Dark Matter as the Curvature Signature of a Living Manifold

This paper develops a structural reinterpretation of dark‑matter phenomena by treating them as expressions of hidden curvature within an evolving spacetime manifold rather than as evidence for undiscovered particles. The central claim is that gravitational anomalies—galactic rotation curves, lensing distortions, cluster dynamics, and early‑universe fluctuations—arise from geometric features of the manifold that do not correspond to visible mass but nonetheless shape motion and light.The work preserves the mathematics of general relativity while shifting its ontology: geometry becomes generative rather than passive, and the manifold is treated as an active relational substrate that updates through global–local coupling. Under this framework, dark matter is not a substance but a structural signature of curvature that is smooth, continuous, and globally constrained. This interpretation reduces the need for free halo parameters, predicts fewer small‑scale substructures than ΛCDM, and aligns gravitational behavior with the manifold’s large‑scale evolution.The paper positions dark matter as one aspect of a broader relational ontology in which systems maintain coherence through reciprocal constraint propagation. It outlines empirical tests—lensing reconstructions, rotation‑curve modeling, and structure‑formation simulations—that can distinguish geometric signatures from particulate ones. The result is a unified, falsifiable account of dark‑matter phenomena grounded in the physics of evolving geometry rather than speculative particle species.