A young boy and a girl with a magic crystal must race against pirates and foreign agents in a search for a legendary floating castle.
Teenage math whiz Kenji Koiso agrees to take a summer job at the Nagano hometown of his crush, Natsuki. When he arrives, he finds that her family have reunited to celebrate the 90th birthday of their matriarch. His job: pretend to be Natsuki's fiancé. Meanwhile, his attempt to solve a mathematical equation causes a parallel world's collision with Earth.
Cyborg detective Batou is assigned to investigate a series of murders committed by gynoids—doll-like cyborgs, which all malfunctioned, killed, then self-destructed afterwards. The brains of the gynoids initialize in order to protect their manufacturer's software, but in one gynoid, which Batou himself neutralized, one file remains: a voice speaking the phrase "Help me."
