In the realm of fictional worlds, mystery often arises not from magic alone, but from the invisible scaffolding of mathematical principles that shape narrative coherence and immersive depth. *Sea of Spirits*—a vivid imagined universe—exemplifies how abstract concepts like Hausdorff spaces and correlation coefficients transform abstract wonder into tangible storytelling. The Hausdorff Property and Narrative Distinctness A foundational idea in topology, the Hausdorff space ensures that distinct points possess separate neighborhoods—preventing

1. Introduction to Human Decision-Making and Game Design Understanding how humans make decisions is a complex field that intersects psychology, economics, and neuroscience. Everyday choices—from small habits to life-altering decisions—are influenced by a myriad of factors including emotions, cognitive biases, and social pressures. Game design, as a structured environment with clear rules and incentives, serves as a powerful tool to model and reveal these underlying decision patterns. By simulating real-world