Sora wo Kakeru Shoujo

Synopsis

Akiha's peaceful breakfast is interrupted when her sister Kazane tries to get Akiha to agree to an arranged marriage. With her younger sister Nami also making derisive remarks, Akiha and her robot servant and friend Imoko flee the house for the spaceport and school. Nami subsequently gives chase only to be stopped in her tracks by both her agoraphobia and lack of a student card. Akiha and Imoko are joined by two of Akiha's classmates who borrow an escape pod for Akiha so she has no need to return home. The escape pod encounters a gravity quake caused by the brain colony Leopard which Akiha and Imoko explore before meeting the eccentric AI face-to-face. Together with ICP officer Itsuki Kannagi who tries to arrest both Akiha and Leopard, they use their QT-Arms to prevent Leopard from crashing into Earth. At the end of the episode, Honoka Kawai shows up on Leopard and calls Akiha "The Girl Who Leapt Through Space".

(Source: Wikipedia)