Nayuta no Kiseki occupies an odd place in the Kiseki series, and fans tend to think of it as an enjoyable outing but not part of the same world as the ‘mainline’ Kiseki storyline. This theory builds on my previous theory (posted to this site under the title ‘The Wizard of Ouroboros’) and includes new hints from Hajimari no Kiseki.
Please note this post includes endgame spoilers for Sen IV and Nayuta as well as partial spoilers for Hajimari.