Karahan Framework v122 — A Nonlinear Torsion–Phase Field Theory with Lagrangian Structure for Galactic Dynamics without Dark Matter

Title:Karahan Framework v122 — A Nonlinear Torsion–Phase Field Theory with Lagrangian Structure for Galactic Dynamics without Dark Matter Abstract:We present the Karahan Framework v122, a nonlinear torsion–phase field theory proposed as a unified alternative to dark matter in galactic dynamics. The model describes galaxies as self-organizing resonance systems arising from the coupled evolution of an effective torsion field and a phase field. The framework is formulated within an effective Lagrangian structure, from which the coupled field equations are derived. In the appropriate macroscopic limit, these equations reduce to a nonlinear reaction–diffusion system capable of generating large-scale coherent structures through phase synchronization and feedback mechanisms. Flat galactic rotation curves emerge naturally from the gradient of a logarithmic torsion profile when combined with a radius-dependent effective acceleration term. Spiral morphology is interpreted as a manifestation of phase-locked resonance channels, while star formation is associated with compressive regions of the coupled field dynamics. The model defines a direct observational interface, enabling quantitative comparison with rotation-curve datasets such as SPARC using a minimal parameter set. Preliminary results indicate promising agreement with observed galactic rotation profiles, while also revealing parameter degeneracies that require further investigation. This version includes a corrected rotational formulation and introduces a consistent Lagrangian field-theoretic foundation, improving the internal coherence of the model. The Karahan Framework provides a unified qualitative description of galactic rotation, morphology, and structure formation within a single field-based approach. While the current implementation remains at a pre-quantitative stage and lacks full hydrodynamic and N-body coupling, it defines a mathematically explicit and falsifiable pathway toward empirical validation.