第 18275 題：Lp收斂

原題與已知條件

同一有限原子probability space、固定整數p大於等於1與symbolic moment tail。操作=lp-moment-at-n；資料={"masses":[[1,2],[1,2]],"coefficients":[25,-26],"shift":2,"p":1,"n":25}。請依 exact_ordered_tuple_declared_by_interface 欄序回答。

• G001 — 同一有限原子probability space、固定整數p大於等於1與symbolic moment tail。操作=lp-moment-at-n；資料={"masses":[[1,2],[1,2]],"coefficients":[25,-26],"shift":2,"p":1,"n":25}。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-lp-convergence

逐步推導

source operation=lp-moment-at-n;original snapshot and mathematics retained

explicit ordered source output fields=[p, n, p_moment, certificate]

Lp complete atomic probability mass := sum(1/2, 1/2)

Lp complete atomic probability mass = 1

Lp coefficient atom0 absolute power product stage1 := mul(1, 25)

Lp coefficient atom0 absolute power product stage1 = 25

Lp constant weighted coefficient atom0 := mul(1/2, 25)

Lp constant weighted coefficient atom0 = 25/2

original atom=0;mass=1/2;SIGNED coefficient=25;fixed integer p=1

absolute coefficient power=25;weighted coefficient power=25/2

Lp coefficient atom1 absolute power product stage1 := mul(1, 26)

Lp coefficient atom1 absolute power product stage1 = 26

Lp constant weighted coefficient atom1 := mul(1/2, 26)

Lp constant weighted coefficient atom1 = 13

original atom=1;mass=1/2;SIGNED coefficient=-26;fixed integer p=1

absolute coefficient power=26;weighted coefficient power=13

Lp full weighted absolute coefficient power sum := sum(25/2, 13)

Lp full weighted absolute coefficient power sum = 51/2

SAME complete probability space;masses=[1/2, 1/2];signed coefficients=[25, -26];shift=2;fixed p=1;weighted constant=51/2

for EVERY n>=0,p-moment E|error_n|^p=(51/2)/(n+2)^1;all moments finite and tend0;this is NOT the p-th-root norm value

selected Lp index common error denominator := sum(25, 2)

selected Lp index common error denominator = 27

selected Lp index atom0 absolute error amplitude := div(25, 27)

selected Lp index atom0 absolute error amplitude = 25/27

selected Lp index atom0 error power product stage1 := mul(1, 25/27)

selected Lp index atom0 error power product stage1 = 25/27

selected Lp index atom0 weighted moment term := mul(1/2, 25/27)

selected Lp index atom0 weighted moment term = 25/54

selected Lp index atom1 absolute error amplitude := div(26, 27)

selected Lp index atom1 absolute error amplitude = 26/27

selected Lp index atom1 error power product stage1 := mul(1, 26/27)

selected Lp index atom1 error power product stage1 = 26/27

selected Lp index atom1 weighted moment term := mul(1/2, 26/27)

selected Lp index atom1 weighted moment term = 13/27

selected Lp index full p-moment := sum(25/54, 13/27)

selected Lp index full p-moment = 17/18

selected Lp index:original n=25;fixed p=1;all weighted absolute-power terms=[25/54, 13/27]

exact p-moment=17/18;neither its p-th root nor unweighted atom mean

逐步反向核對

• 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 — 以精確有理數重算 selected Lp index full p-moment，不以小數近似替代。
• S017 · premise_and_result_audit — 以精確有理數重算 selected Lp index atom1 weighted moment term，不以小數近似替代。
• S016 · premise_and_result_audit — 以精確有理數重算 selected Lp index atom1 error power product stage1，不以小數近似替代。
• S015 · premise_and_result_audit — 以精確有理數重算 selected Lp index atom1 absolute error amplitude，不以小數近似替代。
• S014 · premise_and_result_audit — 以精確有理數重算 selected Lp index atom0 weighted moment term，不以小數近似替代。
• S013 · premise_and_result_audit — 以精確有理數重算 selected Lp index atom0 error power product stage1，不以小數近似替代。
• S012 · premise_and_result_audit — 以精確有理數重算 selected Lp index atom0 absolute error amplitude，不以小數近似替代。
• S011 · premise_and_result_audit — 以精確有理數重算 selected Lp index common error denominator，不以小數近似替代。
• 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 — 以精確有理數重算 Lp full weighted absolute coefficient power sum，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 Lp constant weighted coefficient atom1，不以小數近似替代。
• S006 · premise_and_result_audit — 以精確有理數重算 Lp coefficient atom1 absolute power product stage1，不以小數近似替代。
• 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 — 以精確有理數重算 Lp constant weighted coefficient atom0，不以小數近似替代。
• S003 · premise_and_result_audit — 以精確有理數重算 Lp coefficient atom0 absolute power product stage1，不以小數近似替代。
• S002 · premise_and_result_audit — 以精確有理數重算 Lp complete atomic probability mass，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

(1, 25, 17/18, exact_finite_atomic_moment)

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。