Human–AI Collaboration: Galaxy Rotation Without Dark-Matter Halos — Median Velocity Residual Reduced from 50.3% to 11.6% in 47 Held-Out Disk Galaxies and to 9.3% in 16 Early-Type Galaxies

This work tests a rotation law that predicts galaxy rotation from visible matter alone, without dark-matter halos or galaxy-specific parameters. The law is formulated within a theoretical framework of multi-frequency angular momentum, in which one dynamical law applies across scales. Its single calibration scale was fixed on 102 SPARC galaxies, selected by a predetermined SHA-256 ordering and frozen; 47 other galaxies were predicted with zero free parameters. On their outer halves the pooled median fractional velocity residual is 11.6%, against 50.3% for Newtonian gravity on the same baryons, a 76.9% reduction, and 43 of 47 galaxies improve. Per-galaxy NFW halos reach 2.0% on the same points by fitting 94 parameters to the curves themselves and adding unseen mass, a median 3.6 times the visible mass at the outermost radius (3.2 across all 149 galaxies analysed). The radial acceleration relation (RAR), also free of dark matter, reaches 9.7% under the identical protocol. Both laws use visible matter alone, and the observed rotation of a test galaxy enters only in scoring; the RAR form was inferred empirically from observed accelerations, whereas the law tested here is formulated within the theory. A parameter-free radial-shape test gives a median outer logarithmic-slope offset of 0.28. On 16 rotating early-type galaxies outside the SPARC disk sample, with every constant frozen, the median outer residual is 9.3%, against 11.5% for the RAR and 37.1% for Newtonian gravity. All results were reproduced independently from the archived program and data. The work was carried out through human–AI collaboration.