Algebraic Topology of Natural Numbers: The Eulerian Phase-Bus Model

Key Points

• This research aims to establish a formal mapping of non-zero natural numbers onto a recursive phase-axes system, utilizing Euler's Identity.
• Introduced a mapping of N* onto imaginary phase-axes derived from Euler's Identity.
• Defined a Torque Operator to manage transitions between stability states.
• Developed an algorithmic framework for analyzing discrete information-flow density.
• Demonstrated a systematic approach to transition between planar and volumetric stability states.
• Provided quantitative insights into the information-flow density based on the recursive system.
• Established a foundational algorithm that can be applied in advanced mathematical computations and theoretical frameworks.