Reference for Gittin 9:9
יָצָא שְׁמָהּ בָּעִיר מְקֻדֶּשֶׁת, הֲרֵי זוֹ מְקֻדֶּשֶׁת. מְגֹרֶשֶׁת, הֲרֵי זוֹ מְגֹרֶשֶׁת. וּבִלְבַד שֶׁלֹּא יְהֵא שָׁם אֲמַתְלָא. אֵיזוֹ הִיא אֲמַתְלָא. גֵּרַשׁ אִישׁ פְּלוֹנִי אֶת אִשְׁתּוֹ עַל תְּנַאי, זָרַק לָהּ קִדּוּשֶׁיהָ, סָפֵק קָרוֹב לָהּ סָפֵק קָרוֹב לוֹ, זוֹ הִיא אֲמַתְלָא:
If her name went out in the city as betrothed, [If a report were circulated about a single girl: "This girl was betrothed to this man today" (not where there was a mere rumor, but where lamps were lit and beds were spread, and people went in and out saying: "She was betrothed today"], she is [assumed to be] betrothed. (If a report went out that) she were divorced, she is (assumed to be) divorced. [This refers to the beginning, viz.: This woman about whom a report went out that she was betrothed, which report we entertain, forbidding her to marry any man but that one — if there then went out about her a report that she were divorced, that the man who had married her had divorced her], she is (assumed to be) divorced [and is permitted to all men; for the report that we entertained in the beginning — "its receipt has come with it"]. This, so long as there be no attenuation (amathla) to it [i.e., that there not be with the report of betrothal or of divorce an amathla, a consideration which breaks the power of the report]. What is (an instance of) an amathla? "That man divorced his wife on condition"; "He threw her her (instrument of) betrothal, possibly near her (in which instance she is betrothed); possibly near him" (in which instance she is not betrothed). This is an amathla.