UDCT v7.09 Post Registration — Positive Global Virial Work with Local Jeans Obstructions: Results of the Registered GQUMOND Example-A Test in Three Ultra-Faint Dwarfs

Abstract

UDCT v7.09 Post Registration — This record presents the post-registration results of the registered GQUMOND example-A test in Leo IV, Pegasus III, and Hydrus I, together with a complete Python reproducibility archive. The registered protocol evaluates 36 GQUMOND cases covering three objects, two stellar profiles, and six screening lengths, with six QUMOND controls. Both registered grids yield Outcome B: all 36 GQUMOND global virial values and all six control values are positive, with agreement of their signs across the grids. Supplementary refined-grid calculations provide additional numerical consistency checks. Positive global virial work does not guarantee physically admissible local equilibrium. For the Hydrus I tapered-cusp profile, the conditional isotropic Jeans calculation produces negative radial pressure at screening lengths of 1, 3, and 10 pc. At 10 pc, outward mean force and negative effective enclosed mass also occur within the registered diagnostic interval of 0.1–10 half-light radii. These local obstructions remain despite positive global virial work. The tested model follows Milgrom’s published generalized QUMOND example structure and retains its action-derived Hessian contribution. It is not a new UDCT constitutive law. The results show that negative global virial work is not inevitable merely because such a contribution is present within this protocol. They do not establish a unique cause of the earlier v7.06 problems or cancel those recorded problems. Density profiles and the Galactic field are prescribed. No coupled matter-field evolution, full bidirectional projection, or dynamic back-reaction is simulated. The calculations do not establish agreement with observed stellar velocity dispersions or validate the complete UDCT framework. The complete ZIP includes the report, reproduction runner, unchanged original v7.09 implementation and v7.06 dependency, installation requirements, reference numerical outputs, and file checksums. The README documents execution instructions, assumptions, numerical checks, and interpretation limits. Code and README are provided under the MIT License. Preregistration:https://doi.org/10.5281/zenodo.23120660 Source repository:https://github.com/wspaik5/UDCT_v7.09_Postregistration_Results The report is provided under CC BY 4.0. The Python code and README are provided under the MIT License.