60 years before World War II, mankind found ten alternate worlds that exist but with different other physical laws. The force that supports these alternate worlds is called Concept. At the same time, mankind also discovered that all these alternate worlds are about to collide and the ones without the most amount of Concept will be annihilated.

To survive, a world call Low-G, which has no Positive Concepts of its own, started the Concept War to try to secure the most amount of Concepts. It took all the other worlds', called Gs, positive concepts and destroyed them all. All that remains is Low-G.

Now 60 years later, which is the present, Low-G is facing destruction because of its Negative Concepts are rapidly expanding. To resolve this, Low-G needs Positive Concepts from all the other alternate worlds. UCAT, the team that destroyed the alternate worlds 60 years ago formed the Team Leviathan to begin negotiation with the survivors from all the other worlds.

Mikoto Sayama is the protagonist of the story. After his grandpa, who was a key figure in the Concept War and in the negotiation team, passed away, IAI, UCAT's mother branch in Japan, explained everything to Mikoto and had him take over the negotiation seat.

Carrying the phrase "The family name Sayama is villain itself" and all the hatred, young Mikoto begins his negotiation with the other worlds.