Geometric Leakage: A 5D Holographic Solution to Dark Matter and a Falsifiable Prediction for Euclid

### Falsifiable Observational Predictions 10⁹ M_ | R₅ \; kpc | v₋₄₀₊₀₆₄ \; km/s | _² (5D Model) | _² (NFW DM) | |: --- |: ---: |: ---: |: ---: |: ---: |: ---: | | **DDO 154** (Dwarf) | 0. 3 | 11. 78 5. 34 | 67. 94 12. 39 | **1. 12** | 1. 35 | | **NGC 3198** (Intermediate) | 70. 0 | 4. 11 0. 26 | 134. 06 0. 99 | **0. 53** | 0. 60 | | **UGC 2885** (Giant) | 400. 0 | 26. 17 2. 61 | 259. 67 6. 91 | **1. 18** | 1. 45 | --- ## Abstract We present a radical and unified solution to the dark matter enigma in modern cosmology without invoking non-baryonic cold dark matter (LCDM) or exotic WIMPs. We demonstrate that dark matter is an emergent geometric illusion resulting from "Geometric Leakage" of gravitational strength from a 5D holographic bulk into our 4D spacetime. Building upon this framework, we formulate an exact orbital velocity equation that naturally reproduces galaxy rotation curves across dwarf, intermediate, and giant galaxies from the SPARC database with high statistical precision (chi²ₙu < 1. 2). Furthermore, we prove that the characteristic leakage scale R5 is not a universal constant but obeys a dynamic scaling relation with baryonic mass (AlMuaazab Scaling Law: R5 ~ Mbar^ (1/3) ), explaining the absence of dark matter signatures on Solar System scales. Finally, the model provides a falsifiable prediction: a sharp, non-chemical optical discontinuity in gravitational weak/strong lensing profiles at R5 ~ 300 kpc for galaxy clusters, directly testable by the Euclid space telescope.