Axiomatic Generation of Geometry and Complex Structures from One-Dimensional Defects

Abstract

This paper presents an axiomatic framework showing how one-dimensional defects generate three-dimensional geometric structures and induce two-dimensional complex structures. The theory establishes a necessary generative hierarchy and demonstrates its consistency through hyperbolic and non-hyperbolic knot complements. This work is licensed under the Creative Commons Attribution 4.0 International (CC BY 4.0) license.