The world was once at war with 10 alternate worlds. This was known as the Concept War and our world won 60 years ago. All of this was concealed so no normal people are aware of this fact in the current time. After the death of his grandfather, the high-school student Sayama Mikoto is suddenly summoned by the giant corporation IAI. He learns this world is headed for destruction due to the acceleration of the Minus Concepts. To prevent this, negotiations must be undertaken with the survivors of the other parallel worlds so their 10 concepts can be released. And so Sayama is caught up in the final battle to clean up after the Concept War which left behind so much enmity.
The world is terrorized by the powerful Black Witch who has been sealed in the moon. Every ten years, the night of Hexennacht arrives and a chosen witch must battle the Black Witch in hopes of finally defeating her. As the current decade's Hexennacht approaches, a mysterious girl named Kagami Kagami arrives and meets Horinouchi Mitsuru, the daughter of the previous Hexennacht representative. It takes place between Kyoukai Senjou no Horizon and the City Series, two other series by the author.