R0040-20893 · q-20261014-advance-20261108-r07-finite-directed-graph-0018
完整有限ordered-pair edge set與loop-free simple digraph convention。操作=digraph-qualification；資料={"n":5,"edges":[[0,1],[0,2],[1,2],[2,3],[3,4],[4,0],[4,1]]}。請依 exact_ordered_tuple_declared_by_interface 欄序回答。
G001 — 完整有限ordered-pair edge set與loop-free simple digraph convention。操作=digraph-qualification；資料={"n":5,"edges":[[0,1],[0,2],[1,2],[2,3],[3,4],[4,0],[4,1]]}。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=digraph-qualification;original snapshot and mathematics retained
操作後
explicit ordered source output fields=[vertex_count, edges, loop_free, simple_directed_set_qualified, convention]
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。標籤不自動是數學證據，No保持來源的聲稱範圍。
規則：source_ordered_interface_explicit_without_javascript · 依賴：G001
操作前
ORIGINAL complete directed carrier Fin(5);ORIGINAL lexicographically canonical ORDERED arcs=[[0, 1], [0, 2], [1, 2], [2, 3], [3, 4], [4, 0], [4, 1]]
操作後
all endpoints in range and same-direction arcs unique;actual loops=[];main loop-free directed-set convention qualified
條件：無
只核整張arc列表的from/to排序，不把各arc端點排序。(u,v)與(v,u)不同且可同時存在；main禁止loop，boundary暫收loop用來比對慣例，不作一般digraph不存在的判決。
規則：digraph_ordered_pairs_not_undirected_endpoint_sorting · 依賴：G001, S001
操作前
complete ordered-arc data passed this main loop-free simple-directed convention
操作後
qualification does NOT assert acyclicity,undirectedness,connectivity or any degree convention beyond this signature
條件：無
即使有兩方向arc或有向cycle，仍可是合格loop-free simple digraph。這個True不升格額外graph性質。
規則：digraph_signature_qualification_not_unrequested_graph_properties · 依賴：G001, S002
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。(5, [[0, 1], [0, 2], [1, 2], [2, 3], [3, 4], [4, 0], [4, 1]], 是, 是, ordered_pairs_and_no_parallel_duplicate_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。
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: 6f06b409a60f839b733291dcdd13cad329d214400fcba2814bc0745f748ded0dcandidate record SHA-256: 2e9a9e16d98e7d75fd33a71cdfeaff7b343874e61f42e742dae7e2837f4dea39semantic review receipt SHA-256: c6483ed1229af9183fe5c704a2627b1558ad9a31bfbb0d2ee2d5c1a1c299ab4dquestion-first witness SHA-256: e81f9a560d630fcb23441146f008c4feca7aceab3ebe4de2cf1997c061375ef7Lean: NOT_RUN · human review: NOT_PERFORMED