The Topology of Charge: Deriving Coulomb's Law and the Origin of Repulsion from the Surface Orientation of Recursive Skyrmions

This monograph extends the General Static-Dynamic Recursive Information Space (GSDRIS) framework to derive the geometric origin of Electric Charge and Coulomb's Law. While Paper 7 established charge quantization as a topological defect, the mechanism of electromagnetic interaction - specifically the phenomenon of Electrostatic Repulsion - remains to be derived from the recursive topology.

We redefine electric charge ($q$) not as an intrinsic quantum number, but as the Surface Orientation Vector of a Skyrmion knot. We demonstrate that the recursive flux intersecting the 4D-metric boundary can possess two distinct orientations: divergent (Source/Positive) or convergent (Sink/Negative).

We analytically derive Coulomb's Law ($F \propto q_1 q_2 / r^2$) from the hydrodynamics of these vector fields. Unlike Gravity (Paper 56), which arises from scalar pressure shadowing (Attraction only), the electric force arises from Vector Flux Interference. We prove that parallel flux vectors (Like Charges) generate positive pressure (Repulsion), while anti-parallel flux vectors (Opposite Charges) generate negative pressure (Attraction). This unifies Electrostatics with the topological fluid dynamics of the vacuum.