Constitutional conundrum

[heatmaster]

Does anyone have the answer to this question,  say the President has been reelected to a second term and he/she dies a month before the inauguration; the Vice President assumes the presidency under the constitution; the results are due to be announced on Janusry 6; the question that begs to be asked, is the new president covered constitutionally and politically? Any feedback is welcome.

[heatmaster]

My scenario is around say December 12: The outcome is pretty clear cut; a substantial victory in Electoral College and say a 15 point spread in the incumbent President's favor.
My second scenario, just two weeks or so before the inauguration.