第 18213 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-epsilon-witness；資料={"masses":[[1,2],[1,2]],"coefficients":[13,-14],"shift":2,"p":1,"epsilon":[1,22]}。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-epsilon-witness；資料={"masses":[[1,2],[1,2]],"coefficients":[13,-14],"shift":2,"p":1,"epsilon":[1,22]}。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-epsilon-witness;original snapshot and mathematics retained

explicit ordered source output fields=[p, moment_tolerance, N, p_moment_at_N, strict_tail, 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, 13)

Lp coefficient atom0 absolute power product stage1 = 13

Lp constant weighted coefficient atom0 := mul(1/2, 13)

Lp constant weighted coefficient atom0 = 13/2

original atom=0;mass=1/2;SIGNED coefficient=13;fixed integer p=1

absolute coefficient power=13;weighted coefficient power=13/2

Lp coefficient atom1 absolute power product stage1 := mul(1, 14)

Lp coefficient atom1 absolute power product stage1 = 14

Lp constant weighted coefficient atom1 := mul(1/2, 14)

Lp constant weighted coefficient atom1 = 7

original atom=1;mass=1/2;SIGNED coefficient=-14;fixed integer p=1

absolute coefficient power=14;weighted coefficient power=7

Lp full weighted absolute coefficient power sum := sum(13/2, 7)

Lp full weighted absolute coefficient power sum = 27/2

SAME complete probability space;masses=[1/2, 1/2];signed coefficients=[13, -14];shift=2;fixed p=1;weighted constant=27/2

for EVERY n>=0,p-moment E|error_n|^p=(27/2)/(n+2)^1;all moments finite and tend0;this is NOT the p-th-root norm value

Lp strict moment comparison numerator := mul(27, 22)

Lp strict moment comparison numerator = 594

Lp strict moment comparison coefficient := mul(2, 1)

Lp strict moment comparison coefficient = 2

Lp least cutoff positive denominator := sum(296, 2)

Lp least cutoff positive denominator = 298

Lp cutoff denominator power product stage1 := mul(1, 298)

Lp cutoff denominator power product stage1 = 298

Lp strict cutoff integer right side := mul(2, 298)

Lp strict cutoff integer right side = 596

Lp previous denominator := sub(298, 1)

Lp previous denominator = 297

Lp previous denominator power product stage1 := mul(1, 297)

Lp previous denominator power product stage1 = 297

Lp previous integer right side := mul(2, 297)

Lp previous integer right side = 594

cutoff N=296;denominator=298;integer left=594;current right=596;previous right=594

strict comparison holds at N and fails at N-1;all smaller allowed indices fail

Lp cutoff evaluation common error denominator := sum(296, 2)

Lp cutoff evaluation common error denominator = 298

Lp cutoff evaluation atom0 absolute error amplitude := div(13, 298)

Lp cutoff evaluation atom0 absolute error amplitude = 13/298

Lp cutoff evaluation atom0 error power product stage1 := mul(1, 13/298)

Lp cutoff evaluation atom0 error power product stage1 = 13/298

Lp cutoff evaluation atom0 weighted moment term := mul(1/2, 13/298)

Lp cutoff evaluation atom0 weighted moment term = 13/596

Lp cutoff evaluation atom1 absolute error amplitude := div(14, 298)

Lp cutoff evaluation atom1 absolute error amplitude = 7/149

Lp cutoff evaluation atom1 error power product stage1 := mul(1, 7/149)

Lp cutoff evaluation atom1 error power product stage1 = 7/149

Lp cutoff evaluation atom1 weighted moment term := mul(1/2, 7/149)

Lp cutoff evaluation atom1 weighted moment term = 7/298

Lp cutoff evaluation full p-moment := sum(13/596, 7/298)

Lp cutoff evaluation full p-moment = 27/596

Lp cutoff evaluation:original n=296;fixed p=1;all weighted absolute-power terms=[13/596, 7/298]

exact p-moment=27/596;neither its p-th root nor unweighted atom mean

moment_tolerance epsilon=1/22;fixed p=1;least N=296;EXACT moment at N=27/596

for EVERY later n,moment=K/(n+shift)^p<=moment_at_N<epsilon;norm bound with SAME epsilon would instead require moment<epsilon^1

逐步反向核對

• S029 · 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。
• S028 · 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。
• S027 · premise_and_result_audit — 以精確有理數重算 Lp cutoff evaluation full p-moment，不以小數近似替代。
• S026 · premise_and_result_audit — 以精確有理數重算 Lp cutoff evaluation atom1 weighted moment term，不以小數近似替代。
• S025 · premise_and_result_audit — 以精確有理數重算 Lp cutoff evaluation atom1 error power product stage1，不以小數近似替代。
• S024 · premise_and_result_audit — 以精確有理數重算 Lp cutoff evaluation atom1 absolute error amplitude，不以小數近似替代。
• S023 · premise_and_result_audit — 以精確有理數重算 Lp cutoff evaluation atom0 weighted moment term，不以小數近似替代。
• S022 · premise_and_result_audit — 以精確有理數重算 Lp cutoff evaluation atom0 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 Lp cutoff evaluation atom0 absolute error amplitude，不以小數近似替代。
• S020 · premise_and_result_audit — 以精確有理數重算 Lp cutoff evaluation common error denominator，不以小數近似替代。
• 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 Lp previous integer right side，不以小數近似替代。
• S017 · premise_and_result_audit — 以精確有理數重算 Lp previous denominator power product stage1，不以小數近似替代。
• S016 · premise_and_result_audit — 以精確有理數重算 Lp previous denominator，不以小數近似替代。
• S015 · premise_and_result_audit — 以精確有理數重算 Lp strict cutoff integer right side，不以小數近似替代。
• S014 · premise_and_result_audit — 以精確有理數重算 Lp cutoff denominator power product stage1，不以小數近似替代。
• S013 · premise_and_result_audit — 以精確有理數重算 Lp least cutoff positive denominator，不以小數近似替代。
• S012 · premise_and_result_audit — 以精確有理數重算 Lp strict moment comparison coefficient，不以小數近似替代。
• S011 · premise_and_result_audit — 以精確有理數重算 Lp strict moment comparison numerator，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, 1/22, 296, 27/596, 是, forall_n_ge_N_symbolic_monotone_tail)

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。