We cannot prove a negative, we can only say, correctly, that there is no evidence that Soetoro adopted him. The name used on a school registration form is no evidence of adoption.
Of course, if you want to keep repeating it ad infinitum, that is your right.
Obama has gone to great lengths to conceal all the documents in his life. You claim that the only “evidence” you will accept are documents that you know have been concealed and are not available for review.
There is plenty of other information that shows that Lolo Soetoro adopted Obama. Obama used the name Barry Soetoro shortly after Stanley Ann married Soetoro. His school records record Lolo as the father. His step sister has stated that Lolo adopted Obama.
You arbitrarily and illogically reject all this information. You provide no information whatsoever to support your assertion that Obama was not adopted.
This is a dishonest argument.
Of course, if you want to keep repeating it ad infinitum, that is your right.
My position is that there are reasons to believe Obama was adopted. I do not regard it as a foregone conclusion, I merely point out that the weight of evidence currently supports it, and it seemingly answers a lot of questions if it is true. At the moment I don't regard it as established one way or the other.