The contrast between these two characters centers on whether mastery over information serves as a cage or a key. Because one operates via authority and the other via physical application, a direct YPS comparison between a YPS-3 spirit and a YPS-4 mage is fundamentally flawed. These power types occupy different axes; Beatrice manipulates reality through spiritual contracts and mana dependency, while Mathias optimizes combat through a scientific understanding of physics. For Beatrice, knowledge was a prison. Her centuries spent in the Forbidden Library were not an academic pursuit but a manifestation of her stagnation and trauma. Her power is a byproduct of her waiting, making her effectiveness entirely dependent on the emotional bond she forms with a contractor. In contrast, Mathias treats knowledge as a weapon of liberation. He views the established magical laws of his new world as errors to be corrected, utilizing dust explosions and sympathetic vibrations to bypass the biological ceilings of his previous life. While both characters possess a high degree of technical expertise, they utilize it to solve opposite existential crises. Beatrice’s arc is a journey from intellectual isolation to the courage of human fragility. Mathias’s trajectory is a relentless pursuit of efficiency to avoid the helplessness of his first incarnation. One finds agency by finally letting go of the need for a specific answer, while the other finds it by engineering every possible variable. This reveals a core isekai tension: power is either a burden that requires a relationship to carry, or a tool that requires an obsession to wield.