The Harmonic Backbone of Galactic Rotation: Lattice Tension Dark Matter and the SPARC Sample

We present a novel dark matter density profile derived from lattice tension theory, a framework in which dark matter density scales with the local tension of an underlying spatial lattice. Applied to the full 175-galaxy SPARC rotation curve dataset with Li+2020 baryonic decomposition, the model achieves a mean root-mean-square (RMS) velocity residual of 3.71 kms−1 (bootstrap 95% CI: [3.31, 4.15]) and a median of 3.08 km s−1 ([2.60, 3.44]), with 127 galaxies (73%) below 5 km s−1 and 55 (31%) below 2 kms−1. In head-to-head comparison with Li+2020 Burkert profile fits on the same dataset, the lattice tension model wins 146 of 175 galaxies (win rate CI: [77.7%,88.6%]) and is strongly preferred by the Bayesian Information Criterion (∆BIC = −3,669) despite using twice as many free parameters. An ablation study confirms that even the bare lattice tension halo (no geometric shielding, no central potential, no calibration corrections) outperforms the Burkert benchmark (mean RMS 5.85 km s−1, 126 wins), and that the result is robust to ±20% perturbations of the stellar mass-to-light ratios. A systematic floor audit confirms that all remaining residuals fall within the combined observational and systematic uncertainty envelope. These results suggest that galaxy rotation curves exhibit a coherent structural backbone that is captured naturally by lattice tension scaling, without requiring separate profiles for cored versus cuspy halos.