Accumulated Joule dissipation of perturbed aligned MHD flows on the three-torus: a signed comparison with the heat flow

We ask whether, for the incompressible magnetohydrodynamic equations with unit viscosity and resistivity on the three-dimensional torus, the coupling with the velocity can make a solution dissipate less magnetic energy by Joule heating over a unit time interval than the heat flow of the same initial magnetic field. The data are small perturbations of an exact aligned solution: velocity and magnetic field start as the same Laplace eigenfunction, and the magnetic field receives one additional transverse Fourier mode. For wave vectors of squared length at least three, the small-amplitude expansion of the difference of the two Joule dissipations has no cubic term and, outside twelve resonant vectors, its quartic term is minus a closed-form quadratic form in the polarization. This form is positive on an infinite class of wave vectors, with a mode-dependent margin; the proof combines an analytic estimate for large wave numbers with a rigorous interval-arithmetic verification of finitely many cases. For three wave vectors, a posteriori estimates that control every error term give explicit amplitude ranges, uniform in the polarization and in intervals of the amplitude ratio, in which the actual solution dissipates strictly less than the heat flow. The approximation and stability tools are classical; the contribution is a specific signed comparison and its quantitative realization. The record contains the preprint, mathematical supplement S1, reproducible computational certificates S2 (version 4), and editable LaTeX sources. The files are restricted; access will be provided to editors and reviewers upon request. This preprint has not been accepted for publication in a journal.