Information-Imprinting Geometry and the Origin of Galactic Dynamics and the Baryonic Tully–Fisher Relation

This preprint presents a minimal effective gravitational framework in which galactic-scale dynamics emerge from an information-imprinting mechanism associated with baryonic mass distributions. The model does not invoke dark matter particles or phenomenological acceleration scales such as those assumed in Modified Newtonian Dynamics. An information potential field, sourced by baryonic density, generates an effective information-fluid component through a nonlinear coupling. Within this framework, flat galactic rotation curves and the baryonic Tully–Fisher relation naturally arise from geometric boundary scaling, controlled by the baryonic boundary scale R_b and an information condensation efficiency \eta. The theory is intentionally formulated as an effective model applicable at galactic scales, with an automatic screening mechanism that restores standard Newtonian gravity and General Relativity in small-scale systems such as the Solar System. Cosmological initial conditions and high-energy modifications of gravity are explicitly outside the scope of the present work. This preprint is associated with the OSF project KUTERN-0: Finite-Information Late-Time Cosmology and Tension Alleviation and is currently prepared for journal submission.