第 22892 題：連續實值分布函數

原題與已知條件

CDF本身continuous、nondecreasing、right-continuous且audit query_points嚴格遞增。操作=contcdf-zero-jump-atomlessness；資料={"knots":[-18,0,18],"values":[0,[17,18],1],"point":0}。請依 exact_ordered_tuple_declared_by_interface 欄序回答。

• G001 — CDF本身continuous、nondecreasing、right-continuous且audit query_points嚴格遞增。操作=contcdf-zero-jump-atomlessness；資料={"knots":[-18,0,18],"values":[0,[17,18],1],"point":0}。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-continuous-real-distribution-function

逐步推導

source operation=contcdf-zero-jump-atomlessness;original snapshot and mathematics retained

explicit ordered source output fields=[point, F_at_point, F_left_limit, singleton_probability, zero_jump, certificate]

CDF segment0 positive knot width := sub(0, -18)

CDF segment0 positive knot width = 18

CDF segment0 nonnegative value increment := sub(17/18, 0)

CDF segment0 nonnegative value increment = 17/18

CDF segment0 exact nonnegative slope := div(17/18, 18)

CDF segment0 exact nonnegative slope = 17/324

CDF segment1 positive knot width := sub(18, 0)

CDF segment1 positive knot width = 18

CDF segment1 nonnegative value increment := sub(1, 17/18)

CDF segment1 nonnegative value increment = 1/18

CDF segment1 exact nonnegative slope := div(1/18, 18)

CDF segment1 exact nonnegative slope = 1/324

ORIGINAL strictly increasing knots=[-18, 0, 18];aligned exact nondecreasing values=[0, 17/18, 1];ALL [width,height,slope] rows=[[18, 17/18, 17/324], [18, 1/18, 1/324]]

declare linear interpolation on EVERY segment,constant0 left and1 right;shared knot values make joins continuous;all slopes>=0 allow flats;continuous implies right-continuous and endpoints give limits0/1

CDF ORIGINAL atom query ORIGINAL query minus left knot := sub(0, -18)

CDF ORIGINAL atom query ORIGINAL query minus left knot = 18

CDF ORIGINAL atom query exact interval fraction := div(18, 18)

CDF ORIGINAL atom query exact interval fraction = 1

CDF ORIGINAL atom query fraction times ORIGINAL value increment := mul(1, 17/18)

CDF ORIGINAL atom query fraction times ORIGINAL value increment = 17/18

CDF ORIGINAL atom query plus ORIGINAL left-knot value := sum(0, 17/18)

CDF ORIGINAL atom query plus ORIGINAL left-knot value = 17/18

CDF ORIGINAL atom query:ORIGINAL exact query x=0;knots=[-18, 0, 18];values=[0, 17/18, 1]

case=FIRST source interval containing query,including shared knot;source interval index=0;F(x)=17/18;this is CDF value,NOT singleton mass

CDF actual value minus equal continuous left limit := sub(17/18, 17/18)

CDF actual value minus equal continuous left limit = 0

ORIGINAL point=0;WHOLE-law continuity gives F(x)=17/18=F(x-)

P(X=x)=F(x)-F(x-)=0;zero_jump=是;F(x) may be positive;atomless alone does NOT imply a density

逐步反向核對

• 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 CDF actual value minus equal continuous left limit，不以小數近似替代。
• S013 · 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。
• S012 · premise_and_result_audit — 以精確有理數重算 CDF ORIGINAL atom query plus ORIGINAL left-knot value，不以小數近似替代。
• S011 · premise_and_result_audit — 以精確有理數重算 CDF ORIGINAL atom query fraction times ORIGINAL value increment，不以小數近似替代。
• S010 · premise_and_result_audit — 以精確有理數重算 CDF ORIGINAL atom query exact interval fraction，不以小數近似替代。
• S009 · premise_and_result_audit — 以精確有理數重算 CDF ORIGINAL atom query ORIGINAL query minus left knot，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 CDF segment1 exact nonnegative slope，不以小數近似替代。
• S006 · premise_and_result_audit — 以精確有理數重算 CDF segment1 nonnegative value increment，不以小數近似替代。
• S005 · premise_and_result_audit — 以精確有理數重算 CDF segment1 positive knot width，不以小數近似替代。
• S004 · premise_and_result_audit — 以精確有理數重算 CDF segment0 exact nonnegative slope，不以小數近似替代。
• S003 · premise_and_result_audit — 以精確有理數重算 CDF segment0 nonnegative value increment，不以小數近似替代。
• S002 · premise_and_result_audit — 以精確有理數重算 CDF segment0 positive knot width，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

(0, 17/18, 17/18, 0, 是, continuous_CDF_has_zero_singleton_mass_but_need_not_have_density)

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。