第 11722 題：邊界值問題

原題與已知條件

內部PDE責任與矩形邊界資料分開。操作=bvp-dirichlet-edge-identity；資料={"coefficients":[9,-1,-3,2,-1,-1],"bounds":[-23,23,-22,24],"edge":"right","boundary_coefficients":[1044,-26,-1]}。請依 [bounds,edge,edge_variable,restriction_coefficients,boundary_coefficients,edge_identity,scope] 欄序回答。

• G001 — 內部PDE責任與矩形邊界資料分開。操作=bvp-dirichlet-edge-identity；資料={"coefficients":[9,-1,-3,2,-1,-1],"bounds":[-23,23,-22,24],"edge":"right","boundary_coefficients":[1044,-26,-1]}。請依 [bounds,edge,edge_variable,restriction_coefficients,boundary_coefficients,edge_identity,scope] 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-boundary-value-problem

逐步推導

original coefficients=[9, -1, -3, 2, -1, -1];basis=[1,x,y,x^2,xy,y^2]

u(x,y)=(9)+(-1)*x+(-3)*y+(2)*x^2+(-1)*x*y+(-1)*y^2

selected boundary fixed coordinate squared := mul(23, 23)

selected boundary fixed coordinate squared = 529

selected boundary fixed linear term := mul(-1, 23)

selected boundary fixed linear term = -23

selected boundary fixed square term := mul(2, 529)

selected boundary fixed square term = 1058

selected boundary constant coefficient := sum(9, -23, 1058)

selected boundary constant coefficient = 1044

selected boundary cross contribution := mul(-1, 23)

selected boundary cross contribution = -23

selected boundary linear coefficient := sum(-3, -23)

selected boundary linear coefficient = -26

selected boundary:vary y;fix x=23;original coefficients=[9, -1, -3, 2, -1, -1]

ascending y slice coefficients=[1044, -26, -1]

selected boundary coefficient residual0 := sub(1044, 1044)

selected boundary coefficient residual0 = 0

selected boundary coefficient residual1 := sub(-26, -26)

selected boundary coefficient residual1 = 0

selected boundary coefficient residual2 := sub(-1, -1)

selected boundary coefficient residual2 = 0

selected boundary:edge=right;bounds=[-23, 23, -22, 24];remaining variable=y;restriction=[1044, -26, -1];supplied=[1044, -26, -1]

all coefficient residuals=[0, 0, 0];polynomial identity=是

逐步反向核對

• 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 selected boundary coefficient residual2，不以小數近似替代。
• S010 · premise_and_result_audit — 以精確有理數重算 selected boundary coefficient residual1，不以小數近似替代。
• S009 · premise_and_result_audit — 以精確有理數重算 selected boundary coefficient residual0，不以小數近似替代。
• 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 — 以精確有理數重算 selected boundary linear coefficient，不以小數近似替代。
• S006 · premise_and_result_audit — 以精確有理數重算 selected boundary cross contribution，不以小數近似替代。
• S005 · premise_and_result_audit — 以精確有理數重算 selected boundary constant coefficient，不以小數近似替代。
• S004 · premise_and_result_audit — 以精確有理數重算 selected boundary fixed square term，不以小數近似替代。
• S003 · premise_and_result_audit — 以精確有理數重算 selected boundary fixed linear term，不以小數近似替代。
• S002 · premise_and_result_audit — 以精確有理數重算 selected boundary fixed coordinate squared，不以小數近似替代。
• 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, -22, 24], right, y, [1044, -26, -1], [1044, -26, -1], 是, declared_edge_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。