Einstein–Karahan Framework v122: A Geometric Torsion–Phase Model Confronted with Real SPARC Rotation Curve Data

We present the Einstein–Karahan framework v122, a geometric extension of spacetime dynamics that incorporates an effective torsion–phase field system as an alternative to particle-based dark matter. In this formulation, galactic rotation curves arise from an induced acceleration term associated with a logarithmic torsion profile, rather than from unseen mass components.This master version integrates the theoretical structure of the model—including its effective field equations, covariant embedding within a Riemann–Cartan spacetime, and stability and consistency constraints—with a first direct confrontation with observational data from the SPARC database. A real-data fit is performed for the galaxy NGC 3198, demonstrating that the framework can be applied to astrophysical rotation curves in a fully quantitative manner.The resulting fit parameters show that the model captures the qualitative behavior of flat rotation curves, but also reveal limitations such as parameter degeneracy and a non-optimal goodness-of-fit. These results indicate that, while the framework is empirically accessible and mathematically consistent at the effective level, it remains a proof-of-concept rather than a fully validated alternative to dark matter.We outline the necessary next steps toward full validation, including multi-galaxy SPARC analysis, statistical parameter inference, and consistency checks across gravitational regimes. The Einstein–Karahan framework thus defines a structured and testable research program aimed at reinterpreting galactic dynamics as emergent properties of extended spacetime geometry.