  The relation between the baryon number in QCD at nonzero chemical potential
and the spectral density of the baryon number Dirac operator, $\gamma_0(D+m)$,
is examined. We show that extreme oscillations of the spectral density, caused
by the QCD sign problem, are essential for the formation of the average baryon
number when $\mu>m_\pi/2$. We compute the oscillating region of the spectral
density using chiral perturbation theory. The extreme oscillations have a
microscopic period and are resolved using random matrix theory.
