This side story follows Asama, Kimi and Mitotsudaira aboard Musashi one year before the beginning of the main story, as Asama is considering to create a music band together with her two friends for the next festival in Aki, a territory under the governance of K.P.A. Italia.
 
Note: An official comercial release of the side story volumes of Kyoukaisenjou no Horizon that were bundled with the first press release of the 1st, 3rd, 5th and 7th Blu-ray volume of both seasons of anime.

In the far future, humans abandon a devastated Earth and traveled to outer space. However, due to unknown phenomenon that prevents them from traveling into space, humanity returns to Earth only to find it inhospitable except for Japan. 
To accomodate the entire human population, pocket dimensions are created around Japan to house in the populace. In order to find a way to return to outer space, the humans began reenacting human history according to the Holy book Testament. But in the year 1413 of the Testament Era, the nations of the pocket dimensions invade and conquer Japan, dividing the territory into feudal fiefdoms and forcing the original inhabitants of Japan to leave. 
It is now the year 1648 of the Testament Era, the refugees of Japan now live in the city ship Musashi, where it constantly travels around Japan while being watched by the Testament Union, the authority that runs the re-enactment of history. However, rumors of an apocalypse and war begins to spread when the Testament stops revealing what happens next after 1648. 
Taking advantage of this situation, Toori Aoi, head of Musashi Ariadust Academy's Supreme Federation and President of the student council, leads his fellow classmates to use this opportunity to regain their homeland. 
(Source: Wikipedia)

The story is set in a distant future where Japan is divided into feudal territories and conquered by other countries. There is a floating city named Musashi that is composed of eight ships in the skies. A war that will determine the fate of the world will be fought by students on the Musashi. 
In the far future, humans abandon the devastated Earth and ascend to the upper world "Tenjo", taking on new, god-like form. But even with their newfound "Godhood", humanity eventually fell into war, resulting in the collapse of Tenjo and the very law of causation, and humanity, having lost their divine powers, returns to the Earth, grown largely uninhabitable, with the exception of a portion of the Far-East (modern-day Japan), which they name "Shinshuu" (Divine States").
As Shinshuu alone is too small to accommodate all of humanity, they duplicate the region in a parallel world they called "Juusou Sekai" (Harmonic Realm"), calling their new territories "Juusou Shinshuu" (Harmonic Divine States). In order to rebuild Tenjo and the law of causation, the returned humans start a reenactment of history, starting from 10,000 BC, following the guidance of historical records from a source known as the "Testament". In the year 1413 TE (Testament Era), the reenactment of the Nanboku-cho War in Shinshuu inadvertently damages the mechanisms separating the worlds, causing Juusou Sekai to collapse into the original world. The humans living in the Juusou Shinshuu thus lost their land, and decide to invade the original world. The people of Shinshuu are defeated, and under the terms of their surrender, their territory is divided by the invaders, and discriminatory laws are imposed on them. Reenactment of history is resumed from 1457AD, but the updates to the Testament unexpectedly end at 1648 AD. A rumor of impending apocalypse begins to spread the world.

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