Dark Halos as Geometric Residuals of the Baryonic Transition

Galaxy rotation curves show a mismatch between the observed circular field and that predicted by baryons. Standard closure models this as a dark halo. We test an alternative: dark halos as geometric residuals of the baryonic organization. We define the residual q(R) = g_obs − g_bar and the field m(R) = q(R)/R = (V_obs² − V_bar²)/R². The exterior profile is anchored at the first upward transition where q ≃ g_bar, and its shape is a power law: m(R)/m_t = (R/R_t)^(−γ), with γ the outer residual slope. For SPARC (175 galaxies), 124 show this transition. The correlation between γ and baryonic velocity at the transition is ρ = 0.725 for the quality sample and 0.801 for Q = 1. Leave-one-galaxy-out tests reconstruct held-out outer rotation curves with a mean absolute error of 7.71 km s⁻¹, better than RAR and NFW baselines in the same domain. The outer width usually assigned to the dark halo is not a free shape independent of baryons. It is encoded in the baryonic transition and central depth: compact or deep baryonic structures yield steeper residual slopes, while diffuse structures yield broader ones. A reproducibility package is provided.