Other than the divorce papers between his mother and Lolo Soertero. Those describe him as a child of the marriage. Since we know, from the divorce papers between his mother and Barack H. Obama Sr, that he was also child of that marriage. We must assume that he was legally Soetero's child, via adoption, albeit one over 18 but still needing support for college, we pretty well must assume that he was adopted by Soertero. Might have been in Hawaii, or Indonesia, or elsewhere for that matter.
“We must assume that he was legally Soetero’s child, via adoption...”
Assumption. Lots of folks don’t adopt step-children.