Emergent Fisher Halos

We develop a scalar theory of gravity in which the apparent dark matter halo of a galaxy is the response of a Fisher information vacuum to the presence of baryonic matter. The theory starts from a local Fisher energy functional for a scalar field σF on an information manifold for the vacuum, with baryons entering as a source. A Bogomolny-type completion fixes the halo profile geometrically rather than empirically; the scalar sector is embedded in Universal Information Hydrodynamics through a dissipative Fisher operator GF and a bounded-entropy reversible correction. In spherical symmetry the resulting Fisher Bogomolny equation yields cuspy or cored halos depending on a Fisher temperature parameter, while on realistic SPARC baryon distributions a one-parameter Fisher susceptibility model captures many observed rotation curves and reproduces characteristic acceleration and surface-density scales.