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

This deposit presents version 5 of “Conservation, symmetry, and nonlinear exchange in a shearing self-gravitating magnetofluid,” together with supplementary material, supporting numerical evidence, registered history files, and a separate simulation video companion. Version 5 introduces an exact parameterized integral representation of the retained nonlinear evolution. Based on variation of constants, it separates linear propagation of initial disturbances from the accumulated nonlinear remainder and its subsequent propagation, connecting a family of initial states and physical parameters to the particular numerical experiments. The representation is implicit in the evolving solution and retains the complete nonlinear remainder. It applies at fixed spectral cutoff and product grid over smooth, admissible solution intervals. Its centered form explains the removal of propagated initial even curvature when distinguishing inherited structure from nonlinear generation. This revision develops the mathematical account using the existing simulations. 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 that can nevertheless produce finite complete-state responses, while matched interventions distinguish nonlinear generation of Fourier support from its modulation by shear. A derived reversal recovers refined ideal histories over the tested evolution windows, and imposed forward losses produce measurable return defects. The numerical findings apply to the tested discrete models and finite evolution windows. Spatial-convergence limits and saved-time quadrature sensitivity remain explicit. The supporting package contains 120 compact source records within 179 compact evidence files, together with source code, reproducibility materials, and a 526-member registered history inventory. That inventory comprises 74 preserved originals and 452 deterministic regenerations matching their recorded historical hashes. The separate video companion contains four original movies: two views of an evolving tilted cloud in the related exploratory MAVE 3D pilot, and the V6R Fold 1 soft and joint directional responses of density, compression, magnetic pressure, gravitational potential, and xy stress on two periodic phase coordinates. An illustrated guide, saved response arrays and scalar balance records, and verification scripts explain the plotted quantities and reproduce selected numerical checks. The guide distinguishes these consistency and reproducibility checks from physical-energy residuals, spatial-resolution limits, and the effects of video encoding. For manageable downloads and retries, the complete SHARE ZIP is supplied as 28 numbered parts, PAPER_01_v5_SHARE.zip.001 through .028. Download all parts and the accompanying reassembly and verification files into the same folder. On Windows, run REASSEMBLE_SHARE.cmd, keeping REASSEMBLE_SHARE.ps1 and PARTS_MANIFEST.json alongside it. The script verifies each part and the reconstructed archive using SHA-256 checksums. Full reconstruction has been tested, and the resulting ZIP is byte-for-byte identical to the original SHARE package. Instructions for other operating systems are included in README_REASSEMBLE.txt. The video companion remains a separate ZIP download. Generative AI tools, including OpenAI Codex 5.6 sol and 6.0 astra, assisted with code development and debugging, numerical analysis, mathematical discussion, plotting-code preparation, and manuscript preparation. Jake Campbell directed the research, reviewed AI-assisted outputs against the stated equations, independent numerical checks, thresholds, and preserved failure records, and accepts responsibility for the work. The retained historical record does not permit a complete inventory of model versions.