It takes place alongside the main story
Jin and Nao are pilot of an Valvrave variant called Kagerou
L-Elf learns about this, but keeps it a secret from Haruto and the others
When they leave for earth Jin and Nao stay to project the module.
Kagerou doesn't require a Kamitsuki to pilot
it uses a special engine that is basically an internal rune battery
Near the end Kagerou's battery runs out and it is remodeled into a proper Valvrave
In the end Jin and Nao become Kamitsuki themselves
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"Legitimacy is based on three things. First of all, the people who are asked to obey authority have to feel like they have a voice—that if they speak up, they will be heard. Second, the law has to be predictable. There has to be a reasonable expectation that the rules tomorrow are going to be roughly the same as the rules today. And third, the authority has to be fair. It can’t treat one group differently from another.” Malcolm Gladwell