UDCT v7.09 — Pre-registration: Applying the v7.06 Virial and Jeans Protocol to Milgrom's Published GQUMOND Length-Screening Example, with a QUMOND Control, in Three Ultra-Faint Dwarfs

This record contains the UDCT v7.09 pre-registration and companion Python implementation for testing Milgrom’s published GQUMOND length-screening example against a QUMOND control in three ultra-faint dwarf galaxies: Leo IV, Pegasus III, and Hydrus I. The protocol applies the v7.06 virial and isotropic Jeans methods with fixed stellar profiles, Galactic-field inputs, acceleration scale, screening-length grid, and decision rules. It specifies 36 GQUMOND cases and six QUMOND control cases. The primary diagnostic is the sign of the virial work; additional diagnostics include the Hessian-term contribution, angle-averaged radial force, enclosed effective mass, and Jeans quantities. The purpose is to determine whether the negative virial work previously found for the UDCT integral construction also appears in this particular GQUMOND example. The test addresses one specified example and does not establish a conclusion about GQUMOND theories as a whole or validate UDCT. This deposit contains the pre-registration PDF, the v7.09 implementation, the unchanged v7.06 dependency script, README, and MIT license. As stated in the accompanying documentation, only analytic and geometry self-tests have been performed; the registered calculation has not been run, and no registered numerical results are included. The calculation uses a local Galactic Taylor-field approximation and spherical isotropic Jeans modelling, without a dark halo, LMC potential, or time evolution. Negative effective mass or outward mean force is treated as a static equilibrium diagnostic, not as a prediction of stellar ejection. Licensing: the pre-registration PDF is licensed under CC BY 4.0. The Python scripts and README are licensed under the MIT License. Prepared by Won Shik Paik with assistance from Anthropic Claude; earlier related work also involved OpenAI ChatGPT, Google Gemini, and xAI Grok, as disclosed in the PDF.