Siman 23
Presented here for study, not as a practical ruling. The Shulchan Aruch rules by Sephardi custom, the Rema's glosses by Ashkenazi custom, and the Kitzur follows Ashkenazi custom. For a practical question, ask your rabbi.
א עד מתי נאמן הדיין לומר לזה זכיתי. ובו סעיף אחד: כל זמן שבעלי דינים עומדים לפני הדיין נאמן לומר לזה חייבתי ולזה זכיתי נסתלקו מלפניו אינו נאמן אם אין בידו פסק דין ודוקא בשודא דדייני אבל דין התלוי בטענות לא שייך בו נאמנות שלפי הטענות יזכה הזוכה ובלבד שלא יסתור טענות הראשונות וכל זה דוקא בדיין א' אבל שנים נאמנים לעולם ואפי' אם יש ב' עדים שמכחישים אותם: הגה וה"ה אם קבלו עליהם פשרן לזמן כל מה שאומר תוך זמן נאמן אבל אם כבר כתב ונתן להם הפשרה אין לו רשות להוסיף או לגרוע (אפי' תוך הזמן) אע"פ שאומר שכך היתה כוונתו (ב"י בשם רשב"א):
1 As long as the litigants are [still] standing before the Judge, he is believed when he states, 'I have pronounced this party guilty' and 'I have pronounced that party not guilty.' [As soon as] they are dismissed from his presence, he is not believed. And [this refers to a case] where the written verdict is not in his [the litigant's] possession, and [this ruling is applicable] only to a case of discretionary judgment; but in [the case of] a verdict which depends upon the pleas [of the litigants], reliance [on the Judge] does not apply, for in accordance with [the restatement of] the pleas the one who deserves favourable judgment will be so pronounced provided he [the litigant] does not upset his former pleas. This entire [ruling applies] only to one Judge; but two [Judges] are always believed, even if there are two witnesses who contradict them. Rema: So too, if they [ the litigants ] accepted an arbitrator [ to bring about a settlement ] within a certain time limit, — [ the law is that with respect to ] everything he [ the arbitrator ] states within the time limit, he is believed. However, if he had already recorded the settlement in writing and given [ it ] to them, he [ subsequently ] has no right to add or to subtract [ therefrom ] even within the time limit, although he states that thus was his [ original ] intention.