Toward a Topological Interpretation of the Baryonic Tully-Fisher Relation

We propose a phenomenologically motivated effective field theory (EFT) framework in which galacticscaling relations emerge from topological properties of the vacuum. By introducing a nonlinear consti-tutive coupling between a background field and an effective network current, we suggest a mechanismof dynamical mass generation associated with localized topological solitons. Under a set of physicallymotivated assumptions—specifically topological flux conservation and phase-locking saturation—weshow that a scaling relation of the form R0 ∝M1/2b leads to a deterministic derivation of the BaryonicTully-Fisher Relation (BTFR), V4f ∝Mb. Comprehensive validation across the full SPARC sample of175 disk galaxies demonstrates that the V4.0 q-EFT model outperforms the NFW dark matter profilein 61% of cases and the Simple Interpolating MOND formalism in 86% of cases. Crucially, the 27failure cases exhibit a strong morphological correlation with non-axisymmetric systems, confirming aphysically motivated and testable boundary of model applicability.