“Trump becomes President at the same instant that Obama ceases to be President. At noon.”
100 percent wrong. Trump must swear the Oath correctly before his term can officially begin, per Article II Section 1 of the United States Constitution (not Amendment 20). While Amendment 20 does specify the date and time of when the old term officially ends and the new begins such as:
Amendment XX Section 1. The terms of the President and Vice President shall end at noon on the 20th day of January, and the terms of Senators and Representatives at noon on the 3d day of January, of the years in which such terms would have ended if this article had not been ratified; and the terms of their successors shall then begin.
Article II Section 1 of the United States Constitution specifically states:
“...Before he enter on the execution of his office, he shall take the following oath or affirmation:—’I do solemnly swear (or affirm) that I will faithfully execute the office of President of the United States, and will to the best of my ability, preserve, protect and defend the Constitution of the United States.’”
Therefore, since the 20th Amendment came about when the President originally was sworn into office in March which caused problems due to the needed time it took to install and confirm cabinet members. The 20th Amendment, ratified by 43 states, pushed this back to January. The 20th Amendment does not override the clause in Article II Section 1 of the United States Constitution. This is why the oath is sworn as near to noon on January 20th as is possible. Otherwise, Trump cannot duly execute the office of the President even though Amendment 20 states his term officially begins. Trump must say the Oath in his entirety and correctly before he can be officially President. Without the Oath, he officially and technically can’t do jack.
Trump will have already taken the oath before noon. Therefore he will become President at noon, at the instant Obama’s term ends.
Any limitations as to how early PEOTUS can swear in?
After thinking about this a little more I am going to amend what I said. Kerry cannot be interim President because he is a political appointee by Obama. His term ends at 12:59:59 PM on January 20th. At the same time all Obama’s political appointees also end. The interim President would follow the line of succession until Trump is officially sworn in. Trump doesn’t automatically become President at the end of Obama’s term as he is still President-Elect until he is sworn in even though a new administration term has begun. Since kerry is out of a job at 12;59:59 he is no longer Secretary of State and no longer in the line of succession.
The Supreme Court has ruled on these questions in several cases. There is no practical lapse in the SCOTUS interpretation of US law between one administration and the next.