Black Holes as Nodes of Field Density in the Closed System

This document is the third (https://doi.org/10.5281/zenodo.23479623) in a series. Paper 1 (https://doi.org/10.5281/zenodo.23403699) established the scalar field φ as navigable infrastructure, dark atoms as stable dark matter, and the geometric window as the selection mechanism. Paper 2 (https://doi.org/10.5281/zenodo.23441876) developed the cosmology that follows: a closed system at maximum size with local redistribution of regions. This third paper proposes that black holes are the nodes where field density reaches its critical maximum: the points where baryonic matter is converted into vacuum field and where the field crystallizes back into baryonic matter. The conversion is driven by the elevation of the saddle point: when field density is high enough, all reactions are suppressed, and matter becomes pure field. The process is reversible: when field density decreases, the saddle point lowers, and reactions resume. The model is falsifiable by density anisotropies, contraction regions, and inversion footprints.