The Doomsday (滅日 Horobi, localized as Day of Reckoning) is an event in which the world is destroyed and recreated anew.
The Doomsday is a ceremony which effectively heralds the end of the world, and begins the construction of a new one. The ceremony begins with the living turning into magic element, and their souls being returned to the Blue; following this, the world is reset, and, finally, the Successor of the Blue begins to reconstruct the world. The Qualified, however, still remain in the world as they have been chosen by the Blue. They are able to use Magic Formulas despite the lack of magic element.
The White of Nothingness (虚無の白 Kyomu no Shiro) is the final phase of the Doomsday. It is an altered scenery, a completely white space of nothing.