  We consider the distribution of the complex phase of the fermion determinant
in QCD at nonzero chemical potential and examine the physical conditions under
which the distribution takes a Gaussian form. We then calculate the baryon
number as a function of the complex phase of the fermion determinant and show
1) that the exponential cancellations produced by the sign problem take the
form of total derivatives 2) that the full baryon number is orthogonal to this
noise. These insights allow us to define a self-consistency requirement for
measurements of the baryon number in lattice simulations.
