Complex-time phenomenology and halo-independent galaxy rotation-curve tests

Abstract We perform a halo-independent, prediction-mode test of a minimal complex-time (CT) phenomenology for galaxy rotation curves using the SPARC database. Galaxy rotation curves are commonly interpreted as evidence for dark matter (DM). We focus on the highest-quality subsample (Q = 1; n = 99) and adopt a fixed-rule CT prescription (CTmin) with the CT scale radius set to the photometric disk scale (rc = Rdisk), without any galaxy-by-galaxy halo fitting or parameter tuning. We compare a baryons-only baseline against CTmin using the weighted root-mean-square error (wRMSE) computed from the rotation-curve uncertainties. CTmin improves the fit in 91/99 galaxies, with the error-reduction factor ℛwRMSE ≡ wRMSE (baryons only) / wRMSE (CTmin) having median 2.19 (mean 3.34) and a heavy tail reaching ≈14.8. To diagnose outer confinement directly, we construct the halo-independent required extra support vDM,req (r) from the observed curve once baryons are fixed, and evaluate the outer DM-replacement ratio (vφ/vDM,req) outer, over r ≥ 0.8 Rmax,RC. The distribution has median 0.912 (mean 0.996), with 32/99 galaxies in a near-unity band 0.85–1.15. The ratio shows a positive trend with disk size (slope 0.127 in (vφ/vDM,req) outer vs Rdisk), and the CT-induced and required profiles exhibit good shape agreement (median R2 = 0.921). These results indicate that, under a globally fixed prescription, a CT contribution can systematically reduce predictive errors and can supply a substantial fraction of the outer support otherwise attributed to dark matter, while identifying well-defined mismatch regimes for constrained refinement. Running title: Halo-independent CT test of SPARC rotation curves Keywords: galaxy rotation curves; dark matter; SPARC; halo-independent diagnostics; modified gravity; complex time