# 第 18975 題：Euler trail與circuit [返回所在分頁 95](https://ocme.evemisslab.com/zh-Hant/questions/page/95/) [← 逐題詳解目錄](https://ocme.evemisslab.com/zh-Hant/questions/) · [原題批次](https://ocme.evemisslab.com/zh-Hant/practice/batch-20261014-advance-20261105-r04-eulerian-trail-foundations/#q-20261014-advance-20261105-r04-eulerian-trail-0025) 本頁是已完成第二對話 AI 數理與中英語義覆核的教學詳解，只支持本題明示的模型與前提。沒有人工審查或新 Lean 證明，也不提升原題或 MKO 的 Canonical 真值狀態。 R0036-18975 · q-20261014-advance-20261105-r04-eulerian-trail-0025 ## 原題與已知條件 完整有限簡單無向圖、edge support與明示walk。操作=euler-trail-audit；資料={"n":27,"edges":[[0,1],[0,26],[1,2],[2,3],[3,4],[4,5],[5,6],[6,7],[7,8],[8,9],[9,10],[10,11],[11,12],[12,13],[13,14],[14,15],[15,16],[16,17],[17,18],[18,19],[19,20],[20,21],[21,22],[22,23],[23,24],[24,25],[25,26]],"vertex_walk":[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]}。請依 exact_ordered_tuple_declared_by_interface 欄序回答。 - G001 — 完整有限簡單無向圖、edge support與明示walk。操作=euler-trail-audit；資料={"n":27,"edges":[[0,1],[0,26],[1,2],[2,3],[3,4],[4,5],[5,6],[6,7],[7,8],[8,9],[9,10],[10,11],[11,12],[12,13],[13,14],[14,15],[15,16],[16,17],[17,18],[18,19],[19,20],[20,21],[21,22],[22,23],[23,24],[24,25],[25,26]],"vertex_walk":[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]}。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-eulerian-trail](https://ocme.evemisslab.com/zh-Hant/mko/mko-eulerian-trail/) ## 逐步推導 S001 · implies操作前 source operation=euler-trail-audit;original snapshot and mathematics retained 操作後 explicit ordered source output fields=[vertex_walk, used_edge_indices, length_and_adjacency, recorded_edge_indices_unique, recorded_edges_cover_exactly_once, vertex_revisited, valid_euler_trail, boundary] 條件：無 原題歷史介面標記仍在快照；這裡直接給原始欄位順序，主文不需JavaScript或外部表。描述欄位不自動證成任何數學聲稱。 步驟識別與依賴規則：source_ordered_interface_explicit_without_javascript · 依賴：G001 S002 · implies操作前 complete ORIGINAL carrier Fin(27);canonical ORIGINAL simple undirected edges=[[0, 1], [0, 26], [1, 2], [2, 3], [3, 4], [4, 5], [5, 6], [6, 7], [7, 8], [8, 9], [9, 10], [10, 11], [11, 12], [12, 13], [13, 14], [14, 15], [15, 16], [16, 17], [17, 18], [18, 19], [19, 20], [20, 21], [21, 22], [22, 23], [23, 24], [24, 25], [25, 26]] 操作後 edge indices are EXACT original list positions0..26;retain ALL vertices;no12-vertex or10-edge bound 條件：無 逐原邊位置固定索引，不用頂點對的字串排序代替來源數字順序。此題族允許到60頂點，不沿用前題族上界；零邊圖僅在允許的操作出現。 步驟識別與依賴規則：euler_original_simple_graph_indices_full_carrier · 依賴：G001, S001 S003 · implies操作前 original walk step=0;consecutive vertices=[0, 1];undirected candidate edge=[0, 1] 操作後 matching original edge index=0;recorded edge prefix=[0];length-and-adjacency status=是 條件：無 每個步長都查原圖；不存在的邊只使adjacency失敗，不補一個假索引到used。used只記實際找到的邊，故它的覆蓋檢查不能取代walk完整性。 步驟識別與依賴規則：euler_every_walk_step_missing_edge_not_recorded · 依賴：G001, S002 S004 · implies操作前 original walk step=1;consecutive vertices=[1, 2];undirected candidate edge=[1, 2] 操作後 matching original edge index=2;recorded edge prefix=[0, 2];length-and-adjacency status=是 條件：無 每個步長都查原圖；不存在的邊只使adjacency失敗，不補一個假索引到used。used只記實際找到的邊，故它的覆蓋檢查不能取代walk完整性。 步驟識別與依賴規則：euler_every_walk_step_missing_edge_not_recorded · 依賴：G001, S003 S005 · implies操作前 original walk step=2;consecutive vertices=[2, 3];undirected candidate edge=[2, 3] 操作後 matching original edge index=3;recorded edge prefix=[0, 2, 3];length-and-adjacency status=是 條件：無 每個步長都查原圖；不存在的邊只使adjacency失敗，不補一個假索引到used。used只記實際找到的邊，故它的覆蓋檢查不能取代walk完整性。 步驟識別與依賴規則：euler_every_walk_step_missing_edge_not_recorded · 依賴：G001, S004 S006 · implies操作前 original walk step=3;consecutive vertices=[3, 4];undirected candidate edge=[3, 4] 操作後 matching original edge index=4;recorded edge prefix=[0, 2, 3, 4];length-and-adjacency status=是 條件：無 每個步長都查原圖；不存在的邊只使adjacency失敗，不補一個假索引到used。used只記實際找到的邊，故它的覆蓋檢查不能取代walk完整性。 步驟識別與依賴規則：euler_every_walk_step_missing_edge_not_recorded · 依賴：G001, S005 S007 · implies操作前 original walk step=4;consecutive vertices=[4, 5];undirected candidate edge=[4, 5] 操作後 matching original edge index=5;recorded edge prefix=[0, 2, 3, 4, 5];length-and-adjacency status=是 條件：無 每個步長都查原圖；不存在的邊只使adjacency失敗，不補一個假索引到used。used只記實際找到的邊，故它的覆蓋檢查不能取代walk完整性。 步驟識別與依賴規則：euler_every_walk_step_missing_edge_not_recorded · 依賴：G001, S006 S008 · implies操作前 original walk step=5;consecutive vertices=[5, 6];undirected candidate edge=[5, 6] 操作後 matching original edge index=6;recorded edge prefix=[0, 2, 3, 4, 5, 6];length-and-adjacency status=是 條件：無 每個步長都查原圖；不存在的邊只使adjacency失敗，不補一個假索引到used。used只記實際找到的邊，故它的覆蓋檢查不能取代walk完整性。 步驟識別與依賴規則：euler_every_walk_step_missing_edge_not_recorded · 依賴：G001, S007 S009 · implies操作前 original walk step=6;consecutive vertices=[6, 7];undirected candidate edge=[6, 7] 操作後 matching original edge index=7;recorded edge prefix=[0, 2, 3, 4, 5, 6, 7];length-and-adjacency status=是 條件：無 每個步長都查原圖；不存在的邊只使adjacency失敗，不補一個假索引到used。used只記實際找到的邊，故它的覆蓋檢查不能取代walk完整性。 步驟識別與依賴規則：euler_every_walk_step_missing_edge_not_recorded · 依賴：G001, S008 S010 · implies操作前 original walk step=7;consecutive vertices=[7, 8];undirected candidate edge=[7, 8] 操作後 matching original edge index=8;recorded edge prefix=[0, 2, 3, 4, 5, 6, 7, 8];length-and-adjacency status=是 條件：無 每個步長都查原圖；不存在的邊只使adjacency失敗，不補一個假索引到used。used只記實際找到的邊，故它的覆蓋檢查不能取代walk完整性。 步驟識別與依賴規則：euler_every_walk_step_missing_edge_not_recorded · 依賴：G001, S009 S011 · implies操作前 original walk step=8;consecutive vertices=[8, 9];undirected candidate edge=[8, 9] 操作後 matching original edge index=9;recorded edge prefix=[0, 2, 3, 4, 5, 6, 7, 8, 9];length-and-adjacency status=是 條件：無 每個步長都查原圖；不存在的邊只使adjacency失敗，不補一個假索引到used。used只記實際找到的邊，故它的覆蓋檢查不能取代walk完整性。 步驟識別與依賴規則：euler_every_walk_step_missing_edge_not_recorded · 依賴：G001, S010 S012 · implies操作前 original walk step=9;consecutive vertices=[9, 10];undirected candidate edge=[9, 10] 操作後 matching original edge index=10;recorded edge prefix=[0, 2, 3, 4, 5, 6, 7, 8, 9, 10];length-and-adjacency status=是 條件：無 每個步長都查原圖；不存在的邊只使adjacency失敗，不補一個假索引到used。used只記實際找到的邊，故它的覆蓋檢查不能取代walk完整性。 步驟識別與依賴規則：euler_every_walk_step_missing_edge_not_recorded · 依賴：G001, S011 S013 · implies操作前 original walk step=10;consecutive vertices=[10, 11];undirected candidate edge=[10, 11] 操作後 matching original edge index=11;recorded edge prefix=[0, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11];length-and-adjacency status=是 條件：無 每個步長都查原圖；不存在的邊只使adjacency失敗，不補一個假索引到used。used只記實際找到的邊，故它的覆蓋檢查不能取代walk完整性。 步驟識別與依賴規則：euler_every_walk_step_missing_edge_not_recorded · 依賴：G001, S012 S014 · implies操作前 original walk step=11;consecutive vertices=[11, 12];undirected candidate edge=[11, 12] 操作後 matching original edge index=12;recorded edge prefix=[0, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12];length-and-adjacency status=是 條件：無 每個步長都查原圖；不存在的邊只使adjacency失敗，不補一個假索引到used。used只記實際找到的邊，故它的覆蓋檢查不能取代walk完整性。 步驟識別與依賴規則：euler_every_walk_step_missing_edge_not_recorded · 依賴：G001, S013 S015 · implies操作前 original walk step=12;consecutive vertices=[12, 13];undirected candidate edge=[12, 13] 操作後 matching original edge index=13;recorded edge prefix=[0, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13];length-and-adjacency status=是 條件：無 每個步長都查原圖；不存在的邊只使adjacency失敗，不補一個假索引到used。used只記實際找到的邊，故它的覆蓋檢查不能取代walk完整性。 步驟識別與依賴規則：euler_every_walk_step_missing_edge_not_recorded · 依賴：G001, S014 S016 · implies操作前 original walk step=13;consecutive vertices=[13, 14];undirected candidate edge=[13, 14] 操作後 matching original edge index=14;recorded edge prefix=[0, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14];length-and-adjacency status=是 條件：無 每個步長都查原圖；不存在的邊只使adjacency失敗，不補一個假索引到used。used只記實際找到的邊，故它的覆蓋檢查不能取代walk完整性。 步驟識別與依賴規則：euler_every_walk_step_missing_edge_not_recorded · 依賴：G001, S015 S017 · implies操作前 original walk step=14;consecutive vertices=[14, 15];undirected candidate edge=[14, 15] 操作後 matching original edge index=15;recorded edge prefix=[0, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15];length-and-adjacency status=是 條件：無 每個步長都查原圖；不存在的邊只使adjacency失敗，不補一個假索引到used。used只記實際找到的邊，故它的覆蓋檢查不能取代walk完整性。 步驟識別與依賴規則：euler_every_walk_step_missing_edge_not_recorded · 依賴：G001, S016 S018 · implies操作前 original walk step=15;consecutive vertices=[15, 16];undirected candidate edge=[15, 16] 操作後 matching original edge index=16;recorded edge prefix=[0, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16];length-and-adjacency status=是 條件：無 每個步長都查原圖；不存在的邊只使adjacency失敗，不補一個假索引到used。used只記實際找到的邊，故它的覆蓋檢查不能取代walk完整性。 步驟識別與依賴規則：euler_every_walk_step_missing_edge_not_recorded · 依賴：G001, S017 S019 · implies操作前 original walk step=16;consecutive vertices=[16, 17];undirected candidate edge=[16, 17] 操作後 matching original edge index=17;recorded edge prefix=[0, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17];length-and-adjacency status=是 條件：無 每個步長都查原圖；不存在的邊只使adjacency失敗，不補一個假索引到used。used只記實際找到的邊，故它的覆蓋檢查不能取代walk完整性。 步驟識別與依賴規則：euler_every_walk_step_missing_edge_not_recorded · 依賴：G001, S018 S020 · implies操作前 original walk step=17;consecutive vertices=[17, 18];undirected candidate edge=[17, 18] 操作後 matching original edge index=18;recorded edge prefix=[0, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18];length-and-adjacency status=是 條件：無 每個步長都查原圖；不存在的邊只使adjacency失敗，不補一個假索引到used。used只記實際找到的邊，故它的覆蓋檢查不能取代walk完整性。 步驟識別與依賴規則：euler_every_walk_step_missing_edge_not_recorded · 依賴：G001, S019 S021 · implies操作前 original walk step=18;consecutive vertices=[18, 19];undirected candidate edge=[18, 19] 操作後 matching original edge index=19;recorded edge prefix=[0, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19];length-and-adjacency status=是 條件：無 每個步長都查原圖；不存在的邊只使adjacency失敗，不補一個假索引到used。used只記實際找到的邊，故它的覆蓋檢查不能取代walk完整性。 步驟識別與依賴規則：euler_every_walk_step_missing_edge_not_recorded · 依賴：G001, S020 S022 · implies操作前 original walk step=19;consecutive vertices=[19, 20];undirected candidate edge=[19, 20] 操作後 matching original edge index=20;recorded edge prefix=[0, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20];length-and-adjacency status=是 條件：無 每個步長都查原圖；不存在的邊只使adjacency失敗，不補一個假索引到used。used只記實際找到的邊，故它的覆蓋檢查不能取代walk完整性。 步驟識別與依賴規則：euler_every_walk_step_missing_edge_not_recorded · 依賴：G001, S021 S023 · implies操作前 original walk step=20;consecutive vertices=[20, 21];undirected candidate edge=[20, 21] 操作後 matching original edge index=21;recorded edge prefix=[0, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20, 21];length-and-adjacency status=是 條件：無 每個步長都查原圖；不存在的邊只使adjacency失敗，不補一個假索引到used。used只記實際找到的邊，故它的覆蓋檢查不能取代walk完整性。 步驟識別與依賴規則：euler_every_walk_step_missing_edge_not_recorded · 依賴：G001, S022 S024 · implies操作前 original walk step=21;consecutive vertices=[21, 22];undirected candidate edge=[21, 22] 操作後 matching original edge index=22;recorded edge prefix=[0, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20, 21, 22];length-and-adjacency status=是 條件：無 每個步長都查原圖；不存在的邊只使adjacency失敗，不補一個假索引到used。used只記實際找到的邊，故它的覆蓋檢查不能取代walk完整性。 步驟識別與依賴規則：euler_every_walk_step_missing_edge_not_recorded · 依賴：G001, S023 S025 · implies操作前 original walk step=22;consecutive vertices=[22, 23];undirected candidate edge=[22, 23] 操作後 matching original edge index=23;recorded edge prefix=[0, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20, 21, 22, 23];length-and-adjacency status=是 條件：無 每個步長都查原圖；不存在的邊只使adjacency失敗，不補一個假索引到used。used只記實際找到的邊，故它的覆蓋檢查不能取代walk完整性。 步驟識別與依賴規則：euler_every_walk_step_missing_edge_not_recorded · 依賴：G001, S024 S026 · implies操作前 original walk step=23;consecutive vertices=[23, 24];undirected candidate edge=[23, 24] 操作後 matching original edge index=24;recorded edge prefix=[0, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20, 21, 22, 23, 24];length-and-adjacency status=是 條件：無 每個步長都查原圖；不存在的邊只使adjacency失敗，不補一個假索引到used。used只記實際找到的邊，故它的覆蓋檢查不能取代walk完整性。 步驟識別與依賴規則：euler_every_walk_step_missing_edge_not_recorded · 依賴：G001, S025 S027 · implies操作前 original walk step=24;consecutive vertices=[24, 25];undirected candidate edge=[24, 25] 操作後 matching original edge index=25;recorded edge prefix=[0, 2, 3, 4, 5, 6, 7, 8, 9, 10, 11, 12, 13, 14, 15, 16, 17, 18, 19, 20, 21, 22, 23, 24, 25];length-and-adjacency status=是 條件：無 每個步長都查原圖；不存在的邊只使adjacency失敗，不補一個假索引到used。used只記實際找到的邊，故它的覆蓋檢查不能取代walk完整性。 步驟識別與依賴規則：euler_every_walk_step_missing_edge_not_recorded · 依賴：G001, S026 S028 · implies操作前 original walk step=25;consecutive vertices=[25, 26];undirected candidate edge=[25, 26] 操作後 matching original edge index=26;recorded edge prefix=[0, 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];length-and-adjacency status=是 條件：無 每個步長都查原圖；不存在的邊只使adjacency失敗，不補一個假索引到used。used只記實際找到的邊，故它的覆蓋檢查不能取代walk完整性。 步驟識別與依賴規則：euler_every_walk_step_missing_edge_not_recorded · 依賴：G001, S027 S029 · implies操作前 original walk step=26;consecutive vertices=[26, 0];undirected candidate edge=[0, 26] 操作後 matching original edge index=1;recorded edge prefix=[0, 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, 1];length-and-adjacency status=是 條件：無 每個步長都查原圖；不存在的邊只使adjacency失敗，不補一個假索引到used。used只記實際找到的邊，故它的覆蓋檢查不能取代walk完整性。 步驟識別與依賴規則：euler_every_walk_step_missing_edge_not_recorded · 依賴：G001, S028 S030 · implies操作前 original complete walk=[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];required vertex-list length=28;actual length=28;found ORIGINAL edge indices=[0, 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, 1] 操作後 length-and-all-adjacency=是;recorded indices unique=是;recorded complete single-use coverage=是;vertex revisited=是;VALID Euler trail=是 條件：無 Euler trail可重複頂點，真正禁止重複邊。最後valid是長度／全部adjacency與完整單次用邊的合取；例如沒有找到的額外步仍可能留下used剛好覆蓋全圖，但walk仍無效。一次壞walk不否認此圖另有Euler walk。 步驟識別與依賴規則：euler_trail_full_conjunction_repeated_vertices_permitted · 依賴：G001, S029 ## 逐步反向核對 - S030 · 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。 - S029 · 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。 - S028 · 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。 - S027 · 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。 - S026 · 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。 - S025 · 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。 - S024 · 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。 - S023 · 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。 - S022 · 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。 - S021 · 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。 - S020 · 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。 - S019 · 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。 - S018 · 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。 - S017 · 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。 - S016 · 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。 - S015 · 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。 - S014 · 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。 - S013 · 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。 - S012 · 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。 - S011 · 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。 - S010 · 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。 - S009 · 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。 - 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, 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], [0, 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, 1], 是, 是, 是, 是, 是, trail_allows_repeated_vertices_not_edges) 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: 3e8e594994ef7da211fa2cf8180873040870d170a235e75df66c1544f6c2ffdc - candidate record SHA-256: 267d4e5391c67e906d9e2413b459d5c7a35bfe175b283d9a910f927edeea9751 - semantic review receipt SHA-256: efee5462991619d6ed9f64f11ddb085e5614ef33f9f8fcd8cf29b9329f8fd301 - question-first witness SHA-256: acf91fa1622f01d2cf04b2c513294254323665351f660f2628aaafdb869c4ff2 - Lean: NOT_RUN · human review: NOT_PERFORMED [同源完整 JSON](https://ocme.evemisslab.com/data/question-derivations/questions/q-20261014-advance-20261105-r04-eulerian-trail-0025.json)