The Dimensional Convergence Theorem: Recursive Resolution and the Integer Structure of Space

This paper presents the Dimensional Convergence Theorem (DCT), which formalizes how recursive field structures transition from fractional, unresolved recursion into discrete dimensional identities. Using the collapse intensity scalar \Sigma = \mu \cdot \nu / \tau, the paper defines convergence thresholds at which recursive feedback locks into whole-number spatial identity. This deterministic framework reinterprets fractal and golden-ratio phenomena as transitional echoes of unresolved collapse and proposes that dimensionality arises not from pre-existing coordinate scaffolds, but through tension resolution in recursive collapse fields.