第 24373 題：有限流網路

原題與已知條件

finite loop-free directed network、逐edge capacity與逐internal-vertex conservation。操作=flow-network-qualification；資料={"vertices":["s22","a22","t22","u22"],"edges":[["s22","a22"],["a22","s22"],["a22","t22"],["t22","a22"]],"source":"s22","sink":"t22","capacities":[115,115,115,115],"flows":[92,46,69,23]}。請依 exact_ordered_tuple_declared_by_interface 欄序回答。

• G001 — finite loop-free directed network、逐edge capacity與逐internal-vertex conservation。操作=flow-network-qualification；資料={"vertices":["s22","a22","t22","u22"],"edges":[["s22","a22"],["a22","s22"],["a22","t22"],["t22","a22"]],"source":"s22","sink":"t22","capacities":[115,115,115,115],"flows":[92,46,69,23]}。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-finite-flow-network

逐步推導

source roles = [flow-network-qualification]

derived = [[vertices, source, sink, edge_capacity_flow_rows, antiparallel_pair_count, network_qualified, convention]]

source roles = [[s22, a22, t22, u22], [[s22, a22], [a22, s22], [a22, t22], [t22, a22]], [115, 115, 115, 115], [92, 46, 69, 23], s22, t22]

derived = [[a22, s22, t22, u22], [[[a22, s22], 115, 46], [[a22, t22], 115, 69], [[s22, a22], 115, 92], [[t22, a22], 115, 23]], 2, 是]

source roles = [0, [a22, s22], 46, 115]

derived = [是, 是, 是]

source roles = [1, [a22, t22], 69, 115]

derived = [是, 是, 是]

source roles = [2, [s22, a22], 92, 115]

derived = [是, 是, 是]

source roles = [3, [t22, a22], 23, 115]

derived = [是, 是, 是]

Flow ALL incoming at vertex a22 := sum(92, 23)

Flow ALL incoming at vertex a22 = 115

Flow ALL outgoing at vertex a22 := sum(46, 69)

Flow ALL outgoing at vertex a22 = 115

source roles = [a22, [2, 3], [0, 1]]

derived = [115, 115, 是, 是]

Flow ALL incoming at vertex s22 := sum(46)

Flow ALL incoming at vertex s22 = 46

Flow ALL outgoing at vertex s22 := sum(92)

Flow ALL outgoing at vertex s22 = 92

source roles = [s22, [0], [2]]

derived = [46, 92, 否, 否]

Flow ALL incoming at vertex t22 := sum(69)

Flow ALL incoming at vertex t22 = 69

Flow ALL outgoing at vertex t22 := sum(23)

Flow ALL outgoing at vertex t22 = 23

source roles = [t22, [1], [3]]

derived = [69, 23, 否, 否]

Flow ALL incoming at vertex u22 := sum()

Flow ALL incoming at vertex u22 = 0

Flow ALL outgoing at vertex u22 := sum()

Flow ALL outgoing at vertex u22 = 0

source roles = [u22, [], []]

derived = [0, 0, 是, 是]

Flow source NET outflow not gross outgoing := sub(92, 46)

Flow source NET outflow not gross outgoing = 46

Flow sink NET inflow not gross incoming := sub(69, 23)

Flow sink NET inflow not gross incoming = 46

source roles = [s22, t22, [[[a22, s22], 46, 115, 是], [[a22, t22], 69, 115, 是], [[s22, a22], 92, 115, 是], [[t22, a22], 23, 115, 是]], [[a22, 115, 115, 是], [u22, 0, 0, 是]], 46, 46]

derived = [是, 是, 是, 是, 否]

逐步反向核對

• 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 — 以精確有理數重算 Flow sink NET inflow not gross incoming，不以小數近似替代。
• S019 · premise_and_result_audit — 以精確有理數重算 Flow source NET outflow not gross outgoing，不以小數近似替代。
• 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 — 以精確有理數重算 Flow ALL outgoing at vertex u22，不以小數近似替代。
• S016 · premise_and_result_audit — 以精確有理數重算 Flow ALL incoming at vertex u22，不以小數近似替代。
• 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 — 以精確有理數重算 Flow ALL outgoing at vertex t22，不以小數近似替代。
• S013 · premise_and_result_audit — 以精確有理數重算 Flow ALL incoming at vertex t22，不以小數近似替代。
• 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 — 以精確有理數重算 Flow ALL outgoing at vertex s22，不以小數近似替代。
• S010 · premise_and_result_audit — 以精確有理數重算 Flow ALL incoming at vertex s22，不以小數近似替代。
• 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 — 以精確有理數重算 Flow ALL outgoing at vertex a22，不以小數近似替代。
• S007 · premise_and_result_audit — 以精確有理數重算 Flow ALL incoming at vertex a22，不以小數近似替代。
• 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

([a22, s22, t22, u22], s22, t22, [[[a22, s22], 115, 46], [[a22, t22], 115, 69], [[s22, a22], 115, 92], [[t22, a22], 115, 23]], 2, 是, finite_loop_free_simple_digraph_with_explicit_antiparallel_convention_zero_capacities_and_disconnected_vertices_allowed)

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。