  We prove the main conjecture from [M. R. Douglas, B. Shiffman and S.
Zelditch, Critical points and supersymmetric vacua, II: Asymptotics and
extremal metrics. J. Differential Geom. 72 (2006), no. 3, 381-427] concerning
the metric dependence and asymptotic minimization of the expected number
\mathcal{N}^{crit}_{N,h} of critical points of random holomorphic sections of
the Nth tensor power of a positive line bundle. The first non-topological term
in the asymptotic expansion of \mathcal{N}^{crit}_{N,h} is the the Calabi
functional multiplied by the constant \be_2(m) which depends only on the
dimension of the manifold. We prove that \be_2(m) is strictly positive in all
dimensions, showing that the expansion is non-topological for all m, and that
the Calabi extremal metric, when it exists, asymptotically minimizes
\mathcal{N}^{crit}_{N,h}.
