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[Aleksandr Sigalov:] This is a very correct observation. My friend is absolutely right. As far as I understand, marriage according to the Torah is a voluntary contract between a man and a woman. It is literally a piece of paper that outlines conditions of a particular marriage. See Deuteronomy 24:1, 24:3. As far as terminology goes, I think such contract would be called "sefer khawthan" (scroll of marriage) as opposed to "sefer kereethooth" (scroll of divorce). Sex alone does not automatically make you husband and wife. There has to be physical written contract and at least two witnesses (i.e Deut 19:15).