Topological Network Effective Field Theory: A q-Deformed Variational Model and Asymptotic Galactic Dynamics

We propose a phenomenologically motivated effective field theory (EFT) incorporatinga background 1-form field and an effective network current. A generalized q-deformed ca-pacity parameter, motivated by Tsallis non-extensive statistics, mediates the backgroundinteraction. Treating the phase index q as an auxiliary modulus field, the theory admitsdistinct topological vacuum phases. Through an asymptotic expansion near the macroscopiclimit (q ≈1), the model suggests a mechanism for asymptotically flat rotation curves witha logarithmic correction. We explicitly demonstrate that the framework recovers standardNewtonian dynamics in the q →1 limit, establishing the correspondence principle. Theframework provides a potential phenomenological alternative to dark matter descriptions,subject to the weak-field and spherical symmetry approximations discussed herein.