Einstein–Karahan Framework v122: A Geometric Torsion–Phase Model with First Real-Data Validation from the SPARC Database

We present version v122 of the Einstein–Karahan framework, 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 are interpreted as emergent effects of an induced acceleration associated with a logarithmic torsion profile, rather than as evidence for unseen mass components.This work consolidates the theoretical structure of the framework—including its effective field equations, covariant embedding within a Riemann–Cartan geometry, and stability and local-consistency conditions—with a first direct application to real observational data from the SPARC database. A quantitative fit is performed for the galaxy NGC 3198, demonstrating that the model can be consistently confronted with astrophysical rotation curve data.The resulting parameters reproduce the qualitative behavior of flat rotation curves, while also revealing limitations such as parameter degeneracy and a non-optimal goodness-of-fit. These findings indicate that, although the framework is mathematically consistent and empirically testable at the effective level, it remains a proof-of-concept rather than a fully validated alternative to dark matter.Future work will focus on systematic multi-galaxy analysis, statistical parameter inference, and consistency checks across gravitational regimes. The Einstein–Karahan framework thus defines a structured and falsifiable research program aimed at reinterpreting galactic dynamics as emergent properties of extended spacetime geometry.