8.18 Galaxy Rotation Curves and Falsification of Dark Matter

Starting from the ℳ𝒞ℐ Three-Sector and Coding Orbit compactification, combined with the Permeation Function elliptic PDE framework, this article establishes the nonlinear correction to gravity at galactic scales induced by three-dimensional coherent leakage of the Information Field Dirac Spectral Direction. Core results: the Characteristic Acceleration is uniquely determined by dimensional homogeneity and the Spectral Volume Scale; the gravity correction formula satisfies double limit constraints and the {2,3,5} Interlock Property minimum complexity principle; the rigorous Tully-Fisher form . Dark Matter resolution: the flatness of galaxy rotation curves is a rigorous corollary of three-dimensional coherent leakage of the Information Field Dirac Spectral Direction, and does not correspond to any scatterable particle state. **Keywords:** Galaxy Rotation Curves; Dark Matter; Information Field Dirac Spectral Direction; Characteristic Acceleration; Tully-Fisher Relation; Geometric Gravity