Geometric Resolution of Galactic Rotation Curves: Matrix Tension as a Deterministic Replacement for Dark Matter

The anomalous flattening of galactic rotation curves is historically interpreted as evidence for an invisible "Dark Matter" halo encompassing baryonic galaxies. This paper demonstrates that Dark Matter is an unnecessary mathematical artifact born from the application of a structurally diluted macroscopic gravitational constant (G_macro) beyond its coherent geometric scale. 

By applying the General Theory of Correspondence (GTOC), we show that the vacuum is not an empty void, but a structural matrix constrained by the universal 10^-31 meter baseline floor. We derive the intrinsic geometric stiffness of this lattice, expressing it as a baseline radial acceleration (a_matrix). 

When applied to the extreme outer rim of a galactic halo, the mathematical inclusion of this matrix tension perfectly cancels out the radial distance variable (r), natively forcing the orbital velocity to a constant plateau. This structurally resolves the rotation curve paradox using strictly derived constants and is empirically validated by historical MOND threshold observations, eradicating the need for the dark sector.