The Phantom Metric: Resolving Dark Matter Anomalies in Galactic Kinematics, Strong Lensing, and Galaxy Clusters via Topological Constraints and Topological Metric Deformation (Parameter-Free)

Abstract

We present a unified, parameter-free geometric framework that resolves dark matter anomalies as emergent properties of a macroscopic topological manifold. When local gravitational acceleration drops below the empirical minimal acceleration threshold ($a_0$), the spatial metric undergoes geometric saturation, resolving disparate anomalies through distinct boundary mechanics. In galactic kinematics, the system's physical morphology dictates the outcome. Structural flattening into a quasi-2D plane triggers a metric deformation modulated by a Topological Scaling Constant ($\varphi \approx 1.618$), deterministically flattening rotation curves. Conversely, internal dynamics within 3D spherical structures bypass this constraint, strictly maintaining classical Newtonian decay. Concurrently, in gravitational lensing, spatial saturation forms an absolute 2D topological screen exactly at the minimal acceleration threshold, regardless of the lensing mass's physical morphology. This deterministic 2D boundary routes background photons to natively form precise Einstein rings. This framework undergoes a rigorous, three-pronged empirical audit with zero free parameters: Gravitational Lensing: Tested against 100 strong gravitational lenses from the NASA/HST SLACS dataset, the model predicts the Macroscopic Saturation Boundary radius ($R_{BB}$, Einstein Ring Radius) with a consolidated global accuracy of 99.17% ($R^2 = 0.9917$). Galactic Kinematics: Tested against 100% of the SPARC database spanning 3,391 spatiotemporal measurement points across all 175 Late-Type Galaxies (LTGs), and locking the universal stellar mass-to-light ratio ($\Upsilon_* = 0.46$), the model delivers an unfiltered global goodness-of-fit of 91.5% ($R^2 = 0.9150$) with zero localized curve-fitting. Macroscopic Cluster Lensing: Tested against massive galaxy clusters from the HST CLASH survey. Operating strictly on the observable baryonic mass fraction (~13%) with zero dark matter, the model predicts Einstein Ring radii with an exceptional 97.1% structural parity ($R_{1:1}^2 = 0.9710$) across all morphologically relaxed clusters. This demonstrates that geometric conservation scales flawlessly to the largest bound structures in the universe, provided the system maintains a unified center of mass. These results demonstrate that cosmic anomalies are natively resolved by geometric saturation boundaries, rendering non-baryonic dark matter mathematically redundant.