Spiral Exponential Function — Chapter 3: Uniform Linear Motion

This paper focuses on the behavior of the spiral exponential function at the critical angle θ = π/4. At this point, the acceleration vector becomes purely imaginary, eliminating any real-axis component. As a result, uniform linear motion naturally emerges as a form of structural degeneration of the spiral. This degeneration represents a transition into linear behavior due to the breakdown of rotational structure, marking a key transformation within the spiral space. The study reinterprets linear motion not as a mere special case, but as the structural counterpart to rotation, offering a novel perspective on the hierarchical organization of motion.