Story gap between Manga Arc 2 and 3?
The Manga For Arc 2 and Arc 3 is published at the same time with different Mangaka 

Arc 3,Truth From Zero Mangaka (Daichi Matsue) draw the first ones, A Day in the Capital) also and his work published in Comic Alive. 

The 2nd Manga Arc 2, A Week in The Mansion drawn by Makoto Fugetsu is published by Big Gangan

Both are not finished as of my writing (19/10/2016).