SPARC Galaxies as Closed Relativistic Systems - An Empirical Analysis

We present an alternative geometric approach to the dark matter phenomenon. In the proposed framework, the additional observed stellar velocity originatesfrom the finite Euclidean reconstruction of an underlying relativisticgeometry. We argue that the translation between curvedRiemannian/Lorentzian geometry and an effective Euclidean observationalrepresentation cannot, in general, remain globally unbounded. In this work, we explore the mathematical structure of this transformation, introduce a set of reconstruction constraints, and formalize the resultingFinite Reconstruction Framework. We then test the framework empirically using SPARC rotation-curve data andanalyze the resulting reconstructions statistically across multiple galacticmorphologies. Across the SPARC sample, the first quartile agreement (Q1) yields an averagereduced chi-square value of approximately 0. 79. For several morphologicalfamilies, the fourth quartile (Q4) agreement remains nearchi² ≈ 3. Most of the strongest residual outliers belong to the Sab and S0morphological families. We discuss the possibility that these systems possessgreater baryonic and structural complexity, which may naturally lead to largerresidual structure within the present reconstruction framework.