Black Holes from the Sobolev–Ozok Lattice (SOL):Derivation, Galaxy Occupation Thresholds, and Quasi-Black-Hole Signatures

This paper develops black holes from the Sobolev–Ozok Lattice (SOL) framework and connects fundamental coherence physics to astrophysical observations. It shows that supermassive black holes are inevitable in galactic centers once the stellar velocity dispersion passes a minimum threshold set by the coherence core. This explains why nearly all galaxies above a critical scale host black holes, while smaller systems may only form partial or quasi–black holes.

The work also introduces the concept of quasi–black holes, near-saturated cores that produce measurable deviations in black hole shadow size, innermost stable orbit, and horizon position. These deviations follow simple linear discovery lines that make the model directly testable with current and future Event Horizon Telescope observations. Case studies of Sgr A* and M87* show that the predicted deviations are within present observational limits but become more significant near the occupation threshold.

This unifies three results: a first-principles derivation of black holes from SOL, an explanation of the inevitability of central black holes in galaxies, and a predictive framework for quasi–black holes that links galactic kinematics to strong-field observational signatures.