Geometric Ontology and Fractal Arborescence of Natural Numbers: A Unified Framework for Co-Division Fibers and Affine Chains

This article establishes a comprehensive synthesis of the structural and dynamical properties of the set of natural numbers and odd integers . By integrating the theories of Dimensional Habitation, Co-Division Fibers, and the Inverse Collatz Topology, we propose a non-linear coordinate system based on the duality between 2-adic valuation and affine expansion. We formalize the existence of Equi-level Classes as the fundamental "branches" of a deterministic fractal tree, where the number 1 serves as a dual-state singularity ( "1" Root and "1"  Seed ). The resulting architecture reveals that the apparent chaos in arithmetic sequences is a manifestation of pre-determined geographic paths within a multi-dimensional lattice, exhibiting self-similarity analogous to Barnsley-type fractals.