Valadis Information Geometry (V4): A Graph-Theoretic Discrete Metric and Dynamical Framework

Key Points

• The aim is to present a discrete geometric framework that utilizes graph-theoretic concepts to define space and dynamics.
• Introduced unit-distance graph structures generated by circle intersections.
• Defined space through a graph characterized by vertices and edges.
• Applied graph distance to describe distance metrics and curvature in the framework.
• Analyzed transitions on the graph as a means to understand dynamics.
• Proposed a self-consistent geometric model with structure emerging from discrete rather than continuous coordinate transitions.
• Demonstrated the application of the framework in defining curvature and dynamics effectively.