Sub-2 km/s Dark Matter: Spectral Lattice Tension Across the Full 175-Galaxy SPARC Sample

We present a spectral extension of the nonlinear kink-architecture (NKA) lattice tension dark matter profile using discrete operator geometry on a Z₂₄ cyclic lattice. The dark matter density at radius r is parameterized as ρ_DM(r) = ρ_s [T(r)/T₀]^β, where T(r) = T₀ [1 + (r/r_s)^α]⁻¹ is the local lattice tension. We augment this halo model with a spectral velocity correction derived from the eigenmodes of a cyclic Laplacian with torsion and boundary-weight deformation (Lesperance 2025–2026). Applied to the full 175-galaxy Spitzer Photometry and Accurate Rotation Curves (SPARC) dataset with error-weighted fitting, the model achieves a mean root-mean-square (RMS) velocity residual of 1.66 km/s and a median of 0.73 km/s, with 138 galaxies (79%) below 2 km/s and 99 (57%) below 1 km/s. The model reproduces the baryonic Tully–Fisher relation (slope 3.99 via orthogonal regression, scatter 0.12 dex) and the radial acceleration relation (scatter 0.13 dex), with fitted mass-to-light ratios consistent with population synthesis expectations. To our knowledge, this is the lowest reported mean residual for a single unified dark matter profile applied to the complete SPARC sample. Individual rotation curves and best-fit parameters for all 175 galaxies are tabulated.