第 18256 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":[6,-7],"shift":2,"p":3,"n":6}。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":[6,-7],"shift":2,"p":3,"n":6}。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, 6)

Lp coefficient atom0 absolute power product stage1 = 6

Lp coefficient atom0 absolute power product stage2 := mul(6, 6)

Lp coefficient atom0 absolute power product stage2 = 36

Lp coefficient atom0 absolute power product stage3 := mul(36, 6)

Lp coefficient atom0 absolute power product stage3 = 216

Lp constant weighted coefficient atom0 := mul(1/2, 216)

Lp constant weighted coefficient atom0 = 108

original atom=0;mass=1/2;SIGNED coefficient=6;fixed integer p=3

absolute coefficient power=216;weighted coefficient power=108

Lp coefficient atom1 absolute power product stage1 := mul(1, 7)

Lp coefficient atom1 absolute power product stage1 = 7

Lp coefficient atom1 absolute power product stage2 := mul(7, 7)

Lp coefficient atom1 absolute power product stage2 = 49

Lp coefficient atom1 absolute power product stage3 := mul(49, 7)

Lp coefficient atom1 absolute power product stage3 = 343

Lp constant weighted coefficient atom1 := mul(1/2, 343)

Lp constant weighted coefficient atom1 = 343/2

original atom=1;mass=1/2;SIGNED coefficient=-7;fixed integer p=3

absolute coefficient power=343;weighted coefficient power=343/2

Lp full weighted absolute coefficient power sum := sum(108, 343/2)

Lp full weighted absolute coefficient power sum = 559/2

SAME complete probability space;masses=[1/2, 1/2];signed coefficients=[6, -7];shift=2;fixed p=3;weighted constant=559/2

for EVERY n>=0,p-moment E|error_n|^p=(559/2)/(n+2)^3;all moments finite and tend0;this is NOT the p-th-root norm value

selected Lp index common error denominator := sum(6, 2)

selected Lp index common error denominator = 8

selected Lp index atom0 absolute error amplitude := div(6, 8)

selected Lp index atom0 absolute error amplitude = 3/4

selected Lp index atom0 error power product stage1 := mul(1, 3/4)

selected Lp index atom0 error power product stage1 = 3/4

selected Lp index atom0 error power product stage2 := mul(3/4, 3/4)

selected Lp index atom0 error power product stage2 = 9/16

selected Lp index atom0 error power product stage3 := mul(9/16, 3/4)

selected Lp index atom0 error power product stage3 = 27/64

selected Lp index atom0 weighted moment term := mul(1/2, 27/64)

selected Lp index atom0 weighted moment term = 27/128

selected Lp index atom1 absolute error amplitude := div(7, 8)

selected Lp index atom1 absolute error amplitude = 7/8

selected Lp index atom1 error power product stage1 := mul(1, 7/8)

selected Lp index atom1 error power product stage1 = 7/8

selected Lp index atom1 error power product stage2 := mul(7/8, 7/8)

selected Lp index atom1 error power product stage2 = 49/64

selected Lp index atom1 error power product stage3 := mul(49/64, 7/8)

selected Lp index atom1 error power product stage3 = 343/512

selected Lp index atom1 weighted moment term := mul(1/2, 343/512)

selected Lp index atom1 weighted moment term = 343/1024

selected Lp index full p-moment := sum(27/128, 343/1024)

selected Lp index full p-moment = 559/1024

selected Lp index:original n=6;fixed p=3;all weighted absolute-power terms=[27/128, 343/1024]

exact p-moment=559/1024;neither its p-th root nor unweighted atom mean

逐步反向核對

• 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 — 以精確有理數重算 selected Lp index full p-moment，不以小數近似替代。
• S025 · 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。
• S024 · premise_and_result_audit — 以精確有理數重算 selected Lp index atom1 error power product stage3，不以小數近似替代。
• S023 · premise_and_result_audit — 以精確有理數重算 selected Lp index atom1 error power product stage2，不以小數近似替代。
• S022 · 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。
• S021 · 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。
• S020 · 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。
• S019 · premise_and_result_audit — 以精確有理數重算 selected Lp index atom0 error power product stage3，不以小數近似替代。
• S018 · premise_and_result_audit — 以精確有理數重算 selected Lp index atom0 error power product stage2，不以小數近似替代。
• S017 · 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。
• S016 · 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。
• S015 · 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。
• 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 — 以精確有理數重算 Lp full weighted absolute coefficient power sum，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 Lp constant weighted coefficient atom1，不以小數近似替代。
• S010 · premise_and_result_audit — 以精確有理數重算 Lp coefficient atom1 absolute power product stage3，不以小數近似替代。
• S009 · premise_and_result_audit — 以精確有理數重算 Lp coefficient atom1 absolute power product stage2，不以小數近似替代。
• S008 · 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。
• 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 — 以精確有理數重算 Lp constant weighted coefficient atom0，不以小數近似替代。
• S005 · premise_and_result_audit — 以精確有理數重算 Lp coefficient atom0 absolute power product stage3，不以小數近似替代。
• S004 · premise_and_result_audit — 以精確有理數重算 Lp coefficient atom0 absolute power product stage2，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

(3, 6, 559/1024, 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。