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

We present a unified, parameter-free geometric framework that accounts for observed dark matter anomalies as emergent thermodynamic properties of a discrete spacetime manifold. We demonstrate that when local gravitational acceleration drops below a fundamental cosmic horizon threshold (a₀), the spacetime metric undergoes geometric saturation—strictly contingent upon the system's dimensional reduction to a quasi-2D plane. This framework natively resolves anomalies across disparate astrophysical phenomena without invoking non-baryonic matter: In gravitational lensing, this macroscopic saturation creates a 2D topological screen (analogous to an absolute thin-lens boundary), deterministically routing background photons to form precise Einstein rings. In galactic kinematics, highly flattened spiral galaxies reach maximal spatial saturation. Here, a Topological Scaling Constant (φ ≈ 1.618) emerges not as a universal active force, but as the geometric dispersion ratio of this minimum acceleration, modulating the metric deformation and flattening rotation curves. Conversely, 3D spherical systems fail to reach 2D geometric saturation, naturally bypassing the topological constraint and maintaining classical Newtonian decay. 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% (R² = 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 (ϒ* = 0.46), the model delivers an unfiltered global goodness-of-fit of 91.5% (R² = 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 (R²_1:1 = 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 spherical geometry. These results strongly suggest that cosmic rotation flattening and strong lensing anomalies are fundamental geometric conservation properties triggered by 2D spatial saturation, rendering dark matter mathematically redundant.