We present a geometric approach to the dark matter problem based on theintroduction of a finite local reconstruction boundary. In General Relativity, spacetime is described through curvedRiemannian/Lorentzian geometry. We argue that such a geometry cannot, ingeneral, admit a globally unbounded Euclidean observational representationwithout a finite normalization domain. Otherwise, the distinction betweencurved and Euclidean geometry would lose mathematical meaning. We therefore explore the hypothesis that Euclidean observational frameworkssuch as the SPARC rotation-curve database implicitly require a finitereconstruction boundary. Because the translation between curved geometry and Euclidean representation isnot canonical, the implementation adopted here is approximate and based on asimplified radial shell prescription adapted to the SPARC data. We test this hypothesis empirically using SPARC rotation curves and presentrepresentative reconstructions together with broad statistical diagnostics.The first quartile (Q1) agreement across morphological families is strong,with an average reduced chi-square value of approximately 0.79. In severalmorphological classes, the fourth quartile (Q4) agreement also remains strong,with values near 3. These results suggest that part of the observed galactic velocity discrepancymay originate from the geometric reconstruction itself rather than fromadditional unseen matter components.
Aviad Shetrit (Mon,) studied this question.