Quadratum

Quadratum, also known as Shibuya (シブヤ), is an original world in Kingdom Hearts III. It is a modern, urban world based off of the real-life Shibuya with some distinct variations and differences. Quadratum is the main setting of Verum Rex, a fictional video game that exists in Toy Box.

Settings and Areas
Xehanort describes Quadratum as a world of neither light nor darkness, but somewhere "on the other side", and Ansem the Wise believes it to be a fictional world outside of their reality, an "unreality".

The only part of Quadratum extensively glimpsed so far is a crosswalk located in front of a building with "104" displayed. Quadratum is populated by clothing and tech shops and retailers. In the distance, many high-rise buildings and skyscrapers extend out towards the horizon. Curiously, despite the presence of many automobiles, the city appears to be almost entirely abandoned and desolate.

Some distance away, a large twin building with red aviation lights can be seen.

The minigame Verum Rex: Beat of Lead takes place on a sort of oil-drilling platform located some miles offshore. The platform acts as a battle arena against numerous Gigas. Scattered throughout the platform are spherical fuel containers, and in the center an electric energy field that discharged in continued intervals. Above the energy trap is a suspended glass platform that can be destroyed. In the distance, the city along with a bridge and a golden-lit tower can be seen.

Kingdom Hearts III
Quadratum is first seen when Rex and Hamm watch a Verum Rex video game and action figure trailer upon first entering the Toy Box.

Some time later, Sora and Woody's gang find Rex in the game store looking for Verum Rex merchandise, convinced that Sora is its hero Yozora and looking to prove it. As they are about to leave, Young Xehanort appears and has a Marionette possess Buzz to experiment with the toys' hearts. Young Xehanort then transports Sora into Verum Rex's offshore platform arena to battle the Gigas, but he's able to escape and return to Galaxy Toys.

After the defeat of Master Xehanort, Sora and Riku, separated and disoriented, awaken in Quadratum. The two walk through the streets observing where they are; Sora finds himself at the crosswalk staring at a building with the number "104" displayed, while Riku stares at a large building. As Riku walks past the large building, Yozora sits alone atop watching him down below.

Elsewhere, on the roof of another skyscraper some distance away, The Master of Masters frames the full moon with his hands, then forms a heart shape over it using his fingers, symbolizing Kingdom Hearts.

Kingdom Hearts III Re Mind
One year after Xehanort's ultimate defeat, Sora wakes up in a nighttime version of The Final World, and desperately calls out to whoever he can. He encounters Yozora, whom he learned more about from a girl he met before, and is surprised to discover that Yozora is actually a real person. Yozora appears to know exactly who Sora is and claims that he is tasked to "save" him, but suddenly questions whether that is truly Sora at all. To Sora's shock, he summons his crossbow and sword and the location suddenly changes to the "104" building, where a fearsome battle ensues.

After Sora defeats Yozora, Yozora fades away into light and Sora ends up in the daytime version of The Final World. Meanwhile, Yozora is woken up from his slumber in the back seat of a car by his driver, who asks him, "Impressive, is it not?" Sora and Yozora both wonder whether or not their encounter was real or just a weird dream. Sora then states that none of this makes any sense to him.

Kingdom Hearts Melody of Memory
The name Quadratum is revealed when the Nameless Star in The Final World surmises it must be what Riku is talking about, after he explains his dream about a large city with tall buildings. Using the power of waking, Riku opens a portal to travel there.

Kingdom Hearts 3D: Dream Drop Distance
Neku Sakuraba, Joshua, Daisukenojo Bito, Rhyme, and Shiki all hail from Shibuya. However, Neku's Shibuya and Yozora's are two entirely separate worlds.

Character Design
Sora retains his normal outfits, but his clothes are more detailed and textured, along with having a darker shade.