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For an isolated cold initially resting razor-thin disk, the displayed pointwise bound makes the absolute gravity-equivalent magnetic surface density smaller than its actual surface density. The positive-kernel comparison of thin-disk fields then makes the integrand in the horizontal virial balance of a cold magnetized fluid negative above and below the disk. Consequently its radial second moment begins to decrease. This establishes initial contraction in the global virial sense, not inward acceleration of every individual fluid element or unlimited subsequent collapse.

At the initially resting instant $K_{ij}=0$, and the cold-fluid assumption removes the pressure stress. Sum the $xx$ and $yy$ components of the magnetized-fluid tensor virial theorem. The magnetic and gravitational traces areSince $I_{\perp }=I_{xx}+I_{yy}$ and $g_z=-{\partial }_z\Phi$, this yields the horizontal virial balance of a cold magnetized fluid:Being at rest sets the instantaneous velocity to zero; it does not assert equilibrium or zero acceleration. The fields throughout space contribute to this stress integral, including their vacuum exterior.