Direct Universal Compression Theory (DUCT) IV: The Quantum Compression Limit: Redefining Neutron Stars, Black Holes, and the Schwarzschild Metric through the η-Field

This manuscript extends the Direct Universal Compression Theory (DUCT) into the regime of extreme gravitational fields, applying the non-linear η-field equation to neutron stars and black holes. We propose that the η-field (scalar compression) replaces the standard Schwarzschild metric by redefining acceleration as a function of geometric compression. By anchoring the maximum stable compression of baryonic matter to the Golden Ratio (ϕ), we derive a deterministic "Mass-Radius" relation that deviates from General Relativity (GR) by a factor of √ϕ. Furthermore, we demonstrate that the "singularity" predicted by standard models is replaced by a high-density "Scalar Core" governed by Quantum Compression Inertia (QCI), providing a mathematical floor to volume and solving the infinite density paradox.