As discussed here, here, here, and here, there are different opinions as to when one is allowed to break their fast and end Shabbos, ranging from 36 minutes (mine) to 42 minutes to 60 minutes to 72 minutes to different times for fasts and Shabbos/Yom Kippur/Yom Tov. Where did these different opinions start? I understand that all of them are different calculations for when three stars come out, but why do different communities calculate that differently?
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