family_id":"qf-mod35-uniform-finite-domain-witness","seed":202611042007,"parameters":{"limit":[6,7],"coefficients":[7,-8],"shift":2,"epsilon":[1,16],"domain":"Finite_domain_symbolic_uniform_tail","operation":"uniform-finite-domain-witness","semantic_template":"qf-mod35-uniform-finite-domain-witness/{\"coefficients\":[7,-8],\"epsilon\":[1,16],\"limit\":[6,7],\"shift\":2}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_or_symbolic_model","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"候選須主端重算；不構成人工審定、sampled rank-nullity、infinite-domain uniformity、term-zero convergence、estimator properties、noncoprime CRT shortcut、MST、mode implication、Lean或Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-14","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261014-advance-20261104-r02-uniform-convergence-of-functions-0008","batch_id":"batch-20261014-advance-20261104-r02-uniform-convergence-of-functions-foundations","language":"zh-Hant","source_mko_ids":["mko-uniform-convergence-of-functions"],"title_zh":"一致收斂","stem_zh":"共同有限domain的symbolic tail與同一N(epsilon)。操作=uniform-finite-domain-witness；資料={\"limit\":[7,8],\"coefficients\":[8,-9],\"shift\":2,\"epsilon\":[1,17]}。請依 exact_ordered_tuple_declared_by_interface 欄序回答。","answer":{"kind":"expression","value":"(1/17, [[0, 135], [1, 152]], 152, 是, same_N_for_all_finite_domain_points)","explanation_zh":"Wave5第四層核對=(1/17, [[0, 135], [1, 152]], 152, 是, same_N_for_all_finite_domain_points)；依完整明示資料重算；同一N控制所有x且有限domain可取pointwise witnesses最大值；不可外推無限domain且finite prefix不足。"},"difficulty":{"band":"undergraduate_core","level":1,"skills":["一致收斂"]},"variant":{"family_id":"qf-mod35-uniform-finite-domain-witness","seed":202611042008,"parameters":{"limit":[7,8],"coefficients":[8,-9],"shift":2,"epsilon":[1,17],"domain":"Finite_domain_symbolic_uniform_tail","operation":"uniform-finite-domain-witness","semantic_template":"qf-mod35-uniform-finite-domain-witness/{\"coefficients\":[8,-9],\"epsilon\":[1,17],\"limit\":[7,8],\"shift\":2}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_or_symbolic_model","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"候選須主端重算；不構成人工審定、sampled rank-nullity、infinite-domain uniformity、term-zero convergence、estimator properties、noncoprime CRT shortcut、MST、mode implication、Lean或Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-14","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261014-advance-20261104-r02-uniform-convergence-of-functions-0009","batch_id":"batch-20261014-advance-20261104-r02-uniform-convergence-of-functions-foundations","language":"zh-Hant","source_mko_ids":["mko-uniform-convergence-of-functions"],"title_zh":"一致收斂","stem_zh":"共同有限domain的symbolic tail與同一N(epsilon)。操作=uniform-finite-domain-witness；資料={\"limit\":[8,9],\"coefficients\":[9,-10],\"shift\":2,\"epsilon\":[1,18]}。請依 exact_ordered_tuple_declared_by_interface 欄序回答。","answer":{"kind":"expression","value":"(1/18, [[0, 161], [1, 179]], 179, 是, same_N_for_all_finite_domain_points)","explanation_zh":"Wave5第四層核對=(1/18, [[0, 161], [1, 179]], 179, 是, same_N_for_all_finite_domain_points)；依完整明示資料重算；同一N控制所有x且有限domain可取pointwise witnesses最大值；不可外推無限domain且finite prefix不足。"},"difficulty":{"band":"undergraduate_core","level":2,"skills":["一致收斂"]},"variant":{"family_id":"qf-mod35-uniform-finite-domain-witness","seed":202611042009,"parameters":{"limit":[8,9],"coefficients":[9,-10],"shift":2,"epsilon":[1,18],"domain":"Finite_domain_symbolic_uniform_tail","operation":"uniform-finite-domain-witness","semantic_template":"qf-mod35-uniform-finite-domain-witness/{\"coefficients\":[9,-10],\"epsilon\":[1,18],\"limit\":[8,9],\"shift\":2}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_or_symbolic_model","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"候選須主端重算；不構成人工審定、sampled rank-nullity、infinite-domain uniformity、term-zero convergence、estimator properties、noncoprime CRT shortcut、MST、mode implication、Lean或Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-14","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261014-advance-20261104-r02-uniform-convergence-of-functions-0010","batch_id":"batch-20261014-advance-20261104-r02-uniform-convergence-of-functions-foundations","language":"zh-Hant","source_mko_ids":["mko-uniform-convergence-of-functions"],"title_zh":"一致收斂","stem_zh":"共同有限domain的symbolic tail與同一N(epsilon)。操作=uniform-finite-domain-witness；資料={\"limit\":[9,10],\"coefficients\":[10,-11],\"shift\":2,\"epsilon\":[1,19]}。請依 exact_ordered_tuple_declared_by_interface 欄序回答。","answer":{"kind":"expression","value":"(1/19, [[0, 189], [1, 208]], 208, 是, same_N_for_all_finite_domain_points)","explanation_zh":"Wave5第四層核對=(1/19, [[0, 189], [1, 208]], 208, 是, same_N_for_all_finite_domain_points)；依完整明示資料重算；同一N控制所有x且有限domain可取pointwise witnesses最大值；不可外推無限domain且finite prefix不足。"},"difficulty":{"band":"undergraduate_core","level":2,"skills":["一致收斂"]},"variant":{"family_id":"qf-mod35-uniform-finite-domain-witness","seed":202611042010,"parameters":{"limit":[9,10],"coefficients":[10,-11],"shift":2,"epsilon":[1,19],"domain":"Finite_domain_symbolic_uniform_tail","operation":"uniform-finite-domain-witness","semantic_template":"qf-mod35-uniform-finite-domain-witness/{\"coefficients\":[10,-11],\"epsilon\":[1,19],\"limit\":[9,10],\"shift\":2}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_or_symbolic_model","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"候選須主端重算；不構成人工審定、sampled rank-nullity、infinite-domain uniformity、term-zero convergence、estimator properties、noncoprime CRT shortcut、MST、mode implication、Lean或Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-14","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261014-advance-20261104-r02-uniform-convergence-of-functions-0011","batch_id":"batch-20261014-advance-20261104-r02-uniform-convergence-of-functions-foundations","language":"zh-Hant","source_mko_ids":["mko-uniform-convergence-of-functions"],"title_zh":"一致收斂","stem_zh":"共同有限domain的symbolic tail與同一N(epsilon)。操作=uniform-finite-domain-witness；資料={\"limit\":[10,11],\"coefficients\":[11,-12],\"shift\":2,\"epsilon\":[1,20]}。請依 exact_ordered_tuple_declared_by_interface 欄序回答。","answer":{"kind":"expression","value":"(1/20, [[0, 219], [1, 239]], 239, 是, same_N_for_all_finite_domain_points)","explanation_zh":"Wave5第四層核對=(1/20, [[0, 219], [1, 239]], 239, 是, same_N_for_all_finite_domain_points)；依完整明示資料重算；同一N控制所有x且有限domain可取pointwise witnesses最大值；不可外推無限domain且finite prefix不足。"},"difficulty":{"band":"undergraduate_core","level":2,"skills":["一致收斂"]},"variant":{"family_id":"qf-mod35-uniform-finite-domain-witness","seed":202611042011,"parameters":{"limit":[10,11],"coefficients":[11,-12],"shift":2,"epsilon":[1,20],"domain":"Finite_domain_symbolic_uniform_tail","operation":"uniform-finite-domain-witness","semantic_template":"qf-mod35-uniform-finite-domain-witness/{\"coefficients\":[11,-12],\"epsilon\":[1,20],\"limit\":[10,11],\"shift\":2}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_or_symbolic_model","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"候選須主端重算；不構成人工審定、sampled rank-nullity、infinite-domain uniformity、term-zero convergence、estimator properties、noncoprime CRT shortcut、MST、mode implication、Lean或Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-14","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261014-advance-20261104-r02-uniform-convergence-of-functions-0012","batch_id":"batch-20261014-advance-20261104-r02-uniform-convergence-of-functions-foundations","language":"zh-Hant","source_mko_ids":["mko-uniform-convergence-of-functions"],"title_zh":"一致收斂","stem_zh":"共同有限domain的symbolic tail與同一N(epsilon)。操作=uniform-finite-domain-witness；資料={\"limit\":[11,12],\"coefficients\":[12,-13],\"shift\":2,\"epsilon\":[1,21]}。請依 exact_ordered_tuple_declared_by_interface 欄序回答。","answer":{"kind":"expression","value":"(1/21, [[0, 251], [1, 272]], 272, 是, same_N_for_all_finite_domain_points)","explanation_zh":"Wave5第四層核對=(1/21, [[0, 251], [1, 272]], 272, 是, same_N_for_all_finite_domain_points)；依完整明示資料重算；同一N控制所有x且有限domain可取pointwise witnesses最大值；不可外推無限domain且finite prefix不足。"},"difficulty":{"band":"undergraduate_core","level":2,"skills":["一致收斂"]},"variant":{"family_id":"qf-mod35-uniform-finite-domain-witness","seed":202611042012,"parameters":{"limit":[11,12],"coefficients":[12,-13],"shift":2,"epsilon":[1,21],"domain":"Finite_domain_symbolic_uniform_tail","operation":"uniform-finite-domain-witness","semantic_template":"qf-mod35-uniform-finite-domain-witness/{\"coefficients\":[12,-13],\"epsilon\":[1,21],\"limit\":[11,12],\"shift\":2}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_or_symbolic_model","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"候選須主端重算；不構成人工審定、sampled rank-nullity、infinite-domain uniformity、term-zero convergence、estimator properties、noncoprime CRT shortcut、MST、mode implication、Lean或Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-14","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261014-advance-20261104-r02-uniform-convergence-of-functions-0013","batch_id":"batch-20261014-advance-20261104-r02-uniform-convergence-of-functions-foundations","language":"zh-Hant","source_mko_ids":["mko-uniform-convergence-of-functions"],"title_zh":"一致收斂","stem_zh":"共同有限domain的symbolic tail與同一N(epsilon)。操作=uniform-finite-domain-witness；資料={\"limit\":[12,13],\"coefficients\":[13,-14],\"shift\":2,\"epsilon\":[1,22]}。請依 exact_ordered_tuple_declared_by_interface 欄序回答。","answer":{"kind":"expression","value":"(1/22, [[0, 285], [1, 307]], 307, 是, same_N_for_all_finite_domain_points)","explanation_zh":"Wave5第四層核對=(1/22, [[0, 285], [1, 307]], 307, 是, same_N_for_all_finite_domain_points)；依完整明示資料重算；同一N控制所有x且有限domain可取pointwise witnesses最大值；不可外推無限domain且finite prefix不足。"},"difficulty":{"band":"undergraduate_core","level":2,"skills":["一致收斂"]},"variant":{"family_id":"qf-mod35-uniform-finite-domain-witness","seed":202611042013,"parameters":{"limit":[12,13],"coefficients":[13,-14],"shift":2,"epsilon":[1,22],"domain":"Finite_domain_symbolic_uniform_tail","operation":"uniform-finite-domain-witness","semantic_template":"qf-mod35-uniform-finite-domain-witness/{\"coefficients\":[13,-14],\"epsilon\":[1,22],\"limit\":[12,13],\"shift\":2}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_or_symbolic_model","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"候選須主端重算；不構成人工審定、sampled rank-nullity、infinite-domain uniformity、term-zero convergence、estimator properties、noncoprime CRT shortcut、MST、mode implication、Lean或Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-14","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261014-advance-20261104-r02-uniform-convergence-of-functions-0014","batch_id":"batch-20261014-advance-20261104-r02-uniform-convergence-of-functions-foundations","language":"zh-Hant","source_mko_ids":["mko-uniform-convergence-of-functions"],"title_zh":"一致收斂","stem_zh":"共同有限domain的symbolic tail與同一N(epsilon)。操作=uniform-finite-domain-witness；資料={\"limit\":[13,14],\"coefficients\":[14,-15],\"shift\":2,\"epsilon\":[1,23]}。請依 exact_ordered_tuple_declared_by_interface 欄序回答。","answer":{"kind":"expression","value":"(1/23, [[0, 321], [1, 344]], 344, 是, same_N_for_all_finite_domain_points)","explanation_zh":"Wave5第四層核對=(1/23, [[0, 321], [1, 344]], 344, 是, same_N_for_all_finite_domain_points)；依完整明示資料重算；同一N控制所有x且有限domain可取pointwise witnesses最大值；不可外推無限domain且finite prefix不足。"},"difficulty":{"band":"undergraduate_core","level":2,"skills":["一致收斂"]},"variant":{"family_id":"qf-mod35-uniform-finite-domain-witness","seed":202611042014,"parameters":{"limit":[13,14],"coefficients":[14,-15],"shift":2,"epsilon":[1,23],"domain":"Finite_domain_symbolic_uniform_tail","operation":"uniform-finite-domain-witness","semantic_template":"qf-mod35-uniform-finite-domain-witness/{\"coefficients\":[14,-15],\"epsilon\":[1,23],\"limit\":[13,14],\"shift\":2}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_or_symbolic_model","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"候選須主端重算；不構成人工審定、sampled rank-nullity、infinite-domain uniformity、term-zero convergence、estimator properties、noncoprime CRT shortcut、MST、mode implication、Lean或Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-14","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261014-advance-20261104-r02-uniform-convergence-of-functions-0015","batch_id":"batch-20261014-advance-20261104-r02-uniform-convergence-of-functions-foundations","language":"zh-Hant","source_mko_ids":["mko-uniform-convergence-of-functions"],"title_zh":"一致收斂","stem_zh":"共同有限domain的symbolic tail與同一N(epsilon)。操作=uniform-finite-domain-witness；資料={\"limit\":[14,15],\"coefficients\":[15,-16],\"shift\":2,\"epsilon\":[1,24]}。請依 exact_ordered_tuple_declared_by_interface 欄序回答。","answer":{"kind":"expression","value":"(1/24, [[0, 359], [1, 383]], 383, 是, same_N_for_all_finite_domain_points)","explanation_zh":"Wave5第四層核對=(1/24, [[0, 359], [1, 383]], 383, 是, same_N_for_all_finite_domain_points)；依完整明示資料重算；同一N控制所有x且有限domain可取pointwise witnesses最大值；不可外推無限domain且finite prefix不足。"},"difficulty":{"band":"undergraduate_core","level":2,"skills":["一致收斂"]},"variant":{"family_id":"qf-mod35-uniform-finite-domain-witness","seed":202611042015,"parameters":{"limit":[14,15],"coefficients":[15,-16],"shift":2,"epsilon":[1,24],"domain":"Finite_domain_symbolic_uniform_tail","operation":"uniform-finite-domain-witness","semantic_template":"qf-mod35-uniform-finite-domain-witness/{\"coefficients\":[15,-16],\"epsilon\":[1,24],\"limit\":[14,15],\"shift\":2}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_or_symbolic_model","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"候選須主端重算；不構成人工審定、sampled rank-nullity、infinite-domain uniformity、term-zero convergence、estimator properties、noncoprime CRT shortcut、MST、mode implication、Lean或Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-14","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261014-advance-20261104-r02-uniform-convergence-of-functions-0016","batch_id":"batch-20261014-advance-20261104-r02-uniform-convergence-of-functions-foundations","language":"zh-Hant","source_mko_ids":["mko-uniform-convergence-of-functions"],"title_zh":"一致收斂","stem_zh":"共同有限domain的symbolic tail與同一N(epsilon)。操作=uniform-finite-domain-witness；資料={\"limit\":[15,16],\"coefficients\":[16,-17],\"shift\":2,\"epsilon\":[1,25]}。請依 exact_ordered_tuple_declared_by_interface 欄序回答。","answer":{"kind":"expression","value":"(1/25, [[0, 399], [1, 424]], 424, 是, same_N_for_all_finite_domain_points)","explanation_zh":"Wave5第四層核對=(1/25, [[0, 399], [1, 424]], 424, 是, same_N_for_all_finite_domain_points)；依完整明示資料重算；同一N控制所有x且有限domain可取pointwise witnesses最大值；不可外推無限domain且finite prefix不足。"},"difficulty":{"band":"undergraduate_core","level":2,"skills":["一致收斂"]},"variant":{"family_id":"qf-mod35-uniform-finite-domain-witness","seed":202611042016,"parameters":{"limit":[15,16],"coefficients":[16,-17],"shift":2,"epsilon":[1,25],"domain":"Finite_domain_symbolic_uniform_tail","operation":"uniform-finite-domain-witness","semantic_template":"qf-mod35-uniform-finite-domain-witness/{\"coefficients\":[16,-17],\"epsilon\":[1,25],\"limit\":[15,16],\"shift\":2}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_or_symbolic_model","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"候選須主端重算；不構成人工審定、sampled rank-nullity、infinite-domain uniformity、term-zero convergence、estimator properties、noncoprime CRT shortcut、MST、mode implication、Lean或Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-14","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261014-advance-20261104-r02-uniform-convergence-of-functions-0017","batch_id":"batch-20261014-advance-20261104-r02-uniform-convergence-of-functions-foundations","language":"zh-Hant","source_mko_ids":["mko-uniform-convergence-of-functions"],"title_zh":"一致收斂","stem_zh":"共同有限domain的symbolic tail與同一N(epsilon)。操作=uniform-finite-domain-witness；資料={\"limit\":[16,17],\"coefficients\":[17,-18],\"shift\":2,\"epsilon\":[1,26]}。請依 exact_ordered_tuple_declared_by_interface 欄序回答。","answer":{"kind":"expression","value":"(1/26, [[0, 441], [1, 467]], 467, 是, same_N_for_all_finite_domain_points)","explanation_zh":"Wave5第四層核對=(1/26, [[0, 441], [1, 467]], 467, 是, same_N_for_all_finite_domain_points)；依完整明示資料重算；同一N控制所有x且有限domain可取pointwise witnesses最大值；不可外推無限domain且finite prefix不足。"},"difficulty":{"band":"undergraduate_core","level":2,"skills":["一致收斂"]},"variant":{"family_id":"qf-mod35-uniform-finite-domain-witness","seed":202611042017,"parameters":{"limit":[16,17],"coefficients":[17,-18],"shift":2,"epsilon":[1,26],"domain":"Finite_domain_symbolic_uniform_tail","operation":"uniform-finite-domain-witness","semantic_template":"qf-mod35-uniform-finite-domain-witness/{\"coefficients\":[17,-18],\"epsilon\":[1,26],\"limit\":[16,17],\"shift\":2}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_or_symbolic_model","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"候選須主端重算；不構成人工審定、sampled rank-nullity、infinite-domain uniformity、term-zero convergence、estimator properties、noncoprime CRT shortcut、MST、mode implication、Lean或Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-14","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261014-advance-20261104-r02-uniform-convergence-of-functions-0018","batch_id":"batch-20261014-advance-20261104-r02-uniform-convergence-of-functions-foundations","language":"zh-Hant","source_mko_ids":["mko-uniform-convergence-of-functions"],"title_zh":"一致收斂","stem_zh":"共同有限domain的symbolic tail與同一N(epsilon)。操作=uniform-finite-domain-witness；資料={\"limit\":[17,18],\"coefficients\":[18,-19],\"shift\":2,\"epsilon\":[1,27]}。請依 exact_ordered_tuple_declared_by_interface 欄序回答。","answer":{"kind":"expression","value":"(1/27, [[0, 485], [1, 512]], 512, 是, same_N_for_all_finite_domain_points)","explanation_zh":"Wave5第四層核對=(1/27, [[0, 485], [1, 512]], 512, 是, same_N_for_all_finite_domain_points)；依完整明示資料重算；同一N控制所有x且有限domain可取pointwise witnesses最大值；不可外推無限domain且finite prefix不足。"},"difficulty":{"band":"undergraduate_core","level":3,"skills":["一致收斂"]},"variant":{"family_id":"qf-mod35-uniform-finite-domain-witness","seed":202611042018,"parameters":{"limit":[17,18],"coefficients":[18,-19],"shift":2,"epsilon":[1,27],"domain":"Finite_domain_symbolic_uniform_tail","operation":"uniform-finite-domain-witness","semantic_template":"qf-mod35-uniform-finite-domain-witness/{\"coefficients\":[18,-19],\"epsilon\":[1,27],\"limit\":[17,18],\"shift\":2}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_or_symbolic_model","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"候選須主端重算；不構成人工審定、sampled rank-nullity、infinite-domain uniformity、term-zero convergence、estimator properties、noncoprime CRT shortcut、MST、mode implication、Lean或Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-14","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261014-advance-20261104-r02-uniform-convergence-of-functions-0019","batch_id":"batch-20261014-advance-20261104-r02-uniform-convergence-of-functions-foundations","language":"zh-Hant","source_mko_ids":["mko-uniform-convergence-of-functions"],"title_zh":"一致收斂","stem_zh":"共同有限domain的symbolic tail與同一N(epsilon)。操作=uniform-finite-domain-witness；資料={\"limit\":[18,19],\"coefficients\":[19,-20],\"shift\":2,\"epsilon\":[1,28]}。請依 exact_ordered_tuple_declared_by_interface 欄序回答。","answer":{"kind":"expression","value":"(1/28, [[0, 531], [1, 559]], 559, 是, same_N_for_all_finite_domain_points)","explanation_zh":"Wave5第四層核對=(1/28, [[0, 531], [1, 559]], 559, 是, same_N_for_all_finite_domain_points)；依完整明示資料重算；同一N控制所有x且有限domain可取pointwise witnesses最大值；不可外推無限domain且finite prefix不足。"},"difficulty":{"band":"undergraduate_core","level":3,"skills":["一致收斂"]},"variant":{"family_id":"qf-mod35-uniform-finite-domain-witness","seed":202611042019,"parameters":{"limit":[18,19],"coefficients":[19,-20],"shift":2,"epsilon":[1,28],"domain":"Finite_domain_symbolic_uniform_tail","operation":"uniform-finite-domain-witness","semantic_template":"qf-mod35-uniform-finite-domain-witness/{\"coefficients\":[19,-20],\"epsilon\":[1,28],\"limit\":[18,19],\"shift\":2}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_or_symbolic_model","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"候選須主端重算；不構成人工審定、sampled rank-nullity、infinite-domain uniformity、term-zero convergence、estimator properties、noncoprime CRT shortcut、MST、mode implication、Lean或Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-14","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261014-advance-20261104-r02-uniform-convergence-of-functions-0020","batch_id":"batch-20261014-advance-20261104-r02-uniform-convergence-of-functions-foundations","language":"zh-Hant","source_mko_ids":["mko-uniform-convergence-of-functions"],"title_zh":"一致收斂","stem_zh":"共同有限domain的symbolic tail與同一N(epsilon)。操作=uniform-finite-domain-witness；資料={\"limit\":[19,20],\"coefficients\":[20,-21],\"shift\":2,\"epsilon\":[1,29]}。請依 exact_ordered_tuple_declared_by_interface 欄序回答。","answer":{"kind":"expression","value":"(1/29, [[0, 579], [1, 608]], 608, 是, same_N_for_all_finite_domain_points)","explanation_zh":"Wave5第四層核對=(1/29, [[0, 579], [1, 608]], 608, 是, same_N_for_all_finite_domain_points)；依完整明示資料重算；同一N控制所有x且有限domain可取pointwise witnesses最大值；不可外推無限domain且finite prefix不足。"},"difficulty":{"band":"undergraduate_core","level":3,"skills":["一致收斂"]},"variant":{"family_id":"qf-mod35-uniform-finite-domain-witness","seed":202611042020,"parameters":{"limit":[19,20],"coefficients":[20,-21],"shift":2,"epsilon":[1,29],"domain":"Finite_domain_symbolic_uniform_tail","operation":"uniform-finite-domain-witness","semantic_template":"qf-mod35-uniform-finite-domain-witness/{\"coefficients\":[20,-21],\"epsilon\":[1,29],\"limit\":[19,20],\"shift\":2}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_or_symbolic_model","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"候選須主端重算；不構成人工審定、sampled rank-nullity、infinite-domain uniformity、term-zero convergence、estimator properties、noncoprime CRT shortcut、MST、mode implication、Lean或Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-14","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261014-advance-20261104-r02-uniform-convergence-of-functions-0021","batch_id":"batch-20261014-advance-20261104-r02-uniform-convergence-of-functions-foundations","language":"zh-Hant","source_mko_ids":["mko-uniform-convergence-of-functions"],"title_zh":"一致收斂","stem_zh":"共同有限domain的symbolic tail與同一N(epsilon)。操作=uniform-finite-domain-witness；資料={\"limit\":[20,21],\"coefficients\":[21,-22],\"shift\":2,\"epsilon\":[1,30]}。請依 exact_ordered_tuple_declared_by_interface 欄序回答。","answer":{"kind":"expression","value":"(1/30, [[0, 629], [1, 659]], 659, 是, same_N_for_all_finite_domain_points)","explanation_zh":"Wave5第四層核對=(1/30, [[0, 629], [1, 659]], 659, 是, same_N_for_all_finite_domain_points)；依完整明示資料重算；同一N控制所有x且有限domain可取pointwise witnesses最大值；不可外推無限domain且finite prefix不足。"},"difficulty":{"band":"undergraduate_core","level":3,"skills":["一致收斂"]},"variant":{"family_id":"qf-mod35-uniform-finite-domain-witness","seed":202611042021,"parameters":{"limit":[20,21],"coefficients":[21,-22],"shift":2,"epsilon":[1,30],"domain":"Finite_domain_symbolic_uniform_tail","operation":"uniform-finite-domain-witness","semantic_template":"qf-mod35-uniform-finite-domain-witness/{\"coefficients\":[21,-22],\"epsilon\":[1,30],\"limit\":[20,21],\"shift\":2}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_or_symbolic_model","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"候選須主端重算；不構成人工審定、sampled rank-nullity、infinite-domain uniformity、term-zero convergence、estimator properties、noncoprime CRT shortcut、MST、mode implication、Lean或Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-14","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261014-advance-20261104-r02-uniform-convergence-of-functions-0022","batch_id":"batch-20261014-advance-20261104-r02-uniform-convergence-of-functions-foundations","language":"zh-Hant","source_mko_ids":["mko-uniform-convergence-of-functions"],"title_zh":"一致收斂","stem_zh":"共同有限domain的symbolic tail與同一N(epsilon)。操作=uniform-finite-domain-witness；資料={\"limit\":[21,22],\"coefficients\":[22,-23],\"shift\":2,\"epsilon\":[1,31]}。請依 exact_ordered_tuple_declared_by_interface 欄序回答。","answer":{"kind":"expression","value":"(1/31, [[0, 681], [1, 712]], 712, 是, same_N_for_all_finite_domain_points)","explanation_zh":"Wave5第四層核對=(1/31, [[0, 681], [1, 712]], 712, 是, same_N_for_all_finite_domain_points)；依完整明示資料重算；同一N控制所有x且有限domain可取pointwise witnesses最大值；不可外推無限domain且finite prefix不足。"},"difficulty":{"band":"undergraduate_core","level":3,"skills":["一致收斂"]},"variant":{"family_id":"qf-mod35-uniform-finite-domain-witness","seed":202611042022,"parameters":{"limit":[21,22],"coefficients":[22,-23],"shift":2,"epsilon":[1,31],"domain":"Finite_domain_symbolic_uniform_tail","operation":"uniform-finite-domain-witness","semantic_template":"qf-mod35-uniform-finite-domain-witness/{\"coefficients\":[22,-23],\"epsilon\":[1,31],\"limit\":[21,22],\"shift\":2}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_or_symbolic_model","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"候選須主端重算；不構成人工審定、sampled rank-nullity、infinite-domain uniformity、term-zero convergence、estimator properties、noncoprime CRT shortcut、MST、mode implication、Lean或Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-14","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261014-advance-20261104-r02-uniform-convergence-of-functions-0023","batch_id":"batch-20261014-advance-20261104-r02-uniform-convergence-of-functions-foundations","language":"zh-Hant","source_mko_ids":["mko-uniform-convergence-of-functions"],"title_zh":"一致收斂","stem_zh":"共同有限domain的symbolic tail與同一N(epsilon)。操作=uniform-finite-domain-witness；資料={\"limit\":[22,23],\"coefficients\":[23,-24],\"shift\":2,\"epsilon\":[1,32]}。請依 exact_ordered_tuple_declared_by_interface 欄序回答。","answer":{"kind":"expression","value":"(1/32, [[0, 735], [1, 767]], 767, 是, same_N_for_all_finite_domain_points)","explanation_zh":"Wave5第四層核對=(1/32, [[0, 735], [1, 767]], 767, 是, same_N_for_all_finite_domain_points)；依完整明示資料重算；同一N控制所有x且有限domain可取pointwise witnesses最大值；不可外推無限domain且finite prefix不足。"},"difficulty":{"band":"undergraduate_core","level":3,"skills":["一致收斂"]},"variant":{"family_id":"qf-mod35-uniform-finite-domain-witness","seed":202611042023,"parameters":{"limit":[22,23],"coefficients":[23,-24],"shift":2,"epsilon":[1,32],"domain":"Finite_domain_symbolic_uniform_tail","operation":"uniform-finite-domain-witness","semantic_template":"qf-mod35-uniform-finite-domain-witness/{\"coefficients\":[23,-24],\"epsilon\":[1,32],\"limit\":[22,23],\"shift\":2}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_or_symbolic_model","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"候選須主端重算；不構成人工審定、sampled rank-nullity、infinite-domain uniformity、term-zero convergence、estimator properties、noncoprime CRT shortcut、MST、mode implication、Lean或Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-14","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261014-advance-20261104-r02-uniform-convergence-of-functions-0024","batch_id":"batch-20261014-advance-20261104-r02-uniform-convergence-of-functions-foundations","language":"zh-Hant","source_mko_ids":["mko-uniform-convergence-of-functions"],"title_zh":"一致收斂","stem_zh":"共同有限domain的symbolic tail與同一N(epsilon)。操作=uniform-finite-domain-witness；資料={\"limit\":[23,24],\"coefficients\":[24,-25],\"shift\":2,\"epsilon\":[1,33]}。請依 exact_ordered_tuple_declared_by_interface 欄序回答。","answer":{"kind":"expression","value":"(1/33, [[0, 791], [1, 824]], 824, 是, same_N_for_all_finite_domain_points)","explanation_zh":"Wave5第四層核對=(1/33, [[0, 791], [1, 824]], 824, 是, same_N_for_all_finite_domain_points)；依完整明示資料重算；同一N控制所有x且有限domain可取pointwise witnesses最大值；不可外推無限domain且finite prefix不足。"},"difficulty":{"band":"undergraduate_core","level":3,"skills":["一致收斂"]},"variant":{"family_id":"qf-mod35-uniform-finite-domain-witness","seed":202611042024,"parameters":{"limit":[23,24],"coefficients":[24,-25],"shift":2,"epsilon":[1,33],"domain":"Finite_domain_symbolic_uniform_tail","operation":"uniform-finite-domain-witness","semantic_template":"qf-mod35-uniform-finite-domain-witness/{\"coefficients\":[24,-25],\"epsilon\":[1,33],\"limit\":[23,24],\"shift\":2}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_or_symbolic_model","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"候選須主端重算；不構成人工審定、sampled rank-nullity、infinite-domain uniformity、term-zero convergence、estimator properties、noncoprime CRT shortcut、MST、mode implication、Lean或Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-14","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261014-advance-20261104-r02-uniform-convergence-of-functions-0025","batch_id":"batch-20261014-advance-20261104-r02-uniform-convergence-of-functions-foundations","language":"zh-Hant","source_mko_ids":["mko-uniform-convergence-of-functions"],"title_zh":"一致收斂","stem_zh":"共同有限domain的symbolic tail與同一N(epsilon)。操作=uniform-finite-domain-witness；資料={\"limit\":[24,25],\"coefficients\":[25,-26],\"shift\":2,\"epsilon\":[1,34]}。請依 exact_ordered_tuple_declared_by_interface 欄序回答。","answer":{"kind":"expression","value":"(1/34, [[0, 849], [1, 883]], 883, 是, same_N_for_all_finite_domain_points)","explanation_zh":"Wave5第四層核對=(1/34, [[0, 849], [1, 883]], 883, 是, same_N_for_all_finite_domain_points)；依完整明示資料重算；同一N控制所有x且有限domain可取pointwise witnesses最大值；不可外推無限domain且finite prefix不足。"},"difficulty":{"band":"undergraduate_core","level":3,"skills":["一致收斂"]},"variant":{"family_id":"qf-mod35-uniform-finite-domain-witness","seed":202611042025,"parameters":{"limit":[24,25],"coefficients":[25,-26],"shift":2,"epsilon":[1,34],"domain":"Finite_domain_symbolic_uniform_tail","operation":"uniform-finite-domain-witness","semantic_template":"qf-mod35-uniform-finite-domain-witness/{\"coefficients\":[25,-26],\"epsilon\":[1,34],\"limit\":[24,25],\"shift\":2}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_or_symbolic_model","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"候選須主端重算；不構成人工審定、sampled rank-nullity、infinite-domain uniformity、term-zero convergence、estimator properties、noncoprime CRT shortcut、MST、mode implication、Lean或Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-14","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261014-advance-20261104-r02-uniform-convergence-of-functions-0026","batch_id":"batch-20261014-advance-20261104-r02-uniform-convergence-of-functions-foundations","language":"zh-Hant","source_mko_ids":["mko-uniform-convergence-of-functions"],"title_zh":"一致收斂","stem_zh":"共同有限domain的symbolic tail與同一N(epsilon)。操作=uniform-sup-gap；資料={\"limit\":[0,1],\"coefficients\":[1,-2],\"shift\":2,\"n\":1}。請依 exact_ordered_tuple_declared_by_interface 欄序回答。","answer":{"kind":"expression","value":"(1, 2/3, exact_finite_domain_supremum)","explanation_zh":"Wave5第四層核對=(1, 2/3, exact_finite_domain_supremum)；依完整明示資料重算；同一N控制所有x且有限domain可取pointwise witnesses最大值；不可外推無限domain且finite prefix不足。"},"difficulty":{"band":"undergraduate_core","level":1,"skills":["一致收斂"]},"variant":{"family_id":"qf-mod35-uniform-sup-gap","seed":202611042026,"parameters":{"limit":[0,1],"coefficients":[1,-2],"shift":2,"n":1,"domain":"Finite_domain_symbolic_uniform_tail","operation":"uniform-sup-gap","semantic_template":"qf-mod35-uniform-sup-gap/{\"coefficients\":[1,-2],\"limit\":[0,1],\"n\":1,\"shift\":2}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_or_symbolic_model","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"候選須主端重算；不構成人工審定、sampled rank-nullity、infinite-domain uniformity、term-zero convergence、estimator properties、noncoprime CRT shortcut、MST、mode implication、Lean或Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-14","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261014-advance-20261104-r02-uniform-convergence-of-functions-0027","batch_id":"batch-20261014-advance-20261104-r02-uniform-convergence-of-functions-foundations","language":"zh-Hant","source_mko_ids":["mko-uniform-convergence-of-functions"],"title_zh":"一致收斂","stem_zh":"共同有限domain的symbolic tail與同一N(epsilon)。操作=uniform-sup-gap；資料={\"limit\":[1,2],\"coefficients\":[2,-3],\"shift\":2,\"n\":2}。請依 exact_ordered_tuple_declared_by_interface 欄序回答。","answer":{"kind":"expression","value":"(2, 3/4, exact_finite_domain_supremum)","explanation_zh":"Wave5第四層核對=(2, 3/4, exact_finite_domain_supremum)；依完整明示資料重算；同一N控制所有x且有限domain可取pointwise witnesses最大值；不可外推無限domain且finite prefix不足。"},"difficulty":{"band":"undergraduate_core","level":1,"skills":["一致收斂"]},"variant":{"family_id":"qf-mod35-uniform-sup-gap","seed":202611042027,"parameters":{"limit":[1,2],"coefficients":[2,-3],"shift":2,"n":2,"domain":"Finite_domain_symbolic_uniform_tail","operation":"uniform-sup-gap","semantic_template":"qf-mod35-uniform-sup-gap/{\"coefficients\":[2,-3],\"limit\":[1,2],\"n\":2,\"shift\":2}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_or_symbolic_model","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"候選須主端重算；不構成人工審定、sampled rank-nullity、infinite-domain uniformity、term-zero convergence、estimator properties、noncoprime CRT shortcut、MST、mode implication、Lean或Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-14","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261014-advance-20261104-r02-uniform-convergence-of-functions-0028","batch_id":"batch-20261014-advance-20261104-r02-uniform-convergence-of-functions-foundations","language":"zh-Hant","source_mko_ids":["mko-uniform-convergence-of-functions"],"title_zh":"一致收斂","stem_zh":"共同有限domain的symbolic tail與同一N(epsilon)。操作=uniform-sup-gap；資料={\"limit\":[2,3],\"coefficients\":[3,-4],\"shift\":2,\"n\":3}。請依 exact_ordered_tuple_declared_by_interface 欄序回答。","answer":{"kind":"expression","value":"(3, 4/5, exact_finite_domain_supremum)","explanation_zh":"Wave5第四層核對=(3, 4/5, exact_finite_domain_supremum)；依完整明示資料重算；同一N控制所有x且有限domain可取pointwise witnesses最大值；不可外推無限domain且finite prefix不足。"},"difficulty":{"band":"undergraduate_core","level":1,"skills":["一致收斂"]},"variant":{"family_id":"qf-mod35-uniform-sup-gap","seed":202611042028,"parameters":{"limit":[2,3],"coefficients":[3,-4],"shift":2,"n":3,"domain":"Finite_domain_symbolic_uniform_tail","operation":"uniform-sup-gap","semantic_template":"qf-mod35-uniform-sup-gap/{\"coefficients\":[3,-4],\"limit\":[2,3],\"n\":3,\"shift\":2}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_or_symbolic_model","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"候選須主端重算；不構成人工審定、sampled rank-nullity、infinite-domain uniformity、term-zero convergence、estimator properties、noncoprime CRT shortcut、MST、mode implication、Lean或Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-14","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261014-advance-20261104-r02-uniform-convergence-of-functions-0029","batch_id":"batch-20261014-advance-20261104-r02-uniform-convergence-of-functions-foundations","language":"zh-Hant","source_mko_ids":["mko-uniform-convergence-of-functions"],"title_zh":"一致收斂","stem_zh":"共同有限domain的symbolic tail與同一N(epsilon)。操作=uniform-sup-gap；資料={\"limit\":[3,4],\"coefficients\":[4,-5],\"shift\":2,\"n\":4}。請依 exact_ordered_tuple_declared_by_interface 欄序回答。","answer":{"kind":"expression","value":"(4, 5/6, exact_finite_domain_supremum)","explanation_zh":"Wave5第四層核對=(4, 5/6, exact_finite_domain_supremum)；依完整明示資料重算；同一N控制所有x且有限domain可取pointwise witnesses最大值；不可外推無限domain且finite prefix不足。"},"difficulty":{"band":"undergraduate_core","level":1,"skills":["一致收斂"]},"variant":{"family_id":"qf-mod35-uniform-sup-gap","seed":202611042029,"parameters":{"limit":[3,4],"coefficients":[4,-5],"shift":2,"n":4,"domain":"Finite_domain_symbolic_uniform_tail","operation":"uniform-sup-gap","semantic_template":"qf-mod35-uniform-sup-gap/{\"coefficients\":[4,-5],\"limit\":[3,4],\"n\":4,\"shift\":2}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_or_symbolic_model","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"候選須主端重算；不構成人工審定、sampled rank-nullity、infinite-domain uniformity、term-zero convergence、estimator properties、noncoprime CRT shortcut、MST、mode implication、Lean或Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-14","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261014-advance-20261104-r02-uniform-convergence-of-functions-0030","batch_id":"batch-20261014-advance-20261104-r02-uniform-convergence-of-functions-foundations","language":"zh-Hant","source_mko_ids":["mko-uniform-convergence-of-functions"],"title_zh":"一致收斂","stem_zh":"共同有限domain的symbolic tail與同一N(epsilon)。操作=uniform-sup-gap；資料={\"limit\":[4,5],\"coefficients\":[5,-6],\"shift\":2,\"n\":5}。請依 exact_ordered_tuple_declared_by_interface 欄序回答。","answer":{"kind":"expression","value":"(5, 6/7, exact_finite_domain_supremum)","explanation_zh":"Wave5第四層核對=(5, 6/7, exact_finite_domain_supremum)；依完整明示資料重算；同一N控制所有x且有限domain可取pointwise witnesses最大值；不可外推無限domain且finite prefix不足。"},"difficulty":{"band":"undergraduate_core","level":1,"skills":["一致收斂"]},"variant":{"family_id":"qf-mod35-uniform-sup-gap","seed":202611042030,"parameters":{"limit":[4,5],"coefficients":[5,-6],"shift":2,"n":5,"domain":"Finite_domain_symbolic_uniform_tail","operation":"uniform-sup-gap","semantic_template":"qf-mod35-uniform-sup-gap/{\"coefficients\":[5,-6],\"limit\":[4,5],\"n\":5,\"shift\":2}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_or_symbolic_model","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"候選須主端重算；不構成人工審定、sampled rank-nullity、infinite-domain uniformity、term-zero convergence、estimator properties、noncoprime CRT shortcut、MST、mode implication、Lean或Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-14","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261014-advance-20261104-r02-uniform-convergence-of-functions-0031","batch_id":"batch-20261014-advance-20261104-r02-uniform-convergence-of-functions-foundations","language":"zh-Hant","source_mko_ids":["mko-uniform-convergence-of-functions"],"title_zh":"一致收斂","stem_zh":"共同有限domain的symbolic tail與同一N(epsilon)。操作=uniform-sup-gap；資料={\"limit\":[5,6],\"coefficients\":[6,-7],\"shift\":2,\"n\":6}。請依 exact_ordered_tuple_declared_by_interface 欄序回答。","answer":{"kind":"expression","value":"(6, 7/8, exact_finite_domain_supremum)","explanation_zh":"Wave5第四層核對=(6, 7/8, exact_finite_domain_supremum)；依完整明示資料重算；同一N控制所有x且有限domain可取pointwise witnesses最大值；不可外推無限domain且finite prefix不足。"},"difficulty":{"band":"undergraduate_core","level":1,"skills":["一致收斂"]},"variant":{"family_id":"qf-mod35-uniform-sup-gap","seed":202611042031,"parameters":{"limit":[5,6],"coefficients":[6,-7],"shift":2,"n":6,"domain":"Finite_domain_symbolic_uniform_tail","operation":"uniform-sup-gap","semantic_template":"qf-mod35-uniform-sup-gap/{\"coefficients\":[6,-7],\"limit\":[5,6],\"n\":6,\"shift\":2}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_or_symbolic_model","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"候選須主端重算；不構成人工審定、sampled rank-nullity、infinite-domain uniformity、term-zero convergence、estimator properties、noncoprime CRT shortcut、MST、mode implication、Lean或Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-14","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261014-advance-20261104-r02-uniform-convergence-of-functions-0032","batch_id":"batch-20261014-advance-20261104-r02-uniform-convergence-of-functions-foundations","language":"zh-Hant","source_mko_ids":["mko-uniform-convergence-of-functions"],"title_zh":"一致收斂","stem_zh":"共同有限domain的symbolic tail與同一N(epsilon)。操作=uniform-sup-gap；資料={\"limit\":[6,7],\"coefficients\":[7,-8],\"shift\":2,\"n\":7}。請依 exact_ordered_tuple_declared_by_interface 欄序回答。","answer":{"kind":"expression","value":"(7, 8/9, exact_finite_domain_supremum)","explanation_zh":"Wave5第四層核對=(7, 8/9, exact_finite_domain_supremum)；依完整明示資料重算；同一N控制所有x且有限domain可取pointwise witnesses最大值；不可外推無限domain且finite prefix不足。"},"difficulty":{"band":"undergraduate_core","level":1,"skills":["一致收斂"]},"variant":{"family_id":"qf-mod35-uniform-sup-gap","seed":202611042032,"parameters":{"limit":[6,7],"coefficients":[7,-8],"shift":2,"n":7,"domain":"Finite_domain_symbolic_uniform_tail","operation":"uniform-sup-gap","semantic_template":"qf-mod35-uniform-sup-gap/{\"coefficients\":[7,-8],\"limit\":[6,7],\"n\":7,\"shift\":2}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_or_symbolic_model","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"候選須主端重算；不構成人工審定、sampled rank-nullity、infinite-domain uniformity、term-zero convergence、estimator properties、noncoprime CRT shortcut、MST、mode implication、Lean或Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-14","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261014-advance-20261104-r02-uniform-convergence-of-functions-0033","batch_id":"batch-20261014-advance-20261104-r02-uniform-convergence-of-functions-foundations","language":"zh-Hant","source_mko_ids":["mko-uniform-convergence-of-functions"],"title_zh":"一致收斂","stem_zh":"共同有限domain的symbolic tail與同一N(epsilon)。操作=uniform-sup-gap；資料={\"limit\":[7,8],\"coefficients\":[8,-9],\"shift\":2,\"n\":8}。請依 exact_ordered_tuple_declared_by_interface 欄序回答。","answer":{"kind":"expression","value":"(8, 9/10, exact_finite_domain_supremum)","explanation_zh":"Wave5第四層核對=(8, 9/10, exact_finite_domain_supremum)；依完整明示資料重算；同一N控制所有x且有限domain可取pointwise witnesses最大值；不可外推無限domain且finite prefix不足。"},"difficulty":{"band":"undergraduate_core","level":1,"skills":["一致收斂"]},"variant":{"family_id":"qf-mod35-uniform-sup-gap","seed":202611042033,"parameters":{"limit":[7,8],"coefficients":[8,-9],"shift":2,"n":8,"domain":"Finite_domain_symbolic_uniform_tail","operation":"uniform-sup-gap","semantic_template":"qf-mod35-uniform-sup-gap/{\"coefficients\":[8,-9],\"limit\":[7,8],\"n\":8,\"shift\":2}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_or_symbolic_model","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"候選須主端重算；不構成人工審定、sampled rank-nullity、infinite-domain uniformity、term-zero convergence、estimator properties、noncoprime CRT shortcut、MST、mode implication、Lean或Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-14","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261014-advance-20261104-r02-uniform-convergence-of-functions-0034","batch_id":"batch-20261014-advance-20261104-r02-uniform-convergence-of-functions-foundations","language":"zh-Hant","source_mko_ids":["mko-uniform-convergence-of-functions"],"title_zh":"一致收斂","stem_zh":"共同有限domain的symbolic tail與同一N(epsilon)。操作=uniform-sup-gap；資料={\"limit\":[8,9],\"coefficients\":[9,-10],\"shift\":2,\"n\":9}。請依 exact_ordered_tuple_declared_by_interface 欄序回答。","answer":{"kind":"expression","value":"(9, 10/11, exact_finite_domain_supremum)","explanation_zh":"Wave5第四層核對=(9, 10/11, exact_finite_domain_supremum)；依完整明示資料重算；同一N控制所有x且有限domain可取pointwise witnesses最大值；不可外推無限domain且finite prefix不足。"},"difficulty":{"band":"undergraduate_core","level":2,"skills":["一致收斂"]},"variant":{"family_id":"qf-mod35-uniform-sup-gap","seed":202611042034,"parameters":{"limit":[8,9],"coefficients":[9,-10],"shift":2,"n":9,"domain":"Finite_domain_symbolic_uniform_tail","operation":"uniform-sup-gap","semantic_template":"qf-mod35-uniform-sup-gap/{\"coefficients\":[9,-10],\"limit\":[8,9],\"n\":9,\"shift\":2}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_or_symbolic_model","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"候選須主端重算；不構成人工審定、sampled rank-nullity、infinite-domain uniformity、term-zero convergence、estimator properties、noncoprime CRT shortcut、MST、mode implication、Lean或Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-14","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261014-advance-20261104-r02-uniform-convergence-of-functions-0035","batch_id":"batch-20261014-advance-20261104-r02-uniform-convergence-of-functions-foundations","language":"zh-Hant","source_mko_ids":["mko-uniform-convergence-of-functions"],"title_zh":"一致收斂","stem_zh":"共同有限domain的symbolic tail與同一N(epsilon)。操作=uniform-sup-gap；資料={\"limit\":[9,10],\"coefficients\":[10,-11],\"shift\":2,\"n\":10}。請依 exact_ordered_tuple_declared_by_interface 欄序回答。","answer":{"kind":"expression","value":"(10, 11/12, exact_finite_domain_supremum)","explanation_zh":"Wave5第四層核對=(10, 11/12, exact_finite_domain_supremum)；依完整明示資料重算；同一N控制所有x且有限domain可取pointwise witnesses最大值；不可外推無限domain且finite prefix不足。"},"difficulty":{"band":"undergraduate_core","level":2,"skills":["一致收斂"]},"variant":{"family_id":"qf-mod35-uniform-sup-gap","seed":202611042035,"parameters":{"limit":[9,10],"coefficients":[10,-11],"shift":2,"n":10,"domain":"Finite_domain_symbolic_uniform_tail","operation":"uniform-sup-gap","semantic_template":"qf-mod35-uniform-sup-gap/{\"coefficients\":[10,-11],\"limit\":[9,10],\"n\":10,\"shift\":2}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_or_symbolic_model","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"候選須主端重算；不構成人工審定、sampled rank-nullity、infinite-domain uniformity、term-zero convergence、estimator properties、noncoprime CRT shortcut、MST、mode implication、Lean或Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-14","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261014-advance-20261104-r02-uniform-convergence-of-functions-0036","batch_id":"batch-20261014-advance-20261104-r02-uniform-convergence-of-functions-foundations","language":"zh-Hant","source_mko_ids":["mko-uniform-convergence-of-functions"],"title_zh":"一致收斂","stem_zh":"共同有限domain的symbolic tail與同一N(epsilon)。操作=uniform-sup-gap；資料={\"limit\":[10,11],\"coefficients\":[11,-12],\"shift\":2,\"n\":11}。請依 exact_ordered_tuple_declared_by_interface 欄序回答。","answer":{"kind":"expression","value":"(11, 12/13, exact_finite_domain_supremum)","explanation_zh":"Wave5第四層核對=(11, 12/13, exact_finite_domain_supremum)；依完整明示資料重算；同一N控制所有x且有限domain可取pointwise witnesses最大值；不可外推無限domain且finite prefix不足。"},"difficulty":{"band":"undergraduate_core","level":2,"skills":["一致收斂"]},"variant":{"family_id":"qf-mod35-uniform-sup-gap","seed":202611042036,"parameters":{"limit":[10,11],"coefficients":[11,-12],"shift":2,"n":11,"domain":"Finite_domain_symbolic_uniform_tail","operation":"uniform-sup-gap","semantic_template":"qf-mod35-uniform-sup-gap/{\"coefficients\":[11,-12],\"limit\":[10,11],\"n\":11,\"shift\":2}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_or_symbolic_model","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"候選須主端重算；不構成人工審定、sampled rank-nullity、infinite-domain uniformity、term-zero convergence、estimator properties、noncoprime CRT shortcut、MST、mode implication、Lean或Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-14","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261014-advance-20261104-r02-uniform-convergence-of-functions-0037","batch_id":"batch-20261014-advance-20261104-r02-uniform-convergence-of-functions-foundations","language":"zh-Hant","source_mko_ids":["mko-uniform-convergence-of-functions"],"title_zh":"一致收斂","stem_zh":"共同有限domain的symbolic tail與同一N(epsilon)。操作=uniform-sup-gap；資料={\"limit\":[11,12],\"coefficients\":[12,-13],\"shift\":2,\"n\":12}。請依 exact_ordered_tuple_declared_by_interface 欄序回答。","answer":{"kind":"expression","value":"(12, 13/14, exact_finite_domain_supremum)","explanation_zh":"Wave5第四層核對=(12, 13/14, exact_finite_domain_supremum)；依完整明示資料重算；同一N控制所有x且有限domain可取pointwise witnesses最大值；不可外推無限domain且finite prefix不足。"},"difficulty":{"band":"undergraduate_core","level":2,"skills":["一致收斂"]},"variant":{"family_id":"qf-mod35-uniform-sup-gap","seed":202611042037,"parameters":{"limit":[11,12],"coefficients":[12,-13],"shift":2,"n":12,"domain":"Finite_domain_symbolic_uniform_tail","operation":"uniform-sup-gap","semantic_template":"qf-mod35-uniform-sup-gap/{\"coefficients\":[12,-13],\"limit\":[11,12],\"n\":12,\"shift\":2}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_or_symbolic_model","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"候選須主端重算；不構成人工審定、sampled rank-nullity、infinite-domain uniformity、term-zero convergence、estimator properties、noncoprime CRT shortcut、MST、mode implication、Lean或Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-14","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261014-advance-20261104-r02-uniform-convergence-of-functions-0038","batch_id":"batch-20261014-advance-20261104-r02-uniform-convergence-of-functions-foundations","language":"zh-Hant","source_mko_ids":["mko-uniform-convergence-of-functions"],"title_zh":"一致收斂","stem_zh":"共同有限domain的symbolic tail與同一N(epsilon)。操作=uniform-sup-gap；資料={\"limit\":[12,13],\"coefficients\":[13,-14],\"shift\":2,\"n\":13}。請依 exact_ordered_tuple_declared_by_interface 欄序回答。","answer":{"kind":"expression","value":"(13, 14/15, exact_finite_domain_supremum)","explanation_zh":"Wave5第四層核對=(13, 14/15, exact_finite_domain_supremum)；依完整明示資料重算；同一N控制所有x且有限domain可取pointwise witnesses最大值；不可外推無限domain且finite prefix不足。"},"difficulty":{"band":"undergraduate_core","level":2,"skills":["一致收斂"]},"variant":{"family_id":"qf-mod35-uniform-sup-gap","seed":202611042038,"parameters":{"limit":[12,13],"coefficients":[13,-14],"shift":2,"n":13,"domain":"Finite_domain_symbolic_uniform_tail","operation":"uniform-sup-gap","semantic_template":"qf-mod35-uniform-sup-gap/{\"coefficients\":[13,-14],\"limit\":[12,13],\"n\":13,\"shift\":2}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_or_symbolic_model","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"候選須主端重算；不構成人工審定、sampled rank-nullity、infinite-domain uniformity、term-zero convergence、estimator properties、noncoprime CRT shortcut、MST、mode implication、Lean或Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-14","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261014-advance-20261104-r02-uniform-convergence-of-functions-0039","batch_id":"batch-20261014-advance-20261104-r02-uniform-convergence-of-functions-foundations","language":"zh-Hant","source_mko_ids":["mko-uniform-convergence-of-functions"],"title_zh":"一致收斂","stem_zh":"共同有限domain的symbolic tail與同一N(epsilon)。操作=uniform-sup-gap；資料={\"limit\":[13,14],\"coefficients\":[14,-15],\"shift\":2,\"n\":14}。請依 exact_ordered_tuple_declared_by_interface 欄序回答。","answer":{"kind":"expression","value":"(14, 15/16, exact_finite_domain_supremum)","explanation_zh":"Wave5第四層核對=(14, 15/16, exact_finite_domain_supremum)；依完整明示資料重算；同一N控制所有x且有限domain可取pointwise witnesses最大值；不可外推無限domain且finite prefix不足。"},"difficulty":{"band":"undergraduate_core","level":2,"skills":["一致收斂"]},"variant":{"family_id":"qf-mod35-uniform-sup-gap","seed":202611042039,"parameters":{"limit":[13,14],"coefficients":[14,-15],"shift":2,"n":14,"domain":"Finite_domain_symbolic_uniform_tail","operation":"uniform-sup-gap","semantic_template":"qf-mod35-uniform-sup-gap/{\"coefficients\":[14,-15],\"limit\":[13,14],\"n\":14,\"shift\":2}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_or_symbolic_model","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"候選須主端重算；不構成人工審定、sampled rank-nullity、infinite-domain uniformity、term-zero convergence、estimator properties、noncoprime CRT shortcut、MST、mode implication、Lean或Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-14","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261014-advance-20261104-r02-uniform-convergence-of-functions-0040","batch_id":"batch-20261014-advance-20261104-r02-uniform-convergence-of-functions-foundations","language":"zh-Hant","source_mko_ids":["mko-uniform-convergence-of-functions"],"title_zh":"一致收斂","stem_zh":"共同有限domain的symbolic tail與同一N(epsilon)。操作=uniform-sup-gap；資料={\"limit\":[14,15],\"coefficients\":[15,-16],\"shift\":2,\"n\":15}。請依 exact_ordered_tuple_declared_by_interface 欄序回答。","answer":{"kind":"expression","value":"(15, 16/17, exact_finite_domain_supremum)","explanation_zh":"Wave5第四層核對=(15, 16/17, exact_finite_domain_supremum)；依完整明示資料重算；同一N控制所有x且有限domain可取pointwise witnesses最大值；不可外推無限domain且finite prefix不足。"},"difficulty":{"band":"undergraduate_core","level":2,"skills":["一致收斂"]},"variant":{"family_id":"qf-mod35-uniform-sup-gap","seed":202611042040,"parameters":{"limit":[14,15],"coefficients":[15,-16],"shift":2,"n":15,"domain":"Finite_domain_symbolic_uniform_tail","operation":"uniform-sup-gap","semantic_template":"qf-mod35-uniform-sup-gap/{\"coefficients\":[15,-16],\"limit\":[14,15],\"n\":15,\"shift\":2}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_or_symbolic_model","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"候選須主端重算；不構成人工審定、sampled rank-nullity、infinite-domain uniformity、term-zero convergence、estimator properties、noncoprime CRT shortcut、MST、mode implication、Lean或Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-14","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261014-advance-20261104-r02-uniform-convergence-of-functions-0041","batch_id":"batch-20261014-advance-20261104-r02-uniform-convergence-of-functions-foundations","language":"zh-Hant","source_mko_ids":["mko-uniform-convergence-of-functions"],"title_zh":"一致收斂","stem_zh":"共同有限domain的symbolic tail與同一N(epsilon)。操作=uniform-sup-gap；資料={\"limit\":[15,16],\"coefficients\":[16,-17],\"shift\":2,\"n\":16}。請依 exact_ordered_tuple_declared_by_interface 欄序回答。","answer":{"kind":"expression","value":"(16, 17/18, exact_finite_domain_supremum)","explanation_zh":"Wave5第四層核對=(16, 17/18, exact_finite_domain_supremum)；依完整明示資料重算；同一N控制所有x且有限domain可取pointwise witnesses最大值；不可外推無限domain且finite prefix不足。"},"difficulty":{"band":"undergraduate_core","level":2,"skills":["一致收斂"]},"variant":{"family_id":"qf-mod35-uniform-sup-gap","seed":202611042041,"parameters":{"limit":[15,16],"coefficients":[16,-17],"shift":2,"n":16,"domain":"Finite_domain_symbolic_uniform_tail","operation":"uniform-sup-gap","semantic_template":"qf-mod35-uniform-sup-gap/{\"coefficients\":[16,-17],\"limit\":[15,16],\"n\":16,\"shift\":2}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_or_symbolic_model","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"候選須主端重算；不構成人工審定、sampled rank-nullity、infinite-domain uniformity、term-zero convergence、estimator properties、noncoprime CRT shortcut、MST、mode implication、Lean或Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-14","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261014-advance-20261104-r02-uniform-convergence-of-functions-0042","batch_id":"batch-20261014-advance-20261104-r02-uniform-convergence-of-functions-foundations","language":"zh-Hant","source_mko_ids":["mko-uniform-convergence-of-functions"],"title_zh":"一致收斂","stem_zh":"共同有限domain的symbolic tail與同一N(epsilon)。操作=uniform-sup-gap；資料={\"limit\":[16,17],\"coefficients\":[17,-18],\"shift\":2,\"n\":17}。請依 exact_ordered_tuple_declared_by_interface 欄序回答。","answer":{"kind":"expression","value":"(17, 18/19, exact_finite_domain_supremum)","explanation_zh":"Wave5第四層核對=(17, 18/19, exact_finite_domain_supremum)；依完整明示資料重算；同一N控制所有x且有限domain可取pointwise witnesses最大值；不可外推無限domain且finite prefix不足。"},"difficulty":{"band":"undergraduate_core","level":2,"skills":["一致收斂"]},"variant":{"family_id":"qf-mod35-uniform-sup-gap","seed":202611042042,"parameters":{"limit":[16,17],"coefficients":[17,-18],"shift":2,"n":17,"domain":"Finite_domain_symbolic_uniform_tail","operation":"uniform-sup-gap","semantic_template":"qf-mod35-uniform-sup-gap/{\"coefficients\":[17,-18],\"limit\":[16,17],\"n\":17,\"shift\":2}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_or_symbolic_model","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"候選須主端重算；不構成人工審定、sampled rank-nullity、infinite-domain uniformity、term-zero convergence、estimator properties、noncoprime CRT shortcut、MST、mode implication、Lean或Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-14","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261014-advance-20261104-r02-uniform-convergence-of-functions-0043","batch_id":"batch-20261014-advance-20261104-r02-uniform-convergence-of-functions-foundations","language":"zh-Hant","source_mko_ids":["mko-uniform-convergence-of-functions"],"title_zh":"一致收斂","stem_zh":"共同有限domain的symbolic tail與同一N(epsilon)。操作=uniform-sup-gap；資料={\"limit\":[17,18],\"coefficients\":[18,-19],\"shift\":2,\"n\":18}。請依 exact_ordered_tuple_declared_by_interface 欄序回答。","answer":{"kind":"expression","value":"(18, 19/20, exact_finite_domain_supremum)","explanation_zh":"Wave5第四層核對=(18, 19/20, exact_finite_domain_supremum)；依完整明示資料重算；同一N控制所有x且有限domain可取pointwise witnesses最大值；不可外推無限domain且finite prefix不足。"},"difficulty":{"band":"undergraduate_core","level":3,"skills":["一致收斂"]},"variant":{"family_id":"qf-mod35-uniform-sup-gap","seed":202611042043,"parameters":{"limit":[17,18],"coefficients":[18,-19],"shift":2,"n":18,"domain":"Finite_domain_symbolic_uniform_tail","operation":"uniform-sup-gap","semantic_template":"qf-mod35-uniform-sup-gap/{\"coefficients\":[18,-19],\"limit\":[17,18],\"n\":18,\"shift\":2}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_or_symbolic_model","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"候選須主端重算；不構成人工審定、sampled rank-nullity、infinite-domain uniformity、term-zero convergence、estimator properties、noncoprime CRT shortcut、MST、mode implication、Lean或Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-14","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261014-advance-20261104-r02-uniform-convergence-of-functions-0044","batch_id":"batch-20261014-advance-20261104-r02-uniform-convergence-of-functions-foundations","language":"zh-Hant","source_mko_ids":["mko-uniform-convergence-of-functions"],"title_zh":"一致收斂","stem_zh":"共同有限domain的symbolic tail與同一N(epsilon)。操作=uniform-sup-gap；資料={\"limit\":[18,19],\"coefficients\":[19,-20],\"shift\":2,\"n\":19}。請依 exact_ordered_tuple_declared_by_interface 欄序回答。","answer":{"kind":"expression","value":"(19, 20/21, exact_finite_domain_supremum)","explanation_zh":"Wave5第四層核對=(19, 20/21, exact_finite_domain_supremum)；依完整明示資料重算；同一N控制所有x且有限domain可取pointwise witnesses最大值；不可外推無限domain且finite prefix不足。"},"difficulty":{"band":"undergraduate_core","level":3,"skills":["一致收斂"]},"variant":{"family_id":"qf-mod35-uniform-sup-gap","seed":202611042044,"parameters":{"limit":[18,19],"coefficients":[19,-20],"shift":2,"n":19,"domain":"Finite_domain_symbolic_uniform_tail","operation":"uniform-sup-gap","semantic_template":"qf-mod35-uniform-sup-gap/{\"coefficients\":[19,-20],\"limit\":[18,19],\"n\":19,\"shift\":2}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_or_symbolic_model","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"候選須主端重算；不構成人工審定、sampled rank-nullity、infinite-domain uniformity、term-zero convergence、estimator properties、noncoprime CRT shortcut、MST、mode implication、Lean或Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-14","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261014-advance-20261104-r02-uniform-convergence-of-functions-0045","batch_id":"batch-20261014-advance-20261104-r02-uniform-convergence-of-functions-foundations","language":"zh-Hant","source_mko_ids":["mko-uniform-convergence-of-functions"],"title_zh":"一致收斂","stem_zh":"共同有限domain的symbolic tail與同一N(epsilon)。操作=uniform-sup-gap；資料={\"limit\":[19,20],\"coefficients\":[20,-21],\"shift\":2,\"n\":20}。請依 exact_ordered_tuple_declared_by_interface 欄序回答。","answer":{"kind":"expression","value":"(20, 21/22, exact_finite_domain_supremum)","explanation_zh":"Wave5第四層核對=(20, 21/22, exact_finite_domain_supremum)；依完整明示資料重算；同一N控制所有x且有限domain可取pointwise witnesses最大值；不可外推無限domain且finite prefix不足。"},"difficulty":{"band":"undergraduate_core","level":3,"skills":["一致收斂"]},"variant":{"family_id":"qf-mod35-uniform-sup-gap","seed":202611042045,"parameters":{"limit":[19,20],"coefficients":[20,-21],"shift":2,"n":20,"domain":"Finite_domain_symbolic_uniform_tail","operation":"uniform-sup-gap","semantic_template":"qf-mod35-uniform-sup-gap/{\"coefficients\":[20,-21],\"limit\":[19,20],\"n\":20,\"shift\":2}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_or_symbolic_model","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"候選須主端重算；不構成人工審定、sampled rank-nullity、infinite-domain uniformity、term-zero convergence、estimator properties、noncoprime CRT shortcut、MST、mode implication、Lean或Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-14","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261014-advance-20261104-r02-uniform-convergence-of-functions-0046","batch_id":"batch-20261014-advance-20261104-r02-uniform-convergence-of-functions-foundations","language":"zh-Hant","source_mko_ids":["mko-uniform-convergence-of-functions"],"title_zh":"一致收斂","stem_zh":"共同有限domain的symbolic tail與同一N(epsilon)。操作=uniform-sup-gap；資料={\"limit\":[20,21],\"coefficients\":[21,-22],\"shift\":2,\"n\":21}。請依 exact_ordered_tuple_declared_by_interface 欄序回答。","answer":{"kind":"expression","value":"(21, 22/23, exact_finite_domain_supremum)","explanation_zh":"Wave5第四層核對=(21, 22/23, exact_finite_domain_supremum)；依完整明示資料重算；同一N控制所有x且有限domain可取pointwise witnesses最大值；不可外推無限domain且finite prefix不足。"},"difficulty":{"band":"undergraduate_core","level":3,"skills":["一致收斂"]},"variant":{"family_id":"qf-mod35-uniform-sup-gap","seed":202611042046,"parameters":{"limit":[20,21],"coefficients":[21,-22],"shift":2,"n":21,"domain":"Finite_domain_symbolic_uniform_tail","operation":"uniform-sup-gap","semantic_template":"qf-mod35-uniform-sup-gap/{\"coefficients\":[21,-22],\"limit\":[20,21],\"n\":21,\"shift\":2}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_or_symbolic_model","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"候選須主端重算；不構成人工審定、sampled rank-nullity、infinite-domain uniformity、term-zero convergence、estimator properties、noncoprime CRT shortcut、MST、mode implication、Lean或Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-14","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261014-advance-20261104-r02-uniform-convergence-of-functions-0047","batch_id":"batch-20261014-advance-20261104-r02-uniform-convergence-of-functions-foundations","language":"zh-Hant","source_mko_ids":["mko-uniform-convergence-of-functions"],"title_zh":"一致收斂","stem_zh":"共同有限domain的symbolic tail與同一N(epsilon)。操作=uniform-sup-gap；資料={\"limit\":[21,22],\"coefficients\":[22,-23],\"shift\":2,\"n\":22}。請依 exact_ordered_tuple_declared_by_interface 欄序回答。","answer":{"kind":"expression","value":"(22, 23/24, exact_finite_domain_supremum)","explanation_zh":"Wave5第四層核對=(22, 23/24, exact_finite_domain_supremum)；依完整明示資料重算；同一N控制所有x且有限domain可取pointwise witnesses最大值；不可外推無限domain且finite prefix不足。"},"difficulty":{"band":"undergraduate_core","level":3,"skills":["一致收斂"]},"variant":{"family_id":"qf-mod35-uniform-sup-gap","seed":202611042047,"parameters":{"limit":[21,22],"coefficients":[22,-23],"shift":2,"n":22,"domain":"Finite_domain_symbolic_uniform_tail","operation":"uniform-sup-gap","semantic_template":"qf-mod35-uniform-sup-gap/{\"coefficients\":[22,-23],\"limit\":[21,22],\"n\":22,\"shift\":2}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_or_symbolic_model","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"候選須主端重算；不構成人工審定、sampled rank-nullity、infinite-domain uniformity、term-zero convergence、estimator properties、noncoprime CRT shortcut、MST、mode implication、Lean或Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-14","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261014-advance-20261104-r02-uniform-convergence-of-functions-0048","batch_id":"batch-20261014-advance-20261104-r02-uniform-convergence-of-functions-foundations","language":"zh-Hant","source_mko_ids":["mko-uniform-convergence-of-functions"],"title_zh":"一致收斂","stem_zh":"共同有限domain的symbolic tail與同一N(epsilon)。操作=uniform-sup-gap；資料={\"limit\":[22,23],\"coefficients\":[23,-24],\"shift\":2,\"n\":23}。請依 exact_ordered_tuple_declared_by_interface 欄序回答。","answer":{"kind":"expression","value":"(23, 24/25, exact_finite_domain_supremum)","explanation_zh":"Wave5第四層核對=(23, 24/25, exact_finite_domain_supremum)；依完整明示資料重算；同一N控制所有x且有限domain可取pointwise witnesses最大值；不可外推無限domain且finite prefix不足。"},"difficulty":{"band":"undergraduate_core","level":3,"skills":["一致收斂"]},"variant":{"family_id":"qf-mod35-uniform-sup-gap","seed":202611042048,"parameters":{"limit":[22,23],"coefficients":[23,-24],"shift":2,"n":23,"domain":"Finite_domain_symbolic_uniform_tail","operation":"uniform-sup-gap","semantic_template":"qf-mod35-uniform-sup-gap/{\"coefficients\":[23,-24],\"limit\":[22,23],\"n\":23,\"shift\":2}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_or_symbolic_model","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"候選須主端重算；不構成人工審定、sampled rank-nullity、infinite-domain uniformity、term-zero convergence、estimator properties、noncoprime CRT shortcut、MST、mode implication、Lean或Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-14","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261014-advance-20261104-r02-uniform-convergence-of-functions-0049","batch_id":"batch-20261014-advance-20261104-r02-uniform-convergence-of-functions-foundations","language":"zh-Hant","source_mko_ids":["mko-uniform-convergence-of-functions"],"title_zh":"一致收斂","stem_zh":"共同有限domain的symbolic tail與同一N(epsilon)。操作=uniform-sup-gap；資料={\"limit\":[23,24],\"coefficients\":[24,-25],\"shift\":2,\"n\":24}。請依 exact_ordered_tuple_declared_by_interface 欄序回答。","answer":{"kind":"expression","value":"(24, 25/26, exact_finite_domain_supremum)","explanation_zh":"Wave5第四層核對=(24, 25/26, exact_finite_domain_supremum)；依完整明示資料重算；同一N控制所有x且有限domain可取pointwise witnesses最大值；不可外推無限domain且finite prefix不足。"},"difficulty":{"band":"undergraduate_core","level":3,"skills":["一致收斂"]},"variant":{"family_id":"qf-mod35-uniform-sup-gap","seed":202611042049,"parameters":{"limit":[23,24],"coefficients":[24,-25],"shift":2,"n":24,"domain":"Finite_domain_symbolic_uniform_tail","operation":"uniform-sup-gap","semantic_template":"qf-mod35-uniform-sup-gap/{\"coefficients\":[24,-25],\"limit\":[23,24],\"n\":24,\"shift\":2}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_or_symbolic_model","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"候選須主端重算；不構成人工審定、sampled rank-nullity、infinite-domain uniformity、term-zero convergence、estimator properties、noncoprime CRT shortcut、MST、mode implication、Lean或Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-14","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261014-advance-20261104-r02-uniform-convergence-of-functions-0050","batch_id":"batch-20261014-advance-20261104-r02-uniform-convergence-of-functions-foundations","language":"zh-Hant","source_mko_ids":["mko-uniform-convergence-of-functions"],"title_zh":"一致收斂","stem_zh":"共同有限domain的symbolic tail與同一N(epsilon)。操作=uniform-sup-gap；資料={\"limit\":[24,25],\"coefficients\":[25,-26],\"shift\":2,\"n\":25}。請依 exact_ordered_tuple_declared_by_interface 欄序回答。","answer":{"kind":"expression","value":"(25, 26/27, exact_finite_domain_supremum)","explanation_zh":"Wave5第四層核對=(25, 26/27, exact_finite_domain_supremum)；依完整明示資料重算；同一N控制所有x且有限domain可取pointwise witnesses最大值；不可外推無限domain且finite prefix不足。"},"difficulty":{"band":"undergraduate_core","level":3,"skills":["一致收斂"]},"variant":{"family_id":"qf-mod35-uniform-sup-gap","seed":202611042050,"parameters":{"limit":[24,25],"coefficients":[25,-26],"shift":2,"n":25,"domain":"Finite_domain_symbolic_uniform_tail","operation":"uniform-sup-gap","semantic_template":"qf-mod35-uniform-sup-gap/{\"coefficients\":[25,-26],\"limit\":[24,25],\"n\":25,\"shift\":2}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_or_symbolic_model","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"候選須主端重算；不構成人工審定、sampled rank-nullity、infinite-domain uniformity、term-zero convergence、estimator properties、noncoprime CRT shortcut、MST、mode implication、Lean或Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-14","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261014-advance-20261104-r02-uniform-convergence-of-functions-0051","batch_id":"batch-20261014-advance-20261104-r02-uniform-convergence-of-functions-foundations","language":"zh-Hant","source_mko_ids":["mko-uniform-convergence-of-functions"],"title_zh":"一致收斂","stem_zh":"共同有限domain的symbolic tail與同一N(epsilon)。操作=uniform-pointwise-max；資料={\"limit\":[0,1],\"coefficients\":[1,-2],\"shift\":2,\"epsilon\":[1,10]}。請依 exact_ordered_tuple_declared_by_interface 欄序回答。","answer":{"kind":"expression","value":"([[0, 9], [1, 19]], 19, 是, finite_maximum_only_not_infinite_domain_implication)","explanation_zh":"Wave5第四層核對=([[0, 9], [1, 19]], 19, 是, finite_maximum_only_not_infinite_domain_implication)；依完整明示資料重算；同一N控制所有x且有限domain可取pointwise witnesses最大值；不可外推無限domain且finite prefix不足。"},"difficulty":{"band":"undergraduate_core","level":1,"skills":["一致收斂"]},"variant":{"family_id":"qf-mod35-uniform-pointwise-max","seed":202611042051,"parameters":{"limit":[0,1],"coefficients":[1,-2],"shift":2,"epsilon":[1,10],"domain":"Finite_domain_symbolic_uniform_tail","operation":"uniform-pointwise-max","semantic_template":"qf-mod35-uniform-pointwise-max/{\"coefficients\":[1,-2],\"epsilon\":[1,10],\"limit\":[0,1],\"shift\":2}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_or_symbolic_model","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"候選須主端重算；不構成人工審定、sampled rank-nullity、infinite-domain uniformity、term-zero convergence、estimator properties、noncoprime CRT shortcut、MST、mode implication、Lean或Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-14","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261014-advance-20261104-r02-uniform-convergence-of-functions-0052","batch_id":"batch-20261014-advance-20261104-r02-uniform-convergence-of-functions-foundations","language":"zh-Hant","source_mko_ids":["mko-uniform-convergence-of-functions"],"title_zh":"一致收斂","stem_zh":"共同有限domain的symbolic tail與同一N(epsilon)。操作=uniform-pointwise-max；資料={\"limit\":[1,2],\"coefficients\":[2,-3],\"shift\":2,\"epsilon\":[1,11]}。請依 exact_ordered_tuple_declared_by_interface 欄序回答。","answer":{"kind":"expression","value":"([[0, 21], [1, 32]], 32, 是, finite_maximum_only_not_infinite_domain_implication)","explanation_zh":"Wave5第四層核對=([[0, 21], [1, 32]], 32, 是, finite_maximum_only_not_infinite_domain_implication)；依完整明示資料重算；同一N控制所有x且有限domain可取pointwise witnesses最大值；不可外推無限domain且finite prefix不足。"},"difficulty":{"band":"undergraduate_core","level":1,"skills":["一致收斂"]},"variant":{"family_id":"qf-mod35-uniform-pointwise-max","seed":202611042052,"parameters":{"limit":[1,2],"coefficients":[2,-3],"shift":2,"epsilon":[1,11],"domain":"Finite_domain_symbolic_uniform_tail","operation":"uniform-pointwise-max","semantic_template":"qf-mod35-uniform-pointwise-max/{\"coefficients\":[2,-3],\"epsilon\":[1,11],\"limit\":[1,2],\"shift\":2}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_or_symbolic_model","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"候選須主端重算；不構成人工審定、sampled rank-nullity、infinite-domain uniformity、term-zero convergence、estimator properties、noncoprime CRT shortcut、MST、mode implication、Lean或Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-14","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261014-advance-20261104-r02-uniform-convergence-of-functions-0053","batch_id":"batch-20261014-advance-20261104-r02-uniform-convergence-of-functions-foundations","language":"zh-Hant","source_mko_ids":["mko-uniform-convergence-of-functions"],"title_zh":"一致收斂","stem_zh":"共同有限domain的symbolic tail與同一N(epsilon)。操作=uniform-pointwise-max；資料={\"limit\":[2,3],\"coefficients\":[3,-4],\"shift\":2,\"epsilon\":[1,12]}。請依 exact_ordered_tuple_declared_by_interface 欄序回答。","answer":{"kind":"expression","value":"([[0, 35], [1, 47]], 47, 是, finite_maximum_only_not_infinite_domain_implication)","explanation_zh":"Wave5第四層核對=([[0, 35], [1, 47]], 47, 是, finite_maximum_only_not_infinite_domain_implication)；依完整明示資料重算；同一N控制所有x且有限domain可取pointwise witnesses最大值；不可外推無限domain且finite prefix不足。"},"difficulty":{"band":"undergraduate_core","level":1,"skills":["一致收斂"]},"variant":{"family_id":"qf-mod35-uniform-pointwise-max","seed":202611042053,"parameters":{"limit":[2,3],"coefficients":[3,-4],"shift":2,"epsilon":[1,12],"domain":"Finite_domain_symbolic_uniform_tail","operation":"uniform-pointwise-max","semantic_template":"qf-mod35-uniform-pointwise-max/{\"coefficients\":[3,-4],\"epsilon\":[1,12],\"limit\":[2,3],\"shift\":2}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_or_symbolic_model","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"候選須主端重算；不構成人工審定、sampled rank-nullity、infinite-domain uniformity、term-zero convergence、estimator properties、noncoprime CRT shortcut、MST、mode implication、Lean或Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-14","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261014-advance-20261104-r02-uniform-convergence-of-functions-0054","batch_id":"batch-20261014-advance-20261104-r02-uniform-convergence-of-functions-foundations","language":"zh-Hant","source_mko_ids":["mko-uniform-convergence-of-functions"],"title_zh":"一致收斂","stem_zh":"共同有限domain的symbolic tail與同一N(epsilon)。操作=uniform-pointwise-max；資料={\"limit\":[3,4],\"coefficients\":[4,-5],\"shift\":2,\"epsilon\":[1,13]}。請依 exact_ordered_tuple_declared_by_interface 欄序回答。","answer":{"kind":"expression","value":"([[0, 51], [1, 64]], 64, 是, finite_maximum_only_not_infinite_domain_implication)","explanation_zh":"Wave5第四層核對=([[0, 51], [1, 64]], 64, 是, finite_maximum_only_not_infinite_domain_implication)；依完整明示資料重算；同一N控制所有x且有限domain可取pointwise witnesses最大值；不可外推無限domain且finite prefix不足。"},"difficulty":{"band":"undergraduate_core","level":1,"skills":["一致收斂"]},"variant":{"family_id":"qf-mod35-uniform-pointwise-max","seed":202611042054,"parameters":{"limit":[3,4],"coefficients":[4,-5],"shift":2,"epsilon":[1,13],"domain":"Finite_domain_symbolic_uniform_tail","operation":"uniform-pointwise-max","semantic_template":"qf-mod35-uniform-pointwise-max/{\"coefficients\":[4,-5],\"epsilon\":[1,13],\"limit\":[3,4],\"shift\":2}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_or_symbolic_model","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"候選須主端重算；不構成人工審定、sampled rank-nullity、infinite-domain uniformity、term-zero convergence、estimator properties、noncoprime CRT shortcut、MST、mode implication、Lean或Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-14","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261014-advance-20261104-r02-uniform-convergence-of-functions-0055","batch_id":"batch-20261014-advance-20261104-r02-uniform-convergence-of-functions-foundations","language":"zh-Hant","source_mko_ids":["mko-uniform-convergence-of-functions"],"title_zh":"一致收斂","stem_zh":"共同有限domain的symbolic tail與同一N(epsilon)。操作=uniform-pointwise-max；資料={\"limit\":[4,5],\"coefficients\":[5,-6],\"shift\":2,\"epsilon\":[1,14]}。請依 exact_ordered_tuple_declared_by_interface 欄序回答。","answer":{"kind":"expression","value":"([[0, 69], [1, 83]], 83, 是, finite_maximum_only_not_infinite_domain_implication)","explanation_zh":"Wave5第四層核對=([[0, 69], [1, 83]], 83, 是, finite_maximum_only_not_infinite_domain_implication)；依完整明示資料重算；同一N控制所有x且有限domain可取pointwise witnesses最大值；不可外推無限domain且finite prefix不足。"},"difficulty":{"band":"undergraduate_core","level":1,"skills":["一致收斂"]},"variant":{"family_id":"qf-mod35-uniform-pointwise-max","seed":202611042055,"parameters":{"limit":[4,5],"coefficients":[5,-6],"shift":2,"epsilon":[1,14],"domain":"Finite_domain_symbolic_uniform_tail","operation":"uniform-pointwise-max","semantic_template":"qf-mod35-uniform-pointwise-max/{\"coefficients\":[5,-6],\"epsilon\":[1,14],\"limit\":[4,5],\"shift\":2}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_or_symbolic_model","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"候選須主端重算；不構成人工審定、sampled rank-nullity、infinite-domain uniformity、term-zero convergence、estimator properties、noncoprime CRT shortcut、MST、mode implication、Lean或Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-14","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261014-advance-20261104-r02-uniform-convergence-of-functions-0056","batch_id":"batch-20261014-advance-20261104-r02-uniform-convergence-of-functions-foundations","language":"zh-Hant","source_mko_ids":["mko-uniform-convergence-of-functions"],"title_zh":"一致收斂","stem_zh":"共同有限domain的symbolic tail與同一N(epsilon)。操作=uniform-pointwise-max；資料={\"limit\":[5,6],\"coefficients\":[6,-7],\"shift\":2,\"epsilon\":[1,15]}。請依 exact_ordered_tuple_declared_by_interface 欄序回答。","answer":{"kind":"expression","value":"([[0, 89], [1, 104]], 104, 是, finite_maximum_only_not_infinite_domain_implication)","explanation_zh":"Wave5第四層核對=([[0, 89], [1, 104]], 104, 是, finite_maximum_only_not_infinite_domain_implication)；依完整明示資料重算；同一N控制所有x且有限domain可取pointwise witnesses最大值；不可外推無限domain且finite prefix不足。"},"difficulty":{"band":"undergraduate_core","level":1,"skills":["一致收斂"]},"variant":{"family_id":"qf-mod35-uniform-pointwise-max","seed":202611042056,"parameters":{"limit":[5,6],"coefficients":[6,-7],"shift":2,"epsilon":[1,15],"domain":"Finite_domain_symbolic_uniform_tail","operation":"uniform-pointwise-max","semantic_template":"qf-mod35-uniform-pointwise-max/{\"coefficients\":[6,-7],\"epsilon\":[1,15],\"limit\":[5,6],\"shift\":2}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_or_symbolic_model","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"候選須主端重算；不構成人工審定、sampled rank-nullity、infinite-domain uniformity、term-zero convergence、estimator properties、noncoprime CRT shortcut、MST、mode implication、Lean或Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-14","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261014-advance-20261104-r02-uniform-convergence-of-functions-0057","batch_id":"batch-20261014-advance-20261104-r02-uniform-convergence-of-functions-foundations","language":"zh-Hant","source_mko_ids":["mko-uniform-convergence-of-functions"],"title_zh":"一致收斂","stem_zh":"共同有限domain的symbolic tail與同一N(epsilon)。操作=uniform-pointwise-max；資料={\"limit\":[6,7],\"coefficients\":[7,-8],\"shift\":2,\"epsilon\":[1,16]}。請依 exact_ordered_tuple_declared_by_interface 欄序回答。","answer":{"kind":"expression","value":"([[0, 111], [1, 127]], 127, 是, finite_maximum_only_not_infinite_domain_implication)","explanation_zh":"Wave5第四層核對=([[0, 111], [1, 127]], 127, 是, finite_maximum_only_not_infinite_domain_implication)；依完整明示資料重算；同一N控制所有x且有限domain可取pointwise witnesses最大值；不可外推無限domain且finite prefix不足。"},"difficulty":{"band":"undergraduate_core","level":1,"skills":["一致收斂"]},"variant":{"family_id":"qf-mod35-uniform-pointwise-max","seed":202611042057,"parameters":{"limit":[6,7],"coefficients":[7,-8],"shift":2,"epsilon":[1,16],"domain":"Finite_domain_symbolic_uniform_tail","operation":"uniform-pointwise-max","semantic_template":"qf-mod35-uniform-pointwise-max/{\"coefficients\":[7,-8],\"epsilon\":[1,16],\"limit\":[6,7],\"shift\":2}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_or_symbolic_model","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"候選須主端重算；不構成人工審定、sampled rank-nullity、infinite-domain uniformity、term-zero convergence、estimator properties、noncoprime CRT shortcut、MST、mode implication、Lean或Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-14","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261014-advance-20261104-r02-uniform-convergence-of-functions-0058","batch_id":"batch-20261014-advance-20261104-r02-uniform-convergence-of-functions-foundations","language":"zh-Hant","source_mko_ids":["mko-uniform-convergence-of-functions"],"title_zh":"一致收斂","stem_zh":"共同有限domain的symbolic tail與同一N(epsilon)。操作=uniform-pointwise-max；資料={\"limit\":[7,8],\"coefficients\":[8,-9],\"shift\":2,\"epsilon\":[1,17]}。請依 exact_ordered_tuple_declared_by_interface 欄序回答。","answer":{"kind":"expression","value":"([[0, 135], [1, 152]], 152, 是, finite_maximum_only_not_infinite_domain_implication)","explanation_zh":"Wave5第四層核對=([[0, 135], [1, 152]], 152, 是, finite_maximum_only_not_infinite_domain_implication)；依完整明示資料重算；同一N控制所有x且有限domain可取pointwise witnesses最大值；不可外推無限domain且finite prefix不足。"},"difficulty":{"band":"undergraduate_core","level":1,"skills":["一致收斂"]},"variant":{"family_id":"qf-mod35-uniform-pointwise-max","seed":202611042058,"parameters":{"limit":[7,8],"coefficients":[8,-9],"shift":2,"epsilon":[1,17],"domain":"Finite_domain_symbolic_uniform_tail","operation":"uniform-pointwise-max","semantic_template":"qf-mod35-uniform-pointwise-max/{\"coefficients\":[8,-9],\"epsilon\":[1,17],\"limit\":[7,8],\"shift\":2}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_or_symbolic_model","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"候選須主端重算；不構成人工審定、sampled rank-nullity、infinite-domain uniformity、term-zero convergence、estimator properties、noncoprime CRT shortcut、MST、mode implication、Lean或Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-14","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261014-advance-20261104-r02-uniform-convergence-of-functions-0059","batch_id":"batch-20261014-advance-20261104-r02-uniform-convergence-of-functions-foundations","language":"zh-Hant","source_mko_ids":["mko-uniform-convergence-of-functions"],"title_zh":"一致收斂","stem_zh":"共同有限domain的symbolic tail與同一N(epsilon)。操作=uniform-pointwise-max；資料={\"limit\":[8,9],\"coefficients\":[9,-10],\"shift\":2,\"epsilon\":[1,18]}。請依 exact_ordered_tuple_declared_by_interface 欄序回答。","answer":{"kind":"expression","value":"([[0, 161], [1, 179]], 179, 是, finite_maximum_only_not_infinite_domain_implication)","explanation_zh":"Wave5第四層核對=([[0, 161], [1, 179]], 179, 是, finite_maximum_only_not_infinite_domain_implication)；依完整明示資料重算；同一N控制所有x且有限domain可取pointwise witnesses最大值；不可外推無限domain且finite prefix不足。"},"difficulty":{"band":"undergraduate_core","level":2,"skills":["一致收斂"]},"variant":{"family_id":"qf-mod35-uniform-pointwise-max","seed":202611042059,"parameters":{"limit":[8,9],"coefficients":[9,-10],"shift":2,"epsilon":[1,18],"domain":"Finite_domain_symbolic_uniform_tail","operation":"uniform-pointwise-max","semantic_template":"qf-mod35-uniform-pointwise-max/{\"coefficients\":[9,-10],\"epsilon\":[1,18],\"limit\":[8,9],\"shift\":2}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_or_symbolic_model","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"候選須主端重算；不構成人工審定、sampled rank-nullity、infinite-domain uniformity、term-zero convergence、estimator properties、noncoprime CRT shortcut、MST、mode implication、Lean或Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-14","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261014-advance-20261104-r02-uniform-convergence-of-functions-0060","batch_id":"batch-20261014-advance-20261104-r02-uniform-convergence-of-functions-foundations","language":"zh-Hant","source_mko_ids":["mko-uniform-convergence-of-functions"],"title_zh":"一致收斂","stem_zh":"共同有限domain的symbolic tail與同一N(epsilon)。操作=uniform-pointwise-max；資料={\"limit\":[9,10],\"coefficients\":[10,-11],\"shift\":2,\"epsilon\":[1,19]}。請依 exact_ordered_tuple_declared_by_interface 欄序回答。","answer":{"kind":"expression","value":"([[0, 189], [1, 208]], 208, 是, finite_maximum_only_not_infinite_domain_implication)","explanation_zh":"Wave5第四層核對=([[0, 189], [1, 208]], 208, 是, finite_maximum_only_not_infinite_domain_implication)；依完整明示資料重算；同一N控制所有x且有限domain可取pointwise witnesses最大值；不可外推無限domain且finite prefix不足。"},"difficulty":{"band":"undergraduate_core","level":2,"skills":["一致收斂"]},"variant":{"family_id":"qf-mod35-uniform-pointwise-max","seed":202611042060,"parameters":{"limit":[9,10],"coefficients":[10,-11],"shift":2,"epsilon":[1,19],"domain":"Finite_domain_symbolic_uniform_tail","operation":"uniform-pointwise-max","semantic_template":"qf-mod35-uniform-pointwise-max/{\"coefficients\":[10,-11],\"epsilon\":[1,19],\"limit\":[9,10],\"shift\":2}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_or_symbolic_model","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"候選須主端重算；不構成人工審定、sampled rank-nullity、infinite-domain uniformity、term-zero convergence、estimator properties、noncoprime CRT shortcut、MST、mode implication、Lean或Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-14","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261014-advance-20261104-r02-uniform-convergence-of-functions-0061","batch_id":"batch-20261014-advance-20261104-r02-uniform-convergence-of-functions-foundations","language":"zh-Hant","source_mko_ids":["mko-uniform-convergence-of-functions"],"title_zh":"一致收斂","stem_zh":"共同有限domain的symbolic tail與同一N(epsilon)。操作=uniform-pointwise-max；資料={\"limit\":[10,11],\"coefficients\":[11,-12],\"shift\":2,\"epsilon\":[1,20]}。請依 exact_ordered_tuple_declared_by_interface 欄序回答。","answer":{"kind":"expression","value":"([[0, 219], [1, 239]], 239, 是, finite_maximum_only_not_infinite_domain_implication)","explanation_zh":"Wave5第四層核對=([[0, 219], [1, 239]], 239, 是, finite_maximum_only_not_infinite_domain_implication)；依完整明示資料重算；同一N控制所有x且有限domain可取pointwise witnesses最大值；不可外推無限domain且finite prefix不足。"},"difficulty":{"band":"undergraduate_core","level":2,"skills":["一致收斂"]},"variant":{"family_id":"qf-mod35-uniform-pointwise-max","seed":202611042061,"parameters":{"limit":[10,11],"coefficients":[11,-12],"shift":2,"epsilon":[1,20],"domain":"Finite_domain_symbolic_uniform_tail","operation":"uniform-pointwise-max","semantic_template":"qf-mod35-uniform-pointwise-max/{\"coefficients\":[11,-12],\"epsilon\":[1,20],\"limit\":[10,11],\"shift\":2}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_or_symbolic_model","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"候選須主端重算；不構成人工審定、sampled rank-nullity、infinite-domain uniformity、term-zero convergence、estimator properties、noncoprime CRT shortcut、MST、mode implication、Lean或Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-14","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261014-advance-20261104-r02-uniform-convergence-of-functions-0062","batch_id":"batch-20261014-advance-20261104-r02-uniform-convergence-of-functions-foundations","language":"zh-Hant","source_mko_ids":["mko-uniform-convergence-of-functions"],"title_zh":"一致收斂","stem_zh":"共同有限domain的symbolic tail與同一N(epsilon)。操作=uniform-pointwise-max；資料={\"limit\":[11,12],\"coefficients\":[12,-13],\"shift\":2,\"epsilon\":[1,21]}。請依 exact_ordered_tuple_declared_by_interface 欄序回答。","answer":{"kind":"expression","value":"([[0, 251], [1, 272]], 272, 是, finite_maximum_only_not_infinite_domain_implication)","explanation_zh":"Wave5第四層核對=([[0, 251], [1, 272]], 272, 是, finite_maximum_only_not_infinite_domain_implication)；依完整明示資料重算；同一N控制所有x且有限domain可取pointwise witnesses最大值；不可外推無限domain且finite prefix不足。"},"difficulty":{"band":"undergraduate_core","level":2,"skills":["一致收斂"]},"variant":{"family_id":"qf-mod35-uniform-pointwise-max","seed":202611042062,"parameters":{"limit":[11,12],"coefficients":[12,-13],"shift":2,"epsilon":[1,21],"domain":"Finite_domain_symbolic_uniform_tail","operation":"uniform-pointwise-max","semantic_template":"qf-mod35-uniform-pointwise-max/{\"coefficients\":[12,-13],\"epsilon\":[1,21],\"limit\":[11,12],\"shift\":2}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_or_symbolic_model","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"候選須主端重算；不構成人工審定、sampled rank-nullity、infinite-domain uniformity、term-zero convergence、estimator properties、noncoprime CRT shortcut、MST、mode implication、Lean或Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-14","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261014-advance-20261104-r02-uniform-convergence-of-functions-0063","batch_id":"batch-20261014-advance-20261104-r02-uniform-convergence-of-functions-foundations","language":"zh-Hant","source_mko_ids":["mko-uniform-convergence-of-functions"],"title_zh":"一致收斂","stem_zh":"共同有限domain的symbolic tail與同一N(epsilon)。操作=uniform-pointwise-max；資料={\"limit\":[12,13],\"coefficients\":[13,-14],\"shift\":2,\"epsilon\":[1,22]}。請依 exact_ordered_tuple_declared_by_interface 欄序回答。","answer":{"kind":"expression","value":"([[0, 285], [1, 307]], 307, 是, finite_maximum_only_not_infinite_domain_implication)","explanation_zh":"Wave5第四層核對=([[0, 285], [1, 307]], 307, 是, finite_maximum_only_not_infinite_domain_implication)；依完整明示資料重算；同一N控制所有x且有限domain可取pointwise witnesses最大值；不可外推無限domain且finite prefix不足。"},"difficulty":{"band":"undergraduate_core","level":2,"skills":["一致收斂"]},"variant":{"family_id":"qf-mod35-uniform-pointwise-max","seed":202611042063,"parameters":{"limit":[12,13],"coefficients":[13,-14],"shift":2,"epsilon":[1,22],"domain":"Finite_domain_symbolic_uniform_tail","operation":"uniform-pointwise-max","semantic_template":"qf-mod35-uniform-pointwise-max/{\"coefficients\":[13,-14],\"epsilon\":[1,22],\"limit\":[12,13],\"shift\":2}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_or_symbolic_model","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"候選須主端重算；不構成人工審定、sampled rank-nullity、infinite-domain uniformity、term-zero convergence、estimator properties、noncoprime CRT shortcut、MST、mode implication、Lean或Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-14","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261014-advance-20261104-r02-uniform-convergence-of-functions-0064","batch_id":"batch-20261014-advance-20261104-r02-uniform-convergence-of-functions-foundations","language":"zh-Hant","source_mko_ids":["mko-uniform-convergence-of-functions"],"title_zh":"一致收斂","stem_zh":"共同有限domain的symbolic tail與同一N(epsilon)。操作=uniform-pointwise-max；資料={\"limit\":[13,14],\"coefficients\":[14,-15],\"shift\":2,\"epsilon\":[1,23]}。請依 exact_ordered_tuple_declared_by_interface 欄序回答。","answer":{"kind":"expression","value":"([[0, 321], [1, 344]], 344, 是, finite_maximum_only_not_infinite_domain_implication)","explanation_zh":"Wave5第四層核對=([[0, 321], [1, 344]], 344, 是, finite_maximum_only_not_infinite_domain_implication)；依完整明示資料重算；同一N控制所有x且有限domain可取pointwise witnesses最大值；不可外推無限domain且finite prefix不足。"},"difficulty":{"band":"undergraduate_core","level":2,"skills":["一致收斂"]},"variant":{"family_id":"qf-mod35-uniform-pointwise-max","seed":202611042064,"parameters":{"limit":[13,14],"coefficients":[14,-15],"shift":2,"epsilon":[1,23],"domain":"Finite_domain_symbolic_uniform_tail","operation":"uniform-pointwise-max","semantic_template":"qf-mod35-uniform-pointwise-max/{\"coefficients\":[14,-15],\"epsilon\":[1,23],\"limit\":[13,14],\"shift\":2}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_or_symbolic_model","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"候選須主端重算；不構成人工審定、sampled rank-nullity、infinite-domain uniformity、term-zero convergence、estimator properties、noncoprime CRT shortcut、MST、mode implication、Lean或Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-14","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261014-advance-20261104-r02-uniform-convergence-of-functions-0065","batch_id":"batch-20261014-advance-20261104-r02-uniform-convergence-of-functions-foundations","language":"zh-Hant","source_mko_ids":["mko-uniform-convergence-of-functions"],"title_zh":"一致收斂","stem_zh":"共同有限domain的symbolic tail與同一N(epsilon)。操作=uniform-pointwise-max；資料={\"limit\":[14,15],\"coefficients\":[15,-16],\"shift\":2,\"epsilon\":[1,24]}。請依 exact_ordered_tuple_declared_by_interface 欄序回答。","answer":{"kind":"expression","value":"([[0, 359], [1, 383]], 383, 是, finite_maximum_only_not_infinite_domain_implication)","explanation_zh":"Wave5第四層核對=([[0, 359], [1, 383]], 383, 是, finite_maximum_only_not_infinite_domain_implication)；依完整明示資料重算；同一N控制所有x且有限domain可取pointwise witnesses最大值；不可外推無限domain且finite prefix不足。"},"difficulty":{"band":"undergraduate_core","level":2,"skills":["一致收斂"]},"variant":{"family_id":"qf-mod35-uniform-pointwise-max","seed":202611042065,"parameters":{"limit":[14,15],"coefficients":[15,-16],"shift":2,"epsilon":[1,24],"domain":"Finite_domain_symbolic_uniform_tail","operation":"uniform-pointwise-max","semantic_template":"qf-mod35-uniform-pointwise-max/{\"coefficients\":[15,-16],\"epsilon\":[1,24],\"limit\":[14,15],\"shift\":2}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_or_symbolic_model","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"候選須主端重算；不構成人工審定、sampled rank-nullity、infinite-domain uniformity、term-zero convergence、estimator properties、noncoprime CRT shortcut、MST、mode implication、Lean或Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-14","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261014-advance-20261104-r02-uniform-convergence-of-functions-0066","batch_id":"batch-20261014-advance-20261104-r02-uniform-convergence-of-functions-foundations","language":"zh-Hant","source_mko_ids":["mko-uniform-convergence-of-functions"],"title_zh":"一致收斂","stem_zh":"共同有限domain的symbolic tail與同一N(epsilon)。操作=uniform-pointwise-max；資料={\"limit\":[15,16],\"coefficients\":[16,-17],\"shift\":2,\"epsilon\":[1,25]}。請依 exact_ordered_tuple_declared_by_interface 欄序回答。","answer":{"kind":"expression","value":"([[0, 399], [1, 424]], 424, 是, finite_maximum_only_not_infinite_domain_implication)","explanation_zh":"Wave5第四層核對=([[0, 399], [1, 424]], 424, 是, finite_maximum_only_not_infinite_domain_implication)；依完整明示資料重算；同一N控制所有x且有限domain可取pointwise witnesses最大值；不可外推無限domain且finite prefix不足。"},"difficulty":{"band":"undergraduate_core","level":2,"skills":["一致收斂"]},"variant":{"family_id":"qf-mod35-uniform-pointwise-max","seed":202611042066,"parameters":{"limit":[15,16],"coefficients":[16,-17],"shift":2,"epsilon":[1,25],"domain":"Finite_domain_symbolic_uniform_tail","operation":"uniform-pointwise-max","semantic_template":"qf-mod35-uniform-pointwise-max/{\"coefficients\":[16,-17],\"epsilon\":[1,25],\"limit\":[15,16],\"shift\":2}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_or_symbolic_model","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"候選須主端重算；不構成人工審定、sampled rank-nullity、infinite-domain uniformity、term-zero convergence、estimator properties、noncoprime CRT shortcut、MST、mode implication、Lean或Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-14","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261014-advance-20261104-r02-uniform-convergence-of-functions-0067","batch_id":"batch-20261014-advance-20261104-r02-uniform-convergence-of-functions-foundations","language":"zh-Hant","source_mko_ids":["mko-uniform-convergence-of-functions"],"title_zh":"一致收斂","stem_zh":"共同有限domain的symbolic tail與同一N(epsilon)。操作=uniform-pointwise-max；資料={\"limit\":[16,17],\"coefficients\":[17,-18],\"shift\":2,\"epsilon\":[1,26]}。請依 exact_ordered_tuple_declared_by_interface 欄序回答。","answer":{"kind":"expression","value":"([[0, 441], [1, 467]], 467, 是, finite_maximum_only_not_infinite_domain_implication)","explanation_zh":"Wave5第四層核對=([[0, 441], [1, 467]], 467, 是, finite_maximum_only_not_infinite_domain_implication)；依完整明示資料重算；同一N控制所有x且有限domain可取pointwise witnesses最大值；不可外推無限domain且finite prefix不足。"},"difficulty":{"band":"undergraduate_core","level":2,"skills":["一致收斂"]},"variant":{"family_id":"qf-mod35-uniform-pointwise-max","seed":202611042067,"parameters":{"limit":[16,17],"coefficients":[17,-18],"shift":2,"epsilon":[1,26],"domain":"Finite_domain_symbolic_uniform_tail","operation":"uniform-pointwise-max","semantic_template":"qf-mod35-uniform-pointwise-max/{\"coefficients\":[17,-18],\"epsilon\":[1,26],\"limit\":[16,17],\"shift\":2}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_or_symbolic_model","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"候選須主端重算；不構成人工審定、sampled rank-nullity、infinite-domain uniformity、term-zero convergence、estimator properties、noncoprime CRT shortcut、MST、mode implication、Lean或Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-14","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261014-advance-20261104-r02-uniform-convergence-of-functions-0068","batch_id":"batch-20261014-advance-20261104-r02-uniform-convergence-of-functions-foundations","language":"zh-Hant","source_mko_ids":["mko-uniform-convergence-of-functions"],"title_zh":"一致收斂","stem_zh":"共同有限domain的symbolic tail與同一N(epsilon)。操作=uniform-pointwise-max；資料={\"limit\":[17,18],\"coefficients\":[18,-19],\"shift\":2,\"epsilon\":[1,27]}。請依 exact_ordered_tuple_declared_by_interface 欄序回答。","answer":{"kind":"expression","value":"([[0, 485], [1, 512]], 512, 是, finite_maximum_only_not_infinite_domain_implication)","explanation_zh":"Wave5第四層核對=([[0, 485], [1, 512]], 512, 是, finite_maximum_only_not_infinite_domain_implication)；依完整明示資料重算；同一N控制所有x且有限domain可取pointwise witnesses最大值；不可外推無限domain且finite prefix不足。"},"difficulty":{"band":"undergraduate_core","level":3,"skills":["一致收斂"]},"variant":{"family_id":"qf-mod35-uniform-pointwise-max","seed":202611042068,"parameters":{"limit":[17,18],"coefficients":[18,-19],"shift":2,"epsilon":[1,27],"domain":"Finite_domain_symbolic_uniform_tail","operation":"uniform-pointwise-max","semantic_template":"qf-mod35-uniform-pointwise-max/{\"coefficients\":[18,-19],\"epsilon\":[1,27],\"limit\":[17,18],\"shift\":2}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_or_symbolic_model","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"候選須主端重算；不構成人工審定、sampled rank-nullity、infinite-domain uniformity、term-zero convergence、estimator properties、noncoprime CRT shortcut、MST、mode implication、Lean或Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-14","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261014-advance-20261104-r02-uniform-convergence-of-functions-0069","batch_id":"batch-20261014-advance-20261104-r02-uniform-convergence-of-functions-foundations","language":"zh-Hant","source_mko_ids":["mko-uniform-convergence-of-functions"],"title_zh":"一致收斂","stem_zh":"共同有限domain的symbolic tail與同一N(epsilon)。操作=uniform-pointwise-max；資料={\"limit\":[18,19],\"coefficients\":[19,-20],\"shift\":2,\"epsilon\":[1,28]}。請依 exact_ordered_tuple_declared_by_interface 欄序回答。","answer":{"kind":"expression","value":"([[0, 531], [1, 559]], 559, 是, finite_maximum_only_not_infinite_domain_implication)","explanation_zh":"Wave5第四層核對=([[0, 531], [1, 559]], 559, 是, finite_maximum_only_not_infinite_domain_implication)；依完整明示資料重算；同一N控制所有x且有限domain可取pointwise witnesses最大值；不可外推無限domain且finite prefix不足。"},"difficulty":{"band":"undergraduate_core","level":3,"skills":["一致收斂"]},"variant":{"family_id":"qf-mod35-uniform-pointwise-max","seed":202611042069,"parameters":{"limit":[18,19],"coefficients":[19,-20],"shift":2,"epsilon":[1,28],"domain":"Finite_domain_symbolic_uniform_tail","operation":"uniform-pointwise-max","semantic_template":"qf-mod35-uniform-pointwise-max/{\"coefficients\":[19,-20],\"epsilon\":[1,28],\"limit\":[18,19],\"shift\":2}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_or_symbolic_model","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"候選須主端重算；不構成人工審定、sampled rank-nullity、infinite-domain uniformity、term-zero convergence、estimator properties、noncoprime CRT shortcut、MST、mode implication、Lean或Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-14","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261014-advance-20261104-r02-uniform-convergence-of-functions-0070","batch_id":"batch-20261014-advance-20261104-r02-uniform-convergence-of-functions-foundations","language":"zh-Hant","source_mko_ids":["mko-uniform-convergence-of-functions"],"title_zh":"一致收斂","stem_zh":"共同有限domain的symbolic tail與同一N(epsilon)。操作=uniform-pointwise-max；資料={\"limit\":[19,20],\"coefficients\":[20,-21],\"shift\":2,\"epsilon\":[1,29]}。請依 exact_ordered_tuple_declared_by_interface 欄序回答。","answer":{"kind":"expression","value":"([[0, 579], [1, 608]], 608, 是, finite_maximum_only_not_infinite_domain_implication)","explanation_zh":"Wave5第四層核對=([[0, 579], [1, 608]], 608, 是, finite_maximum_only_not_infinite_domain_implication)；依完整明示資料重算；同一N控制所有x且有限domain可取pointwise witnesses最大值；不可外推無限domain且finite prefix不足。"},"difficulty":{"band":"undergraduate_core","level":3,"skills":["一致收斂"]},"variant":{"family_id":"qf-mod35-uniform-pointwise-max","seed":202611042070,"parameters":{"limit":[19,20],"coefficients":[20,-21],"shift":2,"epsilon":[1,29],"domain":"Finite_domain_symbolic_uniform_tail","operation":"uniform-pointwise-max","semantic_template":"qf-mod35-uniform-pointwise-max/{\"coefficients\":[20,-21],\"epsilon\":[1,29],\"limit\":[19,20],\"shift\":2}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_or_symbolic_model","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"候選須主端重算；不構成人工審定、sampled rank-nullity、infinite-domain uniformity、term-zero convergence、estimator properties、noncoprime CRT shortcut、MST、mode implication、Lean或Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-14","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261014-advance-20261104-r02-uniform-convergence-of-functions-0071","batch_id":"batch-20261014-advance-20261104-r02-uniform-convergence-of-functions-foundations","language":"zh-Hant","source_mko_ids":["mko-uniform-convergence-of-functions"],"title_zh":"一致收斂","stem_zh":"共同有限domain的symbolic tail與同一N(epsilon)。操作=uniform-pointwise-max；資料={\"limit\":[20,21],\"coefficients\":[21,-22],\"shift\":2,\"epsilon\":[1,30]}。請依 exact_ordered_tuple_declared_by_interface 欄序回答。","answer":{"kind":"expression","value":"([[0, 629], [1, 659]], 659, 是, finite_maximum_only_not_infinite_domain_implication)","explanation_zh":"Wave5第四層核對=([[0, 629], [1, 659]], 659, 是, finite_maximum_only_not_infinite_domain_implication)；依完整明示資料重算；同一N控制所有x且有限domain可取pointwise witnesses最大值；不可外推無限domain且finite prefix不足。"},"difficulty":{"band":"undergraduate_core","level":3,"skills":["一致收斂"]},"variant":{"family_id":"qf-mod35-uniform-pointwise-max","seed":202611042071,"parameters":{"limit":[20,21],"coefficients":[21,-22],"shift":2,"epsilon":[1,30],"domain":"Finite_domain_symbolic_uniform_tail","operation":"uniform-pointwise-max","semantic_template":"qf-mod35-uniform-pointwise-max/{\"coefficients\":[21,-22],\"epsilon\":[1,30],\"limit\":[20,21],\"shift\":2}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_or_symbolic_model","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"候選須主端重算；不構成人工審定、sampled rank-nullity、infinite-domain uniformity、term-zero convergence、estimator properties、noncoprime CRT shortcut、MST、mode implication、Lean或Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-14","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261014-advance-20261104-r02-uniform-convergence-of-functions-0072","batch_id":"batch-20261014-advance-20261104-r02-uniform-convergence-of-functions-foundations","language":"zh-Hant","source_mko_ids":["mko-uniform-convergence-of-functions"],"title_zh":"一致收斂","stem_zh":"共同有限domain的symbolic tail與同一N(epsilon)。操作=uniform-pointwise-max；資料={\"limit\":[21,22],\"coefficients\":[22,-23],\"shift\":2,\"epsilon\":[1,31]}。請依 exact_ordered_tuple_declared_by_interface 欄序回答。","answer":{"kind":"expression","value":"([[0, 681], [1, 712]], 712, 是, finite_maximum_only_not_infinite_domain_implication)","explanation_zh":"Wave5第四層核對=([[0, 681], [1, 712]], 712, 是, finite_maximum_only_not_infinite_domain_implication)；依完整明示資料重算；同一N控制所有x且有限domain可取pointwise witnesses最大值；不可外推無限domain且finite prefix不足。"},"difficulty":{"band":"undergraduate_core","level":3,"skills":["一致收斂"]},"variant":{"family_id":"qf-mod35-uniform-pointwise-max","seed":202611042072,"parameters":{"limit":[21,22],"coefficients":[22,-23],"shift":2,"epsilon":[1,31],"domain":"Finite_domain_symbolic_uniform_tail","operation":"uniform-pointwise-max","semantic_template":"qf-mod35-uniform-pointwise-max/{\"coefficients\":[22,-23],\"epsilon\":[1,31],\"limit\":[21,22],\"shift\":2}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_or_symbolic_model","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"候選須主端重算；不構成人工審定、sampled rank-nullity、infinite-domain uniformity、term-zero convergence、estimator properties、noncoprime CRT shortcut、MST、mode implication、Lean或Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-14","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261014-advance-20261104-r02-uniform-convergence-of-functions-0073","batch_id":"batch-20261014-advance-20261104-r02-uniform-convergence-of-functions-foundations","language":"zh-Hant","source_mko_ids":["mko-uniform-convergence-of-functions"],"title_zh":"一致收斂","stem_zh":"共同有限domain的symbolic tail與同一N(epsilon)。操作=uniform-pointwise-max；資料={\"limit\":[22,23],\"coefficients\":[23,-24],\"shift\":2,\"epsilon\":[1,32]}。請依 exact_ordered_tuple_declared_by_interface 欄序回答。","answer":{"kind":"expression","value":"([[0, 735], [1, 767]], 767, 是, finite_maximum_only_not_infinite_domain_implication)","explanation_zh":"Wave5第四層核對=([[0, 735], [1, 767]], 767, 是, finite_maximum_only_not_infinite_domain_implication)；依完整明示資料重算；同一N控制所有x且有限domain可取pointwise witnesses最大值；不可外推無限domain且finite prefix不足。"},"difficulty":{"band":"undergraduate_core","level":3,"skills":["一致收斂"]},"variant":{"family_id":"qf-mod35-uniform-pointwise-max","seed":202611042073,"parameters":{"limit":[22,23],"coefficients":[23,-24],"shift":2,"epsilon":[1,32],"domain":"Finite_domain_symbolic_uniform_tail","operation":"uniform-pointwise-max","semantic_template":"qf-mod35-uniform-pointwise-max/{\"coefficients\":[23,-24],\"epsilon\":[1,32],\"limit\":[22,23],\"shift\":2}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_or_symbolic_model","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"候選須主端重算；不構成人工審定、sampled rank-nullity、infinite-domain uniformity、term-zero convergence、estimator properties、noncoprime CRT shortcut、MST、mode implication、Lean或Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-14","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261014-advance-20261104-r02-uniform-convergence-of-functions-0074","batch_id":"batch-20261014-advance-20261104-r02-uniform-convergence-of-functions-foundations","language":"zh-Hant","source_mko_ids":["mko-uniform-convergence-of-functions"],"title_zh":"一致收斂","stem_zh":"共同有限domain的symbolic tail與同一N(epsilon)。操作=uniform-pointwise-max；資料={\"limit\":[23,24],\"coefficients\":[24,-25],\"shift\":2,\"epsilon\":[1,33]}。請依 exact_ordered_tuple_declared_by_interface 欄序回答。","answer":{"kind":"expression","value":"([[0, 791], [1, 824]], 824, 是, finite_maximum_only_not_infinite_domain_implication)","explanation_zh":"Wave5第四層核對=([[0, 791], [1, 824]], 824, 是, finite_maximum_only_not_infinite_domain_implication)；依完整明示資料重算；同一N控制所有x且有限domain可取pointwise witnesses最大值；不可外推無限domain且finite prefix不足。"},"difficulty":{"band":"undergraduate_core","level":3,"skills":["一致收斂"]},"variant":{"family_id":"qf-mod35-uniform-pointwise-max","seed":202611042074,"parameters":{"limit":[23,24],"coefficients":[24,-25],"shift":2,"epsilon":[1,33],"domain":"Finite_domain_symbolic_uniform_tail","operation":"uniform-pointwise-max","semantic_template":"qf-mod35-uniform-pointwise-max/{\"coefficients\":[24,-25],\"epsilon\":[1,33],\"limit\":[23,24],\"shift\":2}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_or_symbolic_model","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"候選須主端重算；不構成人工審定、sampled rank-nullity、infinite-domain uniformity、term-zero convergence、estimator properties、noncoprime CRT shortcut、MST、mode implication、Lean或Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-14","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261014-advance-20261104-r02-uniform-convergence-of-functions-0075","batch_id":"batch-20261014-advance-20261104-r02-uniform-convergence-of-functions-foundations","language":"zh-Hant","source_mko_ids":["mko-uniform-convergence-of-functions"],"title_zh":"一致收斂","stem_zh":"共同有限domain的symbolic tail與同一N(epsilon)。操作=uniform-pointwise-max；資料={\"limit\":[24,25],\"coefficients\":[25,-26],\"shift\":2,\"epsilon\":[1,34]}。請依 exact_ordered_tuple_declared_by_interface 欄序回答。","answer":{"kind":"expression","value":"([[0, 849], [1, 883]], 883, 是, finite_maximum_only_not_infinite_domain_implication)","explanation_zh":"Wave5第四層核對=([[0, 849], [1, 883]], 883, 是, finite_maximum_only_not_infinite_domain_implication)；依完整明示資料重算；同一N控制所有x且有限domain可取pointwise witnesses最大值；不可外推無限domain且finite prefix不足。"},"difficulty":{"band":"undergraduate_core","level":3,"skills":["一致收斂"]},"variant":{"family_id":"qf-mod35-uniform-pointwise-max","seed":202611042075,"parameters":{"limit":[24,25],"coefficients":[25,-26],"shift":2,"epsilon":[1,34],"domain":"Finite_domain_symbolic_uniform_tail","operation":"uniform-pointwise-max","semantic_template":"qf-mod35-uniform-pointwise-max/{\"coefficients\":[25,-26],\"epsilon\":[1,34],\"limit\":[24,25],\"shift\":2}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_or_symbolic_model","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"候選須主端重算；不構成人工審定、sampled rank-nullity、infinite-domain uniformity、term-zero convergence、estimator properties、noncoprime CRT shortcut、MST、mode implication、Lean或Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-14","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261014-advance-20261104-r02-uniform-convergence-of-functions-0076","batch_id":"batch-20261014-advance-20261104-r02-uniform-convergence-of-functions-foundations","language":"zh-Hant","source_mko_ids":["mko-uniform-convergence-of-functions"],"title_zh":"一致收斂","stem_zh":"共同有限domain的symbolic tail與同一N(epsilon)。操作=uniform-finite-prefix-boundary；資料={\"limit\":[0,1],\"coefficients\":[1,-2],\"shift\":2,\"prefix_length\":1}。請依 exact_ordered_tuple_declared_by_interface 欄序回答。","answer":{"kind":"expression","value":"(1, 否, finite_prefix_not_uniform_convergence_certificate)","explanation_zh":"Wave5第四層核對=(1, 否, finite_prefix_not_uniform_convergence_certificate)；依完整明示資料重算；同一N控制所有x且有限domain可取pointwise witnesses最大值；不可外推無限domain且finite prefix不足。"},"difficulty":{"band":"undergraduate_core","level":1,"skills":["一致收斂"]},"variant":{"family_id":"qf-mod35-uniform-finite-prefix-boundary","seed":202611042076,"parameters":{"limit":[0,1],"coefficients":[1,-2],"shift":2,"prefix_length":1,"domain":"Finite_domain_symbolic_uniform_tail","operation":"uniform-finite-prefix-boundary","semantic_template":"qf-mod35-uniform-finite-prefix-boundary/{\"coefficients\":[1,-2],\"limit\":[0,1],\"prefix_length\":1,\"shift\":2}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_or_symbolic_model","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"候選須主端重算；不構成人工審定、sampled rank-nullity、infinite-domain uniformity、term-zero convergence、estimator properties、noncoprime CRT shortcut、MST、mode implication、Lean或Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-14","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261014-advance-20261104-r02-uniform-convergence-of-functions-0077","batch_id":"batch-20261014-advance-20261104-r02-uniform-convergence-of-functions-foundations","language":"zh-Hant","source_mko_ids":["mko-uniform-convergence-of-functions"],"title_zh":"一致收斂","stem_zh":"共同有限domain的symbolic tail與同一N(epsilon)。操作=uniform-finite-prefix-boundary；資料={\"limit\":[1,2],\"coefficients\":[2,-3],\"shift\":2,\"prefix_length\":2}。請依 exact_ordered_tuple_declared_by_interface 欄序回答。","answer":{"kind":"expression","value":"(2, 否, finite_prefix_not_uniform_convergence_certificate)","explanation_zh":"Wave5第四層核對=(2, 否, finite_prefix_not_uniform_convergence_certificate)；依完整明示資料重算；同一N控制所有x且有限domain可取pointwise witnesses最大值；不可外推無限domain且finite prefix不足。"},"difficulty":{"band":"undergraduate_core","level":1,"skills":["一致收斂"]},"variant":{"family_id":"qf-mod35-uniform-finite-prefix-boundary","seed":202611042077,"parameters":{"limit":[1,2],"coefficients":[2,-3],"shift":2,"prefix_length":2,"domain":"Finite_domain_symbolic_uniform_tail","operation":"uniform-finite-prefix-boundary","semantic_template":"qf-mod35-uniform-finite-prefix-boundary/{\"coefficients\":[2,-3],\"limit\":[1,2],\"prefix_length\":2,\"shift\":2}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_or_symbolic_model","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"候選須主端重算；不構成人工審定、sampled rank-nullity、infinite-domain uniformity、term-zero convergence、estimator properties、noncoprime CRT shortcut、MST、mode implication、Lean或Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-14","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261014-advance-20261104-r02-uniform-convergence-of-functions-0078","batch_id":"batch-20261014-advance-20261104-r02-uniform-convergence-of-functions-foundations","language":"zh-Hant","source_mko_ids":["mko-uniform-convergence-of-functions"],"title_zh":"一致收斂","stem_zh":"共同有限domain的symbolic tail與同一N(epsilon)。操作=uniform-finite-prefix-boundary；資料={\"limit\":[2,3],\"coefficients\":[3,-4],\"shift\":2,\"prefix_length\":3}。請依 exact_ordered_tuple_declared_by_interface 欄序回答。","answer":{"kind":"expression","value":"(3, 否, finite_prefix_not_uniform_convergence_certificate)","explanation_zh":"Wave5第四層核對=(3, 否, finite_prefix_not_uniform_convergence_certificate)；依完整明示資料重算；同一N控制所有x且有限domain可取pointwise witnesses最大值；不可外推無限domain且finite prefix不足。"},"difficulty":{"band":"undergraduate_core","level":1,"skills":["一致收斂"]},"variant":{"family_id":"qf-mod35-uniform-finite-prefix-boundary","seed":202611042078,"parameters":{"limit":[2,3],"coefficients":[3,-4],"shift":2,"prefix_length":3,"domain":"Finite_domain_symbolic_uniform_tail","operation":"uniform-finite-prefix-boundary","semantic_template":"qf-mod35-uniform-finite-prefix-boundary/{\"coefficients\":[3,-4],\"limit\":[2,3],\"prefix_length\":3,\"shift\":2}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_or_symbolic_model","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"候選須主端重算；不構成人工審定、sampled rank-nullity、infinite-domain uniformity、term-zero convergence、estimator properties、noncoprime CRT shortcut、MST、mode implication、Lean或Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-14","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261014-advance-20261104-r02-uniform-convergence-of-functions-0079","batch_id":"batch-20261014-advance-20261104-r02-uniform-convergence-of-functions-foundations","language":"zh-Hant","source_mko_ids":["mko-uniform-convergence-of-functions"],"title_zh":"一致收斂","stem_zh":"共同有限domain的symbolic tail與同一N(epsilon)。操作=uniform-finite-prefix-boundary；資料={\"limit\":[3,4],\"coefficients\":[4,-5],\"shift\":2,\"prefix_length\":4}。請依 exact_ordered_tuple_declared_by_interface 欄序回答。","answer":{"kind":"expression","value":"(4, 否, finite_prefix_not_uniform_convergence_certificate)","explanation_zh":"Wave5第四層核對=(4, 否, finite_prefix_not_uniform_convergence_certificate)；依完整明示資料重算；同一N控制所有x且有限domain可取pointwise witnesses最大值；不可外推無限domain且finite prefix不足。"},"difficulty":{"band":"undergraduate_core","level":1,"skills":["一致收斂"]},"variant":{"family_id":"qf-mod35-uniform-finite-prefix-boundary","seed":202611042079,"parameters":{"limit":[3,4],"coefficients":[4,-5],"shift":2,"prefix_length":4,"domain":"Finite_domain_symbolic_uniform_tail","operation":"uniform-finite-prefix-boundary","semantic_template":"qf-mod35-uniform-finite-prefix-boundary/{\"coefficients\":[4,-5],\"limit\":[3,4],\"prefix_length\":4,\"shift\":2}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_or_symbolic_model","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"候選須主端重算；不構成人工審定、sampled rank-nullity、infinite-domain uniformity、term-zero convergence、estimator properties、noncoprime CRT shortcut、MST、mode implication、Lean或Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-14","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261014-advance-20261104-r02-uniform-convergence-of-functions-0080","batch_id":"batch-20261014-advance-20261104-r02-uniform-convergence-of-functions-foundations","language":"zh-Hant","source_mko_ids":["mko-uniform-convergence-of-functions"],"title_zh":"一致收斂","stem_zh":"共同有限domain的symbolic tail與同一N(epsilon)。操作=uniform-finite-prefix-boundary；資料={\"limit\":[4,5],\"coefficients\":[5,-6],\"shift\":2,\"prefix_length\":5}。請依 exact_ordered_tuple_declared_by_interface 欄序回答。","answer":{"kind":"expression","value":"(5, 否, finite_prefix_not_uniform_convergence_certificate)","explanation_zh":"Wave5第四層核對=(5, 否, finite_prefix_not_uniform_convergence_certificate)；依完整明示資料重算；同一N控制所有x且有限domain可取pointwise witnesses最大值；不可外推無限domain且finite prefix不足。"},"difficulty":{"band":"undergraduate_core","level":1,"skills":["一致收斂"]},"variant":{"family_id":"qf-mod35-uniform-finite-prefix-boundary","seed":202611042080,"parameters":{"limit":[4,5],"coefficients":[5,-6],"shift":2,"prefix_length":5,"domain":"Finite_domain_symbolic_uniform_tail","operation":"uniform-finite-prefix-boundary","semantic_template":"qf-mod35-uniform-finite-prefix-boundary/{\"coefficients\":[5,-6],\"limit\":[4,5],\"prefix_length\":5,\"shift\":2}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_or_symbolic_model","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"候選須主端重算；不構成人工審定、sampled rank-nullity、infinite-domain uniformity、term-zero convergence、estimator properties、noncoprime CRT shortcut、MST、mode implication、Lean或Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-14","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261014-advance-20261104-r02-uniform-convergence-of-functions-0081","batch_id":"batch-20261014-advance-20261104-r02-uniform-convergence-of-functions-foundations","language":"zh-Hant","source_mko_ids":["mko-uniform-convergence-of-functions"],"title_zh":"一致收斂","stem_zh":"共同有限domain的symbolic tail與同一N(epsilon)。操作=uniform-finite-prefix-boundary；資料={\"limit\":[5,6],\"coefficients\":[6,-7],\"shift\":2,\"prefix_length\":6}。請依 exact_ordered_tuple_declared_by_interface 欄序回答。","answer":{"kind":"expression","value":"(6, 否, finite_prefix_not_uniform_convergence_certificate)","explanation_zh":"Wave5第四層核對=(6, 否, finite_prefix_not_uniform_convergence_certificate)；依完整明示資料重算；同一N控制所有x且有限domain可取pointwise witnesses最大值；不可外推無限domain且finite prefix不足。"},"difficulty":{"band":"undergraduate_core","level":1,"skills":["一致收斂"]},"variant":{"family_id":"qf-mod35-uniform-finite-prefix-boundary","seed":202611042081,"parameters":{"limit":[5,6],"coefficients":[6,-7],"shift":2,"prefix_length":6,"domain":"Finite_domain_symbolic_uniform_tail","operation":"uniform-finite-prefix-boundary","semantic_template":"qf-mod35-uniform-finite-prefix-boundary/{\"coefficients\":[6,-7],\"limit\":[5,6],\"prefix_length\":6,\"shift\":2}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_or_symbolic_model","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"候選須主端重算；不構成人工審定、sampled rank-nullity、infinite-domain uniformity、term-zero convergence、estimator properties、noncoprime CRT shortcut、MST、mode implication、Lean或Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-14","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261014-advance-20261104-r02-uniform-convergence-of-functions-0082","batch_id":"batch-20261014-advance-20261104-r02-uniform-convergence-of-functions-foundations","language":"zh-Hant","source_mko_ids":["mko-uniform-convergence-of-functions"],"title_zh":"一致收斂","stem_zh":"共同有限domain的symbolic tail與同一N(epsilon)。操作=uniform-finite-prefix-boundary；資料={\"limit\":[6,7],\"coefficients\":[7,-8],\"shift\":2,\"prefix_length\":7}。請依 exact_ordered_tuple_declared_by_interface 欄序回答。","answer":{"kind":"expression","value":"(7, 否, finite_prefix_not_uniform_convergence_certificate)","explanation_zh":"Wave5第四層核對=(7, 否, finite_prefix_not_uniform_convergence_certificate)；依完整明示資料重算；同一N控制所有x且有限domain可取pointwise witnesses最大值；不可外推無限domain且finite prefix不足。"},"difficulty":{"band":"undergraduate_core","level":1,"skills":["一致收斂"]},"variant":{"family_id":"qf-mod35-uniform-finite-prefix-boundary","seed":202611042082,"parameters":{"limit":[6,7],"coefficients":[7,-8],"shift":2,"prefix_length":7,"domain":"Finite_domain_symbolic_uniform_tail","operation":"uniform-finite-prefix-boundary","semantic_template":"qf-mod35-uniform-finite-prefix-boundary/{\"coefficients\":[7,-8],\"limit\":[6,7],\"prefix_length\":7,\"shift\":2}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_or_symbolic_model","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"候選須主端重算；不構成人工審定、sampled rank-nullity、infinite-domain uniformity、term-zero convergence、estimator properties、noncoprime CRT shortcut、MST、mode implication、Lean或Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-14","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261014-advance-20261104-r02-uniform-convergence-of-functions-0083","batch_id":"batch-20261014-advance-20261104-r02-uniform-convergence-of-functions-foundations","language":"zh-Hant","source_mko_ids":["mko-uniform-convergence-of-functions"],"title_zh":"一致收斂","stem_zh":"共同有限domain的symbolic tail與同一N(epsilon)。操作=uniform-finite-prefix-boundary；資料={\"limit\":[7,8],\"coefficients\":[8,-9],\"shift\":2,\"prefix_length\":8}。請依 exact_ordered_tuple_declared_by_interface 欄序回答。","answer":{"kind":"expression","value":"(8, 否, finite_prefix_not_uniform_convergence_certificate)","explanation_zh":"Wave5第四層核對=(8, 否, finite_prefix_not_uniform_convergence_certificate)；依完整明示資料重算；同一N控制所有x且有限domain可取pointwise witnesses最大值；不可外推無限domain且finite prefix不足。"},"difficulty":{"band":"undergraduate_core","level":1,"skills":["一致收斂"]},"variant":{"family_id":"qf-mod35-uniform-finite-prefix-boundary","seed":202611042083,"parameters":{"limit":[7,8],"coefficients":[8,-9],"shift":2,"prefix_length":8,"domain":"Finite_domain_symbolic_uniform_tail","operation":"uniform-finite-prefix-boundary","semantic_template":"qf-mod35-uniform-finite-prefix-boundary/{\"coefficients\":[8,-9],\"limit\":[7,8],\"prefix_length\":8,\"shift\":2}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_or_symbolic_model","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"候選須主端重算；不構成人工審定、sampled rank-nullity、infinite-domain uniformity、term-zero convergence、estimator properties、noncoprime CRT shortcut、MST、mode implication、Lean或Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-14","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261014-advance-20261104-r02-uniform-convergence-of-functions-0084","batch_id":"batch-20261014-advance-20261104-r02-uniform-convergence-of-functions-foundations","language":"zh-Hant","source_mko_ids":["mko-uniform-convergence-of-functions"],"title_zh":"一致收斂","stem_zh":"共同有限domain的symbolic tail與同一N(epsilon)。操作=uniform-finite-prefix-boundary；資料={\"limit\":[8,9],\"coefficients\":[9,-10],\"shift\":2,\"prefix_length\":9}。請依 exact_ordered_tuple_declared_by_interface 欄序回答。","answer":{"kind":"expression","value":"(9, 否, finite_prefix_not_uniform_convergence_certificate)","explanation_zh":"Wave5第四層核對=(9, 否, finite_prefix_not_uniform_convergence_certificate)；依完整明示資料重算；同一N控制所有x且有限domain可取pointwise witnesses最大值；不可外推無限domain且finite prefix不足。"},"difficulty":{"band":"undergraduate_core","level":2,"skills":["一致收斂"]},"variant":{"family_id":"qf-mod35-uniform-finite-prefix-boundary","seed":202611042084,"parameters":{"limit":[8,9],"coefficients":[9,-10],"shift":2,"prefix_length":9,"domain":"Finite_domain_symbolic_uniform_tail","operation":"uniform-finite-prefix-boundary","semantic_template":"qf-mod35-uniform-finite-prefix-boundary/{\"coefficients\":[9,-10],\"limit\":[8,9],\"prefix_length\":9,\"shift\":2}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_or_symbolic_model","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"候選須主端重算；不構成人工審定、sampled rank-nullity、infinite-domain uniformity、term-zero convergence、estimator properties、noncoprime CRT shortcut、MST、mode implication、Lean或Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-14","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261014-advance-20261104-r02-uniform-convergence-of-functions-0085","batch_id":"batch-20261014-advance-20261104-r02-uniform-convergence-of-functions-foundations","language":"zh-Hant","source_mko_ids":["mko-uniform-convergence-of-functions"],"title_zh":"一致收斂","stem_zh":"共同有限domain的symbolic tail與同一N(epsilon)。操作=uniform-finite-prefix-boundary；資料={\"limit\":[9,10],\"coefficients\":[10,-11],\"shift\":2,\"prefix_length\":10}。請依 exact_ordered_tuple_declared_by_interface 欄序回答。","answer":{"kind":"expression","value":"(10, 否, finite_prefix_not_uniform_convergence_certificate)","explanation_zh":"Wave5第四層核對=(10, 否, finite_prefix_not_uniform_convergence_certificate)；依完整明示資料重算；同一N控制所有x且有限domain可取pointwise witnesses最大值；不可外推無限domain且finite prefix不足。"},"difficulty":{"band":"undergraduate_core","level":2,"skills":["一致收斂"]},"variant":{"family_id":"qf-mod35-uniform-finite-prefix-boundary","seed":202611042085,"parameters":{"limit":[9,10],"coefficients":[10,-11],"shift":2,"prefix_length":10,"domain":"Finite_domain_symbolic_uniform_tail","operation":"uniform-finite-prefix-boundary","semantic_template":"qf-mod35-uniform-finite-prefix-boundary/{\"coefficients\":[10,-11],\"limit\":[9,10],\"prefix_length\":10,\"shift\":2}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_or_symbolic_model","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"候選須主端重算；不構成人工審定、sampled rank-nullity、infinite-domain uniformity、term-zero convergence、estimator properties、noncoprime CRT shortcut、MST、mode implication、Lean或Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-14","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261014-advance-20261104-r02-uniform-convergence-of-functions-0086","batch_id":"batch-20261014-advance-20261104-r02-uniform-convergence-of-functions-foundations","language":"zh-Hant","source_mko_ids":["mko-uniform-convergence-of-functions"],"title_zh":"一致收斂","stem_zh":"共同有限domain的symbolic tail與同一N(epsilon)。操作=uniform-finite-prefix-boundary；資料={\"limit\":[10,11],\"coefficients\":[11,-12],\"shift\":2,\"prefix_length\":11}。請依 exact_ordered_tuple_declared_by_interface 欄序回答。","answer":{"kind":"expression","value":"(11, 否, finite_prefix_not_uniform_convergence_certificate)","explanation_zh":"Wave5第四層核對=(11, 否, finite_prefix_not_uniform_convergence_certificate)；依完整明示資料重算；同一N控制所有x且有限domain可取pointwise witnesses最大值；不可外推無限domain且finite prefix不足。"},"difficulty":{"band":"undergraduate_core","level":2,"skills":["一致收斂"]},"variant":{"family_id":"qf-mod35-uniform-finite-prefix-boundary","seed":202611042086,"parameters":{"limit":[10,11],"coefficients":[11,-12],"shift":2,"prefix_length":11,"domain":"Finite_domain_symbolic_uniform_tail","operation":"uniform-finite-prefix-boundary","semantic_template":"qf-mod35-uniform-finite-prefix-boundary/{\"coefficients\":[11,-12],\"limit\":[10,11],\"prefix_length\":11,\"shift\":2}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_or_symbolic_model","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"候選須主端重算；不構成人工審定、sampled rank-nullity、infinite-domain uniformity、term-zero convergence、estimator properties、noncoprime CRT shortcut、MST、mode implication、Lean或Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-14","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261014-advance-20261104-r02-uniform-convergence-of-functions-0087","batch_id":"batch-20261014-advance-20261104-r02-uniform-convergence-of-functions-foundations","language":"zh-Hant","source_mko_ids":["mko-uniform-convergence-of-functions"],"title_zh":"一致收斂","stem_zh":"共同有限domain的symbolic tail與同一N(epsilon)。操作=uniform-finite-prefix-boundary；資料={\"limit\":[11,12],\"coefficients\":[12,-13],\"shift\":2,\"prefix_length\":12}。請依 exact_ordered_tuple_declared_by_interface 欄序回答。","answer":{"kind":"expression","value":"(12, 否, finite_prefix_not_uniform_convergence_certificate)","explanation_zh":"Wave5第四層核對=(12, 否, finite_prefix_not_uniform_convergence_certificate)；依完整明示資料重算；同一N控制所有x且有限domain可取pointwise witnesses最大值；不可外推無限domain且finite prefix不足。"},"difficulty":{"band":"undergraduate_core","level":2,"skills":["一致收斂"]},"variant":{"family_id":"qf-mod35-uniform-finite-prefix-boundary","seed":202611042087,"parameters":{"limit":[11,12],"coefficients":[12,-13],"shift":2,"prefix_length":12,"domain":"Finite_domain_symbolic_uniform_tail","operation":"uniform-finite-prefix-boundary","semantic_template":"qf-mod35-uniform-finite-prefix-boundary/{\"coefficients\":[12,-13],\"limit\":[11,12],\"prefix_length\":12,\"shift\":2}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_or_symbolic_model","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"候選須主端重算；不構成人工審定、sampled rank-nullity、infinite-domain uniformity、term-zero convergence、estimator properties、noncoprime CRT shortcut、MST、mode implication、Lean或Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-14","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261014-advance-20261104-r02-uniform-convergence-of-functions-0088","batch_id":"batch-20261014-advance-20261104-r02-uniform-convergence-of-functions-foundations","language":"zh-Hant","source_mko_ids":["mko-uniform-convergence-of-functions"],"title_zh":"一致收斂","stem_zh":"共同有限domain的symbolic tail與同一N(epsilon)。操作=uniform-finite-prefix-boundary；資料={\"limit\":[12,13],\"coefficients\":[13,-14],\"shift\":2,\"prefix_length\":13}。請依 exact_ordered_tuple_declared_by_interface 欄序回答。","answer":{"kind":"expression","value":"(13, 否, finite_prefix_not_uniform_convergence_certificate)","explanation_zh":"Wave5第四層核對=(13, 否, finite_prefix_not_uniform_convergence_certificate)；依完整明示資料重算；同一N控制所有x且有限domain可取pointwise witnesses最大值；不可外推無限domain且finite prefix不足。"},"difficulty":{"band":"undergraduate_core","level":2,"skills":["一致收斂"]},"variant":{"family_id":"qf-mod35-uniform-finite-prefix-boundary","seed":202611042088,"parameters":{"limit":[12,13],"coefficients":[13,-14],"shift":2,"prefix_length":13,"domain":"Finite_domain_symbolic_uniform_tail","operation":"uniform-finite-prefix-boundary","semantic_template":"qf-mod35-uniform-finite-prefix-boundary/{\"coefficients\":[13,-14],\"limit\":[12,13],\"prefix_length\":13,\"shift\":2}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_or_symbolic_model","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"候選須主端重算；不構成人工審定、sampled rank-nullity、infinite-domain uniformity、term-zero convergence、estimator properties、noncoprime CRT shortcut、MST、mode implication、Lean或Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-14","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261014-advance-20261104-r02-uniform-convergence-of-functions-0089","batch_id":"batch-20261014-advance-20261104-r02-uniform-convergence-of-functions-foundations","language":"zh-Hant","source_mko_ids":["mko-uniform-convergence-of-functions"],"title_zh":"一致收斂","stem_zh":"共同有限domain的symbolic tail與同一N(epsilon)。操作=uniform-finite-prefix-boundary；資料={\"limit\":[13,14],\"coefficients\":[14,-15],\"shift\":2,\"prefix_length\":14}。請依 exact_ordered_tuple_declared_by_interface 欄序回答。","answer":{"kind":"expression","value":"(14, 否, finite_prefix_not_uniform_convergence_certificate)","explanation_zh":"Wave5第四層核對=(14, 否, finite_prefix_not_uniform_convergence_certificate)；依完整明示資料重算；同一N控制所有x且有限domain可取pointwise witnesses最大值；不可外推無限domain且finite prefix不足。"},"difficulty":{"band":"undergraduate_core","level":2,"skills":["一致收斂"]},"variant":{"family_id":"qf-mod35-uniform-finite-prefix-boundary","seed":202611042089,"parameters":{"limit":[13,14],"coefficients":[14,-15],"shift":2,"prefix_length":14,"domain":"Finite_domain_symbolic_uniform_tail","operation":"uniform-finite-prefix-boundary","semantic_template":"qf-mod35-uniform-finite-prefix-boundary/{\"coefficients\":[14,-15],\"limit\":[13,14],\"prefix_length\":14,\"shift\":2}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_or_symbolic_model","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"候選須主端重算；不構成人工審定、sampled rank-nullity、infinite-domain uniformity、term-zero convergence、estimator properties、noncoprime CRT shortcut、MST、mode implication、Lean或Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-14","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261014-advance-20261104-r02-uniform-convergence-of-functions-0090","batch_id":"batch-20261014-advance-20261104-r02-uniform-convergence-of-functions-foundations","language":"zh-Hant","source_mko_ids":["mko-uniform-convergence-of-functions"],"title_zh":"一致收斂","stem_zh":"共同有限domain的symbolic tail與同一N(epsilon)。操作=uniform-finite-prefix-boundary；資料={\"limit\":[14,15],\"coefficients\":[15,-16],\"shift\":2,\"prefix_length\":15}。請依 exact_ordered_tuple_declared_by_interface 欄序回答。","answer":{"kind":"expression","value":"(15, 否, finite_prefix_not_uniform_convergence_certificate)","explanation_zh":"Wave5第四層核對=(15, 否, finite_prefix_not_uniform_convergence_certificate)；依完整明示資料重算；同一N控制所有x且有限domain可取pointwise witnesses最大值；不可外推無限domain且finite prefix不足。"},"difficulty":{"band":"undergraduate_core","level":2,"skills":["一致收斂"]},"variant":{"family_id":"qf-mod35-uniform-finite-prefix-boundary","seed":202611042090,"parameters":{"limit":[14,15],"coefficients":[15,-16],"shift":2,"prefix_length":15,"domain":"Finite_domain_symbolic_uniform_tail","operation":"uniform-finite-prefix-boundary","semantic_template":"qf-mod35-uniform-finite-prefix-boundary/{\"coefficients\":[15,-16],\"limit\":[14,15],\"prefix_length\":15,\"shift\":2}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_or_symbolic_model","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"候選須主端重算；不構成人工審定、sampled rank-nullity、infinite-domain uniformity、term-zero convergence、estimator properties、noncoprime CRT shortcut、MST、mode implication、Lean或Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-14","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261014-advance-20261104-r02-uniform-convergence-of-functions-0091","batch_id":"batch-20261014-advance-20261104-r02-uniform-convergence-of-functions-foundations","language":"zh-Hant","source_mko_ids":["mko-uniform-convergence-of-functions"],"title_zh":"一致收斂","stem_zh":"共同有限domain的symbolic tail與同一N(epsilon)。操作=uniform-finite-prefix-boundary；資料={\"limit\":[15,16],\"coefficients\":[16,-17],\"shift\":2,\"prefix_length\":16}。請依 exact_ordered_tuple_declared_by_interface 欄序回答。","answer":{"kind":"expression","value":"(16, 否, finite_prefix_not_uniform_convergence_certificate)","explanation_zh":"Wave5第四層核對=(16, 否, finite_prefix_not_uniform_convergence_certificate)；依完整明示資料重算；同一N控制所有x且有限domain可取pointwise witnesses最大值；不可外推無限domain且finite prefix不足。"},"difficulty":{"band":"undergraduate_core","level":2,"skills":["一致收斂"]},"variant":{"family_id":"qf-mod35-uniform-finite-prefix-boundary","seed":202611042091,"parameters":{"limit":[15,16],"coefficients":[16,-17],"shift":2,"prefix_length":16,"domain":"Finite_domain_symbolic_uniform_tail","operation":"uniform-finite-prefix-boundary","semantic_template":"qf-mod35-uniform-finite-prefix-boundary/{\"coefficients\":[16,-17],\"limit\":[15,16],\"prefix_length\":16,\"shift\":2}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_or_symbolic_model","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"候選須主端重算；不構成人工審定、sampled rank-nullity、infinite-domain uniformity、term-zero convergence、estimator properties、noncoprime CRT shortcut、MST、mode implication、Lean或Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-14","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261014-advance-20261104-r02-uniform-convergence-of-functions-0092","batch_id":"batch-20261014-advance-20261104-r02-uniform-convergence-of-functions-foundations","language":"zh-Hant","source_mko_ids":["mko-uniform-convergence-of-functions"],"title_zh":"一致收斂","stem_zh":"共同有限domain的symbolic tail與同一N(epsilon)。操作=uniform-finite-prefix-boundary；資料={\"limit\":[16,17],\"coefficients\":[17,-18],\"shift\":2,\"prefix_length\":17}。請依 exact_ordered_tuple_declared_by_interface 欄序回答。","answer":{"kind":"expression","value":"(17, 否, finite_prefix_not_uniform_convergence_certificate)","explanation_zh":"Wave5第四層核對=(17, 否, finite_prefix_not_uniform_convergence_certificate)；依完整明示資料重算；同一N控制所有x且有限domain可取pointwise witnesses最大值；不可外推無限domain且finite prefix不足。"},"difficulty":{"band":"undergraduate_core","level":2,"skills":["一致收斂"]},"variant":{"family_id":"qf-mod35-uniform-finite-prefix-boundary","seed":202611042092,"parameters":{"limit":[16,17],"coefficients":[17,-18],"shift":2,"prefix_length":17,"domain":"Finite_domain_symbolic_uniform_tail","operation":"uniform-finite-prefix-boundary","semantic_template":"qf-mod35-uniform-finite-prefix-boundary/{\"coefficients\":[17,-18],\"limit\":[16,17],\"prefix_length\":17,\"shift\":2}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_or_symbolic_model","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"候選須主端重算；不構成人工審定、sampled rank-nullity、infinite-domain uniformity、term-zero convergence、estimator properties、noncoprime CRT shortcut、MST、mode implication、Lean或Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-14","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261014-advance-20261104-r02-uniform-convergence-of-functions-0093","batch_id":"batch-20261014-advance-20261104-r02-uniform-convergence-of-functions-foundations","language":"zh-Hant","source_mko_ids":["mko-uniform-convergence-of-functions"],"title_zh":"一致收斂","stem_zh":"共同有限domain的symbolic tail與同一N(epsilon)。操作=uniform-finite-prefix-boundary；資料={\"limit\":[17,18],\"coefficients\":[18,-19],\"shift\":2,\"prefix_length\":18}。請依 exact_ordered_tuple_declared_by_interface 欄序回答。","answer":{"kind":"expression","value":"(18, 否, finite_prefix_not_uniform_convergence_certificate)","explanation_zh":"Wave5第四層核對=(18, 否, finite_prefix_not_uniform_convergence_certificate)；依完整明示資料重算；同一N控制所有x且有限domain可取pointwise witnesses最大值；不可外推無限domain且finite prefix不足。"},"difficulty":{"band":"undergraduate_core","level":3,"skills":["一致收斂"]},"variant":{"family_id":"qf-mod35-uniform-finite-prefix-boundary","seed":202611042093,"parameters":{"limit":[17,18],"coefficients":[18,-19],"shift":2,"prefix_length":18,"domain":"Finite_domain_symbolic_uniform_tail","operation":"uniform-finite-prefix-boundary","semantic_template":"qf-mod35-uniform-finite-prefix-boundary/{\"coefficients\":[18,-19],\"limit\":[17,18],\"prefix_length\":18,\"shift\":2}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_or_symbolic_model","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"候選須主端重算；不構成人工審定、sampled rank-nullity、infinite-domain uniformity、term-zero convergence、estimator properties、noncoprime CRT shortcut、MST、mode implication、Lean或Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-14","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261014-advance-20261104-r02-uniform-convergence-of-functions-0094","batch_id":"batch-20261014-advance-20261104-r02-uniform-convergence-of-functions-foundations","language":"zh-Hant","source_mko_ids":["mko-uniform-convergence-of-functions"],"title_zh":"一致收斂","stem_zh":"共同有限domain的symbolic tail與同一N(epsilon)。操作=uniform-finite-prefix-boundary；資料={\"limit\":[18,19],\"coefficients\":[19,-20],\"shift\":2,\"prefix_length\":19}。請依 exact_ordered_tuple_declared_by_interface 欄序回答。","answer":{"kind":"expression","value":"(19, 否, finite_prefix_not_uniform_convergence_certificate)","explanation_zh":"Wave5第四層核對=(19, 否, finite_prefix_not_uniform_convergence_certificate)；依完整明示資料重算；同一N控制所有x且有限domain可取pointwise witnesses最大值；不可外推無限domain且finite prefix不足。"},"difficulty":{"band":"undergraduate_core","level":3,"skills":["一致收斂"]},"variant":{"family_id":"qf-mod35-uniform-finite-prefix-boundary","seed":202611042094,"parameters":{"limit":[18,19],"coefficients":[19,-20],"shift":2,"prefix_length":19,"domain":"Finite_domain_symbolic_uniform_tail","operation":"uniform-finite-prefix-boundary","semantic_template":"qf-mod35-uniform-finite-prefix-boundary/{\"coefficients\":[19,-20],\"limit\":[18,19],\"prefix_length\":19,\"shift\":2}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_or_symbolic_model","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"候選須主端重算；不構成人工審定、sampled rank-nullity、infinite-domain uniformity、term-zero convergence、estimator properties、noncoprime CRT shortcut、MST、mode implication、Lean或Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-14","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261014-advance-20261104-r02-uniform-convergence-of-functions-0095","batch_id":"batch-20261014-advance-20261104-r02-uniform-convergence-of-functions-foundations","language":"zh-Hant","source_mko_ids":["mko-uniform-convergence-of-functions"],"title_zh":"一致收斂","stem_zh":"共同有限domain的symbolic tail與同一N(epsilon)。操作=uniform-finite-prefix-boundary；資料={\"limit\":[19,20],\"coefficients\":[20,-21],\"shift\":2,\"prefix_length\":20}。請依 exact_ordered_tuple_declared_by_interface 欄序回答。","answer":{"kind":"expression","value":"(20, 否, finite_prefix_not_uniform_convergence_certificate)","explanation_zh":"Wave5第四層核對=(20, 否, finite_prefix_not_uniform_convergence_certificate)；依完整明示資料重算；同一N控制所有x且有限domain可取pointwise witnesses最大值；不可外推無限domain且finite prefix不足。"},"difficulty":{"band":"undergraduate_core","level":3,"skills":["一致收斂"]},"variant":{"family_id":"qf-mod35-uniform-finite-prefix-boundary","seed":202611042095,"parameters":{"limit":[19,20],"coefficients":[20,-21],"shift":2,"prefix_length":20,"domain":"Finite_domain_symbolic_uniform_tail","operation":"uniform-finite-prefix-boundary","semantic_template":"qf-mod35-uniform-finite-prefix-boundary/{\"coefficients\":[20,-21],\"limit\":[19,20],\"prefix_length\":20,\"shift\":2}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_or_symbolic_model","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"候選須主端重算；不構成人工審定、sampled rank-nullity、infinite-domain uniformity、term-zero convergence、estimator properties、noncoprime CRT shortcut、MST、mode implication、Lean或Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-14","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261014-advance-20261104-r02-uniform-convergence-of-functions-0096","batch_id":"batch-20261014-advance-20261104-r02-uniform-convergence-of-functions-foundations","language":"zh-Hant","source_mko_ids":["mko-uniform-convergence-of-functions"],"title_zh":"一致收斂","stem_zh":"共同有限domain的symbolic tail與同一N(epsilon)。操作=uniform-finite-prefix-boundary；資料={\"limit\":[20,21],\"coefficients\":[21,-22],\"shift\":2,\"prefix_length\":21}。請依 exact_ordered_tuple_declared_by_interface 欄序回答。","answer":{"kind":"expression","value":"(21, 否, finite_prefix_not_uniform_convergence_certificate)","explanation_zh":"Wave5第四層核對=(21, 否, finite_prefix_not_uniform_convergence_certificate)；依完整明示資料重算；同一N控制所有x且有限domain可取pointwise witnesses最大值；不可外推無限domain且finite prefix不足。"},"difficulty":{"band":"undergraduate_core","level":3,"skills":["一致收斂"]},"variant":{"family_id":"qf-mod35-uniform-finite-prefix-boundary","seed":202611042096,"parameters":{"limit":[20,21],"coefficients":[21,-22],"shift":2,"prefix_length":21,"domain":"Finite_domain_symbolic_uniform_tail","operation":"uniform-finite-prefix-boundary","semantic_template":"qf-mod35-uniform-finite-prefix-boundary/{\"coefficients\":[21,-22],\"limit\":[20,21],\"prefix_length\":21,\"shift\":2}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_or_symbolic_model","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"候選須主端重算；不構成人工審定、sampled rank-nullity、infinite-domain uniformity、term-zero convergence、estimator properties、noncoprime CRT shortcut、MST、mode implication、Lean或Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-14","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261014-advance-20261104-r02-uniform-convergence-of-functions-0097","batch_id":"batch-20261014-advance-20261104-r02-uniform-convergence-of-functions-foundations","language":"zh-Hant","source_mko_ids":["mko-uniform-convergence-of-functions"],"title_zh":"一致收斂","stem_zh":"共同有限domain的symbolic tail與同一N(epsilon)。操作=uniform-finite-prefix-boundary；資料={\"limit\":[21,22],\"coefficients\":[22,-23],\"shift\":2,\"prefix_length\":22}。請依 exact_ordered_tuple_declared_by_interface 欄序回答。","answer":{"kind":"expression","value":"(22, 否, finite_prefix_not_uniform_convergence_certificate)","explanation_zh":"Wave5第四層核對=(22, 否, finite_prefix_not_uniform_convergence_certificate)；依完整明示資料重算；同一N控制所有x且有限domain可取pointwise witnesses最大值；不可外推無限domain且finite prefix不足。"},"difficulty":{"band":"undergraduate_core","level":3,"skills":["一致收斂"]},"variant":{"family_id":"qf-mod35-uniform-finite-prefix-boundary","seed":202611042097,"parameters":{"limit":[21,22],"coefficients":[22,-23],"shift":2,"prefix_length":22,"domain":"Finite_domain_symbolic_uniform_tail","operation":"uniform-finite-prefix-boundary","semantic_template":"qf-mod35-uniform-finite-prefix-boundary/{\"coefficients\":[22,-23],\"limit\":[21,22],\"prefix_length\":22,\"shift\":2}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_or_symbolic_model","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"候選須主端重算；不構成人工審定、sampled rank-nullity、infinite-domain uniformity、term-zero convergence、estimator properties、noncoprime CRT shortcut、MST、mode implication、Lean或Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-14","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261014-advance-20261104-r02-uniform-convergence-of-functions-0098","batch_id":"batch-20261014-advance-20261104-r02-uniform-convergence-of-functions-foundations","language":"zh-Hant","source_mko_ids":["mko-uniform-convergence-of-functions"],"title_zh":"一致收斂","stem_zh":"共同有限domain的symbolic tail與同一N(epsilon)。操作=uniform-finite-prefix-boundary；資料={\"limit\":[22,23],\"coefficients\":[23,-24],\"shift\":2,\"prefix_length\":23}。請依 exact_ordered_tuple_declared_by_interface 欄序回答。","answer":{"kind":"expression","value":"(23, 否, finite_prefix_not_uniform_convergence_certificate)","explanation_zh":"Wave5第四層核對=(23, 否, finite_prefix_not_uniform_convergence_certificate)；依完整明示資料重算；同一N控制所有x且有限domain可取pointwise witnesses最大值；不可外推無限domain且finite prefix不足。"},"difficulty":{"band":"undergraduate_core","level":3,"skills":["一致收斂"]},"variant":{"family_id":"qf-mod35-uniform-finite-prefix-boundary","seed":202611042098,"parameters":{"limit":[22,23],"coefficients":[23,-24],"shift":2,"prefix_length":23,"domain":"Finite_domain_symbolic_uniform_tail","operation":"uniform-finite-prefix-boundary","semantic_template":"qf-mod35-uniform-finite-prefix-boundary/{\"coefficients\":[23,-24],\"limit\":[22,23],\"prefix_length\":23,\"shift\":2}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_or_symbolic_model","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"候選須主端重算；不構成人工審定、sampled rank-nullity、infinite-domain uniformity、term-zero convergence、estimator properties、noncoprime CRT shortcut、MST、mode implication、Lean或Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-14","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261014-advance-20261104-r02-uniform-convergence-of-functions-0099","batch_id":"batch-20261014-advance-20261104-r02-uniform-convergence-of-functions-foundations","language":"zh-Hant","source_mko_ids":["mko-uniform-convergence-of-functions"],"title_zh":"一致收斂","stem_zh":"共同有限domain的symbolic tail與同一N(epsilon)。操作=uniform-finite-prefix-boundary；資料={\"limit\":[23,24],\"coefficients\":[24,-25],\"shift\":2,\"prefix_length\":24}。請依 exact_ordered_tuple_declared_by_interface 欄序回答。","answer":{"kind":"expression","value":"(24, 否, finite_prefix_not_uniform_convergence_certificate)","explanation_zh":"Wave5第四層核對=(24, 否, finite_prefix_not_uniform_convergence_certificate)；依完整明示資料重算；同一N控制所有x且有限domain可取pointwise witnesses最大值；不可外推無限domain且finite prefix不足。"},"difficulty":{"band":"undergraduate_core","level":3,"skills":["一致收斂"]},"variant":{"family_id":"qf-mod35-uniform-finite-prefix-boundary","seed":202611042099,"parameters":{"limit":[23,24],"coefficients":[24,-25],"shift":2,"prefix_length":24,"domain":"Finite_domain_symbolic_uniform_tail","operation":"uniform-finite-prefix-boundary","semantic_template":"qf-mod35-uniform-finite-prefix-boundary/{\"coefficients\":[24,-25],\"limit\":[23,24],\"prefix_length\":24,\"shift\":2}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_or_symbolic_model","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"候選須主端重算；不構成人工審定、sampled rank-nullity、infinite-domain uniformity、term-zero convergence、estimator properties、noncoprime CRT shortcut、MST、mode implication、Lean或Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-14","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261014-advance-20261104-r02-uniform-convergence-of-functions-0100","batch_id":"batch-20261014-advance-20261104-r02-uniform-convergence-of-functions-foundations","language":"zh-Hant","source_mko_ids":["mko-uniform-convergence-of-functions"],"title_zh":"一致收斂","stem_zh":"共同有限domain的symbolic tail與同一N(epsilon)。操作=uniform-finite-prefix-boundary；資料={\"limit\":[24,25],\"coefficients\":[25,-26],\"shift\":2,\"prefix_length\":25}。請依 exact_ordered_tuple_declared_by_interface 欄序回答。","answer":{"kind":"expression","value":"(25, 否, finite_prefix_not_uniform_convergence_certificate)","explanation_zh":"Wave5第四層核對=(25, 否, finite_prefix_not_uniform_convergence_certificate)；依完整明示資料重算；同一N控制所有x且有限domain可取pointwise witnesses最大值；不可外推無限domain且finite prefix不足。"},"difficulty":{"band":"undergraduate_core","level":3,"skills":["一致收斂"]},"variant":{"family_id":"qf-mod35-uniform-finite-prefix-boundary","seed":202611042100,"parameters":{"limit":[24,25],"coefficients":[25,-26],"shift":2,"prefix_length":25,"domain":"Finite_domain_symbolic_uniform_tail","operation":"uniform-finite-prefix-boundary","semantic_template":"qf-mod35-uniform-finite-prefix-boundary/{\"coefficients\":[25,-26],\"limit\":[24,25],\"prefix_length\":25,\"shift\":2}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_or_symbolic_model","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"候選須主端重算；不構成人工審定、sampled rank-nullity、infinite-domain uniformity、term-zero convergence、estimator properties、noncoprime CRT shortcut、MST、mode implication、Lean或Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-14","contract_version":"ocme-question-factory-v0.1"}}