{"schema_version":"ocme-question-v0.1","id":"q-20261014-advance-20261107-r07-subsequence-0001","batch_id":"batch-20261014-advance-20261107-r07-subsequence-foundations","language":"zh-Hant","source_mko_ids":["mko-subsequence"],"title_zh":"子數列","stem_zh":"自然數索引與symbolic嚴格遞增證書。操作=subseq-index-certificate；資料={\"index_start\":0,\"index_step\":1}。請依 exact_ordered_tuple_declared_by_interface 欄序回答。","answer":{"kind":"expression","value":"(0, 1, k(j)=0+1j, 是, strictly_increasing_for_all_natural_j)","explanation_zh":"Wave6根層核對=(0, 1, k(j)=0+1j, 是, strictly_increasing_for_all_natural_j)；依完整明示資料獨立重算；subsequence索引必須嚴格遞增並保留原數列次序，不是重排或任意子集合；有限索引列表只證finite prefix；無限subsequence需要通用increasing-index certificate。"},"difficulty":{"band":"undergraduate_core","level":1,"skills":["子數列"]},"variant":{"family_id":"qf-mod38-subseq-index-certificate","seed":202611077001,"parameters":{"index_start":0,"index_step":1,"domain":"Symbolic_affine_subsequence_index","operation":"subseq-index-certificate","semantic_template":"qf-mod38-subseq-index-certificate/{\"index_start\":0,\"index_step\":1}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_or_symbolic_model","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"候選須主端重算；不構成人工審定、有限sample群作用、sup等於max、basis等於subbasis、signed Markov、pigeonhole converse、nonunit Euler、finite-prefix subsequence、Lean或Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-14","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261014-advance-20261107-r07-subsequence-0002","batch_id":"batch-20261014-advance-20261107-r07-subsequence-foundations","language":"zh-Hant","source_mko_ids":["mko-subsequence"],"title_zh":"子數列","stem_zh":"自然數索引與symbolic嚴格遞增證書。操作=subseq-index-certificate；資料={\"index_start\":1,\"index_step\":2}。請依 exact_ordered_tuple_declared_by_interface 欄序回答。","answer":{"kind":"expression","value":"(1, 2, k(j)=1+2j, 是, strictly_increasing_for_all_natural_j)","explanation_zh":"Wave6根層核對=(1, 2, k(j)=1+2j, 是, strictly_increasing_for_all_natural_j)；依完整明示資料獨立重算；subsequence索引必須嚴格遞增並保留原數列次序，不是重排或任意子集合；有限索引列表只證finite prefix；無限subsequence需要通用increasing-index certificate。"},"difficulty":{"band":"undergraduate_core","level":1,"skills":["子數列"]},"variant":{"family_id":"qf-mod38-subseq-index-certificate","seed":202611077002,"parameters":{"index_start":1,"index_step":2,"domain":"Symbolic_affine_subsequence_index","operation":"subseq-index-certificate","semantic_template":"qf-mod38-subseq-index-certificate/{\"index_start\":1,\"index_step\":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、有限sample群作用、sup等於max、basis等於subbasis、signed Markov、pigeonhole converse、nonunit Euler、finite-prefix subsequence、Lean或Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-14","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261014-advance-20261107-r07-subsequence-0003","batch_id":"batch-20261014-advance-20261107-r07-subsequence-foundations","language":"zh-Hant","source_mko_ids":["mko-subsequence"],"title_zh":"子數列","stem_zh":"自然數索引與symbolic嚴格遞增證書。操作=subseq-index-certificate；資料={\"index_start\":2,\"index_step\":3}。請依 exact_ordered_tuple_declared_by_interface 欄序回答。","answer":{"kind":"expression","value":"(2, 3, k(j)=2+3j, 是, strictly_increasing_for_all_natural_j)","explanation_zh":"Wave6根層核對=(2, 3, k(j)=2+3j, 是, strictly_increasing_for_all_natural_j)；依完整明示資料獨立重算；subsequence索引必須嚴格遞增並保留原數列次序，不是重排或任意子集合；有限索引列表只證finite prefix；無限subsequence需要通用increasing-index certificate。"},"difficulty":{"band":"undergraduate_core","level":1,"skills":["子數列"]},"variant":{"family_id":"qf-mod38-subseq-index-certificate","seed":202611077003,"parameters":{"index_start":2,"index_step":3,"domain":"Symbolic_affine_subsequence_index","operation":"subseq-index-certificate","semantic_template":"qf-mod38-subseq-index-certificate/{\"index_start\":2,\"index_step\":3}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_or_symbolic_model","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"候選須主端重算；不構成人工審定、有限sample群作用、sup等於max、basis等於subbasis、signed Markov、pigeonhole converse、nonunit Euler、finite-prefix subsequence、Lean或Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-14","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261014-advance-20261107-r07-subsequence-0004","batch_id":"batch-20261014-advance-20261107-r07-subsequence-foundations","language":"zh-Hant","source_mko_ids":["mko-subsequence"],"title_zh":"子數列","stem_zh":"自然數索引與symbolic嚴格遞增證書。操作=subseq-index-certificate；資料={\"index_start\":3,\"index_step\":4}。請依 exact_ordered_tuple_declared_by_interface 欄序回答。","answer":{"kind":"expression","value":"(3, 4, k(j)=3+4j, 是, strictly_increasing_for_all_natural_j)","explanation_zh":"Wave6根層核對=(3, 4, k(j)=3+4j, 是, strictly_increasing_for_all_natural_j)；依完整明示資料獨立重算；subsequence索引必須嚴格遞增並保留原數列次序，不是重排或任意子集合；有限索引列表只證finite prefix；無限subsequence需要通用increasing-index certificate。"},"difficulty":{"band":"undergraduate_core","level":1,"skills":["子數列"]},"variant":{"family_id":"qf-mod38-subseq-index-certificate","seed":202611077004,"parameters":{"index_start":3,"index_step":4,"domain":"Symbolic_affine_subsequence_index","operation":"subseq-index-certificate","semantic_template":"qf-mod38-subseq-index-certificate/{\"index_start\":3,\"index_step\":4}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_or_symbolic_model","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"候選須主端重算；不構成人工審定、有限sample群作用、sup等於max、basis等於subbasis、signed Markov、pigeonhole converse、nonunit Euler、finite-prefix subsequence、Lean或Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-14","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261014-advance-20261107-r07-subsequence-0005","batch_id":"batch-20261014-advance-20261107-r07-subsequence-foundations","language":"zh-Hant","source_mko_ids":["mko-subsequence"],"title_zh":"子數列","stem_zh":"自然數索引與symbolic嚴格遞增證書。操作=subseq-index-certificate；資料={\"index_start\":4,\"index_step\":5}。請依 exact_ordered_tuple_declared_by_interface 欄序回答。","answer":{"kind":"expression","value":"(4, 5, k(j)=4+5j, 是, strictly_increasing_for_all_natural_j)","explanation_zh":"Wave6根層核對=(4, 5, k(j)=4+5j, 是, strictly_increasing_for_all_natural_j)；依完整明示資料獨立重算；subsequence索引必須嚴格遞增並保留原數列次序，不是重排或任意子集合；有限索引列表只證finite prefix；無限subsequence需要通用increasing-index certificate。"},"difficulty":{"band":"undergraduate_core","level":1,"skills":["子數列"]},"variant":{"family_id":"qf-mod38-subseq-index-certificate","seed":202611077005,"parameters":{"index_start":4,"index_step":5,"domain":"Symbolic_affine_subsequence_index","operation":"subseq-index-certificate","semantic_template":"qf-mod38-subseq-index-certificate/{\"index_start\":4,\"index_step\":5}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_or_symbolic_model","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"候選須主端重算；不構成人工審定、有限sample群作用、sup等於max、basis等於subbasis、signed Markov、pigeonhole converse、nonunit Euler、finite-prefix subsequence、Lean或Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-14","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261014-advance-20261107-r07-subsequence-0006","batch_id":"batch-20261014-advance-20261107-r07-subsequence-foundations","language":"zh-Hant","source_mko_ids":["mko-subsequence"],"title_zh":"子數列","stem_zh":"自然數索引與symbolic嚴格遞增證書。操作=subseq-index-certificate；資料={\"index_start\":5,\"index_step\":1}。請依 exact_ordered_tuple_declared_by_interface 欄序回答。","answer":{"kind":"expression","value":"(5, 1, k(j)=5+1j, 是, strictly_increasing_for_all_natural_j)","explanation_zh":"Wave6根層核對=(5, 1, k(j)=5+1j, 是, strictly_increasing_for_all_natural_j)；依完整明示資料獨立重算；subsequence索引必須嚴格遞增並保留原數列次序，不是重排或任意子集合；有限索引列表只證finite prefix；無限subsequence需要通用increasing-index certificate。"},"difficulty":{"band":"undergraduate_core","level":1,"skills":["子數列"]},"variant":{"family_id":"qf-mod38-subseq-index-certificate","seed":202611077006,"parameters":{"index_start":5,"index_step":1,"domain":"Symbolic_affine_subsequence_index","operation":"subseq-index-certificate","semantic_template":"qf-mod38-subseq-index-certificate/{\"index_start\":5,\"index_step\":1}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_or_symbolic_model","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"候選須主端重算；不構成人工審定、有限sample群作用、sup等於max、basis等於subbasis、signed Markov、pigeonhole converse、nonunit Euler、finite-prefix subsequence、Lean或Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-14","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261014-advance-20261107-r07-subsequence-0007","batch_id":"batch-20261014-advance-20261107-r07-subsequence-foundations","language":"zh-Hant","source_mko_ids":["mko-subsequence"],"title_zh":"子數列","stem_zh":"自然數索引與symbolic嚴格遞增證書。操作=subseq-index-certificate；資料={\"index_start\":6,\"index_step\":2}。請依 exact_ordered_tuple_declared_by_interface 欄序回答。","answer":{"kind":"expression","value":"(6, 2, k(j)=6+2j, 是, strictly_increasing_for_all_natural_j)","explanation_zh":"Wave6根層核對=(6, 2, k(j)=6+2j, 是, strictly_increasing_for_all_natural_j)；依完整明示資料獨立重算；subsequence索引必須嚴格遞增並保留原數列次序，不是重排或任意子集合；有限索引列表只證finite prefix；無限subsequence需要通用increasing-index certificate。"},"difficulty":{"band":"undergraduate_core","level":1,"skills":["子數列"]},"variant":{"family_id":"qf-mod38-subseq-index-certificate","seed":202611077007,"parameters":{"index_start":6,"index_step":2,"domain":"Symbolic_affine_subsequence_index","operation":"subseq-index-certificate","semantic_template":"qf-mod38-subseq-index-certificate/{\"index_start\":6,\"index_step\":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、有限sample群作用、sup等於max、basis等於subbasis、signed Markov、pigeonhole converse、nonunit Euler、finite-prefix subsequence、Lean或Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-14","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261014-advance-20261107-r07-subsequence-0008","batch_id":"batch-20261014-advance-20261107-r07-subsequence-foundations","language":"zh-Hant","source_mko_ids":["mko-subsequence"],"title_zh":"子數列","stem_zh":"自然數索引與symbolic嚴格遞增證書。操作=subseq-index-certificate；資料={\"index_start\":7,\"index_step\":3}。請依 exact_ordered_tuple_declared_by_interface 欄序回答。","answer":{"kind":"expression","value":"(7, 3, k(j)=7+3j, 是, strictly_increasing_for_all_natural_j)","explanation_zh":"Wave6根層核對=(7, 3, k(j)=7+3j, 是, strictly_increasing_for_all_natural_j)；依完整明示資料獨立重算；subsequence索引必須嚴格遞增並保留原數列次序，不是重排或任意子集合；有限索引列表只證finite prefix；無限subsequence需要通用increasing-index certificate。"},"difficulty":{"band":"undergraduate_core","level":1,"skills":["子數列"]},"variant":{"family_id":"qf-mod38-subseq-index-certificate","seed":202611077008,"parameters":{"index_start":7,"index_step":3,"domain":"Symbolic_affine_subsequence_index","operation":"subseq-index-certificate","semantic_template":"qf-mod38-subseq-index-certificate/{\"index_start\":7,\"index_step\":3}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_or_symbolic_model","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"候選須主端重算；不構成人工審定、有限sample群作用、sup等於max、basis等於subbasis、signed Markov、pigeonhole converse、nonunit Euler、finite-prefix subsequence、Lean或Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-14","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261014-advance-20261107-r07-subsequence-0009","batch_id":"batch-20261014-advance-20261107-r07-subsequence-foundations","language":"zh-Hant","source_mko_ids":["mko-subsequence"],"title_zh":"子數列","stem_zh":"自然數索引與symbolic嚴格遞增證書。操作=subseq-index-certificate；資料={\"index_start\":8,\"index_step\":4}。請依 exact_ordered_tuple_declared_by_interface 欄序回答。","answer":{"kind":"expression","value":"(8, 4, k(j)=8+4j, 是, strictly_increasing_for_all_natural_j)","explanation_zh":"Wave6根層核對=(8, 4, k(j)=8+4j, 是, strictly_increasing_for_all_natural_j)；依完整明示資料獨立重算；subsequence索引必須嚴格遞增並保留原數列次序，不是重排或任意子集合；有限索引列表只證finite prefix；無限subsequence需要通用increasing-index certificate。"},"difficulty":{"band":"undergraduate_core","level":2,"skills":["子數列"]},"variant":{"family_id":"qf-mod38-subseq-index-certificate","seed":202611077009,"parameters":{"index_start":8,"index_step":4,"domain":"Symbolic_affine_subsequence_index","operation":"subseq-index-certificate","semantic_template":"qf-mod38-subseq-index-certificate/{\"index_start\":8,\"index_step\":4}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_or_symbolic_model","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"候選須主端重算；不構成人工審定、有限sample群作用、sup等於max、basis等於subbasis、signed Markov、pigeonhole converse、nonunit Euler、finite-prefix subsequence、Lean或Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-14","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261014-advance-20261107-r07-subsequence-0010","batch_id":"batch-20261014-advance-20261107-r07-subsequence-foundations","language":"zh-Hant","source_mko_ids":["mko-subsequence"],"title_zh":"子數列","stem_zh":"自然數索引與symbolic嚴格遞增證書。操作=subseq-index-certificate；資料={\"index_start\":9,\"index_step\":5}。請依 exact_ordered_tuple_declared_by_interface 欄序回答。","answer":{"kind":"expression","value":"(9, 5, k(j)=9+5j, 是, strictly_increasing_for_all_natural_j)","explanation_zh":"Wave6根層核對=(9, 5, k(j)=9+5j, 是, strictly_increasing_for_all_natural_j)；依完整明示資料獨立重算；subsequence索引必須嚴格遞增並保留原數列次序，不是重排或任意子集合；有限索引列表只證finite prefix；無限subsequence需要通用increasing-index certificate。"},"difficulty":{"band":"undergraduate_core","level":2,"skills":["子數列"]},"variant":{"family_id":"qf-mod38-subseq-index-certificate","seed":202611077010,"parameters":{"index_start":9,"index_step":5,"domain":"Symbolic_affine_subsequence_index","operation":"subseq-index-certificate","semantic_template":"qf-mod38-subseq-index-certificate/{\"index_start\":9,\"index_step\":5}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_or_symbolic_model","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"候選須主端重算；不構成人工審定、有限sample群作用、sup等於max、basis等於subbasis、signed Markov、pigeonhole converse、nonunit Euler、finite-prefix subsequence、Lean或Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-14","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261014-advance-20261107-r07-subsequence-0011","batch_id":"batch-20261014-advance-20261107-r07-subsequence-foundations","language":"zh-Hant","source_mko_ids":["mko-subsequence"],"title_zh":"子數列","stem_zh":"自然數索引與symbolic嚴格遞增證書。操作=subseq-index-certificate；資料={\"index_start\":10,\"index_step\":1}。請依 exact_ordered_tuple_declared_by_interface 欄序回答。","answer":{"kind":"expression","value":"(10, 1, k(j)=10+1j, 是, strictly_increasing_for_all_natural_j)","explanation_zh":"Wave6根層核對=(10, 1, k(j)=10+1j, 是, strictly_increasing_for_all_natural_j)；依完整明示資料獨立重算；subsequence索引必須嚴格遞增並保留原數列次序，不是重排或任意子集合；有限索引列表只證finite prefix；無限subsequence需要通用increasing-index certificate。"},"difficulty":{"band":"undergraduate_core","level":2,"skills":["子數列"]},"variant":{"family_id":"qf-mod38-subseq-index-certificate","seed":202611077011,"parameters":{"index_start":10,"index_step":1,"domain":"Symbolic_affine_subsequence_index","operation":"subseq-index-certificate","semantic_template":"qf-mod38-subseq-index-certificate/{\"index_start\":10,\"index_step\":1}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_or_symbolic_model","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"候選須主端重算；不構成人工審定、有限sample群作用、sup等於max、basis等於subbasis、signed Markov、pigeonhole converse、nonunit Euler、finite-prefix subsequence、Lean或Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-14","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261014-advance-20261107-r07-subsequence-0012","batch_id":"batch-20261014-advance-20261107-r07-subsequence-foundations","language":"zh-Hant","source_mko_ids":["mko-subsequence"],"title_zh":"子數列","stem_zh":"自然數索引與symbolic嚴格遞增證書。操作=subseq-index-certificate；資料={\"index_start\":11,\"index_step\":2}。請依 exact_ordered_tuple_declared_by_interface 欄序回答。","answer":{"kind":"expression","value":"(11, 2, k(j)=11+2j, 是, strictly_increasing_for_all_natural_j)","explanation_zh":"Wave6根層核對=(11, 2, k(j)=11+2j, 是, strictly_increasing_for_all_natural_j)；依完整明示資料獨立重算；subsequence索引必須嚴格遞增並保留原數列次序，不是重排或任意子集合；有限索引列表只證finite prefix；無限subsequence需要通用increasing-index certificate。"},"difficulty":{"band":"undergraduate_core","level":2,"skills":["子數列"]},"variant":{"family_id":"qf-mod38-subseq-index-certificate","seed":202611077012,"parameters":{"index_start":11,"index_step":2,"domain":"Symbolic_affine_subsequence_index","operation":"subseq-index-certificate","semantic_template":"qf-mod38-subseq-index-certificate/{\"index_start\":11,\"index_step\":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、有限sample群作用、sup等於max、basis等於subbasis、signed Markov、pigeonhole converse、nonunit Euler、finite-prefix subsequence、Lean或Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-14","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261014-advance-20261107-r07-subsequence-0013","batch_id":"batch-20261014-advance-20261107-r07-subsequence-foundations","language":"zh-Hant","source_mko_ids":["mko-subsequence"],"title_zh":"子數列","stem_zh":"自然數索引與symbolic嚴格遞增證書。操作=subseq-index-certificate；資料={\"index_start\":12,\"index_step\":3}。請依 exact_ordered_tuple_declared_by_interface 欄序回答。","answer":{"kind":"expression","value":"(12, 3, k(j)=12+3j, 是, strictly_increasing_for_all_natural_j)","explanation_zh":"Wave6根層核對=(12, 3, k(j)=12+3j, 是, strictly_increasing_for_all_natural_j)；依完整明示資料獨立重算；subsequence索引必須嚴格遞增並保留原數列次序，不是重排或任意子集合；有限索引列表只證finite prefix；無限subsequence需要通用increasing-index certificate。"},"difficulty":{"band":"undergraduate_core","level":2,"skills":["子數列"]},"variant":{"family_id":"qf-mod38-subseq-index-certificate","seed":202611077013,"parameters":{"index_start":12,"index_step":3,"domain":"Symbolic_affine_subsequence_index","operation":"subseq-index-certificate","semantic_template":"qf-mod38-subseq-index-certificate/{\"index_start\":12,\"index_step\":3}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_or_symbolic_model","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"候選須主端重算；不構成人工審定、有限sample群作用、sup等於max、basis等於subbasis、signed Markov、pigeonhole converse、nonunit Euler、finite-prefix subsequence、Lean或Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-14","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261014-advance-20261107-r07-subsequence-0014","batch_id":"batch-20261014-advance-20261107-r07-subsequence-foundations","language":"zh-Hant","source_mko_ids":["mko-subsequence"],"title_zh":"子數列","stem_zh":"自然數索引與symbolic嚴格遞增證書。操作=subseq-index-certificate；資料={\"index_start\":13,\"index_step\":4}。請依 exact_ordered_tuple_declared_by_interface 欄序回答。","answer":{"kind":"expression","value":"(13, 4, k(j)=13+4j, 是, strictly_increasing_for_all_natural_j)","explanation_zh":"Wave6根層核對=(13, 4, k(j)=13+4j, 是, strictly_increasing_for_all_natural_j)；依完整明示資料獨立重算；subsequence索引必須嚴格遞增並保留原數列次序，不是重排或任意子集合；有限索引列表只證finite prefix；無限subsequence需要通用increasing-index certificate。"},"difficulty":{"band":"undergraduate_core","level":2,"skills":["子數列"]},"variant":{"family_id":"qf-mod38-subseq-index-certificate","seed":202611077014,"parameters":{"index_start":13,"index_step":4,"domain":"Symbolic_affine_subsequence_index","operation":"subseq-index-certificate","semantic_template":"qf-mod38-subseq-index-certificate/{\"index_start\":13,\"index_step\":4}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_or_symbolic_model","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"候選須主端重算；不構成人工審定、有限sample群作用、sup等於max、basis等於subbasis、signed Markov、pigeonhole converse、nonunit Euler、finite-prefix subsequence、Lean或Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-14","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261014-advance-20261107-r07-subsequence-0015","batch_id":"batch-20261014-advance-20261107-r07-subsequence-foundations","language":"zh-Hant","source_mko_ids":["mko-subsequence"],"title_zh":"子數列","stem_zh":"自然數索引與symbolic嚴格遞增證書。操作=subseq-index-certificate；資料={\"index_start\":14,\"index_step\":5}。請依 exact_ordered_tuple_declared_by_interface 欄序回答。","answer":{"kind":"expression","value":"(14, 5, k(j)=14+5j, 是, strictly_increasing_for_all_natural_j)","explanation_zh":"Wave6根層核對=(14, 5, k(j)=14+5j, 是, strictly_increasing_for_all_natural_j)；依完整明示資料獨立重算；subsequence索引必須嚴格遞增並保留原數列次序，不是重排或任意子集合；有限索引列表只證finite prefix；無限subsequence需要通用increasing-index certificate。"},"difficulty":{"band":"undergraduate_core","level":2,"skills":["子數列"]},"variant":{"family_id":"qf-mod38-subseq-index-certificate","seed":202611077015,"parameters":{"index_start":14,"index_step":5,"domain":"Symbolic_affine_subsequence_index","operation":"subseq-index-certificate","semantic_template":"qf-mod38-subseq-index-certificate/{\"index_start\":14,\"index_step\":5}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_or_symbolic_model","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"候選須主端重算；不構成人工審定、有限sample群作用、sup等於max、basis等於subbasis、signed Markov、pigeonhole converse、nonunit Euler、finite-prefix subsequence、Lean或Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-14","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261014-advance-20261107-r07-subsequence-0016","batch_id":"batch-20261014-advance-20261107-r07-subsequence-foundations","language":"zh-Hant","source_mko_ids":["mko-subsequence"],"title_zh":"子數列","stem_zh":"自然數索引與symbolic嚴格遞增證書。操作=subseq-index-certificate；資料={\"index_start\":15,\"index_step\":1}。請依 exact_ordered_tuple_declared_by_interface 欄序回答。","answer":{"kind":"expression","value":"(15, 1, k(j)=15+1j, 是, strictly_increasing_for_all_natural_j)","explanation_zh":"Wave6根層核對=(15, 1, k(j)=15+1j, 是, strictly_increasing_for_all_natural_j)；依完整明示資料獨立重算；subsequence索引必須嚴格遞增並保留原數列次序，不是重排或任意子集合；有限索引列表只證finite prefix；無限subsequence需要通用increasing-index certificate。"},"difficulty":{"band":"undergraduate_core","level":2,"skills":["子數列"]},"variant":{"family_id":"qf-mod38-subseq-index-certificate","seed":202611077016,"parameters":{"index_start":15,"index_step":1,"domain":"Symbolic_affine_subsequence_index","operation":"subseq-index-certificate","semantic_template":"qf-mod38-subseq-index-certificate/{\"index_start\":15,\"index_step\":1}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_or_symbolic_model","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"候選須主端重算；不構成人工審定、有限sample群作用、sup等於max、basis等於subbasis、signed Markov、pigeonhole converse、nonunit Euler、finite-prefix subsequence、Lean或Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-14","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261014-advance-20261107-r07-subsequence-0017","batch_id":"batch-20261014-advance-20261107-r07-subsequence-foundations","language":"zh-Hant","source_mko_ids":["mko-subsequence"],"title_zh":"子數列","stem_zh":"自然數索引與symbolic嚴格遞增證書。操作=subseq-index-certificate；資料={\"index_start\":16,\"index_step\":2}。請依 exact_ordered_tuple_declared_by_interface 欄序回答。","answer":{"kind":"expression","value":"(16, 2, k(j)=16+2j, 是, strictly_increasing_for_all_natural_j)","explanation_zh":"Wave6根層核對=(16, 2, k(j)=16+2j, 是, strictly_increasing_for_all_natural_j)；依完整明示資料獨立重算；subsequence索引必須嚴格遞增並保留原數列次序，不是重排或任意子集合；有限索引列表只證finite prefix；無限subsequence需要通用increasing-index certificate。"},"difficulty":{"band":"undergraduate_core","level":2,"skills":["子數列"]},"variant":{"family_id":"qf-mod38-subseq-index-certificate","seed":202611077017,"parameters":{"index_start":16,"index_step":2,"domain":"Symbolic_affine_subsequence_index","operation":"subseq-index-certificate","semantic_template":"qf-mod38-subseq-index-certificate/{\"index_start\":16,\"index_step\":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、有限sample群作用、sup等於max、basis等於subbasis、signed Markov、pigeonhole converse、nonunit Euler、finite-prefix subsequence、Lean或Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-14","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261014-advance-20261107-r07-subsequence-0018","batch_id":"batch-20261014-advance-20261107-r07-subsequence-foundations","language":"zh-Hant","source_mko_ids":["mko-subsequence"],"title_zh":"子數列","stem_zh":"自然數索引與symbolic嚴格遞增證書。操作=subseq-index-certificate；資料={\"index_start\":17,\"index_step\":3}。請依 exact_ordered_tuple_declared_by_interface 欄序回答。","answer":{"kind":"expression","value":"(17, 3, k(j)=17+3j, 是, strictly_increasing_for_all_natural_j)","explanation_zh":"Wave6根層核對=(17, 3, k(j)=17+3j, 是, strictly_increasing_for_all_natural_j)；依完整明示資料獨立重算；subsequence索引必須嚴格遞增並保留原數列次序，不是重排或任意子集合；有限索引列表只證finite prefix；無限subsequence需要通用increasing-index certificate。"},"difficulty":{"band":"undergraduate_core","level":3,"skills":["子數列"]},"variant":{"family_id":"qf-mod38-subseq-index-certificate","seed":202611077018,"parameters":{"index_start":17,"index_step":3,"domain":"Symbolic_affine_subsequence_index","operation":"subseq-index-certificate","semantic_template":"qf-mod38-subseq-index-certificate/{\"index_start\":17,\"index_step\":3}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_or_symbolic_model","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"候選須主端重算；不構成人工審定、有限sample群作用、sup等於max、basis等於subbasis、signed Markov、pigeonhole converse、nonunit Euler、finite-prefix subsequence、Lean或Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-14","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261014-advance-20261107-r07-subsequence-0019","batch_id":"batch-20261014-advance-20261107-r07-subsequence-foundations","language":"zh-Hant","source_mko_ids":["mko-subsequence"],"title_zh":"子數列","stem_zh":"自然數索引與symbolic嚴格遞增證書。操作=subseq-index-certificate；資料={\"index_start\":18,\"index_step\":4}。請依 exact_ordered_tuple_declared_by_interface 欄序回答。","answer":{"kind":"expression","value":"(18, 4, k(j)=18+4j, 是, strictly_increasing_for_all_natural_j)","explanation_zh":"Wave6根層核對=(18, 4, k(j)=18+4j, 是, strictly_increasing_for_all_natural_j)；依完整明示資料獨立重算；subsequence索引必須嚴格遞增並保留原數列次序，不是重排或任意子集合；有限索引列表只證finite prefix；無限subsequence需要通用increasing-index certificate。"},"difficulty":{"band":"undergraduate_core","level":3,"skills":["子數列"]},"variant":{"family_id":"qf-mod38-subseq-index-certificate","seed":202611077019,"parameters":{"index_start":18,"index_step":4,"domain":"Symbolic_affine_subsequence_index","operation":"subseq-index-certificate","semantic_template":"qf-mod38-subseq-index-certificate/{\"index_start\":18,\"index_step\":4}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_or_symbolic_model","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"候選須主端重算；不構成人工審定、有限sample群作用、sup等於max、basis等於subbasis、signed Markov、pigeonhole converse、nonunit Euler、finite-prefix subsequence、Lean或Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-14","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261014-advance-20261107-r07-subsequence-0020","batch_id":"batch-20261014-advance-20261107-r07-subsequence-foundations","language":"zh-Hant","source_mko_ids":["mko-subsequence"],"title_zh":"子數列","stem_zh":"自然數索引與symbolic嚴格遞增證書。操作=subseq-index-certificate；資料={\"index_start\":19,\"index_step\":5}。請依 exact_ordered_tuple_declared_by_interface 欄序回答。","answer":{"kind":"expression","value":"(19, 5, k(j)=19+5j, 是, strictly_increasing_for_all_natural_j)","explanation_zh":"Wave6根層核對=(19, 5, k(j)=19+5j, 是, strictly_increasing_for_all_natural_j)；依完整明示資料獨立重算；subsequence索引必須嚴格遞增並保留原數列次序，不是重排或任意子集合；有限索引列表只證finite prefix；無限subsequence需要通用increasing-index certificate。"},"difficulty":{"band":"undergraduate_core","level":3,"skills":["子數列"]},"variant":{"family_id":"qf-mod38-subseq-index-certificate","seed":202611077020,"parameters":{"index_start":19,"index_step":5,"domain":"Symbolic_affine_subsequence_index","operation":"subseq-index-certificate","semantic_template":"qf-mod38-subseq-index-certificate/{\"index_start\":19,\"index_step\":5}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_or_symbolic_model","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"候選須主端重算；不構成人工審定、有限sample群作用、sup等於max、basis等於subbasis、signed Markov、pigeonhole converse、nonunit Euler、finite-prefix subsequence、Lean或Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-14","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261014-advance-20261107-r07-subsequence-0021","batch_id":"batch-20261014-advance-20261107-r07-subsequence-foundations","language":"zh-Hant","source_mko_ids":["mko-subsequence"],"title_zh":"子數列","stem_zh":"自然數索引與symbolic嚴格遞增證書。操作=subseq-index-certificate；資料={\"index_start\":20,\"index_step\":1}。請依 exact_ordered_tuple_declared_by_interface 欄序回答。","answer":{"kind":"expression","value":"(20, 1, k(j)=20+1j, 是, strictly_increasing_for_all_natural_j)","explanation_zh":"Wave6根層核對=(20, 1, k(j)=20+1j, 是, strictly_increasing_for_all_natural_j)；依完整明示資料獨立重算；subsequence索引必須嚴格遞增並保留原數列次序，不是重排或任意子集合；有限索引列表只證finite prefix；無限subsequence需要通用increasing-index certificate。"},"difficulty":{"band":"undergraduate_core","level":3,"skills":["子數列"]},"variant":{"family_id":"qf-mod38-subseq-index-certificate","seed":202611077021,"parameters":{"index_start":20,"index_step":1,"domain":"Symbolic_affine_subsequence_index","operation":"subseq-index-certificate","semantic_template":"qf-mod38-subseq-index-certificate/{\"index_start\":20,\"index_step\":1}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_or_symbolic_model","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"候選須主端重算；不構成人工審定、有限sample群作用、sup等於max、basis等於subbasis、signed Markov、pigeonhole converse、nonunit Euler、finite-prefix subsequence、Lean或Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-14","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261014-advance-20261107-r07-subsequence-0022","batch_id":"batch-20261014-advance-20261107-r07-subsequence-foundations","language":"zh-Hant","source_mko_ids":["mko-subsequence"],"title_zh":"子數列","stem_zh":"自然數索引與symbolic嚴格遞增證書。操作=subseq-index-certificate；資料={\"index_start\":21,\"index_step\":2}。請依 exact_ordered_tuple_declared_by_interface 欄序回答。","answer":{"kind":"expression","value":"(21, 2, k(j)=21+2j, 是, strictly_increasing_for_all_natural_j)","explanation_zh":"Wave6根層核對=(21, 2, k(j)=21+2j, 是, strictly_increasing_for_all_natural_j)；依完整明示資料獨立重算；subsequence索引必須嚴格遞增並保留原數列次序，不是重排或任意子集合；有限索引列表只證finite prefix；無限subsequence需要通用increasing-index certificate。"},"difficulty":{"band":"undergraduate_core","level":3,"skills":["子數列"]},"variant":{"family_id":"qf-mod38-subseq-index-certificate","seed":202611077022,"parameters":{"index_start":21,"index_step":2,"domain":"Symbolic_affine_subsequence_index","operation":"subseq-index-certificate","semantic_template":"qf-mod38-subseq-index-certificate/{\"index_start\":21,\"index_step\":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、有限sample群作用、sup等於max、basis等於subbasis、signed Markov、pigeonhole converse、nonunit Euler、finite-prefix subsequence、Lean或Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-14","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261014-advance-20261107-r07-subsequence-0023","batch_id":"batch-20261014-advance-20261107-r07-subsequence-foundations","language":"zh-Hant","source_mko_ids":["mko-subsequence"],"title_zh":"子數列","stem_zh":"自然數索引與symbolic嚴格遞增證書。操作=subseq-index-certificate；資料={\"index_start\":22,\"index_step\":3}。請依 exact_ordered_tuple_declared_by_interface 欄序回答。","answer":{"kind":"expression","value":"(22, 3, k(j)=22+3j, 是, strictly_increasing_for_all_natural_j)","explanation_zh":"Wave6根層核對=(22, 3, k(j)=22+3j, 是, strictly_increasing_for_all_natural_j)；依完整明示資料獨立重算；subsequence索引必須嚴格遞增並保留原數列次序，不是重排或任意子集合；有限索引列表只證finite prefix；無限subsequence需要通用increasing-index certificate。"},"difficulty":{"band":"undergraduate_core","level":3,"skills":["子數列"]},"variant":{"family_id":"qf-mod38-subseq-index-certificate","seed":202611077023,"parameters":{"index_start":22,"index_step":3,"domain":"Symbolic_affine_subsequence_index","operation":"subseq-index-certificate","semantic_template":"qf-mod38-subseq-index-certificate/{\"index_start\":22,\"index_step\":3}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_or_symbolic_model","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"候選須主端重算；不構成人工審定、有限sample群作用、sup等於max、basis等於subbasis、signed Markov、pigeonhole converse、nonunit Euler、finite-prefix subsequence、Lean或Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-14","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261014-advance-20261107-r07-subsequence-0024","batch_id":"batch-20261014-advance-20261107-r07-subsequence-foundations","language":"zh-Hant","source_mko_ids":["mko-subsequence"],"title_zh":"子數列","stem_zh":"自然數索引與symbolic嚴格遞增證書。操作=subseq-index-certificate；資料={\"index_start\":23,\"index_step\":4}。請依 exact_ordered_tuple_declared_by_interface 欄序回答。","answer":{"kind":"expression","value":"(23, 4, k(j)=23+4j, 是, strictly_increasing_for_all_natural_j)","explanation_zh":"Wave6根層核對=(23, 4, k(j)=23+4j, 是, strictly_increasing_for_all_natural_j)；依完整明示資料獨立重算；subsequence索引必須嚴格遞增並保留原數列次序，不是重排或任意子集合；有限索引列表只證finite prefix；無限subsequence需要通用increasing-index certificate。"},"difficulty":{"band":"undergraduate_core","level":3,"skills":["子數列"]},"variant":{"family_id":"qf-mod38-subseq-index-certificate","seed":202611077024,"parameters":{"index_start":23,"index_step":4,"domain":"Symbolic_affine_subsequence_index","operation":"subseq-index-certificate","semantic_template":"qf-mod38-subseq-index-certificate/{\"index_start\":23,\"index_step\":4}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_or_symbolic_model","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"候選須主端重算；不構成人工審定、有限sample群作用、sup等於max、basis等於subbasis、signed Markov、pigeonhole converse、nonunit Euler、finite-prefix subsequence、Lean或Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-14","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261014-advance-20261107-r07-subsequence-0025","batch_id":"batch-20261014-advance-20261107-r07-subsequence-foundations","language":"zh-Hant","source_mko_ids":["mko-subsequence"],"title_zh":"子數列","stem_zh":"自然數索引與symbolic嚴格遞增證書。操作=subseq-index-certificate；資料={\"index_start\":24,\"index_step\":5}。請依 exact_ordered_tuple_declared_by_interface 欄序回答。","answer":{"kind":"expression","value":"(24, 5, k(j)=24+5j, 是, strictly_increasing_for_all_natural_j)","explanation_zh":"Wave6根層核對=(24, 5, k(j)=24+5j, 是, strictly_increasing_for_all_natural_j)；依完整明示資料獨立重算；subsequence索引必須嚴格遞增並保留原數列次序，不是重排或任意子集合；有限索引列表只證finite prefix；無限subsequence需要通用increasing-index certificate。"},"difficulty":{"band":"undergraduate_core","level":3,"skills":["子數列"]},"variant":{"family_id":"qf-mod38-subseq-index-certificate","seed":202611077025,"parameters":{"index_start":24,"index_step":5,"domain":"Symbolic_affine_subsequence_index","operation":"subseq-index-certificate","semantic_template":"qf-mod38-subseq-index-certificate/{\"index_start\":24,\"index_step\":5}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_or_symbolic_model","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"候選須主端重算；不構成人工審定、有限sample群作用、sup等於max、basis等於subbasis、signed Markov、pigeonhole converse、nonunit Euler、finite-prefix subsequence、Lean或Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-14","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261014-advance-20261107-r07-subsequence-0026","batch_id":"batch-20261014-advance-20261107-r07-subsequence-foundations","language":"zh-Hant","source_mko_ids":["mko-subsequence"],"title_zh":"子數列","stem_zh":"自然數索引與symbolic嚴格遞增證書。操作=subseq-arithmetic-term；資料={\"source_start\":1,\"source_step\":1,\"index_start\":0,\"index_step\":1,\"j\":2}。請依 exact_ordered_tuple_declared_by_interface 欄序回答。","answer":{"kind":"expression","value":"(2, 2, 3, a_of_k_j_preserves_original_order)","explanation_zh":"Wave6根層核對=(2, 2, 3, a_of_k_j_preserves_original_order)；依完整明示資料獨立重算；subsequence索引必須嚴格遞增並保留原數列次序，不是重排或任意子集合；有限索引列表只證finite prefix；無限subsequence需要通用increasing-index certificate。"},"difficulty":{"band":"undergraduate_core","level":1,"skills":["子數列"]},"variant":{"family_id":"qf-mod38-subseq-arithmetic-term","seed":202611077026,"parameters":{"source_start":1,"source_step":1,"index_start":0,"index_step":1,"j":2,"domain":"Symbolic_affine_subsequence_index","operation":"subseq-arithmetic-term","semantic_template":"qf-mod38-subseq-arithmetic-term/{\"index_start\":0,\"index_step\":1,\"j\":2,\"source_start\":1,\"source_step\":1}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_or_symbolic_model","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"候選須主端重算；不構成人工審定、有限sample群作用、sup等於max、basis等於subbasis、signed Markov、pigeonhole converse、nonunit Euler、finite-prefix subsequence、Lean或Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-14","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261014-advance-20261107-r07-subsequence-0027","batch_id":"batch-20261014-advance-20261107-r07-subsequence-foundations","language":"zh-Hant","source_mko_ids":["mko-subsequence"],"title_zh":"子數列","stem_zh":"自然數索引與symbolic嚴格遞增證書。操作=subseq-arithmetic-term；資料={\"source_start\":2,\"source_step\":2,\"index_start\":1,\"index_step\":2,\"j\":3}。請依 exact_ordered_tuple_declared_by_interface 欄序回答。","answer":{"kind":"expression","value":"(3, 7, 16, a_of_k_j_preserves_original_order)","explanation_zh":"Wave6根層核對=(3, 7, 16, a_of_k_j_preserves_original_order)；依完整明示資料獨立重算；subsequence索引必須嚴格遞增並保留原數列次序，不是重排或任意子集合；有限索引列表只證finite prefix；無限subsequence需要通用increasing-index certificate。"},"difficulty":{"band":"undergraduate_core","level":1,"skills":["子數列"]},"variant":{"family_id":"qf-mod38-subseq-arithmetic-term","seed":202611077027,"parameters":{"source_start":2,"source_step":2,"index_start":1,"index_step":2,"j":3,"domain":"Symbolic_affine_subsequence_index","operation":"subseq-arithmetic-term","semantic_template":"qf-mod38-subseq-arithmetic-term/{\"index_start\":1,\"index_step\":2,\"j\":3,\"source_start\":2,\"source_step\":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、有限sample群作用、sup等於max、basis等於subbasis、signed Markov、pigeonhole converse、nonunit Euler、finite-prefix subsequence、Lean或Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-14","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261014-advance-20261107-r07-subsequence-0028","batch_id":"batch-20261014-advance-20261107-r07-subsequence-foundations","language":"zh-Hant","source_mko_ids":["mko-subsequence"],"title_zh":"子數列","stem_zh":"自然數索引與symbolic嚴格遞增證書。操作=subseq-arithmetic-term；資料={\"source_start\":3,\"source_step\":3,\"index_start\":2,\"index_step\":3,\"j\":4}。請依 exact_ordered_tuple_declared_by_interface 欄序回答。","answer":{"kind":"expression","value":"(4, 14, 45, a_of_k_j_preserves_original_order)","explanation_zh":"Wave6根層核對=(4, 14, 45, a_of_k_j_preserves_original_order)；依完整明示資料獨立重算；subsequence索引必須嚴格遞增並保留原數列次序，不是重排或任意子集合；有限索引列表只證finite prefix；無限subsequence需要通用increasing-index certificate。"},"difficulty":{"band":"undergraduate_core","level":1,"skills":["子數列"]},"variant":{"family_id":"qf-mod38-subseq-arithmetic-term","seed":202611077028,"parameters":{"source_start":3,"source_step":3,"index_start":2,"index_step":3,"j":4,"domain":"Symbolic_affine_subsequence_index","operation":"subseq-arithmetic-term","semantic_template":"qf-mod38-subseq-arithmetic-term/{\"index_start\":2,\"index_step\":3,\"j\":4,\"source_start\":3,\"source_step\":3}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_or_symbolic_model","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"候選須主端重算；不構成人工審定、有限sample群作用、sup等於max、basis等於subbasis、signed Markov、pigeonhole converse、nonunit Euler、finite-prefix subsequence、Lean或Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-14","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261014-advance-20261107-r07-subsequence-0029","batch_id":"batch-20261014-advance-20261107-r07-subsequence-foundations","language":"zh-Hant","source_mko_ids":["mko-subsequence"],"title_zh":"子數列","stem_zh":"自然數索引與symbolic嚴格遞增證書。操作=subseq-arithmetic-term；資料={\"source_start\":4,\"source_step\":4,\"index_start\":3,\"index_step\":4,\"j\":5}。請依 exact_ordered_tuple_declared_by_interface 欄序回答。","answer":{"kind":"expression","value":"(5, 23, 96, a_of_k_j_preserves_original_order)","explanation_zh":"Wave6根層核對=(5, 23, 96, a_of_k_j_preserves_original_order)；依完整明示資料獨立重算；subsequence索引必須嚴格遞增並保留原數列次序，不是重排或任意子集合；有限索引列表只證finite prefix；無限subsequence需要通用increasing-index certificate。"},"difficulty":{"band":"undergraduate_core","level":1,"skills":["子數列"]},"variant":{"family_id":"qf-mod38-subseq-arithmetic-term","seed":202611077029,"parameters":{"source_start":4,"source_step":4,"index_start":3,"index_step":4,"j":5,"domain":"Symbolic_affine_subsequence_index","operation":"subseq-arithmetic-term","semantic_template":"qf-mod38-subseq-arithmetic-term/{\"index_start\":3,\"index_step\":4,\"j\":5,\"source_start\":4,\"source_step\":4}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_or_symbolic_model","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"候選須主端重算；不構成人工審定、有限sample群作用、sup等於max、basis等於subbasis、signed Markov、pigeonhole converse、nonunit Euler、finite-prefix subsequence、Lean或Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-14","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261014-advance-20261107-r07-subsequence-0030","batch_id":"batch-20261014-advance-20261107-r07-subsequence-foundations","language":"zh-Hant","source_mko_ids":["mko-subsequence"],"title_zh":"子數列","stem_zh":"自然數索引與symbolic嚴格遞增證書。操作=subseq-arithmetic-term；資料={\"source_start\":5,\"source_step\":5,\"index_start\":0,\"index_step\":5,\"j\":6}。請依 exact_ordered_tuple_declared_by_interface 欄序回答。","answer":{"kind":"expression","value":"(6, 30, 155, a_of_k_j_preserves_original_order)","explanation_zh":"Wave6根層核對=(6, 30, 155, a_of_k_j_preserves_original_order)；依完整明示資料獨立重算；subsequence索引必須嚴格遞增並保留原數列次序，不是重排或任意子集合；有限索引列表只證finite prefix；無限subsequence需要通用increasing-index certificate。"},"difficulty":{"band":"undergraduate_core","level":1,"skills":["子數列"]},"variant":{"family_id":"qf-mod38-subseq-arithmetic-term","seed":202611077030,"parameters":{"source_start":5,"source_step":5,"index_start":0,"index_step":5,"j":6,"domain":"Symbolic_affine_subsequence_index","operation":"subseq-arithmetic-term","semantic_template":"qf-mod38-subseq-arithmetic-term/{\"index_start\":0,\"index_step\":5,\"j\":6,\"source_start\":5,\"source_step\":5}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_or_symbolic_model","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"候選須主端重算；不構成人工審定、有限sample群作用、sup等於max、basis等於subbasis、signed Markov、pigeonhole converse、nonunit Euler、finite-prefix subsequence、Lean或Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-14","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261014-advance-20261107-r07-subsequence-0031","batch_id":"batch-20261014-advance-20261107-r07-subsequence-foundations","language":"zh-Hant","source_mko_ids":["mko-subsequence"],"title_zh":"子數列","stem_zh":"自然數索引與symbolic嚴格遞增證書。操作=subseq-arithmetic-term；資料={\"source_start\":6,\"source_step\":6,\"index_start\":1,\"index_step\":1,\"j\":7}。請依 exact_ordered_tuple_declared_by_interface 欄序回答。","answer":{"kind":"expression","value":"(7, 8, 54, a_of_k_j_preserves_original_order)","explanation_zh":"Wave6根層核對=(7, 8, 54, a_of_k_j_preserves_original_order)；依完整明示資料獨立重算；subsequence索引必須嚴格遞增並保留原數列次序，不是重排或任意子集合；有限索引列表只證finite prefix；無限subsequence需要通用increasing-index certificate。"},"difficulty":{"band":"undergraduate_core","level":1,"skills":["子數列"]},"variant":{"family_id":"qf-mod38-subseq-arithmetic-term","seed":202611077031,"parameters":{"source_start":6,"source_step":6,"index_start":1,"index_step":1,"j":7,"domain":"Symbolic_affine_subsequence_index","operation":"subseq-arithmetic-term","semantic_template":"qf-mod38-subseq-arithmetic-term/{\"index_start\":1,\"index_step\":1,\"j\":7,\"source_start\":6,\"source_step\":6}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_or_symbolic_model","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"候選須主端重算；不構成人工審定、有限sample群作用、sup等於max、basis等於subbasis、signed Markov、pigeonhole converse、nonunit Euler、finite-prefix subsequence、Lean或Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-14","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261014-advance-20261107-r07-subsequence-0032","batch_id":"batch-20261014-advance-20261107-r07-subsequence-foundations","language":"zh-Hant","source_mko_ids":["mko-subsequence"],"title_zh":"子數列","stem_zh":"自然數索引與symbolic嚴格遞增證書。操作=subseq-arithmetic-term；資料={\"source_start\":7,\"source_step\":7,\"index_start\":2,\"index_step\":2,\"j\":8}。請依 exact_ordered_tuple_declared_by_interface 欄序回答。","answer":{"kind":"expression","value":"(8, 18, 133, a_of_k_j_preserves_original_order)","explanation_zh":"Wave6根層核對=(8, 18, 133, a_of_k_j_preserves_original_order)；依完整明示資料獨立重算；subsequence索引必須嚴格遞增並保留原數列次序，不是重排或任意子集合；有限索引列表只證finite prefix；無限subsequence需要通用increasing-index certificate。"},"difficulty":{"band":"undergraduate_core","level":1,"skills":["子數列"]},"variant":{"family_id":"qf-mod38-subseq-arithmetic-term","seed":202611077032,"parameters":{"source_start":7,"source_step":7,"index_start":2,"index_step":2,"j":8,"domain":"Symbolic_affine_subsequence_index","operation":"subseq-arithmetic-term","semantic_template":"qf-mod38-subseq-arithmetic-term/{\"index_start\":2,\"index_step\":2,\"j\":8,\"source_start\":7,\"source_step\":7}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_or_symbolic_model","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"候選須主端重算；不構成人工審定、有限sample群作用、sup等於max、basis等於subbasis、signed Markov、pigeonhole converse、nonunit Euler、finite-prefix subsequence、Lean或Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-14","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261014-advance-20261107-r07-subsequence-0033","batch_id":"batch-20261014-advance-20261107-r07-subsequence-foundations","language":"zh-Hant","source_mko_ids":["mko-subsequence"],"title_zh":"子數列","stem_zh":"自然數索引與symbolic嚴格遞增證書。操作=subseq-arithmetic-term；資料={\"source_start\":8,\"source_step\":1,\"index_start\":3,\"index_step\":3,\"j\":9}。請依 exact_ordered_tuple_declared_by_interface 欄序回答。","answer":{"kind":"expression","value":"(9, 30, 38, a_of_k_j_preserves_original_order)","explanation_zh":"Wave6根層核對=(9, 30, 38, a_of_k_j_preserves_original_order)；依完整明示資料獨立重算；subsequence索引必須嚴格遞增並保留原數列次序，不是重排或任意子集合；有限索引列表只證finite prefix；無限subsequence需要通用increasing-index certificate。"},"difficulty":{"band":"undergraduate_core","level":1,"skills":["子數列"]},"variant":{"family_id":"qf-mod38-subseq-arithmetic-term","seed":202611077033,"parameters":{"source_start":8,"source_step":1,"index_start":3,"index_step":3,"j":9,"domain":"Symbolic_affine_subsequence_index","operation":"subseq-arithmetic-term","semantic_template":"qf-mod38-subseq-arithmetic-term/{\"index_start\":3,\"index_step\":3,\"j\":9,\"source_start\":8,\"source_step\":1}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_or_symbolic_model","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"候選須主端重算；不構成人工審定、有限sample群作用、sup等於max、basis等於subbasis、signed Markov、pigeonhole converse、nonunit Euler、finite-prefix subsequence、Lean或Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-14","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261014-advance-20261107-r07-subsequence-0034","batch_id":"batch-20261014-advance-20261107-r07-subsequence-foundations","language":"zh-Hant","source_mko_ids":["mko-subsequence"],"title_zh":"子數列","stem_zh":"自然數索引與symbolic嚴格遞增證書。操作=subseq-arithmetic-term；資料={\"source_start\":9,\"source_step\":2,\"index_start\":0,\"index_step\":4,\"j\":10}。請依 exact_ordered_tuple_declared_by_interface 欄序回答。","answer":{"kind":"expression","value":"(10, 40, 89, a_of_k_j_preserves_original_order)","explanation_zh":"Wave6根層核對=(10, 40, 89, a_of_k_j_preserves_original_order)；依完整明示資料獨立重算；subsequence索引必須嚴格遞增並保留原數列次序，不是重排或任意子集合；有限索引列表只證finite prefix；無限subsequence需要通用increasing-index certificate。"},"difficulty":{"band":"undergraduate_core","level":2,"skills":["子數列"]},"variant":{"family_id":"qf-mod38-subseq-arithmetic-term","seed":202611077034,"parameters":{"source_start":9,"source_step":2,"index_start":0,"index_step":4,"j":10,"domain":"Symbolic_affine_subsequence_index","operation":"subseq-arithmetic-term","semantic_template":"qf-mod38-subseq-arithmetic-term/{\"index_start\":0,\"index_step\":4,\"j\":10,\"source_start\":9,\"source_step\":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、有限sample群作用、sup等於max、basis等於subbasis、signed Markov、pigeonhole converse、nonunit Euler、finite-prefix subsequence、Lean或Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-14","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261014-advance-20261107-r07-subsequence-0035","batch_id":"batch-20261014-advance-20261107-r07-subsequence-foundations","language":"zh-Hant","source_mko_ids":["mko-subsequence"],"title_zh":"子數列","stem_zh":"自然數索引與symbolic嚴格遞增證書。操作=subseq-arithmetic-term；資料={\"source_start\":10,\"source_step\":3,\"index_start\":1,\"index_step\":5,\"j\":11}。請依 exact_ordered_tuple_declared_by_interface 欄序回答。","answer":{"kind":"expression","value":"(11, 56, 178, a_of_k_j_preserves_original_order)","explanation_zh":"Wave6根層核對=(11, 56, 178, a_of_k_j_preserves_original_order)；依完整明示資料獨立重算；subsequence索引必須嚴格遞增並保留原數列次序，不是重排或任意子集合；有限索引列表只證finite prefix；無限subsequence需要通用increasing-index certificate。"},"difficulty":{"band":"undergraduate_core","level":2,"skills":["子數列"]},"variant":{"family_id":"qf-mod38-subseq-arithmetic-term","seed":202611077035,"parameters":{"source_start":10,"source_step":3,"index_start":1,"index_step":5,"j":11,"domain":"Symbolic_affine_subsequence_index","operation":"subseq-arithmetic-term","semantic_template":"qf-mod38-subseq-arithmetic-term/{\"index_start\":1,\"index_step\":5,\"j\":11,\"source_start\":10,\"source_step\":3}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_or_symbolic_model","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"候選須主端重算；不構成人工審定、有限sample群作用、sup等於max、basis等於subbasis、signed Markov、pigeonhole converse、nonunit Euler、finite-prefix subsequence、Lean或Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-14","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261014-advance-20261107-r07-subsequence-0036","batch_id":"batch-20261014-advance-20261107-r07-subsequence-foundations","language":"zh-Hant","source_mko_ids":["mko-subsequence"],"title_zh":"子數列","stem_zh":"自然數索引與symbolic嚴格遞增證書。操作=subseq-arithmetic-term；資料={\"source_start\":11,\"source_step\":4,\"index_start\":2,\"index_step\":1,\"j\":12}。請依 exact_ordered_tuple_declared_by_interface 欄序回答。","answer":{"kind":"expression","value":"(12, 14, 67, a_of_k_j_preserves_original_order)","explanation_zh":"Wave6根層核對=(12, 14, 67, a_of_k_j_preserves_original_order)；依完整明示資料獨立重算；subsequence索引必須嚴格遞增並保留原數列次序，不是重排或任意子集合；有限索引列表只證finite prefix；無限subsequence需要通用increasing-index certificate。"},"difficulty":{"band":"undergraduate_core","level":2,"skills":["子數列"]},"variant":{"family_id":"qf-mod38-subseq-arithmetic-term","seed":202611077036,"parameters":{"source_start":11,"source_step":4,"index_start":2,"index_step":1,"j":12,"domain":"Symbolic_affine_subsequence_index","operation":"subseq-arithmetic-term","semantic_template":"qf-mod38-subseq-arithmetic-term/{\"index_start\":2,\"index_step\":1,\"j\":12,\"source_start\":11,\"source_step\":4}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_or_symbolic_model","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"候選須主端重算；不構成人工審定、有限sample群作用、sup等於max、basis等於subbasis、signed Markov、pigeonhole converse、nonunit Euler、finite-prefix subsequence、Lean或Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-14","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261014-advance-20261107-r07-subsequence-0037","batch_id":"batch-20261014-advance-20261107-r07-subsequence-foundations","language":"zh-Hant","source_mko_ids":["mko-subsequence"],"title_zh":"子數列","stem_zh":"自然數索引與symbolic嚴格遞增證書。操作=subseq-arithmetic-term；資料={\"source_start\":12,\"source_step\":5,\"index_start\":3,\"index_step\":2,\"j\":13}。請依 exact_ordered_tuple_declared_by_interface 欄序回答。","answer":{"kind":"expression","value":"(13, 29, 157, a_of_k_j_preserves_original_order)","explanation_zh":"Wave6根層核對=(13, 29, 157, a_of_k_j_preserves_original_order)；依完整明示資料獨立重算；subsequence索引必須嚴格遞增並保留原數列次序，不是重排或任意子集合；有限索引列表只證finite prefix；無限subsequence需要通用increasing-index certificate。"},"difficulty":{"band":"undergraduate_core","level":2,"skills":["子數列"]},"variant":{"family_id":"qf-mod38-subseq-arithmetic-term","seed":202611077037,"parameters":{"source_start":12,"source_step":5,"index_start":3,"index_step":2,"j":13,"domain":"Symbolic_affine_subsequence_index","operation":"subseq-arithmetic-term","semantic_template":"qf-mod38-subseq-arithmetic-term/{\"index_start\":3,\"index_step\":2,\"j\":13,\"source_start\":12,\"source_step\":5}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_or_symbolic_model","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"候選須主端重算；不構成人工審定、有限sample群作用、sup等於max、basis等於subbasis、signed Markov、pigeonhole converse、nonunit Euler、finite-prefix subsequence、Lean或Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-14","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261014-advance-20261107-r07-subsequence-0038","batch_id":"batch-20261014-advance-20261107-r07-subsequence-foundations","language":"zh-Hant","source_mko_ids":["mko-subsequence"],"title_zh":"子數列","stem_zh":"自然數索引與symbolic嚴格遞增證書。操作=subseq-arithmetic-term；資料={\"source_start\":13,\"source_step\":6,\"index_start\":0,\"index_step\":3,\"j\":14}。請依 exact_ordered_tuple_declared_by_interface 欄序回答。","answer":{"kind":"expression","value":"(14, 42, 265, a_of_k_j_preserves_original_order)","explanation_zh":"Wave6根層核對=(14, 42, 265, a_of_k_j_preserves_original_order)；依完整明示資料獨立重算；subsequence索引必須嚴格遞增並保留原數列次序，不是重排或任意子集合；有限索引列表只證finite prefix；無限subsequence需要通用increasing-index certificate。"},"difficulty":{"band":"undergraduate_core","level":2,"skills":["子數列"]},"variant":{"family_id":"qf-mod38-subseq-arithmetic-term","seed":202611077038,"parameters":{"source_start":13,"source_step":6,"index_start":0,"index_step":3,"j":14,"domain":"Symbolic_affine_subsequence_index","operation":"subseq-arithmetic-term","semantic_template":"qf-mod38-subseq-arithmetic-term/{\"index_start\":0,\"index_step\":3,\"j\":14,\"source_start\":13,\"source_step\":6}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_or_symbolic_model","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"候選須主端重算；不構成人工審定、有限sample群作用、sup等於max、basis等於subbasis、signed Markov、pigeonhole converse、nonunit Euler、finite-prefix subsequence、Lean或Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-14","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261014-advance-20261107-r07-subsequence-0039","batch_id":"batch-20261014-advance-20261107-r07-subsequence-foundations","language":"zh-Hant","source_mko_ids":["mko-subsequence"],"title_zh":"子數列","stem_zh":"自然數索引與symbolic嚴格遞增證書。操作=subseq-arithmetic-term；資料={\"source_start\":14,\"source_step\":7,\"index_start\":1,\"index_step\":4,\"j\":15}。請依 exact_ordered_tuple_declared_by_interface 欄序回答。","answer":{"kind":"expression","value":"(15, 61, 441, a_of_k_j_preserves_original_order)","explanation_zh":"Wave6根層核對=(15, 61, 441, a_of_k_j_preserves_original_order)；依完整明示資料獨立重算；subsequence索引必須嚴格遞增並保留原數列次序，不是重排或任意子集合；有限索引列表只證finite prefix；無限subsequence需要通用increasing-index certificate。"},"difficulty":{"band":"undergraduate_core","level":2,"skills":["子數列"]},"variant":{"family_id":"qf-mod38-subseq-arithmetic-term","seed":202611077039,"parameters":{"source_start":14,"source_step":7,"index_start":1,"index_step":4,"j":15,"domain":"Symbolic_affine_subsequence_index","operation":"subseq-arithmetic-term","semantic_template":"qf-mod38-subseq-arithmetic-term/{\"index_start\":1,\"index_step\":4,\"j\":15,\"source_start\":14,\"source_step\":7}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_or_symbolic_model","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"候選須主端重算；不構成人工審定、有限sample群作用、sup等於max、basis等於subbasis、signed Markov、pigeonhole converse、nonunit Euler、finite-prefix subsequence、Lean或Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-14","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261014-advance-20261107-r07-subsequence-0040","batch_id":"batch-20261014-advance-20261107-r07-subsequence-foundations","language":"zh-Hant","source_mko_ids":["mko-subsequence"],"title_zh":"子數列","stem_zh":"自然數索引與symbolic嚴格遞增證書。操作=subseq-arithmetic-term；資料={\"source_start\":15,\"source_step\":1,\"index_start\":2,\"index_step\":5,\"j\":16}。請依 exact_ordered_tuple_declared_by_interface 欄序回答。","answer":{"kind":"expression","value":"(16, 82, 97, a_of_k_j_preserves_original_order)","explanation_zh":"Wave6根層核對=(16, 82, 97, a_of_k_j_preserves_original_order)；依完整明示資料獨立重算；subsequence索引必須嚴格遞增並保留原數列次序，不是重排或任意子集合；有限索引列表只證finite prefix；無限subsequence需要通用increasing-index certificate。"},"difficulty":{"band":"undergraduate_core","level":2,"skills":["子數列"]},"variant":{"family_id":"qf-mod38-subseq-arithmetic-term","seed":202611077040,"parameters":{"source_start":15,"source_step":1,"index_start":2,"index_step":5,"j":16,"domain":"Symbolic_affine_subsequence_index","operation":"subseq-arithmetic-term","semantic_template":"qf-mod38-subseq-arithmetic-term/{\"index_start\":2,\"index_step\":5,\"j\":16,\"source_start\":15,\"source_step\":1}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_or_symbolic_model","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"候選須主端重算；不構成人工審定、有限sample群作用、sup等於max、basis等於subbasis、signed Markov、pigeonhole converse、nonunit Euler、finite-prefix subsequence、Lean或Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-14","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261014-advance-20261107-r07-subsequence-0041","batch_id":"batch-20261014-advance-20261107-r07-subsequence-foundations","language":"zh-Hant","source_mko_ids":["mko-subsequence"],"title_zh":"子數列","stem_zh":"自然數索引與symbolic嚴格遞增證書。操作=subseq-arithmetic-term；資料={\"source_start\":16,\"source_step\":2,\"index_start\":3,\"index_step\":1,\"j\":17}。請依 exact_ordered_tuple_declared_by_interface 欄序回答。","answer":{"kind":"expression","value":"(17, 20, 56, a_of_k_j_preserves_original_order)","explanation_zh":"Wave6根層核對=(17, 20, 56, a_of_k_j_preserves_original_order)；依完整明示資料獨立重算；subsequence索引必須嚴格遞增並保留原數列次序，不是重排或任意子集合；有限索引列表只證finite prefix；無限subsequence需要通用increasing-index certificate。"},"difficulty":{"band":"undergraduate_core","level":2,"skills":["子數列"]},"variant":{"family_id":"qf-mod38-subseq-arithmetic-term","seed":202611077041,"parameters":{"source_start":16,"source_step":2,"index_start":3,"index_step":1,"j":17,"domain":"Symbolic_affine_subsequence_index","operation":"subseq-arithmetic-term","semantic_template":"qf-mod38-subseq-arithmetic-term/{\"index_start\":3,\"index_step\":1,\"j\":17,\"source_start\":16,\"source_step\":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、有限sample群作用、sup等於max、basis等於subbasis、signed Markov、pigeonhole converse、nonunit Euler、finite-prefix subsequence、Lean或Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-14","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261014-advance-20261107-r07-subsequence-0042","batch_id":"batch-20261014-advance-20261107-r07-subsequence-foundations","language":"zh-Hant","source_mko_ids":["mko-subsequence"],"title_zh":"子數列","stem_zh":"自然數索引與symbolic嚴格遞增證書。操作=subseq-arithmetic-term；資料={\"source_start\":17,\"source_step\":3,\"index_start\":0,\"index_step\":2,\"j\":18}。請依 exact_ordered_tuple_declared_by_interface 欄序回答。","answer":{"kind":"expression","value":"(18, 36, 125, a_of_k_j_preserves_original_order)","explanation_zh":"Wave6根層核對=(18, 36, 125, a_of_k_j_preserves_original_order)；依完整明示資料獨立重算；subsequence索引必須嚴格遞增並保留原數列次序，不是重排或任意子集合；有限索引列表只證finite prefix；無限subsequence需要通用increasing-index certificate。"},"difficulty":{"band":"undergraduate_core","level":2,"skills":["子數列"]},"variant":{"family_id":"qf-mod38-subseq-arithmetic-term","seed":202611077042,"parameters":{"source_start":17,"source_step":3,"index_start":0,"index_step":2,"j":18,"domain":"Symbolic_affine_subsequence_index","operation":"subseq-arithmetic-term","semantic_template":"qf-mod38-subseq-arithmetic-term/{\"index_start\":0,\"index_step\":2,\"j\":18,\"source_start\":17,\"source_step\":3}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_or_symbolic_model","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"候選須主端重算；不構成人工審定、有限sample群作用、sup等於max、basis等於subbasis、signed Markov、pigeonhole converse、nonunit Euler、finite-prefix subsequence、Lean或Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-14","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261014-advance-20261107-r07-subsequence-0043","batch_id":"batch-20261014-advance-20261107-r07-subsequence-foundations","language":"zh-Hant","source_mko_ids":["mko-subsequence"],"title_zh":"子數列","stem_zh":"自然數索引與symbolic嚴格遞增證書。操作=subseq-arithmetic-term；資料={\"source_start\":18,\"source_step\":4,\"index_start\":1,\"index_step\":3,\"j\":19}。請依 exact_ordered_tuple_declared_by_interface 欄序回答。","answer":{"kind":"expression","value":"(19, 58, 250, a_of_k_j_preserves_original_order)","explanation_zh":"Wave6根層核對=(19, 58, 250, a_of_k_j_preserves_original_order)；依完整明示資料獨立重算；subsequence索引必須嚴格遞增並保留原數列次序，不是重排或任意子集合；有限索引列表只證finite prefix；無限subsequence需要通用increasing-index certificate。"},"difficulty":{"band":"undergraduate_core","level":3,"skills":["子數列"]},"variant":{"family_id":"qf-mod38-subseq-arithmetic-term","seed":202611077043,"parameters":{"source_start":18,"source_step":4,"index_start":1,"index_step":3,"j":19,"domain":"Symbolic_affine_subsequence_index","operation":"subseq-arithmetic-term","semantic_template":"qf-mod38-subseq-arithmetic-term/{\"index_start\":1,\"index_step\":3,\"j\":19,\"source_start\":18,\"source_step\":4}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_or_symbolic_model","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"候選須主端重算；不構成人工審定、有限sample群作用、sup等於max、basis等於subbasis、signed Markov、pigeonhole converse、nonunit Euler、finite-prefix subsequence、Lean或Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-14","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261014-advance-20261107-r07-subsequence-0044","batch_id":"batch-20261014-advance-20261107-r07-subsequence-foundations","language":"zh-Hant","source_mko_ids":["mko-subsequence"],"title_zh":"子數列","stem_zh":"自然數索引與symbolic嚴格遞增證書。操作=subseq-arithmetic-term；資料={\"source_start\":19,\"source_step\":5,\"index_start\":2,\"index_step\":4,\"j\":20}。請依 exact_ordered_tuple_declared_by_interface 欄序回答。","answer":{"kind":"expression","value":"(20, 82, 429, a_of_k_j_preserves_original_order)","explanation_zh":"Wave6根層核對=(20, 82, 429, a_of_k_j_preserves_original_order)；依完整明示資料獨立重算；subsequence索引必須嚴格遞增並保留原數列次序，不是重排或任意子集合；有限索引列表只證finite prefix；無限subsequence需要通用increasing-index certificate。"},"difficulty":{"band":"undergraduate_core","level":3,"skills":["子數列"]},"variant":{"family_id":"qf-mod38-subseq-arithmetic-term","seed":202611077044,"parameters":{"source_start":19,"source_step":5,"index_start":2,"index_step":4,"j":20,"domain":"Symbolic_affine_subsequence_index","operation":"subseq-arithmetic-term","semantic_template":"qf-mod38-subseq-arithmetic-term/{\"index_start\":2,\"index_step\":4,\"j\":20,\"source_start\":19,\"source_step\":5}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_or_symbolic_model","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"候選須主端重算；不構成人工審定、有限sample群作用、sup等於max、basis等於subbasis、signed Markov、pigeonhole converse、nonunit Euler、finite-prefix subsequence、Lean或Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-14","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261014-advance-20261107-r07-subsequence-0045","batch_id":"batch-20261014-advance-20261107-r07-subsequence-foundations","language":"zh-Hant","source_mko_ids":["mko-subsequence"],"title_zh":"子數列","stem_zh":"自然數索引與symbolic嚴格遞增證書。操作=subseq-arithmetic-term；資料={\"source_start\":20,\"source_step\":6,\"index_start\":3,\"index_step\":5,\"j\":21}。請依 exact_ordered_tuple_declared_by_interface 欄序回答。","answer":{"kind":"expression","value":"(21, 108, 668, a_of_k_j_preserves_original_order)","explanation_zh":"Wave6根層核對=(21, 108, 668, a_of_k_j_preserves_original_order)；依完整明示資料獨立重算；subsequence索引必須嚴格遞增並保留原數列次序，不是重排或任意子集合；有限索引列表只證finite prefix；無限subsequence需要通用increasing-index certificate。"},"difficulty":{"band":"undergraduate_core","level":3,"skills":["子數列"]},"variant":{"family_id":"qf-mod38-subseq-arithmetic-term","seed":202611077045,"parameters":{"source_start":20,"source_step":6,"index_start":3,"index_step":5,"j":21,"domain":"Symbolic_affine_subsequence_index","operation":"subseq-arithmetic-term","semantic_template":"qf-mod38-subseq-arithmetic-term/{\"index_start\":3,\"index_step\":5,\"j\":21,\"source_start\":20,\"source_step\":6}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_or_symbolic_model","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"候選須主端重算；不構成人工審定、有限sample群作用、sup等於max、basis等於subbasis、signed Markov、pigeonhole converse、nonunit Euler、finite-prefix subsequence、Lean或Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-14","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261014-advance-20261107-r07-subsequence-0046","batch_id":"batch-20261014-advance-20261107-r07-subsequence-foundations","language":"zh-Hant","source_mko_ids":["mko-subsequence"],"title_zh":"子數列","stem_zh":"自然數索引與symbolic嚴格遞增證書。操作=subseq-arithmetic-term；資料={\"source_start\":21,\"source_step\":7,\"index_start\":0,\"index_step\":1,\"j\":22}。請依 exact_ordered_tuple_declared_by_interface 欄序回答。","answer":{"kind":"expression","value":"(22, 22, 175, a_of_k_j_preserves_original_order)","explanation_zh":"Wave6根層核對=(22, 22, 175, a_of_k_j_preserves_original_order)；依完整明示資料獨立重算；subsequence索引必須嚴格遞增並保留原數列次序，不是重排或任意子集合；有限索引列表只證finite prefix；無限subsequence需要通用increasing-index certificate。"},"difficulty":{"band":"undergraduate_core","level":3,"skills":["子數列"]},"variant":{"family_id":"qf-mod38-subseq-arithmetic-term","seed":202611077046,"parameters":{"source_start":21,"source_step":7,"index_start":0,"index_step":1,"j":22,"domain":"Symbolic_affine_subsequence_index","operation":"subseq-arithmetic-term","semantic_template":"qf-mod38-subseq-arithmetic-term/{\"index_start\":0,\"index_step\":1,\"j\":22,\"source_start\":21,\"source_step\":7}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_or_symbolic_model","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"候選須主端重算；不構成人工審定、有限sample群作用、sup等於max、basis等於subbasis、signed Markov、pigeonhole converse、nonunit Euler、finite-prefix subsequence、Lean或Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-14","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261014-advance-20261107-r07-subsequence-0047","batch_id":"batch-20261014-advance-20261107-r07-subsequence-foundations","language":"zh-Hant","source_mko_ids":["mko-subsequence"],"title_zh":"子數列","stem_zh":"自然數索引與symbolic嚴格遞增證書。操作=subseq-arithmetic-term；資料={\"source_start\":22,\"source_step\":1,\"index_start\":1,\"index_step\":2,\"j\":23}。請依 exact_ordered_tuple_declared_by_interface 欄序回答。","answer":{"kind":"expression","value":"(23, 47, 69, a_of_k_j_preserves_original_order)","explanation_zh":"Wave6根層核對=(23, 47, 69, a_of_k_j_preserves_original_order)；依完整明示資料獨立重算；subsequence索引必須嚴格遞增並保留原數列次序，不是重排或任意子集合；有限索引列表只證finite prefix；無限subsequence需要通用increasing-index certificate。"},"difficulty":{"band":"undergraduate_core","level":3,"skills":["子數列"]},"variant":{"family_id":"qf-mod38-subseq-arithmetic-term","seed":202611077047,"parameters":{"source_start":22,"source_step":1,"index_start":1,"index_step":2,"j":23,"domain":"Symbolic_affine_subsequence_index","operation":"subseq-arithmetic-term","semantic_template":"qf-mod38-subseq-arithmetic-term/{\"index_start\":1,\"index_step\":2,\"j\":23,\"source_start\":22,\"source_step\":1}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_or_symbolic_model","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"候選須主端重算；不構成人工審定、有限sample群作用、sup等於max、basis等於subbasis、signed Markov、pigeonhole converse、nonunit Euler、finite-prefix subsequence、Lean或Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-14","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261014-advance-20261107-r07-subsequence-0048","batch_id":"batch-20261014-advance-20261107-r07-subsequence-foundations","language":"zh-Hant","source_mko_ids":["mko-subsequence"],"title_zh":"子數列","stem_zh":"自然數索引與symbolic嚴格遞增證書。操作=subseq-arithmetic-term；資料={\"source_start\":23,\"source_step\":2,\"index_start\":2,\"index_step\":3,\"j\":24}。請依 exact_ordered_tuple_declared_by_interface 欄序回答。","answer":{"kind":"expression","value":"(24, 74, 171, a_of_k_j_preserves_original_order)","explanation_zh":"Wave6根層核對=(24, 74, 171, a_of_k_j_preserves_original_order)；依完整明示資料獨立重算；subsequence索引必須嚴格遞增並保留原數列次序，不是重排或任意子集合；有限索引列表只證finite prefix；無限subsequence需要通用increasing-index certificate。"},"difficulty":{"band":"undergraduate_core","level":3,"skills":["子數列"]},"variant":{"family_id":"qf-mod38-subseq-arithmetic-term","seed":202611077048,"parameters":{"source_start":23,"source_step":2,"index_start":2,"index_step":3,"j":24,"domain":"Symbolic_affine_subsequence_index","operation":"subseq-arithmetic-term","semantic_template":"qf-mod38-subseq-arithmetic-term/{\"index_start\":2,\"index_step\":3,\"j\":24,\"source_start\":23,\"source_step\":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、有限sample群作用、sup等於max、basis等於subbasis、signed Markov、pigeonhole converse、nonunit Euler、finite-prefix subsequence、Lean或Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-14","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261014-advance-20261107-r07-subsequence-0049","batch_id":"batch-20261014-advance-20261107-r07-subsequence-foundations","language":"zh-Hant","source_mko_ids":["mko-subsequence"],"title_zh":"子數列","stem_zh":"自然數索引與symbolic嚴格遞增證書。操作=subseq-arithmetic-term；資料={\"source_start\":24,\"source_step\":3,\"index_start\":3,\"index_step\":4,\"j\":25}。請依 exact_ordered_tuple_declared_by_interface 欄序回答。","answer":{"kind":"expression","value":"(25, 103, 333, a_of_k_j_preserves_original_order)","explanation_zh":"Wave6根層核對=(25, 103, 333, a_of_k_j_preserves_original_order)；依完整明示資料獨立重算；subsequence索引必須嚴格遞增並保留原數列次序，不是重排或任意子集合；有限索引列表只證finite prefix；無限subsequence需要通用increasing-index certificate。"},"difficulty":{"band":"undergraduate_core","level":3,"skills":["子數列"]},"variant":{"family_id":"qf-mod38-subseq-arithmetic-term","seed":202611077049,"parameters":{"source_start":24,"source_step":3,"index_start":3,"index_step":4,"j":25,"domain":"Symbolic_affine_subsequence_index","operation":"subseq-arithmetic-term","semantic_template":"qf-mod38-subseq-arithmetic-term/{\"index_start\":3,\"index_step\":4,\"j\":25,\"source_start\":24,\"source_step\":3}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_or_symbolic_model","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"候選須主端重算；不構成人工審定、有限sample群作用、sup等於max、basis等於subbasis、signed Markov、pigeonhole converse、nonunit Euler、finite-prefix subsequence、Lean或Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-14","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261014-advance-20261107-r07-subsequence-0050","batch_id":"batch-20261014-advance-20261107-r07-subsequence-foundations","language":"zh-Hant","source_mko_ids":["mko-subsequence"],"title_zh":"子數列","stem_zh":"自然數索引與symbolic嚴格遞增證書。操作=subseq-arithmetic-term；資料={\"source_start\":25,\"source_step\":4,\"index_start\":0,\"index_step\":5,\"j\":26}。請依 exact_ordered_tuple_declared_by_interface 欄序回答。","answer":{"kind":"expression","value":"(26, 130, 545, a_of_k_j_preserves_original_order)","explanation_zh":"Wave6根層核對=(26, 130, 545, a_of_k_j_preserves_original_order)；依完整明示資料獨立重算；subsequence索引必須嚴格遞增並保留原數列次序，不是重排或任意子集合；有限索引列表只證finite prefix；無限subsequence需要通用increasing-index certificate。"},"difficulty":{"band":"undergraduate_core","level":3,"skills":["子數列"]},"variant":{"family_id":"qf-mod38-subseq-arithmetic-term","seed":202611077050,"parameters":{"source_start":25,"source_step":4,"index_start":0,"index_step":5,"j":26,"domain":"Symbolic_affine_subsequence_index","operation":"subseq-arithmetic-term","semantic_template":"qf-mod38-subseq-arithmetic-term/{\"index_start\":0,\"index_step\":5,\"j\":26,\"source_start\":25,\"source_step\":4}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_or_symbolic_model","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"候選須主端重算；不構成人工審定、有限sample群作用、sup等於max、basis等於subbasis、signed Markov、pigeonhole converse、nonunit Euler、finite-prefix subsequence、Lean或Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-14","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261014-advance-20261107-r07-subsequence-0051","batch_id":"batch-20261014-advance-20261107-r07-subsequence-foundations","language":"zh-Hant","source_mko_ids":["mko-subsequence"],"title_zh":"子數列","stem_zh":"自然數索引與symbolic嚴格遞增證書。操作=subseq-composed-index；資料={\"outer_start\":0,\"outer_step\":1,\"inner_start\":0,\"inner_step\":1,\"j\":1}。請依 exact_ordered_tuple_declared_by_interface 欄序回答。","answer":{"kind":"expression","value":"(1, 1, 1, 1, 是, composition_remains_strictly_increasing)","explanation_zh":"Wave6根層核對=(1, 1, 1, 1, 是, composition_remains_strictly_increasing)；依完整明示資料獨立重算；subsequence索引必須嚴格遞增並保留原數列次序，不是重排或任意子集合；有限索引列表只證finite prefix；無限subsequence需要通用increasing-index certificate。"},"difficulty":{"band":"undergraduate_core","level":1,"skills":["子數列"]},"variant":{"family_id":"qf-mod38-subseq-composed-index","seed":202611077051,"parameters":{"outer_start":0,"outer_step":1,"inner_start":0,"inner_step":1,"j":1,"domain":"Symbolic_affine_subsequence_index","operation":"subseq-composed-index","semantic_template":"qf-mod38-subseq-composed-index/{\"inner_start\":0,\"inner_step\":1,\"j\":1,\"outer_start\":0,\"outer_step\":1}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_or_symbolic_model","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"候選須主端重算；不構成人工審定、有限sample群作用、sup等於max、basis等於subbasis、signed Markov、pigeonhole converse、nonunit Euler、finite-prefix subsequence、Lean或Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-14","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261014-advance-20261107-r07-subsequence-0052","batch_id":"batch-20261014-advance-20261107-r07-subsequence-foundations","language":"zh-Hant","source_mko_ids":["mko-subsequence"],"title_zh":"子數列","stem_zh":"自然數索引與symbolic嚴格遞增證書。操作=subseq-composed-index；資料={\"outer_start\":1,\"outer_step\":2,\"inner_start\":1,\"inner_step\":2,\"j\":2}。請依 exact_ordered_tuple_declared_by_interface 欄序回答。","answer":{"kind":"expression","value":"(2, 5, 11, 4, 是, composition_remains_strictly_increasing)","explanation_zh":"Wave6根層核對=(2, 5, 11, 4, 是, composition_remains_strictly_increasing)；依完整明示資料獨立重算；subsequence索引必須嚴格遞增並保留原數列次序，不是重排或任意子集合；有限索引列表只證finite prefix；無限subsequence需要通用increasing-index certificate。"},"difficulty":{"band":"undergraduate_core","level":1,"skills":["子數列"]},"variant":{"family_id":"qf-mod38-subseq-composed-index","seed":202611077052,"parameters":{"outer_start":1,"outer_step":2,"inner_start":1,"inner_step":2,"j":2,"domain":"Symbolic_affine_subsequence_index","operation":"subseq-composed-index","semantic_template":"qf-mod38-subseq-composed-index/{\"inner_start\":1,\"inner_step\":2,\"j\":2,\"outer_start\":1,\"outer_step\":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、有限sample群作用、sup等於max、basis等於subbasis、signed Markov、pigeonhole converse、nonunit Euler、finite-prefix subsequence、Lean或Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-14","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261014-advance-20261107-r07-subsequence-0053","batch_id":"batch-20261014-advance-20261107-r07-subsequence-foundations","language":"zh-Hant","source_mko_ids":["mko-subsequence"],"title_zh":"子數列","stem_zh":"自然數索引與symbolic嚴格遞增證書。操作=subseq-composed-index；資料={\"outer_start\":2,\"outer_step\":3,\"inner_start\":2,\"inner_step\":3,\"j\":3}。請依 exact_ordered_tuple_declared_by_interface 欄序回答。","answer":{"kind":"expression","value":"(3, 11, 35, 9, 是, composition_remains_strictly_increasing)","explanation_zh":"Wave6根層核對=(3, 11, 35, 9, 是, composition_remains_strictly_increasing)；依完整明示資料獨立重算；subsequence索引必須嚴格遞增並保留原數列次序，不是重排或任意子集合；有限索引列表只證finite prefix；無限subsequence需要通用increasing-index certificate。"},"difficulty":{"band":"undergraduate_core","level":1,"skills":["子數列"]},"variant":{"family_id":"qf-mod38-subseq-composed-index","seed":202611077053,"parameters":{"outer_start":2,"outer_step":3,"inner_start":2,"inner_step":3,"j":3,"domain":"Symbolic_affine_subsequence_index","operation":"subseq-composed-index","semantic_template":"qf-mod38-subseq-composed-index/{\"inner_start\":2,\"inner_step\":3,\"j\":3,\"outer_start\":2,\"outer_step\":3}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_or_symbolic_model","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"候選須主端重算；不構成人工審定、有限sample群作用、sup等於max、basis等於subbasis、signed Markov、pigeonhole converse、nonunit Euler、finite-prefix subsequence、Lean或Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-14","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261014-advance-20261107-r07-subsequence-0054","batch_id":"batch-20261014-advance-20261107-r07-subsequence-foundations","language":"zh-Hant","source_mko_ids":["mko-subsequence"],"title_zh":"子數列","stem_zh":"自然數索引與symbolic嚴格遞增證書。操作=subseq-composed-index；資料={\"outer_start\":0,\"outer_step\":4,\"inner_start\":3,\"inner_step\":4,\"j\":4}。請依 exact_ordered_tuple_declared_by_interface 欄序回答。","answer":{"kind":"expression","value":"(4, 19, 76, 16, 是, composition_remains_strictly_increasing)","explanation_zh":"Wave6根層核對=(4, 19, 76, 16, 是, composition_remains_strictly_increasing)；依完整明示資料獨立重算；subsequence索引必須嚴格遞增並保留原數列次序，不是重排或任意子集合；有限索引列表只證finite prefix；無限subsequence需要通用increasing-index certificate。"},"difficulty":{"band":"undergraduate_core","level":1,"skills":["子數列"]},"variant":{"family_id":"qf-mod38-subseq-composed-index","seed":202611077054,"parameters":{"outer_start":0,"outer_step":4,"inner_start":3,"inner_step":4,"j":4,"domain":"Symbolic_affine_subsequence_index","operation":"subseq-composed-index","semantic_template":"qf-mod38-subseq-composed-index/{\"inner_start\":3,\"inner_step\":4,\"j\":4,\"outer_start\":0,\"outer_step\":4}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_or_symbolic_model","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"候選須主端重算；不構成人工審定、有限sample群作用、sup等於max、basis等於subbasis、signed Markov、pigeonhole converse、nonunit Euler、finite-prefix subsequence、Lean或Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-14","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261014-advance-20261107-r07-subsequence-0055","batch_id":"batch-20261014-advance-20261107-r07-subsequence-foundations","language":"zh-Hant","source_mko_ids":["mko-subsequence"],"title_zh":"子數列","stem_zh":"自然數索引與symbolic嚴格遞增證書。操作=subseq-composed-index；資料={\"outer_start\":1,\"outer_step\":5,\"inner_start\":0,\"inner_step\":5,\"j\":5}。請依 exact_ordered_tuple_declared_by_interface 欄序回答。","answer":{"kind":"expression","value":"(5, 25, 126, 25, 是, composition_remains_strictly_increasing)","explanation_zh":"Wave6根層核對=(5, 25, 126, 25, 是, composition_remains_strictly_increasing)；依完整明示資料獨立重算；subsequence索引必須嚴格遞增並保留原數列次序，不是重排或任意子集合；有限索引列表只證finite prefix；無限subsequence需要通用increasing-index certificate。"},"difficulty":{"band":"undergraduate_core","level":1,"skills":["子數列"]},"variant":{"family_id":"qf-mod38-subseq-composed-index","seed":202611077055,"parameters":{"outer_start":1,"outer_step":5,"inner_start":0,"inner_step":5,"j":5,"domain":"Symbolic_affine_subsequence_index","operation":"subseq-composed-index","semantic_template":"qf-mod38-subseq-composed-index/{\"inner_start\":0,\"inner_step\":5,\"j\":5,\"outer_start\":1,\"outer_step\":5}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_or_symbolic_model","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"候選須主端重算；不構成人工審定、有限sample群作用、sup等於max、basis等於subbasis、signed Markov、pigeonhole converse、nonunit Euler、finite-prefix subsequence、Lean或Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-14","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261014-advance-20261107-r07-subsequence-0056","batch_id":"batch-20261014-advance-20261107-r07-subsequence-foundations","language":"zh-Hant","source_mko_ids":["mko-subsequence"],"title_zh":"子數列","stem_zh":"自然數索引與symbolic嚴格遞增證書。操作=subseq-composed-index；資料={\"outer_start\":2,\"outer_step\":1,\"inner_start\":1,\"inner_step\":6,\"j\":6}。請依 exact_ordered_tuple_declared_by_interface 欄序回答。","answer":{"kind":"expression","value":"(6, 37, 39, 6, 是, composition_remains_strictly_increasing)","explanation_zh":"Wave6根層核對=(6, 37, 39, 6, 是, composition_remains_strictly_increasing)；依完整明示資料獨立重算；subsequence索引必須嚴格遞增並保留原數列次序，不是重排或任意子集合；有限索引列表只證finite prefix；無限subsequence需要通用increasing-index certificate。"},"difficulty":{"band":"undergraduate_core","level":1,"skills":["子數列"]},"variant":{"family_id":"qf-mod38-subseq-composed-index","seed":202611077056,"parameters":{"outer_start":2,"outer_step":1,"inner_start":1,"inner_step":6,"j":6,"domain":"Symbolic_affine_subsequence_index","operation":"subseq-composed-index","semantic_template":"qf-mod38-subseq-composed-index/{\"inner_start\":1,\"inner_step\":6,\"j\":6,\"outer_start\":2,\"outer_step\":1}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_or_symbolic_model","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"候選須主端重算；不構成人工審定、有限sample群作用、sup等於max、basis等於subbasis、signed Markov、pigeonhole converse、nonunit Euler、finite-prefix subsequence、Lean或Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-14","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261014-advance-20261107-r07-subsequence-0057","batch_id":"batch-20261014-advance-20261107-r07-subsequence-foundations","language":"zh-Hant","source_mko_ids":["mko-subsequence"],"title_zh":"子數列","stem_zh":"自然數索引與symbolic嚴格遞增證書。操作=subseq-composed-index；資料={\"outer_start\":0,\"outer_step\":2,\"inner_start\":2,\"inner_step\":1,\"j\":7}。請依 exact_ordered_tuple_declared_by_interface 欄序回答。","answer":{"kind":"expression","value":"(7, 9, 18, 2, 是, composition_remains_strictly_increasing)","explanation_zh":"Wave6根層核對=(7, 9, 18, 2, 是, composition_remains_strictly_increasing)；依完整明示資料獨立重算；subsequence索引必須嚴格遞增並保留原數列次序，不是重排或任意子集合；有限索引列表只證finite prefix；無限subsequence需要通用increasing-index certificate。"},"difficulty":{"band":"undergraduate_core","level":1,"skills":["子數列"]},"variant":{"family_id":"qf-mod38-subseq-composed-index","seed":202611077057,"parameters":{"outer_start":0,"outer_step":2,"inner_start":2,"inner_step":1,"j":7,"domain":"Symbolic_affine_subsequence_index","operation":"subseq-composed-index","semantic_template":"qf-mod38-subseq-composed-index/{\"inner_start\":2,\"inner_step\":1,\"j\":7,\"outer_start\":0,\"outer_step\":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、有限sample群作用、sup等於max、basis等於subbasis、signed Markov、pigeonhole converse、nonunit Euler、finite-prefix subsequence、Lean或Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-14","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261014-advance-20261107-r07-subsequence-0058","batch_id":"batch-20261014-advance-20261107-r07-subsequence-foundations","language":"zh-Hant","source_mko_ids":["mko-subsequence"],"title_zh":"子數列","stem_zh":"自然數索引與symbolic嚴格遞增證書。操作=subseq-composed-index；資料={\"outer_start\":1,\"outer_step\":3,\"inner_start\":3,\"inner_step\":2,\"j\":8}。請依 exact_ordered_tuple_declared_by_interface 欄序回答。","answer":{"kind":"expression","value":"(8, 19, 58, 6, 是, composition_remains_strictly_increasing)","explanation_zh":"Wave6根層核對=(8, 19, 58, 6, 是, composition_remains_strictly_increasing)；依完整明示資料獨立重算；subsequence索引必須嚴格遞增並保留原數列次序，不是重排或任意子集合；有限索引列表只證finite prefix；無限subsequence需要通用increasing-index certificate。"},"difficulty":{"band":"undergraduate_core","level":1,"skills":["子數列"]},"variant":{"family_id":"qf-mod38-subseq-composed-index","seed":202611077058,"parameters":{"outer_start":1,"outer_step":3,"inner_start":3,"inner_step":2,"j":8,"domain":"Symbolic_affine_subsequence_index","operation":"subseq-composed-index","semantic_template":"qf-mod38-subseq-composed-index/{\"inner_start\":3,\"inner_step\":2,\"j\":8,\"outer_start\":1,\"outer_step\":3}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_or_symbolic_model","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"候選須主端重算；不構成人工審定、有限sample群作用、sup等於max、basis等於subbasis、signed Markov、pigeonhole converse、nonunit Euler、finite-prefix subsequence、Lean或Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-14","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261014-advance-20261107-r07-subsequence-0059","batch_id":"batch-20261014-advance-20261107-r07-subsequence-foundations","language":"zh-Hant","source_mko_ids":["mko-subsequence"],"title_zh":"子數列","stem_zh":"自然數索引與symbolic嚴格遞增證書。操作=subseq-composed-index；資料={\"outer_start\":2,\"outer_step\":4,\"inner_start\":0,\"inner_step\":3,\"j\":9}。請依 exact_ordered_tuple_declared_by_interface 欄序回答。","answer":{"kind":"expression","value":"(9, 27, 110, 12, 是, composition_remains_strictly_increasing)","explanation_zh":"Wave6根層核對=(9, 27, 110, 12, 是, composition_remains_strictly_increasing)；依完整明示資料獨立重算；subsequence索引必須嚴格遞增並保留原數列次序，不是重排或任意子集合；有限索引列表只證finite prefix；無限subsequence需要通用increasing-index certificate。"},"difficulty":{"band":"undergraduate_core","level":2,"skills":["子數列"]},"variant":{"family_id":"qf-mod38-subseq-composed-index","seed":202611077059,"parameters":{"outer_start":2,"outer_step":4,"inner_start":0,"inner_step":3,"j":9,"domain":"Symbolic_affine_subsequence_index","operation":"subseq-composed-index","semantic_template":"qf-mod38-subseq-composed-index/{\"inner_start\":0,\"inner_step\":3,\"j\":9,\"outer_start\":2,\"outer_step\":4}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_or_symbolic_model","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"候選須主端重算；不構成人工審定、有限sample群作用、sup等於max、basis等於subbasis、signed Markov、pigeonhole converse、nonunit Euler、finite-prefix subsequence、Lean或Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-14","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261014-advance-20261107-r07-subsequence-0060","batch_id":"batch-20261014-advance-20261107-r07-subsequence-foundations","language":"zh-Hant","source_mko_ids":["mko-subsequence"],"title_zh":"子數列","stem_zh":"自然數索引與symbolic嚴格遞增證書。操作=subseq-composed-index；資料={\"outer_start\":0,\"outer_step\":5,\"inner_start\":1,\"inner_step\":4,\"j\":10}。請依 exact_ordered_tuple_declared_by_interface 欄序回答。","answer":{"kind":"expression","value":"(10, 41, 205, 20, 是, composition_remains_strictly_increasing)","explanation_zh":"Wave6根層核對=(10, 41, 205, 20, 是, composition_remains_strictly_increasing)；依完整明示資料獨立重算；subsequence索引必須嚴格遞增並保留原數列次序，不是重排或任意子集合；有限索引列表只證finite prefix；無限subsequence需要通用increasing-index certificate。"},"difficulty":{"band":"undergraduate_core","level":2,"skills":["子數列"]},"variant":{"family_id":"qf-mod38-subseq-composed-index","seed":202611077060,"parameters":{"outer_start":0,"outer_step":5,"inner_start":1,"inner_step":4,"j":10,"domain":"Symbolic_affine_subsequence_index","operation":"subseq-composed-index","semantic_template":"qf-mod38-subseq-composed-index/{\"inner_start\":1,\"inner_step\":4,\"j\":10,\"outer_start\":0,\"outer_step\":5}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_or_symbolic_model","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"候選須主端重算；不構成人工審定、有限sample群作用、sup等於max、basis等於subbasis、signed Markov、pigeonhole converse、nonunit Euler、finite-prefix subsequence、Lean或Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-14","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261014-advance-20261107-r07-subsequence-0061","batch_id":"batch-20261014-advance-20261107-r07-subsequence-foundations","language":"zh-Hant","source_mko_ids":["mko-subsequence"],"title_zh":"子數列","stem_zh":"自然數索引與symbolic嚴格遞增證書。操作=subseq-composed-index；資料={\"outer_start\":1,\"outer_step\":1,\"inner_start\":2,\"inner_step\":5,\"j\":11}。請依 exact_ordered_tuple_declared_by_interface 欄序回答。","answer":{"kind":"expression","value":"(11, 57, 58, 5, 是, composition_remains_strictly_increasing)","explanation_zh":"Wave6根層核對=(11, 57, 58, 5, 是, composition_remains_strictly_increasing)；依完整明示資料獨立重算；subsequence索引必須嚴格遞增並保留原數列次序，不是重排或任意子集合；有限索引列表只證finite prefix；無限subsequence需要通用increasing-index certificate。"},"difficulty":{"band":"undergraduate_core","level":2,"skills":["子數列"]},"variant":{"family_id":"qf-mod38-subseq-composed-index","seed":202611077061,"parameters":{"outer_start":1,"outer_step":1,"inner_start":2,"inner_step":5,"j":11,"domain":"Symbolic_affine_subsequence_index","operation":"subseq-composed-index","semantic_template":"qf-mod38-subseq-composed-index/{\"inner_start\":2,\"inner_step\":5,\"j\":11,\"outer_start\":1,\"outer_step\":1}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_or_symbolic_model","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"候選須主端重算；不構成人工審定、有限sample群作用、sup等於max、basis等於subbasis、signed Markov、pigeonhole converse、nonunit Euler、finite-prefix subsequence、Lean或Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-14","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261014-advance-20261107-r07-subsequence-0062","batch_id":"batch-20261014-advance-20261107-r07-subsequence-foundations","language":"zh-Hant","source_mko_ids":["mko-subsequence"],"title_zh":"子數列","stem_zh":"自然數索引與symbolic嚴格遞增證書。操作=subseq-composed-index；資料={\"outer_start\":2,\"outer_step\":2,\"inner_start\":3,\"inner_step\":6,\"j\":12}。請依 exact_ordered_tuple_declared_by_interface 欄序回答。","answer":{"kind":"expression","value":"(12, 75, 152, 12, 是, composition_remains_strictly_increasing)","explanation_zh":"Wave6根層核對=(12, 75, 152, 12, 是, composition_remains_strictly_increasing)；依完整明示資料獨立重算；subsequence索引必須嚴格遞增並保留原數列次序，不是重排或任意子集合；有限索引列表只證finite prefix；無限subsequence需要通用increasing-index certificate。"},"difficulty":{"band":"undergraduate_core","level":2,"skills":["子數列"]},"variant":{"family_id":"qf-mod38-subseq-composed-index","seed":202611077062,"parameters":{"outer_start":2,"outer_step":2,"inner_start":3,"inner_step":6,"j":12,"domain":"Symbolic_affine_subsequence_index","operation":"subseq-composed-index","semantic_template":"qf-mod38-subseq-composed-index/{\"inner_start\":3,\"inner_step\":6,\"j\":12,\"outer_start\":2,\"outer_step\":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、有限sample群作用、sup等於max、basis等於subbasis、signed Markov、pigeonhole converse、nonunit Euler、finite-prefix subsequence、Lean或Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-14","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261014-advance-20261107-r07-subsequence-0063","batch_id":"batch-20261014-advance-20261107-r07-subsequence-foundations","language":"zh-Hant","source_mko_ids":["mko-subsequence"],"title_zh":"子數列","stem_zh":"自然數索引與symbolic嚴格遞增證書。操作=subseq-composed-index；資料={\"outer_start\":0,\"outer_step\":3,\"inner_start\":0,\"inner_step\":1,\"j\":13}。請依 exact_ordered_tuple_declared_by_interface 欄序回答。","answer":{"kind":"expression","value":"(13, 13, 39, 3, 是, composition_remains_strictly_increasing)","explanation_zh":"Wave6根層核對=(13, 13, 39, 3, 是, composition_remains_strictly_increasing)；依完整明示資料獨立重算；subsequence索引必須嚴格遞增並保留原數列次序，不是重排或任意子集合；有限索引列表只證finite prefix；無限subsequence需要通用increasing-index certificate。"},"difficulty":{"band":"undergraduate_core","level":2,"skills":["子數列"]},"variant":{"family_id":"qf-mod38-subseq-composed-index","seed":202611077063,"parameters":{"outer_start":0,"outer_step":3,"inner_start":0,"inner_step":1,"j":13,"domain":"Symbolic_affine_subsequence_index","operation":"subseq-composed-index","semantic_template":"qf-mod38-subseq-composed-index/{\"inner_start\":0,\"inner_step\":1,\"j\":13,\"outer_start\":0,\"outer_step\":3}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_or_symbolic_model","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"候選須主端重算；不構成人工審定、有限sample群作用、sup等於max、basis等於subbasis、signed Markov、pigeonhole converse、nonunit Euler、finite-prefix subsequence、Lean或Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-14","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261014-advance-20261107-r07-subsequence-0064","batch_id":"batch-20261014-advance-20261107-r07-subsequence-foundations","language":"zh-Hant","source_mko_ids":["mko-subsequence"],"title_zh":"子數列","stem_zh":"自然數索引與symbolic嚴格遞增證書。操作=subseq-composed-index；資料={\"outer_start\":1,\"outer_step\":4,\"inner_start\":1,\"inner_step\":2,\"j\":14}。請依 exact_ordered_tuple_declared_by_interface 欄序回答。","answer":{"kind":"expression","value":"(14, 29, 117, 8, 是, composition_remains_strictly_increasing)","explanation_zh":"Wave6根層核對=(14, 29, 117, 8, 是, composition_remains_strictly_increasing)；依完整明示資料獨立重算；subsequence索引必須嚴格遞增並保留原數列次序，不是重排或任意子集合；有限索引列表只證finite prefix；無限subsequence需要通用increasing-index certificate。"},"difficulty":{"band":"undergraduate_core","level":2,"skills":["子數列"]},"variant":{"family_id":"qf-mod38-subseq-composed-index","seed":202611077064,"parameters":{"outer_start":1,"outer_step":4,"inner_start":1,"inner_step":2,"j":14,"domain":"Symbolic_affine_subsequence_index","operation":"subseq-composed-index","semantic_template":"qf-mod38-subseq-composed-index/{\"inner_start\":1,\"inner_step\":2,\"j\":14,\"outer_start\":1,\"outer_step\":4}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_or_symbolic_model","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"候選須主端重算；不構成人工審定、有限sample群作用、sup等於max、basis等於subbasis、signed Markov、pigeonhole converse、nonunit Euler、finite-prefix subsequence、Lean或Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-14","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261014-advance-20261107-r07-subsequence-0065","batch_id":"batch-20261014-advance-20261107-r07-subsequence-foundations","language":"zh-Hant","source_mko_ids":["mko-subsequence"],"title_zh":"子數列","stem_zh":"自然數索引與symbolic嚴格遞增證書。操作=subseq-composed-index；資料={\"outer_start\":2,\"outer_step\":5,\"inner_start\":2,\"inner_step\":3,\"j\":15}。請依 exact_ordered_tuple_declared_by_interface 欄序回答。","answer":{"kind":"expression","value":"(15, 47, 237, 15, 是, composition_remains_strictly_increasing)","explanation_zh":"Wave6根層核對=(15, 47, 237, 15, 是, composition_remains_strictly_increasing)；依完整明示資料獨立重算；subsequence索引必須嚴格遞增並保留原數列次序，不是重排或任意子集合；有限索引列表只證finite prefix；無限subsequence需要通用increasing-index certificate。"},"difficulty":{"band":"undergraduate_core","level":2,"skills":["子數列"]},"variant":{"family_id":"qf-mod38-subseq-composed-index","seed":202611077065,"parameters":{"outer_start":2,"outer_step":5,"inner_start":2,"inner_step":3,"j":15,"domain":"Symbolic_affine_subsequence_index","operation":"subseq-composed-index","semantic_template":"qf-mod38-subseq-composed-index/{\"inner_start\":2,\"inner_step\":3,\"j\":15,\"outer_start\":2,\"outer_step\":5}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_or_symbolic_model","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"候選須主端重算；不構成人工審定、有限sample群作用、sup等於max、basis等於subbasis、signed Markov、pigeonhole converse、nonunit Euler、finite-prefix subsequence、Lean或Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-14","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261014-advance-20261107-r07-subsequence-0066","batch_id":"batch-20261014-advance-20261107-r07-subsequence-foundations","language":"zh-Hant","source_mko_ids":["mko-subsequence"],"title_zh":"子數列","stem_zh":"自然數索引與symbolic嚴格遞增證書。操作=subseq-composed-index；資料={\"outer_start\":0,\"outer_step\":1,\"inner_start\":3,\"inner_step\":4,\"j\":16}。請依 exact_ordered_tuple_declared_by_interface 欄序回答。","answer":{"kind":"expression","value":"(16, 67, 67, 4, 是, composition_remains_strictly_increasing)","explanation_zh":"Wave6根層核對=(16, 67, 67, 4, 是, composition_remains_strictly_increasing)；依完整明示資料獨立重算；subsequence索引必須嚴格遞增並保留原數列次序，不是重排或任意子集合；有限索引列表只證finite prefix；無限subsequence需要通用increasing-index certificate。"},"difficulty":{"band":"undergraduate_core","level":2,"skills":["子數列"]},"variant":{"family_id":"qf-mod38-subseq-composed-index","seed":202611077066,"parameters":{"outer_start":0,"outer_step":1,"inner_start":3,"inner_step":4,"j":16,"domain":"Symbolic_affine_subsequence_index","operation":"subseq-composed-index","semantic_template":"qf-mod38-subseq-composed-index/{\"inner_start\":3,\"inner_step\":4,\"j\":16,\"outer_start\":0,\"outer_step\":1}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_or_symbolic_model","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"候選須主端重算；不構成人工審定、有限sample群作用、sup等於max、basis等於subbasis、signed Markov、pigeonhole converse、nonunit Euler、finite-prefix subsequence、Lean或Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-14","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261014-advance-20261107-r07-subsequence-0067","batch_id":"batch-20261014-advance-20261107-r07-subsequence-foundations","language":"zh-Hant","source_mko_ids":["mko-subsequence"],"title_zh":"子數列","stem_zh":"自然數索引與symbolic嚴格遞增證書。操作=subseq-composed-index；資料={\"outer_start\":1,\"outer_step\":2,\"inner_start\":0,\"inner_step\":5,\"j\":17}。請依 exact_ordered_tuple_declared_by_interface 欄序回答。","answer":{"kind":"expression","value":"(17, 85, 171, 10, 是, composition_remains_strictly_increasing)","explanation_zh":"Wave6根層核對=(17, 85, 171, 10, 是, composition_remains_strictly_increasing)；依完整明示資料獨立重算；subsequence索引必須嚴格遞增並保留原數列次序，不是重排或任意子集合；有限索引列表只證finite prefix；無限subsequence需要通用increasing-index certificate。"},"difficulty":{"band":"undergraduate_core","level":2,"skills":["子數列"]},"variant":{"family_id":"qf-mod38-subseq-composed-index","seed":202611077067,"parameters":{"outer_start":1,"outer_step":2,"inner_start":0,"inner_step":5,"j":17,"domain":"Symbolic_affine_subsequence_index","operation":"subseq-composed-index","semantic_template":"qf-mod38-subseq-composed-index/{\"inner_start\":0,\"inner_step\":5,\"j\":17,\"outer_start\":1,\"outer_step\":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、有限sample群作用、sup等於max、basis等於subbasis、signed Markov、pigeonhole converse、nonunit Euler、finite-prefix subsequence、Lean或Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-14","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261014-advance-20261107-r07-subsequence-0068","batch_id":"batch-20261014-advance-20261107-r07-subsequence-foundations","language":"zh-Hant","source_mko_ids":["mko-subsequence"],"title_zh":"子數列","stem_zh":"自然數索引與symbolic嚴格遞增證書。操作=subseq-composed-index；資料={\"outer_start\":2,\"outer_step\":3,\"inner_start\":1,\"inner_step\":6,\"j\":18}。請依 exact_ordered_tuple_declared_by_interface 欄序回答。","answer":{"kind":"expression","value":"(18, 109, 329, 18, 是, composition_remains_strictly_increasing)","explanation_zh":"Wave6根層核對=(18, 109, 329, 18, 是, composition_remains_strictly_increasing)；依完整明示資料獨立重算；subsequence索引必須嚴格遞增並保留原數列次序，不是重排或任意子集合；有限索引列表只證finite prefix；無限subsequence需要通用increasing-index certificate。"},"difficulty":{"band":"undergraduate_core","level":3,"skills":["子數列"]},"variant":{"family_id":"qf-mod38-subseq-composed-index","seed":202611077068,"parameters":{"outer_start":2,"outer_step":3,"inner_start":1,"inner_step":6,"j":18,"domain":"Symbolic_affine_subsequence_index","operation":"subseq-composed-index","semantic_template":"qf-mod38-subseq-composed-index/{\"inner_start\":1,\"inner_step\":6,\"j\":18,\"outer_start\":2,\"outer_step\":3}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_or_symbolic_model","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"候選須主端重算；不構成人工審定、有限sample群作用、sup等於max、basis等於subbasis、signed Markov、pigeonhole converse、nonunit Euler、finite-prefix subsequence、Lean或Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-14","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261014-advance-20261107-r07-subsequence-0069","batch_id":"batch-20261014-advance-20261107-r07-subsequence-foundations","language":"zh-Hant","source_mko_ids":["mko-subsequence"],"title_zh":"子數列","stem_zh":"自然數索引與symbolic嚴格遞增證書。操作=subseq-composed-index；資料={\"outer_start\":0,\"outer_step\":4,\"inner_start\":2,\"inner_step\":1,\"j\":19}。請依 exact_ordered_tuple_declared_by_interface 欄序回答。","answer":{"kind":"expression","value":"(19, 21, 84, 4, 是, composition_remains_strictly_increasing)","explanation_zh":"Wave6根層核對=(19, 21, 84, 4, 是, composition_remains_strictly_increasing)；依完整明示資料獨立重算；subsequence索引必須嚴格遞增並保留原數列次序，不是重排或任意子集合；有限索引列表只證finite prefix；無限subsequence需要通用increasing-index certificate。"},"difficulty":{"band":"undergraduate_core","level":3,"skills":["子數列"]},"variant":{"family_id":"qf-mod38-subseq-composed-index","seed":202611077069,"parameters":{"outer_start":0,"outer_step":4,"inner_start":2,"inner_step":1,"j":19,"domain":"Symbolic_affine_subsequence_index","operation":"subseq-composed-index","semantic_template":"qf-mod38-subseq-composed-index/{\"inner_start\":2,\"inner_step\":1,\"j\":19,\"outer_start\":0,\"outer_step\":4}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_or_symbolic_model","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"候選須主端重算；不構成人工審定、有限sample群作用、sup等於max、basis等於subbasis、signed Markov、pigeonhole converse、nonunit Euler、finite-prefix subsequence、Lean或Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-14","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261014-advance-20261107-r07-subsequence-0070","batch_id":"batch-20261014-advance-20261107-r07-subsequence-foundations","language":"zh-Hant","source_mko_ids":["mko-subsequence"],"title_zh":"子數列","stem_zh":"自然數索引與symbolic嚴格遞增證書。操作=subseq-composed-index；資料={\"outer_start\":1,\"outer_step\":5,\"inner_start\":3,\"inner_step\":2,\"j\":20}。請依 exact_ordered_tuple_declared_by_interface 欄序回答。","answer":{"kind":"expression","value":"(20, 43, 216, 10, 是, composition_remains_strictly_increasing)","explanation_zh":"Wave6根層核對=(20, 43, 216, 10, 是, composition_remains_strictly_increasing)；依完整明示資料獨立重算；subsequence索引必須嚴格遞增並保留原數列次序，不是重排或任意子集合；有限索引列表只證finite prefix；無限subsequence需要通用increasing-index certificate。"},"difficulty":{"band":"undergraduate_core","level":3,"skills":["子數列"]},"variant":{"family_id":"qf-mod38-subseq-composed-index","seed":202611077070,"parameters":{"outer_start":1,"outer_step":5,"inner_start":3,"inner_step":2,"j":20,"domain":"Symbolic_affine_subsequence_index","operation":"subseq-composed-index","semantic_template":"qf-mod38-subseq-composed-index/{\"inner_start\":3,\"inner_step\":2,\"j\":20,\"outer_start\":1,\"outer_step\":5}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_or_symbolic_model","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"候選須主端重算；不構成人工審定、有限sample群作用、sup等於max、basis等於subbasis、signed Markov、pigeonhole converse、nonunit Euler、finite-prefix subsequence、Lean或Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-14","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261014-advance-20261107-r07-subsequence-0071","batch_id":"batch-20261014-advance-20261107-r07-subsequence-foundations","language":"zh-Hant","source_mko_ids":["mko-subsequence"],"title_zh":"子數列","stem_zh":"自然數索引與symbolic嚴格遞增證書。操作=subseq-composed-index；資料={\"outer_start\":2,\"outer_step\":1,\"inner_start\":0,\"inner_step\":3,\"j\":21}。請依 exact_ordered_tuple_declared_by_interface 欄序回答。","answer":{"kind":"expression","value":"(21, 63, 65, 3, 是, composition_remains_strictly_increasing)","explanation_zh":"Wave6根層核對=(21, 63, 65, 3, 是, composition_remains_strictly_increasing)；依完整明示資料獨立重算；subsequence索引必須嚴格遞增並保留原數列次序，不是重排或任意子集合；有限索引列表只證finite prefix；無限subsequence需要通用increasing-index certificate。"},"difficulty":{"band":"undergraduate_core","level":3,"skills":["子數列"]},"variant":{"family_id":"qf-mod38-subseq-composed-index","seed":202611077071,"parameters":{"outer_start":2,"outer_step":1,"inner_start":0,"inner_step":3,"j":21,"domain":"Symbolic_affine_subsequence_index","operation":"subseq-composed-index","semantic_template":"qf-mod38-subseq-composed-index/{\"inner_start\":0,\"inner_step\":3,\"j\":21,\"outer_start\":2,\"outer_step\":1}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_or_symbolic_model","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"候選須主端重算；不構成人工審定、有限sample群作用、sup等於max、basis等於subbasis、signed Markov、pigeonhole converse、nonunit Euler、finite-prefix subsequence、Lean或Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-14","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261014-advance-20261107-r07-subsequence-0072","batch_id":"batch-20261014-advance-20261107-r07-subsequence-foundations","language":"zh-Hant","source_mko_ids":["mko-subsequence"],"title_zh":"子數列","stem_zh":"自然數索引與symbolic嚴格遞增證書。操作=subseq-composed-index；資料={\"outer_start\":0,\"outer_step\":2,\"inner_start\":1,\"inner_step\":4,\"j\":22}。請依 exact_ordered_tuple_declared_by_interface 欄序回答。","answer":{"kind":"expression","value":"(22, 89, 178, 8, 是, composition_remains_strictly_increasing)","explanation_zh":"Wave6根層核對=(22, 89, 178, 8, 是, composition_remains_strictly_increasing)；依完整明示資料獨立重算；subsequence索引必須嚴格遞增並保留原數列次序，不是重排或任意子集合；有限索引列表只證finite prefix；無限subsequence需要通用increasing-index certificate。"},"difficulty":{"band":"undergraduate_core","level":3,"skills":["子數列"]},"variant":{"family_id":"qf-mod38-subseq-composed-index","seed":202611077072,"parameters":{"outer_start":0,"outer_step":2,"inner_start":1,"inner_step":4,"j":22,"domain":"Symbolic_affine_subsequence_index","operation":"subseq-composed-index","semantic_template":"qf-mod38-subseq-composed-index/{\"inner_start\":1,\"inner_step\":4,\"j\":22,\"outer_start\":0,\"outer_step\":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、有限sample群作用、sup等於max、basis等於subbasis、signed Markov、pigeonhole converse、nonunit Euler、finite-prefix subsequence、Lean或Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-14","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261014-advance-20261107-r07-subsequence-0073","batch_id":"batch-20261014-advance-20261107-r07-subsequence-foundations","language":"zh-Hant","source_mko_ids":["mko-subsequence"],"title_zh":"子數列","stem_zh":"自然數索引與symbolic嚴格遞增證書。操作=subseq-composed-index；資料={\"outer_start\":1,\"outer_step\":3,\"inner_start\":2,\"inner_step\":5,\"j\":23}。請依 exact_ordered_tuple_declared_by_interface 欄序回答。","answer":{"kind":"expression","value":"(23, 117, 352, 15, 是, composition_remains_strictly_increasing)","explanation_zh":"Wave6根層核對=(23, 117, 352, 15, 是, composition_remains_strictly_increasing)；依完整明示資料獨立重算；subsequence索引必須嚴格遞增並保留原數列次序，不是重排或任意子集合；有限索引列表只證finite prefix；無限subsequence需要通用increasing-index certificate。"},"difficulty":{"band":"undergraduate_core","level":3,"skills":["子數列"]},"variant":{"family_id":"qf-mod38-subseq-composed-index","seed":202611077073,"parameters":{"outer_start":1,"outer_step":3,"inner_start":2,"inner_step":5,"j":23,"domain":"Symbolic_affine_subsequence_index","operation":"subseq-composed-index","semantic_template":"qf-mod38-subseq-composed-index/{\"inner_start\":2,\"inner_step\":5,\"j\":23,\"outer_start\":1,\"outer_step\":3}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_or_symbolic_model","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"候選須主端重算；不構成人工審定、有限sample群作用、sup等於max、basis等於subbasis、signed Markov、pigeonhole converse、nonunit Euler、finite-prefix subsequence、Lean或Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-14","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261014-advance-20261107-r07-subsequence-0074","batch_id":"batch-20261014-advance-20261107-r07-subsequence-foundations","language":"zh-Hant","source_mko_ids":["mko-subsequence"],"title_zh":"子數列","stem_zh":"自然數索引與symbolic嚴格遞增證書。操作=subseq-composed-index；資料={\"outer_start\":2,\"outer_step\":4,\"inner_start\":3,\"inner_step\":6,\"j\":24}。請依 exact_ordered_tuple_declared_by_interface 欄序回答。","answer":{"kind":"expression","value":"(24, 147, 590, 24, 是, composition_remains_strictly_increasing)","explanation_zh":"Wave6根層核對=(24, 147, 590, 24, 是, composition_remains_strictly_increasing)；依完整明示資料獨立重算；subsequence索引必須嚴格遞增並保留原數列次序，不是重排或任意子集合；有限索引列表只證finite prefix；無限subsequence需要通用increasing-index certificate。"},"difficulty":{"band":"undergraduate_core","level":3,"skills":["子數列"]},"variant":{"family_id":"qf-mod38-subseq-composed-index","seed":202611077074,"parameters":{"outer_start":2,"outer_step":4,"inner_start":3,"inner_step":6,"j":24,"domain":"Symbolic_affine_subsequence_index","operation":"subseq-composed-index","semantic_template":"qf-mod38-subseq-composed-index/{\"inner_start\":3,\"inner_step\":6,\"j\":24,\"outer_start\":2,\"outer_step\":4}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_or_symbolic_model","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"候選須主端重算；不構成人工審定、有限sample群作用、sup等於max、basis等於subbasis、signed Markov、pigeonhole converse、nonunit Euler、finite-prefix subsequence、Lean或Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-14","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261014-advance-20261107-r07-subsequence-0075","batch_id":"batch-20261014-advance-20261107-r07-subsequence-foundations","language":"zh-Hant","source_mko_ids":["mko-subsequence"],"title_zh":"子數列","stem_zh":"自然數索引與symbolic嚴格遞增證書。操作=subseq-composed-index；資料={\"outer_start\":0,\"outer_step\":5,\"inner_start\":0,\"inner_step\":1,\"j\":25}。請依 exact_ordered_tuple_declared_by_interface 欄序回答。","answer":{"kind":"expression","value":"(25, 25, 125, 5, 是, composition_remains_strictly_increasing)","explanation_zh":"Wave6根層核對=(25, 25, 125, 5, 是, composition_remains_strictly_increasing)；依完整明示資料獨立重算；subsequence索引必須嚴格遞增並保留原數列次序，不是重排或任意子集合；有限索引列表只證finite prefix；無限subsequence需要通用increasing-index certificate。"},"difficulty":{"band":"undergraduate_core","level":3,"skills":["子數列"]},"variant":{"family_id":"qf-mod38-subseq-composed-index","seed":202611077075,"parameters":{"outer_start":0,"outer_step":5,"inner_start":0,"inner_step":1,"j":25,"domain":"Symbolic_affine_subsequence_index","operation":"subseq-composed-index","semantic_template":"qf-mod38-subseq-composed-index/{\"inner_start\":0,\"inner_step\":1,\"j\":25,\"outer_start\":0,\"outer_step\":5}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_or_symbolic_model","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"候選須主端重算；不構成人工審定、有限sample群作用、sup等於max、basis等於subbasis、signed Markov、pigeonhole converse、nonunit Euler、finite-prefix subsequence、Lean或Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-14","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261014-advance-20261107-r07-subsequence-0076","batch_id":"batch-20261014-advance-20261107-r07-subsequence-foundations","language":"zh-Hant","source_mko_ids":["mko-subsequence"],"title_zh":"子數列","stem_zh":"自然數索引與symbolic嚴格遞增證書。操作=subseq-finite-prefix-boundary；資料={\"indices\":[0,1,2,3]}。請依 exact_ordered_tuple_declared_by_interface 欄序回答。","answer":{"kind":"expression","value":"([0, 1, 2, 3], 是, 否, finite_increasing_prefix_not_infinite_subsequence_certificate)","explanation_zh":"Wave6根層核對=([0, 1, 2, 3], 是, 否, finite_increasing_prefix_not_infinite_subsequence_certificate)；依完整明示資料獨立重算；subsequence索引必須嚴格遞增並保留原數列次序，不是重排或任意子集合；有限索引列表只證finite prefix；無限subsequence需要通用increasing-index certificate。"},"difficulty":{"band":"undergraduate_core","level":1,"skills":["子數列"]},"variant":{"family_id":"qf-mod38-subseq-finite-prefix-boundary","seed":202611077076,"parameters":{"indices":[0,1,2,3],"domain":"Symbolic_affine_subsequence_index","operation":"subseq-finite-prefix-boundary","semantic_template":"qf-mod38-subseq-finite-prefix-boundary/{\"indices\":[0,1,2,3]}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_or_symbolic_model","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"候選須主端重算；不構成人工審定、有限sample群作用、sup等於max、basis等於subbasis、signed Markov、pigeonhole converse、nonunit Euler、finite-prefix subsequence、Lean或Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-14","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261014-advance-20261107-r07-subsequence-0077","batch_id":"batch-20261014-advance-20261107-r07-subsequence-foundations","language":"zh-Hant","source_mko_ids":["mko-subsequence"],"title_zh":"子數列","stem_zh":"自然數索引與symbolic嚴格遞增證書。操作=subseq-finite-prefix-boundary；資料={\"indices\":[1,3,5,7,9]}。請依 exact_ordered_tuple_declared_by_interface 欄序回答。","answer":{"kind":"expression","value":"([1, 3, 5, 7, 9], 是, 否, finite_increasing_prefix_not_infinite_subsequence_certificate)","explanation_zh":"Wave6根層核對=([1, 3, 5, 7, 9], 是, 否, finite_increasing_prefix_not_infinite_subsequence_certificate)；依完整明示資料獨立重算；subsequence索引必須嚴格遞增並保留原數列次序，不是重排或任意子集合；有限索引列表只證finite prefix；無限subsequence需要通用increasing-index certificate。"},"difficulty":{"band":"undergraduate_core","level":1,"skills":["子數列"]},"variant":{"family_id":"qf-mod38-subseq-finite-prefix-boundary","seed":202611077077,"parameters":{"indices":[1,3,5,7,9],"domain":"Symbolic_affine_subsequence_index","operation":"subseq-finite-prefix-boundary","semantic_template":"qf-mod38-subseq-finite-prefix-boundary/{\"indices\":[1,3,5,7,9]}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_or_symbolic_model","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"候選須主端重算；不構成人工審定、有限sample群作用、sup等於max、basis等於subbasis、signed Markov、pigeonhole converse、nonunit Euler、finite-prefix subsequence、Lean或Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-14","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261014-advance-20261107-r07-subsequence-0078","batch_id":"batch-20261014-advance-20261107-r07-subsequence-foundations","language":"zh-Hant","source_mko_ids":["mko-subsequence"],"title_zh":"子數列","stem_zh":"自然數索引與symbolic嚴格遞增證書。操作=subseq-finite-prefix-boundary；資料={\"indices\":[2,5,8,11,14,17]}。請依 exact_ordered_tuple_declared_by_interface 欄序回答。","answer":{"kind":"expression","value":"([2, 5, 8, 11, 14, 17], 是, 否, finite_increasing_prefix_not_infinite_subsequence_certificate)","explanation_zh":"Wave6根層核對=([2, 5, 8, 11, 14, 17], 是, 否, finite_increasing_prefix_not_infinite_subsequence_certificate)；依完整明示資料獨立重算；subsequence索引必須嚴格遞增並保留原數列次序，不是重排或任意子集合；有限索引列表只證finite prefix；無限subsequence需要通用increasing-index certificate。"},"difficulty":{"band":"undergraduate_core","level":1,"skills":["子數列"]},"variant":{"family_id":"qf-mod38-subseq-finite-prefix-boundary","seed":202611077078,"parameters":{"indices":[2,5,8,11,14,17],"domain":"Symbolic_affine_subsequence_index","operation":"subseq-finite-prefix-boundary","semantic_template":"qf-mod38-subseq-finite-prefix-boundary/{\"indices\":[2,5,8,11,14,17]}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_or_symbolic_model","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"候選須主端重算；不構成人工審定、有限sample群作用、sup等於max、basis等於subbasis、signed Markov、pigeonhole converse、nonunit Euler、finite-prefix subsequence、Lean或Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-14","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261014-advance-20261107-r07-subsequence-0079","batch_id":"batch-20261014-advance-20261107-r07-subsequence-foundations","language":"zh-Hant","source_mko_ids":["mko-subsequence"],"title_zh":"子數列","stem_zh":"自然數索引與symbolic嚴格遞增證書。操作=subseq-finite-prefix-boundary；資料={\"indices\":[3,7,11,15]}。請依 exact_ordered_tuple_declared_by_interface 欄序回答。","answer":{"kind":"expression","value":"([3, 7, 11, 15], 是, 否, finite_increasing_prefix_not_infinite_subsequence_certificate)","explanation_zh":"Wave6根層核對=([3, 7, 11, 15], 是, 否, finite_increasing_prefix_not_infinite_subsequence_certificate)；依完整明示資料獨立重算；subsequence索引必須嚴格遞增並保留原數列次序，不是重排或任意子集合；有限索引列表只證finite prefix；無限subsequence需要通用increasing-index certificate。"},"difficulty":{"band":"undergraduate_core","level":1,"skills":["子數列"]},"variant":{"family_id":"qf-mod38-subseq-finite-prefix-boundary","seed":202611077079,"parameters":{"indices":[3,7,11,15],"domain":"Symbolic_affine_subsequence_index","operation":"subseq-finite-prefix-boundary","semantic_template":"qf-mod38-subseq-finite-prefix-boundary/{\"indices\":[3,7,11,15]}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_or_symbolic_model","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"候選須主端重算；不構成人工審定、有限sample群作用、sup等於max、basis等於subbasis、signed Markov、pigeonhole converse、nonunit Euler、finite-prefix subsequence、Lean或Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-14","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261014-advance-20261107-r07-subsequence-0080","batch_id":"batch-20261014-advance-20261107-r07-subsequence-foundations","language":"zh-Hant","source_mko_ids":["mko-subsequence"],"title_zh":"子數列","stem_zh":"自然數索引與symbolic嚴格遞增證書。操作=subseq-finite-prefix-boundary；資料={\"indices\":[4,9,14,19,24]}。請依 exact_ordered_tuple_declared_by_interface 欄序回答。","answer":{"kind":"expression","value":"([4, 9, 14, 19, 24], 是, 否, finite_increasing_prefix_not_infinite_subsequence_certificate)","explanation_zh":"Wave6根層核對=([4, 9, 14, 19, 24], 是, 否, finite_increasing_prefix_not_infinite_subsequence_certificate)；依完整明示資料獨立重算；subsequence索引必須嚴格遞增並保留原數列次序，不是重排或任意子集合；有限索引列表只證finite prefix；無限subsequence需要通用increasing-index certificate。"},"difficulty":{"band":"undergraduate_core","level":1,"skills":["子數列"]},"variant":{"family_id":"qf-mod38-subseq-finite-prefix-boundary","seed":202611077080,"parameters":{"indices":[4,9,14,19,24],"domain":"Symbolic_affine_subsequence_index","operation":"subseq-finite-prefix-boundary","semantic_template":"qf-mod38-subseq-finite-prefix-boundary/{\"indices\":[4,9,14,19,24]}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_or_symbolic_model","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"候選須主端重算；不構成人工審定、有限sample群作用、sup等於max、basis等於subbasis、signed Markov、pigeonhole converse、nonunit Euler、finite-prefix subsequence、Lean或Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-14","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261014-advance-20261107-r07-subsequence-0081","batch_id":"batch-20261014-advance-20261107-r07-subsequence-foundations","language":"zh-Hant","source_mko_ids":["mko-subsequence"],"title_zh":"子數列","stem_zh":"自然數索引與symbolic嚴格遞增證書。操作=subseq-finite-prefix-boundary；資料={\"indices\":[5,6,7,8,9,10]}。請依 exact_ordered_tuple_declared_by_interface 欄序回答。","answer":{"kind":"expression","value":"([5, 6, 7, 8, 9, 10], 是, 否, finite_increasing_prefix_not_infinite_subsequence_certificate)","explanation_zh":"Wave6根層核對=([5, 6, 7, 8, 9, 10], 是, 否, finite_increasing_prefix_not_infinite_subsequence_certificate)；依完整明示資料獨立重算；subsequence索引必須嚴格遞增並保留原數列次序，不是重排或任意子集合；有限索引列表只證finite prefix；無限subsequence需要通用increasing-index certificate。"},"difficulty":{"band":"undergraduate_core","level":1,"skills":["子數列"]},"variant":{"family_id":"qf-mod38-subseq-finite-prefix-boundary","seed":202611077081,"parameters":{"indices":[5,6,7,8,9,10],"domain":"Symbolic_affine_subsequence_index","operation":"subseq-finite-prefix-boundary","semantic_template":"qf-mod38-subseq-finite-prefix-boundary/{\"indices\":[5,6,7,8,9,10]}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_or_symbolic_model","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"候選須主端重算；不構成人工審定、有限sample群作用、sup等於max、basis等於subbasis、signed Markov、pigeonhole converse、nonunit Euler、finite-prefix subsequence、Lean或Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-14","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261014-advance-20261107-r07-subsequence-0082","batch_id":"batch-20261014-advance-20261107-r07-subsequence-foundations","language":"zh-Hant","source_mko_ids":["mko-subsequence"],"title_zh":"子數列","stem_zh":"自然數索引與symbolic嚴格遞增證書。操作=subseq-finite-prefix-boundary；資料={\"indices\":[6,8,10,12]}。請依 exact_ordered_tuple_declared_by_interface 欄序回答。","answer":{"kind":"expression","value":"([6, 8, 10, 12], 是, 否, finite_increasing_prefix_not_infinite_subsequence_certificate)","explanation_zh":"Wave6根層核對=([6, 8, 10, 12], 是, 否, finite_increasing_prefix_not_infinite_subsequence_certificate)；依完整明示資料獨立重算；subsequence索引必須嚴格遞增並保留原數列次序，不是重排或任意子集合；有限索引列表只證finite prefix；無限subsequence需要通用increasing-index certificate。"},"difficulty":{"band":"undergraduate_core","level":1,"skills":["子數列"]},"variant":{"family_id":"qf-mod38-subseq-finite-prefix-boundary","seed":202611077082,"parameters":{"indices":[6,8,10,12],"domain":"Symbolic_affine_subsequence_index","operation":"subseq-finite-prefix-boundary","semantic_template":"qf-mod38-subseq-finite-prefix-boundary/{\"indices\":[6,8,10,12]}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_or_symbolic_model","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"候選須主端重算；不構成人工審定、有限sample群作用、sup等於max、basis等於subbasis、signed Markov、pigeonhole converse、nonunit Euler、finite-prefix subsequence、Lean或Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-14","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261014-advance-20261107-r07-subsequence-0083","batch_id":"batch-20261014-advance-20261107-r07-subsequence-foundations","language":"zh-Hant","source_mko_ids":["mko-subsequence"],"title_zh":"子數列","stem_zh":"自然數索引與symbolic嚴格遞增證書。操作=subseq-finite-prefix-boundary；資料={\"indices\":[7,10,13,16,19]}。請依 exact_ordered_tuple_declared_by_interface 欄序回答。","answer":{"kind":"expression","value":"([7, 10, 13, 16, 19], 是, 否, finite_increasing_prefix_not_infinite_subsequence_certificate)","explanation_zh":"Wave6根層核對=([7, 10, 13, 16, 19], 是, 否, finite_increasing_prefix_not_infinite_subsequence_certificate)；依完整明示資料獨立重算；subsequence索引必須嚴格遞增並保留原數列次序，不是重排或任意子集合；有限索引列表只證finite prefix；無限subsequence需要通用increasing-index certificate。"},"difficulty":{"band":"undergraduate_core","level":1,"skills":["子數列"]},"variant":{"family_id":"qf-mod38-subseq-finite-prefix-boundary","seed":202611077083,"parameters":{"indices":[7,10,13,16,19],"domain":"Symbolic_affine_subsequence_index","operation":"subseq-finite-prefix-boundary","semantic_template":"qf-mod38-subseq-finite-prefix-boundary/{\"indices\":[7,10,13,16,19]}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_or_symbolic_model","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"候選須主端重算；不構成人工審定、有限sample群作用、sup等於max、basis等於subbasis、signed Markov、pigeonhole converse、nonunit Euler、finite-prefix subsequence、Lean或Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-14","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261014-advance-20261107-r07-subsequence-0084","batch_id":"batch-20261014-advance-20261107-r07-subsequence-foundations","language":"zh-Hant","source_mko_ids":["mko-subsequence"],"title_zh":"子數列","stem_zh":"自然數索引與symbolic嚴格遞增證書。操作=subseq-finite-prefix-boundary；資料={\"indices\":[8,12,16,20,24,28]}。請依 exact_ordered_tuple_declared_by_interface 欄序回答。","answer":{"kind":"expression","value":"([8, 12, 16, 20, 24, 28], 是, 否, finite_increasing_prefix_not_infinite_subsequence_certificate)","explanation_zh":"Wave6根層核對=([8, 12, 16, 20, 24, 28], 是, 否, finite_increasing_prefix_not_infinite_subsequence_certificate)；依完整明示資料獨立重算；subsequence索引必須嚴格遞增並保留原數列次序，不是重排或任意子集合；有限索引列表只證finite prefix；無限subsequence需要通用increasing-index certificate。"},"difficulty":{"band":"undergraduate_core","level":2,"skills":["子數列"]},"variant":{"family_id":"qf-mod38-subseq-finite-prefix-boundary","seed":202611077084,"parameters":{"indices":[8,12,16,20,24,28],"domain":"Symbolic_affine_subsequence_index","operation":"subseq-finite-prefix-boundary","semantic_template":"qf-mod38-subseq-finite-prefix-boundary/{\"indices\":[8,12,16,20,24,28]}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_or_symbolic_model","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"候選須主端重算；不構成人工審定、有限sample群作用、sup等於max、basis等於subbasis、signed Markov、pigeonhole converse、nonunit Euler、finite-prefix subsequence、Lean或Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-14","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261014-advance-20261107-r07-subsequence-0085","batch_id":"batch-20261014-advance-20261107-r07-subsequence-foundations","language":"zh-Hant","source_mko_ids":["mko-subsequence"],"title_zh":"子數列","stem_zh":"自然數索引與symbolic嚴格遞增證書。操作=subseq-finite-prefix-boundary；資料={\"indices\":[9,14,19,24]}。請依 exact_ordered_tuple_declared_by_interface 欄序回答。","answer":{"kind":"expression","value":"([9, 14, 19, 24], 是, 否, finite_increasing_prefix_not_infinite_subsequence_certificate)","explanation_zh":"Wave6根層核對=([9, 14, 19, 24], 是, 否, finite_increasing_prefix_not_infinite_subsequence_certificate)；依完整明示資料獨立重算；subsequence索引必須嚴格遞增並保留原數列次序，不是重排或任意子集合；有限索引列表只證finite prefix；無限subsequence需要通用increasing-index certificate。"},"difficulty":{"band":"undergraduate_core","level":2,"skills":["子數列"]},"variant":{"family_id":"qf-mod38-subseq-finite-prefix-boundary","seed":202611077085,"parameters":{"indices":[9,14,19,24],"domain":"Symbolic_affine_subsequence_index","operation":"subseq-finite-prefix-boundary","semantic_template":"qf-mod38-subseq-finite-prefix-boundary/{\"indices\":[9,14,19,24]}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_or_symbolic_model","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"候選須主端重算；不構成人工審定、有限sample群作用、sup等於max、basis等於subbasis、signed Markov、pigeonhole converse、nonunit Euler、finite-prefix subsequence、Lean或Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-14","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261014-advance-20261107-r07-subsequence-0086","batch_id":"batch-20261014-advance-20261107-r07-subsequence-foundations","language":"zh-Hant","source_mko_ids":["mko-subsequence"],"title_zh":"子數列","stem_zh":"自然數索引與symbolic嚴格遞增證書。操作=subseq-finite-prefix-boundary；資料={\"indices\":[10,11,12,13,14]}。請依 exact_ordered_tuple_declared_by_interface 欄序回答。","answer":{"kind":"expression","value":"([10, 11, 12, 13, 14], 是, 否, finite_increasing_prefix_not_infinite_subsequence_certificate)","explanation_zh":"Wave6根層核對=([10, 11, 12, 13, 14], 是, 否, finite_increasing_prefix_not_infinite_subsequence_certificate)；依完整明示資料獨立重算；subsequence索引必須嚴格遞增並保留原數列次序，不是重排或任意子集合；有限索引列表只證finite prefix；無限subsequence需要通用increasing-index certificate。"},"difficulty":{"band":"undergraduate_core","level":2,"skills":["子數列"]},"variant":{"family_id":"qf-mod38-subseq-finite-prefix-boundary","seed":202611077086,"parameters":{"indices":[10,11,12,13,14],"domain":"Symbolic_affine_subsequence_index","operation":"subseq-finite-prefix-boundary","semantic_template":"qf-mod38-subseq-finite-prefix-boundary/{\"indices\":[10,11,12,13,14]}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_or_symbolic_model","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"候選須主端重算；不構成人工審定、有限sample群作用、sup等於max、basis等於subbasis、signed Markov、pigeonhole converse、nonunit Euler、finite-prefix subsequence、Lean或Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-14","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261014-advance-20261107-r07-subsequence-0087","batch_id":"batch-20261014-advance-20261107-r07-subsequence-foundations","language":"zh-Hant","source_mko_ids":["mko-subsequence"],"title_zh":"子數列","stem_zh":"自然數索引與symbolic嚴格遞增證書。操作=subseq-finite-prefix-boundary；資料={\"indices\":[11,13,15,17,19,21]}。請依 exact_ordered_tuple_declared_by_interface 欄序回答。","answer":{"kind":"expression","value":"([11, 13, 15, 17, 19, 21], 是, 否, finite_increasing_prefix_not_infinite_subsequence_certificate)","explanation_zh":"Wave6根層核對=([11, 13, 15, 17, 19, 21], 是, 否, finite_increasing_prefix_not_infinite_subsequence_certificate)；依完整明示資料獨立重算；subsequence索引必須嚴格遞增並保留原數列次序，不是重排或任意子集合；有限索引列表只證finite prefix；無限subsequence需要通用increasing-index certificate。"},"difficulty":{"band":"undergraduate_core","level":2,"skills":["子數列"]},"variant":{"family_id":"qf-mod38-subseq-finite-prefix-boundary","seed":202611077087,"parameters":{"indices":[11,13,15,17,19,21],"domain":"Symbolic_affine_subsequence_index","operation":"subseq-finite-prefix-boundary","semantic_template":"qf-mod38-subseq-finite-prefix-boundary/{\"indices\":[11,13,15,17,19,21]}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_or_symbolic_model","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"候選須主端重算；不構成人工審定、有限sample群作用、sup等於max、basis等於subbasis、signed Markov、pigeonhole converse、nonunit Euler、finite-prefix subsequence、Lean或Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-14","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261014-advance-20261107-r07-subsequence-0088","batch_id":"batch-20261014-advance-20261107-r07-subsequence-foundations","language":"zh-Hant","source_mko_ids":["mko-subsequence"],"title_zh":"子數列","stem_zh":"自然數索引與symbolic嚴格遞增證書。操作=subseq-finite-prefix-boundary；資料={\"indices\":[12,15,18,21]}。請依 exact_ordered_tuple_declared_by_interface 欄序回答。","answer":{"kind":"expression","value":"([12, 15, 18, 21], 是, 否, finite_increasing_prefix_not_infinite_subsequence_certificate)","explanation_zh":"Wave6根層核對=([12, 15, 18, 21], 是, 否, finite_increasing_prefix_not_infinite_subsequence_certificate)；依完整明示資料獨立重算；subsequence索引必須嚴格遞增並保留原數列次序，不是重排或任意子集合；有限索引列表只證finite prefix；無限subsequence需要通用increasing-index certificate。"},"difficulty":{"band":"undergraduate_core","level":2,"skills":["子數列"]},"variant":{"family_id":"qf-mod38-subseq-finite-prefix-boundary","seed":202611077088,"parameters":{"indices":[12,15,18,21],"domain":"Symbolic_affine_subsequence_index","operation":"subseq-finite-prefix-boundary","semantic_template":"qf-mod38-subseq-finite-prefix-boundary/{\"indices\":[12,15,18,21]}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_or_symbolic_model","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"候選須主端重算；不構成人工審定、有限sample群作用、sup等於max、basis等於subbasis、signed Markov、pigeonhole converse、nonunit Euler、finite-prefix subsequence、Lean或Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-14","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261014-advance-20261107-r07-subsequence-0089","batch_id":"batch-20261014-advance-20261107-r07-subsequence-foundations","language":"zh-Hant","source_mko_ids":["mko-subsequence"],"title_zh":"子數列","stem_zh":"自然數索引與symbolic嚴格遞增證書。操作=subseq-finite-prefix-boundary；資料={\"indices\":[13,17,21,25,29]}。請依 exact_ordered_tuple_declared_by_interface 欄序回答。","answer":{"kind":"expression","value":"([13, 17, 21, 25, 29], 是, 否, finite_increasing_prefix_not_infinite_subsequence_certificate)","explanation_zh":"Wave6根層核對=([13, 17, 21, 25, 29], 是, 否, finite_increasing_prefix_not_infinite_subsequence_certificate)；依完整明示資料獨立重算；subsequence索引必須嚴格遞增並保留原數列次序，不是重排或任意子集合；有限索引列表只證finite prefix；無限subsequence需要通用increasing-index certificate。"},"difficulty":{"band":"undergraduate_core","level":2,"skills":["子數列"]},"variant":{"family_id":"qf-mod38-subseq-finite-prefix-boundary","seed":202611077089,"parameters":{"indices":[13,17,21,25,29],"domain":"Symbolic_affine_subsequence_index","operation":"subseq-finite-prefix-boundary","semantic_template":"qf-mod38-subseq-finite-prefix-boundary/{\"indices\":[13,17,21,25,29]}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_or_symbolic_model","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"候選須主端重算；不構成人工審定、有限sample群作用、sup等於max、basis等於subbasis、signed Markov、pigeonhole converse、nonunit Euler、finite-prefix subsequence、Lean或Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-14","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261014-advance-20261107-r07-subsequence-0090","batch_id":"batch-20261014-advance-20261107-r07-subsequence-foundations","language":"zh-Hant","source_mko_ids":["mko-subsequence"],"title_zh":"子數列","stem_zh":"自然數索引與symbolic嚴格遞增證書。操作=subseq-finite-prefix-boundary；資料={\"indices\":[14,19,24,29,34,39]}。請依 exact_ordered_tuple_declared_by_interface 欄序回答。","answer":{"kind":"expression","value":"([14, 19, 24, 29, 34, 39], 是, 否, finite_increasing_prefix_not_infinite_subsequence_certificate)","explanation_zh":"Wave6根層核對=([14, 19, 24, 29, 34, 39], 是, 否, finite_increasing_prefix_not_infinite_subsequence_certificate)；依完整明示資料獨立重算；subsequence索引必須嚴格遞增並保留原數列次序，不是重排或任意子集合；有限索引列表只證finite prefix；無限subsequence需要通用increasing-index certificate。"},"difficulty":{"band":"undergraduate_core","level":2,"skills":["子數列"]},"variant":{"family_id":"qf-mod38-subseq-finite-prefix-boundary","seed":202611077090,"parameters":{"indices":[14,19,24,29,34,39],"domain":"Symbolic_affine_subsequence_index","operation":"subseq-finite-prefix-boundary","semantic_template":"qf-mod38-subseq-finite-prefix-boundary/{\"indices\":[14,19,24,29,34,39]}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_or_symbolic_model","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"候選須主端重算；不構成人工審定、有限sample群作用、sup等於max、basis等於subbasis、signed Markov、pigeonhole converse、nonunit Euler、finite-prefix subsequence、Lean或Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-14","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261014-advance-20261107-r07-subsequence-0091","batch_id":"batch-20261014-advance-20261107-r07-subsequence-foundations","language":"zh-Hant","source_mko_ids":["mko-subsequence"],"title_zh":"子數列","stem_zh":"自然數索引與symbolic嚴格遞增證書。操作=subseq-finite-prefix-boundary；資料={\"indices\":[15,16,17,18]}。請依 exact_ordered_tuple_declared_by_interface 欄序回答。","answer":{"kind":"expression","value":"([15, 16, 17, 18], 是, 否, finite_increasing_prefix_not_infinite_subsequence_certificate)","explanation_zh":"Wave6根層核對=([15, 16, 17, 18], 是, 否, finite_increasing_prefix_not_infinite_subsequence_certificate)；依完整明示資料獨立重算；subsequence索引必須嚴格遞增並保留原數列次序，不是重排或任意子集合；有限索引列表只證finite prefix；無限subsequence需要通用increasing-index certificate。"},"difficulty":{"band":"undergraduate_core","level":2,"skills":["子數列"]},"variant":{"family_id":"qf-mod38-subseq-finite-prefix-boundary","seed":202611077091,"parameters":{"indices":[15,16,17,18],"domain":"Symbolic_affine_subsequence_index","operation":"subseq-finite-prefix-boundary","semantic_template":"qf-mod38-subseq-finite-prefix-boundary/{\"indices\":[15,16,17,18]}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_or_symbolic_model","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"候選須主端重算；不構成人工審定、有限sample群作用、sup等於max、basis等於subbasis、signed Markov、pigeonhole converse、nonunit Euler、finite-prefix subsequence、Lean或Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-14","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261014-advance-20261107-r07-subsequence-0092","batch_id":"batch-20261014-advance-20261107-r07-subsequence-foundations","language":"zh-Hant","source_mko_ids":["mko-subsequence"],"title_zh":"子數列","stem_zh":"自然數索引與symbolic嚴格遞增證書。操作=subseq-finite-prefix-boundary；資料={\"indices\":[16,18,20,22,24]}。請依 exact_ordered_tuple_declared_by_interface 欄序回答。","answer":{"kind":"expression","value":"([16, 18, 20, 22, 24], 是, 否, finite_increasing_prefix_not_infinite_subsequence_certificate)","explanation_zh":"Wave6根層核對=([16, 18, 20, 22, 24], 是, 否, finite_increasing_prefix_not_infinite_subsequence_certificate)；依完整明示資料獨立重算；subsequence索引必須嚴格遞增並保留原數列次序，不是重排或任意子集合；有限索引列表只證finite prefix；無限subsequence需要通用increasing-index certificate。"},"difficulty":{"band":"undergraduate_core","level":2,"skills":["子數列"]},"variant":{"family_id":"qf-mod38-subseq-finite-prefix-boundary","seed":202611077092,"parameters":{"indices":[16,18,20,22,24],"domain":"Symbolic_affine_subsequence_index","operation":"subseq-finite-prefix-boundary","semantic_template":"qf-mod38-subseq-finite-prefix-boundary/{\"indices\":[16,18,20,22,24]}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_or_symbolic_model","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"候選須主端重算；不構成人工審定、有限sample群作用、sup等於max、basis等於subbasis、signed Markov、pigeonhole converse、nonunit Euler、finite-prefix subsequence、Lean或Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-14","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261014-advance-20261107-r07-subsequence-0093","batch_id":"batch-20261014-advance-20261107-r07-subsequence-foundations","language":"zh-Hant","source_mko_ids":["mko-subsequence"],"title_zh":"子數列","stem_zh":"自然數索引與symbolic嚴格遞增證書。操作=subseq-finite-prefix-boundary；資料={\"indices\":[17,20,23,26,29,32]}。請依 exact_ordered_tuple_declared_by_interface 欄序回答。","answer":{"kind":"expression","value":"([17, 20, 23, 26, 29, 32], 是, 否, finite_increasing_prefix_not_infinite_subsequence_certificate)","explanation_zh":"Wave6根層核對=([17, 20, 23, 26, 29, 32], 是, 否, finite_increasing_prefix_not_infinite_subsequence_certificate)；依完整明示資料獨立重算；subsequence索引必須嚴格遞增並保留原數列次序，不是重排或任意子集合；有限索引列表只證finite prefix；無限subsequence需要通用increasing-index certificate。"},"difficulty":{"band":"undergraduate_core","level":3,"skills":["子數列"]},"variant":{"family_id":"qf-mod38-subseq-finite-prefix-boundary","seed":202611077093,"parameters":{"indices":[17,20,23,26,29,32],"domain":"Symbolic_affine_subsequence_index","operation":"subseq-finite-prefix-boundary","semantic_template":"qf-mod38-subseq-finite-prefix-boundary/{\"indices\":[17,20,23,26,29,32]}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_or_symbolic_model","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"候選須主端重算；不構成人工審定、有限sample群作用、sup等於max、basis等於subbasis、signed Markov、pigeonhole converse、nonunit Euler、finite-prefix subsequence、Lean或Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-14","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261014-advance-20261107-r07-subsequence-0094","batch_id":"batch-20261014-advance-20261107-r07-subsequence-foundations","language":"zh-Hant","source_mko_ids":["mko-subsequence"],"title_zh":"子數列","stem_zh":"自然數索引與symbolic嚴格遞增證書。操作=subseq-finite-prefix-boundary；資料={\"indices\":[18,22,26,30]}。請依 exact_ordered_tuple_declared_by_interface 欄序回答。","answer":{"kind":"expression","value":"([18, 22, 26, 30], 是, 否, finite_increasing_prefix_not_infinite_subsequence_certificate)","explanation_zh":"Wave6根層核對=([18, 22, 26, 30], 是, 否, finite_increasing_prefix_not_infinite_subsequence_certificate)；依完整明示資料獨立重算；subsequence索引必須嚴格遞增並保留原數列次序，不是重排或任意子集合；有限索引列表只證finite prefix；無限subsequence需要通用increasing-index certificate。"},"difficulty":{"band":"undergraduate_core","level":3,"skills":["子數列"]},"variant":{"family_id":"qf-mod38-subseq-finite-prefix-boundary","seed":202611077094,"parameters":{"indices":[18,22,26,30],"domain":"Symbolic_affine_subsequence_index","operation":"subseq-finite-prefix-boundary","semantic_template":"qf-mod38-subseq-finite-prefix-boundary/{\"indices\":[18,22,26,30]}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_or_symbolic_model","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"候選須主端重算；不構成人工審定、有限sample群作用、sup等於max、basis等於subbasis、signed Markov、pigeonhole converse、nonunit Euler、finite-prefix subsequence、Lean或Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-14","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261014-advance-20261107-r07-subsequence-0095","batch_id":"batch-20261014-advance-20261107-r07-subsequence-foundations","language":"zh-Hant","source_mko_ids":["mko-subsequence"],"title_zh":"子數列","stem_zh":"自然數索引與symbolic嚴格遞增證書。操作=subseq-finite-prefix-boundary；資料={\"indices\":[19,24,29,34,39]}。請依 exact_ordered_tuple_declared_by_interface 欄序回答。","answer":{"kind":"expression","value":"([19, 24, 29, 34, 39], 是, 否, finite_increasing_prefix_not_infinite_subsequence_certificate)","explanation_zh":"Wave6根層核對=([19, 24, 29, 34, 39], 是, 否, finite_increasing_prefix_not_infinite_subsequence_certificate)；依完整明示資料獨立重算；subsequence索引必須嚴格遞增並保留原數列次序，不是重排或任意子集合；有限索引列表只證finite prefix；無限subsequence需要通用increasing-index certificate。"},"difficulty":{"band":"undergraduate_core","level":3,"skills":["子數列"]},"variant":{"family_id":"qf-mod38-subseq-finite-prefix-boundary","seed":202611077095,"parameters":{"indices":[19,24,29,34,39],"domain":"Symbolic_affine_subsequence_index","operation":"subseq-finite-prefix-boundary","semantic_template":"qf-mod38-subseq-finite-prefix-boundary/{\"indices\":[19,24,29,34,39]}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_or_symbolic_model","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"候選須主端重算；不構成人工審定、有限sample群作用、sup等於max、basis等於subbasis、signed Markov、pigeonhole converse、nonunit Euler、finite-prefix subsequence、Lean或Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-14","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261014-advance-20261107-r07-subsequence-0096","batch_id":"batch-20261014-advance-20261107-r07-subsequence-foundations","language":"zh-Hant","source_mko_ids":["mko-subsequence"],"title_zh":"子數列","stem_zh":"自然數索引與symbolic嚴格遞增證書。操作=subseq-finite-prefix-boundary；資料={\"indices\":[20,21,22,23,24,25]}。請依 exact_ordered_tuple_declared_by_interface 欄序回答。","answer":{"kind":"expression","value":"([20, 21, 22, 23, 24, 25], 是, 否, finite_increasing_prefix_not_infinite_subsequence_certificate)","explanation_zh":"Wave6根層核對=([20, 21, 22, 23, 24, 25], 是, 否, finite_increasing_prefix_not_infinite_subsequence_certificate)；依完整明示資料獨立重算；subsequence索引必須嚴格遞增並保留原數列次序，不是重排或任意子集合；有限索引列表只證finite prefix；無限subsequence需要通用increasing-index certificate。"},"difficulty":{"band":"undergraduate_core","level":3,"skills":["子數列"]},"variant":{"family_id":"qf-mod38-subseq-finite-prefix-boundary","seed":202611077096,"parameters":{"indices":[20,21,22,23,24,25],"domain":"Symbolic_affine_subsequence_index","operation":"subseq-finite-prefix-boundary","semantic_template":"qf-mod38-subseq-finite-prefix-boundary/{\"indices\":[20,21,22,23,24,25]}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_or_symbolic_model","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"候選須主端重算；不構成人工審定、有限sample群作用、sup等於max、basis等於subbasis、signed Markov、pigeonhole converse、nonunit Euler、finite-prefix subsequence、Lean或Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-14","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261014-advance-20261107-r07-subsequence-0097","batch_id":"batch-20261014-advance-20261107-r07-subsequence-foundations","language":"zh-Hant","source_mko_ids":["mko-subsequence"],"title_zh":"子數列","stem_zh":"自然數索引與symbolic嚴格遞增證書。操作=subseq-finite-prefix-boundary；資料={\"indices\":[21,23,25,27]}。請依 exact_ordered_tuple_declared_by_interface 欄序回答。","answer":{"kind":"expression","value":"([21, 23, 25, 27], 是, 否, finite_increasing_prefix_not_infinite_subsequence_certificate)","explanation_zh":"Wave6根層核對=([21, 23, 25, 27], 是, 否, finite_increasing_prefix_not_infinite_subsequence_certificate)；依完整明示資料獨立重算；subsequence索引必須嚴格遞增並保留原數列次序，不是重排或任意子集合；有限索引列表只證finite prefix；無限subsequence需要通用increasing-index certificate。"},"difficulty":{"band":"undergraduate_core","level":3,"skills":["子數列"]},"variant":{"family_id":"qf-mod38-subseq-finite-prefix-boundary","seed":202611077097,"parameters":{"indices":[21,23,25,27],"domain":"Symbolic_affine_subsequence_index","operation":"subseq-finite-prefix-boundary","semantic_template":"qf-mod38-subseq-finite-prefix-boundary/{\"indices\":[21,23,25,27]}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_or_symbolic_model","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"候選須主端重算；不構成人工審定、有限sample群作用、sup等於max、basis等於subbasis、signed Markov、pigeonhole converse、nonunit Euler、finite-prefix subsequence、Lean或Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-14","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261014-advance-20261107-r07-subsequence-0098","batch_id":"batch-20261014-advance-20261107-r07-subsequence-foundations","language":"zh-Hant","source_mko_ids":["mko-subsequence"],"title_zh":"子數列","stem_zh":"自然數索引與symbolic嚴格遞增證書。操作=subseq-finite-prefix-boundary；資料={\"indices\":[22,25,28,31,34]}。請依 exact_ordered_tuple_declared_by_interface 欄序回答。","answer":{"kind":"expression","value":"([22, 25, 28, 31, 34], 是, 否, finite_increasing_prefix_not_infinite_subsequence_certificate)","explanation_zh":"Wave6根層核對=([22, 25, 28, 31, 34], 是, 否, finite_increasing_prefix_not_infinite_subsequence_certificate)；依完整明示資料獨立重算；subsequence索引必須嚴格遞增並保留原數列次序，不是重排或任意子集合；有限索引列表只證finite prefix；無限subsequence需要通用increasing-index certificate。"},"difficulty":{"band":"undergraduate_core","level":3,"skills":["子數列"]},"variant":{"family_id":"qf-mod38-subseq-finite-prefix-boundary","seed":202611077098,"parameters":{"indices":[22,25,28,31,34],"domain":"Symbolic_affine_subsequence_index","operation":"subseq-finite-prefix-boundary","semantic_template":"qf-mod38-subseq-finite-prefix-boundary/{\"indices\":[22,25,28,31,34]}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_or_symbolic_model","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"候選須主端重算；不構成人工審定、有限sample群作用、sup等於max、basis等於subbasis、signed Markov、pigeonhole converse、nonunit Euler、finite-prefix subsequence、Lean或Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-14","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261014-advance-20261107-r07-subsequence-0099","batch_id":"batch-20261014-advance-20261107-r07-subsequence-foundations","language":"zh-Hant","source_mko_ids":["mko-subsequence"],"title_zh":"子數列","stem_zh":"自然數索引與symbolic嚴格遞增證書。操作=subseq-finite-prefix-boundary；資料={\"indices\":[23,27,31,35,39,43]}。請依 exact_ordered_tuple_declared_by_interface 欄序回答。","answer":{"kind":"expression","value":"([23, 27, 31, 35, 39, 43], 是, 否, finite_increasing_prefix_not_infinite_subsequence_certificate)","explanation_zh":"Wave6根層核對=([23, 27, 31, 35, 39, 43], 是, 否, finite_increasing_prefix_not_infinite_subsequence_certificate)；依完整明示資料獨立重算；subsequence索引必須嚴格遞增並保留原數列次序，不是重排或任意子集合；有限索引列表只證finite prefix；無限subsequence需要通用increasing-index certificate。"},"difficulty":{"band":"undergraduate_core","level":3,"skills":["子數列"]},"variant":{"family_id":"qf-mod38-subseq-finite-prefix-boundary","seed":202611077099,"parameters":{"indices":[23,27,31,35,39,43],"domain":"Symbolic_affine_subsequence_index","operation":"subseq-finite-prefix-boundary","semantic_template":"qf-mod38-subseq-finite-prefix-boundary/{\"indices\":[23,27,31,35,39,43]}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_or_symbolic_model","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"候選須主端重算；不構成人工審定、有限sample群作用、sup等於max、basis等於subbasis、signed Markov、pigeonhole converse、nonunit Euler、finite-prefix subsequence、Lean或Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-14","contract_version":"ocme-question-factory-v0.1"}}
{"schema_version":"ocme-question-v0.1","id":"q-20261014-advance-20261107-r07-subsequence-0100","batch_id":"batch-20261014-advance-20261107-r07-subsequence-foundations","language":"zh-Hant","source_mko_ids":["mko-subsequence"],"title_zh":"子數列","stem_zh":"自然數索引與symbolic嚴格遞增證書。操作=subseq-finite-prefix-boundary；資料={\"indices\":[24,29,34,39]}。請依 exact_ordered_tuple_declared_by_interface 欄序回答。","answer":{"kind":"expression","value":"([24, 29, 34, 39], 是, 否, finite_increasing_prefix_not_infinite_subsequence_certificate)","explanation_zh":"Wave6根層核對=([24, 29, 34, 39], 是, 否, finite_increasing_prefix_not_infinite_subsequence_certificate)；依完整明示資料獨立重算；subsequence索引必須嚴格遞增並保留原數列次序，不是重排或任意子集合；有限索引列表只證finite prefix；無限subsequence需要通用increasing-index certificate。"},"difficulty":{"band":"undergraduate_core","level":3,"skills":["子數列"]},"variant":{"family_id":"qf-mod38-subseq-finite-prefix-boundary","seed":202611077100,"parameters":{"indices":[24,29,34,39],"domain":"Symbolic_affine_subsequence_index","operation":"subseq-finite-prefix-boundary","semantic_template":"qf-mod38-subseq-finite-prefix-boundary/{\"indices\":[24,29,34,39]}"}},"verification":{"status":"candidate","checks":["producer_exact_finite_or_symbolic_model","producer_source_snapshot_check","producer_substantive_template_deduplication","producer_json_schema"],"warning_zh":"候選須主端重算；不構成人工審定、有限sample群作用、sup等於max、basis等於subbasis、signed Markov、pigeonhole converse、nonunit Euler、finite-prefix subsequence、Lean或Evidence。"},"provenance":{"generator_role":"question_producer","generator_model":"model_unknown","generated_at":"2026-10-14","contract_version":"ocme-question-factory-v0.1"}}