20 C.F.R. § 404.734
In many States, the law will treat someone as a child of another if he or she agreed to adopt the child, the natural parents or the person caring for the child were parties to the agreement, he or she and the child then lived together as parent and child, and certain other requirements are met. If you are a child who had this kind or relationship to the insured person (or to the insured persons's wife, widow, or husband), we will ask for evidence of the agreement if it is in writing. If it is not in writing or cannot be gotten, other evidence may be accepted. Also, the following evidence will be asked for: Written statements of your natural parents and the adopting parents and other evidence of the child's relationship to the adopting parents.
20 C.F.R. §404.734