Title: Karahan Framework v121 — A Nonlinear Torsion–Phase Field Theory for Galactic Dynamics, Structure Formation, and Star Formation without Dark Matter

Title:Karahan Framework v121 — A Nonlinear Torsion–Phase Field Theory for Galactic Dynamics, Structure Formation, and Star Formation without Dark Matter Subtitle:Complete Unified Model Including Mathematical Formulation, Dynamical Simulation, and First Observational Interface Abstract:We present the Karahan Framework v121, 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 as a nonlinear reaction–diffusion system incorporating diffusion, damping, self-interaction, and phase synchronization. Within this structure, flat galactic rotation curves emerge naturally from the gradient of a logarithmic torsion profile, eliminating the need for non-baryonic matter components. Spiral morphology is generated dynamically through phase-locking and large-scale coherence, while star formation is modeled as a threshold-driven response to compressive field regions. A time-dependent simulation demonstrates that coherent spiral structures can arise spontaneously from initially disordered field configurations. The model further establishes a direct observational interface, enabling quantitative comparison with rotation-curve datasets such as SPARC via a minimal parameter set. The Karahan Framework provides a unified qualitative description of galactic rotation, morphology, and star formation within a single field-theoretic structure. While the current implementation remains at a pre-quantitative stage and lacks full hydrodynamic and N-body coupling, it defines a mathematically explicit and testable pathway toward empirical validation. This work positions the framework as a falsifiable physical model, offering concrete predictions including spiral arm drift, dynamic star formation patterns, and measurable deviations from circular symmetry in black hole shadow observations.