When verifying a person’s status with respect to Halachic matters, the highest form of proof is the testimony of two valid witnesses. For example, if a man and woman engage in relations, and two witnesses testify to the fact that they are brother and sister, this testimony authorizes Bet Din to administer capital punishment to the man and woman for an incestuous relationship – even though Bet Din does not know them or their family. In Torah law, there is no stronger proof than the formal testimony of two valid witnesses.
However, testimony is not the only means of verifying personal status. The Halachic concept of "Hazaka" refers to a situation where a person’s status, or the relationship between two people, is widely known and accepted. For example, if there is a family which everybody in the community assumes to be a father, mother and their children, then this widely-acknowledged presumption suffices as proof to their status with respect to Halacha. Therefore, if a boy and girl from the same family have relations, they are liable to capital punishment even without formal testimony to their relationship as siblings. Since they grew up in the same family and were known to everybody in the community as brother and sister, they are treated as such by Halacha, even with respect to capital punishment.
The Rambam (Rabbi Moshe Maimonides, Spain-Egypt, 1135-1204) proves this Halachic concept from the law in the Torah that one who curses or beats his father or mother, Heaven forbid, is liable to capital punishment. The Torah authorizes a Bet Din to administer capital punishment to somebody who curses or beats his father even though there is no possibility of proving that the he is actually his father. This relationship is established based on the common presumption by all who know them that they are father and son. Clearly, then, "Hazaka" suffices to verify a person’s relationship to somebody else, even in the absence of testimony.
The Shulhan Aruch (Eben Ha’ezer 19) applies this principle to the case of adultery. If a man and woman are presumed to be married to one another, and the woman has a relationship with another man, she and that man are liable to capital punishment. Since the woman has a "Hazaka" – the presumed status of a married woman, she is liable to punishment for adultery. The Shulhan Aruch rules that if a man and woman come to a community from afar and claim they are married, and nobody knows them or can verify their status as a married couple, they establish a "Hazaka" after living in the community as a married couple for thirty days. Even though there are no witnesses to their marriage, the woman and the man with whom she had the forbidden relationship are liable to capital punishment on the basis of the "Hazaka" that was established by their living together as a married couple for thirty days.
Summary: The Halachic concept of "Hazaka" allows us to presume a familial or marital relationship between two people for Halachic purposes even without formal testimony. Thus, if a couple and children live together as a family, the children are considered siblings, and the adults are considered their parents and married to one another, with respect to Halacha. If a man and woman move into a community and claim to be married, and nobody knows them or can verify their married status, they establish a "Hazaka" as a married couple after living as a married couple in the community for thirty days. Therefore, after that point, if the woman has an extramarital affair, she is considered an adulteress and is thus liable to capital punishment.
