Summary
Sudachi, unable to attend regular classes, lives and studies with Livia and Yozuru in Livia's trailer house while training as a Coordinator. During a fractions lesson, Sudachi struggles with the math problems while communicating through her nonverbal sounds and telepathy, choosing not to speak mentally with Livia despite considering her a savior who gave her shelter and purpose. When Livia leaves abruptly with a dark expression, Sudachi worries she angered her, but Yozuru notes Livia has been preoccupied lately, suggesting she's burdened by Coordinator responsibilities in Kamihama. Though wanting to help, Sudachi decides not to pry into Livia's personal matters.
Seeking advice, Sudachi consults Mikage about cheering up Livia. Mikage suggests demonstrating growth as a Coordinator would please Livia. Inspired, Sudachi volunteers to perform her first emotion fragment adjustment for the clients, Yuna and Hikaru, a task she'd previously pretended inability at to receive Livia's attention. She succeeds effortlessly, but feels this achievement alone is insufficient.
Determined to gather useful intelligence, Sudachi partners with Mikage to investigate the Kamihama Magia Union and Tokime Clan's movements. After being rebuffed by Mitama, they target former Neo-Magius members Shigure and Hagumu now aligned with the Union. By offering free adjustments, Sudachi learns the Union operates through a small core group while most members focus on self-preservation, which would be valuable intel for Livia.
Their activities draw suspicion from hostile Magical Girls who accuse them of breaching Coordinator neutrality. Though Mikage initially defends her, Sudachi finds courage to assert herself telepathically until Juri intervenes to defuse the confrontation. This makes Sudachi hopeful for Livia's approval.
Returning late past study time, Sudachi faces Livia's anger and momentarily flees. Livia tracks her down and reveals her "worry" was actually concern over Sudachi's development - frustrated by her own inadequate teaching and fearing Sudachi wouldn't become independent. Learning of Sudachi's accomplishments through Yozuru and Mikage, Livia praises her and motivates her to finally master fractions with promised additional praise.
With renewed determination, Sudachi solves the math problems correctly. As Livia commends her success, they prepare for Sudachi's visit to her parents' home - now able to appreciate both her original family and her new life clearing sins alongside Livia.
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