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第 24946 題:有限群同態的核

本頁導覽
  1. 原題與已知條件
  2. 定義與適用範圍
  3. 逐步推導
  4. 逐步反向核對
  5. 結論
  6. 本題覆核與來源綁定

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← 逐題詳解目錄 · 原題批次

R0048-24946 · q-20261015-advance-20261114-r01-finite-group-homomorphism-kernel-0021

原題與已知條件

完整來源/目標Cayley table與complete total map逐對同態核對。操作=kernel-homomorphism-qualification;資料={"source_table":[[0,1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,19,20,21,22],[1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,19,20,21,22,0],[2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,19,20,21,22,0,1],[3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,19,20,21,22,0,1,2],[4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,19,20,21,22,0,1,2,3],[5,6,7,8,9,10,11,12,13,14,15,16,17,18,19,20,21,22,0,1,2,3,4],[6,7,8,9,10,11,12,13,14,15,16,17,18,19,20,21,22,0,1,2,3,4,5],[7,8,9,10,11,12,13,14,15,16,17,18,19,20,21,22,0,1,2,3,4,5,6],[8,9,10,11,12,13,14,15,16,17,18,19,20,21,22,0,1,2,3,4,5,6,7],[9,10,11,12,13,14,15,16,17,18,19,20,21,22,0,1,2,3,4,5,6,7,8],[10,11,12,13,14,15,16,17,18,19,20,21,22,0,1,2,3,4,5,6,7,8,9],[11,12,13,14,15,16,17,18,19,20,21,22,0,1,2,3,4,5,6,7,8,9,10],[12,13,14,15,16,17,18,19,20,21,22,0,1,2,3,4,5,6,7,8,9,10,11],[13,14,15,16,17,18,19,20,21,22,0,1,2,3,4,5,6,7,8,9,10,11,12],[14,15,16,17,18,19,20,21,22,0,1,2,3,4,5,6,7,8,9,10,11,12,13],[15,16,17,18,19,20,21,22,0,1,2,3,4,5,6,7,8,9,10,11,12,13,14],[16,17,18,19,20,21,22,0,1,2,3,4,5,6,7,8,9,10,11,12,13,14,15],[17,18,19,20,21,22,0,1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16],[18,19,20,21,22,0,1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17],[19,20,21,22,0,1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18],[20,21,22,0,1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,19],[21,22,0,1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,19,20],[22,0,1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,19,20,21]],"source_identity":0,"target_table":[[0,1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,19,20,21,22],[1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,19,20,21,22,0],[2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,19,20,21,22,0,1],[3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,19,20,21,22,0,1,2],[4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,19,20,21,22,0,1,2,3],[5,6,7,8,9,10,11,12,13,14,15,16,17,18,19,20,21,22,0,1,2,3,4],[6,7,8,9,10,11,12,13,14,15,16,17,18,19,20,21,22,0,1,2,3,4,5],[7,8,9,10,11,12,13,14,15,16,17,18,19,20,21,22,0,1,2,3,4,5,6],[8,9,10,11,12,13,14,15,16,17,18,19,20,21,22,0,1,2,3,4,5,6,7],[9,10,11,12,13,14,15,16,17,18,19,20,21,22,0,1,2,3,4,5,6,7,8],[10,11,12,13,14,15,16,17,18,19,20,21,22,0,1,2,3,4,5,6,7,8,9],[11,12,13,14,15,16,17,18,19,20,21,22,0,1,2,3,4,5,6,7,8,9,10],[12,13,14,15,16,17,18,19,20,21,22,0,1,2,3,4,5,6,7,8,9,10,11],[13,14,15,16,17,18,19,20,21,22,0,1,2,3,4,5,6,7,8,9,10,11,12],[14,15,16,17,18,19,20,21,22,0,1,2,3,4,5,6,7,8,9,10,11,12,13],[15,16,17,18,19,20,21,22,0,1,2,3,4,5,6,7,8,9,10,11,12,13,14],[16,17,18,19,20,21,22,0,1,2,3,4,5,6,7,8,9,10,11,12,13,14,15],[17,18,19,20,21,22,0,1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16],[18,19,20,21,22,0,1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17],[19,20,21,22,0,1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18],[20,21,22,0,1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,19],[21,22,0,1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,19,20],[22,0,1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,19,20,21]],"target_identity":0,"mapping":[0,22,21,20,19,18,17,16,15,14,13,12,11,10,9,8,7,6,5,4,3,2,1]}。請依 exact_ordered_tuple_declared_by_interface 欄序回答。

  • G001 — 完整來源/目標Cayley table與complete total map逐對同態核對。操作=kernel-homomorphism-qualification;資料={"source_table":[[0,1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,19,20,21,22],[1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,19,20,21,22,0],[2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,19,20,21,22,0,1],[3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,19,20,21,22,0,1,2],[4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,19,20,21,22,0,1,2,3],[5,6,7,8,9,10,11,12,13,14,15,16,17,18,19,20,21,22,0,1,2,3,4],[6,7,8,9,10,11,12,13,14,15,16,17,18,19,20,21,22,0,1,2,3,4,5],[7,8,9,10,11,12,13,14,15,16,17,18,19,20,21,22,0,1,2,3,4,5,6],[8,9,10,11,12,13,14,15,16,17,18,19,20,21,22,0,1,2,3,4,5,6,7],[9,10,11,12,13,14,15,16,17,18,19,20,21,22,0,1,2,3,4,5,6,7,8],[10,11,12,13,14,15,16,17,18,19,20,21,22,0,1,2,3,4,5,6,7,8,9],[11,12,13,14,15,16,17,18,19,20,21,22,0,1,2,3,4,5,6,7,8,9,10],[12,13,14,15,16,17,18,19,20,21,22,0,1,2,3,4,5,6,7,8,9,10,11],[13,14,15,16,17,18,19,20,21,22,0,1,2,3,4,5,6,7,8,9,10,11,12],[14,15,16,17,18,19,20,21,22,0,1,2,3,4,5,6,7,8,9,10,11,12,13],[15,16,17,18,19,20,21,22,0,1,2,3,4,5,6,7,8,9,10,11,12,13,14],[16,17,18,19,20,21,22,0,1,2,3,4,5,6,7,8,9,10,11,12,13,14,15],[17,18,19,20,21,22,0,1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16],[18,19,20,21,22,0,1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17],[19,20,21,22,0,1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18],[20,21,22,0,1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,19],[21,22,0,1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,19,20],[22,0,1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,19,20,21]],"source_identity":0,"target_table":[[0,1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,19,20,21,22],[1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,19,20,21,22,0],[2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,19,20,21,22,0,1],[3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,19,20,21,22,0,1,2],[4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,19,20,21,22,0,1,2,3],[5,6,7,8,9,10,11,12,13,14,15,16,17,18,19,20,21,22,0,1,2,3,4],[6,7,8,9,10,11,12,13,14,15,16,17,18,19,20,21,22,0,1,2,3,4,5],[7,8,9,10,11,12,13,14,15,16,17,18,19,20,21,22,0,1,2,3,4,5,6],[8,9,10,11,12,13,14,15,16,17,18,19,20,21,22,0,1,2,3,4,5,6,7],[9,10,11,12,13,14,15,16,17,18,19,20,21,22,0,1,2,3,4,5,6,7,8],[10,11,12,13,14,15,16,17,18,19,20,21,22,0,1,2,3,4,5,6,7,8,9],[11,12,13,14,15,16,17,18,19,20,21,22,0,1,2,3,4,5,6,7,8,9,10],[12,13,14,15,16,17,18,19,20,21,22,0,1,2,3,4,5,6,7,8,9,10,11],[13,14,15,16,17,18,19,20,21,22,0,1,2,3,4,5,6,7,8,9,10,11,12],[14,15,16,17,18,19,20,21,22,0,1,2,3,4,5,6,7,8,9,10,11,12,13],[15,16,17,18,19,20,21,22,0,1,2,3,4,5,6,7,8,9,10,11,12,13,14],[16,17,18,19,20,21,22,0,1,2,3,4,5,6,7,8,9,10,11,12,13,14,15],[17,18,19,20,21,22,0,1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16],[18,19,20,21,22,0,1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17],[19,20,21,22,0,1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18],[20,21,22,0,1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,19],[21,22,0,1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,19,20],[22,0,1,2,3,4,5,6,7,8,9,10,11,12,13,14,15,16,17,18,19,20,21]],"target_identity":0,"mapping":[0,22,21,20,19,18,17,16,15,14,13,12,11,10,9,8,7,6,5,4,3,2,1]}。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。

逐步推導

S001 · implies

操作前

source roles = [kernel-homomorphism-qualification]

操作後

derived = [[source_order, target_order, mapping, product_law_rows, homomorphism, first_failed_pair_or_null, certificate]]

條件:無

直接列來源完整欄序,不需JavaScript;原題、布林旗標、數學物件與非聲稱保持分層。

步驟識別與依賴

規則:source_ordered_fields_without_JS · 依賴:G001

S002 · implies

操作前

source roles = [Kernel ORIGINAL SOURCE group, 64, [[0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20, 21, 22], [1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20, 21, 22, 0], [2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20, 21, 22, 0, 1], [3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20, 21, 22, 0, 1, 2], [4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20, 21, 22, 0, 1, 2, 3], [5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20, 21, 22, 0, 1, 2, 3, 4], [6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20, 21, 22, 0, 1, 2, 3, 4, 5], [7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20, 21, 22, 0, 1, 2, 3, 4, 5, 6], [8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20, 21, 22, 0, 1, 2, 3, 4, 5, 6, 7], [9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20, 21, 22, 0, 1, 2, 3, 4, 5, 6, 7, 8], [10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20, 21, 22, 0, 1, 2, 3, 4, 5, 6, 7, 8, 9], [11, 12, 13, 14, 15, 16, 17, 18, 19, 20, 21, 22, 0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10], [12, 13, 14, 15, 16, 17, 18, 19, 20, 21, 22, 0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11], [13, 14, 15, 16, 17, 18, 19, 20, 21, 22, 0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12], [14, 15, 16, 17, 18, 19, 20, 21, 22, 0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13], [15, 16, 17, 18, 19, 20, 21, 22, 0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14], [16, 17, 18, 19, 20, 21, 22, 0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15], [17, 18, 19, 20, 21, 22, 0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16], [18, 19, 20, 21, 22, 0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17], [19, 20, 21, 22, 0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18], [20, 21, 22, 0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19], [21, 22, 0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20], [22, 0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20, 21]], 0]

操作後

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

條件:無

先驗完整n×n閉合表與實際identity標籤,非預設0。mod44上限32,mod45上限64;同一carrier不能混入另一表。

步驟識別與依賴

規則:Group_complete_Cayley_signature_actual_identity · 依賴:G001, S001

S003 · implies

操作前

source roles = [Kernel ORIGINAL SOURCE group, 23, FOR EVERY x,y,z in0..n-1]

操作後

derived = [[[是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是], [是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是], [是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是], [是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是], [是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是], [是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是], [是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是], [是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是], [是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是], [是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是], [是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是], [是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是], [是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是], [是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是], [是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是], [是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是], [是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是], [是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是], [是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是], [是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是], [是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是], [是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是], [是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是]], 12167, 是]

條件:無

矩陣(x,y)逐全部z核(xy)z=x(yz),故涵蓋全部n³三元組,不是抽樣。表已在前步完整列出,不重印數百萬同義查表項。

步驟識別與依賴

規則:Group_ALL_associativity_triples_compact_complete_pair_matrix · 依賴:G001, S002

S004 · implies

操作前

source roles = [Kernel ORIGINAL SOURCE group, 0]

操作後

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

條件:無

每個元素的左、右逆都要回到同一實際identity;結合律使兩側逆唯一。這才完成群前提。

步驟識別與依賴

規則:Group_ALL_two_sided_inverses · 依賴:G001, S003

S005 · implies

操作前

source roles = [Kernel ORIGINAL TARGET group, 64, [[0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20, 21, 22], [1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20, 21, 22, 0], [2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20, 21, 22, 0, 1], [3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20, 21, 22, 0, 1, 2], [4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20, 21, 22, 0, 1, 2, 3], [5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20, 21, 22, 0, 1, 2, 3, 4], [6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20, 21, 22, 0, 1, 2, 3, 4, 5], [7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20, 21, 22, 0, 1, 2, 3, 4, 5, 6], [8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20, 21, 22, 0, 1, 2, 3, 4, 5, 6, 7], [9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20, 21, 22, 0, 1, 2, 3, 4, 5, 6, 7, 8], [10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20, 21, 22, 0, 1, 2, 3, 4, 5, 6, 7, 8, 9], [11, 12, 13, 14, 15, 16, 17, 18, 19, 20, 21, 22, 0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10], [12, 13, 14, 15, 16, 17, 18, 19, 20, 21, 22, 0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11], [13, 14, 15, 16, 17, 18, 19, 20, 21, 22, 0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12], [14, 15, 16, 17, 18, 19, 20, 21, 22, 0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13], [15, 16, 17, 18, 19, 20, 21, 22, 0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14], [16, 17, 18, 19, 20, 21, 22, 0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15], [17, 18, 19, 20, 21, 22, 0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16], [18, 19, 20, 21, 22, 0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17], [19, 20, 21, 22, 0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18], [20, 21, 22, 0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19], [21, 22, 0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20], [22, 0, 1, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20, 21]], 0]

操作後

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

條件:無

先驗完整n×n閉合表與實際identity標籤,非預設0。mod44上限32,mod45上限64;同一carrier不能混入另一表。

步驟識別與依賴

規則:Group_complete_Cayley_signature_actual_identity · 依賴:G001, S004

S006 · implies

操作前

source roles = [Kernel ORIGINAL TARGET group, 23, FOR EVERY x,y,z in0..n-1]

操作後

derived = [[[是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是], [是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是], [是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是], [是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是], [是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是], [是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是], [是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是], [是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是], [是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是], [是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是], [是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是], [是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是], [是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是], [是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是], [是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是], [是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是], [是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是], [是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是], [是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是], [是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是], [是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是], [是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是], [是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是, 是]], 12167, 是]

條件:無

矩陣(x,y)逐全部z核(xy)z=x(yz),故涵蓋全部n³三元組,不是抽樣。表已在前步完整列出,不重印數百萬同義查表項。

步驟識別與依賴

規則:Group_ALL_associativity_triples_compact_complete_pair_matrix · 依賴:G001, S005

S007 · implies

操作前

source roles = [Kernel ORIGINAL TARGET group, 0]

操作後

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

條件:無

每個元素的左、右逆都要回到同一實際identity;結合律使兩側逆唯一。這才完成群前提。

步驟識別與依賴

規則:Group_ALL_two_sided_inverses · 依賴:G001, S006

S008 · implies

操作前

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

操作後

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

條件:無

先對同一source/target每對(x,y)驗f(xy)=f(x)f(y),保首failed row/null。total map不是homomorphism;失敗即擋所有kernel定理,不把內部fallback當真正identity preimage。

步驟識別與依賴

規則:Kernel_complete_TOTAL_map_ALL_product_pairs_before_theorems · 依賴:G001, S007

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

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

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。

來源雜湊與覆核憑證
  • input commit: 0f7be61e2c22317a4075561dc822c87d881a50db
  • original question SHA-256: 95c254e41605b356504f4c7e1d9cc0dabed367f1ddd337146828f43561dc1415
  • candidate record SHA-256: 8a2080d5c13573285dc55c3aa146600582fe5cb9deb7d7df79c116f607a48aca
  • semantic review receipt SHA-256: 049a9e07e69fead88d93b34f0937b9470a06d71c1a8d097058fc83554529bdd0
  • question-first witness SHA-256: 0c71ebb418f3de347d232d159fc25e93036f4ab9166bcfb5ee5b4be86d5c55b9
  • Lean: NOT_RUN · human review: NOT_PERFORMED
同源完整 JSON