{"schema_version":"ocme-question-v0.1","id":"q-20261014-advance-20261104-r07-lp-convergence-0001","batch_id":"batch-20261014-advance-20261104-r07-lp-convergence-foundations","language":"zh-Hant","source_mko_ids":["mko-lp-convergence"],"title_zh":"Lp收斂","stem_zh":"同一有限原子probability space、固定整數p大於等於1與symbolic moment tail。操作=lp-moment-at-n；資料={\"masses\":[[1,2],[1,2]],\"coefficients\":[1,-2],\"shift\":2,\"p\":1,\"n\":1}。請依 exact_ordered_tuple_declared_by_interface 欄序回答。","answer":{"kind":"expression","value":"(1, 1, 1/2, exact_finite_atomic_moment)","explanation_zh":"Wave5第四層核對=(1, 1, 1/2, exact_finite_atomic_moment)；依完整明示資料重算；核E absolute error power p趨零且moments有限；finite prefix不足，a.s. probability或其他Lq implications另需假設。"},"difficulty":{"band":"undergraduate_core","level":1,"skills":["Lp收斂"]},"variant":{"family_id":"qf-mod35-lp-moment-at-n","seed":202611047001,"parameters":{"masses":[[1,2],[1,2]],"coefficients":[1,-2],"shift":2,"p":1,"n":1,"domain":"Finite_atomic_symbolic_Lp_tail","operation":"lp-moment-at-n","semantic_template":"qf-mod35-lp-moment-at-n/{\"coefficients\":[1,-2],\"masses\":[[1,2],[1,2]],\"n\":1,\"p\":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-r07-lp-convergence-0002","batch_id":"batch-20261014-advance-20261104-r07-lp-convergence-foundations","language":"zh-Hant","source_mko_ids":["mko-lp-convergence"],"title_zh":"Lp收斂","stem_zh":"同一有限原子probability space、固定整數p大於等於1與symbolic moment tail。操作=lp-moment-at-n；資料={\"masses\":[[1,2],[1,2]],\"coefficients\":[2,-3],\"shift\":2,\"p\":2,\"n\":2}。請依 exact_ordered_tuple_declared_by_interface 欄序回答。","answer":{"kind":"expression","value":"(2, 2, 13/32, exact_finite_atomic_moment)","explanation_zh":"Wave5第四層核對=(2, 2, 13/32, exact_finite_atomic_moment)；依完整明示資料重算；核E absolute error power p趨零且moments有限；finite prefix不足，a.s. probability或其他Lq implications另需假設。"},"difficulty":{"band":"undergraduate_core","level":1,"skills":["Lp收斂"]},"variant":{"family_id":"qf-mod35-lp-moment-at-n","seed":202611047002,"parameters":{"masses":[[1,2],[1,2]],"coefficients":[2,-3],"shift":2,"p":2,"n":2,"domain":"Finite_atomic_symbolic_Lp_tail","operation":"lp-moment-at-n","semantic_template":"qf-mod35-lp-moment-at-n/{\"coefficients\":[2,-3],\"masses\":[[1,2],[1,2]],\"n\":2,\"p\":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-r07-lp-convergence-0003","batch_id":"batch-20261014-advance-20261104-r07-lp-convergence-foundations","language":"zh-Hant","source_mko_ids":["mko-lp-convergence"],"title_zh":"Lp收斂","stem_zh":"同一有限原子probability space、固定整數p大於等於1與symbolic moment tail。操作=lp-moment-at-n；資料={\"masses\":[[1,2],[1,2]],\"coefficients\":[3,-4],\"shift\":2,\"p\":3,\"n\":3}。請依 exact_ordered_tuple_declared_by_interface 欄序回答。","answer":{"kind":"expression","value":"(3, 3, 91/250, exact_finite_atomic_moment)","explanation_zh":"Wave5第四層核對=(3, 3, 91/250, exact_finite_atomic_moment)；依完整明示資料重算；核E absolute error power p趨零且moments有限；finite prefix不足，a.s. probability或其他Lq implications另需假設。"},"difficulty":{"band":"undergraduate_core","level":1,"skills":["Lp收斂"]},"variant":{"family_id":"qf-mod35-lp-moment-at-n","seed":202611047003,"parameters":{"masses":[[1,2],[1,2]],"coefficients":[3,-4],"shift":2,"p":3,"n":3,"domain":"Finite_atomic_symbolic_Lp_tail","operation":"lp-moment-at-n","semantic_template":"qf-mod35-lp-moment-at-n/{\"coefficients\":[3,-4],\"masses\":[[1,2],[1,2]],\"n\":3,\"p\":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-r07-lp-convergence-0004","batch_id":"batch-20261014-advance-20261104-r07-lp-convergence-foundations","language":"zh-Hant","source_mko_ids":["mko-lp-convergence"],"title_zh":"Lp收斂","stem_zh":"同一有限原子probability space、固定整數p大於等於1與symbolic moment tail。操作=lp-moment-at-n；資料={\"masses\":[[1,2],[1,2]],\"coefficients\":[4,-5],\"shift\":2,\"p\":1,\"n\":4}。請依 exact_ordered_tuple_declared_by_interface 欄序回答。","answer":{"kind":"expression","value":"(1, 4, 3/4, exact_finite_atomic_moment)","explanation_zh":"Wave5第四層核對=(1, 4, 3/4, exact_finite_atomic_moment)；依完整明示資料重算；核E absolute error power p趨零且moments有限；finite prefix不足，a.s. probability或其他Lq implications另需假設。"},"difficulty":{"band":"undergraduate_core","level":1,"skills":["Lp收斂"]},"variant":{"family_id":"qf-mod35-lp-moment-at-n","seed":202611047004,"parameters":{"masses":[[1,2],[1,2]],"coefficients":[4,-5],"shift":2,"p":1,"n":4,"domain":"Finite_atomic_symbolic_Lp_tail","operation":"lp-moment-at-n","semantic_template":"qf-mod35-lp-moment-at-n/{\"coefficients\":[4,-5],\"masses\":[[1,2],[1,2]],\"n\":4,\"p\":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-r07-lp-convergence-0005","batch_id":"batch-20261014-advance-20261104-r07-lp-convergence-foundations","language":"zh-Hant","source_mko_ids":["mko-lp-convergence"],"title_zh":"Lp收斂","stem_zh":"同一有限原子probability space、固定整數p大於等於1與symbolic moment tail。操作=lp-moment-at-n；資料={\"masses\":[[1,2],[1,2]],\"coefficients\":[5,-6],\"shift\":2,\"p\":2,\"n\":5}。請依 exact_ordered_tuple_declared_by_interface 欄序回答。","answer":{"kind":"expression","value":"(2, 5, 61/98, exact_finite_atomic_moment)","explanation_zh":"Wave5第四層核對=(2, 5, 61/98, exact_finite_atomic_moment)；依完整明示資料重算；核E absolute error power p趨零且moments有限；finite prefix不足，a.s. probability或其他Lq implications另需假設。"},"difficulty":{"band":"undergraduate_core","level":1,"skills":["Lp收斂"]},"variant":{"family_id":"qf-mod35-lp-moment-at-n","seed":202611047005,"parameters":{"masses":[[1,2],[1,2]],"coefficients":[5,-6],"shift":2,"p":2,"n":5,"domain":"Finite_atomic_symbolic_Lp_tail","operation":"lp-moment-at-n","semantic_template":"qf-mod35-lp-moment-at-n/{\"coefficients\":[5,-6],\"masses\":[[1,2],[1,2]],\"n\":5,\"p\":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-r07-lp-convergence-0006","batch_id":"batch-20261014-advance-20261104-r07-lp-convergence-foundations","language":"zh-Hant","source_mko_ids":["mko-lp-convergence"],"title_zh":"Lp收斂","stem_zh":"同一有限原子probability space、固定整數p大於等於1與symbolic moment tail。操作=lp-moment-at-n；資料={\"masses\":[[1,2],[1,2]],\"coefficients\":[6,-7],\"shift\":2,\"p\":3,\"n\":6}。請依 exact_ordered_tuple_declared_by_interface 欄序回答。","answer":{"kind":"expression","value":"(3, 6, 559/1024, exact_finite_atomic_moment)","explanation_zh":"Wave5第四層核對=(3, 6, 559/1024, exact_finite_atomic_moment)；依完整明示資料重算；核E absolute error power p趨零且moments有限；finite prefix不足，a.s. probability或其他Lq implications另需假設。"},"difficulty":{"band":"undergraduate_core","level":1,"skills":["Lp收斂"]},"variant":{"family_id":"qf-mod35-lp-moment-at-n","seed":202611047006,"parameters":{"masses":[[1,2],[1,2]],"coefficients":[6,-7],"shift":2,"p":3,"n":6,"domain":"Finite_atomic_symbolic_Lp_tail","operation":"lp-moment-at-n","semantic_template":"qf-mod35-lp-moment-at-n/{\"coefficients\":[6,-7],\"masses\":[[1,2],[1,2]],\"n\":6,\"p\":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-r07-lp-convergence-0007","batch_id":"batch-20261014-advance-20261104-r07-lp-convergence-foundations","language":"zh-Hant","source_mko_ids":["mko-lp-convergence"],"title_zh":"Lp收斂","stem_zh":"同一有限原子probability space、固定整數p大於等於1與symbolic moment tail。操作=lp-moment-at-n；資料={\"masses\":[[1,2],[1,2]],\"coefficients\":[7,-8],\"shift\":2,\"p\":1,\"n\":7}。請依 exact_ordered_tuple_declared_by_interface 欄序回答。","answer":{"kind":"expression","value":"(1, 7, 5/6, exact_finite_atomic_moment)","explanation_zh":"Wave5第四層核對=(1, 7, 5/6, exact_finite_atomic_moment)；依完整明示資料重算；核E absolute error power p趨零且moments有限；finite prefix不足，a.s. probability或其他Lq implications另需假設。"},"difficulty":{"band":"undergraduate_core","level":1,"skills":["Lp收斂"]},"variant":{"family_id":"qf-mod35-lp-moment-at-n","seed":202611047007,"parameters":{"masses":[[1,2],[1,2]],"coefficients":[7,-8],"shift":2,"p":1,"n":7,"domain":"Finite_atomic_symbolic_Lp_tail","operation":"lp-moment-at-n","semantic_template":"qf-mod35-lp-moment-at-n/{\"coefficients\":[7,-8],\"masses\":[[1,2],[1,2]],\"n\":7,\"p\":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-r07-lp-convergence-0008","batch_id":"batch-20261014-advance-20261104-r07-lp-convergence-foundations","language":"zh-Hant","source_mko_ids":["mko-lp-convergence"],"title_zh":"Lp收斂","stem_zh":"同一有限原子probability space、固定整數p大於等於1與symbolic moment tail。操作=lp-moment-at-n；資料={\"masses\":[[1,2],[1,2]],\"coefficients\":[8,-9],\"shift\":2,\"p\":2,\"n\":8}。請依 exact_ordered_tuple_declared_by_interface 欄序回答。","answer":{"kind":"expression","value":"(2, 8, 29/40, exact_finite_atomic_moment)","explanation_zh":"Wave5第四層核對=(2, 8, 29/40, exact_finite_atomic_moment)；依完整明示資料重算；核E absolute error power p趨零且moments有限；finite prefix不足，a.s. probability或其他Lq implications另需假設。"},"difficulty":{"band":"undergraduate_core","level":1,"skills":["Lp收斂"]},"variant":{"family_id":"qf-mod35-lp-moment-at-n","seed":202611047008,"parameters":{"masses":[[1,2],[1,2]],"coefficients":[8,-9],"shift":2,"p":2,"n":8,"domain":"Finite_atomic_symbolic_Lp_tail","operation":"lp-moment-at-n","semantic_template":"qf-mod35-lp-moment-at-n/{\"coefficients\":[8,-9],\"masses\":[[1,2],[1,2]],\"n\":8,\"p\":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-r07-lp-convergence-0009","batch_id":"batch-20261014-advance-20261104-r07-lp-convergence-foundations","language":"zh-Hant","source_mko_ids":["mko-lp-convergence"],"title_zh":"Lp收斂","stem_zh":"同一有限原子probability space、固定整數p大於等於1與symbolic moment tail。操作=lp-moment-at-n；資料={\"masses\":[[1,2],[1,2]],\"coefficients\":[9,-10],\"shift\":2,\"p\":3,\"n\":9}。請依 exact_ordered_tuple_declared_by_interface 欄序回答。","answer":{"kind":"expression","value":"(3, 9, 1729/2662, exact_finite_atomic_moment)","explanation_zh":"Wave5第四層核對=(3, 9, 1729/2662, exact_finite_atomic_moment)；依完整明示資料重算；核E absolute error power p趨零且moments有限；finite prefix不足，a.s. probability或其他Lq implications另需假設。"},"difficulty":{"band":"undergraduate_core","level":2,"skills":["Lp收斂"]},"variant":{"family_id":"qf-mod35-lp-moment-at-n","seed":202611047009,"parameters":{"masses":[[1,2],[1,2]],"coefficients":[9,-10],"shift":2,"p":3,"n":9,"domain":"Finite_atomic_symbolic_Lp_tail","operation":"lp-moment-at-n","semantic_template":"qf-mod35-lp-moment-at-n/{\"coefficients\":[9,-10],\"masses\":[[1,2],[1,2]],\"n\":9,\"p\":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-r07-lp-convergence-0010","batch_id":"batch-20261014-advance-20261104-r07-lp-convergence-foundations","language":"zh-Hant","source_mko_ids":["mko-lp-convergence"],"title_zh":"Lp收斂","stem_zh":"同一有限原子probability space、固定整數p大於等於1與symbolic moment tail。操作=lp-moment-at-n；資料={\"masses\":[[1,2],[1,2]],\"coefficients\":[10,-11],\"shift\":2,\"p\":1,\"n\":10}。請依 exact_ordered_tuple_declared_by_interface 欄序回答。","answer":{"kind":"expression","value":"(1, 10, 7/8, exact_finite_atomic_moment)","explanation_zh":"Wave5第四層核對=(1, 10, 7/8, exact_finite_atomic_moment)；依完整明示資料重算；核E absolute error power p趨零且moments有限；finite prefix不足，a.s. probability或其他Lq implications另需假設。"},"difficulty":{"band":"undergraduate_core","level":2,"skills":["Lp收斂"]},"variant":{"family_id":"qf-mod35-lp-moment-at-n","seed":202611047010,"parameters":{"masses":[[1,2],[1,2]],"coefficients":[10,-11],"shift":2,"p":1,"n":10,"domain":"Finite_atomic_symbolic_Lp_tail","operation":"lp-moment-at-n","semantic_template":"qf-mod35-lp-moment-at-n/{\"coefficients\":[10,-11],\"masses\":[[1,2],[1,2]],\"n\":10,\"p\":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-r07-lp-convergence-0011","batch_id":"batch-20261014-advance-20261104-r07-lp-convergence-foundations","language":"zh-Hant","source_mko_ids":["mko-lp-convergence"],"title_zh":"Lp收斂","stem_zh":"同一有限原子probability space、固定整數p大於等於1與symbolic moment tail。操作=lp-moment-at-n；資料={\"masses\":[[1,2],[1,2]],\"coefficients\":[11,-12],\"shift\":2,\"p\":2,\"n\":11}。請依 exact_ordered_tuple_declared_by_interface 欄序回答。","answer":{"kind":"expression","value":"(2, 11, 265/338, exact_finite_atomic_moment)","explanation_zh":"Wave5第四層核對=(2, 11, 265/338, exact_finite_atomic_moment)；依完整明示資料重算；核E absolute error power p趨零且moments有限；finite prefix不足，a.s. probability或其他Lq implications另需假設。"},"difficulty":{"band":"undergraduate_core","level":2,"skills":["Lp收斂"]},"variant":{"family_id":"qf-mod35-lp-moment-at-n","seed":202611047011,"parameters":{"masses":[[1,2],[1,2]],"coefficients":[11,-12],"shift":2,"p":2,"n":11,"domain":"Finite_atomic_symbolic_Lp_tail","operation":"lp-moment-at-n","semantic_template":"qf-mod35-lp-moment-at-n/{\"coefficients\":[11,-12],\"masses\":[[1,2],[1,2]],\"n\":11,\"p\":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-r07-lp-convergence-0012","batch_id":"batch-20261014-advance-20261104-r07-lp-convergence-foundations","language":"zh-Hant","source_mko_ids":["mko-lp-convergence"],"title_zh":"Lp收斂","stem_zh":"同一有限原子probability space、固定整數p大於等於1與symbolic moment tail。操作=lp-moment-at-n；資料={\"masses\":[[1,2],[1,2]],\"coefficients\":[12,-13],\"shift\":2,\"p\":3,\"n\":12}。請依 exact_ordered_tuple_declared_by_interface 欄序回答。","answer":{"kind":"expression","value":"(3, 12, 3925/5488, exact_finite_atomic_moment)","explanation_zh":"Wave5第四層核對=(3, 12, 3925/5488, exact_finite_atomic_moment)；依完整明示資料重算；核E absolute error power p趨零且moments有限；finite prefix不足，a.s. probability或其他Lq implications另需假設。"},"difficulty":{"band":"undergraduate_core","level":2,"skills":["Lp收斂"]},"variant":{"family_id":"qf-mod35-lp-moment-at-n","seed":202611047012,"parameters":{"masses":[[1,2],[1,2]],"coefficients":[12,-13],"shift":2,"p":3,"n":12,"domain":"Finite_atomic_symbolic_Lp_tail","operation":"lp-moment-at-n","semantic_template":"qf-mod35-lp-moment-at-n/{\"coefficients\":[12,-13],\"masses\":[[1,2],[1,2]],\"n\":12,\"p\":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-r07-lp-convergence-0013","batch_id":"batch-20261014-advance-20261104-r07-lp-convergence-foundations","language":"zh-Hant","source_mko_ids":["mko-lp-convergence"],"title_zh":"Lp收斂","stem_zh":"同一有限原子probability space、固定整數p大於等於1與symbolic moment tail。操作=lp-moment-at-n；資料={\"masses\":[[1,2],[1,2]],\"coefficients\":[13,-14],\"shift\":2,\"p\":1,\"n\":13}。請依 exact_ordered_tuple_declared_by_interface 欄序回答。","answer":{"kind":"expression","value":"(1, 13, 9/10, exact_finite_atomic_moment)","explanation_zh":"Wave5第四層核對=(1, 13, 9/10, exact_finite_atomic_moment)；依完整明示資料重算；核E absolute error power p趨零且moments有限；finite prefix不足，a.s. probability或其他Lq implications另需假設。"},"difficulty":{"band":"undergraduate_core","level":2,"skills":["Lp收斂"]},"variant":{"family_id":"qf-mod35-lp-moment-at-n","seed":202611047013,"parameters":{"masses":[[1,2],[1,2]],"coefficients":[13,-14],"shift":2,"p":1,"n":13,"domain":"Finite_atomic_symbolic_Lp_tail","operation":"lp-moment-at-n","semantic_template":"qf-mod35-lp-moment-at-n/{\"coefficients\":[13,-14],\"masses\":[[1,2],[1,2]],\"n\":13,\"p\":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-r07-lp-convergence-0014","batch_id":"batch-20261014-advance-20261104-r07-lp-convergence-foundations","language":"zh-Hant","source_mko_ids":["mko-lp-convergence"],"title_zh":"Lp收斂","stem_zh":"同一有限原子probability space、固定整數p大於等於1與symbolic moment tail。操作=lp-moment-at-n；資料={\"masses\":[[1,2],[1,2]],\"coefficients\":[14,-15],\"shift\":2,\"p\":2,\"n\":14}。請依 exact_ordered_tuple_declared_by_interface 欄序回答。","answer":{"kind":"expression","value":"(2, 14, 421/512, exact_finite_atomic_moment)","explanation_zh":"Wave5第四層核對=(2, 14, 421/512, exact_finite_atomic_moment)；依完整明示資料重算；核E absolute error power p趨零且moments有限；finite prefix不足，a.s. probability或其他Lq implications另需假設。"},"difficulty":{"band":"undergraduate_core","level":2,"skills":["Lp收斂"]},"variant":{"family_id":"qf-mod35-lp-moment-at-n","seed":202611047014,"parameters":{"masses":[[1,2],[1,2]],"coefficients":[14,-15],"shift":2,"p":2,"n":14,"domain":"Finite_atomic_symbolic_Lp_tail","operation":"lp-moment-at-n","semantic_template":"qf-mod35-lp-moment-at-n/{\"coefficients\":[14,-15],\"masses\":[[1,2],[1,2]],\"n\":14,\"p\":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-r07-lp-convergence-0015","batch_id":"batch-20261014-advance-20261104-r07-lp-convergence-foundations","language":"zh-Hant","source_mko_ids":["mko-lp-convergence"],"title_zh":"Lp收斂","stem_zh":"同一有限原子probability space、固定整數p大於等於1與symbolic moment tail。操作=lp-moment-at-n；資料={\"masses\":[[1,2],[1,2]],\"coefficients\":[15,-16],\"shift\":2,\"p\":3,\"n\":15}。請依 exact_ordered_tuple_declared_by_interface 欄序回答。","answer":{"kind":"expression","value":"(3, 15, 7471/9826, exact_finite_atomic_moment)","explanation_zh":"Wave5第四層核對=(3, 15, 7471/9826, exact_finite_atomic_moment)；依完整明示資料重算；核E absolute error power p趨零且moments有限；finite prefix不足，a.s. probability或其他Lq implications另需假設。"},"difficulty":{"band":"undergraduate_core","level":2,"skills":["Lp收斂"]},"variant":{"family_id":"qf-mod35-lp-moment-at-n","seed":202611047015,"parameters":{"masses":[[1,2],[1,2]],"coefficients":[15,-16],"shift":2,"p":3,"n":15,"domain":"Finite_atomic_symbolic_Lp_tail","operation":"lp-moment-at-n","semantic_template":"qf-mod35-lp-moment-at-n/{\"coefficients\":[15,-16],\"masses\":[[1,2],[1,2]],\"n\":15,\"p\":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-r07-lp-convergence-0016","batch_id":"batch-20261014-advance-20261104-r07-lp-convergence-foundations","language":"zh-Hant","source_mko_ids":["mko-lp-convergence"],"title_zh":"Lp收斂","stem_zh":"同一有限原子probability space、固定整數p大於等於1與symbolic moment tail。操作=lp-moment-at-n；資料={\"masses\":[[1,2],[1,2]],\"coefficients\":[16,-17],\"shift\":2,\"p\":1,\"n\":16}。請依 exact_ordered_tuple_declared_by_interface 欄序回答。","answer":{"kind":"expression","value":"(1, 16, 11/12, exact_finite_atomic_moment)","explanation_zh":"Wave5第四層核對=(1, 16, 11/12, exact_finite_atomic_moment)；依完整明示資料重算；核E absolute error power p趨零且moments有限；finite prefix不足，a.s. probability或其他Lq implications另需假設。"},"difficulty":{"band":"undergraduate_core","level":2,"skills":["Lp收斂"]},"variant":{"family_id":"qf-mod35-lp-moment-at-n","seed":202611047016,"parameters":{"masses":[[1,2],[1,2]],"coefficients":[16,-17],"shift":2,"p":1,"n":16,"domain":"Finite_atomic_symbolic_Lp_tail","operation":"lp-moment-at-n","semantic_template":"qf-mod35-lp-moment-at-n/{\"coefficients\":[16,-17],\"masses\":[[1,2],[1,2]],\"n\":16,\"p\":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-r07-lp-convergence-0017","batch_id":"batch-20261014-advance-20261104-r07-lp-convergence-foundations","language":"zh-Hant","source_mko_ids":["mko-lp-convergence"],"title_zh":"Lp收斂","stem_zh":"同一有限原子probability space、固定整數p大於等於1與symbolic moment tail。操作=lp-moment-at-n；資料={\"masses\":[[1,2],[1,2]],\"coefficients\":[17,-18],\"shift\":2,\"p\":2,\"n\":17}。請依 exact_ordered_tuple_declared_by_interface 欄序回答。","answer":{"kind":"expression","value":"(2, 17, 613/722, exact_finite_atomic_moment)","explanation_zh":"Wave5第四層核對=(2, 17, 613/722, exact_finite_atomic_moment)；依完整明示資料重算；核E absolute error power p趨零且moments有限；finite prefix不足，a.s. probability或其他Lq implications另需假設。"},"difficulty":{"band":"undergraduate_core","level":2,"skills":["Lp收斂"]},"variant":{"family_id":"qf-mod35-lp-moment-at-n","seed":202611047017,"parameters":{"masses":[[1,2],[1,2]],"coefficients":[17,-18],"shift":2,"p":2,"n":17,"domain":"Finite_atomic_symbolic_Lp_tail","operation":"lp-moment-at-n","semantic_template":"qf-mod35-lp-moment-at-n/{\"coefficients\":[17,-18],\"masses\":[[1,2],[1,2]],\"n\":17,\"p\":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-r07-lp-convergence-0018","batch_id":"batch-20261014-advance-20261104-r07-lp-convergence-foundations","language":"zh-Hant","source_mko_ids":["mko-lp-convergence"],"title_zh":"Lp收斂","stem_zh":"同一有限原子probability space、固定整數p大於等於1與symbolic moment tail。操作=lp-moment-at-n；資料={\"masses\":[[1,2],[1,2]],\"coefficients\":[18,-19],\"shift\":2,\"p\":3,\"n\":18}。請依 exact_ordered_tuple_declared_by_interface 欄序回答。","answer":{"kind":"expression","value":"(3, 18, 12691/16000, exact_finite_atomic_moment)","explanation_zh":"Wave5第四層核對=(3, 18, 12691/16000, exact_finite_atomic_moment)；依完整明示資料重算；核E absolute error power p趨零且moments有限；finite prefix不足，a.s. probability或其他Lq implications另需假設。"},"difficulty":{"band":"undergraduate_core","level":3,"skills":["Lp收斂"]},"variant":{"family_id":"qf-mod35-lp-moment-at-n","seed":202611047018,"parameters":{"masses":[[1,2],[1,2]],"coefficients":[18,-19],"shift":2,"p":3,"n":18,"domain":"Finite_atomic_symbolic_Lp_tail","operation":"lp-moment-at-n","semantic_template":"qf-mod35-lp-moment-at-n/{\"coefficients\":[18,-19],\"masses\":[[1,2],[1,2]],\"n\":18,\"p\":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-r07-lp-convergence-0019","batch_id":"batch-20261014-advance-20261104-r07-lp-convergence-foundations","language":"zh-Hant","source_mko_ids":["mko-lp-convergence"],"title_zh":"Lp收斂","stem_zh":"同一有限原子probability space、固定整數p大於等於1與symbolic moment tail。操作=lp-moment-at-n；資料={\"masses\":[[1,2],[1,2]],\"coefficients\":[19,-20],\"shift\":2,\"p\":1,\"n\":19}。請依 exact_ordered_tuple_declared_by_interface 欄序回答。","answer":{"kind":"expression","value":"(1, 19, 13/14, exact_finite_atomic_moment)","explanation_zh":"Wave5第四層核對=(1, 19, 13/14, exact_finite_atomic_moment)；依完整明示資料重算；核E absolute error power p趨零且moments有限；finite prefix不足，a.s. probability或其他Lq implications另需假設。"},"difficulty":{"band":"undergraduate_core","level":3,"skills":["Lp收斂"]},"variant":{"family_id":"qf-mod35-lp-moment-at-n","seed":202611047019,"parameters":{"masses":[[1,2],[1,2]],"coefficients":[19,-20],"shift":2,"p":1,"n":19,"domain":"Finite_atomic_symbolic_Lp_tail","operation":"lp-moment-at-n","semantic_template":"qf-mod35-lp-moment-at-n/{\"coefficients\":[19,-20],\"masses\":[[1,2],[1,2]],\"n\":19,\"p\":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-r07-lp-convergence-0020","batch_id":"batch-20261014-advance-20261104-r07-lp-convergence-foundations","language":"zh-Hant","source_mko_ids":["mko-lp-convergence"],"title_zh":"Lp收斂","stem_zh":"同一有限原子probability space、固定整數p大於等於1與symbolic moment tail。操作=lp-moment-at-n；資料={\"masses\":[[1,2],[1,2]],\"coefficients\":[20,-21],\"shift\":2,\"p\":2,\"n\":20}。請依 exact_ordered_tuple_declared_by_interface 欄序回答。","answer":{"kind":"expression","value":"(2, 20, 841/968, exact_finite_atomic_moment)","explanation_zh":"Wave5第四層核對=(2, 20, 841/968, exact_finite_atomic_moment)；依完整明示資料重算；核E absolute error power p趨零且moments有限；finite prefix不足，a.s. probability或其他Lq implications另需假設。"},"difficulty":{"band":"undergraduate_core","level":3,"skills":["Lp收斂"]},"variant":{"family_id":"qf-mod35-lp-moment-at-n","seed":202611047020,"parameters":{"masses":[[1,2],[1,2]],"coefficients":[20,-21],"shift":2,"p":2,"n":20,"domain":"Finite_atomic_symbolic_Lp_tail","operation":"lp-moment-at-n","semantic_template":"qf-mod35-lp-moment-at-n/{\"coefficients\":[20,-21],\"masses\":[[1,2],[1,2]],\"n\":20,\"p\":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-r07-lp-convergence-0021","batch_id":"batch-20261014-advance-20261104-r07-lp-convergence-foundations","language":"zh-Hant","source_mko_ids":["mko-lp-convergence"],"title_zh":"Lp收斂","stem_zh":"同一有限原子probability space、固定整數p大於等於1與symbolic moment tail。操作=lp-moment-at-n；資料={\"masses\":[[1,2],[1,2]],\"coefficients\":[21,-22],\"shift\":2,\"p\":3,\"n\":21}。請依 exact_ordered_tuple_declared_by_interface 欄序回答。","answer":{"kind":"expression","value":"(3, 21, 19909/24334, exact_finite_atomic_moment)","explanation_zh":"Wave5第四層核對=(3, 21, 19909/24334, exact_finite_atomic_moment)；依完整明示資料重算；核E absolute error power p趨零且moments有限；finite prefix不足，a.s. probability或其他Lq implications另需假設。"},"difficulty":{"band":"undergraduate_core","level":3,"skills":["Lp收斂"]},"variant":{"family_id":"qf-mod35-lp-moment-at-n","seed":202611047021,"parameters":{"masses":[[1,2],[1,2]],"coefficients":[21,-22],"shift":2,"p":3,"n":21,"domain":"Finite_atomic_symbolic_Lp_tail","operation":"lp-moment-at-n","semantic_template":"qf-mod35-lp-moment-at-n/{\"coefficients\":[21,-22],\"masses\":[[1,2],[1,2]],\"n\":21,\"p\":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-r07-lp-convergence-0022","batch_id":"batch-20261014-advance-20261104-r07-lp-convergence-foundations","language":"zh-Hant","source_mko_ids":["mko-lp-convergence"],"title_zh":"Lp收斂","stem_zh":"同一有限原子probability space、固定整數p大於等於1與symbolic moment tail。操作=lp-moment-at-n；資料={\"masses\":[[1,2],[1,2]],\"coefficients\":[22,-23],\"shift\":2,\"p\":1,\"n\":22}。請依 exact_ordered_tuple_declared_by_interface 欄序回答。","answer":{"kind":"expression","value":"(1, 22, 15/16, exact_finite_atomic_moment)","explanation_zh":"Wave5第四層核對=(1, 22, 15/16, exact_finite_atomic_moment)；依完整明示資料重算；核E absolute error power p趨零且moments有限；finite prefix不足，a.s. probability或其他Lq implications另需假設。"},"difficulty":{"band":"undergraduate_core","level":3,"skills":["Lp收斂"]},"variant":{"family_id":"qf-mod35-lp-moment-at-n","seed":202611047022,"parameters":{"masses":[[1,2],[1,2]],"coefficients":[22,-23],"shift":2,"p":1,"n":22,"domain":"Finite_atomic_symbolic_Lp_tail","operation":"lp-moment-at-n","semantic_template":"qf-mod35-lp-moment-at-n/{\"coefficients\":[22,-23],\"masses\":[[1,2],[1,2]],\"n\":22,\"p\":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-r07-lp-convergence-0023","batch_id":"batch-20261014-advance-20261104-r07-lp-convergence-foundations","language":"zh-Hant","source_mko_ids":["mko-lp-convergence"],"title_zh":"Lp收斂","stem_zh":"同一有限原子probability space、固定整數p大於等於1與symbolic moment tail。操作=lp-moment-at-n；資料={\"masses\":[[1,2],[1,2]],\"coefficients\":[23,-24],\"shift\":2,\"p\":2,\"n\":23}。請依 exact_ordered_tuple_declared_by_interface 欄序回答。","answer":{"kind":"expression","value":"(2, 23, 221/250, exact_finite_atomic_moment)","explanation_zh":"Wave5第四層核對=(2, 23, 221/250, exact_finite_atomic_moment)；依完整明示資料重算；核E absolute error power p趨零且moments有限；finite prefix不足，a.s. probability或其他Lq implications另需假設。"},"difficulty":{"band":"undergraduate_core","level":3,"skills":["Lp收斂"]},"variant":{"family_id":"qf-mod35-lp-moment-at-n","seed":202611047023,"parameters":{"masses":[[1,2],[1,2]],"coefficients":[23,-24],"shift":2,"p":2,"n":23,"domain":"Finite_atomic_symbolic_Lp_tail","operation":"lp-moment-at-n","semantic_template":"qf-mod35-lp-moment-at-n/{\"coefficients\":[23,-24],\"masses\":[[1,2],[1,2]],\"n\":23,\"p\":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-r07-lp-convergence-0024","batch_id":"batch-20261014-advance-20261104-r07-lp-convergence-foundations","language":"zh-Hant","source_mko_ids":["mko-lp-convergence"],"title_zh":"Lp收斂","stem_zh":"同一有限原子probability space、固定整數p大於等於1與symbolic moment tail。操作=lp-moment-at-n；資料={\"masses\":[[1,2],[1,2]],\"coefficients\":[24,-25],\"shift\":2,\"p\":3,\"n\":24}。請依 exact_ordered_tuple_declared_by_interface 欄序回答。","answer":{"kind":"expression","value":"(3, 24, 29449/35152, exact_finite_atomic_moment)","explanation_zh":"Wave5第四層核對=(3, 24, 29449/35152, exact_finite_atomic_moment)；依完整明示資料重算；核E absolute error power p趨零且moments有限；finite prefix不足，a.s. probability或其他Lq implications另需假設。"},"difficulty":{"band":"undergraduate_core","level":3,"skills":["Lp收斂"]},"variant":{"family_id":"qf-mod35-lp-moment-at-n","seed":202611047024,"parameters":{"masses":[[1,2],[1,2]],"coefficients":[24,-25],"shift":2,"p":3,"n":24,"domain":"Finite_atomic_symbolic_Lp_tail","operation":"lp-moment-at-n","semantic_template":"qf-mod35-lp-moment-at-n/{\"coefficients\":[24,-25],\"masses\":[[1,2],[1,2]],\"n\":24,\"p\":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-r07-lp-convergence-0025","batch_id":"batch-20261014-advance-20261104-r07-lp-convergence-foundations","language":"zh-Hant","source_mko_ids":["mko-lp-convergence"],"title_zh":"Lp收斂","stem_zh":"同一有限原子probability space、固定整數p大於等於1與symbolic moment tail。操作=lp-moment-at-n；資料={\"masses\":[[1,2],[1,2]],\"coefficients\":[25,-26],\"shift\":2,\"p\":1,\"n\":25}。請依 exact_ordered_tuple_declared_by_interface 欄序回答。","answer":{"kind":"expression","value":"(1, 25, 17/18, exact_finite_atomic_moment)","explanation_zh":"Wave5第四層核對=(1, 25, 17/18, exact_finite_atomic_moment)；依完整明示資料重算；核E absolute error power p趨零且moments有限；finite prefix不足，a.s. probability或其他Lq implications另需假設。"},"difficulty":{"band":"undergraduate_core","level":3,"skills":["Lp收斂"]},"variant":{"family_id":"qf-mod35-lp-moment-at-n","seed":202611047025,"parameters":{"masses":[[1,2],[1,2]],"coefficients":[25,-26],"shift":2,"p":1,"n":25,"domain":"Finite_atomic_symbolic_Lp_tail","operation":"lp-moment-at-n","semantic_template":"qf-mod35-lp-moment-at-n/{\"coefficients\":[25,-26],\"masses\":[[1,2],[1,2]],\"n\":25,\"p\":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-r07-lp-convergence-0026","batch_id":"batch-20261014-advance-20261104-r07-lp-convergence-foundations","language":"zh-Hant","source_mko_ids":["mko-lp-convergence"],"title_zh":"Lp收斂","stem_zh":"同一有限原子probability space、固定整數p大於等於1與symbolic moment tail。操作=lp-epsilon-witness；資料={\"masses\":[[1,2],[1,2]],\"coefficients\":[1,-2],\"shift\":2,\"p\":1,\"epsilon\":[1,10]}。請依 exact_ordered_tuple_declared_by_interface 欄序回答。","answer":{"kind":"expression","value":"(1, 1/10, 14, 3/32, 是, forall_n_ge_N_symbolic_monotone_tail)","explanation_zh":"Wave5第四層核對=(1, 1/10, 14, 3/32, 是, forall_n_ge_N_symbolic_monotone_tail)；依完整明示資料重算；核E absolute error power p趨零且moments有限；finite prefix不足，a.s. probability或其他Lq implications另需假設。"},"difficulty":{"band":"undergraduate_core","level":1,"skills":["Lp收斂"]},"variant":{"family_id":"qf-mod35-lp-epsilon-witness","seed":202611047026,"parameters":{"masses":[[1,2],[1,2]],"coefficients":[1,-2],"shift":2,"p":1,"epsilon":[1,10],"domain":"Finite_atomic_symbolic_Lp_tail","operation":"lp-epsilon-witness","semantic_template":"qf-mod35-lp-epsilon-witness/{\"coefficients\":[1,-2],\"epsilon\":[1,10],\"masses\":[[1,2],[1,2]],\"p\":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-r07-lp-convergence-0027","batch_id":"batch-20261014-advance-20261104-r07-lp-convergence-foundations","language":"zh-Hant","source_mko_ids":["mko-lp-convergence"],"title_zh":"Lp收斂","stem_zh":"同一有限原子probability space、固定整數p大於等於1與symbolic moment tail。操作=lp-epsilon-witness；資料={\"masses\":[[1,2],[1,2]],\"coefficients\":[2,-3],\"shift\":2,\"p\":2,\"epsilon\":[1,11]}。請依 exact_ordered_tuple_declared_by_interface 欄序回答。","answer":{"kind":"expression","value":"(2, 1/11, 7, 13/162, 是, forall_n_ge_N_symbolic_monotone_tail)","explanation_zh":"Wave5第四層核對=(2, 1/11, 7, 13/162, 是, forall_n_ge_N_symbolic_monotone_tail)；依完整明示資料重算；核E absolute error power p趨零且moments有限；finite prefix不足，a.s. probability或其他Lq implications另需假設。"},"difficulty":{"band":"undergraduate_core","level":1,"skills":["Lp收斂"]},"variant":{"family_id":"qf-mod35-lp-epsilon-witness","seed":202611047027,"parameters":{"masses":[[1,2],[1,2]],"coefficients":[2,-3],"shift":2,"p":2,"epsilon":[1,11],"domain":"Finite_atomic_symbolic_Lp_tail","operation":"lp-epsilon-witness","semantic_template":"qf-mod35-lp-epsilon-witness/{\"coefficients\":[2,-3],\"epsilon\":[1,11],\"masses\":[[1,2],[1,2]],\"p\":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-r07-lp-convergence-0028","batch_id":"batch-20261014-advance-20261104-r07-lp-convergence-foundations","language":"zh-Hant","source_mko_ids":["mko-lp-convergence"],"title_zh":"Lp收斂","stem_zh":"同一有限原子probability space、固定整數p大於等於1與symbolic moment tail。操作=lp-epsilon-witness；資料={\"masses\":[[1,2],[1,2]],\"coefficients\":[3,-4],\"shift\":2,\"p\":3,\"epsilon\":[1,12]}。請依 exact_ordered_tuple_declared_by_interface 欄序回答。","answer":{"kind":"expression","value":"(3, 1/12, 7, 91/1458, 是, forall_n_ge_N_symbolic_monotone_tail)","explanation_zh":"Wave5第四層核對=(3, 1/12, 7, 91/1458, 是, forall_n_ge_N_symbolic_monotone_tail)；依完整明示資料重算；核E absolute error power p趨零且moments有限；finite prefix不足，a.s. probability或其他Lq implications另需假設。"},"difficulty":{"band":"undergraduate_core","level":1,"skills":["Lp收斂"]},"variant":{"family_id":"qf-mod35-lp-epsilon-witness","seed":202611047028,"parameters":{"masses":[[1,2],[1,2]],"coefficients":[3,-4],"shift":2,"p":3,"epsilon":[1,12],"domain":"Finite_atomic_symbolic_Lp_tail","operation":"lp-epsilon-witness","semantic_template":"qf-mod35-lp-epsilon-witness/{\"coefficients\":[3,-4],\"epsilon\":[1,12],\"masses\":[[1,2],[1,2]],\"p\":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-r07-lp-convergence-0029","batch_id":"batch-20261014-advance-20261104-r07-lp-convergence-foundations","language":"zh-Hant","source_mko_ids":["mko-lp-convergence"],"title_zh":"Lp收斂","stem_zh":"同一有限原子probability space、固定整數p大於等於1與symbolic moment tail。操作=lp-epsilon-witness；資料={\"masses\":[[1,2],[1,2]],\"coefficients\":[4,-5],\"shift\":2,\"p\":1,\"epsilon\":[1,13]}。請依 exact_ordered_tuple_declared_by_interface 欄序回答。","answer":{"kind":"expression","value":"(1, 1/13, 57, 9/118, 是, forall_n_ge_N_symbolic_monotone_tail)","explanation_zh":"Wave5第四層核對=(1, 1/13, 57, 9/118, 是, forall_n_ge_N_symbolic_monotone_tail)；依完整明示資料重算；核E absolute error power p趨零且moments有限；finite prefix不足，a.s. probability或其他Lq implications另需假設。"},"difficulty":{"band":"undergraduate_core","level":1,"skills":["Lp收斂"]},"variant":{"family_id":"qf-mod35-lp-epsilon-witness","seed":202611047029,"parameters":{"masses":[[1,2],[1,2]],"coefficients":[4,-5],"shift":2,"p":1,"epsilon":[1,13],"domain":"Finite_atomic_symbolic_Lp_tail","operation":"lp-epsilon-witness","semantic_template":"qf-mod35-lp-epsilon-witness/{\"coefficients\":[4,-5],\"epsilon\":[1,13],\"masses\":[[1,2],[1,2]],\"p\":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-r07-lp-convergence-0030","batch_id":"batch-20261014-advance-20261104-r07-lp-convergence-foundations","language":"zh-Hant","source_mko_ids":["mko-lp-convergence"],"title_zh":"Lp收斂","stem_zh":"同一有限原子probability space、固定整數p大於等於1與symbolic moment tail。操作=lp-epsilon-witness；資料={\"masses\":[[1,2],[1,2]],\"coefficients\":[5,-6],\"shift\":2,\"p\":2,\"epsilon\":[1,14]}。請依 exact_ordered_tuple_declared_by_interface 欄序回答。","answer":{"kind":"expression","value":"(2, 1/14, 19, 61/882, 是, forall_n_ge_N_symbolic_monotone_tail)","explanation_zh":"Wave5第四層核對=(2, 1/14, 19, 61/882, 是, forall_n_ge_N_symbolic_monotone_tail)；依完整明示資料重算；核E absolute error power p趨零且moments有限；finite prefix不足，a.s. probability或其他Lq implications另需假設。"},"difficulty":{"band":"undergraduate_core","level":1,"skills":["Lp收斂"]},"variant":{"family_id":"qf-mod35-lp-epsilon-witness","seed":202611047030,"parameters":{"masses":[[1,2],[1,2]],"coefficients":[5,-6],"shift":2,"p":2,"epsilon":[1,14],"domain":"Finite_atomic_symbolic_Lp_tail","operation":"lp-epsilon-witness","semantic_template":"qf-mod35-lp-epsilon-witness/{\"coefficients\":[5,-6],\"epsilon\":[1,14],\"masses\":[[1,2],[1,2]],\"p\":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-r07-lp-convergence-0031","batch_id":"batch-20261014-advance-20261104-r07-lp-convergence-foundations","language":"zh-Hant","source_mko_ids":["mko-lp-convergence"],"title_zh":"Lp收斂","stem_zh":"同一有限原子probability space、固定整數p大於等於1與symbolic moment tail。操作=lp-epsilon-witness；資料={\"masses\":[[1,2],[1,2]],\"coefficients\":[6,-7],\"shift\":2,\"p\":3,\"epsilon\":[1,15]}。請依 exact_ordered_tuple_declared_by_interface 欄序回答。","answer":{"kind":"expression","value":"(3, 1/15, 15, 559/9826, 是, forall_n_ge_N_symbolic_monotone_tail)","explanation_zh":"Wave5第四層核對=(3, 1/15, 15, 559/9826, 是, forall_n_ge_N_symbolic_monotone_tail)；依完整明示資料重算；核E absolute error power p趨零且moments有限；finite prefix不足，a.s. probability或其他Lq implications另需假設。"},"difficulty":{"band":"undergraduate_core","level":1,"skills":["Lp收斂"]},"variant":{"family_id":"qf-mod35-lp-epsilon-witness","seed":202611047031,"parameters":{"masses":[[1,2],[1,2]],"coefficients":[6,-7],"shift":2,"p":3,"epsilon":[1,15],"domain":"Finite_atomic_symbolic_Lp_tail","operation":"lp-epsilon-witness","semantic_template":"qf-mod35-lp-epsilon-witness/{\"coefficients\":[6,-7],\"epsilon\":[1,15],\"masses\":[[1,2],[1,2]],\"p\":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-r07-lp-convergence-0032","batch_id":"batch-20261014-advance-20261104-r07-lp-convergence-foundations","language":"zh-Hant","source_mko_ids":["mko-lp-convergence"],"title_zh":"Lp收斂","stem_zh":"同一有限原子probability space、固定整數p大於等於1與symbolic moment tail。操作=lp-epsilon-witness；資料={\"masses\":[[1,2],[1,2]],\"coefficients\":[7,-8],\"shift\":2,\"p\":1,\"epsilon\":[1,16]}。請依 exact_ordered_tuple_declared_by_interface 欄序回答。","answer":{"kind":"expression","value":"(1, 1/16, 119, 15/242, 是, forall_n_ge_N_symbolic_monotone_tail)","explanation_zh":"Wave5第四層核對=(1, 1/16, 119, 15/242, 是, forall_n_ge_N_symbolic_monotone_tail)；依完整明示資料重算；核E absolute error power p趨零且moments有限；finite prefix不足，a.s. probability或其他Lq implications另需假設。"},"difficulty":{"band":"undergraduate_core","level":1,"skills":["Lp收斂"]},"variant":{"family_id":"qf-mod35-lp-epsilon-witness","seed":202611047032,"parameters":{"masses":[[1,2],[1,2]],"coefficients":[7,-8],"shift":2,"p":1,"epsilon":[1,16],"domain":"Finite_atomic_symbolic_Lp_tail","operation":"lp-epsilon-witness","semantic_template":"qf-mod35-lp-epsilon-witness/{\"coefficients\":[7,-8],\"epsilon\":[1,16],\"masses\":[[1,2],[1,2]],\"p\":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-r07-lp-convergence-0033","batch_id":"batch-20261014-advance-20261104-r07-lp-convergence-foundations","language":"zh-Hant","source_mko_ids":["mko-lp-convergence"],"title_zh":"Lp收斂","stem_zh":"同一有限原子probability space、固定整數p大於等於1與symbolic moment tail。操作=lp-epsilon-witness；資料={\"masses\":[[1,2],[1,2]],\"coefficients\":[8,-9],\"shift\":2,\"p\":2,\"epsilon\":[1,17]}。請依 exact_ordered_tuple_declared_by_interface 欄序回答。","answer":{"kind":"expression","value":"(2, 1/17, 34, 145/2592, 是, forall_n_ge_N_symbolic_monotone_tail)","explanation_zh":"Wave5第四層核對=(2, 1/17, 34, 145/2592, 是, forall_n_ge_N_symbolic_monotone_tail)；依完整明示資料重算；核E absolute error power p趨零且moments有限；finite prefix不足，a.s. probability或其他Lq implications另需假設。"},"difficulty":{"band":"undergraduate_core","level":1,"skills":["Lp收斂"]},"variant":{"family_id":"qf-mod35-lp-epsilon-witness","seed":202611047033,"parameters":{"masses":[[1,2],[1,2]],"coefficients":[8,-9],"shift":2,"p":2,"epsilon":[1,17],"domain":"Finite_atomic_symbolic_Lp_tail","operation":"lp-epsilon-witness","semantic_template":"qf-mod35-lp-epsilon-witness/{\"coefficients\":[8,-9],\"epsilon\":[1,17],\"masses\":[[1,2],[1,2]],\"p\":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-r07-lp-convergence-0034","batch_id":"batch-20261014-advance-20261104-r07-lp-convergence-foundations","language":"zh-Hant","source_mko_ids":["mko-lp-convergence"],"title_zh":"Lp收斂","stem_zh":"同一有限原子probability space、固定整數p大於等於1與symbolic moment tail。操作=lp-epsilon-witness；資料={\"masses\":[[1,2],[1,2]],\"coefficients\":[9,-10],\"shift\":2,\"p\":3,\"epsilon\":[1,18]}。請依 exact_ordered_tuple_declared_by_interface 欄序回答。","answer":{"kind":"expression","value":"(3, 1/18, 23, 1729/31250, 是, forall_n_ge_N_symbolic_monotone_tail)","explanation_zh":"Wave5第四層核對=(3, 1/18, 23, 1729/31250, 是, forall_n_ge_N_symbolic_monotone_tail)；依完整明示資料重算；核E absolute error power p趨零且moments有限；finite prefix不足，a.s. probability或其他Lq implications另需假設。"},"difficulty":{"band":"undergraduate_core","level":2,"skills":["Lp收斂"]},"variant":{"family_id":"qf-mod35-lp-epsilon-witness","seed":202611047034,"parameters":{"masses":[[1,2],[1,2]],"coefficients":[9,-10],"shift":2,"p":3,"epsilon":[1,18],"domain":"Finite_atomic_symbolic_Lp_tail","operation":"lp-epsilon-witness","semantic_template":"qf-mod35-lp-epsilon-witness/{\"coefficients\":[9,-10],\"epsilon\":[1,18],\"masses\":[[1,2],[1,2]],\"p\":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-r07-lp-convergence-0035","batch_id":"batch-20261014-advance-20261104-r07-lp-convergence-foundations","language":"zh-Hant","source_mko_ids":["mko-lp-convergence"],"title_zh":"Lp收斂","stem_zh":"同一有限原子probability space、固定整數p大於等於1與symbolic moment tail。操作=lp-epsilon-witness；資料={\"masses\":[[1,2],[1,2]],\"coefficients\":[10,-11],\"shift\":2,\"p\":1,\"epsilon\":[1,19]}。請依 exact_ordered_tuple_declared_by_interface 欄序回答。","answer":{"kind":"expression","value":"(1, 1/19, 198, 21/400, 是, forall_n_ge_N_symbolic_monotone_tail)","explanation_zh":"Wave5第四層核對=(1, 1/19, 198, 21/400, 是, forall_n_ge_N_symbolic_monotone_tail)；依完整明示資料重算；核E absolute error power p趨零且moments有限；finite prefix不足，a.s. probability或其他Lq implications另需假設。"},"difficulty":{"band":"undergraduate_core","level":2,"skills":["Lp收斂"]},"variant":{"family_id":"qf-mod35-lp-epsilon-witness","seed":202611047035,"parameters":{"masses":[[1,2],[1,2]],"coefficients":[10,-11],"shift":2,"p":1,"epsilon":[1,19],"domain":"Finite_atomic_symbolic_Lp_tail","operation":"lp-epsilon-witness","semantic_template":"qf-mod35-lp-epsilon-witness/{\"coefficients\":[10,-11],\"epsilon\":[1,19],\"masses\":[[1,2],[1,2]],\"p\":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-r07-lp-convergence-0036","batch_id":"batch-20261014-advance-20261104-r07-lp-convergence-foundations","language":"zh-Hant","source_mko_ids":["mko-lp-convergence"],"title_zh":"Lp收斂","stem_zh":"同一有限原子probability space、固定整數p大於等於1與symbolic moment tail。操作=lp-epsilon-witness；資料={\"masses\":[[1,2],[1,2]],\"coefficients\":[11,-12],\"shift\":2,\"p\":2,\"epsilon\":[1,20]}。請依 exact_ordered_tuple_declared_by_interface 欄序回答。","answer":{"kind":"expression","value":"(2, 1/20, 50, 265/5408, 是, forall_n_ge_N_symbolic_monotone_tail)","explanation_zh":"Wave5第四層核對=(2, 1/20, 50, 265/5408, 是, forall_n_ge_N_symbolic_monotone_tail)；依完整明示資料重算；核E absolute error power p趨零且moments有限；finite prefix不足，a.s. probability或其他Lq implications另需假設。"},"difficulty":{"band":"undergraduate_core","level":2,"skills":["Lp收斂"]},"variant":{"family_id":"qf-mod35-lp-epsilon-witness","seed":202611047036,"parameters":{"masses":[[1,2],[1,2]],"coefficients":[11,-12],"shift":2,"p":2,"epsilon":[1,20],"domain":"Finite_atomic_symbolic_Lp_tail","operation":"lp-epsilon-witness","semantic_template":"qf-mod35-lp-epsilon-witness/{\"coefficients\":[11,-12],\"epsilon\":[1,20],\"masses\":[[1,2],[1,2]],\"p\":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-r07-lp-convergence-0037","batch_id":"batch-20261014-advance-20261104-r07-lp-convergence-foundations","language":"zh-Hant","source_mko_ids":["mko-lp-convergence"],"title_zh":"Lp收斂","stem_zh":"同一有限原子probability space、固定整數p大於等於1與symbolic moment tail。操作=lp-epsilon-witness；資料={\"masses\":[[1,2],[1,2]],\"coefficients\":[12,-13],\"shift\":2,\"p\":3,\"epsilon\":[1,21]}。請依 exact_ordered_tuple_declared_by_interface 欄序回答。","answer":{"kind":"expression","value":"(3, 1/21, 33, 157/3430, 是, forall_n_ge_N_symbolic_monotone_tail)","explanation_zh":"Wave5第四層核對=(3, 1/21, 33, 157/3430, 是, forall_n_ge_N_symbolic_monotone_tail)；依完整明示資料重算；核E absolute error power p趨零且moments有限；finite prefix不足，a.s. probability或其他Lq implications另需假設。"},"difficulty":{"band":"undergraduate_core","level":2,"skills":["Lp收斂"]},"variant":{"family_id":"qf-mod35-lp-epsilon-witness","seed":202611047037,"parameters":{"masses":[[1,2],[1,2]],"coefficients":[12,-13],"shift":2,"p":3,"epsilon":[1,21],"domain":"Finite_atomic_symbolic_Lp_tail","operation":"lp-epsilon-witness","semantic_template":"qf-mod35-lp-epsilon-witness/{\"coefficients\":[12,-13],\"epsilon\":[1,21],\"masses\":[[1,2],[1,2]],\"p\":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-r07-lp-convergence-0038","batch_id":"batch-20261014-advance-20261104-r07-lp-convergence-foundations","language":"zh-Hant","source_mko_ids":["mko-lp-convergence"],"title_zh":"Lp收斂","stem_zh":"同一有限原子probability space、固定整數p大於等於1與symbolic moment tail。操作=lp-epsilon-witness；資料={\"masses\":[[1,2],[1,2]],\"coefficients\":[13,-14],\"shift\":2,\"p\":1,\"epsilon\":[1,22]}。請依 exact_ordered_tuple_declared_by_interface 欄序回答。","answer":{"kind":"expression","value":"(1, 1/22, 296, 27/596, 是, forall_n_ge_N_symbolic_monotone_tail)","explanation_zh":"Wave5第四層核對=(1, 1/22, 296, 27/596, 是, forall_n_ge_N_symbolic_monotone_tail)；依完整明示資料重算；核E absolute error power p趨零且moments有限；finite prefix不足，a.s. probability或其他Lq implications另需假設。"},"difficulty":{"band":"undergraduate_core","level":2,"skills":["Lp收斂"]},"variant":{"family_id":"qf-mod35-lp-epsilon-witness","seed":202611047038,"parameters":{"masses":[[1,2],[1,2]],"coefficients":[13,-14],"shift":2,"p":1,"epsilon":[1,22],"domain":"Finite_atomic_symbolic_Lp_tail","operation":"lp-epsilon-witness","semantic_template":"qf-mod35-lp-epsilon-witness/{\"coefficients\":[13,-14],\"epsilon\":[1,22],\"masses\":[[1,2],[1,2]],\"p\":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-r07-lp-convergence-0039","batch_id":"batch-20261014-advance-20261104-r07-lp-convergence-foundations","language":"zh-Hant","source_mko_ids":["mko-lp-convergence"],"title_zh":"Lp收斂","stem_zh":"同一有限原子probability space、固定整數p大於等於1與symbolic moment tail。操作=lp-epsilon-witness；資料={\"masses\":[[1,2],[1,2]],\"coefficients\":[14,-15],\"shift\":2,\"p\":2,\"epsilon\":[1,23]}。請依 exact_ordered_tuple_declared_by_interface 欄序回答。","answer":{"kind":"expression","value":"(2, 1/23, 68, 421/9800, 是, forall_n_ge_N_symbolic_monotone_tail)","explanation_zh":"Wave5第四層核對=(2, 1/23, 68, 421/9800, 是, forall_n_ge_N_symbolic_monotone_tail)；依完整明示資料重算；核E absolute error power p趨零且moments有限；finite prefix不足，a.s. probability或其他Lq implications另需假設。"},"difficulty":{"band":"undergraduate_core","level":2,"skills":["Lp收斂"]},"variant":{"family_id":"qf-mod35-lp-epsilon-witness","seed":202611047039,"parameters":{"masses":[[1,2],[1,2]],"coefficients":[14,-15],"shift":2,"p":2,"epsilon":[1,23],"domain":"Finite_atomic_symbolic_Lp_tail","operation":"lp-epsilon-witness","semantic_template":"qf-mod35-lp-epsilon-witness/{\"coefficients\":[14,-15],\"epsilon\":[1,23],\"masses\":[[1,2],[1,2]],\"p\":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-r07-lp-convergence-0040","batch_id":"batch-20261014-advance-20261104-r07-lp-convergence-foundations","language":"zh-Hant","source_mko_ids":["mko-lp-convergence"],"title_zh":"Lp收斂","stem_zh":"同一有限原子probability space、固定整數p大於等於1與symbolic moment tail。操作=lp-epsilon-witness；資料={\"masses\":[[1,2],[1,2]],\"coefficients\":[15,-16],\"shift\":2,\"p\":3,\"epsilon\":[1,24]}。請依 exact_ordered_tuple_declared_by_interface 欄序回答。","answer":{"kind":"expression","value":"(3, 1/24, 43, 7471/182250, 是, forall_n_ge_N_symbolic_monotone_tail)","explanation_zh":"Wave5第四層核對=(3, 1/24, 43, 7471/182250, 是, forall_n_ge_N_symbolic_monotone_tail)；依完整明示資料重算；核E absolute error power p趨零且moments有限；finite prefix不足，a.s. probability或其他Lq implications另需假設。"},"difficulty":{"band":"undergraduate_core","level":2,"skills":["Lp收斂"]},"variant":{"family_id":"qf-mod35-lp-epsilon-witness","seed":202611047040,"parameters":{"masses":[[1,2],[1,2]],"coefficients":[15,-16],"shift":2,"p":3,"epsilon":[1,24],"domain":"Finite_atomic_symbolic_Lp_tail","operation":"lp-epsilon-witness","semantic_template":"qf-mod35-lp-epsilon-witness/{\"coefficients\":[15,-16],\"epsilon\":[1,24],\"masses\":[[1,2],[1,2]],\"p\":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-r07-lp-convergence-0041","batch_id":"batch-20261014-advance-20261104-r07-lp-convergence-foundations","language":"zh-Hant","source_mko_ids":["mko-lp-convergence"],"title_zh":"Lp收斂","stem_zh":"同一有限原子probability space、固定整數p大於等於1與symbolic moment tail。操作=lp-epsilon-witness；資料={\"masses\":[[1,2],[1,2]],\"coefficients\":[16,-17],\"shift\":2,\"p\":1,\"epsilon\":[1,25]}。請依 exact_ordered_tuple_declared_by_interface 欄序回答。","answer":{"kind":"expression","value":"(1, 1/25, 411, 33/826, 是, forall_n_ge_N_symbolic_monotone_tail)","explanation_zh":"Wave5第四層核對=(1, 1/25, 411, 33/826, 是, forall_n_ge_N_symbolic_monotone_tail)；依完整明示資料重算；核E absolute error power p趨零且moments有限；finite prefix不足，a.s. probability或其他Lq implications另需假設。"},"difficulty":{"band":"undergraduate_core","level":2,"skills":["Lp收斂"]},"variant":{"family_id":"qf-mod35-lp-epsilon-witness","seed":202611047041,"parameters":{"masses":[[1,2],[1,2]],"coefficients":[16,-17],"shift":2,"p":1,"epsilon":[1,25],"domain":"Finite_atomic_symbolic_Lp_tail","operation":"lp-epsilon-witness","semantic_template":"qf-mod35-lp-epsilon-witness/{\"coefficients\":[16,-17],\"epsilon\":[1,25],\"masses\":[[1,2],[1,2]],\"p\":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-r07-lp-convergence-0042","batch_id":"batch-20261014-advance-20261104-r07-lp-convergence-foundations","language":"zh-Hant","source_mko_ids":["mko-lp-convergence"],"title_zh":"Lp收斂","stem_zh":"同一有限原子probability space、固定整數p大於等於1與symbolic moment tail。操作=lp-epsilon-witness；資料={\"masses\":[[1,2],[1,2]],\"coefficients\":[17,-18],\"shift\":2,\"p\":2,\"epsilon\":[1,26]}。請依 exact_ordered_tuple_declared_by_interface 欄序回答。","answer":{"kind":"expression","value":"(2, 1/26, 88, 613/16200, 是, forall_n_ge_N_symbolic_monotone_tail)","explanation_zh":"Wave5第四層核對=(2, 1/26, 88, 613/16200, 是, forall_n_ge_N_symbolic_monotone_tail)；依完整明示資料重算；核E absolute error power p趨零且moments有限；finite prefix不足，a.s. probability或其他Lq implications另需假設。"},"difficulty":{"band":"undergraduate_core","level":2,"skills":["Lp收斂"]},"variant":{"family_id":"qf-mod35-lp-epsilon-witness","seed":202611047042,"parameters":{"masses":[[1,2],[1,2]],"coefficients":[17,-18],"shift":2,"p":2,"epsilon":[1,26],"domain":"Finite_atomic_symbolic_Lp_tail","operation":"lp-epsilon-witness","semantic_template":"qf-mod35-lp-epsilon-witness/{\"coefficients\":[17,-18],\"epsilon\":[1,26],\"masses\":[[1,2],[1,2]],\"p\":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-r07-lp-convergence-0043","batch_id":"batch-20261014-advance-20261104-r07-lp-convergence-foundations","language":"zh-Hant","source_mko_ids":["mko-lp-convergence"],"title_zh":"Lp收斂","stem_zh":"同一有限原子probability space、固定整數p大於等於1與symbolic moment tail。操作=lp-epsilon-witness；資料={\"masses\":[[1,2],[1,2]],\"coefficients\":[18,-19],\"shift\":2,\"p\":3,\"epsilon\":[1,27]}。請依 exact_ordered_tuple_declared_by_interface 欄序回答。","answer":{"kind":"expression","value":"(3, 1/27, 54, 37/1024, 是, forall_n_ge_N_symbolic_monotone_tail)","explanation_zh":"Wave5第四層核對=(3, 1/27, 54, 37/1024, 是, forall_n_ge_N_symbolic_monotone_tail)；依完整明示資料重算；核E absolute error power p趨零且moments有限；finite prefix不足，a.s. probability或其他Lq implications另需假設。"},"difficulty":{"band":"undergraduate_core","level":3,"skills":["Lp收斂"]},"variant":{"family_id":"qf-mod35-lp-epsilon-witness","seed":202611047043,"parameters":{"masses":[[1,2],[1,2]],"coefficients":[18,-19],"shift":2,"p":3,"epsilon":[1,27],"domain":"Finite_atomic_symbolic_Lp_tail","operation":"lp-epsilon-witness","semantic_template":"qf-mod35-lp-epsilon-witness/{\"coefficients\":[18,-19],\"epsilon\":[1,27],\"masses\":[[1,2],[1,2]],\"p\":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-r07-lp-convergence-0044","batch_id":"batch-20261014-advance-20261104-r07-lp-convergence-foundations","language":"zh-Hant","source_mko_ids":["mko-lp-convergence"],"title_zh":"Lp收斂","stem_zh":"同一有限原子probability space、固定整數p大於等於1與symbolic moment tail。操作=lp-epsilon-witness；資料={\"masses\":[[1,2],[1,2]],\"coefficients\":[19,-20],\"shift\":2,\"p\":1,\"epsilon\":[1,28]}。請依 exact_ordered_tuple_declared_by_interface 欄序回答。","answer":{"kind":"expression","value":"(1, 1/28, 545, 39/1094, 是, forall_n_ge_N_symbolic_monotone_tail)","explanation_zh":"Wave5第四層核對=(1, 1/28, 545, 39/1094, 是, forall_n_ge_N_symbolic_monotone_tail)；依完整明示資料重算；核E absolute error power p趨零且moments有限；finite prefix不足，a.s. probability或其他Lq implications另需假設。"},"difficulty":{"band":"undergraduate_core","level":3,"skills":["Lp收斂"]},"variant":{"family_id":"qf-mod35-lp-epsilon-witness","seed":202611047044,"parameters":{"masses":[[1,2],[1,2]],"coefficients":[19,-20],"shift":2,"p":1,"epsilon":[1,28],"domain":"Finite_atomic_symbolic_Lp_tail","operation":"lp-epsilon-witness","semantic_template":"qf-mod35-lp-epsilon-witness/{\"coefficients\":[19,-20],\"epsilon\":[1,28],\"masses\":[[1,2],[1,2]],\"p\":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-r07-lp-convergence-0045","batch_id":"batch-20261014-advance-20261104-r07-lp-convergence-foundations","language":"zh-Hant","source_mko_ids":["mko-lp-convergence"],"title_zh":"Lp收斂","stem_zh":"同一有限原子probability space、固定整數p大於等於1與symbolic moment tail。操作=lp-epsilon-witness；資料={\"masses\":[[1,2],[1,2]],\"coefficients\":[20,-21],\"shift\":2,\"p\":2,\"epsilon\":[1,29]}。請依 exact_ordered_tuple_declared_by_interface 欄序回答。","answer":{"kind":"expression","value":"(2, 1/29, 109, 841/24642, 是, forall_n_ge_N_symbolic_monotone_tail)","explanation_zh":"Wave5第四層核對=(2, 1/29, 109, 841/24642, 是, forall_n_ge_N_symbolic_monotone_tail)；依完整明示資料重算；核E absolute error power p趨零且moments有限；finite prefix不足，a.s. probability或其他Lq implications另需假設。"},"difficulty":{"band":"undergraduate_core","level":3,"skills":["Lp收斂"]},"variant":{"family_id":"qf-mod35-lp-epsilon-witness","seed":202611047045,"parameters":{"masses":[[1,2],[1,2]],"coefficients":[20,-21],"shift":2,"p":2,"epsilon":[1,29],"domain":"Finite_atomic_symbolic_Lp_tail","operation":"lp-epsilon-witness","semantic_template":"qf-mod35-lp-epsilon-witness/{\"coefficients\":[20,-21],\"epsilon\":[1,29],\"masses\":[[1,2],[1,2]],\"p\":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-r07-lp-convergence-0046","batch_id":"batch-20261014-advance-20261104-r07-lp-convergence-foundations","language":"zh-Hant","source_mko_ids":["mko-lp-convergence"],"title_zh":"Lp收斂","stem_zh":"同一有限原子probability space、固定整數p大於等於1與symbolic moment tail。操作=lp-epsilon-witness；資料={\"masses\":[[1,2],[1,2]],\"coefficients\":[21,-22],\"shift\":2,\"p\":3,\"epsilon\":[1,30]}。請依 exact_ordered_tuple_declared_by_interface 欄序回答。","answer":{"kind":"expression","value":"(3, 1/30, 65, 19909/601526, 是, forall_n_ge_N_symbolic_monotone_tail)","explanation_zh":"Wave5第四層核對=(3, 1/30, 65, 19909/601526, 是, forall_n_ge_N_symbolic_monotone_tail)；依完整明示資料重算；核E absolute error power p趨零且moments有限；finite prefix不足，a.s. probability或其他Lq implications另需假設。"},"difficulty":{"band":"undergraduate_core","level":3,"skills":["Lp收斂"]},"variant":{"family_id":"qf-mod35-lp-epsilon-witness","seed":202611047046,"parameters":{"masses":[[1,2],[1,2]],"coefficients":[21,-22],"shift":2,"p":3,"epsilon":[1,30],"domain":"Finite_atomic_symbolic_Lp_tail","operation":"lp-epsilon-witness","semantic_template":"qf-mod35-lp-epsilon-witness/{\"coefficients\":[21,-22],\"epsilon\":[1,30],\"masses\":[[1,2],[1,2]],\"p\":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-r07-lp-convergence-0047","batch_id":"batch-20261014-advance-20261104-r07-lp-convergence-foundations","language":"zh-Hant","source_mko_ids":["mko-lp-convergence"],"title_zh":"Lp收斂","stem_zh":"同一有限原子probability space、固定整數p大於等於1與symbolic moment tail。操作=lp-epsilon-witness；資料={\"masses\":[[1,2],[1,2]],\"coefficients\":[22,-23],\"shift\":2,\"p\":1,\"epsilon\":[1,31]}。請依 exact_ordered_tuple_declared_by_interface 欄序回答。","answer":{"kind":"expression","value":"(1, 1/31, 696, 45/1396, 是, forall_n_ge_N_symbolic_monotone_tail)","explanation_zh":"Wave5第四層核對=(1, 1/31, 696, 45/1396, 是, forall_n_ge_N_symbolic_monotone_tail)；依完整明示資料重算；核E absolute error power p趨零且moments有限；finite prefix不足，a.s. probability或其他Lq implications另需假設。"},"difficulty":{"band":"undergraduate_core","level":3,"skills":["Lp收斂"]},"variant":{"family_id":"qf-mod35-lp-epsilon-witness","seed":202611047047,"parameters":{"masses":[[1,2],[1,2]],"coefficients":[22,-23],"shift":2,"p":1,"epsilon":[1,31],"domain":"Finite_atomic_symbolic_Lp_tail","operation":"lp-epsilon-witness","semantic_template":"qf-mod35-lp-epsilon-witness/{\"coefficients\":[22,-23],\"epsilon\":[1,31],\"masses\":[[1,2],[1,2]],\"p\":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-r07-lp-convergence-0048","batch_id":"batch-20261014-advance-20261104-r07-lp-convergence-foundations","language":"zh-Hant","source_mko_ids":["mko-lp-convergence"],"title_zh":"Lp收斂","stem_zh":"同一有限原子probability space、固定整數p大於等於1與symbolic moment tail。操作=lp-epsilon-witness；資料={\"masses\":[[1,2],[1,2]],\"coefficients\":[23,-24],\"shift\":2,\"p\":2,\"epsilon\":[1,32]}。請依 exact_ordered_tuple_declared_by_interface 欄序回答。","answer":{"kind":"expression","value":"(2, 1/32, 131, 1105/35378, 是, forall_n_ge_N_symbolic_monotone_tail)","explanation_zh":"Wave5第四層核對=(2, 1/32, 131, 1105/35378, 是, forall_n_ge_N_symbolic_monotone_tail)；依完整明示資料重算；核E absolute error power p趨零且moments有限；finite prefix不足，a.s. probability或其他Lq implications另需假設。"},"difficulty":{"band":"undergraduate_core","level":3,"skills":["Lp收斂"]},"variant":{"family_id":"qf-mod35-lp-epsilon-witness","seed":202611047048,"parameters":{"masses":[[1,2],[1,2]],"coefficients":[23,-24],"shift":2,"p":2,"epsilon":[1,32],"domain":"Finite_atomic_symbolic_Lp_tail","operation":"lp-epsilon-witness","semantic_template":"qf-mod35-lp-epsilon-witness/{\"coefficients\":[23,-24],\"epsilon\":[1,32],\"masses\":[[1,2],[1,2]],\"p\":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-r07-lp-convergence-0049","batch_id":"batch-20261014-advance-20261104-r07-lp-convergence-foundations","language":"zh-Hant","source_mko_ids":["mko-lp-convergence"],"title_zh":"Lp收斂","stem_zh":"同一有限原子probability space、固定整數p大於等於1與symbolic moment tail。操作=lp-epsilon-witness；資料={\"masses\":[[1,2],[1,2]],\"coefficients\":[24,-25],\"shift\":2,\"p\":3,\"epsilon\":[1,33]}。請依 exact_ordered_tuple_declared_by_interface 欄序回答。","answer":{"kind":"expression","value":"(3, 1/33, 77, 29449/986078, 是, forall_n_ge_N_symbolic_monotone_tail)","explanation_zh":"Wave5第四層核對=(3, 1/33, 77, 29449/986078, 是, forall_n_ge_N_symbolic_monotone_tail)；依完整明示資料重算；核E absolute error power p趨零且moments有限；finite prefix不足，a.s. probability或其他Lq implications另需假設。"},"difficulty":{"band":"undergraduate_core","level":3,"skills":["Lp收斂"]},"variant":{"family_id":"qf-mod35-lp-epsilon-witness","seed":202611047049,"parameters":{"masses":[[1,2],[1,2]],"coefficients":[24,-25],"shift":2,"p":3,"epsilon":[1,33],"domain":"Finite_atomic_symbolic_Lp_tail","operation":"lp-epsilon-witness","semantic_template":"qf-mod35-lp-epsilon-witness/{\"coefficients\":[24,-25],\"epsilon\":[1,33],\"masses\":[[1,2],[1,2]],\"p\":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-r07-lp-convergence-0050","batch_id":"batch-20261014-advance-20261104-r07-lp-convergence-foundations","language":"zh-Hant","source_mko_ids":["mko-lp-convergence"],"title_zh":"Lp收斂","stem_zh":"同一有限原子probability space、固定整數p大於等於1與symbolic moment tail。操作=lp-epsilon-witness；資料={\"masses\":[[1,2],[1,2]],\"coefficients\":[25,-26],\"shift\":2,\"p\":1,\"epsilon\":[1,34]}。請依 exact_ordered_tuple_declared_by_interface 欄序回答。","answer":{"kind":"expression","value":"(1, 1/34, 866, 51/1736, 是, forall_n_ge_N_symbolic_monotone_tail)","explanation_zh":"Wave5第四層核對=(1, 1/34, 866, 51/1736, 是, forall_n_ge_N_symbolic_monotone_tail)；依完整明示資料重算；核E absolute error power p趨零且moments有限；finite prefix不足，a.s. probability或其他Lq implications另需假設。"},"difficulty":{"band":"undergraduate_core","level":3,"skills":["Lp收斂"]},"variant":{"family_id":"qf-mod35-lp-epsilon-witness","seed":202611047050,"parameters":{"masses":[[1,2],[1,2]],"coefficients":[25,-26],"shift":2,"p":1,"epsilon":[1,34],"domain":"Finite_atomic_symbolic_Lp_tail","operation":"lp-epsilon-witness","semantic_template":"qf-mod35-lp-epsilon-witness/{\"coefficients\":[25,-26],\"epsilon\":[1,34],\"masses\":[[1,2],[1,2]],\"p\":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-r07-lp-convergence-0051","batch_id":"batch-20261014-advance-20261104-r07-lp-convergence-foundations","language":"zh-Hant","source_mko_ids":["mko-lp-convergence"],"title_zh":"Lp收斂","stem_zh":"同一有限原子probability space、固定整數p大於等於1與symbolic moment tail。操作=lp-qualification；資料={\"masses\":[[1,2],[1,2]],\"coefficients\":[1,-2],\"shift\":2,\"p\":1}。請依 exact_ordered_tuple_declared_by_interface 欄序回答。","answer":{"kind":"expression","value":"(1, [1/2, 1/2], [1, -2], 2, 是, common_probability_space_and_finite_integer_p_moments)","explanation_zh":"Wave5第四層核對=(1, [1/2, 1/2], [1, -2], 2, 是, common_probability_space_and_finite_integer_p_moments)；依完整明示資料重算；核E absolute error power p趨零且moments有限；finite prefix不足，a.s. probability或其他Lq implications另需假設。"},"difficulty":{"band":"undergraduate_core","level":1,"skills":["Lp收斂"]},"variant":{"family_id":"qf-mod35-lp-qualification","seed":202611047051,"parameters":{"masses":[[1,2],[1,2]],"coefficients":[1,-2],"shift":2,"p":1,"domain":"Finite_atomic_symbolic_Lp_tail","operation":"lp-qualification","semantic_template":"qf-mod35-lp-qualification/{\"coefficients\":[1,-2],\"masses\":[[1,2],[1,2]],\"p\":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-r07-lp-convergence-0052","batch_id":"batch-20261014-advance-20261104-r07-lp-convergence-foundations","language":"zh-Hant","source_mko_ids":["mko-lp-convergence"],"title_zh":"Lp收斂","stem_zh":"同一有限原子probability space、固定整數p大於等於1與symbolic moment tail。操作=lp-qualification；資料={\"masses\":[[1,2],[1,2]],\"coefficients\":[2,-3],\"shift\":2,\"p\":2}。請依 exact_ordered_tuple_declared_by_interface 欄序回答。","answer":{"kind":"expression","value":"(2, [1/2, 1/2], [2, -3], 2, 是, common_probability_space_and_finite_integer_p_moments)","explanation_zh":"Wave5第四層核對=(2, [1/2, 1/2], [2, -3], 2, 是, common_probability_space_and_finite_integer_p_moments)；依完整明示資料重算；核E absolute error power p趨零且moments有限；finite prefix不足，a.s. probability或其他Lq implications另需假設。"},"difficulty":{"band":"undergraduate_core","level":1,"skills":["Lp收斂"]},"variant":{"family_id":"qf-mod35-lp-qualification","seed":202611047052,"parameters":{"masses":[[1,2],[1,2]],"coefficients":[2,-3],"shift":2,"p":2,"domain":"Finite_atomic_symbolic_Lp_tail","operation":"lp-qualification","semantic_template":"qf-mod35-lp-qualification/{\"coefficients\":[2,-3],\"masses\":[[1,2],[1,2]],\"p\":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-r07-lp-convergence-0053","batch_id":"batch-20261014-advance-20261104-r07-lp-convergence-foundations","language":"zh-Hant","source_mko_ids":["mko-lp-convergence"],"title_zh":"Lp收斂","stem_zh":"同一有限原子probability space、固定整數p大於等於1與symbolic moment tail。操作=lp-qualification；資料={\"masses\":[[1,2],[1,2]],\"coefficients\":[3,-4],\"shift\":2,\"p\":3}。請依 exact_ordered_tuple_declared_by_interface 欄序回答。","answer":{"kind":"expression","value":"(3, [1/2, 1/2], [3, -4], 2, 是, common_probability_space_and_finite_integer_p_moments)","explanation_zh":"Wave5第四層核對=(3, [1/2, 1/2], [3, -4], 2, 是, common_probability_space_and_finite_integer_p_moments)；依完整明示資料重算；核E absolute error power p趨零且moments有限；finite prefix不足，a.s. probability或其他Lq implications另需假設。"},"difficulty":{"band":"undergraduate_core","level":1,"skills":["Lp收斂"]},"variant":{"family_id":"qf-mod35-lp-qualification","seed":202611047053,"parameters":{"masses":[[1,2],[1,2]],"coefficients":[3,-4],"shift":2,"p":3,"domain":"Finite_atomic_symbolic_Lp_tail","operation":"lp-qualification","semantic_template":"qf-mod35-lp-qualification/{\"coefficients\":[3,-4],\"masses\":[[1,2],[1,2]],\"p\":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-r07-lp-convergence-0054","batch_id":"batch-20261014-advance-20261104-r07-lp-convergence-foundations","language":"zh-Hant","source_mko_ids":["mko-lp-convergence"],"title_zh":"Lp收斂","stem_zh":"同一有限原子probability space、固定整數p大於等於1與symbolic moment tail。操作=lp-qualification；資料={\"masses\":[[1,2],[1,2]],\"coefficients\":[4,-5],\"shift\":2,\"p\":1}。請依 exact_ordered_tuple_declared_by_interface 欄序回答。","answer":{"kind":"expression","value":"(1, [1/2, 1/2], [4, -5], 2, 是, common_probability_space_and_finite_integer_p_moments)","explanation_zh":"Wave5第四層核對=(1, [1/2, 1/2], [4, -5], 2, 是, common_probability_space_and_finite_integer_p_moments)；依完整明示資料重算；核E absolute error power p趨零且moments有限；finite prefix不足，a.s. probability或其他Lq implications另需假設。"},"difficulty":{"band":"undergraduate_core","level":1,"skills":["Lp收斂"]},"variant":{"family_id":"qf-mod35-lp-qualification","seed":202611047054,"parameters":{"masses":[[1,2],[1,2]],"coefficients":[4,-5],"shift":2,"p":1,"domain":"Finite_atomic_symbolic_Lp_tail","operation":"lp-qualification","semantic_template":"qf-mod35-lp-qualification/{\"coefficients\":[4,-5],\"masses\":[[1,2],[1,2]],\"p\":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-r07-lp-convergence-0055","batch_id":"batch-20261014-advance-20261104-r07-lp-convergence-foundations","language":"zh-Hant","source_mko_ids":["mko-lp-convergence"],"title_zh":"Lp收斂","stem_zh":"同一有限原子probability space、固定整數p大於等於1與symbolic moment tail。操作=lp-qualification；資料={\"masses\":[[1,2],[1,2]],\"coefficients\":[5,-6],\"shift\":2,\"p\":2}。請依 exact_ordered_tuple_declared_by_interface 欄序回答。","answer":{"kind":"expression","value":"(2, [1/2, 1/2], [5, -6], 2, 是, common_probability_space_and_finite_integer_p_moments)","explanation_zh":"Wave5第四層核對=(2, [1/2, 1/2], [5, -6], 2, 是, common_probability_space_and_finite_integer_p_moments)；依完整明示資料重算；核E absolute error power p趨零且moments有限；finite prefix不足，a.s. probability或其他Lq implications另需假設。"},"difficulty":{"band":"undergraduate_core","level":1,"skills":["Lp收斂"]},"variant":{"family_id":"qf-mod35-lp-qualification","seed":202611047055,"parameters":{"masses":[[1,2],[1,2]],"coefficients":[5,-6],"shift":2,"p":2,"domain":"Finite_atomic_symbolic_Lp_tail","operation":"lp-qualification","semantic_template":"qf-mod35-lp-qualification/{\"coefficients\":[5,-6],\"masses\":[[1,2],[1,2]],\"p\":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-r07-lp-convergence-0056","batch_id":"batch-20261014-advance-20261104-r07-lp-convergence-foundations","language":"zh-Hant","source_mko_ids":["mko-lp-convergence"],"title_zh":"Lp收斂","stem_zh":"同一有限原子probability space、固定整數p大於等於1與symbolic moment tail。操作=lp-qualification；資料={\"masses\":[[1,2],[1,2]],\"coefficients\":[6,-7],\"shift\":2,\"p\":3}。請依 exact_ordered_tuple_declared_by_interface 欄序回答。","answer":{"kind":"expression","value":"(3, [1/2, 1/2], [6, -7], 2, 是, common_probability_space_and_finite_integer_p_moments)","explanation_zh":"Wave5第四層核對=(3, [1/2, 1/2], [6, -7], 2, 是, common_probability_space_and_finite_integer_p_moments)；依完整明示資料重算；核E absolute error power p趨零且moments有限；finite prefix不足，a.s. probability或其他Lq implications另需假設。"},"difficulty":{"band":"undergraduate_core","level":1,"skills":["Lp收斂"]},"variant":{"family_id":"qf-mod35-lp-qualification","seed":202611047056,"parameters":{"masses":[[1,2],[1,2]],"coefficients":[6,-7],"shift":2,"p":3,"domain":"Finite_atomic_symbolic_Lp_tail","operation":"lp-qualification","semantic_template":"qf-mod35-lp-qualification/{\"coefficients\":[6,-7],\"masses\":[[1,2],[1,2]],\"p\":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-r07-lp-convergence-0057","batch_id":"batch-20261014-advance-20261104-r07-lp-convergence-foundations","language":"zh-Hant","source_mko_ids":["mko-lp-convergence"],"title_zh":"Lp收斂","stem_zh":"同一有限原子probability space、固定整數p大於等於1與symbolic moment tail。操作=lp-qualification；資料={\"masses\":[[1,2],[1,2]],\"coefficients\":[7,-8],\"shift\":2,\"p\":1}。請依 exact_ordered_tuple_declared_by_interface 欄序回答。","answer":{"kind":"expression","value":"(1, [1/2, 1/2], [7, -8], 2, 是, common_probability_space_and_finite_integer_p_moments)","explanation_zh":"Wave5第四層核對=(1, [1/2, 1/2], [7, -8], 2, 是, common_probability_space_and_finite_integer_p_moments)；依完整明示資料重算；核E absolute error power p趨零且moments有限；finite prefix不足，a.s. probability或其他Lq implications另需假設。"},"difficulty":{"band":"undergraduate_core","level":1,"skills":["Lp收斂"]},"variant":{"family_id":"qf-mod35-lp-qualification","seed":202611047057,"parameters":{"masses":[[1,2],[1,2]],"coefficients":[7,-8],"shift":2,"p":1,"domain":"Finite_atomic_symbolic_Lp_tail","operation":"lp-qualification","semantic_template":"qf-mod35-lp-qualification/{\"coefficients\":[7,-8],\"masses\":[[1,2],[1,2]],\"p\":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-r07-lp-convergence-0058","batch_id":"batch-20261014-advance-20261104-r07-lp-convergence-foundations","language":"zh-Hant","source_mko_ids":["mko-lp-convergence"],"title_zh":"Lp收斂","stem_zh":"同一有限原子probability space、固定整數p大於等於1與symbolic moment tail。操作=lp-qualification；資料={\"masses\":[[1,2],[1,2]],\"coefficients\":[8,-9],\"shift\":2,\"p\":2}。請依 exact_ordered_tuple_declared_by_interface 欄序回答。","answer":{"kind":"expression","value":"(2, [1/2, 1/2], [8, -9], 2, 是, common_probability_space_and_finite_integer_p_moments)","explanation_zh":"Wave5第四層核對=(2, [1/2, 1/2], [8, -9], 2, 是, common_probability_space_and_finite_integer_p_moments)；依完整明示資料重算；核E absolute error power p趨零且moments有限；finite prefix不足，a.s. probability或其他Lq implications另需假設。"},"difficulty":{"band":"undergraduate_core","level":1,"skills":["Lp收斂"]},"variant":{"family_id":"qf-mod35-lp-qualification","seed":202611047058,"parameters":{"masses":[[1,2],[1,2]],"coefficients":[8,-9],"shift":2,"p":2,"domain":"Finite_atomic_symbolic_Lp_tail","operation":"lp-qualification","semantic_template":"qf-mod35-lp-qualification/{\"coefficients\":[8,-9],\"masses\":[[1,2],[1,2]],\"p\":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-r07-lp-convergence-0059","batch_id":"batch-20261014-advance-20261104-r07-lp-convergence-foundations","language":"zh-Hant","source_mko_ids":["mko-lp-convergence"],"title_zh":"Lp收斂","stem_zh":"同一有限原子probability space、固定整數p大於等於1與symbolic moment tail。操作=lp-qualification；資料={\"masses\":[[1,2],[1,2]],\"coefficients\":[9,-10],\"shift\":2,\"p\":3}。請依 exact_ordered_tuple_declared_by_interface 欄序回答。","answer":{"kind":"expression","value":"(3, [1/2, 1/2], [9, -10], 2, 是, common_probability_space_and_finite_integer_p_moments)","explanation_zh":"Wave5第四層核對=(3, [1/2, 1/2], [9, -10], 2, 是, common_probability_space_and_finite_integer_p_moments)；依完整明示資料重算；核E absolute error power p趨零且moments有限；finite prefix不足，a.s. probability或其他Lq implications另需假設。"},"difficulty":{"band":"undergraduate_core","level":2,"skills":["Lp收斂"]},"variant":{"family_id":"qf-mod35-lp-qualification","seed":202611047059,"parameters":{"masses":[[1,2],[1,2]],"coefficients":[9,-10],"shift":2,"p":3,"domain":"Finite_atomic_symbolic_Lp_tail","operation":"lp-qualification","semantic_template":"qf-mod35-lp-qualification/{\"coefficients\":[9,-10],\"masses\":[[1,2],[1,2]],\"p\":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-r07-lp-convergence-0060","batch_id":"batch-20261014-advance-20261104-r07-lp-convergence-foundations","language":"zh-Hant","source_mko_ids":["mko-lp-convergence"],"title_zh":"Lp收斂","stem_zh":"同一有限原子probability space、固定整數p大於等於1與symbolic moment tail。操作=lp-qualification；資料={\"masses\":[[1,2],[1,2]],\"coefficients\":[10,-11],\"shift\":2,\"p\":1}。請依 exact_ordered_tuple_declared_by_interface 欄序回答。","answer":{"kind":"expression","value":"(1, [1/2, 1/2], [10, -11], 2, 是, common_probability_space_and_finite_integer_p_moments)","explanation_zh":"Wave5第四層核對=(1, [1/2, 1/2], [10, -11], 2, 是, common_probability_space_and_finite_integer_p_moments)；依完整明示資料重算；核E absolute error power p趨零且moments有限；finite prefix不足，a.s. probability或其他Lq implications另需假設。"},"difficulty":{"band":"undergraduate_core","level":2,"skills":["Lp收斂"]},"variant":{"family_id":"qf-mod35-lp-qualification","seed":202611047060,"parameters":{"masses":[[1,2],[1,2]],"coefficients":[10,-11],"shift":2,"p":1,"domain":"Finite_atomic_symbolic_Lp_tail","operation":"lp-qualification","semantic_template":"qf-mod35-lp-qualification/{\"coefficients\":[10,-11],\"masses\":[[1,2],[1,2]],\"p\":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-r07-lp-convergence-0061","batch_id":"batch-20261014-advance-20261104-r07-lp-convergence-foundations","language":"zh-Hant","source_mko_ids":["mko-lp-convergence"],"title_zh":"Lp收斂","stem_zh":"同一有限原子probability space、固定整數p大於等於1與symbolic moment tail。操作=lp-qualification；資料={\"masses\":[[1,2],[1,2]],\"coefficients\":[11,-12],\"shift\":2,\"p\":2}。請依 exact_ordered_tuple_declared_by_interface 欄序回答。","answer":{"kind":"expression","value":"(2, [1/2, 1/2], [11, -12], 2, 是, common_probability_space_and_finite_integer_p_moments)","explanation_zh":"Wave5第四層核對=(2, [1/2, 1/2], [11, -12], 2, 是, common_probability_space_and_finite_integer_p_moments)；依完整明示資料重算；核E absolute error power p趨零且moments有限；finite prefix不足，a.s. probability或其他Lq implications另需假設。"},"difficulty":{"band":"undergraduate_core","level":2,"skills":["Lp收斂"]},"variant":{"family_id":"qf-mod35-lp-qualification","seed":202611047061,"parameters":{"masses":[[1,2],[1,2]],"coefficients":[11,-12],"shift":2,"p":2,"domain":"Finite_atomic_symbolic_Lp_tail","operation":"lp-qualification","semantic_template":"qf-mod35-lp-qualification/{\"coefficients\":[11,-12],\"masses\":[[1,2],[1,2]],\"p\":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-r07-lp-convergence-0062","batch_id":"batch-20261014-advance-20261104-r07-lp-convergence-foundations","language":"zh-Hant","source_mko_ids":["mko-lp-convergence"],"title_zh":"Lp收斂","stem_zh":"同一有限原子probability space、固定整數p大於等於1與symbolic moment tail。操作=lp-qualification；資料={\"masses\":[[1,2],[1,2]],\"coefficients\":[12,-13],\"shift\":2,\"p\":3}。請依 exact_ordered_tuple_declared_by_interface 欄序回答。","answer":{"kind":"expression","value":"(3, [1/2, 1/2], [12, -13], 2, 是, common_probability_space_and_finite_integer_p_moments)","explanation_zh":"Wave5第四層核對=(3, [1/2, 1/2], [12, -13], 2, 是, common_probability_space_and_finite_integer_p_moments)；依完整明示資料重算；核E absolute error power p趨零且moments有限；finite prefix不足，a.s. probability或其他Lq implications另需假設。"},"difficulty":{"band":"undergraduate_core","level":2,"skills":["Lp收斂"]},"variant":{"family_id":"qf-mod35-lp-qualification","seed":202611047062,"parameters":{"masses":[[1,2],[1,2]],"coefficients":[12,-13],"shift":2,"p":3,"domain":"Finite_atomic_symbolic_Lp_tail","operation":"lp-qualification","semantic_template":"qf-mod35-lp-qualification/{\"coefficients\":[12,-13],\"masses\":[[1,2],[1,2]],\"p\":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-r07-lp-convergence-0063","batch_id":"batch-20261014-advance-20261104-r07-lp-convergence-foundations","language":"zh-Hant","source_mko_ids":["mko-lp-convergence"],"title_zh":"Lp收斂","stem_zh":"同一有限原子probability space、固定整數p大於等於1與symbolic moment tail。操作=lp-qualification；資料={\"masses\":[[1,2],[1,2]],\"coefficients\":[13,-14],\"shift\":2,\"p\":1}。請依 exact_ordered_tuple_declared_by_interface 欄序回答。","answer":{"kind":"expression","value":"(1, [1/2, 1/2], [13, -14], 2, 是, common_probability_space_and_finite_integer_p_moments)","explanation_zh":"Wave5第四層核對=(1, [1/2, 1/2], [13, -14], 2, 是, common_probability_space_and_finite_integer_p_moments)；依完整明示資料重算；核E absolute error power p趨零且moments有限；finite prefix不足，a.s. probability或其他Lq implications另需假設。"},"difficulty":{"band":"undergraduate_core","level":2,"skills":["Lp收斂"]},"variant":{"family_id":"qf-mod35-lp-qualification","seed":202611047063,"parameters":{"masses":[[1,2],[1,2]],"coefficients":[13,-14],"shift":2,"p":1,"domain":"Finite_atomic_symbolic_Lp_tail","operation":"lp-qualification","semantic_template":"qf-mod35-lp-qualification/{\"coefficients\":[13,-14],\"masses\":[[1,2],[1,2]],\"p\":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-r07-lp-convergence-0064","batch_id":"batch-20261014-advance-20261104-r07-lp-convergence-foundations","language":"zh-Hant","source_mko_ids":["mko-lp-convergence"],"title_zh":"Lp收斂","stem_zh":"同一有限原子probability space、固定整數p大於等於1與symbolic moment tail。操作=lp-qualification；資料={\"masses\":[[1,2],[1,2]],\"coefficients\":[14,-15],\"shift\":2,\"p\":2}。請依 exact_ordered_tuple_declared_by_interface 欄序回答。","answer":{"kind":"expression","value":"(2, [1/2, 1/2], [14, -15], 2, 是, common_probability_space_and_finite_integer_p_moments)","explanation_zh":"Wave5第四層核對=(2, [1/2, 1/2], [14, -15], 2, 是, common_probability_space_and_finite_integer_p_moments)；依完整明示資料重算；核E absolute error power p趨零且moments有限；finite prefix不足，a.s. probability或其他Lq implications另需假設。"},"difficulty":{"band":"undergraduate_core","level":2,"skills":["Lp收斂"]},"variant":{"family_id":"qf-mod35-lp-qualification","seed":202611047064,"parameters":{"masses":[[1,2],[1,2]],"coefficients":[14,-15],"shift":2,"p":2,"domain":"Finite_atomic_symbolic_Lp_tail","operation":"lp-qualification","semantic_template":"qf-mod35-lp-qualification/{\"coefficients\":[14,-15],\"masses\":[[1,2],[1,2]],\"p\":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-r07-lp-convergence-0065","batch_id":"batch-20261014-advance-20261104-r07-lp-convergence-foundations","language":"zh-Hant","source_mko_ids":["mko-lp-convergence"],"title_zh":"Lp收斂","stem_zh":"同一有限原子probability space、固定整數p大於等於1與symbolic moment tail。操作=lp-qualification；資料={\"masses\":[[1,2],[1,2]],\"coefficients\":[15,-16],\"shift\":2,\"p\":3}。請依 exact_ordered_tuple_declared_by_interface 欄序回答。","answer":{"kind":"expression","value":"(3, [1/2, 1/2], [15, -16], 2, 是, common_probability_space_and_finite_integer_p_moments)","explanation_zh":"Wave5第四層核對=(3, [1/2, 1/2], [15, -16], 2, 是, common_probability_space_and_finite_integer_p_moments)；依完整明示資料重算；核E absolute error power p趨零且moments有限；finite prefix不足，a.s. probability或其他Lq implications另需假設。"},"difficulty":{"band":"undergraduate_core","level":2,"skills":["Lp收斂"]},"variant":{"family_id":"qf-mod35-lp-qualification","seed":202611047065,"parameters":{"masses":[[1,2],[1,2]],"coefficients":[15,-16],"shift":2,"p":3,"domain":"Finite_atomic_symbolic_Lp_tail","operation":"lp-qualification","semantic_template":"qf-mod35-lp-qualification/{\"coefficients\":[15,-16],\"masses\":[[1,2],[1,2]],\"p\":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-r07-lp-convergence-0066","batch_id":"batch-20261014-advance-20261104-r07-lp-convergence-foundations","language":"zh-Hant","source_mko_ids":["mko-lp-convergence"],"title_zh":"Lp收斂","stem_zh":"同一有限原子probability space、固定整數p大於等於1與symbolic moment tail。操作=lp-qualification；資料={\"masses\":[[1,2],[1,2]],\"coefficients\":[16,-17],\"shift\":2,\"p\":1}。請依 exact_ordered_tuple_declared_by_interface 欄序回答。","answer":{"kind":"expression","value":"(1, [1/2, 1/2], [16, -17], 2, 是, common_probability_space_and_finite_integer_p_moments)","explanation_zh":"Wave5第四層核對=(1, [1/2, 1/2], [16, -17], 2, 是, common_probability_space_and_finite_integer_p_moments)；依完整明示資料重算；核E absolute error power p趨零且moments有限；finite prefix不足，a.s. probability或其他Lq implications另需假設。"},"difficulty":{"band":"undergraduate_core","level":2,"skills":["Lp收斂"]},"variant":{"family_id":"qf-mod35-lp-qualification","seed":202611047066,"parameters":{"masses":[[1,2],[1,2]],"coefficients":[16,-17],"shift":2,"p":1,"domain":"Finite_atomic_symbolic_Lp_tail","operation":"lp-qualification","semantic_template":"qf-mod35-lp-qualification/{\"coefficients\":[16,-17],\"masses\":[[1,2],[1,2]],\"p\":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-r07-lp-convergence-0067","batch_id":"batch-20261014-advance-20261104-r07-lp-convergence-foundations","language":"zh-Hant","source_mko_ids":["mko-lp-convergence"],"title_zh":"Lp收斂","stem_zh":"同一有限原子probability space、固定整數p大於等於1與symbolic moment tail。操作=lp-qualification；資料={\"masses\":[[1,2],[1,2]],\"coefficients\":[17,-18],\"shift\":2,\"p\":2}。請依 exact_ordered_tuple_declared_by_interface 欄序回答。","answer":{"kind":"expression","value":"(2, [1/2, 1/2], [17, -18], 2, 是, common_probability_space_and_finite_integer_p_moments)","explanation_zh":"Wave5第四層核對=(2, [1/2, 1/2], [17, -18], 2, 是, common_probability_space_and_finite_integer_p_moments)；依完整明示資料重算；核E absolute error power p趨零且moments有限；finite prefix不足，a.s. probability或其他Lq implications另需假設。"},"difficulty":{"band":"undergraduate_core","level":2,"skills":["Lp收斂"]},"variant":{"family_id":"qf-mod35-lp-qualification","seed":202611047067,"parameters":{"masses":[[1,2],[1,2]],"coefficients":[17,-18],"shift":2,"p":2,"domain":"Finite_atomic_symbolic_Lp_tail","operation":"lp-qualification","semantic_template":"qf-mod35-lp-qualification/{\"coefficients\":[17,-18],\"masses\":[[1,2],[1,2]],\"p\":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-r07-lp-convergence-0068","batch_id":"batch-20261014-advance-20261104-r07-lp-convergence-foundations","language":"zh-Hant","source_mko_ids":["mko-lp-convergence"],"title_zh":"Lp收斂","stem_zh":"同一有限原子probability space、固定整數p大於等於1與symbolic moment tail。操作=lp-qualification；資料={\"masses\":[[1,2],[1,2]],\"coefficients\":[18,-19],\"shift\":2,\"p\":3}。請依 exact_ordered_tuple_declared_by_interface 欄序回答。","answer":{"kind":"expression","value":"(3, [1/2, 1/2], [18, -19], 2, 是, common_probability_space_and_finite_integer_p_moments)","explanation_zh":"Wave5第四層核對=(3, [1/2, 1/2], [18, -19], 2, 是, common_probability_space_and_finite_integer_p_moments)；依完整明示資料重算；核E absolute error power p趨零且moments有限；finite prefix不足，a.s. probability或其他Lq implications另需假設。"},"difficulty":{"band":"undergraduate_core","level":3,"skills":["Lp收斂"]},"variant":{"family_id":"qf-mod35-lp-qualification","seed":202611047068,"parameters":{"masses":[[1,2],[1,2]],"coefficients":[18,-19],"shift":2,"p":3,"domain":"Finite_atomic_symbolic_Lp_tail","operation":"lp-qualification","semantic_template":"qf-mod35-lp-qualification/{\"coefficients\":[18,-19],\"masses\":[[1,2],[1,2]],\"p\":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-r07-lp-convergence-0069","batch_id":"batch-20261014-advance-20261104-r07-lp-convergence-foundations","language":"zh-Hant","source_mko_ids":["mko-lp-convergence"],"title_zh":"Lp收斂","stem_zh":"同一有限原子probability space、固定整數p大於等於1與symbolic moment tail。操作=lp-qualification；資料={\"masses\":[[1,2],[1,2]],\"coefficients\":[19,-20],\"shift\":2,\"p\":1}。請依 exact_ordered_tuple_declared_by_interface 欄序回答。","answer":{"kind":"expression","value":"(1, [1/2, 1/2], [19, -20], 2, 是, common_probability_space_and_finite_integer_p_moments)","explanation_zh":"Wave5第四層核對=(1, [1/2, 1/2], [19, -20], 2, 是, common_probability_space_and_finite_integer_p_moments)；依完整明示資料重算；核E absolute error power p趨零且moments有限；finite prefix不足，a.s. probability或其他Lq implications另需假設。"},"difficulty":{"band":"undergraduate_core","level":3,"skills":["Lp收斂"]},"variant":{"family_id":"qf-mod35-lp-qualification","seed":202611047069,"parameters":{"masses":[[1,2],[1,2]],"coefficients":[19,-20],"shift":2,"p":1,"domain":"Finite_atomic_symbolic_Lp_tail","operation":"lp-qualification","semantic_template":"qf-mod35-lp-qualification/{\"coefficients\":[19,-20],\"masses\":[[1,2],[1,2]],\"p\":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-r07-lp-convergence-0070","batch_id":"batch-20261014-advance-20261104-r07-lp-convergence-foundations","language":"zh-Hant","source_mko_ids":["mko-lp-convergence"],"title_zh":"Lp收斂","stem_zh":"同一有限原子probability space、固定整數p大於等於1與symbolic moment tail。操作=lp-qualification；資料={\"masses\":[[1,2],[1,2]],\"coefficients\":[20,-21],\"shift\":2,\"p\":2}。請依 exact_ordered_tuple_declared_by_interface 欄序回答。","answer":{"kind":"expression","value":"(2, [1/2, 1/2], [20, -21], 2, 是, common_probability_space_and_finite_integer_p_moments)","explanation_zh":"Wave5第四層核對=(2, [1/2, 1/2], [20, -21], 2, 是, common_probability_space_and_finite_integer_p_moments)；依完整明示資料重算；核E absolute error power p趨零且moments有限；finite prefix不足，a.s. probability或其他Lq implications另需假設。"},"difficulty":{"band":"undergraduate_core","level":3,"skills":["Lp收斂"]},"variant":{"family_id":"qf-mod35-lp-qualification","seed":202611047070,"parameters":{"masses":[[1,2],[1,2]],"coefficients":[20,-21],"shift":2,"p":2,"domain":"Finite_atomic_symbolic_Lp_tail","operation":"lp-qualification","semantic_template":"qf-mod35-lp-qualification/{\"coefficients\":[20,-21],\"masses\":[[1,2],[1,2]],\"p\":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-r07-lp-convergence-0071","batch_id":"batch-20261014-advance-20261104-r07-lp-convergence-foundations","language":"zh-Hant","source_mko_ids":["mko-lp-convergence"],"title_zh":"Lp收斂","stem_zh":"同一有限原子probability space、固定整數p大於等於1與symbolic moment tail。操作=lp-qualification；資料={\"masses\":[[1,2],[1,2]],\"coefficients\":[21,-22],\"shift\":2,\"p\":3}。請依 exact_ordered_tuple_declared_by_interface 欄序回答。","answer":{"kind":"expression","value":"(3, [1/2, 1/2], [21, -22], 2, 是, common_probability_space_and_finite_integer_p_moments)","explanation_zh":"Wave5第四層核對=(3, [1/2, 1/2], [21, -22], 2, 是, common_probability_space_and_finite_integer_p_moments)；依完整明示資料重算；核E absolute error power p趨零且moments有限；finite prefix不足，a.s. probability或其他Lq implications另需假設。"},"difficulty":{"band":"undergraduate_core","level":3,"skills":["Lp收斂"]},"variant":{"family_id":"qf-mod35-lp-qualification","seed":202611047071,"parameters":{"masses":[[1,2],[1,2]],"coefficients":[21,-22],"shift":2,"p":3,"domain":"Finite_atomic_symbolic_Lp_tail","operation":"lp-qualification","semantic_template":"qf-mod35-lp-qualification/{\"coefficients\":[21,-22],\"masses\":[[1,2],[1,2]],\"p\":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-r07-lp-convergence-0072","batch_id":"batch-20261014-advance-20261104-r07-lp-convergence-foundations","language":"zh-Hant","source_mko_ids":["mko-lp-convergence"],"title_zh":"Lp收斂","stem_zh":"同一有限原子probability space、固定整數p大於等於1與symbolic moment tail。操作=lp-qualification；資料={\"masses\":[[1,2],[1,2]],\"coefficients\":[22,-23],\"shift\":2,\"p\":1}。請依 exact_ordered_tuple_declared_by_interface 欄序回答。","answer":{"kind":"expression","value":"(1, [1/2, 1/2], [22, -23], 2, 是, common_probability_space_and_finite_integer_p_moments)","explanation_zh":"Wave5第四層核對=(1, [1/2, 1/2], [22, -23], 2, 是, common_probability_space_and_finite_integer_p_moments)；依完整明示資料重算；核E absolute error power p趨零且moments有限；finite prefix不足，a.s. probability或其他Lq implications另需假設。"},"difficulty":{"band":"undergraduate_core","level":3,"skills":["Lp收斂"]},"variant":{"family_id":"qf-mod35-lp-qualification","seed":202611047072,"parameters":{"masses":[[1,2],[1,2]],"coefficients":[22,-23],"shift":2,"p":1,"domain":"Finite_atomic_symbolic_Lp_tail","operation":"lp-qualification","semantic_template":"qf-mod35-lp-qualification/{\"coefficients\":[22,-23],\"masses\":[[1,2],[1,2]],\"p\":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-r07-lp-convergence-0073","batch_id":"batch-20261014-advance-20261104-r07-lp-convergence-foundations","language":"zh-Hant","source_mko_ids":["mko-lp-convergence"],"title_zh":"Lp收斂","stem_zh":"同一有限原子probability space、固定整數p大於等於1與symbolic moment tail。操作=lp-qualification；資料={\"masses\":[[1,2],[1,2]],\"coefficients\":[23,-24],\"shift\":2,\"p\":2}。請依 exact_ordered_tuple_declared_by_interface 欄序回答。","answer":{"kind":"expression","value":"(2, [1/2, 1/2], [23, -24], 2, 是, common_probability_space_and_finite_integer_p_moments)","explanation_zh":"Wave5第四層核對=(2, [1/2, 1/2], [23, -24], 2, 是, common_probability_space_and_finite_integer_p_moments)；依完整明示資料重算；核E absolute error power p趨零且moments有限；finite prefix不足，a.s. probability或其他Lq implications另需假設。"},"difficulty":{"band":"undergraduate_core","level":3,"skills":["Lp收斂"]},"variant":{"family_id":"qf-mod35-lp-qualification","seed":202611047073,"parameters":{"masses":[[1,2],[1,2]],"coefficients":[23,-24],"shift":2,"p":2,"domain":"Finite_atomic_symbolic_Lp_tail","operation":"lp-qualification","semantic_template":"qf-mod35-lp-qualification/{\"coefficients\":[23,-24],\"masses\":[[1,2],[1,2]],\"p\":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-r07-lp-convergence-0074","batch_id":"batch-20261014-advance-20261104-r07-lp-convergence-foundations","language":"zh-Hant","source_mko_ids":["mko-lp-convergence"],"title_zh":"Lp收斂","stem_zh":"同一有限原子probability space、固定整數p大於等於1與symbolic moment tail。操作=lp-qualification；資料={\"masses\":[[1,2],[1,2]],\"coefficients\":[24,-25],\"shift\":2,\"p\":3}。請依 exact_ordered_tuple_declared_by_interface 欄序回答。","answer":{"kind":"expression","value":"(3, [1/2, 1/2], [24, -25], 2, 是, common_probability_space_and_finite_integer_p_moments)","explanation_zh":"Wave5第四層核對=(3, [1/2, 1/2], [24, -25], 2, 是, common_probability_space_and_finite_integer_p_moments)；依完整明示資料重算；核E absolute error power p趨零且moments有限；finite prefix不足，a.s. probability或其他Lq implications另需假設。"},"difficulty":{"band":"undergraduate_core","level":3,"skills":["Lp收斂"]},"variant":{"family_id":"qf-mod35-lp-qualification","seed":202611047074,"parameters":{"masses":[[1,2],[1,2]],"coefficients":[24,-25],"shift":2,"p":3,"domain":"Finite_atomic_symbolic_Lp_tail","operation":"lp-qualification","semantic_template":"qf-mod35-lp-qualification/{\"coefficients\":[24,-25],\"masses\":[[1,2],[1,2]],\"p\":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-r07-lp-convergence-0075","batch_id":"batch-20261014-advance-20261104-r07-lp-convergence-foundations","language":"zh-Hant","source_mko_ids":["mko-lp-convergence"],"title_zh":"Lp收斂","stem_zh":"同一有限原子probability space、固定整數p大於等於1與symbolic moment tail。操作=lp-qualification；資料={\"masses\":[[1,2],[1,2]],\"coefficients\":[25,-26],\"shift\":2,\"p\":1}。請依 exact_ordered_tuple_declared_by_interface 欄序回答。","answer":{"kind":"expression","value":"(1, [1/2, 1/2], [25, -26], 2, 是, common_probability_space_and_finite_integer_p_moments)","explanation_zh":"Wave5第四層核對=(1, [1/2, 1/2], [25, -26], 2, 是, common_probability_space_and_finite_integer_p_moments)；依完整明示資料重算；核E absolute error power p趨零且moments有限；finite prefix不足，a.s. probability或其他Lq implications另需假設。"},"difficulty":{"band":"undergraduate_core","level":3,"skills":["Lp收斂"]},"variant":{"family_id":"qf-mod35-lp-qualification","seed":202611047075,"parameters":{"masses":[[1,2],[1,2]],"coefficients":[25,-26],"shift":2,"p":1,"domain":"Finite_atomic_symbolic_Lp_tail","operation":"lp-qualification","semantic_template":"qf-mod35-lp-qualification/{\"coefficients\":[25,-26],\"masses\":[[1,2],[1,2]],\"p\":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-r07-lp-convergence-0076","batch_id":"batch-20261014-advance-20261104-r07-lp-convergence-foundations","language":"zh-Hant","source_mko_ids":["mko-lp-convergence"],"title_zh":"Lp收斂","stem_zh":"同一有限原子probability space、固定整數p大於等於1與symbolic moment tail。操作=lp-finite-prefix-boundary；資料={\"masses\":[[1,2],[1,2]],\"coefficients\":[1,-2],\"shift\":2,\"p\":1,\"prefix_length\":1}。請依 exact_ordered_tuple_declared_by_interface 欄序回答。","answer":{"kind":"expression","value":"(1, 否, finite_prefix_not_Lp_convergence_certificate_or_mode_implication)","explanation_zh":"Wave5第四層核對=(1, 否, finite_prefix_not_Lp_convergence_certificate_or_mode_implication)；依完整明示資料重算；核E absolute error power p趨零且moments有限；finite prefix不足，a.s. probability或其他Lq implications另需假設。"},"difficulty":{"band":"undergraduate_core","level":1,"skills":["Lp收斂"]},"variant":{"family_id":"qf-mod35-lp-finite-prefix-boundary","seed":202611047076,"parameters":{"masses":[[1,2],[1,2]],"coefficients":[1,-2],"shift":2,"p":1,"prefix_length":1,"domain":"Finite_atomic_symbolic_Lp_tail","operation":"lp-finite-prefix-boundary","semantic_template":"qf-mod35-lp-finite-prefix-boundary/{\"coefficients\":[1,-2],\"masses\":[[1,2],[1,2]],\"p\":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-r07-lp-convergence-0077","batch_id":"batch-20261014-advance-20261104-r07-lp-convergence-foundations","language":"zh-Hant","source_mko_ids":["mko-lp-convergence"],"title_zh":"Lp收斂","stem_zh":"同一有限原子probability space、固定整數p大於等於1與symbolic moment tail。操作=lp-finite-prefix-boundary；資料={\"masses\":[[1,2],[1,2]],\"coefficients\":[2,-3],\"shift\":2,\"p\":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_Lp_convergence_certificate_or_mode_implication)","explanation_zh":"Wave5第四層核對=(2, 否, finite_prefix_not_Lp_convergence_certificate_or_mode_implication)；依完整明示資料重算；核E absolute error power p趨零且moments有限；finite prefix不足，a.s. probability或其他Lq implications另需假設。"},"difficulty":{"band":"undergraduate_core","level":1,"skills":["Lp收斂"]},"variant":{"family_id":"qf-mod35-lp-finite-prefix-boundary","seed":202611047077,"parameters":{"masses":[[1,2],[1,2]],"coefficients":[2,-3],"shift":2,"p":2,"prefix_length":2,"domain":"Finite_atomic_symbolic_Lp_tail","operation":"lp-finite-prefix-boundary","semantic_template":"qf-mod35-lp-finite-prefix-boundary/{\"coefficients\":[2,-3],\"masses\":[[1,2],[1,2]],\"p\":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-r07-lp-convergence-0078","batch_id":"batch-20261014-advance-20261104-r07-lp-convergence-foundations","language":"zh-Hant","source_mko_ids":["mko-lp-convergence"],"title_zh":"Lp收斂","stem_zh":"同一有限原子probability space、固定整數p大於等於1與symbolic moment tail。操作=lp-finite-prefix-boundary；資料={\"masses\":[[1,2],[1,2]],\"coefficients\":[3,-4],\"shift\":2,\"p\":3,\"prefix_length\":3}。請依 exact_ordered_tuple_declared_by_interface 欄序回答。","answer":{"kind":"expression","value":"(3, 否, finite_prefix_not_Lp_convergence_certificate_or_mode_implication)","explanation_zh":"Wave5第四層核對=(3, 否, finite_prefix_not_Lp_convergence_certificate_or_mode_implication)；依完整明示資料重算；核E absolute error power p趨零且moments有限；finite prefix不足，a.s. probability或其他Lq implications另需假設。"},"difficulty":{"band":"undergraduate_core","level":1,"skills":["Lp收斂"]},"variant":{"family_id":"qf-mod35-lp-finite-prefix-boundary","seed":202611047078,"parameters":{"masses":[[1,2],[1,2]],"coefficients":[3,-4],"shift":2,"p":3,"prefix_length":3,"domain":"Finite_atomic_symbolic_Lp_tail","operation":"lp-finite-prefix-boundary","semantic_template":"qf-mod35-lp-finite-prefix-boundary/{\"coefficients\":[3,-4],\"masses\":[[1,2],[1,2]],\"p\":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-r07-lp-convergence-0079","batch_id":"batch-20261014-advance-20261104-r07-lp-convergence-foundations","language":"zh-Hant","source_mko_ids":["mko-lp-convergence"],"title_zh":"Lp收斂","stem_zh":"同一有限原子probability space、固定整數p大於等於1與symbolic moment tail。操作=lp-finite-prefix-boundary；資料={\"masses\":[[1,2],[1,2]],\"coefficients\":[4,-5],\"shift\":2,\"p\":1,\"prefix_length\":4}。請依 exact_ordered_tuple_declared_by_interface 欄序回答。","answer":{"kind":"expression","value":"(4, 否, finite_prefix_not_Lp_convergence_certificate_or_mode_implication)","explanation_zh":"Wave5第四層核對=(4, 否, finite_prefix_not_Lp_convergence_certificate_or_mode_implication)；依完整明示資料重算；核E absolute error power p趨零且moments有限；finite prefix不足，a.s. probability或其他Lq implications另需假設。"},"difficulty":{"band":"undergraduate_core","level":1,"skills":["Lp收斂"]},"variant":{"family_id":"qf-mod35-lp-finite-prefix-boundary","seed":202611047079,"parameters":{"masses":[[1,2],[1,2]],"coefficients":[4,-5],"shift":2,"p":1,"prefix_length":4,"domain":"Finite_atomic_symbolic_Lp_tail","operation":"lp-finite-prefix-boundary","semantic_template":"qf-mod35-lp-finite-prefix-boundary/{\"coefficients\":[4,-5],\"masses\":[[1,2],[1,2]],\"p\":1,\"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-r07-lp-convergence-0080","batch_id":"batch-20261014-advance-20261104-r07-lp-convergence-foundations","language":"zh-Hant","source_mko_ids":["mko-lp-convergence"],"title_zh":"Lp收斂","stem_zh":"同一有限原子probability space、固定整數p大於等於1與symbolic moment tail。操作=lp-finite-prefix-boundary；資料={\"masses\":[[1,2],[1,2]],\"coefficients\":[5,-6],\"shift\":2,\"p\":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_Lp_convergence_certificate_or_mode_implication)","explanation_zh":"Wave5第四層核對=(5, 否, finite_prefix_not_Lp_convergence_certificate_or_mode_implication)；依完整明示資料重算；核E absolute error power p趨零且moments有限；finite prefix不足，a.s. probability或其他Lq implications另需假設。"},"difficulty":{"band":"undergraduate_core","level":1,"skills":["Lp收斂"]},"variant":{"family_id":"qf-mod35-lp-finite-prefix-boundary","seed":202611047080,"parameters":{"masses":[[1,2],[1,2]],"coefficients":[5,-6],"shift":2,"p":2,"prefix_length":5,"domain":"Finite_atomic_symbolic_Lp_tail","operation":"lp-finite-prefix-boundary","semantic_template":"qf-mod35-lp-finite-prefix-boundary/{\"coefficients\":[5,-6],\"masses\":[[1,2],[1,2]],\"p\":2,\"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-r07-lp-convergence-0081","batch_id":"batch-20261014-advance-20261104-r07-lp-convergence-foundations","language":"zh-Hant","source_mko_ids":["mko-lp-convergence"],"title_zh":"Lp收斂","stem_zh":"同一有限原子probability space、固定整數p大於等於1與symbolic moment tail。操作=lp-finite-prefix-boundary；資料={\"masses\":[[1,2],[1,2]],\"coefficients\":[6,-7],\"shift\":2,\"p\":3,\"prefix_length\":6}。請依 exact_ordered_tuple_declared_by_interface 欄序回答。","answer":{"kind":"expression","value":"(6, 否, finite_prefix_not_Lp_convergence_certificate_or_mode_implication)","explanation_zh":"Wave5第四層核對=(6, 否, finite_prefix_not_Lp_convergence_certificate_or_mode_implication)；依完整明示資料重算；核E absolute error power p趨零且moments有限；finite prefix不足，a.s. probability或其他Lq implications另需假設。"},"difficulty":{"band":"undergraduate_core","level":1,"skills":["Lp收斂"]},"variant":{"family_id":"qf-mod35-lp-finite-prefix-boundary","seed":202611047081,"parameters":{"masses":[[1,2],[1,2]],"coefficients":[6,-7],"shift":2,"p":3,"prefix_length":6,"domain":"Finite_atomic_symbolic_Lp_tail","operation":"lp-finite-prefix-boundary","semantic_template":"qf-mod35-lp-finite-prefix-boundary/{\"coefficients\":[6,-7],\"masses\":[[1,2],[1,2]],\"p\":3,\"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-r07-lp-convergence-0082","batch_id":"batch-20261014-advance-20261104-r07-lp-convergence-foundations","language":"zh-Hant","source_mko_ids":["mko-lp-convergence"],"title_zh":"Lp收斂","stem_zh":"同一有限原子probability space、固定整數p大於等於1與symbolic moment tail。操作=lp-finite-prefix-boundary；資料={\"masses\":[[1,2],[1,2]],\"coefficients\":[7,-8],\"shift\":2,\"p\":1,\"prefix_length\":7}。請依 exact_ordered_tuple_declared_by_interface 欄序回答。","answer":{"kind":"expression","value":"(7, 否, finite_prefix_not_Lp_convergence_certificate_or_mode_implication)","explanation_zh":"Wave5第四層核對=(7, 否, finite_prefix_not_Lp_convergence_certificate_or_mode_implication)；依完整明示資料重算；核E absolute error power p趨零且moments有限；finite prefix不足，a.s. probability或其他Lq implications另需假設。"},"difficulty":{"band":"undergraduate_core","level":1,"skills":["Lp收斂"]},"variant":{"family_id":"qf-mod35-lp-finite-prefix-boundary","seed":202611047082,"parameters":{"masses":[[1,2],[1,2]],"coefficients":[7,-8],"shift":2,"p":1,"prefix_length":7,"domain":"Finite_atomic_symbolic_Lp_tail","operation":"lp-finite-prefix-boundary","semantic_template":"qf-mod35-lp-finite-prefix-boundary/{\"coefficients\":[7,-8],\"masses\":[[1,2],[1,2]],\"p\":1,\"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-r07-lp-convergence-0083","batch_id":"batch-20261014-advance-20261104-r07-lp-convergence-foundations","language":"zh-Hant","source_mko_ids":["mko-lp-convergence"],"title_zh":"Lp收斂","stem_zh":"同一有限原子probability space、固定整數p大於等於1與symbolic moment tail。操作=lp-finite-prefix-boundary；資料={\"masses\":[[1,2],[1,2]],\"coefficients\":[8,-9],\"shift\":2,\"p\":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_Lp_convergence_certificate_or_mode_implication)","explanation_zh":"Wave5第四層核對=(8, 否, finite_prefix_not_Lp_convergence_certificate_or_mode_implication)；依完整明示資料重算；核E absolute error power p趨零且moments有限；finite prefix不足，a.s. probability或其他Lq implications另需假設。"},"difficulty":{"band":"undergraduate_core","level":1,"skills":["Lp收斂"]},"variant":{"family_id":"qf-mod35-lp-finite-prefix-boundary","seed":202611047083,"parameters":{"masses":[[1,2],[1,2]],"coefficients":[8,-9],"shift":2,"p":2,"prefix_length":8,"domain":"Finite_atomic_symbolic_Lp_tail","operation":"lp-finite-prefix-boundary","semantic_template":"qf-mod35-lp-finite-prefix-boundary/{\"coefficients\":[8,-9],\"masses\":[[1,2],[1,2]],\"p\":2,\"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-r07-lp-convergence-0084","batch_id":"batch-20261014-advance-20261104-r07-lp-convergence-foundations","language":"zh-Hant","source_mko_ids":["mko-lp-convergence"],"title_zh":"Lp收斂","stem_zh":"同一有限原子probability space、固定整數p大於等於1與symbolic moment tail。操作=lp-finite-prefix-boundary；資料={\"masses\":[[1,2],[1,2]],\"coefficients\":[9,-10],\"shift\":2,\"p\":3,\"prefix_length\":9}。請依 exact_ordered_tuple_declared_by_interface 欄序回答。","answer":{"kind":"expression","value":"(9, 否, finite_prefix_not_Lp_convergence_certificate_or_mode_implication)","explanation_zh":"Wave5第四層核對=(9, 否, finite_prefix_not_Lp_convergence_certificate_or_mode_implication)；依完整明示資料重算；核E absolute error power p趨零且moments有限；finite prefix不足，a.s. probability或其他Lq implications另需假設。"},"difficulty":{"band":"undergraduate_core","level":2,"skills":["Lp收斂"]},"variant":{"family_id":"qf-mod35-lp-finite-prefix-boundary","seed":202611047084,"parameters":{"masses":[[1,2],[1,2]],"coefficients":[9,-10],"shift":2,"p":3,"prefix_length":9,"domain":"Finite_atomic_symbolic_Lp_tail","operation":"lp-finite-prefix-boundary","semantic_template":"qf-mod35-lp-finite-prefix-boundary/{\"coefficients\":[9,-10],\"masses\":[[1,2],[1,2]],\"p\":3,\"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-r07-lp-convergence-0085","batch_id":"batch-20261014-advance-20261104-r07-lp-convergence-foundations","language":"zh-Hant","source_mko_ids":["mko-lp-convergence"],"title_zh":"Lp收斂","stem_zh":"同一有限原子probability space、固定整數p大於等於1與symbolic moment tail。操作=lp-finite-prefix-boundary；資料={\"masses\":[[1,2],[1,2]],\"coefficients\":[10,-11],\"shift\":2,\"p\":1,\"prefix_length\":10}。請依 exact_ordered_tuple_declared_by_interface 欄序回答。","answer":{"kind":"expression","value":"(10, 否, finite_prefix_not_Lp_convergence_certificate_or_mode_implication)","explanation_zh":"Wave5第四層核對=(10, 否, finite_prefix_not_Lp_convergence_certificate_or_mode_implication)；依完整明示資料重算；核E absolute error power p趨零且moments有限；finite prefix不足，a.s. probability或其他Lq implications另需假設。"},"difficulty":{"band":"undergraduate_core","level":2,"skills":["Lp收斂"]},"variant":{"family_id":"qf-mod35-lp-finite-prefix-boundary","seed":202611047085,"parameters":{"masses":[[1,2],[1,2]],"coefficients":[10,-11],"shift":2,"p":1,"prefix_length":10,"domain":"Finite_atomic_symbolic_Lp_tail","operation":"lp-finite-prefix-boundary","semantic_template":"qf-mod35-lp-finite-prefix-boundary/{\"coefficients\":[10,-11],\"masses\":[[1,2],[1,2]],\"p\":1,\"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-r07-lp-convergence-0086","batch_id":"batch-20261014-advance-20261104-r07-lp-convergence-foundations","language":"zh-Hant","source_mko_ids":["mko-lp-convergence"],"title_zh":"Lp收斂","stem_zh":"同一有限原子probability space、固定整數p大於等於1與symbolic moment tail。操作=lp-finite-prefix-boundary；資料={\"masses\":[[1,2],[1,2]],\"coefficients\":[11,-12],\"shift\":2,\"p\":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_Lp_convergence_certificate_or_mode_implication)","explanation_zh":"Wave5第四層核對=(11, 否, finite_prefix_not_Lp_convergence_certificate_or_mode_implication)；依完整明示資料重算；核E absolute error power p趨零且moments有限；finite prefix不足，a.s. probability或其他Lq implications另需假設。"},"difficulty":{"band":"undergraduate_core","level":2,"skills":["Lp收斂"]},"variant":{"family_id":"qf-mod35-lp-finite-prefix-boundary","seed":202611047086,"parameters":{"masses":[[1,2],[1,2]],"coefficients":[11,-12],"shift":2,"p":2,"prefix_length":11,"domain":"Finite_atomic_symbolic_Lp_tail","operation":"lp-finite-prefix-boundary","semantic_template":"qf-mod35-lp-finite-prefix-boundary/{\"coefficients\":[11,-12],\"masses\":[[1,2],[1,2]],\"p\":2,\"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-r07-lp-convergence-0087","batch_id":"batch-20261014-advance-20261104-r07-lp-convergence-foundations","language":"zh-Hant","source_mko_ids":["mko-lp-convergence"],"title_zh":"Lp收斂","stem_zh":"同一有限原子probability space、固定整數p大於等於1與symbolic moment tail。操作=lp-finite-prefix-boundary；資料={\"masses\":[[1,2],[1,2]],\"coefficients\":[12,-13],\"shift\":2,\"p\":3,\"prefix_length\":12}。請依 exact_ordered_tuple_declared_by_interface 欄序回答。","answer":{"kind":"expression","value":"(12, 否, finite_prefix_not_Lp_convergence_certificate_or_mode_implication)","explanation_zh":"Wave5第四層核對=(12, 否, finite_prefix_not_Lp_convergence_certificate_or_mode_implication)；依完整明示資料重算；核E absolute error power p趨零且moments有限；finite prefix不足，a.s. probability或其他Lq implications另需假設。"},"difficulty":{"band":"undergraduate_core","level":2,"skills":["Lp收斂"]},"variant":{"family_id":"qf-mod35-lp-finite-prefix-boundary","seed":202611047087,"parameters":{"masses":[[1,2],[1,2]],"coefficients":[12,-13],"shift":2,"p":3,"prefix_length":12,"domain":"Finite_atomic_symbolic_Lp_tail","operation":"lp-finite-prefix-boundary","semantic_template":"qf-mod35-lp-finite-prefix-boundary/{\"coefficients\":[12,-13],\"masses\":[[1,2],[1,2]],\"p\":3,\"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-r07-lp-convergence-0088","batch_id":"batch-20261014-advance-20261104-r07-lp-convergence-foundations","language":"zh-Hant","source_mko_ids":["mko-lp-convergence"],"title_zh":"Lp收斂","stem_zh":"同一有限原子probability space、固定整數p大於等於1與symbolic moment tail。操作=lp-finite-prefix-boundary；資料={\"masses\":[[1,2],[1,2]],\"coefficients\":[13,-14],\"shift\":2,\"p\":1,\"prefix_length\":13}。請依 exact_ordered_tuple_declared_by_interface 欄序回答。","answer":{"kind":"expression","value":"(13, 否, finite_prefix_not_Lp_convergence_certificate_or_mode_implication)","explanation_zh":"Wave5第四層核對=(13, 否, finite_prefix_not_Lp_convergence_certificate_or_mode_implication)；依完整明示資料重算；核E absolute error power p趨零且moments有限；finite prefix不足，a.s. probability或其他Lq implications另需假設。"},"difficulty":{"band":"undergraduate_core","level":2,"skills":["Lp收斂"]},"variant":{"family_id":"qf-mod35-lp-finite-prefix-boundary","seed":202611047088,"parameters":{"masses":[[1,2],[1,2]],"coefficients":[13,-14],"shift":2,"p":1,"prefix_length":13,"domain":"Finite_atomic_symbolic_Lp_tail","operation":"lp-finite-prefix-boundary","semantic_template":"qf-mod35-lp-finite-prefix-boundary/{\"coefficients\":[13,-14],\"masses\":[[1,2],[1,2]],\"p\":1,\"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-r07-lp-convergence-0089","batch_id":"batch-20261014-advance-20261104-r07-lp-convergence-foundations","language":"zh-Hant","source_mko_ids":["mko-lp-convergence"],"title_zh":"Lp收斂","stem_zh":"同一有限原子probability space、固定整數p大於等於1與symbolic moment tail。操作=lp-finite-prefix-boundary；資料={\"masses\":[[1,2],[1,2]],\"coefficients\":[14,-15],\"shift\":2,\"p\":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_Lp_convergence_certificate_or_mode_implication)","explanation_zh":"Wave5第四層核對=(14, 否, finite_prefix_not_Lp_convergence_certificate_or_mode_implication)；依完整明示資料重算；核E absolute error power p趨零且moments有限；finite prefix不足，a.s. probability或其他Lq implications另需假設。"},"difficulty":{"band":"undergraduate_core","level":2,"skills":["Lp收斂"]},"variant":{"family_id":"qf-mod35-lp-finite-prefix-boundary","seed":202611047089,"parameters":{"masses":[[1,2],[1,2]],"coefficients":[14,-15],"shift":2,"p":2,"prefix_length":14,"domain":"Finite_atomic_symbolic_Lp_tail","operation":"lp-finite-prefix-boundary","semantic_template":"qf-mod35-lp-finite-prefix-boundary/{\"coefficients\":[14,-15],\"masses\":[[1,2],[1,2]],\"p\":2,\"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-r07-lp-convergence-0090","batch_id":"batch-20261014-advance-20261104-r07-lp-convergence-foundations","language":"zh-Hant","source_mko_ids":["mko-lp-convergence"],"title_zh":"Lp收斂","stem_zh":"同一有限原子probability space、固定整數p大於等於1與symbolic moment tail。操作=lp-finite-prefix-boundary；資料={\"masses\":[[1,2],[1,2]],\"coefficients\":[15,-16],\"shift\":2,\"p\":3,\"prefix_length\":15}。請依 exact_ordered_tuple_declared_by_interface 欄序回答。","answer":{"kind":"expression","value":"(15, 否, finite_prefix_not_Lp_convergence_certificate_or_mode_implication)","explanation_zh":"Wave5第四層核對=(15, 否, finite_prefix_not_Lp_convergence_certificate_or_mode_implication)；依完整明示資料重算；核E absolute error power p趨零且moments有限；finite prefix不足，a.s. probability或其他Lq implications另需假設。"},"difficulty":{"band":"undergraduate_core","level":2,"skills":["Lp收斂"]},"variant":{"family_id":"qf-mod35-lp-finite-prefix-boundary","seed":202611047090,"parameters":{"masses":[[1,2],[1,2]],"coefficients":[15,-16],"shift":2,"p":3,"prefix_length":15,"domain":"Finite_atomic_symbolic_Lp_tail","operation":"lp-finite-prefix-boundary","semantic_template":"qf-mod35-lp-finite-prefix-boundary/{\"coefficients\":[15,-16],\"masses\":[[1,2],[1,2]],\"p\":3,\"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-r07-lp-convergence-0091","batch_id":"batch-20261014-advance-20261104-r07-lp-convergence-foundations","language":"zh-Hant","source_mko_ids":["mko-lp-convergence"],"title_zh":"Lp收斂","stem_zh":"同一有限原子probability space、固定整數p大於等於1與symbolic moment tail。操作=lp-finite-prefix-boundary；資料={\"masses\":[[1,2],[1,2]],\"coefficients\":[16,-17],\"shift\":2,\"p\":1,\"prefix_length\":16}。請依 exact_ordered_tuple_declared_by_interface 欄序回答。","answer":{"kind":"expression","value":"(16, 否, finite_prefix_not_Lp_convergence_certificate_or_mode_implication)","explanation_zh":"Wave5第四層核對=(16, 否, finite_prefix_not_Lp_convergence_certificate_or_mode_implication)；依完整明示資料重算；核E absolute error power p趨零且moments有限；finite prefix不足，a.s. probability或其他Lq implications另需假設。"},"difficulty":{"band":"undergraduate_core","level":2,"skills":["Lp收斂"]},"variant":{"family_id":"qf-mod35-lp-finite-prefix-boundary","seed":202611047091,"parameters":{"masses":[[1,2],[1,2]],"coefficients":[16,-17],"shift":2,"p":1,"prefix_length":16,"domain":"Finite_atomic_symbolic_Lp_tail","operation":"lp-finite-prefix-boundary","semantic_template":"qf-mod35-lp-finite-prefix-boundary/{\"coefficients\":[16,-17],\"masses\":[[1,2],[1,2]],\"p\":1,\"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-r07-lp-convergence-0092","batch_id":"batch-20261014-advance-20261104-r07-lp-convergence-foundations","language":"zh-Hant","source_mko_ids":["mko-lp-convergence"],"title_zh":"Lp收斂","stem_zh":"同一有限原子probability space、固定整數p大於等於1與symbolic moment tail。操作=lp-finite-prefix-boundary；資料={\"masses\":[[1,2],[1,2]],\"coefficients\":[17,-18],\"shift\":2,\"p\":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_Lp_convergence_certificate_or_mode_implication)","explanation_zh":"Wave5第四層核對=(17, 否, finite_prefix_not_Lp_convergence_certificate_or_mode_implication)；依完整明示資料重算；核E absolute error power p趨零且moments有限；finite prefix不足，a.s. probability或其他Lq implications另需假設。"},"difficulty":{"band":"undergraduate_core","level":2,"skills":["Lp收斂"]},"variant":{"family_id":"qf-mod35-lp-finite-prefix-boundary","seed":202611047092,"parameters":{"masses":[[1,2],[1,2]],"coefficients":[17,-18],"shift":2,"p":2,"prefix_length":17,"domain":"Finite_atomic_symbolic_Lp_tail","operation":"lp-finite-prefix-boundary","semantic_template":"qf-mod35-lp-finite-prefix-boundary/{\"coefficients\":[17,-18],\"masses\":[[1,2],[1,2]],\"p\":2,\"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-r07-lp-convergence-0093","batch_id":"batch-20261014-advance-20261104-r07-lp-convergence-foundations","language":"zh-Hant","source_mko_ids":["mko-lp-convergence"],"title_zh":"Lp收斂","stem_zh":"同一有限原子probability space、固定整數p大於等於1與symbolic moment tail。操作=lp-finite-prefix-boundary；資料={\"masses\":[[1,2],[1,2]],\"coefficients\":[18,-19],\"shift\":2,\"p\":3,\"prefix_length\":18}。請依 exact_ordered_tuple_declared_by_interface 欄序回答。","answer":{"kind":"expression","value":"(18, 否, finite_prefix_not_Lp_convergence_certificate_or_mode_implication)","explanation_zh":"Wave5第四層核對=(18, 否, finite_prefix_not_Lp_convergence_certificate_or_mode_implication)；依完整明示資料重算；核E absolute error power p趨零且moments有限；finite prefix不足，a.s. probability或其他Lq implications另需假設。"},"difficulty":{"band":"undergraduate_core","level":3,"skills":["Lp收斂"]},"variant":{"family_id":"qf-mod35-lp-finite-prefix-boundary","seed":202611047093,"parameters":{"masses":[[1,2],[1,2]],"coefficients":[18,-19],"shift":2,"p":3,"prefix_length":18,"domain":"Finite_atomic_symbolic_Lp_tail","operation":"lp-finite-prefix-boundary","semantic_template":"qf-mod35-lp-finite-prefix-boundary/{\"coefficients\":[18,-19],\"masses\":[[1,2],[1,2]],\"p\":3,\"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-r07-lp-convergence-0094","batch_id":"batch-20261014-advance-20261104-r07-lp-convergence-foundations","language":"zh-Hant","source_mko_ids":["mko-lp-convergence"],"title_zh":"Lp收斂","stem_zh":"同一有限原子probability space、固定整數p大於等於1與symbolic moment tail。操作=lp-finite-prefix-boundary；資料={\"masses\":[[1,2],[1,2]],\"coefficients\":[19,-20],\"shift\":2,\"p\":1,\"prefix_length\":19}。請依 exact_ordered_tuple_declared_by_interface 欄序回答。","answer":{"kind":"expression","value":"(19, 否, finite_prefix_not_Lp_convergence_certificate_or_mode_implication)","explanation_zh":"Wave5第四層核對=(19, 否, finite_prefix_not_Lp_convergence_certificate_or_mode_implication)；依完整明示資料重算；核E absolute error power p趨零且moments有限；finite prefix不足，a.s. probability或其他Lq implications另需假設。"},"difficulty":{"band":"undergraduate_core","level":3,"skills":["Lp收斂"]},"variant":{"family_id":"qf-mod35-lp-finite-prefix-boundary","seed":202611047094,"parameters":{"masses":[[1,2],[1,2]],"coefficients":[19,-20],"shift":2,"p":1,"prefix_length":19,"domain":"Finite_atomic_symbolic_Lp_tail","operation":"lp-finite-prefix-boundary","semantic_template":"qf-mod35-lp-finite-prefix-boundary/{\"coefficients\":[19,-20],\"masses\":[[1,2],[1,2]],\"p\":1,\"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-r07-lp-convergence-0095","batch_id":"batch-20261014-advance-20261104-r07-lp-convergence-foundations","language":"zh-Hant","source_mko_ids":["mko-lp-convergence"],"title_zh":"Lp收斂","stem_zh":"同一有限原子probability space、固定整數p大於等於1與symbolic moment tail。操作=lp-finite-prefix-boundary；資料={\"masses\":[[1,2],[1,2]],\"coefficients\":[20,-21],\"shift\":2,\"p\":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_Lp_convergence_certificate_or_mode_implication)","explanation_zh":"Wave5第四層核對=(20, 否, finite_prefix_not_Lp_convergence_certificate_or_mode_implication)；依完整明示資料重算；核E absolute error power p趨零且moments有限；finite prefix不足，a.s. probability或其他Lq implications另需假設。"},"difficulty":{"band":"undergraduate_core","level":3,"skills":["Lp收斂"]},"variant":{"family_id":"qf-mod35-lp-finite-prefix-boundary","seed":202611047095,"parameters":{"masses":[[1,2],[1,2]],"coefficients":[20,-21],"shift":2,"p":2,"prefix_length":20,"domain":"Finite_atomic_symbolic_Lp_tail","operation":"lp-finite-prefix-boundary","semantic_template":"qf-mod35-lp-finite-prefix-boundary/{\"coefficients\":[20,-21],\"masses\":[[1,2],[1,2]],\"p\":2,\"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-r07-lp-convergence-0096","batch_id":"batch-20261014-advance-20261104-r07-lp-convergence-foundations","language":"zh-Hant","source_mko_ids":["mko-lp-convergence"],"title_zh":"Lp收斂","stem_zh":"同一有限原子probability space、固定整數p大於等於1與symbolic moment tail。操作=lp-finite-prefix-boundary；資料={\"masses\":[[1,2],[1,2]],\"coefficients\":[21,-22],\"shift\":2,\"p\":3,\"prefix_length\":21}。請依 exact_ordered_tuple_declared_by_interface 欄序回答。","answer":{"kind":"expression","value":"(21, 否, finite_prefix_not_Lp_convergence_certificate_or_mode_implication)","explanation_zh":"Wave5第四層核對=(21, 否, finite_prefix_not_Lp_convergence_certificate_or_mode_implication)；依完整明示資料重算；核E absolute error power p趨零且moments有限；finite prefix不足，a.s. probability或其他Lq implications另需假設。"},"difficulty":{"band":"undergraduate_core","level":3,"skills":["Lp收斂"]},"variant":{"family_id":"qf-mod35-lp-finite-prefix-boundary","seed":202611047096,"parameters":{"masses":[[1,2],[1,2]],"coefficients":[21,-22],"shift":2,"p":3,"prefix_length":21,"domain":"Finite_atomic_symbolic_Lp_tail","operation":"lp-finite-prefix-boundary","semantic_template":"qf-mod35-lp-finite-prefix-boundary/{\"coefficients\":[21,-22],\"masses\":[[1,2],[1,2]],\"p\":3,\"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-r07-lp-convergence-0097","batch_id":"batch-20261014-advance-20261104-r07-lp-convergence-foundations","language":"zh-Hant","source_mko_ids":["mko-lp-convergence"],"title_zh":"Lp收斂","stem_zh":"同一有限原子probability space、固定整數p大於等於1與symbolic moment tail。操作=lp-finite-prefix-boundary；資料={\"masses\":[[1,2],[1,2]],\"coefficients\":[22,-23],\"shift\":2,\"p\":1,\"prefix_length\":22}。請依 exact_ordered_tuple_declared_by_interface 欄序回答。","answer":{"kind":"expression","value":"(22, 否, finite_prefix_not_Lp_convergence_certificate_or_mode_implication)","explanation_zh":"Wave5第四層核對=(22, 否, finite_prefix_not_Lp_convergence_certificate_or_mode_implication)；依完整明示資料重算；核E absolute error power p趨零且moments有限；finite prefix不足，a.s. probability或其他Lq implications另需假設。"},"difficulty":{"band":"undergraduate_core","level":3,"skills":["Lp收斂"]},"variant":{"family_id":"qf-mod35-lp-finite-prefix-boundary","seed":202611047097,"parameters":{"masses":[[1,2],[1,2]],"coefficients":[22,-23],"shift":2,"p":1,"prefix_length":22,"domain":"Finite_atomic_symbolic_Lp_tail","operation":"lp-finite-prefix-boundary","semantic_template":"qf-mod35-lp-finite-prefix-boundary/{\"coefficients\":[22,-23],\"masses\":[[1,2],[1,2]],\"p\":1,\"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-r07-lp-convergence-0098","batch_id":"batch-20261014-advance-20261104-r07-lp-convergence-foundations","language":"zh-Hant","source_mko_ids":["mko-lp-convergence"],"title_zh":"Lp收斂","stem_zh":"同一有限原子probability space、固定整數p大於等於1與symbolic moment tail。操作=lp-finite-prefix-boundary；資料={\"masses\":[[1,2],[1,2]],\"coefficients\":[23,-24],\"shift\":2,\"p\":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_Lp_convergence_certificate_or_mode_implication)","explanation_zh":"Wave5第四層核對=(23, 否, finite_prefix_not_Lp_convergence_certificate_or_mode_implication)；依完整明示資料重算；核E absolute error power p趨零且moments有限；finite prefix不足，a.s. probability或其他Lq implications另需假設。"},"difficulty":{"band":"undergraduate_core","level":3,"skills":["Lp收斂"]},"variant":{"family_id":"qf-mod35-lp-finite-prefix-boundary","seed":202611047098,"parameters":{"masses":[[1,2],[1,2]],"coefficients":[23,-24],"shift":2,"p":2,"prefix_length":23,"domain":"Finite_atomic_symbolic_Lp_tail","operation":"lp-finite-prefix-boundary","semantic_template":"qf-mod35-lp-finite-prefix-boundary/{\"coefficients\":[23,-24],\"masses\":[[1,2],[1,2]],\"p\":2,\"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-r07-lp-convergence-0099","batch_id":"batch-20261014-advance-20261104-r07-lp-convergence-foundations","language":"zh-Hant","source_mko_ids":["mko-lp-convergence"],"title_zh":"Lp收斂","stem_zh":"同一有限原子probability space、固定整數p大於等於1與symbolic moment tail。操作=lp-finite-prefix-boundary；資料={\"masses\":[[1,2],[1,2]],\"coefficients\":[24,-25],\"shift\":2,\"p\":3,\"prefix_length\":24}。請依 exact_ordered_tuple_declared_by_interface 欄序回答。","answer":{"kind":"expression","value":"(24, 否, finite_prefix_not_Lp_convergence_certificate_or_mode_implication)","explanation_zh":"Wave5第四層核對=(24, 否, finite_prefix_not_Lp_convergence_certificate_or_mode_implication)；依完整明示資料重算；核E absolute error power p趨零且moments有限；finite prefix不足，a.s. probability或其他Lq implications另需假設。"},"difficulty":{"band":"undergraduate_core","level":3,"skills":["Lp收斂"]},"variant":{"family_id":"qf-mod35-lp-finite-prefix-boundary","seed":202611047099,"parameters":{"masses":[[1,2],[1,2]],"coefficients":[24,-25],"shift":2,"p":3,"prefix_length":24,"domain":"Finite_atomic_symbolic_Lp_tail","operation":"lp-finite-prefix-boundary","semantic_template":"qf-mod35-lp-finite-prefix-boundary/{\"coefficients\":[24,-25],\"masses\":[[1,2],[1,2]],\"p\":3,\"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-r07-lp-convergence-0100","batch_id":"batch-20261014-advance-20261104-r07-lp-convergence-foundations","language":"zh-Hant","source_mko_ids":["mko-lp-convergence"],"title_zh":"Lp收斂","stem_zh":"同一有限原子probability space、固定整數p大於等於1與symbolic moment tail。操作=lp-finite-prefix-boundary；資料={\"masses\":[[1,2],[1,2]],\"coefficients\":[25,-26],\"shift\":2,\"p\":1,\"prefix_length\":25}。請依 exact_ordered_tuple_declared_by_interface 欄序回答。","answer":{"kind":"expression","value":"(25, 否, finite_prefix_not_Lp_convergence_certificate_or_mode_implication)","explanation_zh":"Wave5第四層核對=(25, 否, finite_prefix_not_Lp_convergence_certificate_or_mode_implication)；依完整明示資料重算；核E absolute error power p趨零且moments有限；finite prefix不足，a.s. probability或其他Lq implications另需假設。"},"difficulty":{"band":"undergraduate_core","level":3,"skills":["Lp收斂"]},"variant":{"family_id":"qf-mod35-lp-finite-prefix-boundary","seed":202611047100,"parameters":{"masses":[[1,2],[1,2]],"coefficients":[25,-26],"shift":2,"p":1,"prefix_length":25,"domain":"Finite_atomic_symbolic_Lp_tail","operation":"lp-finite-prefix-boundary","semantic_template":"qf-mod35-lp-finite-prefix-boundary/{\"coefficients\":[25,-26],\"masses\":[[1,2],[1,2]],\"p\":1,\"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"}}