= No-scale volume runaway criterion
{title2=$V=A/y^3+B/y^2,\quad \partial_yV=-3A/y^4-2B/y^3$}
If a <no-scale supergravity> <scalar potential> has the displayed form with $y>0$ and nonnegative $A,B$ independent of the volume coordinate $y$, every point with $A+B>0$ has a direction of strictly decreasing potential. Thus a finite stationary vacuum requires $A=B=0$. If that common zero set is empty, the potential has infimum zero along $y\to\infty$ but no finite minimum. If the common zero set is nonempty, varying $y$ on it is a <flat direction of a scalar potential>. This distinguishes an attained zero-energy vacuum from a decompactification runaway.
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