>He is the sitting President until the Judiciary and Congress say otherwise.
You’re forgetting one other key group: the people.
“The United States Code Annotated includes the Declaration of Independence under the heading ‘The Organic Laws of the United States of America’ along with the Articles of Confederation, the Constitution, and the Northwest Ordinance. Enabling acts frequently require states to adhere to the principles of the Declaration; in the Enabling Act of June 16, 1906, Congress authorized Oklahoma Territory to take steps to become a state. Section 3 provides that the Oklahoma Constitution ‘shall not be repugnant to the Constitution of the United States and the principles of the Declaration of Independence.’”
—[ http://www.nccs.net/newsletter/jun98nl.html ]
If the Declaration of Independence is law, and it WAS codified by Congress 04 Jul 1776, then the following IS law:
“That whenever any form of government becomes destructive to these ends, it is the right of the people to alter or to abolish it, and to institute new government, laying its foundation on such principles and organizing its powers in such form, as to them shall seem most likely to effect their safety and happiness.”
I’m not forgetting that. I think about it often. We the People haven’t abolished the current government. Unless and until we do, the current government retains our consent ... and Obama remains the sitting POTUS.