本批已通過 Schema、去重、來源快照與獨立答案重算；仍未標記為人工審定。
本題庫已有對應的中英逐步詳解。原題的 candidate 與英文 ai_candidate 狀態保留；AI 覆核、有限計算與 Lean 形式證明分開標示。
batch-20261014-advance-20261107-r07-subsequence-foundations · 2026-10-14 · 100 題
欄序為來源綁定的呈現補充；原始 JSONL 與數學答案不變。
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 [index_start, index_step, index_formula, strictly_increasing, certificate] 欄序回答。
(0, 1, k(j)=0+1j, 是, strictly_increasing_for_all_natural_j)
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。
子數列 · qf-mod38-subseq-index-certificate · candidate
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 [index_start, index_step, index_formula, strictly_increasing, certificate] 欄序回答。
(1, 2, k(j)=1+2j, 是, strictly_increasing_for_all_natural_j)
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。
子數列 · qf-mod38-subseq-index-certificate · candidate
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 [index_start, index_step, index_formula, strictly_increasing, certificate] 欄序回答。
(2, 3, k(j)=2+3j, 是, strictly_increasing_for_all_natural_j)
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。
子數列 · qf-mod38-subseq-index-certificate · candidate
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 [index_start, index_step, index_formula, strictly_increasing, certificate] 欄序回答。
(3, 4, k(j)=3+4j, 是, strictly_increasing_for_all_natural_j)
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。
子數列 · qf-mod38-subseq-index-certificate · candidate
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 [index_start, index_step, index_formula, strictly_increasing, certificate] 欄序回答。
(4, 5, k(j)=4+5j, 是, strictly_increasing_for_all_natural_j)
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。
子數列 · qf-mod38-subseq-index-certificate · candidate
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 [index_start, index_step, index_formula, strictly_increasing, certificate] 欄序回答。
(5, 1, k(j)=5+1j, 是, strictly_increasing_for_all_natural_j)
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。
子數列 · qf-mod38-subseq-index-certificate · candidate
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 [index_start, index_step, index_formula, strictly_increasing, certificate] 欄序回答。
(6, 2, k(j)=6+2j, 是, strictly_increasing_for_all_natural_j)
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。
子數列 · qf-mod38-subseq-index-certificate · candidate
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 [index_start, index_step, index_formula, strictly_increasing, certificate] 欄序回答。
(7, 3, k(j)=7+3j, 是, strictly_increasing_for_all_natural_j)
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。
子數列 · qf-mod38-subseq-index-certificate · candidate
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 [index_start, index_step, index_formula, strictly_increasing, certificate] 欄序回答。
(8, 4, k(j)=8+4j, 是, strictly_increasing_for_all_natural_j)
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。
子數列 · qf-mod38-subseq-index-certificate · candidate
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 [index_start, index_step, index_formula, strictly_increasing, certificate] 欄序回答。
(9, 5, k(j)=9+5j, 是, strictly_increasing_for_all_natural_j)
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。
子數列 · qf-mod38-subseq-index-certificate · candidate
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 [index_start, index_step, index_formula, strictly_increasing, certificate] 欄序回答。
(10, 1, k(j)=10+1j, 是, strictly_increasing_for_all_natural_j)
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。
子數列 · qf-mod38-subseq-index-certificate · candidate
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 [index_start, index_step, index_formula, strictly_increasing, certificate] 欄序回答。
(11, 2, k(j)=11+2j, 是, strictly_increasing_for_all_natural_j)
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。
子數列 · qf-mod38-subseq-index-certificate · candidate
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 [index_start, index_step, index_formula, strictly_increasing, certificate] 欄序回答。
(12, 3, k(j)=12+3j, 是, strictly_increasing_for_all_natural_j)
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。
子數列 · qf-mod38-subseq-index-certificate · candidate
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 [index_start, index_step, index_formula, strictly_increasing, certificate] 欄序回答。
(13, 4, k(j)=13+4j, 是, strictly_increasing_for_all_natural_j)
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。
子數列 · qf-mod38-subseq-index-certificate · candidate
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 [index_start, index_step, index_formula, strictly_increasing, certificate] 欄序回答。
(14, 5, k(j)=14+5j, 是, strictly_increasing_for_all_natural_j)
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。
子數列 · qf-mod38-subseq-index-certificate · candidate
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 [index_start, index_step, index_formula, strictly_increasing, certificate] 欄序回答。
(15, 1, k(j)=15+1j, 是, strictly_increasing_for_all_natural_j)
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。
子數列 · qf-mod38-subseq-index-certificate · candidate
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 [index_start, index_step, index_formula, strictly_increasing, certificate] 欄序回答。
(16, 2, k(j)=16+2j, 是, strictly_increasing_for_all_natural_j)
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。
子數列 · qf-mod38-subseq-index-certificate · candidate
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 [index_start, index_step, index_formula, strictly_increasing, certificate] 欄序回答。
(17, 3, k(j)=17+3j, 是, strictly_increasing_for_all_natural_j)
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。
子數列 · qf-mod38-subseq-index-certificate · candidate
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 [index_start, index_step, index_formula, strictly_increasing, certificate] 欄序回答。
(18, 4, k(j)=18+4j, 是, strictly_increasing_for_all_natural_j)
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。
子數列 · qf-mod38-subseq-index-certificate · candidate
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 [index_start, index_step, index_formula, strictly_increasing, certificate] 欄序回答。
(19, 5, k(j)=19+5j, 是, strictly_increasing_for_all_natural_j)
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。
子數列 · qf-mod38-subseq-index-certificate · candidate
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 [index_start, index_step, index_formula, strictly_increasing, certificate] 欄序回答。
(20, 1, k(j)=20+1j, 是, strictly_increasing_for_all_natural_j)
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。
子數列 · qf-mod38-subseq-index-certificate · candidate
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 [index_start, index_step, index_formula, strictly_increasing, certificate] 欄序回答。
(21, 2, k(j)=21+2j, 是, strictly_increasing_for_all_natural_j)
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。
子數列 · qf-mod38-subseq-index-certificate · candidate
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 [index_start, index_step, index_formula, strictly_increasing, certificate] 欄序回答。
(22, 3, k(j)=22+3j, 是, strictly_increasing_for_all_natural_j)
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。
子數列 · qf-mod38-subseq-index-certificate · candidate
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 [index_start, index_step, index_formula, strictly_increasing, certificate] 欄序回答。
(23, 4, k(j)=23+4j, 是, strictly_increasing_for_all_natural_j)
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。
子數列 · qf-mod38-subseq-index-certificate · candidate
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 [index_start, index_step, index_formula, strictly_increasing, certificate] 欄序回答。
(24, 5, k(j)=24+5j, 是, strictly_increasing_for_all_natural_j)
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。
子數列 · qf-mod38-subseq-index-certificate · candidate
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 [j, source_index, subsequence_term, certificate] 欄序回答。
(2, 2, 3, a_of_k_j_preserves_original_order)
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。
子數列 · qf-mod38-subseq-arithmetic-term · candidate
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 [j, source_index, subsequence_term, certificate] 欄序回答。
(3, 7, 16, a_of_k_j_preserves_original_order)
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。
子數列 · qf-mod38-subseq-arithmetic-term · candidate
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 [j, source_index, subsequence_term, certificate] 欄序回答。
(4, 14, 45, a_of_k_j_preserves_original_order)
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。
子數列 · qf-mod38-subseq-arithmetic-term · candidate
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 [j, source_index, subsequence_term, certificate] 欄序回答。
(5, 23, 96, a_of_k_j_preserves_original_order)
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。
子數列 · qf-mod38-subseq-arithmetic-term · candidate
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 [j, source_index, subsequence_term, certificate] 欄序回答。
(6, 30, 155, a_of_k_j_preserves_original_order)
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。
子數列 · qf-mod38-subseq-arithmetic-term · candidate
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 [j, source_index, subsequence_term, certificate] 欄序回答。
(7, 8, 54, a_of_k_j_preserves_original_order)
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。
子數列 · qf-mod38-subseq-arithmetic-term · candidate
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 [j, source_index, subsequence_term, certificate] 欄序回答。
(8, 18, 133, a_of_k_j_preserves_original_order)
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。
子數列 · qf-mod38-subseq-arithmetic-term · candidate
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 [j, source_index, subsequence_term, certificate] 欄序回答。
(9, 30, 38, a_of_k_j_preserves_original_order)
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。
子數列 · qf-mod38-subseq-arithmetic-term · candidate
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 [j, source_index, subsequence_term, certificate] 欄序回答。
(10, 40, 89, a_of_k_j_preserves_original_order)
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。
子數列 · qf-mod38-subseq-arithmetic-term · candidate
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 [j, source_index, subsequence_term, certificate] 欄序回答。
(11, 56, 178, a_of_k_j_preserves_original_order)
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。
子數列 · qf-mod38-subseq-arithmetic-term · candidate
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 [j, source_index, subsequence_term, certificate] 欄序回答。
(12, 14, 67, a_of_k_j_preserves_original_order)
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。
子數列 · qf-mod38-subseq-arithmetic-term · candidate
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 [j, source_index, subsequence_term, certificate] 欄序回答。
(13, 29, 157, a_of_k_j_preserves_original_order)
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。
子數列 · qf-mod38-subseq-arithmetic-term · candidate
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 [j, source_index, subsequence_term, certificate] 欄序回答。
(14, 42, 265, a_of_k_j_preserves_original_order)
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。
子數列 · qf-mod38-subseq-arithmetic-term · candidate
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 [j, source_index, subsequence_term, certificate] 欄序回答。
(15, 61, 441, a_of_k_j_preserves_original_order)
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。
子數列 · qf-mod38-subseq-arithmetic-term · candidate
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 [j, source_index, subsequence_term, certificate] 欄序回答。
(16, 82, 97, a_of_k_j_preserves_original_order)
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。
子數列 · qf-mod38-subseq-arithmetic-term · candidate
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 [j, source_index, subsequence_term, certificate] 欄序回答。
(17, 20, 56, a_of_k_j_preserves_original_order)
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。
子數列 · qf-mod38-subseq-arithmetic-term · candidate
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 [j, source_index, subsequence_term, certificate] 欄序回答。
(18, 36, 125, a_of_k_j_preserves_original_order)
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。
子數列 · qf-mod38-subseq-arithmetic-term · candidate
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 [j, source_index, subsequence_term, certificate] 欄序回答。
(19, 58, 250, a_of_k_j_preserves_original_order)
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。
子數列 · qf-mod38-subseq-arithmetic-term · candidate
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 [j, source_index, subsequence_term, certificate] 欄序回答。
(20, 82, 429, a_of_k_j_preserves_original_order)
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。
子數列 · qf-mod38-subseq-arithmetic-term · candidate
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 [j, source_index, subsequence_term, certificate] 欄序回答。
(21, 108, 668, a_of_k_j_preserves_original_order)
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。
子數列 · qf-mod38-subseq-arithmetic-term · candidate
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 [j, source_index, subsequence_term, certificate] 欄序回答。
(22, 22, 175, a_of_k_j_preserves_original_order)
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。
子數列 · qf-mod38-subseq-arithmetic-term · candidate
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 [j, source_index, subsequence_term, certificate] 欄序回答。
(23, 47, 69, a_of_k_j_preserves_original_order)
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。
子數列 · qf-mod38-subseq-arithmetic-term · candidate
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 [j, source_index, subsequence_term, certificate] 欄序回答。
(24, 74, 171, a_of_k_j_preserves_original_order)
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。
子數列 · qf-mod38-subseq-arithmetic-term · candidate
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 [j, source_index, subsequence_term, certificate] 欄序回答。
(25, 103, 333, a_of_k_j_preserves_original_order)
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。
子數列 · qf-mod38-subseq-arithmetic-term · candidate
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 [j, source_index, subsequence_term, certificate] 欄序回答。
(26, 130, 545, a_of_k_j_preserves_original_order)
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。
子數列 · qf-mod38-subseq-arithmetic-term · candidate
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 [j, inner_index, source_index, composed_step, strictly_increasing, certificate] 欄序回答。
(1, 1, 1, 1, 是, composition_remains_strictly_increasing)
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。
子數列 · qf-mod38-subseq-composed-index · candidate
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 [j, inner_index, source_index, composed_step, strictly_increasing, certificate] 欄序回答。
(2, 5, 11, 4, 是, composition_remains_strictly_increasing)
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。
子數列 · qf-mod38-subseq-composed-index · candidate
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 [j, inner_index, source_index, composed_step, strictly_increasing, certificate] 欄序回答。
(3, 11, 35, 9, 是, composition_remains_strictly_increasing)
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。
子數列 · qf-mod38-subseq-composed-index · candidate
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 [j, inner_index, source_index, composed_step, strictly_increasing, certificate] 欄序回答。
(4, 19, 76, 16, 是, composition_remains_strictly_increasing)
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。
子數列 · qf-mod38-subseq-composed-index · candidate
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 [j, inner_index, source_index, composed_step, strictly_increasing, certificate] 欄序回答。
(5, 25, 126, 25, 是, composition_remains_strictly_increasing)
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。
子數列 · qf-mod38-subseq-composed-index · candidate
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 [j, inner_index, source_index, composed_step, strictly_increasing, certificate] 欄序回答。
(6, 37, 39, 6, 是, composition_remains_strictly_increasing)
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。
子數列 · qf-mod38-subseq-composed-index · candidate
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 [j, inner_index, source_index, composed_step, strictly_increasing, certificate] 欄序回答。
(7, 9, 18, 2, 是, composition_remains_strictly_increasing)
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。
子數列 · qf-mod38-subseq-composed-index · candidate
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 [j, inner_index, source_index, composed_step, strictly_increasing, certificate] 欄序回答。
(8, 19, 58, 6, 是, composition_remains_strictly_increasing)
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。
子數列 · qf-mod38-subseq-composed-index · candidate
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 [j, inner_index, source_index, composed_step, strictly_increasing, certificate] 欄序回答。
(9, 27, 110, 12, 是, composition_remains_strictly_increasing)
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。
子數列 · qf-mod38-subseq-composed-index · candidate
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 [j, inner_index, source_index, composed_step, strictly_increasing, certificate] 欄序回答。
(10, 41, 205, 20, 是, composition_remains_strictly_increasing)
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。
子數列 · qf-mod38-subseq-composed-index · candidate
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 [j, inner_index, source_index, composed_step, strictly_increasing, certificate] 欄序回答。
(11, 57, 58, 5, 是, composition_remains_strictly_increasing)
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。
子數列 · qf-mod38-subseq-composed-index · candidate
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 [j, inner_index, source_index, composed_step, strictly_increasing, certificate] 欄序回答。
(12, 75, 152, 12, 是, composition_remains_strictly_increasing)
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。
子數列 · qf-mod38-subseq-composed-index · candidate
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 [j, inner_index, source_index, composed_step, strictly_increasing, certificate] 欄序回答。
(13, 13, 39, 3, 是, composition_remains_strictly_increasing)
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。
子數列 · qf-mod38-subseq-composed-index · candidate
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 [j, inner_index, source_index, composed_step, strictly_increasing, certificate] 欄序回答。
(14, 29, 117, 8, 是, composition_remains_strictly_increasing)
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。
子數列 · qf-mod38-subseq-composed-index · candidate
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 [j, inner_index, source_index, composed_step, strictly_increasing, certificate] 欄序回答。
(15, 47, 237, 15, 是, composition_remains_strictly_increasing)
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。
子數列 · qf-mod38-subseq-composed-index · candidate
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 [j, inner_index, source_index, composed_step, strictly_increasing, certificate] 欄序回答。
(16, 67, 67, 4, 是, composition_remains_strictly_increasing)
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。
子數列 · qf-mod38-subseq-composed-index · candidate
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 [j, inner_index, source_index, composed_step, strictly_increasing, certificate] 欄序回答。
(17, 85, 171, 10, 是, composition_remains_strictly_increasing)
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。
子數列 · qf-mod38-subseq-composed-index · candidate
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 [j, inner_index, source_index, composed_step, strictly_increasing, certificate] 欄序回答。
(18, 109, 329, 18, 是, composition_remains_strictly_increasing)
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。
子數列 · qf-mod38-subseq-composed-index · candidate
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 [j, inner_index, source_index, composed_step, strictly_increasing, certificate] 欄序回答。
(19, 21, 84, 4, 是, composition_remains_strictly_increasing)
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。
子數列 · qf-mod38-subseq-composed-index · candidate
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 [j, inner_index, source_index, composed_step, strictly_increasing, certificate] 欄序回答。
(20, 43, 216, 10, 是, composition_remains_strictly_increasing)
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。
子數列 · qf-mod38-subseq-composed-index · candidate
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 [j, inner_index, source_index, composed_step, strictly_increasing, certificate] 欄序回答。
(21, 63, 65, 3, 是, composition_remains_strictly_increasing)
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。
子數列 · qf-mod38-subseq-composed-index · candidate
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 [j, inner_index, source_index, composed_step, strictly_increasing, certificate] 欄序回答。
(22, 89, 178, 8, 是, composition_remains_strictly_increasing)
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。
子數列 · qf-mod38-subseq-composed-index · candidate
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 [j, inner_index, source_index, composed_step, strictly_increasing, certificate] 欄序回答。
(23, 117, 352, 15, 是, composition_remains_strictly_increasing)
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。
子數列 · qf-mod38-subseq-composed-index · candidate
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 [j, inner_index, source_index, composed_step, strictly_increasing, certificate] 欄序回答。
(24, 147, 590, 24, 是, composition_remains_strictly_increasing)
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。
子數列 · qf-mod38-subseq-composed-index · candidate
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 [j, inner_index, source_index, composed_step, strictly_increasing, certificate] 欄序回答。
(25, 25, 125, 5, 是, composition_remains_strictly_increasing)
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。
子數列 · qf-mod38-subseq-composed-index · candidate
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 [indices, finite_prefix_increasing, infinite_certificate_supplied, boundary] 欄序回答。
沒有提供無限索引證書，不等於不能把遞增有限prefix延伸為無限遞增索引。
([0, 1, 2, 3], 是, 否, finite_increasing_prefix_not_infinite_subsequence_certificate)
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。
子數列 · qf-mod38-subseq-finite-prefix-boundary · candidate
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 [indices, finite_prefix_increasing, infinite_certificate_supplied, boundary] 欄序回答。
沒有提供無限索引證書，不等於不能把遞增有限prefix延伸為無限遞增索引。
([1, 3, 5, 7, 9], 是, 否, finite_increasing_prefix_not_infinite_subsequence_certificate)
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。
子數列 · qf-mod38-subseq-finite-prefix-boundary · candidate
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 [indices, finite_prefix_increasing, infinite_certificate_supplied, boundary] 欄序回答。
沒有提供無限索引證書，不等於不能把遞增有限prefix延伸為無限遞增索引。
([2, 5, 8, 11, 14, 17], 是, 否, finite_increasing_prefix_not_infinite_subsequence_certificate)
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。
子數列 · qf-mod38-subseq-finite-prefix-boundary · candidate
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 [indices, finite_prefix_increasing, infinite_certificate_supplied, boundary] 欄序回答。
沒有提供無限索引證書，不等於不能把遞增有限prefix延伸為無限遞增索引。
([3, 7, 11, 15], 是, 否, finite_increasing_prefix_not_infinite_subsequence_certificate)
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。
子數列 · qf-mod38-subseq-finite-prefix-boundary · candidate
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 [indices, finite_prefix_increasing, infinite_certificate_supplied, boundary] 欄序回答。
沒有提供無限索引證書，不等於不能把遞增有限prefix延伸為無限遞增索引。
([4, 9, 14, 19, 24], 是, 否, finite_increasing_prefix_not_infinite_subsequence_certificate)
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。
子數列 · qf-mod38-subseq-finite-prefix-boundary · candidate
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 [indices, finite_prefix_increasing, infinite_certificate_supplied, boundary] 欄序回答。
沒有提供無限索引證書，不等於不能把遞增有限prefix延伸為無限遞增索引。
([5, 6, 7, 8, 9, 10], 是, 否, finite_increasing_prefix_not_infinite_subsequence_certificate)
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。
子數列 · qf-mod38-subseq-finite-prefix-boundary · candidate
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 [indices, finite_prefix_increasing, infinite_certificate_supplied, boundary] 欄序回答。
沒有提供無限索引證書，不等於不能把遞增有限prefix延伸為無限遞增索引。
([6, 8, 10, 12], 是, 否, finite_increasing_prefix_not_infinite_subsequence_certificate)
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。
子數列 · qf-mod38-subseq-finite-prefix-boundary · candidate
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 [indices, finite_prefix_increasing, infinite_certificate_supplied, boundary] 欄序回答。
沒有提供無限索引證書，不等於不能把遞增有限prefix延伸為無限遞增索引。
([7, 10, 13, 16, 19], 是, 否, finite_increasing_prefix_not_infinite_subsequence_certificate)
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。
子數列 · qf-mod38-subseq-finite-prefix-boundary · candidate
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 [indices, finite_prefix_increasing, infinite_certificate_supplied, boundary] 欄序回答。
沒有提供無限索引證書，不等於不能把遞增有限prefix延伸為無限遞增索引。
([8, 12, 16, 20, 24, 28], 是, 否, finite_increasing_prefix_not_infinite_subsequence_certificate)
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。
子數列 · qf-mod38-subseq-finite-prefix-boundary · candidate
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 [indices, finite_prefix_increasing, infinite_certificate_supplied, boundary] 欄序回答。
沒有提供無限索引證書，不等於不能把遞增有限prefix延伸為無限遞增索引。
([9, 14, 19, 24], 是, 否, finite_increasing_prefix_not_infinite_subsequence_certificate)
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。
子數列 · qf-mod38-subseq-finite-prefix-boundary · candidate
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 [indices, finite_prefix_increasing, infinite_certificate_supplied, boundary] 欄序回答。
沒有提供無限索引證書，不等於不能把遞增有限prefix延伸為無限遞增索引。
([10, 11, 12, 13, 14], 是, 否, finite_increasing_prefix_not_infinite_subsequence_certificate)
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。
子數列 · qf-mod38-subseq-finite-prefix-boundary · candidate
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 [indices, finite_prefix_increasing, infinite_certificate_supplied, boundary] 欄序回答。
沒有提供無限索引證書，不等於不能把遞增有限prefix延伸為無限遞增索引。
([11, 13, 15, 17, 19, 21], 是, 否, finite_increasing_prefix_not_infinite_subsequence_certificate)
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。
子數列 · qf-mod38-subseq-finite-prefix-boundary · candidate
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 [indices, finite_prefix_increasing, infinite_certificate_supplied, boundary] 欄序回答。
沒有提供無限索引證書，不等於不能把遞增有限prefix延伸為無限遞增索引。
([12, 15, 18, 21], 是, 否, finite_increasing_prefix_not_infinite_subsequence_certificate)
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。
子數列 · qf-mod38-subseq-finite-prefix-boundary · candidate
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 [indices, finite_prefix_increasing, infinite_certificate_supplied, boundary] 欄序回答。
沒有提供無限索引證書，不等於不能把遞增有限prefix延伸為無限遞增索引。
([13, 17, 21, 25, 29], 是, 否, finite_increasing_prefix_not_infinite_subsequence_certificate)
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。
子數列 · qf-mod38-subseq-finite-prefix-boundary · candidate
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 [indices, finite_prefix_increasing, infinite_certificate_supplied, boundary] 欄序回答。
沒有提供無限索引證書，不等於不能把遞增有限prefix延伸為無限遞增索引。
([14, 19, 24, 29, 34, 39], 是, 否, finite_increasing_prefix_not_infinite_subsequence_certificate)
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。
子數列 · qf-mod38-subseq-finite-prefix-boundary · candidate
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 [indices, finite_prefix_increasing, infinite_certificate_supplied, boundary] 欄序回答。
沒有提供無限索引證書，不等於不能把遞增有限prefix延伸為無限遞增索引。
([15, 16, 17, 18], 是, 否, finite_increasing_prefix_not_infinite_subsequence_certificate)
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。
子數列 · qf-mod38-subseq-finite-prefix-boundary · candidate
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 [indices, finite_prefix_increasing, infinite_certificate_supplied, boundary] 欄序回答。
沒有提供無限索引證書，不等於不能把遞增有限prefix延伸為無限遞增索引。
([16, 18, 20, 22, 24], 是, 否, finite_increasing_prefix_not_infinite_subsequence_certificate)
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。
子數列 · qf-mod38-subseq-finite-prefix-boundary · candidate
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 [indices, finite_prefix_increasing, infinite_certificate_supplied, boundary] 欄序回答。
沒有提供無限索引證書，不等於不能把遞增有限prefix延伸為無限遞增索引。
([17, 20, 23, 26, 29, 32], 是, 否, finite_increasing_prefix_not_infinite_subsequence_certificate)
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。
子數列 · qf-mod38-subseq-finite-prefix-boundary · candidate
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 [indices, finite_prefix_increasing, infinite_certificate_supplied, boundary] 欄序回答。
沒有提供無限索引證書，不等於不能把遞增有限prefix延伸為無限遞增索引。
([18, 22, 26, 30], 是, 否, finite_increasing_prefix_not_infinite_subsequence_certificate)
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。
子數列 · qf-mod38-subseq-finite-prefix-boundary · candidate
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 [indices, finite_prefix_increasing, infinite_certificate_supplied, boundary] 欄序回答。
沒有提供無限索引證書，不等於不能把遞增有限prefix延伸為無限遞增索引。
([19, 24, 29, 34, 39], 是, 否, finite_increasing_prefix_not_infinite_subsequence_certificate)
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。
子數列 · qf-mod38-subseq-finite-prefix-boundary · candidate
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 [indices, finite_prefix_increasing, infinite_certificate_supplied, boundary] 欄序回答。
沒有提供無限索引證書，不等於不能把遞增有限prefix延伸為無限遞增索引。
([20, 21, 22, 23, 24, 25], 是, 否, finite_increasing_prefix_not_infinite_subsequence_certificate)
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。
子數列 · qf-mod38-subseq-finite-prefix-boundary · candidate
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 [indices, finite_prefix_increasing, infinite_certificate_supplied, boundary] 欄序回答。
沒有提供無限索引證書，不等於不能把遞增有限prefix延伸為無限遞增索引。
([21, 23, 25, 27], 是, 否, finite_increasing_prefix_not_infinite_subsequence_certificate)
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。
子數列 · qf-mod38-subseq-finite-prefix-boundary · candidate
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 [indices, finite_prefix_increasing, infinite_certificate_supplied, boundary] 欄序回答。
沒有提供無限索引證書，不等於不能把遞增有限prefix延伸為無限遞增索引。
([22, 25, 28, 31, 34], 是, 否, finite_increasing_prefix_not_infinite_subsequence_certificate)
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。
子數列 · qf-mod38-subseq-finite-prefix-boundary · candidate
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 [indices, finite_prefix_increasing, infinite_certificate_supplied, boundary] 欄序回答。
沒有提供無限索引證書，不等於不能把遞增有限prefix延伸為無限遞增索引。
([23, 27, 31, 35, 39, 43], 是, 否, finite_increasing_prefix_not_infinite_subsequence_certificate)
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。
子數列 · qf-mod38-subseq-finite-prefix-boundary · candidate
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 [indices, finite_prefix_increasing, infinite_certificate_supplied, boundary] 欄序回答。
沒有提供無限索引證書，不等於不能把遞增有限prefix延伸為無限遞增索引。
([24, 29, 34, 39], 是, 否, finite_increasing_prefix_not_infinite_subsequence_certificate)
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。
子數列 · qf-mod38-subseq-finite-prefix-boundary · candidate