The Harmonic Backbone of Galactic Rotation: A Lattice Tension Dark Matter Profile for the SPARC Sample

We present a novel dark matter density profile derived from lattice tension theory and benchmark it against the full 175-galaxy SPARC rotation curve dataset. The NKA lattice tension model achieves a mean RMS velocity residual of 3.71 km/s (bootstrap 95% CI: 3.31, 4.15) and a median of 3.08 km/s, winning 146 of 175 head-to-head galaxy comparisons against Li+2020 Burkert profile fits (ΔBIC = −3,669). An ablation study confirms that even the bare core halo outperforms the Burkert benchmark, and the result is robust to ±20% perturbations of stellar mass-to-light ratios. The Lesperance Residual Diagnostic Framework and spine analysis demonstrate that remaining residuals organize into coherent structural families rather than random noise. This preprint accompanies the full LaTeX source and figures.