Galactic Dynamics from a Principle of Least Informational Cost

We show that observed galactic dynamics that challenge existing frameworks may emerge from a variational principle of least informational cost. In this framework, information is encoded in a real, 2π-periodic relational phase (ψ), in which inertia is the dynamic cost to write new information (change of state), and gravity is the static cost to store that information as persistent spatial gradients (state itself). In the weak/static, nonrelativistic regime, applying consistency and gauge-symmetry requirements to these principles leads to a formally covariant informational action. Varying this action recovers Newtonian gravity at high acceleration, and in spherical symmetry reproduces the Radial Acceleration Relation (RAR) and, as a corollary, the baryonic Tully–Fisher relation, without particulate dark halos. The resulting field equation is identical to the well-known and empirically successful AQUAL (MOND) operator ∇·μ (|∇Φ|/a₀) ∇Φ=4πGρbar, but here derived from an informational action with a fixed interpolation function μ and with a₀ set by the cosmological background. We also outline concrete observational tests capable of falsifying the framework.