Conservation, symmetry, and nonlinear exchange in a shearing self-gravitating magnetofluid

This deposit presents “Conservation, symmetry, and nonlinear exchange in a shearing self-gravitating magnetofluid,” together with supplementary material and compact supporting evidence.The study connects conservation accounting, symmetry-dependent observability, and controlled nonlinear evolution in an eight-component magnetohydrodynamic model. A thirteen-channel momentum budget closes across 196 trajectories. Symmetry identifies scalar-null directions, while matched interventions distinguish nonlinear generation of Fourier support from its modulation by shear. A derived reversal recovers refined ideal histories, and imposed forward losses produce measurable return defects.Results apply to the tested discrete models and finite evolution windows. Spatial-convergence limits and saved-time quadrature sensitivity remain explicit. The package includes 120 compact source records, figures, provenance hashes, and preserved failed results. Full trajectory archives and complete reproduction environments are available upon request, while missing histories require regeneration.