Galaxy Disks, Central Black Holes, and an Extra-Dimensional Tidal Hypothesis: A constraint-first research note

This exploratory research note separates established galaxy dynamics from a speculative higher-dimensional coupling. It proves a limited stable planar-orbit counterexample in a spherical Kepler potential; derives local gas pressure-support, disk-thickness, and black-hole force-fraction relations; and defines anisotropic and isotropic bulk-tide amplitudes with conditional rotation, thickness, and lensing responses. Selected five-dimensional brane-world studies already explore related galaxy rotation and lensing predictions. The proposed extra-dimensional correction remains an unclosed ansatz, is not fitted to data, and does not prove M-theory or a multiverse.