第 26125 題：多對一歸約

原題與已知條件

明示decision predicates與complete total map的雙向membership equivalence。操作=mreduction-composition-direction；資料={"source_carrier":[0,1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,19,20,21,22,23,24,25,26],"middle_carrier":[0,1],"target_carrier":[10,11],"source_yes":[1,3,5,7,9,11,13,15,17,19,21,23,25],"middle_yes":[1],"target_yes":[11],"mapping_ab":[0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0],"mapping_bc":[10,11]}。請依 exact_ordered_tuple_declared_by_interface 欄序回答。

• G001 — 明示decision predicates與complete total map的雙向membership equivalence。操作=mreduction-composition-direction；資料={"source_carrier":[0,1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,19,20,21,22,23,24,25,26],"middle_carrier":[0,1],"target_carrier":[10,11],"source_yes":[1,3,5,7,9,11,13,15,17,19,21,23,25],"middle_yes":[1],"target_yes":[11],"mapping_ab":[0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0,1,0],"mapping_bc":[10,11]}。請依 exact_ordered_tuple_declared_by_interface 欄序回答。

定義與適用範圍

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。

• mko-many-one-reduction

逐步推導

source roles = [mreduction-composition-direction]

derived = [[first_membership_rows, second_membership_rows, composed_images, composed_membership_rows, composed_reduction, certificate]]

source roles = [Reduction ORIGINAL A-to-B, [0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20, 21, 22, 23, 24, 25, 26], [0, 1], [0, 1, 0, 1, 0, 1, 0, 1, 0, 1, 0, 1, 0, 1, 0, 1, 0, 1, 0, 1, 0, 1, 0, 1, 0, 1, 0]]

derived = [[0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20, 21, 22, 23, 24, 25, 26], [0, 1], [0, 1, 0, 1, 0, 1, 0, 1, 0, 1, 0, 1, 0, 1, 0, 1, 0, 1, 0, 1, 0, 1, 0, 1, 0, 1, 0], [[0, 0, 是], [1, 1, 是], [2, 0, 是], [3, 1, 是], [4, 0, 是], [5, 1, 是], [6, 0, 是], [7, 1, 是], [8, 0, 是], [9, 1, 是], [10, 0, 是], [11, 1, 是], [12, 0, 是], [13, 1, 是], [14, 0, 是], [15, 1, 是], [16, 0, 是], [17, 1, 是], [18, 0, 是], [19, 1, 是], [20, 0, 是], [21, 1, 是], [22, 0, 是], [23, 1, 是], [24, 0, 是], [25, 1, 是], [26, 0, 是]], 是, null]

source roles = [Reduction ORIGINAL A-to-B, [1, 3, 5, 7, 9, 11, 13, 15, 17, 19, 21, 23, 25], [1], [0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20, 21, 22, 23, 24, 25, 26], [0, 1], [0, 1, 0, 1, 0, 1, 0, 1, 0, 1, 0, 1, 0, 1, 0, 1, 0, 1, 0, 1, 0, 1, 0, 1, 0, 1, 0]]

derived = [[[0, 否, 0, 否, 是], [1, 是, 1, 是, 是], [2, 否, 0, 否, 是], [3, 是, 1, 是, 是], [4, 否, 0, 否, 是], [5, 是, 1, 是, 是], [6, 否, 0, 否, 是], [7, 是, 1, 是, 是], [8, 否, 0, 否, 是], [9, 是, 1, 是, 是], [10, 否, 0, 否, 是], [11, 是, 1, 是, 是], [12, 否, 0, 否, 是], [13, 是, 1, 是, 是], [14, 否, 0, 否, 是], [15, 是, 1, 是, 是], [16, 否, 0, 否, 是], [17, 是, 1, 是, 是], [18, 否, 0, 否, 是], [19, 是, 1, 是, 是], [20, 否, 0, 否, 是], [21, 是, 1, 是, 是], [22, 否, 0, 否, 是], [23, 是, 1, 是, 是], [24, 否, 0, 否, 是], [25, 是, 1, 是, 是], [26, 否, 0, 否, 是]], 是, 是]

source roles = [Reduction ORIGINAL B-to-C, [0, 1], [10, 11], [10, 11]]

derived = [[0, 1], [10, 11], [10, 11], [[0, 10, 是], [1, 11, 是]], 是, null]

source roles = [Reduction ORIGINAL B-to-C, [1], [11], [0, 1], [10, 11], [10, 11]]

derived = [[[0, 否, 10, 否, 是], [1, 是, 11, 是, 是]], 是, 是]

source roles = [Reduction ACTUAL B-after-A composition, [0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20, 21, 22, 23, 24, 25, 26], [10, 11], [10, 11, 10, 11, 10, 11, 10, 11, 10, 11, 10, 11, 10, 11, 10, 11, 10, 11, 10, 11, 10, 11, 10, 11, 10, 11, 10]]

derived = [[0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20, 21, 22, 23, 24, 25, 26], [10, 11], [10, 11, 10, 11, 10, 11, 10, 11, 10, 11, 10, 11, 10, 11, 10, 11, 10, 11, 10, 11, 10, 11, 10, 11, 10, 11, 10], [[0, 10, 是], [1, 11, 是], [2, 10, 是], [3, 11, 是], [4, 10, 是], [5, 11, 是], [6, 10, 是], [7, 11, 是], [8, 10, 是], [9, 11, 是], [10, 10, 是], [11, 11, 是], [12, 10, 是], [13, 11, 是], [14, 10, 是], [15, 11, 是], [16, 10, 是], [17, 11, 是], [18, 10, 是], [19, 11, 是], [20, 10, 是], [21, 11, 是], [22, 10, 是], [23, 11, 是], [24, 10, 是], [25, 11, 是], [26, 10, 是]], 是, null]

source roles = [Reduction ACTUAL B-after-A composition, [1, 3, 5, 7, 9, 11, 13, 15, 17, 19, 21, 23, 25], [11], [0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20, 21, 22, 23, 24, 25, 26], [10, 11], [10, 11, 10, 11, 10, 11, 10, 11, 10, 11, 10, 11, 10, 11, 10, 11, 10, 11, 10, 11, 10, 11, 10, 11, 10, 11, 10]]

derived = [[[0, 否, 10, 否, 是], [1, 是, 11, 是, 是], [2, 否, 10, 否, 是], [3, 是, 11, 是, 是], [4, 否, 10, 否, 是], [5, 是, 11, 是, 是], [6, 否, 10, 否, 是], [7, 是, 11, 是, 是], [8, 否, 10, 否, 是], [9, 是, 11, 是, 是], [10, 否, 10, 否, 是], [11, 是, 11, 是, 是], [12, 否, 10, 否, 是], [13, 是, 11, 是, 是], [14, 否, 10, 否, 是], [15, 是, 11, 是, 是], [16, 否, 10, 否, 是], [17, 是, 11, 是, 是], [18, 否, 10, 否, 是], [19, 是, 11, 是, 是], [20, 否, 10, 否, 是], [21, 是, 11, 是, 是], [22, 否, 10, 否, 是], [23, 是, 11, 是, 是], [24, 否, 10, 否, 是], [25, 是, 11, 是, 是], [26, 否, 10, 否, 是]], 是, 是]

source roles = [[[0, 否, 0, 否, 是], [1, 是, 1, 是, 是], [2, 否, 0, 否, 是], [3, 是, 1, 是, 是], [4, 否, 0, 否, 是], [5, 是, 1, 是, 是], [6, 否, 0, 否, 是], [7, 是, 1, 是, 是], [8, 否, 0, 否, 是], [9, 是, 1, 是, 是], [10, 否, 0, 否, 是], [11, 是, 1, 是, 是], [12, 否, 0, 否, 是], [13, 是, 1, 是, 是], [14, 否, 0, 否, 是], [15, 是, 1, 是, 是], [16, 否, 0, 否, 是], [17, 是, 1, 是, 是], [18, 否, 0, 否, 是], [19, 是, 1, 是, 是], [20, 否, 0, 否, 是], [21, 是, 1, 是, 是], [22, 否, 0, 否, 是], [23, 是, 1, 是, 是], [24, 否, 0, 否, 是], [25, 是, 1, 是, 是], [26, 否, 0, 否, 是]], [[0, 否, 10, 否, 是], [1, 是, 11, 是, 是]]]

derived = [[10, 11, 10, 11, 10, 11, 10, 11, 10, 11, 10, 11, 10, 11, 10, 11, 10, 11, 10, 11, 10, 11, 10, 11, 10, 11, 10], [[0, 否, 10, 否, 是], [1, 是, 11, 是, 是], [2, 否, 10, 否, 是], [3, 是, 11, 是, 是], [4, 否, 10, 否, 是], [5, 是, 11, 是, 是], [6, 否, 10, 否, 是], [7, 是, 11, 是, 是], [8, 否, 10, 否, 是], [9, 是, 11, 是, 是], [10, 否, 10, 否, 是], [11, 是, 11, 是, 是], [12, 否, 10, 否, 是], [13, 是, 11, 是, 是], [14, 否, 10, 否, 是], [15, 是, 11, 是, 是], [16, 否, 10, 否, 是], [17, 是, 11, 是, 是], [18, 否, 10, 否, 是], [19, 是, 11, 是, 是], [20, 否, 10, 否, 是], [21, 是, 11, 是, 是], [22, 否, 10, 否, 是], [23, 是, 11, 是, 是], [24, 否, 10, 否, 是], [25, 是, 11, 是, 是], [26, 否, 10, 否, 是]], 是]

逐步反向核對

• 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 — 回到原始資料與本步條件核對，不把單向推論誤稱等價。
• 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 — 回到原始資料與本步條件核對，不把單向推論誤稱等價。
• 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 — 回到原始資料與本步條件核對，不把單向推論誤稱等價。
• 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。

結論

([[0, 否, 0, 否, 是], [1, 是, 1, 是, 是], [2, 否, 0, 否, 是], [3, 是, 1, 是, 是], [4, 否, 0, 否, 是], [5, 是, 1, 是, 是], [6, 否, 0, 否, 是], [7, 是, 1, 是, 是], [8, 否, 0, 否, 是], [9, 是, 1, 是, 是], [10, 否, 0, 否, 是], [11, 是, 1, 是, 是], [12, 否, 0, 否, 是], [13, 是, 1, 是, 是], [14, 否, 0, 否, 是], [15, 是, 1, 是, 是], [16, 否, 0, 否, 是], [17, 是, 1, 是, 是], [18, 否, 0, 否, 是], [19, 是, 1, 是, 是], [20, 否, 0, 否, 是], [21, 是, 1, 是, 是], [22, 否, 0, 否, 是], [23, 是, 1, 是, 是], [24, 否, 0, 否, 是], [25, 是, 1, 是, 是], [26, 否, 0, 否, 是]], [[0, 否, 10, 否, 是], [1, 是, 11, 是, 是]], [10, 11, 10, 11, 10, 11, 10, 11, 10, 11, 10, 11, 10, 11, 10, 11, 10, 11, 10, 11, 10, 11, 10, 11, 10, 11, 10], [[0, 否, 10, 否, 是], [1, 是, 11, 是, 是], [2, 否, 10, 否, 是], [3, 是, 11, 是, 是], [4, 否, 10, 否, 是], [5, 是, 11, 是, 是], [6, 否, 10, 否, 是], [7, 是, 11, 是, 是], [8, 否, 10, 否, 是], [9, 是, 11, 是, 是], [10, 否, 10, 否, 是], [11, 是, 11, 是, 是], [12, 否, 10, 否, 是], [13, 是, 11, 是, 是], [14, 否, 10, 否, 是], [15, 是, 11, 是, 是], [16, 否, 10, 否, 是], [17, 是, 11, 是, 是], [18, 否, 10, 否, 是], [19, 是, 11, 是, 是], [20, 否, 10, 否, 是], [21, 是, 11, 是, 是], [22, 否, 10, 否, 是], [23, 是, 11, 是, 是], [24, 否, 10, 否, 是], [25, 是, 11, 是, 是], [26, 否, 10, 否, 是]], 是, A_le_m_B_and_B_le_m_C_imply_A_le_m_C_in_that_direction_only)

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。

本題覆核與來源綁定

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。