First numerical demonstration of negative density-weighted virial work in three ultra-faint dwarfs under an unregistered Hessian-augmented field law

This technical note records the first numerical demonstration of strongly negative density-weighted virial work in Leo IV, Pegasus III and Hydrus I under one unregistered Hessian-augmented field law. Accompanying reproducibility code is included. The result is a diagnostic for this specific candidate, not a general statement about standard MOND.