The Radial Address of the NFW Cusp Failure: Stacked Rotation Curve Residuals Across 149 SPARC Galaxies

The Navarro–Frenk–White (NFW) density profile is known to overpredict dark matter density in the inner regions of many galaxies — the core–cusp problem. We localize this failure to a specific radius in disk-scaled coordinates. By fitting NFW, pseudo-isothermal (CIS), and Burkert dark matter profiles to 149 late-type galaxies from the SPARC database, computing fractional velocity residuals (V_obs − V_model)/V_obs at every measured radius, and stacking across all galaxies with radii normalized by the photometric disk scale length r_d, we identify a systematic overprediction of rotation velocity by the NFW profile at r/r_d ≈ 0.6. The per-galaxy median residual in the zone 0.4 < r/r_d < 0.8 is −0.099 (Wilcoxon signed-rank p = 4 × 10⁻¹³), with 72% of galaxies individually showing the overprediction. The CIS profile shows a weaker feature at the same location (median −0.021, p = 0.001). The Burkert profile shows no feature (median +0.006, p = 0.98), confirming the signal is cusp-specific. The NFW feature persists across Hubble types (not driven by bars), stellar mass-to-light ratios (Υ_* = 0.3–0.8), gas fractions (present in gas-poor galaxies), and disk morphology (present in smooth, regular spirals as well as irregular systems). A control zone at r/r_d = 2–4 shows no systematic CIS residual (p = 0.45). These results provide a quantitative radial benchmark for hydrodynamical simulations of cusp-to-core transformation: the NFW cusp's inner mass excess manifests most strongly at r/r_d = 0.6 ± 0.1, a location set by the baryonic disk scale, not by halo properties alone.