R0039-20454 · q-20261014-advance-20261107-r07-subsequence-0079
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。
G001 — 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。沿用原題明示的論域、假設與來源 MKO 定義。本題已完成第二對話數理與中英語義覆核，並由原始參數逐題獨立重算模型、答案與每個算術步驟；原題仍為 candidate。
操作前
source operation=subseq-finite-prefix-boundary;original snapshot and mathematics retained
操作後
explicit ordered source output fields=[indices, finite_prefix_increasing, infinite_certificate_supplied, boundary]
條件：無
原題快照保留歷史介面標記；本頁直接列來源欄位順序，不需JavaScript或外部表。欄位標籤不是額外數學證據，No保持原題的聲稱範圍。
規則：source_ordered_interface_explicit_without_javascript · 依賴：G001
操作前
subsequence finite prefix adjacent index1 difference := sub(7, 3)
操作後
subsequence finite prefix adjacent index1 difference = 4
條件：無
依原始角色與已核中間量精確代值，保留索引、正負號、分母與證明適用條件。
規則：exact_rational_arithmetic · 依賴：G001, S001
操作前
ORIGINAL finite adjacent positions=[0, 1];actual indices=[3, 7]
操作後
exact forward difference=4;strictly increasing here=是
條件：無
逐原順序核每一對相鄰索引，不先排序或刪重複來修好prefix。有限全部相鄰正差才給此prefix嚴格遞增。
規則：subseq_finite_order_each_actual_adjacent_pair · 依賴：G001, S002
操作前
subsequence finite prefix adjacent index2 difference := sub(11, 7)
操作後
subsequence finite prefix adjacent index2 difference = 4
條件：無
依原始角色與已核中間量精確代值，保留索引、正負號、分母與證明適用條件。
規則：exact_rational_arithmetic · 依賴：G001, S003
操作前
ORIGINAL finite adjacent positions=[1, 2];actual indices=[7, 11]
操作後
exact forward difference=4;strictly increasing here=是
條件：無
逐原順序核每一對相鄰索引，不先排序或刪重複來修好prefix。有限全部相鄰正差才給此prefix嚴格遞增。
規則：subseq_finite_order_each_actual_adjacent_pair · 依賴：G001, S004
操作前
subsequence finite prefix adjacent index3 difference := sub(15, 11)
操作後
subsequence finite prefix adjacent index3 difference = 4
條件：無
依原始角色與已核中間量精確代值，保留索引、正負號、分母與證明適用條件。
規則：exact_rational_arithmetic · 依賴：G001, S005
操作前
ORIGINAL finite adjacent positions=[2, 3];actual indices=[11, 15]
操作後
exact forward difference=4;strictly increasing here=是
條件：無
逐原順序核每一對相鄰索引，不先排序或刪重複來修好prefix。有限全部相鄰正差才給此prefix嚴格遞增。
規則：subseq_finite_order_each_actual_adjacent_pair · 依賴：G001, S006
操作前
ORIGINAL finite index list=[3, 7, 11, 15];ALL adjacent strict flags=[是, 是, 是]
操作後
this finite prefix increasing=是;INFINITE certificate supplied by original data=否;finite_prefix_not_infinite_subsequence_certificate
條件：無
No指原資料沒指定所有後續索引的通用law。合格有限prefix可另構造延伸，例如最後值後逐次加1，但這不確定原未指定continuation；若prefix本身已不遞增，其實際相鄰違例才是阻礙。
規則：subseq_prefix_No_not_nonextendability_or_sorting · 依賴：G001, S007
S008 · premise_and_result_audit — 回到原始資料與本步條件核對，不把單向推論誤稱等價。S007 · premise_and_result_audit — 回到原始資料與本步條件核對，不把單向推論誤稱等價。S006 · premise_and_result_audit — 以精確有理數重算 subsequence finite prefix adjacent index3 difference，不以小數近似替代。S005 · premise_and_result_audit — 回到原始資料與本步條件核對，不把單向推論誤稱等價。S004 · premise_and_result_audit — 以精確有理數重算 subsequence finite prefix adjacent index2 difference，不以小數近似替代。S003 · premise_and_result_audit — 回到原始資料與本步條件核對，不把單向推論誤稱等價。S002 · premise_and_result_audit — 以精確有理數重算 subsequence finite prefix adjacent index1 difference，不以小數近似替代。S001 · premise_and_result_audit — 回到原始資料與本步條件核對，不把單向推論誤稱等價。([3, 7, 11, 15], 是, 否, finite_increasing_prefix_not_infinite_subsequence_certificate)
依上列完整代值及條件核對得到原題答案；原題編號、格式與狀態保持不變。
覆核日期：2026-10-26
原題、答案、步驟表達式、數值 AST 與既有歷史保持原樣；原來的候選狀態屬於來源歷史，不覆寫為形式化證明。
input commit: 0f7be61e2c22317a4075561dc822c87d881a50dboriginal question SHA-256: c1e5776076d4cc09050e307625d2d4d24d8971af4560ba33be76045cbabadcbdcandidate record SHA-256: 9f33c2edded165c7127c4235ed1419c4db270f29faaf062f9426f4c826ed4415semantic review receipt SHA-256: 6e11e35fafe32f16900ce9b522d01acb7b2ee6b463ab179392076cfbe1af8034question-first witness SHA-256: cc0fa361fc25151729e70264340d2eae94f179f6f2a2edfe80ba5704fbbd0682Lean: NOT_RUN · human review: NOT_PERFORMED