Consistency, Stability, and Dimensional Selection: Why the Universe Has Three Spatial Dimensions

This paper completes the pregeometric foundations of Radial Coherential Dynamics (RCD) by establishing three fundamental consistency results. First, we prove that the primordial coherential state C = 1 is an asymptotic limit reached only at infinite physical time, eliminating finite-time initial singularities. Second, we demonstrate the dynamical stability of emergent spacetime under perturbations of the coherence field. Third, we show that three spatial dimensions (d = 3) are uniquely selected as the only dimension for which the coherential graph admits a stable, non-degenerate continuum limit; lower dimensions fail to support causal structure, while higher dimensions exhibit dynamical instabilities. The paper also provides preliminary results toward quantization, showing that the discrete coherential graph introduces a natural ultraviolet cutoff, suggesting perturbative finiteness without conventional renormalization. This work constitutes Paper IV in the RCD Pregeometric Foundations series and closes the consistency and stability analysis of the framework.