Eiji Hayase is a globally recognized scientist and the father of Mari Hayase, the main protagonist of the story. He is also the husband of Akira Hayase and father to his younger daughter, Rika. Eiji is characterized by an intense and passionate dedication to his scientific research, often to the point of obsession. His overwhelming curiosity drives him to become excessively engrossed in his studies and expeditions, a trait that sometimes causes him to neglect his family obligations. For example, his commitment to his work was evident early in his marriage, as he disappeared for an extended period the very day after his wedding.

This pattern of behavior sets the central mystery of the narrative in motion. Eiji has been missing from his family's life for three years prior to the events of the anime, having not contacted his wife or daughters during that entire time. Before his disappearance, he left behind a significant artifact for his daughter: a pendant known as the armillary compass. This device, which is linked to his time travel research, becomes the key that allows Mari to journey into the past. Eiji’s role in the story is that of the absent, sought-after figure. As Mari travels through history, she finds that her father has been present in many of the past eras she visits, leaving traces of his journey through time. His research into time travel and his subsequent disappearance are the primary drivers of the plot.

Beyond his scientific genius, Eiji is depicted as a man who genuinely loves his family despite his physical and emotional absences. This love is demonstrated through a pivotal event in the narrative. When he learns that his daughter Mari has been captured by the antagonist Jou Mikage during one of her trips to the past, Eiji takes direct action. He attempts to save her, a decision that leads to a confrontation with the fabric of time itself, resulting in a time paradox. This action reveals that his motivations are not purely academic; when faced with a direct threat to his child, his paternal instincts override all other considerations, even the laws of physics. His notable abilities include his extensive knowledge of science and magnetism, which allowed him to construct a time machine and create the armillary compass. Through his recorded work and his appearances in the past, he serves as a guide for Mari, helping her understand the scientific principles of the great inventors she meets, even as she works to unlock the mystery of his fate.